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Molecular Engineering 11

Sustainable material selection for additive manufacturing technologies: A critical analysis of rank reversal approachThe world is moving towards a situation where resource scarcity leads to increased material cost, and the government is bound to dispose of heavy wastes generated by the growing population. Additive Manufacturing (AM) has bought a significant revolution in the current manufacturing processes. AM can fabricate complex and intricate shapes with ease. Material selection is an essential aspect in AM as a wide range of compatible materials available for AM. Appropriate material selection is necessary for cleaner production and sustainable development. Sustainable material selection considering various material properties and varied criteria can be effectively managed by Multi-Criteria Decision Making (MCDM) approach. However, several MCDM methods have a rank reversal problem, in which the rank of alternatives got changed when an alternative is added or removed from all considered alternatives. In this regard, this work presents a sustainable material selection of AM technologies. Sustainable material selection has been made for 3 a.m. technologies, namely Fused Deposition Modelling (FDM), Selective Laser Sintering (SLS), and Stereolithography (SLA). Four MCDM techniques have been used to analyze and compare AM materials, namely SAW (Simple Additive Weighting), MOORA (Multi-Objective Optimization based on Ratio Analysis), TOPSIS (Technique for order performance by similarity to ideal solution), and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje). Rank reversal problems associated with MCDM methods are also highlighted in the material selection stage. The results reveal that ‘TPU Elastomer’, ‘Accura HPC′, and ‘Duraform EX′ are identified as the best material for FDM, SLA, and SLS based AM technologies. Further, practical and research implications have been derived based on the study to help industrial practitioners, researchers, and decision-makers for the selection of the best materials in the product development stage to support cleaner production.Advanced technology like AM can help manufacturing firms enhance their capabilities and become more competitive (). Globally 54% of energy is consumed by the industrial sector (), a major concern for society and needed massive transformation in technologies to make it more sustainable. The forecasting study on resource consumption done by the UN reveals that by 2030, the existing resources need to be double to deal with increasing resource consumption due to the vast population growth rate (). Nowadays, AM is gaining vital growth because it is a widely used technique for producing a complex structure with ease and multi-material (). More industries are adopting AM technologies as they are becoming familiar with the benefits of adopting AM technologies, which accelerate the product development phase and with cost-effectiveness (). AM can fabricate complex structures and geometry with lesser cost and time with multi-material properties (). AM can provide an immediate customized product, complex and intricate shapes, innovative product design to the customer, increasing competition in the market (). Apart from its advantages and opportunities, AM provides several sustainable benefits () and can act as a critical technology to sustain the future (). Recently, several studies have been done to evaluate the sustainable performance of AM processes (). It is found that the common method adopted in assessing sustainability is the LCA study and SDM approach (). As the demand for new product development increases, Additive Manufacturing (AM) is gaining vital importance in the new product development process. Various additive manufacturing technologies available are Fused Deposition Modelling (FDM), Selective Laser Sintering (SLS), Stereolithography (SLA), and so on …A report on plastic economy presented by Ellen MacArthur Foundation (EMF) shows that by 2050, plastic wastes will be more by weight compared to fish in the ocean because of current waste generation and resource consumption (). Sustainable material selection plays a vital role in minimizing resource consumption. Sustainable material selection ensures the recycling of material for further use. Several benefits associated with the recycling of material are reduced weight, resource conservation, and cleaner production. Sustainable material selection enables triple-bottom-line sustainability benefits, namely, social, economic, and environmental benefits (Materials play an essential role throughout the life span of a product. Current developments and industrial globalization reach the planetary threshold, where a small increment in carbon emissions will significantly increase global warming (). It generates many environmental problems such as degradation of fresh water, biodiversity loss, land degradation, and an increase in greenhouse gas emissions. The existence of various researches in material selection () shows the importance of material selection for sustainable development. Appropriate material selection is essential in the product development stage. Each material has different properties, so proper criteria must be selected based on the application to analyze alternate materials. For sustainable material selection, not only mechanical properties but environmental properties are also important.The selection of material can be effectively managed by a multi-criteria decision making (MCDM) approach. Many MCDM methods are available to solve such problems (). Like AHP (Analytic Hierarchical Process), VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje), SAW (Simple Additive Weighting), MOORA (Multi-Objective Optimization based on Ratio Analysis), IEM (Information Entropy Method), TOPSIS (a technique for order performance by similarity to ideal solution), COPRAS (complex proportional assessment) and BWM (Best Worst Method). However, several MCDM methods have a rank reversal problem, in which the rank of alternatives got changed when an alternative is added or removed from all considered alternatives (). To deal with growing demand and resource consumption, sustainable material selection for AM is essential. In this context, this work addressed three research questions;RQ1: What are the potential materials available for AM applications?RQ2: What are the critical material selection criteria for different AM technologies?RQ3: How materials can be analyzed to identify the priority order using MCDM methods?As per developed research questions, the objectives of this work is as follows:To identify potential materials available for AM applications.To identify critical material selection criteria for different AM technologies.To analyze materials using different MCDM applicationsTo propose materials priority order for different AM technologies for cleaner production.To achieve these objectives, this work starts with the identification of potential materials for different AM technologies through a literature review. Several criteria have been considered both from traditional and sustainable perspective to compare AM materials. Sustainable material selection has been made for widely used AM technologies, namely FDM, SLS, and SLA. The mentioned 3 a.m. technologies are commonly used in various applications (). Previous studies on AM process selection show that FDM, SLS, and SLA are considered the best AM technologies (). So, this work finds FDM, SLS, and SLA based AM technologies for analyzing sustainable materials. This work uses widely used MCDM methods, namely SAW, MOORA, VIKOR, and TOPSIS.Further, the rank reversal problem associated with considered MCDM methods is also included in this study. The main contribution of the study is the prioritization of materials for FDM, SLS, and SLA based AM technologies by considering both traditional and sustainable criteria. Practical and research implications have been derived based on the study to help industrial practitioners, researchers, and decision-makers for the selection of the best materials in the product development stage to support cleaner production.This paper is organized in the following manner. A summary of the previous literature on materials of AM is presented in section . Description of considered methodology for material selection is discussed in Section includes an analysis of materials of different AM technologies. Section contains results and discussions on findings. Section contains discussions and implications of the study. Section presents conclusions, limitations, and future works.This section includes a review of previous articles to support this work. This section is further divided into three subsections, a literature review on AM materials, a literature review on sustainable material selection, and a research gap.A wide range of materials is available in the field of AM manufacturing. Various researchers have discussed and analyzed materials available for AM ( discussed several materials of AM technologies. The study analyses different properties of AM materials for the proper selection of materials to minimize defects related to AM processes. Further, discussed the abilities of FDM-based 3D printers and analyzed their materials. The study considered twelve material suitable for FDM printer and analyzed based on biocompatibility and solvent compatibility. The adoption of the circular economy in the AM process was discussed by through a case study of the Netherlands. The study suggested searching for local materials that can be recycled and act as input material for AM part fabrication. This will leads to cleaner production and enhance sustainable development.A review on AM process, materials, and their applications in different sectors was presented by . The study discusses materials development in the field of AM, including metals, polymer, ceramics, and concretes. Further, the study presents a survey on the benefits and limitations of AM processes. aimed to fabricate the 3D printed composite material part. The study uses ABS, PLA, and HIPS material to fabricate composite parts and investigate the thermal and mechanical properties of printed parts. The study also analyzed the microstructure of the composite structure produced pieces to confirm the result. Later, developed a metal matrix composite for FDM feedstock by reinforcing ceramic material to low-density polyethylene (LDPE). The study highlights different process parameters on the fabricated part with Taguchi’s L9 orthogonal array.A study to fabricate high-strength punches using AM processes was presented by . The study considered three material and fabricated holes using powder bed fusion based AM process. Different mechanical properties were tested, and Energy Dispersive Spectra (EDS) and Scanning Electron Microscopic (SEM) imaging were also studied to analyze the microstructure of fabricated parts. studied the environmental impact of AM products by considering electricity, fluid, and material consumption. For evaluating ecological implications, the study focused not only on the processing stage but also considers preprocessing and post-processing steps as well.A mathematical algorithm to optimize the material selection of AM processes was proposed by . The study considers three materials: ABS, silicon carbide, and aluminum, and analyzed using AHP methodology. The considered criteria were material cost, manufacturability, and recyclability and the result showed that aluminum has the highest cost-effectiveness value compared to other considered material. Further, in 2020, discussed various AM processes for their applications. The study presents material selection for energy storage devices printed using AM technology. Later, presented a review on biodegradable polymer material used by AM processes for biomedical applications. The study also discussed various biodegradable classes of polymer material used in the AM process by considering their extraction and physical and chemical properties. presented a review of available polymer materials related to AM technologies. The study discusses various AM technologies along with their development. A recent development in AM materials, along with their application areas, is also highlighted. reviewed the current literature on polymer chemistry to achieve sustainability in the field of AM through a proper focus on biodegradable polymer. presented a review on commercially available materials along with high-performance polymer composites that are used in AM applications. Materials pertaining to four technologies of AM, namely, FDM, SLS, Multijet fusion, and SLA was discussed by authors.Sustainable material selection is an essential aspect of sustainable development. Many researches discussed the importance of material selection for new product development under a sustainable environment ( analyzed sustainable material selection for construction materials using the fuzzy AHP method. The study considered six criteria based on the triple bottom line approach to sustainability. A model based on the AHP approach to analyze fiber-reinforced composites material was presented by . The study used an expert choice software tool for analysis and found propylene as the best material. This study helps automotive firms to enable green technology by the sustainable selection of materials. Further, presented challenges associated with sustainable material selection and suggested using LCA packages for effective decision making in sustainable material selection. analyzed the construction material by considering sustainable indicators and uses the hybrid MCDM method for analysis. The indicators were collected from the literature review and proposed a model to analyze the construction material. Further, the developed model was validated through a construction company in the UAE. Further, in 2017, aimed to develop automotive parts remanufacture by properly selecting material in the design stage. A list of criteria was shortlisted for analyzing materials related to automotive parts and used a fuzzy TOPSIS approach to analyze alternative materials. Further, the developed concept was validated by presenting two case studies in the automotive sector.An analysis of sustainable material selection for automobile door panels was presented by . The study integrated LCA, TOPSIS, and IEM method to analyze alternative materials. LCA was used to identify potential categories, IEM was used to calculate weights of criteria, and TOPSIS was used to prioritize alternatives based on selected criteria. Further, presented the rank reversal problem associated with MCDM methods. The study showed several material selection problems by using TOPSIS, VIKOR, and COPRAS based MCDM methods to analyze rank reversal associated with MCDM methods. Later, a hybrid MCDM approach for sustainable material selection for construction was proposed by . Sustainability criteria were considered in the study based on TBL. The study uses DEMATEL to analyze the weights of criteria for analyzing materials and uses fuzzy ANP to prioritize construction materials.A material selection tool based on software support that helps the designer select a suitable composite configuration for aircraft structures was developed by . The study uses LCA and Life Cycle Costing (LCC) to analyze the economic and environmental performance of the material. Further, results reveal that the developed tool helps in significant weight reduction and enhance sustainable development. analyzed materials for construction work by considering sustainable aspects. The study used the LCA module to analyze the environmental impact of construction materials and uses the ANP method for sustainable material selection.Further, in 2020, Maghsoodi et al. show the importance of material selection for sustainable development. The study highlights BWM, Combined Compromise Solution (CoCoSo), and multi MOORA method for optimum selection phase change material used in construction sectors. Later, presented an approach for material selection based on environmental and durability indicators. Further, a case study was presented for polymer material selection based on developed indicators to show developed indicators’ applicability.AM is rapidly growing from the last decade and shows a higher potential for reducing material consumption and enabling cleaner production. AM can fabricate complex and intricate shapes with ease. Material selection is an essential aspect in AM as a wide range of compatible materials available for AM. Sustainable material selection is necessary for cleaner production and sustainable development. Sustainable material selection enables triple-bottom-line benefits of sustainability, namely, social, economic, and environmental benefits. From the existing literature survey, it is found that many studies are available pertaining to the selection of AM materials (). Various authors have discussed polymer-based materials (), and many have studied ceramic, metal, composites-based materials (). But, Specific studies pertaining to different AM technologies are rare. Some studies are available on materials analysis based on their properties, but very few studies are available on AM materials’ ranking. Studies on AM material selection considering sustainability criteria are rare, and rank reversal problems in AM material selection using MCDM methods have not been reported.In this regard, this study attempts to fulfill all research gaps. Sustainable material selection has been made for widely used AM technologies, namely FDM, SLS, and SLA. The mentioned 3 a.m. technologies are commonly used in various applications (). Previous studies on AM process selection show that FDM, SLS, and SLA are considered the best AM technologies (). So, this work finds FDM, SLS, and SLA based AM technologies for analyzing sustainable materials. Four MCDM techniques have been used to analyze and compare AM materials, namely SAW, MOORA, TOPSIS, and VIKOR. Also, the rank reversal problem associated with MCDM applications is discussed. The main contribution of the study is the prioritization of materials for FDM, SLS, and SLA based AM technologies by considering both traditional and sustainable criteria.In this section, the different methodologies used in this work have been demonstrated. IEM was used to analyze the weights of other criteria used in sustainable material selection for AM. For the sustainable material selection of AM technologies, this work considers four MCDM methodology, namely SAW, MOORA, TOPSIS, and VIKOR. MCDM method starts with developing the decision matrix, where selected alternatives are compared with all criteria. The decision matrix is presented in the model (X=[C1C2…CnA1X11X12…X1nA2X21X22…X2n⋮⋮⋮⋱⋮AmXm1Xm2⋯Xmn]Xij presents a rating of ith alternative with respect to jth criteria. A (1,2, ….m) are m alternatives and C(1,2, ….n) are n criteria.Based on this decision matrix, the decision-maker provides the best alternative among all considered alternatives. For analysis, criteria are divided into two categories; beneficial criteria and non-beneficial criteria.The first step of any MCDM method is to identify the weights of criteria. There are many available methods to calculate weights of criteria: IEM, Digital logic, BWM, and AHP (). IEM is used in this study to calculate the weights of criteria because of its broad applicability in real-time data.The next step in the MCDM method is normalization. Different normalization steps are followed in other MCDM methods. After identifying the weights of criteria and normalization of the decision matrix, the final step is to calculate the performance of each alternative based on the criteria. As MCDM methods have different normalization steps and different ways of calculating the performance of alternatives, the ranking achieved by other MCDM methods may vary. The spearman rank correlation method is used to analyze the similarity between MCDM methods (). A detailed description of methodologies are described in further subsections.IEM is mainly used to analyze the criteria and to calculate the weights of criteria in MCDM problems. Steps of IEM are as follows (Step1: Normalize the criteria values using equations Where, Xij′ is normalized value and Xij is the original value.Step 2: Calculate the entropy of each criterion.The entropy of each criterion can be calculated using equation m is the number of the object under each criterion.Step 3: Calculate the redundancy of entropy of each criteria using equation Step 4: Final step is to calculate weight of criteria using equation Step1: Normalize the decision matrix (1) using equations Xij′ is normalized performance value of ith alternative with respect to jth criteria.Xj+ is the maximum value of Xij for criteria j.Xj− is the minimum value of Xij for criteria j.Step 2: Assign weights to each criterion.Step 3: Calculate the performance score of each alternative.In this step of the SAW method, the normalized value of all criteria are multiplied with their criteria weight and added for each alternative. The performance score for each alternative can be calculated using equation Yi is the performance score of ith alternative with respect to all criteria.The ranking of alternatives is given based on values ofYi. The alternative with the highest Yi value is given as ranked first.Step1: Normalize the decision matrix (1) using equation Xij′ is normalized performance value of ith alternative with respect to jth criteria.Step 2: Assign weights to each criterion.Step 3: Calculate the performance score of each alternative.In this step of the MOORA method, the normalized value of all beneficial or maximizing criteria are added, and non-beneficial or minimizing criteria are subtracted for each alternative. The performance score for each alternative can be calculated using equation g is the number of beneficial or maximizing criteria, and (n-g) is the number of non-beneficial or minimizing criteria.Yi is the performance score of ith alternative with respect to all criteria.The ranking of alternatives is given based on values ofYi. The alternative with the highest Yi value is given as ranked first.Step1: Normalize the decision matrix (1) using equation Xij′ is normalized performance value of ith alternative with respect to jth criteria.Xj+ is the maximum value of Xij for criteria j.Xj− is the minimum value of Xij for criteria j.Step 2: Assign weights to each criterion.Step 3: Next step is to develop a weighted normalized decision matrix using equation D=[D11D12…D1nD21D22…D2n⋮⋮⋱⋮Dm1Dm2⋯Dmn]Where,Dij=Xij′×WjStep 4: Next step is to identify the ideal solutions of TOPSIS. I+ represents positive Ideal Solution (PIS), and Negative Ideal Solution (NIS) is represented by I−. PIS and NIS can be calculated using equation Ij+=(maxDi1, maxDi2,maxDi3…maxDin)(1≤i≤m)Ij−=(minDi1,minDi2,minDi3…minDin)(1≤i≤m)Step 5: Calculate the distance of all alternatives with PIS and NIS using equation Step 5: Calculate the closeness rating of all alternatives with respect to PIS. The closeness rating of alternatives can be calculated using equation Step 6: The final stage of TOPSIS is assigning a rank to alternatives. The ranking of alternatives is based on closeness value. The alternative with the highest closeness value is given as ranked first.Step 1: Calculation of best and worst values of all criteria using equation Where f∗j and f−j are the PIS and NIS for criteria j.Step 2: Calculation of utility value (Si) and regret value (Ri)The utility value can be calculated using equation Regret value can be calculated using equation Step 3: Calculation for VIKOR index value (Qi) using equation Qi=vj(Si−S∗)(S−−S∗)+(1−vj)(Ri−R∗)(R−−R∗)S∗=min(Si),S−=max(Si),R∗=min(Ri),andR−=max(Ri)Step 4: The final stage of VIKOR is assigning a rank to alternatives. Ranking of alternatives is based on VIKOR index value (Qi). The alternative with the lowest Qi value is given as ranked first.There are various reasons for selecting SAW, MOORA, TOPSIS, and VIKOR method over other MCDM methods. discussed that for a particular problem, an MCDM method could not be considered at the start of a decision-making process. The first decision-maker should understand the problem by considering alternatives, varied outcomes, and conflicting solutions. Further, presented a review of the material selection problem and found that TOPSIS is the most suitable method for the material selection problem. Further, SAW and MOORA are the most general and straightforward method used for material selection problem (). Similarly, VIKOR is an important MCDM method that provides compromising solutions to decision-making problems (). So, these MCDM methods are found to be very useful, reliable, and widely used in decision making problem. In this regard, this work uses SAW, MOORA, TOPSIS, and VIKOR methods for the sustainable material selection of AM materials.In this section, we illustrate real case studies on sustainable material selection for different AM technologies. The flow of the study is presented in . Four MCDM techniques have been used to analyze and compare AM materials, namely SAW, MOORA, TOPSIS, and VIKOR. Also, the rank reversal problem associated with MCDM applications is discussed in material selection studies. This study presents material selection for 3 a.m. technologies, namely FDM, SLA, and SLS. The mentioned 3 a.m. technologies are widely used in various applications (). Three case studies have been demonstrated in further sub-sections.This case study presents sustainable material selection for FDM based AM technology. For FDM technology, 15 critical criteria considered for sustainable material selection are as follows:Among these 15 criteria, Cost of material, GWP, and Energy consumption are the non-beneficial criteria, and the remaining all are beneficial criteria.Also, the six most widely used FDM printing materials are considered for analysis. The considered materials are Acrylonitrile Butadiene Styrene (ABS), Poly Lactic Acid (PLA), Polycarbonate (PC), Acrylonitrile Styrene Acrylate (ASA), Synthetic Polyamide (Nylon), Thermoplastic Polyurethane Elastomer (TPU Elastomer). The materials data are presented in . The weights of criteria are calculated using the IEM method and are as follows:wa = 0.037, wb= 0.046, wc=0.283, wd=0.037, we=0.061, wf=0.058, wg = 0.054, wh=0.05, wi = 0.083, wj = 0.051, wk = 0.045, wl = 0.056, wm = 0.054, wn = 0.039, wo=0.045.First, this case study is solved by the SAW method. The ranking of materials of FDM using the SAW method is generated as 2-1-6-4-3-5. Material 2 (PLA) is the best option, whereas material 5 (nylon) is the worst option for FDM printers. To analyze rank reversal in the SAW method, the worst material (material 5) is removed from the study. Again, the new ranking of material using the SAW method is 2-1-6-4-3. Therefore, it can be said that the SAW method is not having a rank reversal problem for this case study.Now, this case study is solved by the MOORA method. The ranking of materials is generated as 6-2-3-1-4-5. Material 6 (TPU Elastomer) is the best option, whereas material 5 (Nylon) is the worst option. To analyze rank reversal in the MOORA method, the worst material (material 5) is removed from the study. Again, the new ranking of material using the MOORA method is 6-2-3-1-4. Therefore, it can be said that the MOORA method is not having a rank reversal problem for this case study.Similarly, by using the TOPSIS method, the rank is generated as 6-3-5-2-4-1. Material 6 (TPU Elastomer) is the best option, whereas material 1 (ABS) is the worst option for FDM printers. To analyze rank reversal in the TOPSIS method, the worst material (material 1) is removed from the study. Again, the new ranking of material using the SAW method is 6-3-5-2-4. Therefore, it can be said that the TOPSIS method is not having a rank reversal problem for this case study.Similarly, by using the VIKOR method, the rank is generated as 6-2-3-1-4-5. Material 6 (TPU Elastomer) is the best option, whereas material 5 (Nylon) is the worst option for FDM printers. To analyze rank reversal in the VIKOR method, the worst material (material 5) is removed from the study. Again, the new ranking of material using the VIKOR method is 6-2-3-1-4. Therefore, it can be said that the VIKOR method is not having a rank reversal problem for this case study. compares the ranking of FDM materials using different MCDM methods.This case study presents sustainable material selection for SLA based AM technology. For SLA printer, ten critical criteria considered for sustainable material selection are as follows:Also, the five most widely used SLA printing materials are considered for analysis. The considered materials are Accura Polypropylene (Accura PP), Accura Acrylonitrile Butadiene Styrene (Accura ABS), Accura High Temperature (Accura 48 HTR), Accura High-Performance Composite (Accura HPC), Accura polycarbonate (Accura PC 60). The materials data are presented in . The weights of criteria are calculated using the IEM method and are as follows:wa = 0.092, wb= 0.083, wc=0.142, wd=0.153, we=0.059, wf=0.151, wg = 0.137, wh=0.043, wi = 0.097, wj = 0.043.First, the SAW method is used to solve this case study. The ranking of materials of SLA using the SAW method is generated as 4-3-2-1-5. It means material 4 (Accura HPC) is the best option, whereas material 5 (Accura PC 60) is the worst option for SLA printers. To analyze rank reversal in the SAW method, the worst material (material 5) is removed from the study. Again, the new ranking of material using the SAW method is 4-3-2-1. Therefore, it can be said that the SAW method did not generate the rank reversal problem for this case study.Now, this case study is solved by the MOORA method. The ranking of materials is generated as 4-3-2-1-5. It means material 4 (Accura HPC) is the best option, whereas material 5 (Accura PC 60) is the worst option for SLA printers. To analyze rank reversal in the MOORA method, the worst material (material 5) is removed from the study. Again, the new ranking of material using the MOORA method is 4-3-2-1. Therefore, it can be said that the MOORA method is not having a rank reversal problem for this case study.Similarly, by using the TOPSIS method, the rank is generated as 4-3-1-2-5. It means material 4 (Accura HPC) is the best option, whereas material 5 (Accura PC 60) is the worst option for SLA printers. To analyze rank reversal in the TOPSIS method, the worst material (material 5) is removed from the study. Again, the new ranking of material using the TOPSIS method is 4-3-1-2. Therefore, it can be said that the TOPSIS method is not having a rank reversal problem for this case study.Finally, by using the VIKOR method, the ranking of materials is generated as 4-3-2-1-5. It means material 4 (Accura HPC) is the best option, whereas material 5 (Accura PC 60) is the worst option for SLA printers. To analyze rank reversal in the VIKOR method, the worst material (material 5) is removed from the study. Again, the new ranking of material using the VIKOR method is 4-3-2-1. Therefore, it can be said that the VIKOR method is not having a rank reversal problem for this case study. compares the ranking of SLA materials using different MCDM methods.This case study presents sustainable material selection for SLS based AM technology. For SLS printer, seven critical criteria considered for sustainable material selection are as follows:Also, the six most widely used SLS printing materials are considered for analysis. The considered materials are Castform Polystyrene (Castform PS), Duraform Thermoplastic Elastomer (Duraform FLEX), Duraform Thermoplastic Polyurethane (Duraform TPU), Duraform Flame Retardent (Duraform FR1200), Duraform Polypropylene (Duraform EX), Duraform Glass Filled (Duraform GF). The materials data are presented in . The weights of criteria are calculated using the IEM method and are as follows:wa = 0.091, wb= 0.189, wc=0.098, wd=0.173, we=0.147, wf=0.163, wg = 0.139.First, this case study is solved by the SAW method. The ranking of materials of SLS using the SAW method is generated as 5-6-4-3-1-2. It means material 5 (Duraform EX) is the best option, whereas material 2 (Duraform FLEX) is the worst option for SLS printers. To analyze rank reversal in the SAW method, the worst material (material 2) is removed from the study. Again, the new ranking of material using the SAW method is 5-6-4-3-1. Therefore, it can be said that the SAW method is not having a rank reversal problem for this case study.Now, this case study is solved by the MOORA method. The ranking of materials is generated as 5-6-4-3-2-1. It means material 5 (Duraform EX) is the best option, whereas material 1 (Castform PS) is the worst option. To analyze rank reversal in the MOORA method, the worst material (material 1) is removed from the study. Again, the new ranking of material using the MOORA method is 6-5-4-3-2. It can be seen that the ranking of ‘material 5′ and ‘material 6′ got changes. Therefore, the MOORA method shows the rank reversal problem for this case study.Similarly, by using the TOPSIS method, the rank is generated as 3-5-6-4-2-1. Material 3 (Duraform TPU) is the best option, whereas material 1 (Castform PS) is the worst option for SLS printers. To analyze rank reversal in the TOPSIS method, the worst material (material 1) is removed from the study. Again, the new ranking of material using the TOPSIS method is 3-6-5-4-2. The ranking between ‘material 5′ and ‘material 6′ got changed. Therefore, it can be said that TOPSIS shows a rank reversal problem for this case study.Finally, by using the VIKOR method, the rank is generated as 5-4-6-3-1-2. It means material 5 (Duraform EX) is the best option, whereas material 2 (Duraform FLEX) is the worst option for SLS printers. To analyze rank reversal in the VIKOR method, the worst material (material 2) is removed from the study. Again, the new ranking of material using the VIKOR method is 5-4-6-3-1. Therefore, it can be said that the VIKOR method is not having a rank reversal problem for this case study. compares the ranking of SLS materials using different MCDM methods.In this work, a sustainable material selection of AM technologies has been made using different MCDM applications. Three a.m. technologies have been considered case studies in this work, namely, FDM, SLA, and SLS. IEM based MCDM method is used to calculate weights of all considered criteria. Further, four MCDM methods have been used for the sustainable selection of AM materials, namely, SAW, MOORA, TOPSIS, and VIKOR. Rank reversal problems associated with MCDM methods are also highlighted in the material selection stage. Based on the three case studies, the following observations have been summarized:Out of four MCDM methods, three methods shows ‘TPU Elastomer’ as the best material for FDM based AM technology.Accura HPC is identified as the best material for SLA based AM technology.Out of four MCDM methods, three methods shows ‘Duraform EX′ as the best material for SLS based AM technology.Rank reversal problem has occurred in MOORA and TOPSISSAW and VIKOR method did not show any rank reversal problem in all presented case studies.MOORA shows a rank reversal in one case study out of three.TOPSIS also shows a rank reversal in one case study out of three.The result shows that the SAW and VIKOR method did not show any rank reversal problem (). So, it is clear that the simplest MCDM method, i.e., the SAW method performs best under the rank reversal problem.The result shows that ‘TPU Elastomer’ is the best material for FDM based AM technology. In the literature, several materials have been used in FDM based AM technologies. However, some researchers have mentioned the practical application and advantages of using TPU Elastomer over other FDM materials (). TPU elastomer has the highest flexibility and rubber-like structure () with a high degree of elongation, which makes it advantageous over other FDM materials.For SLA based AM technology, Accura HPC is evaluated as the best material over other SLA materials. The studies by show that Accura HPC is a nanocomposite material used for different manufacturing applications. The essential properties of Accura HPC, which makes it advantageous over other SLA materials are, it has the highest accuracy and flexural strength () as compared to other considered SLA materials.For SLS based AM technology, Duraform EX is identified as the best material over other considered SLS material. Several literatures show the application of Duraform EX (). It has several benefits over other SLA materials, such as it provides the highest surface finish and has the highest tensile strength () as compared to other considered SLS materials.The result shows that the TOPSIS and MOORA method suffers from the rank reversal problem reported that TOPSIS shows a severe rank reversal problem. showed that the rank reversal problem associated with the TOPSIS method is due to the vector normalization method. present a new normalization method that avoids the rank reversal problem in TOPSIS.In the present study, the SAW and VIKOR methods did not show any rank reversal problem in the presented case studies. also reported that the SAW method is ideal and shows the least rank reversal problem. show the least rank reversal problem in the SAW method, whereas the VIKOR method shows the rank reversal problem in material selection studies.From the presented study, it can be seen that the selection of the MCDM method for material analysis is a challenging area. And so, it is recommended to use multiple MCDM techniques to analyze the same problem. Moreover, in some cases, different MCDM gives different results, and it is difficult to analyze the correctness of MCDM methods. So, it is recommended to compare the ranking of alternatives based on other MCDM methods through the Spearman rank correlation method. Equation is used for Spearman rank correlation analysisWhere, Diis the difference in ranking between alternatives obtain using two different MCDM methods, and m is the number of alternatives. shows the ranking of alternative materials for first, second, and third case studies using different MCDM methods. The spearman correlation among other MCDM methods can be analyzed using rank data from The rank correlation obtained between different MCDM methods using . It can be seen that the highest rank correlation is obtained between SAW and MOORA (RS= 1), SAW and VIKOR (RS= 1), and MOORA and VIKOR (RS= 1).The present study aims at selecting sustainable materials for additive manufacturing technologies. The material selection had been made considering 3 a.m. technologies, namely FDM, SLS, and SLA, using various MCDM techniques. Material selection is one of the critical factors for managers to take advantage of sustainability. Also, for any manufacturing organization, the cost incurred by materials will be half of the total operating cost. Thus it becomes difficult for key decision-makers or managers to select sustainable material for the manufacturing process.In this study, an attempt to select sustainable material would help managers to take benefits of sustainability and cleaner production. Improper material selection may impact the design of the product making it more vulnerable to failure. Thus the present study allows decision-makers to select material that enhances additively manufactured product design performance, durability, and output. Moreover, sustainable material selection plays a significant role in the entire design manufacturing process, which provides guaranteed product performance and reduce harmful environmental impacts throughout its life cycle. The present study can be beneficial for the researchers to understand the methodology for the sustainable material selection for additive manufacturing and design a better sustainable design assessment system.AM is gaining vital growth because it is a widely used technique for producing a complex structure with ease. More industries are adopting AM technologies to accelerate the product development phase with cost-effectiveness. Appropriate material selection is necessary for cleaner production and sustainable development. Sustainable material selection plays a vital role in minimizing resource consumption. Existing literature shows that there is a gap in reliable methodologies for AM material selection. Studies on AM material selection considering sustainability criteria are rare, and rank reversal problems in AM material selection using MCDM methods have not been reported.This paper focused on the sustainable material selection of AM technologies. Sustainable material selection has been made for 3 a.m. technologies, namely FDM, SLS, and SLA. The considered 3 a.m. technologies are widely used in a variety of applications. Four MCDM techniques have been used to analyze and compare AM materials, namely SAW, MOORA, TOPSIS, and VIKOR. Further, the rank reversal problem associated with considered MCDM methods is also included in this study. The main contribution of the study is the prioritization of materials for FDM, SLS, and SLA based AM technologies by considering both traditional and sustainable criteria. The study showed that ‘TPU Elastomer’, ‘Accura HPC′, and ‘Duraform EX′ are identified as the best materials for FDM, SLA, and SLS based AM technologies by considering both traditional and environmental criteria. This article helps industrial practitioners, decision-makers, and AM experts with the selection of the best AM materials in the product development stage to support cleaner production.The significant contributions of the study are:This work has filled the current literature gap; very few studies were available on AM material selection considering sustainability criteria, and rank reversal problem in AM material selection using MCDM methods has not been reported.This study provides a priority order of material for three important AM technologies: FDM, SLA, and SLS.This work considers four MCDM methods for prioritization of AM materials considering both traditional and sustainable criteria. Also, the rank reversal problem associated with MCDM applications is discussed.The study has certain limitations in terms of materials, selection criteria, and methodology used. The present study considers some important, widely used materials pertaining to AM technologies. Future studies can be performed by considering more AM materials. Three a.m. technologies, namely FDM, SLS, and SLA, have been considered in the present study. In the future, sustainable material selection studies can be done on other AM technologies. In the present study, the TOPSIS and MOORA methods show the problem of rank reversal. So, in the future other MCDM methods could be used to mitigate the rank reversal problem.Rohit Agrawal: Conceptualization, Methodology, Data curation, Writing – review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Novel polyurethane produced from canola oil based poly(ether ester) polyols: Synthesis, characterization and properties► Novel bio-based poly(ether ester) polyols were synthesized from canola oil. ► The synthesized polyols had high functionality and low viscosity. ► The utilization of these polyols for polyurethanes production was demonstrated. ► Canola oil derived polyurethanes had high glass transition temperatures. ► These polyurethanes had improved hydrolytic stability and alkali resistance.Two novel bio-based poly(ether ester) polyols (Liprol™ 270 and Liprol™ 320) with high functionality and low viscosity were synthesized from canola oil. A simple, two-step reaction sequence of epoxidation followed by hydroxylation and transesterification with 1,3-propanediol or 1,2-propanediol was used resulting in a versatile, low cost process. The chemical structures of the low molecular weight compounds in the polyols produced were identified by liquid chromatography–mass spectrometry (LC–MS) while the distribution of oligomers was elucidated by size exclusion chromatography (SEC). The feasibility of utilizing these polyols for the production of polyurethanes (PUs) was demonstrated by reacting them with commercial petrochemical derived diisocyanate. The physical properties of the PUs prepared were characterized by FTIR, dynamic mechanical analysis (DMA), modulated differential scanning calorimetry (MDSC), and thermo gravimetric analysis (TGA). It was found that Liprol derived PUs had high glass transition temperatures, good hydrolytic stability and alkali resistance, and formed highly cross-linked networks. This work is the first that establishes the production of polyols and their corresponding PUs from vegetable oil starting materials whose glycerol backbone was removed explicitly during the polyol synthesis reaction.Polyurethanes (PUs) are used by a wide range of industries including the construction, automotive and consumers goods industries, and in many diverse applications ranging from medical devices to coatings, etc. Polyols normally used in PU synthesis are made from chemical intermediates derived from petroleum or natural gas. Recently, with the increasing emphasis on issues concerning waste disposal and depletion of non-renewable resources, the importance of using renewable resources in industrial processes has become very clear from a standpoint of sustainability. In the quest for sustainable chemistry, there are in particular, increasing demands for replacing or complementing the traditional petrochemical raw materials with renewable raw materials in the production of polymers In this work, bio-based poly(ether ester) polyols were synthesized through epoxidation followed by hydroxylation (esterification) reactions, starting from canola oil and other renewable content (i.e. 1,3-propanediol and 1,2-propanediol) and using a cheap and efficient procedure, and a strong acid catalyst. An important consideration in selecting 1,3-propanediol and 1,2-propanediol is that both of these diols derived from renewable resources are currently commercially available The canola oil (Safeway® or Canola Harvest® brand or equivalent) used in this study was purchased from a local grocery store. Unrefined crude castor oil was obtained from CasChem Company, USA. Hydrogen peroxide (35%), formic acid (85%), sodium sulfate anhydrous, sodium bicarbonate and 1,2-propanediol (propylene glycol, technical grade) were obtained from Univar, Canada. Ethyl acetate (ACS grade), sodium hydroxide (ACS grade), sodium chloride (ACS grade) and sulfuric acid (ACS grade) were obtained from Fisher Scientific, USA. 1,3-propanediol was obtained from DuPont Tate and Lyle, USA. Tritricosanoin (Mw = 1,101.88 g/mol), distearin (Mw = 625.00 g/mol) and monostearin (Mw = 358.56 g/mol) with purity ⩾99% were obtained from Nu-Chek Prep. Inc. (USA) and used as calibration standards for size-exclusion chromatography (SEC). The polymeric aromatic diphenylmethylene diisocyanate (pMDI, Mondur MRS) was sourced from Bayer Corporation, Pittsburgh, PA, USA. The NCO content of pMDI was 31.5 wt% and its functionality was 2.6 as provided by the supplier.Canola oil was epoxidized by performic acid generated in situ by reaction of hydrogen peroxide with formic acid, as described elsewhere A suitable amount of polyol and pMDI based on an NCO/OH ratio of 1.1/1.0, were weighed into a plastic container, mixed thoroughly for 5 min, poured in a plastic mold previously greased with silicone release agent, and placed in a vacuum oven at 50 °C for 10–20 min to remove bubbles. Air was then introduced to the oven to avoid the deformation of the sample under vacuum and the sample was cured for about 24 h at 50 °C then post-cured for 24 h at 100 °C to complete the reaction. The sample was then cooled to room temperature and demolded. Based on the different types of polyols used, the PUs prepared were coded as Liprol™ 270-MDI and Liprol™ 320-MDI, respectively.The structures of the main compounds in the polyols that are amenable to analysis by electrospray ionization mass spectrometry were identified by LC–MS analysis using normal phase chromatography. A 1200 Agilent high performance liquid chromatography (HPLC) system (Agilent Technologies; CA, USA) was coupled to an Applied Biosystems/MDS Sciex QSTAR Elite mass spectrometer with an electrospray ion source. The injected samples were dissolved in dichloromethane to concentrations of 0.1% (w/v). The samples were separated using an Ascentis silica column (15 × 0.21 cm, 3 μm) and using a binary gradient where mobile phase A was composed of hexane and mobile phase B was isopropanol. The gradient program was as follows: 0.1 min, 2% B; 0.1–20 min, 18% B; 20–25 min: 40% B; 25.1 min, 2% B. The re-equilibrium time was 6 min. The injection volume was 2 μl and flow rate was 200 μl/min. 40 mM ammonium acetate in methanol/isopropanol (3:1, v:v) was added post-column using an isocratic Agilent 1100 pump (Agilent Technologies; CA, USA) at a flow rate of 20 μl/min.MS analysis of the analytes was performed using positive electrospray ionization. Analyst QS 2.0 software was used for data acquisition and analysis. Nitrogen was used as curtain gas, nebulizing gas, and drying gas. The mass range recorded was from m/z 50–1300. The other instrumental conditions were as follows: ionspray voltage 5500 V; curtain gas setting 25; gas 1 setting 25 and gas 2 setting 55; declustering potential (DP), 80 V; focusing potential (FP), 300; second declustering potential (DP2), 15 V; and ion source temperature: 400 °C.The hydroxyl numbers of the polyols were determined according to ASTM D1957-86 and their acid values were determined according to the ASTM D4662-98. The average values and standard deviations of triplicate measurements are reported in . The viscosity of the polyols was measured in shearing mode with the TA advanced rheometer AR 2000 (TA Instruments, DE, USA) using a constant shearing rate of 51.6 s−1 at 25 °C. The viscosity results are listed in The molecular weight distributions of the epoxides and polyols were determined by SEC. The chromatograms were acquired using an isocratic Agilent 1100 pump (Agilent Technologies; CA, USA) equipped with an evaporative light scattering detector (Alltech ELSD 2000, Mandel Scientific Company Inc, Canada). A gel permeation chromatography (GPC) column (300 × 7.8 mm i.d.) with particle size of 5 μm (Styragel HR1, Waters Corporation, USA) was used under the following conditions: tetrahydrofuran as the mobile phase; flow rate of 1 mL/min; sample concentrations of 0.5% (w/v) and injection volumes of 10 μL. Lipids standards with known molecular weight were used to generate a calibration curve.The FTIR spectra were recorded on a Nicolet Magna 750 FTIR (Thermo Nicolet, WI, USA), equipped with an MCT-A detector and a Nicolet Nic-Plan IR microscope by ATR. The spectra were recorded in the range 650–4000 cm−1 with a nominal resolution of 4 cm−1. A background spectrum was first collected before each absorbance spectrum. A total of 128 interferograms were summed before Fourier transformation using the Nicolet Omnic software. To record the polyurethane spectra, a tiny piece of solid specimen was cut off from the bulk sample and placed on the top of the ATR crystal, whereas for polyols, a tiny drop of liquid specimen was placed on the sample holder directly.The gel time of the polyurethane was measured using an AR2000 Advanced Rheometer equipped with the Environmental Test Chamber (ETC). Due to the thermosetting nature of the material, 25 mm disposable plates were used as the test geometry. Isothermal time sweeps were run at a constant temperature of 50 °C to investigate the storage modulus and loss modulus change. The point at which the two curves intersect is typically taken as the gel point of the system and is the point at which the system begins cross-linking ASTM D543 was followed to measure swelling ratio of PUs by immersing them in toluene at 23 °C. Specimens were taken out and both surfaces were dried with paper before weighting every 24 h until constant weight. The swelling ratio was calculated from the difference in equilibrium weights of the swollen and dry sample.ASTM D570 was followed to measure water absorption of PUs by immersing them in water at 23 °C for 24 h. Specimens were taken out and both surfaces were dried with paper before weighting every 24 h until constant weight. Water absorption was calculated from the difference in equilibrium weights of the swollen and dry sample.Dynamic mechanical analysis (DMA) measurements were carried out on a DMA Q800 (TA Instruments, DE, USA), equipped with a liquid-nitrogen cooling apparatus, in the single cantilever mode with a constant heating rate of 2 °C/min from −40 to +180 °C. The size of the samples was 18 × 7 × 2 mm. The measurements were performed under dry nitrogen gas with 2 L/min flow following ASTM E1640-99 standard at a fixed frequency of 1 Hz and a fixed oscillation displacement of 0.015 mm.Modulated differential scanning calorimetry (MDSC) measurements were carried out on a DSC Q100 (TA Instruments, DE, USA), equipped with a refrigerated cooling system. The samples were heated at a rate of 10 °C/min from 25 to 160 °C to erase thermal history, then cooled down to −20 °C at a cooling rate of 5 °C/min. MDSC measurements were performed with a modulation amplitude of 1 °C/min and a modulation period of 60 s at a heating rate of 2 °C/min to 200 °C. The second heating stage was selected for the analysis of heating data. All the DSC measurements were performed following the ASTM E1356-03 standard procedure under a dry nitrogen gas atmosphere.Thermo gravimetric analysis (TGA) was carried out on a TGA Q50 (TA Instruments, DE, USA) following the ASTM D3850-94 standard. The sample was ground to a powder after chilling with liquid nitrogen, and approximately 10 mg of the specimen was loaded in the open platinum pan. The samples were heated from 25 to 600 °C under dry nitrogen with 100 mL/min purging flow at constant heating rates of 10 °C/min.Mechanical properties were tested using an Instron (MA, USA) tensile testing machine (model 4202) equipped with a 500 Kgf load cell and activated grips that prevented slippage of the sample before break. Specimens were cut out from the PU sheets using an ASTM D638 Type V cutter. For hydrolytic stability test, the cut specimens were fully immersed into water at 80 °C for 7 days, whereas for alkali resistance measurement, the specimens were submerged in 3.3% NaOH solution at 80 °C for 7 days. All the samples were dried the tensile test was performed. The measurements were carried out at room temperature with cross-head speed of 100 mm/min, as suggested by the above-mentioned ASTM standard. The data presented are an average of five different measurements. The reported errors are the associated standard deviations.ECO was synthesized using in situ generated performic acid (formic acid reacting with hydrogen peroxide) in the reaction medium. The performic acid adds oxygen to the double bonds of the fatty acid components of the oil to yield an epoxide group and thereby regenerating formic acid for the further reaction. Therefore, a low amount of formic acid is required which also reduces the production of di-hydroxy and hydroxy carboxylate byproducts formed due to an acid catalyzed ring-opening reaction. This conversion of the double bonds into the epoxides was monitored and quantified by LC–MS as described elsewhere C double bonds were converted into epoxides, based on uncorrected peak areas for unsaturated triglycerides and their epoxide products. ECO was then further reacted with diols in the present of sulphuric acid as a catalyst through acid catalyzed ring-opening hydroxylation of the epoxide groups and transesterification of the glycerides to produce polyols. The resultant polyols were characterized by LC–MS analysis, as shown in (a) and (b). This indicates that the molecular weight of the main component in these polyols is at m/z 433, consistent with the structures proposed in . This is much lower than the molecular weight (around 1000) of the main component of the polyols prepared when tetrafluoroboric acid was used as the catalyst ). In addition, these reactions also result in the addition of extra hydroxyl groups (). As a result, the hydroxyl number of such polyols is about 270 and 320 mg KOH/g, which is higher than the traditional vegetable oil-derived polyols produced via the epoxidation reaction (around 200 mg KOH/g) However, it is known that during the ring opening reaction some of the newly formed hydroxyl groups react with existing epoxy groups on other molecules resulting in oligomerization of the polyol (i.e. the formation of dimers, trimers, tetramers, and higher order oligomers) . By comparing the two chromatograms, it was found that the amount of multiple oligomers of Liprol 320 polyol opened by 1,2-propanediol was considerably less than that of Liprol 270 polyol opened by 1,3-propanediol. This is because the polyols produced with 1,2-propanediol have one secondary hydroxyl group which is significantly less reactive compared to a primary hydroxyl group. Hence, Liprol 320 polyols form oligomers less readily than Liprol 270 polyol, and in turn, a lower percentage of the available hydroxyl groups in Liprol 320 are consumed in forming oligomers. As a result, the hydroxyl value of Liprol 320 polyol is higher than that of Liprol 270 polyol formed under similar reaction conditions, as listed in . It was also expected that the viscosity of Liprol 320 polyol should be high due to its high hydroxyl value. However, the viscosity of Liprol 320 was found to be very close to that of Liprol 270 polyol, as shown in . Again, this can be explained by the low amount of oligomerization in Liprol 320 polyol, the predominance of lower molecular weight compounds resulting in lower viscosity. The high hydroxyl number as along with the low viscosity of such polyols will be beneficial in the preparation of polyurethane materials.The thermal properties of Liprol 270 and Liprol 320 polyols were investigated by MDSC measurements (data not shown). Unlike most of the current commercial available bio-based polyols The presence of free functional hydroxyl groups in Liprol 270 and Liprol 320 polyols and the expected structure of the PUs were confirmed qualitatively by FTIR spectroscopy as shown in . For both polyols, a strong stretching band at 3440 cm−1 (O–H group), a stretching band at 1740 cm−1 (CO group), an antisymmetrical stretching band at 1180 cm−1 (C–O–C group) and a stretching band at 1100 cm−1 (secondary O–H group) are present in both FTIR spectra ((a) and (b)). After the polyols are cross-linked with pMDI, the characteristic urethane N–H stretching bands at 3340 cm−1 are evident. In addition, the characteristic broadness of the CO vibration band at 1740 cm−1, attributed to the hydrogen bonding between CO groups and N–H groups, is observed. These changes indicate the formation of urethane linkages in both PU samples ((c) and (d)). Furthermore, the presence of an –NO band centered at 2270 cm−1 indicates that both PU samples still contain unreacted –NO groups. However, a 10% excess of diisocyanate was deliberately used in both PU preparations in order to ensure complete conversion of polyols to urethanes, given the occurrence of the unavoidable isocyanate-consuming side reactions such as the formation of allophanates, ureas or biurets. For the same NCO/OH molar ratio, the relative intensity of the –NO band was higher in Liprol 320-MDI PU than in Liprol 270-MDI PU sample. In addition, there was a shoulder at even higher wavenumbers (3400 cm−1) around N-H vibration region for Liprol 320-MDI PU, which might be attributed to unreacted –OH groups. These clear differences, even if precise quantitative analyses of the FTIR results are lacking, show that both –OH and –NCO amounts left after the reaction was higher in the case of Liprol 320-MDI PU. They are evidence of the strong effect of the steric hindrance of secondary hydroxyl group in cross-linking, resulting in less complete reactions with isocyanates than is the case with Liprol 270 polyol. It can be seen in that for the monomer structures, Liprol 320 contains three secondary hydroxyl groups whereas Liprol 270 contains only one. Of course, with the addition of a suitable catalyst to the polyurethane preparation, as well as the adjustment of the NCO/OH molar ratio, full consumption of the NCO groups during curing of Liprol 320 polyol could likely be achieved, but this is not the purpose of the present study.The gelation time for both Liprol 270-MDI and Liprol 320-MDI polyurethane was measured by monitoring the evolution of storage modulus (G′) and loss modulus (G″) with time at 50 °C. The point at which the two curves intersect is taken as the gel point of the system and is the point at which the system begins cross-linking. Usually, the magnitude of the modulus at the gel point is several thousand Pascal’s. The gel time is 20 min for Liprol 270-MDI and 100 min for Liprol 320-MDI PU, indicating that the former sample reacts faster than the latter one. This was attributed to the difference between the polyols’ structure as illustrated in . Thus, Liprol 270 polyol contains both primary and secondary hydroxyl groups, whereas Liprol 320 polyol contain only secondary functional hydroxyl groups and it is known that isocyanate generally reacts faster with primary hydroxyl groups than with secondary hydroxyl groups Sol fractions, amounting to <0.5% for both Liprol 270-MDI and Liprol 320-MDI PU, were obtained by multiple extractions with toluene. Hence, the extraction experiments showed clearly that the major fraction in both networks is the gel fraction. compares the SEC traces for the sol fractions of Liprol 270-MDI and Liprol 320-MDI PU with that of the starting Liprol 270 polyol. It can be seen that the molecular weight range of the three traces is similar, spanning from approximately 102 to greater than 104 Daltons. Thus, when comparing the PU SEC traces with those of the pure polyol, it was found that no peaks of higher molecular weight than those of the polyols were observed. This suggests that Liprol polyols have a very low mono-hydroxyl content, resulting in a low abundance of the sol fraction, at <0.5% of the weight of the PU.An attempt to evaluate the cross-linking density values through the swelling experiment was made using Flory–Rehner theory. It involves the determination of the polymer–solvent interaction parameter and the solubility parameter of the network; see Eq. . According to the Flory–Rehner theory for equilibrium swollen networks, the average molecular weight of the portion of the chain between cross-links, Mc and cross-linking density, νe can be calculated:1/νe=Mc/ρ2=[-V1(Aϕ21/3-2Bϕ2/f)][ln(1-ϕ2)+ϕ2+χ12ϕ22]where ρ2 is the density of the dry polymer, V1 is the molar volume of the solvent, ϕ2 is the volume fraction of the polymer in the swollen sample, f is the functionality of the network branch points, and χ12 is the polymer–solvent interaction parameter. A and B within the junction-fluctuation theory of Flory (JFF theory) The polymer–solvent interaction parameter, χ12, was calculated from the solubility parameters of the solvent, δ1, and the polymer network, δ2.The solubility parameter of toluene, δ1

= 18.2 (J/cm3)1/2, was obtained from the Polymer Handbook The swelling of Liprol 270-MDI PU in toluene, measured at room temperature is 32%, whereas that of Liprol 320-MDI PU is 35%. Surprisingly, Mc calculated from Eq is only around 200 g/mol for both PU networks when applying the affine model. By comparison with conventional PU networks, these values are unrealistically low. This could be due to the assumptions inherent in the network model, as well as to the irregular chemical structures that both polyols possess. In an affine network, the cross-links are fixed and consequently their positions deform affinely with macroscopic strain. In other words, the junction points are pinned to an elastic background and do not fluctuate during deformation. Consequently, this model neglects the defects that normally occur in a real network, such as dangling chain ends and temporary or permanent chain entanglements. Thus, deviations from the ideal molecular structure could result in an unrealistic value of Mc. In addition, it is of note that some of the reactive hydroxyl groups in both Liprol polyols are in the middle of the chain. These hydroxyl groups may not all be completely reacted with isocyanate, due to steric hindrance effects. A consequence of this would likely be the formation of networks with a large distribution of molecular weights between cross-links. In the case of a polyol monomer originating from linolenic acid, the most unsaturated fatty acid present in canola oil, the hydroxyl groups could be located at C9, C10, C12, C13, C15 and C16 positions on the fatty acyl chain. Therefore, the possibility of several distinct Mc values exists. For instance, Mc could be as low as 26 g/mol, in the event that two adjacent hydroxyls in the same chain react with isocyanate. In another example, an Mc value of 292 g/mol could occur if the primary hydroxyl groups (in the case of Liprol 270-MDI PU) at C9 from each of two fatty acyl chains were reacted to isocyanate. Hence, due to the irregular network, the possible number of Mc values is large, so the calculated value may not be accurate. A similar result was reported by Ryan et al. The Tg for both PUs was determined from the temperature dependence of tan δ (the temperature at the maximum tan δ) in DMA measurements (see ). Tg of Liprol 320-MDI PU is 100 °C, whereas that of Liprol 270-MDI PU is 86 °C. Both values are higher than the Tg values generally reported for PUs made with other vegetable oil polyols, such as those made by the hydroformylation of soybean oil (48 °C) or by the ozonolysis of canola oil (41 °C) ), which showed the same trend: the Tg of Liprol 320-MDI PU is about 15 °C higher than that of Liprol 270-MDI PU.The glass transition of a polymer network is affected by cross-linking density as well as chemical structure. The increase of Tg (∼15 °C) indicated that the flexibility of the polymer chains was reduced for Liprol 320-MDI PU networks shifting the rubbery state to higher temperatures. This could be explained by the higher hydroxyl value of Liprol 320 polyol (), which yields a more highly cross-linked network upon reaction with isocyanate. In addition, the lower oligomer content of Liprol 320 would lead to an increase in the rigidity of the resulting PU and hence, a polymer network with a higher value of Tg. The highly cross-linked network of Liprol 320-MDI PU also gives rise to higher Young’s modulus than Liprol 270-MDI PU, as listed in Plots from TGA and its derivative (DTGA) for Liprol 270-MDI and Liprol 320-MDI PU plastic sheets are shown in (a) and (b), respectively. For both samples, decomposition started at approximately 200 °C and ended at 500 °C. DTGA curves revealed three main degradation processes with noticeable differences in the whole temperature range. For Liprol 320-MDI, the temperatures of 5% mass loss was observed at 273 °C and the fastest mass loss in the first stage was observed at 315 °C. In contrast, Liprol 270-MDI showed higher thermal stability at this stage, with its 5% mass loss and fastest mass loss at 290 and 350 °C, respectively. However, Liprol 320-MDI showed better thermal stability in the second step, with the observation of 50% mass loss at 390 °C versus at 370 °C for Liprol 270-MDI.The thermal stabilities of PUs are dependent on the reactants, additives and conditions in which they are used. It is known that the first stage of degradation is related to urethane bond decomposition , Liprol 270-MDI PU displayed a tensile strength, a Young’s modulus and an elongation at break of 61 ± 1, 1430 ± 8 MPa and 5.9 ± 0.7%, respectively. Liprol 320-MDI PU displayed a tensile strength, a Young’s modulus and an elongation at break of 67 ± 2, 1700 ± 10 MPa and 4.6 ± 0.4%, respectively. The results are compared with that of PU made from castor oil, a widely available natural vegetable oil polyol. In all of these experiments, the isocyanate selected, as well as the NCO/OH molar ratio, were kept constant. As expected, castor oil based PU which has an intact glycerol backbone, displayed lower initial tensile strength (9.3 ± 0.3 MPa), Young’s modulus (8.3 ± 0.2 MPa) and longer elongation at break (62.3 ± 0.6%), compared to both Liprol PU samples. In addition, the tensile strengths of both Liprol PU were of higher values but lower elongation at break than of rhodium catalyzed hydroformylated soybean oil based PUs (38 MPa of tensile strength, 17% of elongation at break), and epoxidized soybean oil based PUs (46 MPa of tensile strength, 7% of elongation at break) Vegetable oils have three ester bonds that are susceptible to hydrolysis, particularly under alkali conditions. Most of the commercially produced vegetable oil derived polyols retain these ester bonds and would therefore, also be susceptible to hydrolysis. In addition, in the corresponding PUs, urethane bonds may hydrolyze when exposed to high humidity to give an amine and carbon dioxide in which the chemical stability of PU made using the test Liprol polyols from this study are compared with that of PU made from castor oil. As expected, castor oil based PU which has an intact glycerol backbone, displayed lower initial tensile strength and poor retention of strength and elongation on exposure to hot water and alkali, compared to both Liprol PU samples. In addition, the water absorption of castor oil PU was about 3% vs. 0.5% for the two Liprols. This is because diffusion of water through polymers is faster in the rubbery state castor oil based PUs, than in the glassy state Liprol based PUs. Higher water absorption leads to the observed greater decrease in strength and elongation in castor oil based PUs. This deficiency was partially overcome by removing the glycerol backbone from the polyol molecules and introducing ether groups during the ring opening reaction. As a result, both Liprol 270-MDI and Liprol 320-MDI PUs displayed an improved retention of strength and elongation after exposure to hot water and alkali solution at 80 °C for 7 days (). Overall, the results indicate that both Liprol polyols can be used in making tough, hard and rigid polyurethanes.Bio-based poly(ether ester) polyols (Liprol 270 and Liprol 320) with high hydroxyl numbers and low viscosity were synthesized from canola oil by epoxidation followed by acid catalyzed ring opening and transesterification reactions with 1,3-propanediol or 1,2-propanediol. The optimized procedure Experimental study on the seismic performance of steel–concrete beam–column connections for prefabricated concrete framesA novel type of prefabricated steel–concrete beam–column connection with different configurations for moment-resisting frames was developed for better constructability. Five beam–column connections, four prefabricated steel–concrete specimens, and one reference monolithic joint were tested under reversed cyclic load–displacement controlled conditions. The main variables were the steel form in beams and columns, fabrication method, and use of steel fiber reinforced concrete (SFRC) in the joint and connection parts. The cracking patterns and load–displacement hysteresis curves were recorded during the test. The efficiency of the developed connection was compared based on bearing capacity, energy dissipation, ductility, and stiffness. The results revealed that the prefabricated specimens with welded reinforcement connection exhibited flexural failure at the prefabricated beam, whereas the specimens with bolted end plates or weld-bolted H-steel beam connecting method failed through joint shear failure. The proposed prefabricated H-steel concrete connection with bolted end plates and SFRC had higher strengths and stiffnesses, more stable load–displacement cycles, and better energy dissipation capabilities. Moreover, the concrete spalling in the joint was adequately controlled, and shear deformation was also reduced. The H-steel beam connector in the proposed connection could effectively transfer loads under earthquakes.Prefabricated concrete members that are created in a factory exhibit better quality control and higher production efficiency than cast-in-place ones []. After being prefabricated, the members are transported to a construction site and fabricated into monolithic structures using different connection methods, resulting in a shorter construction period and better economic profits []. Thus, prefabricated structures have predictable significance in promoting the development of building industrialization and have been widely used in many countries []. The connection has an important function in transferring loads between one prefabricated component and another and is considered the vital part. The type of beam–column connection significantly influences the strength, stability, integrity, and constructability of a prefabricated concrete structure. If the prefabricated beam–column connections are reliable and stable, the fabricated concrete frame can achieve considerable seismic behavior, which has been demonstrated by many research studies. However, the behavior of prefabricated connections does not fully satisfy the requirements under earthquake action, resulting in beam–column connection failures []. Therefore, a reasonable and practical connection with adequate energy dissipation, stiffness, and strength has become a challenge for fabricated concrete moment-resisting frame structures.Currently, many studies have been conducted to evaluate the performance of different types of beam–column connections, including monolithic, welded, bolted, pretensioned, and hybrid joints []. Generally, the continuity of reinforcements between beams and columns is frequently achieved by anchoring or splicing steel bars, grouting sleeves, and cast-in-place concrete [] designed connections with U-shaped beam shells and experimentally revealed good deformation capacities but decreased hysteretic energy dissipation. Yan et al. [] experimented on five beam–column connections using grout sleeves under low-reversed cyclic loading. They reported that the specimens using grout sleeves had a slightly lower energy dissipation capacity than the monolithic connection. Moreover, the use of materials such as steel strands, steel angles, externally embedded rods, and shaped steel was proposed to connect the prefabricated members []. Moreover, experimental studies were performed and the results demonstrated that prefabricated specimens with adequate seismic capacity behave as monolithic connections. In addition, the connection measures were confirmed to be effective and reliable. However, anchoring or splicing reinforcements, and cast-in-place concrete might result in construction difficulty during the on-site assembly process. Additionally, the use of high-performance fiber-reinforced materials, instead of normal concrete, in the joint region is an attractive solution to delay crack propagation []. Recently, high-performance fiber-reinforced materials have been used in prefabricated beam–column connections []. These studies indicated that the deformation performance of connections improved.When a prefabricated beam–column connection is connected by a steel connector, welded or bolted connections are considered feasible methods [] studied the effect and seismic performance of reinforced concrete (RC) slabs, weld connection, and bolt connection for a new precast steel RC beam–column joint with steel beam brackets. They observed that the joint with a slab exhibited better seismic performance, but peak strength decreased owing to the bolt slip. Bahramia et al. analyzed the seismic performance of two new beams to precast column connections connected by welding or bolting with a corbel using nonlinear finite element analysis []. The analytical results revealed that the prefabricated connections exhibited a similar seismic behavior to a corresponding monolithic connection. Ghayeb et al. [] proposed a new type of hybrid beam–column connection and experimentally proved the steel angles significantly improved the seismic performance of precast concrete connections.Steel–RC connections make fabricated concrete frame structures a promising option, but studies of the seismic performance of connections with steel connectors are limited. Their fabrication and post-poured concrete in joint regions have been studied. However, the performance of specimens with steel connections outside the joint region that are reliable and compatible for construction is on high demand. Thus, this study developed a new hybrid prefabricated concrete beam–column connection characterized by H-steel beams, end plates, and steel fiber reinforced concrete (SFRC), which have advantages of easy construction, continuity of column longitudinal reinforcements, and improved seismic behavior. The continuity of the longitudinal reinforcements of the column may improve the integrity of beam–column connections. The H-steel beams and end plates used in the prefabricated beams and columns of the developed specimens have sufficient strength to ensure the continuity of the beam longitudinal reinforcements, and they can be easily assembled through bolting on site. Five specimens including monolithic and prefabricated connections were created and reverse cyclic loading was applied. The efficiency of the developed connection was evaluated in terms of failure mode, hysteretic curves, strength, stiffness, energy dissipation, strains, and shear deformation. The test results indicated that the proposed hybrid beam–column connections can be used in seismic zones.The configurations of the newly proposed prefabricated connection, which consisted of a prefabricated beam, prefabricated column, and connecting segment are shown in . The prefabricated beam and prefabricated column were connected using an H-steel beam, H-steel beam with end plates, or H-steel beam with web connecting plates. These steel connectors can reliably transfer stress from the beam ends to the column to elevate the strength and improve the constructability. Moreover, SFRC was poured into the joint core segment and the connecting segment to enhance the tensile strength.(d)). Four types of configurations used in the prefabricated beam were suggested: partly embedded H-steel beam with grooves inside the beam ((a)), partly embedded connecting plate and protruding longitudinal reinforcements of the beam ((c)), protruding longitudinal reinforcements of the beam ((b)), and partly embedded H-steel beam with a welded end plate ((d)). For the prefabricated column, two types of configurations were developed: an H-steel beam embedded partly in the prefabricated column ((a–c)) and an H-steel beam embedded partly and an end plate welded to the H-steel beam (The developed prefabricated beam–column connection employed steel connectors and welded/bolted connection methods used in steel structures to connect beams and columns that were fabricated in a factory for concrete moment-resisting frames, which have the advantages of rapid construction speed and high assembly efficiency. The connection position was located at a certain distance from the column face; thus, the plastic damage might be moved outward, and the damage of the joint could be avoided. The use of cantilevered H-steel beams through the column avoided the discontinuity of column longitudinal reinforcements and congestion of reinforcement bars in the joint area; thus, it improved the integrity of the joint and effectively transferred the load. The assembly process of the proposed beam–column connection was as follows. After the prefabricated column was installed on site, the prefabricated beams were lifted to the required position. Subsequently, the beam and column were connected through bolting or welding to form the H-steel beam concrete beam–column connections with variable configurations. Finally, the concrete was poured on site for the connecting segment.To understand the seismic performance of the proposed prefabricated beam–column connections visually and clearly, we designed one monolithic connection specimen (denoted as ZJ1) and four prefabricated connection specimens (ZHJ1, ZHJ2, ZHJ3, and ZHJ4) for comparative study. All connections in the test were designed as full-scale specimens based on a prototype moment-resisting frame with a story height of 2.8 m and a beam span length of 3.4 m. The reinforcement configuration of specimens conformed to the requirements of Chinese specifications GB 50011-2010 []. Moreover, to analyze the enhancement effect of different configurations on the proposed connections, we constructed the monolithic connection to initiate failure in the joint for comparison by increasing the interval of the transverse reinforcements. The sectional dimensions of the beam and columns in the test were 400 mm × 250 mm and 350 mm × 350 mm, respectively. The column height was 2800 mm and the beam length was 3550 mm.The dimensions and reinforcement details of each specimen are shown in . The main aim of this study was to compare the prefabricated connections with different connection configurations with the monolithic connection. Therefore, the same reinforcement details were used for the beams and columns of all specimens except for the connection configurations. Eight HRB600 bars with a diameter of 18 mm were placed in the beams as longitudinal bars, and 10 bars of the same grade with a diameter of 20 mm were arranged in the columns as the longitudinal bars through the joint area. The transverse reinforcements were HRB400, of which the intervals were 100 mm in beams and columns. The transverse reinforcement intervals were reduced to 55 and 50 mm for the beam and column ends, respectively, to prevent the premature damage of the beam and column ends from adversely affecting the test results. The yield strength standard value of the H-steel, end plate, connecting plate, and stiffener was Q235.The test variables were the connecting method, SFRC usage, steel skeleton in the beam, steel skeleton in the column, and fabrication method (). Normal concrete was poured into the prefabricated beams and columns of specimens ZJ1 and ZHJ1. For specimens ZHJ2, ZHJ3, and ZHJ4, SFRC was poured into the joint core segment and connecting segment, and normal concrete was poured into the other segments. Cantilevered H-steel beam with cross-sectional dimensions of 354 mm × 200 mm × 6 mm × 12 mm were embedded in the prefabricated columns. The lengths of the cantilever H-steel beams of ZHJ1, ZHJ2, ZHJ3, and ZHJ4 were 750, 950, 750, 710 mm.A 1.0% volume fraction of steel fiber with a diameter of 0.5 mm and length of 30 mm was used to provide resistance against shear stress []. The tensile strength of steel fiber was 1100 MPa, and the density was 7850 kg/m3. The proportion of normal concrete and SFRC is shown in . When the prefabricated beams and columns were poured, 150 mm cubic blocks were fabricated. After the curing period, the test blocks were tested under compression based on GB/T 50152-2012 [], the material properties of the steel bars and steel plates configured in the specimens were tested subjected to tensile tests. The test results are shown in The schematic and photograph of the test setup used in this test are depicted in , respectively. The bottom of the column was connected to the strong floor using a spherical hinge and the top of the column was connected using roller supports. The stability of the column during loading was ensured by lateral bracings at both ends of the column. All the constraints were designed to simulate the practical boundary conditions of the members. First, a constant axial load of 460 kN was applied at the top of the column using a hydraulic jack with a capacity of 1000 kN. The axial compressive ratio of the column was 0.15, which was equal to the ratio of the column axial compression force to the cross-sectional area and the concrete compressive strength. Second, the cyclic load was applied using actuators with a loading range from −500 to 500 kN and a displacement of 500 mm at the left and right beam ends. The left and right actuators applied the load in opposite directions., the loading history was divided into two stages according to JGJ/T101-2015 []: the load-controlled and displacement-controlled stages. Each loading cycle was repeated once at loads of 0.4Py, 0.8Py, and 1.0Py during the load-controlled stage before the specimen yielded, where Py is the yield load, which was obtained by observing the strains of the longitudinal bars in the beam. After the specimen yielded, displacement control was used. The displacement amplitudes of each loading cycle were integral multiples of the yield displacement. Each loading cycle was repeated three times. Finally, loading was stopped when the maximum load value at a certain loading cycle was less than 80% of the peak load. The loading rate was 1 mm/s.During the loading process, the joint shear deformation and rotation were measured using 14 linear variable differential transformers (LVDTs) (). Strain gauges were attached at the corresponding locations for measurement to understand the distribution of strain in the reinforcement, H-steel beam, and steel plate under cyclic loading (The crack patterns and failure modes of the monolithic and prefabricated specimens are shown in . The connections experienced four stages of cracking and failure: the appearance of flexural and diagonal cracks, yielding of reinforcements and steel plates, development of cracks and formation of the plastic hinge, and final failure.For the monolithic specimen ZJ1, four flexural cracks first appeared at the top and bottom of the beams near the column surface at a load of 50.7 kN. When the load increased to 90.8 kN, the first diagonal crack formed in the joint core. Moreover, flexural cracks propagated towards the beam axis. When the specimen yielded, the quantity and width of the cracks on the beam and in the joint continuously propagated, followed by several splitting cracks. As the displacement increased to 69.8 mm, the initial crushed concrete occurred at the joint region owing to a higher shear force. Finally, extensive concrete crushing and spalling caused the final shear failure of the joint owing to increased displacement.For prefabricated connections ZHJ1 and ZHJ4, the crack propagations were similar to those of the monolithic ZJ1 specimen at the initial loading stage. The initial flexural crack of ZHJ1 appeared at the right beam near the column face at a load of 60.5 kN. When the load increased to 90.4 kN, the initial flexural crack of ZHJ4 appeared at the beams away from the embedded H-steel on the beam. Meanwhile, diagonal shear cracks occurred in the joint core area. Compared with specimen ZJ1, fewer flexural cracks occurred on the beam of specimens ZHJ1 and ZHJ4 as the embedded H-steel enhanced the flexural resistance. However, the diagonal cracks rapidly propagated, followed by several splitting cracks resulting from the opening and closing of cracks caused by increased cyclic displacement. With further cyclic loading, concrete spalling occurred in the joint zone along with the diagonal directions and then was fully restrained by the H-steel, which resisted the joint shear force. Finally, both ZHJ1 and ZHJ4 failed through joint shear failure, and the longitudinal reinforcements in the prefabricated beams and columns did not yield. Additionally, there were few minor cracks in the connecting section of specimen ZHJ4 because of the slip caused by the fully bolted connection.Compared with specimens ZHJ1 and ZHJ4, similar crack patterns occurred in specimens ZHJ2 and ZHJ3 under initial cyclic loading. However, significantly more flexural cracks concentrated on the prefabricated beams without the strengthening of the H-steel after the displacement reached 69.5 mm. These cracks at the longitudinal reinforcement–H-steel interface were significantly wider than those at other locations. Subsequently, splitting cracks occurred in the prefabricated beam near the connecting segment, followed by the formation of plastic hinges. With increasing displacement, significant concrete crushing occurred in the plastic hinge region, accompanied by the fracturing of longitudinal reinforcements due to repeated tensile–compression buckling, resulting in the final bending failure of specimens ZHJ2 and ZHJ3.Monolithic specimen ZJ1 and prefabricated specimens ZHJ1 and ZHJ4 suffered from shear failure due to concrete crushing in the core of joints. However, ZHJ1 and ZHJ4 had less damaged concrete in the joint core area than ZJ1 did. This was primarily because of the embedded cantilevered H-steel beam in the columns, which resulted in enhanced shear resistance of the joints. Compared with ZJ1 and ZHJ1, the appearance of initial cracks in ZHJ4 delayed. Moreover, the diagonal cracks of connection ZHJ4 were significantly smaller in width than those of the monolithic connection ZJ1 and prefabricated connection ZHJ1 owing to the steel fibers restraining against the development of cracks. Thus, adding steel fibers in the joint region decreases the width and restrains the propagation of cracks. SFRC is necessary to control the cracks in the proposed connection core region. Therefore, specimen ZHJ4 experienced slight damage in the joint region, resulting from the combination of H-steel beams and steel fibers.The plastic hinges of ZHJ2 and ZHJ3 were located within a certain range around the connection on the beam. The main reason was that the longitudinal bars of ZHJ2 and ZHJ3 were welded to the cantilevered H-steel beam, which produced an abrupt change in stiffness at the connection, resulting in a higher stress of the longitudinal bars. Furthermore, crushed concrete was observed in the prefabricated beams of specimens ZHJ2 and ZHJ3, which was caused by longitudinal reinforcement fracture owing to the increased moment capacity. If the stirrup spacing of the steel–concrete transition section was decreased, the influence of shear force decreased and the specimens suffered a large deformation.The load–displacement curves are depicted in , which also shows the envelope lines of the specimens in blue. shows the comparison of skeleton curves for all connections. As shown in , the yield displacement was obtained using Park's method and defined as the intersection between the horizontal line at peak load and the line that passes through the origin and 75% of the peak load []. The ultimate displacement is equal to the load point in the post peak displacement stage when it corresponds to 80% of the peak load [In prefabricated connections ZHJ1–ZHJ4, the hysteretic loops were fuller, and the pinching phenomenon was less than that of the monolithic specimen. This was because the cantilever H-steel beam enhanced the elastic range, thereby dissipating more energy. Moreover, the average peak load was higher by over 30% than the monolithic connection ZJ1, indicating that the H-steel beam significantly increased the bearing capacity. However, the ultimate displacement was significantly lower than ZJ1 as the H-steel beam provided higher stiffness.Prefabricated connections ZHJ2 and ZHJ3 with welded reinforcement connections exhibited smaller hysteretic responses than specimens ZHJ1 and ZHJ4 with the bolted end plate connections. The pinching phenomenon was larger owing to the more severe damage to the plastic hinge on the prefabricated beam degrading the energy dissipation. The prefabricated beam types and cantilever H-steel beam length of specimens ZHJ2 and ZHJ3 were different, but their load–displacement hysteretic curves were essentially similar. After reaching the peak load, the two curves had a steep decrease in loading resistance caused by the fracturing of the longitudinal reinforcements. As the difference between ZHJ1 and ZHJ4 lay within whether the connection used end plates and SFRC, the bolted end plates and SFRC were important factors affecting the strength degradation, stiffness degradation, energy dissipation, and bearing capacity for this new type of connection. Among all the specimens, the ultimate displacement of the prefabricated specimen ZHJ4 was the largest. This increased maximum displacement was primarily because the SFRC and bolted end plates improved the concrete spalling and enhanced the deformation resistance capacity. For prefabricated connections, when H-steel beams were used in the precast column to connect the precast beam, the stress was transferred effectively from the beam ends to the joint, resulting in a fuller hysteretic response, regardless of steel skeleton in the beam and fabrication method.The ductility of a beam–column connection, reflecting the plastic deformation capacity without significant loss of strength after yielding, is a vital index of seismic performance. The ductility of the connection is frequently quantified using the ductility factor calculated as the ratio of the ultimate displacement to yield displacement. The ductility factors for all connections are listed in The average ductility factors for the monolithic connection and four prefabricated connections were 2.4, 2.1, 2.1, 2.0, and 2.4, respectively. According to ASCE/SEI 41-06 classification standards [The strength degradation ratio (SDR) is a vital indicator of assessing the seismic behavior of specimens under cyclic loading, and it is calculated using Equation , where Pfi and Psi are the strengths of the first and second loading cycles at the ith displacement level, respectively., specimens ZHJ2 and ZHJ3 with welded reinforcement connections exhibited the larger strength degradation ratio, followed by specimens ZHJ1 and ZHJ4 with the bolted end plate connections. The monolithic connection had the lowest SDR. Prefabricated specimens ZHJ2 and ZHJ3 exhibited a steep strength degradation at the final loading stage owing to the fracturing of the welded longitudinal reinforcements and severe crushing of concrete caused by the high stress at the connecting section. The strength degradation ratio curves of prefabricated specimens ZHJ1 and ZHJ4 were stable and had slight fluctuations. This could be attributed to the connection method between the cantilevered H-steel beam and anchored H-steel beam being more reliable. Additionally, the strength degradation of ZHJ4 was more stable owing to the pouring of SFRC, which could adequately restrain the crack development in the joint region. Moreover, the bolted end plates might have a positive effect on the strength degradation owing to the slight slippage caused by the fully bolted connection. To avoid the steep strength degradation, H-steel were required in the precast beam to connect with the precast column, regardless of SFRC usage and fabrication method.The strength degradation ratio of the monolithic connection and four prefabricated specimens was in the range of 0.8–1.0. The strength degradation of all specimens was less than 20%, which satisfied the requirements of ACI 374.1-05 []. The prefabricated specimens with H-steel connectors had less strength degradation owing to the H-steel having larger stiffnesses and bearing higher loads without significant strength loss under the reversed cyclic loading.A structure with sufficient stiffness can avoid excessive deformation and maintain stability under earthquake loads. Therefore, assessing the stiffness and stiffness degradation of the specimens is important to understanding the seismic performance of specimens. Stiffness degradation can be characterized by the variation in the scant stiffness during the loading process. The scant stiffness is defined as the peak load at the ith loading level by the corresponding displacement, calculated using Equation where + Pi and +Δi indicate the peak load and corresponding displacement at the ith loading level in the positive direction, respectively. Similarly, −Pi and −Δi are in the negative direction, respectively.). At each displacement level, the scant stiffness of the prefabricated specimens was greater than that of the monolithic specimen with the aid of the cantilever H-steel beam in increasing the bearing capacity. For the monolithic specimen, the yielding of the reinforcement bars and aggravation of the concrete cracks in the joint core severely affected the stiffness degradation. Similarly, the yielding of the H-steel web and damaged concrete in the joint core resulted in stiffness degradation of specimens ZHJ1 and ZHJ4. The stiffness degradation of specimens ZHJ2 and ZHJ3 was caused by the damaged concrete and fracturing of the longitudinal reinforcements at the connection segment at the beam, which should be considered to be strengthened at the steel–concrete transition section via decreasing the stirrup intervals.To better understand the trend of stiffness degradation, we define the stiffness degradation ratio as the ratio of the secant stiffness to the initial secant stiffness. shows the stiffness degradation ratio curves. The stiffness degradation ratios of the prefabricated connections ZHJ1–ZHJ4 were larger than that of the monolithic specimen after yielding, indicating the developed connecting methods alleviated stiffness degradation owing to the use of the H-steel beam, which had a larger elastic stiffness and can effectively transfer the load under earthquake actions.The inelastic deformation of the connection results in a large amount of energy dissipation. It reduces the energy transmission from a seismic action to other structural components to prevent structural collapse. Cumulative energy dissipation, which is frequently used to evaluate energy dissipation capacity, can be expressed by the sum of the areas enclosed by the load–displacement hysteretic loops., the cumulative energy dissipation of all specimens increased gradually owing to small concrete cracks before the displacement reached 40 mm. Subsequently, the cumulative energy dissipation increased rapidly due to the development of concrete cracks and the yielding of reinforcements and steel connectors. The cumulative energy dissipation of four prefabricated connections was greater than the monolithic specimen because H-steel beams were used in the prefabricated connections, indicating that the former had better energy dissipation owing to fuller hysteretic curves with smaller shrinks and a larger load-carrying capacity caused by less damage in the joint (). Additionally, specimen ZHJ4 with SFRC dissipated less energy than connection ZHJ1 owing to less concrete damage in the joint region. We deduced that SFRC restrained the concrete cracks and had a beneficial effect on concrete damage.The viscous damping ratio (he) is defined by Equation where SABCD is the area enclosed by curve ABCD, and SOEB + SOFD is the summation of triangular areas OEB and OFD., the four prefabricated specimens exhibited higher viscous damping ratios than the monolithic specimen because of the fuller hysteresis loops owing to the use of H-steel beams, which had a larger elastic stiffness and higher load-carrying capacity, resulting in effectively resisting earthquake loads. Specimens ZHJ1 and ZHJ4 with the bolted end plates exhibited the largest viscous damping ratio, followed by specimens ZHJ2 and ZHJ3 with welded reinforcements. Therefore, the H-steel used both in the precast beam and precast column connected through welding or bolting had positive a positive impact on energy dissipation. If the H-steel at the beam end dissipated much greater energy under reversed cyclic loading after yielding, the connections exhibited higher energy dissipation capacities. Similar results were reported by Xu et al. [The rotation capacity in the plastic hinge region can be estimated using moment–rotation hysteretic curves. The rotations of the specimens were measured using LVDTs 1–12 (). The bending moment at the beam end of the specimens was equal to the applied force (P) multiplied by the number of lever arms. shows the moment–rotation hysteresis curves for each specimen.Compared with the monolithic specimen, the four prefabricated specimens exhibited higher ultimate bending moments but lower maximum rotations. The results revealed that the increased moment capacity and rotation stiffness of the prefabricated specimens was caused by the cantilever H-steel beam in the columns. Compared with ZHJ1, ZHJ3, and ZHJ4, the length of the cantilever H-steel beam of the prefabricated connection ZHJ2 was larger, which decreased the rotation due to enhanced stiffness caused by H-steel. The length of the cantilever H-steel beam significantly influenced the rotation capacity. Additionally, specimen ZHJ3 exhibited a larger rotation at the final stage owing to the fracturing of the longitudinal reinforcements at the beam. Specimens ZHJ1 and ZHJ4 with the bolted end plates exhibited fuller moment–rotation hysteretic loops than other specimens. We can deduce that the proposed connection using H-steel can effectively transfer a load to increase the plastic deformation at the beam end. When the stiffness in the steel–concrete section changes abruptly, the stirrup spacing should be adequately decreased to achieve a ductility failure mode.The strain–displacement hysteretic curves of the H-steel beam web in the joint region are shown in The yield and ultimate strains of H-steel beam web were approximately 1492 and 2227 με, respectively, according to the material properties test results. The strain in the H-steel beams web of specimens ZHJ1 and ZHJ4 with the bolted end plates exceeded the yield strain at the displacement of 50 mm, which was consistent with the phenomenon of initial splitting cracks. After the displacement reached 70 mm, the strain in the H-steel beam web of the specimen ZHJ4 exceeded the ultimate value in the negative loading direction, and it was lower than the specimen ZHJ1 in the same displacement level. This was attributed to the phenomenon in which SFRC delayed crack propagation owing to the bridging mechanism. The maximum strain in the H-steel beam web of specimen ZHJ2 with welded reinforcement connection exceeded the ultimate strain, and it had a smaller strain in the positive loading direction. The average maximum strain of both ZHJ2 and ZHJ3 was close to the ultimate value because concrete was not damaged in the joint core region. The longitudinal reinforcements of the beam and column in specimens ZHJ1 and ZHJ4 did not yield, while the transverse reinforcements were yielded owing to the joint failure. For connections ZHJ2 and ZHJ3, the column longitudinal reinforcements and transverse reinforcements did not yield, but the beam longitudinal reinforcements were fracture resulted in flexural failure. shows the schematic shear deformation in the joint region. The shear deformation was measured using LVDTs 13 and 14 (where |AB| and |AD| are the horizontal and vertical distances between the diagonal LVDTs, respectively; Δ|AC| and Δ|BD| are the lengths AC and BD after joint occurred deformation, respectively. The shear force can be defined by Equation depicts shear force–shear deformation curves for beam–column connections.The ultimate shear forces of the four prefabricated connections were greater than the monolithic joint, indicating better shear bearing capability. The four prefabricated specimens had lower maximum shear deformations than the monolithic specimen owing to improved concrete spalling in the joint region at failure. The H-steel beams and SFRC restricted the joint shear deformation and enhanced the shear strength. At the same shear force level, the prefabricated connections exhibited less shear deformation than the monolithic specimen, which indicated that H-steel improved the stiffness in the joint region. Prefabricated specimens ZHJ1 and ZHJ4 with the bolted end plates experienced a larger maximum shear deformation than prefabricated specimens ZHJ2 and ZHJ3 with welded reinforcement connections, which was related to their failure modes. Before the joint shear failure, specimens ZHJ2 and ZHJ3 failed through flexural failure due to a significant change in stiffness caused by the fracturing of the welded longitudinal reinforcements.The shear demand (Vu) and shear strength (Vn) were calculated using Equations , respectively according to JGJ 138–2016 []. The shear strength was the sum of the contributions of the H-steel web, concrete, and stirrup in the core area. Particularly for the contributions of the steel web, the test result indicated that the H-steel web was in the shear yield state when the specimen reached the peak load, which was not local buckling owing to the effective constraints of concrete. Because the influence of axial compressive force was small, and the H-steel web was subjected to force in the plane, the shear strength provided by the H-steel web could be determined using 0.58fatwhw in Equation , which could significantly affect the joint shear strength.Vn=1γRE[2.3φjηjftbjhj+fyvAsvs(h0−as′)+0.58fatwhw]where Mar and Mal are the beam moments; Z is the distance from the upper reinforcement center to the lower one; Hc is the column height (2800 mm); ft is the concrete tensile strength (2.99 MPa); fyv is the transverse reinforcement tensile strength; fa is the steel yield strength; Asv and s are the sectional area and interval of the transverse reinforcements, respectively; tw and hw are the web thickness and web height of steel beam, respectively; h0 is the effective column depth; bj and hj are the effective joint width and depth, respectively; as' is the distance from the column compressive reinforcements to extreme compression layer; φj and ηj are the joint type coefficient and beam constraint influence coefficient, respectively (1.0); γRE is the seismic adjustment coefficient (0.85).The shear demands for ZHJ1, ZHJ2, ZHJ3, and ZHJ4 were 1722, 1760, 1790, and 1757 kN, respectively. The difference in shear demand for all prefabricated connections with different connecting configurations was small. The SFRC also slightly affected the shear demand. Based on JGJ 138–2016, the contribution of SFRC to the shear strength was neglected. Thus, the connections ZHJ2–ZHJ4 with SFRC had the same shear strength with specimen ZHJ1. The value of shear strength was 1646 kN, which was approximate to the shear demand of prefabricated connections. Specimens ZHJ1 and ZHJ4 with H-steel both in the precast beam and column were evaluated to be unsafe because the shear demand was larger than the shear strength, which was consistent with the failure mode (This paper proposes prefabricated steel–concrete beam–column connections with different configurations that are suitable for moment-resisting concrete frames. The following conclusions of the cyclic loading test conducted for five beam–column specimens can be drawn:The monolithic specimen and prefabricated connections with bolted end plates or weld-bolted H-steel connections failed via joint shear failure, whereas the prefabricated connections had less concrete crushing. The prefabricated connections with welded reinforcement connections exhibited flexural failure owing to a dramatic change in stiffness.The prefabricated H-steel concrete connections with different configurations demonstrated high energy dissipation capacities and shear strengths. Moreover, the prefabricated connections with the bolted end plates and SFRC exhibited larger deformation capacities and more stable load–displacement hysteretic responses.The proposed prefabricated H-steel concrete beam–column connections with different configurations were reliable, and the H-steel connector can effectively transfer loads under earthquake action. The different connecting forms had only a slight influence on strength and stiffness, while it significantly affected the failure modes and ductility.SFRC, instead of the normal concrete, is an attractive method of delaying crack propagation. Thus, it can be used in the vital region of the prefabricated connections.Jianxin Zhang: Conceptualization, Investigation, Writing-Original draft, Writing- Review & Editing.Chenchen Li: Investigation, Writing-Original draft, Writing-Review & Editing.Xiaowei Zhang: Investigation, Validation.Yanyan Li: Visualization, Investigation.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Reliability analysis for cementless hip prosthesis using a new optimized formulation of yield stress against elasticity modulus relationshipUsing classical design optimization methods for implant-bone studies does not completely guarantee a safety and satisfactory performance, due in part to the randomness of bone properties and loading. Here, the material properties of the different bone layers are considered as uncertain parameters. So their corresponding yield stress values will not be deterministic, that leads to integrate variable limitations into the optimization process. Here there is a strong need to find a reliable mathematical relationship between yield stress and material properties of the different bone layers. In this work, a new optimized formulation for yield stress against elasticity modulus relationship is first developed. This model is based on some experimental results. A validation of the proposed formulation is next carried out to show its accuracy for both bone layers (cortical and cancellous). A probabilistic sensitivity analysis is then carried out to show the role of each input parameter with respect to the limit state function. The new optimized formulation is next integrated into a reliability analysis problem in order to assess the reliability level of the stem–bone study where we deal with variable boundary limitations. An illustrative application is considered as a bi-dimensional example (contains only two variables) in order to present the results in an illustrative 2D space. Finally, a multi-variable problem considering several daily loading cases on a hip prosthesis shows the applicability of the proposed strategy.Traditional deterministic design methods have accounted for uncertainties through empirical safety factors. The designer does not take into account uncertainties concerning materials, geometry and loading. A number of uncertainties are encountered during the design of osteo-articular systems. These uncertainties are resulted from the variability of applied loads and materials properties, in addition to that resulting from the design modeling. They can be grouped in three main categories, namely irreducible, reducible and statistical uncertainties Design variables xi: the design variables are deterministic variables defined in order to optimize the system. They represent control parameters of the mechanical system (e.g., dimensions, materials, loads) and of the probabilistic model (e.g., mean values and/or standard-deviations of random variables).Random variables yi: the uncertainties are modeled by stochastic physical variables affecting the failure scenario. These variables can represent geometrical dimensions, material characteristics or applied external loading. The knowledge of these variables is not, at best, more than statistical information and it can be admitted as a representation in the form of random variables. The random physical variables represent the structural uncertainties, which are identified by probabilistic distributions.Normalized variables ui: they represent the transformation of the random variables from the physical space to a normalized one according to certain probabilistic distribution laws.The material of this paper is organized as follows: some objectives concerning reliability analysis are first presented in Section . A review of the previous formulations of material properties, especially, Young’s modulus and yield stress against density relationship, are presented in Section with our generalized formulation of the yield stress against Young’s modulus relationship in Section . Using some experimental results, the generalized formulation is next developed to find our optimized constants of proportionality in Section . A numerical validation of the proposed formulation for cortical and cancellous experimental results is carried out in Section . Two numerical stem–bone examples considering several daily loading cases are presented in Section . The first numerical example of a bi-dimensional variable case is considered as an illustrative 2D space modeling and the second one is a multi-dimensional variable case to show applicability of the reliability integration using the proposed formulation and Section The notion of reliability is very old. Ancient civilizations constructed huge buildings and mechanisms and many of these structures still exist, i.e., they have proven to be very reliable designs. However, the cost of construction of these structures was tremendous. Nowadays, the two main objectives in the design of structural systems are to design systems that have satisfactory reliability and are as inexpensive as possible There is no way to make a perfectly safe design. Ignoring uncertainty and using safety factors usually leads to designs with inconsistent reliability levels. Three types of uncertainties can be considered Irreducible uncertainty: irreducible (or Inherent) uncertainty is due to the inherent randomness in physical phenomena and processes. It arises during the description of a physical process and still exists even if unlimited data is available.Reducible uncertainty: reducible (or model) uncertainty may happen due to the use of imperfect models to predict outcomes of an action. It results from the simplification of modeling a true physical process and can be minimized by using more sophisticated model.Statistical uncertainty: it is due to the lack of data for modeling uncertainty. Or, it is related to the fitting of a parametric distribution and this uncertainty can be decreased by increasing the number of fitting data points. shows a simplified diagram for design under uncertainty. The design optimization process controls the input parameters (quantified uncertainties) presented by statistical diagram in order to satisfy the required output parameters (calculated uncertainties). The test process is a comparative process between the calculated output and the quantified input until convergence, as shown in Several strategies can be used for uncertainty measurements such as: Safety factor, Worst case scenario-convex models, Taguchi methods, Fuzzy set methods, Probabilistic methods… These strategies lead a high computing time to compute the probability of failure. An efficient optimization method based on reliability index can be easily implemented and perform the reliability analysis with a reasonable computing time.To estimate the reliability index, several techniques have been developed during the last 40 years, namely FORM (First Order Reliability Methods), SORM (Second Order Reliability Method) and simulation techniques ). For a given failure scenario, the reliability index β is evaluated by solving a constrained minimization problem:where u is the vector modulus in the normalized space (or so-called distribution parameters), measured from the origin see . In FORM approximation, the probability of failure is simply evaluated bywhere Φ(⋅) is the standard Gaussian cumulated function given as follows: gives sufficiently accurate estimation of the failure probability. defines the most probable failure point (MPP) see b. The resulting minimum distance between the limit state function H(u) = 0 and the origin, is called the reliability index βThe mechanical properties of bone depend on composition and structure. However, composition is not constant in living tissues. It changes permanently in terms of the mechanical environment, ageing, disease, nutrition and other factors. Kopperdahl and Keaveny where ρα is the ash density. This expression explains over 96% of the statistical variation in the mechanical behavior of combined vertebral and femoral data over the range of ash density (ρα

= (0.03–1.22 g/cm3)). Using the previous equations, the Young’s modulus and the yield stress in compression are respectively: E

= (1.47–17643.65 MPa) and σC

= (0.15–173.12 MPa). Furthermore, Keyak et al. For a simple test, let us consider an acceptable value of the ash density for trabecular bone, as: ρα

= 0.25 g/cm3. According to the model of Keller In this work, the relationship between the yield stress and the Young’s modulus is first generalized to meet the different design requests. Let us present the developed models or equations using some constants. The Young’s modulus and the yield stress against the ash density relationship can be respectively generalized as follows:where AE and Aσ are constants of proportionality, nE and nσ are exponents of proportionality. Since both Young’s modulus and yield stress are related with the ash density or apparent one, the Young’s modulus with yield stress can be related using a logarithmic transformation. Eq. After having simple developments, a generalized relationship between the yield stress in compression and the Young’s modulus can be written as follows:where Rσ/E

=

nσ/nE is the ratio of exponents. The different studies indicate that the mathematical dependency of bone compressive mechanical properties on composition is closely dependent upon the density and mineral content range examined and, in terms of a single compositional measure, is best predicted by apparent ash density expressed as a power function. We have focused on compression strength because the ultimate tension strength of bone tissue is usually established as a percentage of the compression strength. The tension yield stress can be written:Different values have been used for this ratio, from 0.5 to 0.7 for cortical bone and from 0.7 to 1 for cancellous bone According to some experiments, the constants of Eq. can be determined. It is also easy to determine the ratio of exponents Rσ/E

=

nσ/nE using two experiment points: (σCi,Ei) and (σCi+1,Ei+1). Eq. This way the ratio of exponents can be written as follows:In order to get all constants with an optimum fitting curve, an iterative (optimization) method can be used for at least three given experiment points: (σCi,Ei),(σCi+1,Ei+1) and (σCi+2,Ei+2).Let us consider the three experimental results for cortical bone presented in . Three logarithmic equations can be formulated as follows:The three logarithmic equations are optimized in order to find the constant values with an optimum fitness. The resulting optimum constants are presented in . Here, the relationship can be written as follows.When using the new model for both cortical and cancellous layers (), the results seem to be much closer to the experimental values than those produced by the classical model of Keller Thus, when designing a stem, we recommend optimizing the developed model to obtain the different constants for different bone material behaviors (isotropic, orthotropic…). To show the importance of the proposed model, two numerical applications are next carried out.a shows a 3D model of the studied stem, however, for simplicity a 2D model will be considered during the optimization process. An illustration of the studied stem with different layers is shown in The number of elements considered for optimization is 1476 nonlinear elements (8-node/PLANE82) and the total number of nodes is 4825 nodes. According to , the cortical (or compact) bone part is assumed to be a homogeneous and isotropic material with Young’s modulus E

= 17 GPa and Poisson’s ratio ν

= 0.3. The corresponding experimental yield stress is: σy

= 132 MPa where ɛ is the strain tensor and D is the elastic tensor. According to Huiskes et al. , the minimum stress value can be computed as follows:where E is the uniaxial Young’s modulus. To ensure long-term fixation, the minimum stress value in the surrounding bone has to exceed the threshold value σTar. Thus, the corresponding number of elements for metal region is 557 elements. In the present work three representative daily loading conditions of one-legged stance (L1), extreme ranges of motion of abduction (L2), and adduction (L3) are assumed . The boundary conditions at the distal end have no effect on the stresses in the proximal region. The fixation is carried out on lower bone cut (on the cortical layer) to avoid rigid-body motion.In order to evaluate the reliability level, the limit state function and the random variables should be determined. To determine the limit state function, a direct simulation can be carried out to get the different response results. To determine the most effective variable a sensitivity analysis is required. The random variables are presented by their mean and standard-deviation values.The output parameters can be represented by an indication of fracture stresses and loosening of prosthesis. The von-Mises stresses give an indication of the fracture stress at the different layers of the studied structure. The minimum stress value in the surrounding bone has to be kept above a certain minimum levels (Eq. ) to avoid the loosening of prosthesis functionality. According to , the third loading case is the most critical one. The limit state function is represented by the cancellous region stresses. Here, we note that the maximum von-Mises stress (σmax2=5.63MPa) is the closet one to the fracture ( shows the von-Mises stress distribution for the three loading cases. In the first and second cases, the maximum stresses are located in the metallic stem. But in the third one, the maximum von-Mises stress is located at the bottom right region of the cortical layer. Here, we can distinguish a tension failure case.The evaluation of the probabilistic sensitivities is based on the correlation coefficients between all random input variables and a particular random output parameter. The sensitivity plots only include the significant random input variables. shows the sensitivity measurements of the limit state function (output parameter) with respect to the input random variables (6 variables). When considering the three daily loading cases, there is a variant influence of the input parameters. However, the Young’s modulus of the cancellous and cortical regions has a higher influence relative to the other input parameters. This way when decreasing the Young’s modulus of the cortical bone, the maximum stress of cancellous regions will decrease (positive influence). In contrast, when decreasing the Young’s modulus of the cancellous bone, the maximum stress of cancellous regions will increase (negative influence).The objective is to find the Most Probable Point (MPP) which is represented by the minimum distance between of the origin of the normalized space and the most critical failure surface (limit state function). According to the previous stem–bone simulation, the limit state function is represented by the von-Mises stress at the cancellous layer. In order to formulate the reliability problem, Eqs. can be integrated to problem 1. Thus, for the given failure scenario (cancellous layer), the reliability index β is obtained by solving a constrained minimization problem:min:d(ui)=∑i=1nui2s.t.:H(ui,yi)=σmaxCan(ui,yi)-RT/C.AσeRσ/Elny2AE=0:g1(ui,yi)=σmaxCor(ui,yi)-RT/C.AσeRσ/Elny1AE⩽0:g2(ui,yi)=σmaxM(ui,yi)-σyM⩽0:g3(ui,yi)=σmaxM/B(ui,yi)-2y2U⩽0b) rather than in the space of physical variables (a). Hence, we adopt the law for a normal distribution, and define a normalized variable ui by the transformationwhere yi is a random variable with the mean value myi and standard-deviation σyi. The mean value myi may be adopted as a design variable xi (a). The standard deviations σyi are proposed proportional to the mean values (10%). According to the sensitivity analysis, we find two random variables are the most effective in the structure. Here, the physical space and normalized one in a pedagogical way (bi-dimensional space) can modeled in order to get the global optimum. However, when considering several random variables, the results are subject to classical difficulties in nonlinear programming: existence of local minima, gradient approximation and computational time. Since the reliability analysis is carried out in a normalized space (b), a special technique is developed in order to take advantage of the particular form of the reliability problem using APDL (ANSYS Parametric Design Language). The optimization algorithm, which is illustrated in , supplies us all information about the objective and constraint functions. This algorithm minimizes the minimum distance d(ui), which is carried out in the normalized space.For simplicity, the random variables xi corresponding to the Young’s modulus of the cortical and cancellous bone (E1,

E2) are normally considered distributed. Their mean values are presented in and their standard deviations are proposed proportional to the mean values (10%). shows the reliability indices for three different loading cases when considering 2 parameters.a shows the optimization problem modeling in a physical space where the limit state functions are presented by G(E1,

E2) = 0, however b shows the problem modeling in a normalized space where the limit state functions are presented by H(u1,

u2) = 0. In the physical space, the mean value is presented by the coordinates (x1,

x2), the MPP is represented by the coordinates (y1,

y2) and the reliability levels are presented by ellipses. We model the tension limit states by three limitation curves (continuous lines: GL1T(E1,E2)=0,GL2T(E1,E2)=0 and GL3T(E1,E2)=0) corresponding to the three loading cases and the compression limit states by three limitation curves (intermittent lines: GL1C(E1,E2)=0,GL2C(E1,E2)=0 and GL3C(E1,E2)=0) corresponding to the three loading cases. Here, the MPP is located on the minimum distance between the mean value and the failure limit L3 for tension limit state curve (GL3T(E1,E2)=0). However, in the normalized space, the mean value is presented by the origin (0, 0), the MPP is represented by the coordinates (u1,

u2) and the reliability levels are presented by circles according to Eq. . We model the tension limit states by three limitation curves (continuous lines: HL1T(E1,E2)=0,HL2T(E1,E2)=0 and HL3T(E1,E2)=0) corresponding to the three loading cases and the compression limit states by three limitation curves (intermittent lines: HL1C(E1,E2)=0,HL2C(E1,E2)=0 and HL3C(E1,E2)=0) corresponding to the three loading cases. Here, the MPP is located on the minimum distance between the origin and the failure limit L3 for tension limit state curve (HL3T(E1,E2)=0). We can also note that the third loading case L3 in tension is the most critical case. It is called the failure limit (or surface) and divides the space into safe and failure regions. The most probable failure point (MPP) is then found for βL3T=2.16 when considering tension failure case that leads to a reasonable level of probability of failure: Pf=1.54% using Eqs. . The reliability index is bigger when considering compression failure case: βL3C=4.38 that leads to a very small probability of failure: Pf

= 5.93 × 10−6.In this case, the random variables xi corresponding to the Young’s modulus and the Poisson’s ratio of different layers (E1,

E2,

E3,

ν1,

ν2,

ν3) are normally considered distributed. Their mean values are presented in and their standard deviations are proposed proportional to the mean values (10%). shows the reliability indices for three different loading cases when considering 6 parameters.For this six parameter optimization process, the most probable failure point (MPP) is also found for β

= 2.16 when considering tension failure case that leads to a reasonable level of probability of failure: Pf=1.54%. The reliability index is bigger when considering compression failure case: βL3C=5.28 that leads to a very small probability of failure: Pf

= 6.46 × 10−8. shows that the most effective parameter is the Young’s modulus of the cancellous layer. According to the experimental test of Aleixo et al. ). The experimental results are also prone to different errors (testing protocols…). To improve our design, the ratio of RT/C

≈ 0.7 is considered during the optimization process. Furthermore, the composition of bone materials can be changed according to several factors such as ageing, and disease. It is strongly recommended to integrate the randomness of material behaviors into the prosthesis design strategy. In the literature, several works correlate mechanical properties of bone materials with its composition The proposed strategy essentially consists in integrating reliability analysis into prosthesis design. When considering the randomness or uncertainty on the material properties of the bone, the change of these properties leads to change of its resistance. For example, when changing the elasticity modulus of the bone, the corresponding yield strength will be changed. In general, the composite structure of bone contains organic and inorganic components. Inorganic components are essentially responsible for the compression strength and stiffness, while organic components provide the corresponding tension properties. The developed formulation is mainly based on the inorganic component effects (explicit relationship). According to several experimental works, some coefficients are added to the proposed model in order to take in account the organic component effects (implicit relationship). The optimized formulation for yield stress against elasticity modulus relationship is then developed. Some experimental results are next used to show the proposed model accuracy relative to existing ones. To integrate the reliability concept, a sensitivity analysis is carried out to identify all material parameter roles. Two numerical examples considering several daily loading cases are optimized in order to show the importance of the proposed optimized model (formulation) and also the reliability integration during the design process. In both studied cases, the elasticity modulus of the cancellous layer is the most sensitive parameter. The different results lead to a reasonable level of probability of failure for tension failure case (most dangerous case). The new optimized formulation can be considered as a practical tool for osteoarticular system designers and can be easily implemented into design optimization process. For future developments of this model, the different bone behaviors (orthotropic, anisotropic…) can be considered in order to get realistic results. This integration also allows us finding the optimum position of the implant relative to bone layers with object of insuring a high reliability (confidence) level.Type and orientation of yielded trabeculae during overloading of trabecular bone along orthogonal directionsTrabecular architecture plays a major role in bone mechanics. Osteoporosis leads to a transition from a plate-like to a more rod-like trabecular morphology, which may contribute to fracture risk beyond that predicted by changes in density. In this study, microstructural finite element analysis results were analyzed using individual trabeculae segmentation (ITS) to identify the type and orientation of trabeculae where tissue yielded during compressive overloads in two orthogonal directions. For both apparent loading conditions, most of the yielded tissue was found in longitudinally oriented plates. However, the primary loading mode of yielded trabeculae was axial compression with superposed bending for on-axis loading in contrast to bending for transverse loading. For either loading direction, most plate-like trabeculae yielded in the same loading mode, regardless of their orientation. In contrast, rods oriented parallel to the loading axis yielded in compression, while rods oblique or perpendicular to the loading axis yielded in combined bending and tension. The predominance of tissue yielding in plates during both on-axis and transverse overloading explains why on-axis overloading is detrimental to the off-axis mechanical properties. At the same time, a large fraction of the tissue in rod-like trabeculae parallel to the loading direction yielded in both on-axis and transverse loading. Hence, rods may be more likely to be damaged and potentially resorbed by damage mediated remodeling.Trabecular tissue loss in osteoporotic and aging patients is accompanied by topological changes in microstructure, including the conversion of trabecular plates to rods (). Such changes negatively affect the elastic, yield, and damage behaviors, as trabecular plates play more crucial roles than rods in apparent modulus, apparent yield strength, and microdamage formation (). More rod-like morphologies, characterized by an increase in structure model index (SMI), are associated with a decrease in toughness and strength () and increased microdamage susceptibility during overloading of bovine tibiae (). SMI is also positively correlated with in vivo microdamage burden in human vertebrae (). If microdamage stimulates increased remodeling () that in turn leads to more rod-like morphologies (), unstable degradation of the mechanical properties may result.Trabecular bone is subjected to a variety of loads during activities of daily living, and the orientation of the applied strains with respect to the trabecular orientation plays an important role in trabecular tissue yielding. Thinning of trabeculae and perforation of plates are not uniform in osteoporotic bone, resulting in disproportionate changes in the mechanical properties along the longitudinal and horizontal directions. Trabeculae oriented horizontally tend to be perforated, become thinner, or eventually disappear (), while those oriented longitudinally tend to retain their thickness (). Such structures are more susceptible to buckling under normal axial compressive loads and damage from unusual or off-axis loading (). Computational models have been used to successfully study apparent level yielding () in trabecular bone. In bovine trabecular bone, computational simulations indicate less tissue level yielding for transverse loading than on-axis loading (). These results are consistent with experiments where an on-axis overload caused a 35% reduction in the elastic modulus of human vertebral trabecular bone along the transverse direction, while transverse overloading caused only a statistically insignificant 10% decrease in the on-axis properties (Understanding the effects of trabecular architecture on the mechanics of trabecular bone under various loading conditions should provide insight into bone quality, which will be useful in the development and evaluation of treatments for osteoporosis. The objective of this study was to identify the trabecular morphologies that are susceptible to tissue level yielding in trabecular bone. Specifically, the aims of this study were to (1) identify the yielded tissue in trabecular bone samples overloaded in on-axis and transverse compression using microstructural finite element analysis (micro-FEA) models; (2) decompose the samples into individual plate and rod elements that contained yielded tissue using individual trabeculae segmentation (ITS) technique (); (3) categorize the failure modes of individual trabeculae according to the predominant stress states; (4) compare the failure modes between the two apparent loading modes.Ten cylindrical bovine proximal tibial trabecular bone specimens from a previous study () were analyzed. The orientation of the specimens was controlled using micro-CT imaging to ensure that the principal trabecular orientation was aligned with the axis of the specimens (). The specimens were scanned at 20 μm isotropic resolution in a micro-CT scanner (μCT-80, Scanco Medical AG, Brüttisellen, Switzerland) and the architecture was quantified using the standard software (μCT Evaluation Program V4.3, Scanco Medical AG, Brüttisellen, Switzerland, ). The threshold for evaluation and subsequent finite element modeling was chosen to match the image volume fraction with that measured by Archimedes’s principle.Microstructural finite element models were created for each specimen by directly converting bone voxels into eight-node finite elements (). Cuboid regions, 5×5×6 mm3 in size, were taken from the center of the cylindrical specimens, allowing application of boundary conditions for uniform transverse loading. The images were downsampled to 40 μm isotropic resolution by region-averaging in order to reduce computational time while satisfying the requirements for numerical convergence (). The trabecular tissue was modeled as a homogenous isotropic material with a specimen-specific back-calculated tissue modulus. Briefly, a single step linear FEA was performed to calculate the ratio of tissue modulus to apparent modulus for each specimen. The specimen-specific tissue modulus was obtained by multiplying this ratio with the experimentally determined apparent modulus for each specimen (). A bilinear elastic tissue constitutive model with an asymmetric principal strain yield criterion () was applied with compressive and tensile tissue yield strains of 0.83% and 0.41%, respectively (). The Poisson’s ratio was set to 0.3. Each sample was analyzed twice, first with boundary conditions corresponding to 1.2% on-axis compressive strain, then with 1.2% transverse compressive strain. Geometric nonlinearity was not included, but the effects would be small for the dense plate-like samples and low apparent strains used in this study (ITS was used to identify individual plates and rods within each sample (), and the amount of bone tissue in each trabecular type – plate or rod – was quantified. Trabeculae were further classified as longitudinal, oblique, or horizontal based on their orientation with respect to the specimen axis, which was aligned with the principal trabecular orientation (The tissue strains were calculated from the models, and regions that exceeded the yield strains were identified. Due to the porous architecture of trabecular bone, bone tissue can yield due to either compressive or tensile strain under apparent compressive loading. As such, tissue that yielded due to exceeding the compressive or tensile strain limit was detected and segmented separately. The distribution of the yielded tissue within trabecular types and orientations, and the fraction of the total tissue within each trabecular type and orientation combination that yielded was calculated.Failed trabeculae were identified, and the fraction of trabeculae of each type or orientation that failed was quantified. Most trabeculae contained some yielded tissue due to the irregular mesh boundary introducing artificial stress concentrations (). As such, a threshold of 15% of the tissue within a trabecula was used to identify trabeculae that had failed. A parameter study was conducted to determine the effect of using different thresholds, and the results were not sensitive to this parameter when varied over a range from 5% to 20%. The trabeculae were further categorized as having failed in compression, bending, or tension based on the volume ratio of tissue that yielded in tension to compression being less than 1/4, from 1/4 to 3/4, or greater than 3/4.Statistical analysis was performed with Student’s t-test in Microsoft Excel. The Tukey post-hoc test was used to identify groups with significant differences for ANOVA using JMP 7.0 (SAS Institute Inc., Cary, NC).The samples were primarily composed of longitudinally oriented plates. On average, 80±10% (Mean±SD) of the tissue was found in plates, over 70% of which were oriented in the longitudinal direction. In contrast, over 70% of the rods were oriented in the horizontal direction. Longitudinal trabeculae had a greater volume than horizontal trabeculae (). Visualization software AVS (Advanced Visual Systems Inc., Waltham, MA) was used to verify the rod- and plate-like morphologies of the segmented trabeculae and their orientations (Most of the tissue that yielded was in plates and longitudinally oriented trabeculae for both loading conditions. Plates contained 81±11% of the yielded tissue for on-axis loading, and 69±12% of the yielded tissue was found in plates for transverse loading (a). Similarly, 78±8% of the yielded tissue was found in longitudinal trabeculae for on-axis and 63±10% for transverse loading (b). Combining these data, longitudinally oriented plates were the primary site of yielding, accounting for 73±11% of the total yielded tissue in apparent on-axis compression and 60±12% in apparent transverse compression, respectively.The apparent loading direction affected whether tissue yielded due to compressive vs. tensile strain. When compressed on-axis, over twice as much tissue yielded due to compressive vs. tensile strain in plates (p<0.01, a). In contrast, tensile yielding was more common in plates for apparent level transverse compression. Similarly, in rods over 1.3 times as much tissue yielded due to compressive vs. tensile strain for apparent level on-axis compression, while compressive and tensile yielding were equally common for apparent level transverse compression.When compared by trabecular orientation, the yielding modes differed for the two apparent loading directions. During apparent level on-axis compression, the ratio of tissue that yielded in compression to tension was greater than two in longitudinal trabeculae, but tensile yielding was predominant in horizontal trabeculae (b). In contrast, during transverse compression, tensile yielding dominated in longitudinal trabeculae (p<0.05), while there was similar amount of tissue yielded in both compression and tension for horizontal trabeculae (p>0.15).The fraction of tissue that yielded due to compressive vs. tensile strain within each trabecular type depended on apparent loading direction and trabecular orientation. In plates, there was a higher fraction of tissue that yielded due to compressive strain than tensile strain for on-axis loading (a), while tensile yielding dominated for transverse loading (b), regardless of the plate orientation. However, the yielding modes of rods depended on both the loading direction and their orientations. Following on-axis compression, the volume ratio of the yielded tissue that was strained in compression to tension was over four in longitudinal rods, between one and two in oblique rods, and less than one in horizontal rods during on-axis loading (a). This trend was reversed for transverse loading (In trabeculae oriented parallel to the apparent loading direction, the volume ratio of tissue that yielded due to compressive vs. tensile strain was higher in rods than in plates. During on-axis loading, the ratio was 5.2±2.4 for longitudinal rods, in contrast to 2.2±0.6 for longitudinal plates (p=0.001, a). During transverse loading, the ratios were 1.2±0.3 for horizontal rods and 0.6±0.3 for horizontal plates (p=0.002, b). When considering all yielded tissue, a higher fraction of the total tissue in rods parallel to the loading direction yielded than for similarly oriented plates for both apparent loading modes (p<0.05).The distribution of the failed trabeculae – those where more than 15% of the tissue yielded – depended on trabecular type and orientation for on-axis loading but not transverse loading (). Following on-axis overloading, the fraction of trabeculae that failed in compression and bending was higher than that in tension in plates and longitudinal trabeculae, while the fraction of trabeculae that failed in bending was the highest in rods and oblique trabeculae (p<0.05, a, c). The fraction of trabeculae that failed in tension and bending was the highest in horizontal trabeculae (p<0.05, c). In contrast, during transverse loading, there was no preferred trabecular failure mode, although a slightly smaller fraction of trabeculae failed in compression than in tension or bending for plates, longitudinal and oblique trabeculae (p<0.05, Understanding which trabecular microstructures are most susceptible to damage and failure under various loading conditions should provide insight into bone quality and the mechanisms of osteoporosis treatments. Longitudinal plates were the main site of trabecular yielding for both apparent on-axis and transverse compression in dense plate-like architectures, revealing the structural importance of these trabecular elements. However, during on-axis loading, longitudinal plates were axially compressed with superposed bending – as indicated by the predominance of compressive yielding – while during transverse loading, the plates were primarily bent as indicated by more tensile yielding. Bending was the most important failure mode in rods and off-axis trabeculae for both on-axis and transverse loading.The main strength of this study was the identification of the specific trabecular types and orientations using the ITS technique where yielded tissue was predicted by micro-FEA. The quantity of data and the need to investigate the trends for a population make such methods invaluable for post-processing micro-FEA results. However, there are also important limitations that must be considered when interpreting the results. First, bovine tibial trabecular bone specimens, which are plate-dominated structures, were used in the study, and the results may differ in rod-dominated structures, such as vertebral trabecular bone. Second, the relationships between tissue level yielding and microdamage formation or modulus decreases have not been fully established. As such, further studies of these correlations are needed.An important limitation of this study is the tissue level constitutive model. This constitutive model results in correct prediction of the apparent level yield behavior (), and the strain limits in the tissue level constitutive model are consistent with the yield limits measured in cortical bone tissue (). While these factors support its validity, there has been no direct correlation of the yielded tissue in the models to either permanent deformation or microdamage in actual samples. There is a correlation between the proportion of the predicted yielded tissue that occurs in longitudinal rods and the measured microcrack density (), but in general tissue level yielding does not correlate with microcrack density. Indeed, while microdamage occurs in regions of higher local stress and strain calculated by linear finite element models (), not all high-stress regions are damaged. As such, the yielded regions do not necessarily represent regions of visible microdamage. Neither permanent deformation nor submicroscopic forms of tissue damage have been quantified and compared to finite element models. As such, the constitutive model is a plausible, but not a proven model.The findings further explain the differences in the morphology of the predicted yielded regions between on-axis and transverse overloading (). Yielded regions are larger and more oriented during on-axis compression, because they occur in plates. In transverse compression, the plates do not have a single yielded region of a single mode, but instead have adjacent tensile and compressive yielded regions. In general, plates provide most of the mechanical support in the trabecular structure, and their yielding modes differ between apparent loading modes but are similar for all trabecular orientations. Recent studies that reached similar conclusions did not explore the yielding modes (). In contrast, rods of each orientation have different proportions of tensile and compressive yielding. When taking into account the loading orientation, rods parallel and perpendicular to the apparent loading direction always have greater fractions of compressive and tensile yielding, respectively.The results complement experimental studies of damage and overloading in trabecular bone. The major contribution from longitudinal plates during both on-axis and transverse loading suggests that damage caused by on-axis compression may also affect transverse mechanical properties. This is consistent with the experiments that found on-axis overloading caused a significant decrease in the shear modulus of bovine trabecular bone (), and a 35% reduction in the transverse apparent elastic modulus in human vertebral trabecular bone (). As such, in vivo microdamage that is associated with normal loading during activities of daily living may be detrimental to the mechanical properties for shear or other abnormal loads (The results also complement recent work by , which found that human femoral trabecular bone, when loaded off-axis has lower levels of tissue yielding and a higher proportion of tissue that yielded in tension than compression. Our results further confirm the concept of increased bending of the plate-like trabeculae when the apparent level loading is transverse to the principal trabecular orientation.The results extend our understanding of the relative roles of trabecular plates and rods beyond the elastic range () to the yielding stage. Although rods play a role in both on-axis and transverse compressive loading depending on their orientation relative to the loading direction, the greatest volume of yielded tissue occurs in trabecular plates for both loading modes. In osteoporotic and aging trabecular bone, horizontal trabeculae are preferentially thinned and perforated while longitudinal trabeculae maintain their thickness, leading to a more anisotropic structure that has a greater susceptibility to fractures (). This altered structure has a decreased number of plates along the horizontal direction, and the present results show that rods oriented along the apparent loading axis are more likely to fail than plates. Since yielding in rods is directly correlated to increased microcrack density (), the transition of horizontal trabeculae to a more rod-like morphology in osteoporotic bone may make the whole structure more vulnerable to damage from unusual or off-axis loading.None of the authors have any financial or personal interests with organizations that may benefit from this work.Supplementary data associated with this article can be found in the online version at The role of sclerotic changes in the starting mechanisms of collapse: A histomorphometric and FEM study on the femoral head of osteonecrosisTo assess the distributions of stress, strain, and fractured areas using a finite element model (FEM), and examine the osteoclastic activity histopathologically in osteonecrosis of the femoral head.Three femoral heads were obtained during hip arthroplasty for femoral head osteonecrosis. One sample with a normal area, two samples with a non-sclerotic boundary without collapse (Type 1), two samples with a non-collapsed sclerotic boundary (Type 2), and two samples with a collapsed sclerotic boundary (Type 3) were collected from each femoral head for the FEM and histopathological analyses. FEM was performed using CT data, and the distributions of von Mises equivalent stress, octahedral shear stress, octahedral shear strain, and simulated fractured area were evaluated. Furthermore, the osteoclast count at the boundary was compared for each type.In normal and Type 1 samples, the distributions of von Mises equivalent stress, octahedral shear stress, octahedral shear strain, and the fractured area were equally concentrated along the whole analytical range; however, in the Type 2 and 3 samples, they were concentrated along the thickened bone trabeculae at the boundary, which corresponded to the fractured area. Histopathologically, a significantly increased osteoclast number was observed only at the collapsed sclerotic boundary.These results demonstrated that both shear stress and shear strain tend to be concentrated on thickened bone trabeculae at the boundary. Fracture analyses revealed that the boundary of sclerotic changes, which results from the repair process, may be the starting point of the fracture. Additionally, the osteoclastic activity increases after collapse.Osteonecrosis of the femoral head (ONFH) is considered to be a bone infarction caused by ischemia To date, there are two hypotheses regarding the mechanism of collapse. One is based on the effects of shear stress at the boundary of necrotic and normal areas The three-dimensional finite element model (FEM) can be used to analyze the stress distribution by simulating loading and force In this study, we assessed the distributions of stress, strain, and the simulated fractured area in normal and boundary areas by FEM analyses. In addition, the osteoclastic activity in each area was examined using a histopathological examination.This study was approved by the institutional review board. Three femoral heads were used in this study. The femoral heads were obtained during hip arthroplasty for association research circulation osseous (ARCO) stage-3 ONFH from two males and one female with a mean age of 53 years (range: 34–63) The femoral heads were fixed in 4% para-formalin for three days and cut into 3-mm-thick sections parallel to the cervical axis. All three femoral heads were used for both the FEM and histopathological analyses, which were performed to examine osteoclastic activity. From the cut slices of one femoral head, the following samples (Width: 20 mm × Height: 15 mm × Depth: 3 mm) were collected based on both a macroscopic examination and specimen radiographs: one sample of a normal area, two samples with a non-sclerotic boundary without collapse (Type 1), two samples with a non-collapsed sclerotic boundary (Type 2), and two samples with a collapsed sclerotic boundary (Type 3) (). In total, 21 samples were collected from 3 femoral heads. Regarding the conditions at the boundaries, the samples that included a boundary were classified into three types: a non-sclerotic boundary without collapse (Type 1), a non-collapsed sclerotic boundary (Type 2), and a collapsed sclerotic boundary (Type 3).All of the 21 samples were scanned with high-resolution μCT (R_mCT T1, Rigaku, Tokyo, Japan). CT was performed at a voltage of 60 kV, current of 60 μA, resolution of 50 μm per pixel, and a slice thickness of 0.4 mm. Structural indices of trabecular bone were calculated using a 3D image analysis system (TRI/3D-BON; RATOC System Engineering, Tokyo, Japan). The parameters were calculated in 3D as follows: the trabecular volumetric bone mineral density (vBMD) was determined using a reference phantom (Kyoto Kagaku, Kyoto, Japan) b). In the fracture analysis, von Mises equivalent stress > 4.2 MPa was defined as the stress that induces trabecular fracture After obtaining measurements of FEM, all samples were soaked in 70% ethanol to remove fat from the bone marrow for one day. Thereafter, the samples were decalcified using EDTA for seven days, embedded in paraffin and cut into 3 μm sections. Hematoxylin and eosin (HE) staining was performed in all samples. In addition, tartrate-resistant acid phosphatase (TRAP) staining was performed in 21 samples to count the number of osteoclasts using a TRAP staining kit (WAKO, Osaka, Japan). Osteoclasts were defined as TRAP-positive multinucleated cells with more than three nuclei that existed around the trabecular bone The average numbers of osteoclasts among the three boundary types (Types 1, 2, and 3) were compared using a Poisson regression analysis. The statistical analysis was performed using the JMP 11.0 software package (SAS Institute, Cary, NC, USA). A p-value of < 0.05 was considered to be statistically significant.In three normal area samples, the distributions of von Mises equivalent stress, octahedral shear stress, and octahedral shear strain were equally concentrated along the whole analytical range (). In Type 1 samples (n = 6), the distributions of these mechanical properties were equally concentrated along the whole analytical range, including the necrotic, normal and boundary areas (g–k). In contrast, these mechanical properties were concentrated at the boundary in Type 2 samples (n = 6), (m–q), where the thickened bone trabeculae were observed. In Type 3 samples (n = 6), the distributions of these mechanical properties were also concentrated at the boundary (s–w). In fracture analysis, the simulated fractured area was distributed along the whole analytical range in the normal area and Type 1 samples (f, l), whereas it was mainly seen at the sclerotic boundary in Type 2 and Type 3 samples (In Type 1, no thickened bone trabeculae were observed at the boundary, where only small number of osteoclasts was present, similar to that seen in the normal area (). In Type 2, the number of osteoclasts remained small (c), even at the boundary where the thickened bone trabeculae were observed. On the other hand, in Type 3, a significantly increased number of osteoclasts was observed along the fractured bone trabeculae (To our knowledge, this is the first study to demonstrate the distributions of stress and strain at the non-collapsed boundary, where the concentration of these mechanical properties was observed along the thickened bone trabeculae; in contrast to the equal distributions noted in the normal area. The type classifications that were used to represent the conditions at the boundary in the present study seem to correspond to the ARCO stage, with ARCO stages 1, 2 and 3 corresponding to Type 1 (non-sclerotic boundary without collapse), Type 2 (non-collapsed sclerotic boundary), and Type 3 (collapsed sclerotic boundary), respectively. In Type 1, the distributions of shear stress and shear strain were equivalent in each area, which was completely different from the concentration of shear stress and shear strain seen at the sclerotic boundary in Type 2. These results suggest that the concentration of shear stress and shear strain at the non-collapsed boundary may depend on the degree of sclerotic changes due to thickening of the bone trabeculae. Furthermore, the results of the fracture analysis suggest that the non-collapsed sclerotic boundary may be the starting point of the fracture. In our recent study using SPECT/CT with 99 m technetium hydroxymethylene diphosphonate, the osteoblastic activity in the pre-collapsed stage was found to gradually increase around the necrotic lesion Based on the hypothesis that osteoclastic bone resorption at the boundary may be a cause of collapse, several studies have reported that alendronate, a bisphosphonate compound, shows effectiveness for the prevention of femoral head collapse in cases of ONFH Although the distributions of both shear stress and shear strain were found to be concentrated along the sclerotic boundary in this study, these distributions may not necessarily correspond to the site of collapse in clinical cases. Collapse is known to appear not only inside the necrotic lesion, but also in the subchondral region In this study, plain radiographs showed the sclerotic line in all of the femoral heads before the surgery. Nevertheless, no sclerotic line was observed in some of the slice samples that included the boundary, which might indicate differences in the progression of the sclerotic changes in each sample. The location and extent of the necrotic area are considered to be the most important factors affecting the occurrence of collapse. The rate of collapse in cases where the necrotic area involves more than two-thirds of the weight-bearing portion of the femoral head is reported to be around 94% This study is associated with several limitations. Each sample was collected from a collapsed femoral head, although an ideal analysis of the distributions of stress and strain at the boundary should involve analyses of the whole femoral head before collapse. However, it is impossible to obtain such specimens of the entire femoral head prior to collapse, since the patient has no pain. Therefore, surgically resected femoral heads containing a non-collapsed medial boundary were used in this study. The second limitation is the small number of samples that were examined, mainly due to the rarity of femoral head specimens containing a non-collapsed medial boundary. Furthermore, it was difficult to collect samples containing a boundary corresponding to each type from the same femoral head. Although the data of the current study were not sufficient for proving whether the concentration of stress and strain at the sclerotic boundary of the necrotic lesion actually causes collapse, our results may at least serve as basic data for future studies designed to clarify the mechanisms of collapse.In conclusion, the current study demonstrated that both shear stress and shear strain tend to be concentrated on thickened bone trabeculae at the boundary along with the progression of sclerotic changes, whereas increased osteoclastic activity is not observed unless collapse has occurred. The results of the fracture analysis revealed that boundary areas, in which sclerotic changes resulting from the repair process are present, may be the starting point of fracture. We therefore consider that sclerotic changes at the boundary may play an important role in the pathomechanism of collapse.The authors declare no conflicts of interest in association with the present study.Study design: KK, TY, and GM. Acquisition of samples: KK, TY, GM, KS, and YK. Study conduct: KK, TY, GM, KS, and YK. Drafting manuscript: KK. Revising manuscript: TY and GM. Approving final version of manuscript: KK, TY, GM, KS, YK, and YI. KK and TY take responsibility for integrity of the data analysis.Photothermally enabled MXene hydrogel membrane with integrated solar-driven evaporation and photodegradation for efficient water purificationSustainable and energy-efficient water purification making use of solar energy is highly desirable to address water scarcity and pollution crisis. However, it remains a challenge to achieve full solar spectrum utilization with photothermal and photodegradation capability. Herein, inspired by the unique optical property of MXene, a novel assembly of MXene hydrogel membrane with synergistic photothermal and photocatalysis effect is proposed for integrated water purification. The MXene hydrogel membrane is fabricated based on the structure-directing of self-stacking MXene nanosheets and its abundant molecular interactions with the polymer matrix, polyvinyl alcohol (PVA), and the multifunctional layer-crosslinker, porphyrin. The obtained MXene hydrogel membrane exhibits fascinating physicochemical properties combining dynamic hydrophilic network of hydrogel and permeability of membrane, making it a preferred medium for both vapor generation and photodegradation. Moreover, calculation and experimental results illustrates the charge redistributions and coupling interactions between MXene and porphyrin, which imparts enhanced photothermal effect and photocatalytic activitiy. As a result, the MXene hydrogel membrane exhibits an high solar-driven water evaporation rate (1.82 kg m−2

h−1) and a photodegradation efficiency (90.5 %), rendering an integrated water purification capability under one sun irradiation. This work presents a feasible and effective route towards develop of MXene-mediated cooperative photochemical and photothermal solar energy conversion for sustainable water purification.Freshwater scarcity is a daunting challenge which will continue to aggregate in the future with the development of global economy and society. This situation can be further exacerbated by the on-going water pollutions, which poses great threats to the environment and human health due to the presence of hazardous organic pollutants in wastewater Fundamentally, to achieve efficient water purification by integrated solar-driven evaporation and photodegradation, functional materials with cooperative photothermal conversion and photocatalytic activity is highly sought after Recently, titanium carbide (Ti3C2Tx, T = –F, –O, and –OH), a kind of two-dimensional (2D) MXene materials, has drawn considerable attention due to its broad solar-spectrum absorption, outstanding photothermal effect, and hydrophilic 2D interlayered channels In this work, we present a novel and versatile application of MXene for the assembly of hydrogel membrane (MAP) for photothermally enabled integrated water purification. Our design mainly makes use of the fascinating physicochemical properties of hydorgel membrane that combinesd dynamic hydrophilic network of hydrogel and permeability of membrane, which makes it a preferred medium for both vapor generation and photodegradation All working solutions were prepared using American Chemical Society-grade chemicals and Milli-Q water. Ti3AlC2 (MAX, purity > 98 wt%). Nylon filter film and PVDF filter film (pore size ∼ 0.22 μm) was purchased from Millipore. Meso-tetra(4-carboxyphenyl) porphyrin (H2TCPP) suspension was purchased from Frontier Scientific Co., Ltd, and Polyvinyl Alcohol (PVA) was purchased from Alfa Aesar.Ti3C2Tx nanosheets were synthesised based on an LiF and HCl etching method. In this process, 0.5 g Ti3AlC2 was immersed in an HCl (9 M) and LiF (0.5 g) aqueous solution and the resulting mixture was magnetically stirred at 35 °C for 24 h. The resulting Ti3C2Tx solution was extensively washed and then dispersed in deionised water (DI), followed by a mild ultrasonication process. After a further centrifugation and washing process, the Ti3C2Tx MXene dispersion colloids was obtained.Typically, an optimized MXene dispersion colloids (10.0 mg) was first fully stirred and mixed with Polyvinyl alcohol (PVA) in an optimized ratio of 1.0:0.3 (w/w), followed by the addition of porphyrin. The resulting mixtures were fully stirred and subjected to a further filtration process on filter film (∼0.22 μm), leading to formation of the MXene-PVA-Porphyrin (MAP) hydrogel membranes. After being washed three times with DI and dried at 60 °C under vacuum for 24 h, the dry MAP hydrogel membrane could be peeled off after the fully self-crosslinking. Series of MAP hydrogel membranes consist of different mass ratios of MXene and porphyrin (1.0:0.05, 1.0:0.1, and 1.0:0.2) were fabricated, denoted as MAP5, MAP10, and MAP20, respectively. The MAP20 hydrogel membrane was chosen as the typical membrane after a comprehensive optimization. As a comparison, MXene membrane without porphyrin content was also fabricated based on the same process.Material structures were characterized by transmission electron microscopy (TEM; JEOL 2011F) and field-emission scanning electron microscopy (FESEM; FEI Quanta 450). Grazing incidence X-ray diffraction (GIXRD; Ultima IV) was used to determine the crystalline structure of the membrane samples. Water contact-angle measurements were carried on the sessile drop method using a drop-shape analyser (FM 4000, Krüss, Germany). Optical coherence tomography (OCT, THORLABS) was used to obtain 3D optical sections of the internal structure. Raman spectrometry was conducted with a Renishaw-200 visual Raman microscope using a 633 nm laser beam. Elemental chemical states were detected using X-ray photoelectron spectroscopy (XPS; GESCALAB220i-XL). Absorption spectra were measured on an ultraviolet–visible spectrometer (UV–Vis 3600, Shimadzu) incorporating an attached integrating sphere. The membrane’s thermal conductivity was measured by a Mathis TCi thermal conductivity analyser (C-Therm). Swelling properties of the membranes were evaluated by immersing a ∼0.01 g dry membrane in 100 g DI water at room temperature. The swelling ratio, SW, was calculated based on the equation:where W0, and Wt represent the mass of the membrane at the initial and time t, respectively.Photothermal evaporation experiments were carried out using a Xe short-arc lamp (CEL-HXF300) as the illuminator, equipped with an optical filter for standard AM 1.5G spectrum. RhB solution (5 mg L−1), seawater (3.5 wt%, Science Park, Hong Kong), and high salinity water (10.0 % NaCl) were treated. Before test, the membrane was fully wetted to achieve the adsorption–desorption equilibrium. During these tests, the indoor test humidity and temperature were ∼ 60% and ∼ 25 °C, respectively. Weight changes were monitored using an electronic analytical scale (accurate to 0.1 mg) and were recorded in real-time. Surface temperature and IR thermographs were captured using an IR camera (FLIR E5).Photodegradation tests were carried out in a 100 mL quartz beaker containing an aqueous suspension of Rhodamine B (RhB, 30 mL, 5 mg L−1), and a piece of membrane about ∼ 10.0 mg. The light intensity was kept at one-sun (1 kW m−2) using Xe short-arc lamp (CEL-HXF300) as the light source for the duration. Before being subjected to sunlight irradiation, the membranes were kept in the RhB solution in the dark for 120 mins to get the adsorption–desorption equilibrium. For studying RhB photodegradation, the maximum UV–Vis absorption peak (553 nm) was selected for concentration monitoring. The total organic carbon (TOC) of the system was measured using a TOC analyser (TOC-VCSH, Shimadzu). The photocatalytic capability was evaluated using phenol (30 mL, 5 mg L−1) as as another model pollutant, and its degradation rate was measured by monitoring absorbance peak at 270 nm. Direct confirmation of the generation of radical species, trapped by 5, 5-dimethyl-1-pyrroline N-oxide (DMPO) was done using an electron spin resonance spectrometer (ESR, Bruker Elexsys A200).Density Functional Theory (DFT) calculation was performed by using the VASP package. The exchange correlation energy was depicted based on generalized gradient approximation by functional of PBE. The plane wave basis set of 550 eV cutoff and spin polarization were used in all calculations. The k-point grids of 2 × 2 × 1 and vacuum space>12 Å were used. The zero damping DFT-D3 dispersion correction method of Grimme was applied to illustrate the van der Waals (VdW) interactions of the system. The tolerance convergence accuracy with the total energy less than 2.0 × 10−5 eV/atom was set, the maximum force on per atom was less than 0.01 eV/nm. The charges transferred in the system was computed by Bader charge analysis.a displays the fabrication process of MAP hydrogel membrane. Typically, Ti3C2Tx MXene colloid dispersion was firstly prepared though selective etching of Al layers from the Ti3AlC2 phase (), followed by being exfoliated in DI water under ultrasonication (). Then, the optimized amount of PVA and porphyrin () was added to MXene colloid dispersion, yielding a stable MAP hydrogel membrane after a filtration process. The self-stacking Ti3C2Tx serves as efficient structure-directing based on abundant molecular interactions during the assembly process. Besides, the flexible PVA acts as effective polymer matrix, which provides sufficient mechanical strength and hydrophilic groups. Also, porphyrin, characterized by the conjugated π-π interactions and ring-shaped distribution of –COOH groups, contributes largely to hydrophilic network as a multifunctional crosslinker and photothermal and photocatalytic activity.b and c, the exfoliated Ti3C2Tx nanosheets demonstrates an interlayer distance of approximately 14.8 Å. The slightly broadened interlayer spacing provides abundant channels for the water transport. As shown in the SEM image (d and inset), the MAP hydrogel membrane at dry state displays a relatively smooth surface topology with porphyrin uniformly distributed within interlayers. The membrane had an observed average thickness of ∼ 12.0 μm, with abundant inter-layered channels created by the stacking of MXene nanosheets. In addition, the elemental mapping of MAP hydrogel membrane shows a uniform distribution of C, Ti, and N (e), further verifying the homogeneous distribution of porphyrin and MXene. Also, the swelling behaviour of MAP hydrogel membrane is schematically illustrated in f, and the corresponding images of membranes before and after swelling were shown in g and the inset. The membrane area increased from 4.15 cm2 in the dry state to 9.62 cm2 in the swollen state, indicating a favourable hydrophilic network. Especially, the sufficient water transport channels and good hydrophilicity of hydrogel membrane can be further verified by the SEM image of sample freeze-dried at swollen state (h), initial contact angle (55.1°, inset of a, the characteristic peaks corresponding to (2 0 0) planes of MXene demonstrates a low angle shift in comparison with control MXene (), indicating a broaden interlayer spacing. This interlayer spacing can be further broadened after fully swelling in water, while still maintains a stable structure. Further evidence can be obtained by the OCT images (b), in which MAP hydrogel membrane displays stable structure with much more green pixels at swollen state, compared with the original state. The swelling behaviour and hydrophilicity of the MAP hydrogel membrane in DI water was investigated. exhibits a good water absorption dynamic and a swelling equilibrium ratio of about 85.0 % in 60 mins, which is equivalent to a high-water absorption rate of 21.6 kg m-2h−1. In comparison, the control MXene membrane exhibits much slower swelling behaviour with low swelling ratio of 30.0 %, which cannot be classified as hydrogel membrane.In addition, the structural interactions of MAP hydrogel membrane were characterized by XPS spectra. shows MAP hydrogel membrane displays the characteristic peaks of Ti3C2Tx, corresponding to the C–Ti (281.7 eV) and O–Ti (529.5 eV). Further, more characteristic peaks of C = O (285.9 eV) and O = C (531.9 eV) can be detected, related to the –COOH group of porphyrins. Besides, the FTIR-ATR spectra () exhibit the characteristic peaks of Ti-C, Ti-O, Ti-F, and C-F bonds that related to Ti3C2Tx MXene, as well as a red shift of C-O, –COO-, and C = O bonds as a result of the strong interactions generated in MAP. Taking advantage of these strong molecular interactions between porphyrin and MXene, the MAP assures stable structure with enabled electron density shift and enhanced localized electric field. The increased local electric fields of MAP can be well illustrated by the enhanced Raman signals (f), which reveals enhanced characteristic peaks at 399.3 and 620.8 cm−1, corresponding to the Eg group vibrations of Ti, C and the surface functional groups. Peaks assigned to D band (1320 cm−1) and G band (1570 cm−1) that related to the highly disordered (amorphous) carbon structure and defects, are also greatly increased in the MAP at the presence of porphyrin. Noted that these abundant interactions of MAP simultaneously ensure a stable mechanical property, exhibiting a high tensile strength of 68.2 ± 2 MPa, with a Young modulus of 31.2 ± 1 MPa (To evaluate the solar absorption ability of membranes, UV–Vis-NIR absorption and reflection spectra were measured (). All the MXene based membranes display the distinct absorption of Ti3C2Tx, which consist of two characteristic strong absorption peaks centred at 610 nm and 1148 nm. These absorptions fit well with the AM 1.5G solar spectrum and covers the UV–Vis-NIR region, which could harvest the maximum amount of distributed light energy of the sun. Moreover, the MAP exhibits much stronger and broader bandwidth of solar absorption compared with the control MXene membrane. This is mainly due to the enhanced absorption in UV–vis bandwidths (≤600 nm), and absorption in the high near-infrared bandwidths (≥1148 nm) after coupling with porphyrin. As a result, the MAP was endowed with outstanding photothermal effect, which can be further quantified in terms of the temperature increase under one-sun illumination (1.0 kW m−2). As shown in b, the surface temperature of MAP increases rapidly to 60. 4 °C in 60 s, much higher than that of control MXene membrane (40.9 °C). Accordingly, the same trend can be verified by the surface temperature profiles as a function of time (c). Especially, the highest ΔT of MAP is 39.3 °C after 5 mins, which is nearly 1.6 times that of MXene (24.6 °C), indicating largely enhanced photothermal conversion.The efficient photothermal effect of MAP is largely attributable to the synergistic effects of MXene and porphyrin, which generate coupling physicochemical environment based on plasmonic MXene and the π-conjugated porphyrin. This favourable coupling interactions and charge redistribution can be further illustrated by density functional theory (DFT) calculations. According to difference charge distribution map (d-f), the yellow isosurface surrounding porphyrin and between the interface of porphyrin-MXeen layer demonstrates strong positive charge accumulation, while the blue isosurface appears near the top of MXene layer exhibts the charge depletion, indicating significant charge redistribution. Based on the Bader analysis results, there are approximately 4.4 electrons transfered from Ti3C2Tx to per porphyrin molecule. Moreover, the calculated projected density of states (PDOS) of porphyrin-MXene system (g) exhibits greatly increased electron states and a high value of local states across the Fermi level, further indicating enhanced electron motilities and metallic behaviour.Fundamentally, taking advantaging of the coupling physicochemical environment, the conjugated porphyrin ring could behave as the electron collector and antenna, which contributes to photothermal conversion and generation of high-energy state of photoinduced charge. Moreover, the unique plasmonic MXene could enable the high-density metal-like free electron to induce the localized surface plasmon resonances generation in forms of collective oscillation of photoexcited hot electrons. It therefore not only imparts efficient localized photothermal heating, but also promotes the transfer dynamic of active photon carriers for enhanced photocatalytic capability h, the band gaps of membrane were calculated based on the extrapolation of the linear range obtained from modified Kubelka–Munk function [A(hν)]2 versus photon energy (hν). MAP exhibits a band gap (Eg) narrowing (1.0 eV) compared with the control MXene (1.25 eV), which could absorb more photons with higher energy greater than the bandgap value, indicating more efficient photocatalytic activity.On one hand, solar-driven evaporation performance was evaluated using a lab-designed solar-thermal device () under one-sun irradiation. During test, the membrane, which had a thermal conductivity of 6.5 W m−1 K−1, was placed on top of a piece of cotton cloth-wrapped polystyrene foam that could float on top of the solution as a thermal insulator and support. a shows the surface temperature monitored using an IR camera. The MAP hydrogel membrane demonstrates a rapid increase of temperature within 10 min and reaches a steady state at about 41.8 °C after 60 mins, which is much higher than that of the bulk water (29.6 °C). The corresponding time-dependent IR images (Inset of a) further verify this temperature increase process. b and c shows the time-dependent mass changes within 120 mins. Results shows that the evaporation rate of MAP hydrogel membrane is as high as 1.82 kg m−2

h−1, which is about 1.5 times and 6 times of that of MXene membrane and bulk water, respectively. Additionally, the solar-to-vapour conversion efficiency (η) of the MAP hydrogel membrane was calculated based on the following Equation: where ṁ denotes the evaporation rate under illumination,

hLV

represents the apparent liquid–vapor phase change enthalpy (including the sensible heat Hs and phase change enthalpy Hv), and

qi

is the solar illumination. Like the hydrogel materials, the apparent enthalpy of the hydrogel membrane was evaluated based on the darkness experiment with pure water, which exhibited an evaporation rate of 0.086 and 0.156 kg m−2

h−1, respectively (). Therefore, the MAP20 hydrogel membrane exhibited a η value of 73.5%. The outstanding solar evaporation performance is largely attributable to the superior features of the hydrogel membrane, which not only assures efficient photothermal conversion for heat localization, but also provides a stable hydrophilic network for continuous water pumping.On the other hand, photocatalytic capability was first evaluated based on a photodegradation experiment using RhB solution as a typical model pollutant. d shows the UV–vis absorption spectra of RhB solution as function of time during photodegradation at present of MAP hydrogel membrane. The typical absorbance peak for RhB (554 nm) which is proportional to the concentration, gradually decreases due to the degradation of RhB. Moreover, the degradation dynamics were calculated based on the following equation:where Co and Ct are the concentrations of dye at time 0 and t, respectively. e exhibits that photodegradation of RhB at the presence of the MAP drops rapidly from 1 to about 0.095, indicating a high degradation efficiency of 90.5 %. It is much higher than that of control MXene membrane (76.0 %) and the blank RhB solution without any photocatalyst (4.5%). Moreover, the long-term cycling test () further verifies good photocatalytic stability and reusability of the MAP. Considering photothermal conversion occurs concurrently with the photocatalysis process, which induces a temperature increase in the system, photodegradation process under a constant temperature, controlled by cooling water (25 °C), was also studied for comparison. As expected, e shows that both MAP and MXene membrane under a constant cooling temperature of 25 °C demonstrate a relatively lower degradation efficiency, which in turns indicates strong photothermal effect on photocatalytic capability.We further evaluate the photocatalytic efficiency based on the pseudo-first-order model according to the following equation:where k is related to the photodegradation rate constant. As shown in f, the value of k for MAP is about 0.0116 min−1, which is much higher than that of the control MXene (0.0072 min−1) and for the blank RhB solution (0.0002 min−1). Particularly, when compared with the k values obtained at constant temperature (25 °C, 0.0036 min−1), the MAP demonstrates a photodegradation rate enhancement of 222.2 %. It can also be noted that the relationship between ln(C0/C) and t is not so linear as the slope increases for MAP, indicating a photothermal-enhanced photocatalytic capability. Meanwhile, the MAP hydrogel membrane demonstrates a TOC removal efficiency of 81.2% (), indicating good mineralization performance. Also, when treating a phenol solution as the typical pollution, a degradation efficiency of 72.2% was achieved (The photocatalytic mechanism process of RhB can be summarized in the following steps (1–5). Specifically, the ESR spectra of the MAP () indicates the generation of the hydroxyl radicals (·OH–) and the superoxide radicals (·O2–) during the photocatalytic reaction in the system The synergetic process of MAP hydrogel membrane during water purification can be illustrated in g. Combing with the DFT calculation in Part 3.3, MXene, by virtue of its unique metal-like electronic structure and plasmonic effect, plays the base role to absorb sunlight, induce localized photothermal heating, and generate active species for photocatalytic functions. Moreover, coupling with the conjugated porphyrin enables MXene hydrogel membrane a preferred photothermal and photocatalyst medium to induce more efficient localized photothermal heating and accelerate dynamic and efficiency of photoexcitation for enhanced photocatalytic capability. Therefore, the MAP hydrogel membrane demonstrates great potential for integrated water purification by solar-driven evaporation and photodegradation. Under one-sun irradiation, the setup could generate 1.82 kg m−2

h−1 freshwater by evaporation and achieves 10.5 kg m−2

h−1 by wastewater purification photodegradation. According to , the color of the treated solution is initially dark pink, which fades gradually during the photocatalysis process, while the water produced by solar evaporation is totally transparent. This efficient photodegradation performance in turn endows the MAP membrane with good self-cleaning performance and ensures stable long-term evaporation stability (). The well-maintained structural and functional stability can be verified by the XRD, SEM and UV–vis-NIR result after long term testing (), further indicating its good chemical of MXene. In addition to the wastewater, the MAP hydrogel membrane also works well in real seawater (3.5 wt%, Science Park, Kong), exhibiting a stable water evaporation rate of 1.72 ± 0.4 kg m-2h−1 (). The salt-rejection behaviour is largely attributed to the excellent hydrophilic network of the hydrogel membrane which imparts it with an efficient capillarity force, osmotic expansion effect, and transpiration effect, which allows the concentrated salt could diffuse down back into the bulk water and avoid salt precipitation [62]. The TOC values decrease from the original 56.616 ppm to 1.303 ppm in the condensed water by evaporation and 9.488 ppm in the degradation water by photodegradation, respectively. However, currently it is not much suitable for high salinity seawater desalination due to salt-deposition without other assisting strategies, i.e., structural optimization or salt crystallization inhibition.In conclusion, we have demonstrated a feasible fabrication of MXene hydrogel membrane based on the structure-directing role of self-stacking MXene nanosheets and its molecular interactions with porphyrin and polyvinyl alcohol, for efficient integrated water purification. Taking advantage of the coupling interactions and charge redistribution between MXene and porphyrin, the hydrogel membrane was endowed with fascinating physicochemical properties combining stable hydrophilic dynamic networks, synergistically enhanced photothermal effect, and photothermal-enabled photocatalytic activity. When evaluated for water purification process, the hydrogel membrane exhibited outstanding solar-driven water evaporation of 1.82 kg m−2

h−1 and photocatalytic degradation efficiency of 90.5 %, rendering a high freshwater production capability under one sun irradiation. This work presented a facile and effective route towards the fabrication of high-performance photothermally enabled MXene hydrogel membrane for full solar spectrum driven water purification.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary data to this article can be found online at The following are the Supplementary data to this article:A stabilized formulation for incompressible plasticity using linear triangles and tetrahedraReceived in final revised form 5 May 2003In this paper, a stabilized finite element method to deal with incompressibility in solid mechanics is presented. Both elastic and J2-plastic constitutive behavior have been considered. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To circumvent the Babuška–Brezzi condition a stabilization technique based on the orthogonal sub-scale method is introduced. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate for real industrial applications. Results are compared with standard Galerkin and Q1P0 mixed formulations in either elastic or elasto-plastic incompressible problems.This paper proposes a possible solution to the problem of incompressibility observed in solid mechanics in case of either elastic incompressibility or J2 plasticity. The objective is to avoid the so called volumetric locking, an undesirable effect exhibited by all low order elements based on the standard Galerkin formulation. Many successful strategies to avoid volumetric locking based on both mixed and enhanced formulations can be found in the literature, , but they generally fail in the case of linear triangular or tetrahedral elements due to the lack of satisfaction of the Babuška–Brezzi condition (). Other formulations have been proposed by , etc. to deal with such elements, mainly motivated by the fact that nowadays, for real life geometries, tetrahedral meshes are relatively easy to generate. Techniques based on the sub-grid scale approach proposed by , have been applied in the context of solid mechanics in strain localization problems by the fine scale is represented by additional ad-hoc variables, which are introduced in the same fashion than in the assumed enhanced method. Recently a method based on the orthogonal sub-scales method, introduced by , has been applied to incompressible elasticity by the authors, see . Effectiveness and robustness of the technique have encouraged the authors to extend the approach to non-linear problems. An equal order interpolation of the mixed pressure and displacements fields is introduced followed by a decomposition of the unknowns into resolvable and sub-grid scales orthogonal to the finite element space. The basic idea is to approximate the effect of the component of the continuous solution which cannot be captured by the finite element solution and is the cause of the volumetric locking.In the next section, the equations that define the mechanical problem including the condition of incompressibility will be presented. Later on, the stabilization model using the orthogonal sub-grid scale approach will be presented taking into account the non-linear behavior induced by the plastic model. Finally, some numerical benchmarks will compare the standard Galerkin formulation as well as the mixed Q1P0 approach with the present formulation.It is well known that elements coming from standard displacement formulation often lock in constrained media problems, such as incompressible problems. A possible alternative can be stated introducing a mixed variational formulation. Within this framework it is possible to design more robust and flexible elements such as the assumed stress elements where pressure is interpolated independently of the displacement field.In this section a mixed formulation to deal with an elasto-plastic behavior is introduced. The finite element discretization is presented to point out the restrictions of this formulation coming from the Babuška–Brezzi stability condition. Furthermore, the sub-grid scale approach is presented as an alternative to circumvent this condition to be able to use continuous linear interpolations for both displacements and pressure fields. Finally, the stabilized system of equations that solve the problem of incompressibility is presented, assuming as a particular choice the orthogonal sub-grid scales.The formulation of the mechanical problem to deal with the quasi-incompressible behavior can be written in a mixed format considering the hydrostatic pressure p as an independent unknown, additional to the displacement field, u. The stress tensor σ can be expressed in terms of these two independent variables such as:where p and s(u) are the volumetric and the deviatoric parts of the stress tensor, respectively.If we refer to J2 plasticity then the volumetric and the deviatoric constitutive behavior can be split and treated independently. In particular, the hydrostatic pressure p can be expressed as:where K is the bulk modulus, also referred to as modulus of volumetric compressibility and ευ=tr (ε)=∇·u is the volumetric part of the total deformation ε=∇su. On the other hand, the deviatoric part of the stress tensor s can be introduced as:where G is the shear modulus and ee and e are the deviatoric components of the elastic and the total strain tensors, respectively. According to J2-plastic model, plastic deformation, ep, is assumed to be only deviatoric and it has been computed according to the J2-plastic constitutive model summarized in Therefore, the strong form of the mixed problem that we want to solve, can be formulated as: find the displacement field u and the pressure field p, for given prescribed body forces f, such that:where Ω stands for an open and bounded domain of are subjected to appropriate Diritchlet and Neumann boundary conditions in terms of prescribed displacements, u=Note that the formulation is valid for both compressible and incompressible cases. In particular, in case of incompressibility, that is when K→∞, Denoting by (·,·) the inner product in the space of square integrable functions L2 (Ω), the associated weak form of the problem where v and q are the variations of the displacements and pressure fields, respectively. involve the first derivative of the displacements and only the primal function of the pressure field. Hence, the natural spaces for displacements and pressure continuum fields are: u∈=L2 (Ω), respectively. The corresponding variations are defined in: v∈. Hm (Ω) denotes the space of functions of which its derivatives up to order m⩾0 (integer) belong to L2 (Ω). Roughly speaking, H1 (Ω) involves continuous functions with discontinuous derivatives, while L2 (Ω) includes even discontinuous functions.Using a compact notation, the above problem can be stated as the following bilinear form: are the vector of unknowns and its variation, respectively.h ⊃ L2 (Ω) be the finite element spaces for displacement and the pressure discrete fields uh and ph, respectively.h are the vector of unknowns and its variation, respectively.Up to now, no hypotheses have been made on the interpolation functions chosen for the displacement and pressure fields. However, the stability of the discrete formulation depends on appropriate compatibility restrictions on this choice, as stated by the well-known Babuška–Brezzi, BB-condition, . Also, several authors have deduced necessary but not sufficient conditions for the stability of the pressure approximation, such as the constraint counts [see and references there in]. According to these restrictions, standard mixed elements with continuous equal order linear/linear interpolation for both fields are not stable, but a stable mixed finite element can be constructed using quadratic interpolation for the displacement field and constant interpolation for the pressure.However, the BB-condition can be circumvented by using non-standard mixed interpolation or, for instance, stabilization techniques. The objective of this work is to introduce the so-called sub-grid scale approach to stabilize the discrete formulation of the mixed problem allowing the use of linear interpolations in both displacements and pressure.The basic idea of the sub-grid scale approach () is to consider that the continuous displacement field can be approximated considering two components, one coarse and a finer one, corresponding to different scales or levels of resolution. The solution of the continuous problem contains components from both scales. For the solution of the discrete problem to be stable it is necessary to, somehow, include the effect of both scales in the approximation. The coarse scale can be appropriately solved by a standard finite element interpolation, which however cannot solve the finer scale. Nevertheless, the effect of this finer scale can be included, at least locally, to enhance the stability of the pressure in the mixed formulation.Therefore, the solution of the mixed problem will be approximated aswhere uh is the displacement component of the coarse scale and is the enhancement of the displacement field corresponding to the finer scale. It must be pointed out that no sub-grid scale contribution has been considered on the pressure field. the finite element and the sub-grid scale space, respectively. It is important to observe that we are considering , that is the subgrid scale displacements vanishes all over the boundary ∂Ω. Hence, the solution U belongs to the refined space:Assuming an additive split of the total deviatoric strain tensor e=ee+ep, it is reasonable to assume the elastic and plastic components as: is sufficiently small, compared to the coarse solution uh, so that the deformations induced by the sub-grid displacements as a perturbation of the finite element field uh, which cannot be resolved in h. As a consequence, the deviatoric stress tensor s(uh+) can be split as the sum of a first contribution sh (uh), coming from the elasto-plastic behavior induced by the coarse solution uh, and a second contribution are the vectors of variations, defined onto is defined in the finite element space h and it solves the balance of momentum including a stabilization effect depending on the sub-grid is defined in the sub-grid scale space and it will be used to define the sub-scale displacement field together with the above assumption, it follows that:where the integral over the boundary ∂Ωt involves the prescribed traction . Finally, expressing the total deviatoric stress tensor s in terms of sh, we obtain:Note that it is possible to split these equations in the same way as for the purely elastic case (see where R (Uh, Vh) is the standard term of the weak form of the problem, Vh) is the stabilization term, that can be expressed as and it vanishes all over the boundary ∂Ω, the result isThe pending subject for the next section is how to approximate the sub-scale displacements The objective in this section is to obtain a useful expression for the sub-grid scale displacements . To achieve this result, let us manipulate problem , introducing the split of the stress tensor where the second equation vanishes due to the fact that ]. Observe that also in this case it is possible to split the problem into:where the first term only depends on Uh, while the second term includes the effect of . The above equation can be rewritten as:where the following operator has been introduced:Having in mind the expression of the deviatoric part of the stress tensor Taking into account that for a given a function (·) the order of its gradient is , where h is the characteristic length of the finite element mesh, can be approximated within each element Ωe by the following linear expression: is a parameter defined as a function of the characteristic length of the element he and the shear modulus G; coefficient c=c1·c2, is a coefficient depending on the element interpolation, to be appropriately chosen.Moreover, as a particularization of the general form of the sub-grid scale method detailed in the previous section, let us choose as sub-grid scale space , the space orthogonal to the standard finite element space is generally referred as the space of orthogonal sub-scales. It was introduced in , and applied to incompressible elasticity by the following approximation can be established:where Ph⊥ is the orthogonal projection onto h and therefore Ph⊥ (f)=0. On the other hand, ∇·sh also in (), involves second derivatives of finite element functions which vanish when linear elements are used. As a result can be approximated within each element Ωe, as:where the orthogonal projection Ph⊥ of a variable (·) has been computed as:where Ph (·) is the projection onto the finite element space In particular, calling IIh=Ph (∇Ph) the projection onto Vh of the pressure gradient, it can been computed as:leading to a final expression for the approximation of the sub-grid scale, within each element, such as:Observe that, according to the objective of this work, the use of element-wise linear interpolation for the pressure, implies a discontinuous field for the pressure gradient and, consequently, for the sub-grid scale solution . On the other hand, Πh is defined as a continuous field, leading to an expression for which cannot be condensed element by element. into the expression of the stabilization term As a result of the above procedure, the stabilized system of equations proposed by the authors to solve the problem of incompressibility in case of elasto-plastic behavior, is the following:It is important to point out that under these hypotheses the stabilization term , which can be solved as in a standard mixed finite element formulation. On the other hand, the incompressibility is stabilized element by element, using a term that depends on the difference between the continuous (projected) and the discontinuous (elemental) pressure gradient. This means that the finer is the mesh, smaller is the contribution to the stabilization term to be added to this equation to make possible a stable solution. Finally, it must be observed that in this formulation a third nodal variable Πh has to be solved. However, in the next section we will show that it is possible to overcome this drawback and achieve a robust and efficient solution.Many alternatives can be considered to solve the proposed system of . The strategy preferred by the authors consists of a simultaneous solution at time t=t(n+1) of the balance of momentum together with the pressure equation. The projection of the pressure gradient Πh obtained at time t=t(n) is used during the equilibrium iterations of the next time step. This strategy has proved to be effective without loss of precision or robustness. A brief summary of the algorithm and matrix format implemented is presented in in Box 2 are the residuals vectors associated to , respectively. Moreover, the elemental sub-matrices corresponding to local nodes A and B that must be assembled for the solution of the global system of equations are the following:where Ddev is the deviatoric part of the constitutive tensor; G and GT are the gradient and the divergence operators, respectively; L is the Laplacian operator and My Mp are the “mass” matrices associated to the displacement and pressure fields, respectively.Finally, note that using a lumped projection operator in Box 2 into a trivial vector operation leading to a really efficient solution algorithm.The formulation presented in the preceding sections is illustrated below in a number of numerical simulations. The objective is to show the performance of the proposed algorithm when a J2-elasto-plastic constitutive behavior is considered. Incompressibility condition are assumed in all the benchmark proposed. Performance of the method is tested considering either 2D plane-strain triangular meshes or 3D tetrahedral meshes. To show the behavior of the element under extreme situations, coarse meshes are used in all the tests. Newton–Rapbson method combined with a line search optimization procedure, is used to solve the non-linear system of equations arising from the spatial and temporal discretization of the weak form of the stabilized problem. Calculations are performed with an enhanced version of the finite element code COMET (see ) developed by the authors at the International Center for Numerical Methods in Engineering (CIMNE).The benchmark proposed consists of a square specimen (10×10 cm2) in plane-strain conditions. Two rigid plates have been fixed to the top and the bottom of the specimen. The loading condition consists of a prescribed displacement of the top plate of 1 mm in the vertical direction. The bottom plate is fixed. Young's modulus is E=2.0×105 MPa and the incompressibility condition is enforced by setting Poisson's ratio to υ=0.4999. A perfect plasticity model is assumed considering an elastic limit of σo=150 MPa. The proposed formulation T1P1 is compared to the solution of the mixed mean dilatation/pressure quadrilateral element, generally referred to as Q1P0 element () and the standard Galerkin formulation for triangular elements T1. that pressure contourfills present similarity for the proposed T1P1 and Q1P0 formulations, even if coarse meshes are used. Locking effects induced by the standard Galerkin formulation can be clearly observed in the same figure. shows the equivalent plastic strain contours obtained with the different formulations. Also in this case there is good agreement between the proposed and the Q1P0 formulations. Observe that plastic deformations for the standard Galerkin formulation are localizing incorrectly along a fictitious shear band induced by the finite element mesh. The same phenomenon has been observed in other problems, leading to the conclusion that the proposed formulation is able to produce results that do not depend on the orientation of the mesh used. shows the global response of the specimen in terms of vertical reaction versus vertical displacement. The proposed mixed stabilized formulation compares very well with the results achieved using the Q1P0 formulation. The standard formulation shows a very clear locking effect both in the elastic and in the plastic regimes, with incorrect load–displacement slopes in both situations. Finally, compares the same plots in case of compressible elastic behavior (Poisson's ratio υ=0.3). It is possible to appreciate how the formulation proposed by the authors is still valid in this case. More examples showing the performance of the formulation in compressible and incompressible elasticity can be found in The Cook's membrane problem is a bending dominated example that has been used by many authors as a reference test to check their element formulations, see among others. Here it will be used to compare results for incompressible J2-plasticity, showing the behavior of the algorithm for triangular elements. As a reference solution, the mixed mean dilatation/pressure quadrilateral element, generally referred to as Q1P0 () is used. The problem consists of a tapered panel, clamped on one side and subjected to a shearing load at the free end. In order to test the convergence behavior of the different formulations, the problem has been discretized into 2×2, 5×5, 10×10, 20×20 and 50×50 triangular and quadrilateral finite element meshes. Young's modulus is E=70. the elastic limit is σo=0.243, linear isotropic and kinematic hardening are h=0.135 and Kh=0.015, respectively, and the incompressibility condition is enforced by setting Poisson's ratio to υ=0.4999. the comparison among different formulations in case of incompressible plasticity is shown. Q1P0 mixed mean dilatation/pressure approach, T1 standard elements and the proposed mixed formulation for triangular elements are compared. The same figure shows how the proposed formulation converges to the exact solution faster than the Q1P0 mixed approach, even if triangular meshes are used. The figure also shows the poor performance of T1 standard elements within the context of nearly incompressible plasticity, due to an extreme locking effect. shows the pressure contour fills obtained with the three formulations, using the finest 50×50 quadrilateral (Q1P0) and triangular (T1 and T1P1 stabilized) meshes. It is possible to observe the similarity between the Q1P0 pressure field and the one obtained using the formulation proposed by the authors and on the other hand, the terrible locking effects of a standard Galerkin formulation.The objective of this problem is to show the performance of the proposed formulation when a tetrahedral mesh is used to solve a 3D problem. It has been observed that the sensitivity of enhanced element formulations causes difficulties in compression problems, due to numerical instabilities referred to as hourglassing effect. The performance of the proposed formulation has been checked also in that situation. A 0.3×0.3×0.2 m3 block is incrementally subjected to a compression load (F=1.0E4 MPa) applied on its upper surface (see ). Elasto-plastic constitutive behavior has been assumed (Young's modulus: E=2.0×105 MPa; elastic limit: σo=150 MPa) together with incompressibility condition (Poisson's ratio: ν=0.4999). Results obtained with the Q1P0 formulation using a 15×15×10 hexahedral mesh are compared with a 15×15×10 unstructured tetrahedral mesh based on the proposed formulation. shows the deformed shapes obtained mesh while compares the pressure contour fill being this variable the most sensitive to the any stabilization technique adopted. It is possible to appreciate in both figure the similarity in terms of deformability and stress response for comparable finite element discretizations.In this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented. The method is based on the orthogonal sub-grid scales approach and circumvents the Babuška–Brezzi condition, allowing an accurate and robust formulation suitable for linear triangular and tetrahedral elements. The formulation, presented in a previous work for incompressible elasticity () is extended here to the context of incompressible J2-plasticity. A staggered algorithm together with an explicit solution of the protection of the pressure gradient lead to a competitive procedure suitable for industrial applications. Extension of this technology to the context of large-strain elasto-plasticity will be published soon.Development of a practical model for selection of stable tooling system configurations in internal turningWhen machining high precision mechanical parts, self-excited chatter vibrations must be absolutely avoided since they cause unacceptable surface finish and dimensional errors. Such unstable vibrational phenomena typically arise when the overall machining system stiffness is relatively low, as in the case of internal turning operations performed with slender boring bars. In general, it is not easy to select stable tooling system configurations for a given workpiece material, since data available in literature are often incomplete or inapplicable, especially for modern boring bars made of high-damping carbides. In this paper, an experimental study on the influence of boring bar material, boring bar geometry, cutting edge geometry, workpiece material and cutting parameters on process stability in internal finish turning is illustrated. From the analysis of experimental results, process stability mainly depends on the ratio of boring bar overhang L to bar external diameter D, independently of cutting parameters. Accordingly, the critical ratio (L/D)cr can be defined as the maximum L/D ratio assuring process stability for most cutting parameters combinations. A semi-empirical model of the critical ratio (L/D)cr as a function of boring bar material and geometry, cutting edge geometry and workpiece material was finally obtained, which is in good accordance with experimental data (accuracy of ±10%) and it can be practically applied for optimal selection of stable tooling system configurations in internal turning.► Experimental study on max. stable boring bar aspect ratio L/D in internal turning. ► Different bar materials and geometries, workpiece materials and tools are tested. ► Modal analysis is carried out on the considered tooling system configurations. ► A model based on chatter theory is calibrated by means of experimental data.When machining high-precision mechanical components, the static and dynamic behavior of the machining system during the cutting process plays a fundamental role, since it greatly affects the obtained surface quality.Basically, machining system vibrations can be split into the sum of forced and chatter vibrations. Forced vibrations are generated during a regular cutting process and they cannot be completely avoided due to the compliance of the machining system. However, their effect is usually small. On the contrary, chatter vibrations negatively affect part precision and surface quality, since they are unstable and chaotic. Also, they can cause abnormal tool wear, tool breakage, damage of the tooling structure and of the spindle bearings. For these reasons, avoidance of chatter vibrations is crucial.Main physical mechanisms responsible for chatter in turning is the regenerative effect, deriving from the combination of the instantaneous tool–workpiece relative vibration with the waviness of machined surface left by the cutting tool at the previous round Research works dealing with chatter can be roughly split into three main categories, depending on their focus on chatter detection, suppression or prediction. Chatter detection is based on the application of single or multisensor systems installed on the machine tool and on the development of special algorithms for in-process chatter identification Alternatively, chatter prediction algorithms can be used for a preventive identification of stable machining system configurations Generally, several experimental tests would be required for calibrating and validating the aforesaid methodologies. Nevertheless, only a few experimental tests are reported in literature, especially in the case of internal turning, see . On the contrary, the accent is mostly placed on numerical simulation of cutting process dynamics.In internal turning, the boring bar is generally the most flexible element of the machining system, thus it is mainly responsible for chatter onset. Therefore, boring bar material and geometry may significantly affect chatter occurrence, as well as cutting edge geometry and workpiece material.In this work, the influence on process stability of different bar materials (conventional alloy steel and high-damping boring bar), bar geometries (external diameter D and overhang L, see ), cutting edge geometries (tool nose radius rε), workpiece material (represented by its cutting pressure ks) and cutting parameters (spindle speed n and depth of cut ap) were experimentally investigated.Surprisingly, experimental results showed that the stability of a given combination of bar type, cutting edge geometry and workpiece material mainly depends on the adopted aspect ratio L/D, independently of cutting parameters. Therefore, the critical ratio (L/D)cr was defined as the maximum aspect ratio assuring process stability for most cutting parameters combinations. A semi-empirical model of (L/D)cr as a function of boring bar material and diameter D, tool nose radius rε and cutting pressure ks of the workpiece material was finally proposed and validated through experimental data.In this research work, a mechanistic cutting force model was adopted, see where dFc is the main cutting force, dFn is the normal cutting force acting on the infinitesimal cutting edge dl, while dA is the infinitesimal uncut chip section area depending on the local uncut chip thickness h(l), see (a). Shearing and Plowing – S&P – cutting force coefficients were used to model the influence of dl and dA on the cutting force components. The influence of cutting speed vc on S&P cutting force coefficients was neglected.Cutting force components were obtained by integration along the cutting edge, as follows:{Fc=∫0BdFc=kcsA+kcpBFp=∫0BcosχdFn=kcs[∫0BcosχdA]+kcp[∫0Bcosχdl]Ff=∫0BsinχdFn=kcs[∫0BsinχdA]+kcp[∫0Bsinχdl].It has to be pointed out that the total uncut chip section area A, the total length of contact B and the arguments between square brackets were computed numerically in order to take into account the effective shape of the uncut chip section area, which can be very complicated, especially when feed f is of the same order of magnitude of nose radius rε.S&P cutting force coefficients were estimated experimentally for the selected combinations of workpiece materials–cutting tools, as described in Tooling system dynamics are represented in (b). Let us assume that the tooling system dynamic compliance measured at tool tip in the radial direction x can be approximated by the modelWx(jω)=ux(jω)Fx(jω)≅G(jω/jωn)2+2ξ(jω/jωn)+1,where G is the static compliance expressed in (m/N), ωn is the main natural pulsation expressed in (rad/s) and ξ is the (adimensional) damping coefficient. The influence of tangential vibrations uy on process stability was neglected, in accordance with literature.Let τ be the spindle rotation period. Let us introduce the notationhence ux,τ is the tool tip displacement at the previous round.The radial back force Fx can be expressed as a function of the following independent variables:Let us define the nominal radial back force asLet us suppose that the tooling system position has been already corrected for compensating the static displacement caused by Fx0Under these hypotheses, the equilibrium configuration is achieved whenand the effective depth of cut ap is equal to the nominal value. The variation of the radial back force δFx due to tool tip vibrations ux and ux,τ can be determined as follows:δFx=Fx−Fx0=∂Fx∂uxux+∂Fx∂ux,τux,τ≈−(∂Fx∂ux,τ)︸kτ(ux−ux,τ),where kτ is the regenerative, radial cutting force coefficient, which has a strong influence on the stability of the cutting process Theoretical regenerative radial cutting force coefficient kτ is usually computed by neglecting the influence of nose radius rε, since depth of cut ap is supposed to be considerably greater than nose radius. Also, the feed f is generally assumed to be small in comparison with nose radius rε. Moreover, the calculation is carried out by considering infinitesimal vibrations dux of the tool tip and by neglecting the variation of the radial back force due to the variation of the cutting edge contact length B. As a result, the estimated radial cutting force coefficient kτ depends on depth of cut ap, nose radius rε (when considered), nominal working cutting edge angle χ and shearing normal cutting force coefficient kns.Here a numerical approach was preferred, similar to that presented in non-zero nose radius rε, i.e. the effect of ap≈rε;realistic values of feed f, even when rε is small;finite, i.e. non-infinitesimal tool tip vibrations δu;the variation of cutting edge contact length B, i.e. the influence of plowing normal cutting force coefficient knp, see For this purpose, the following numerical procedure was conceived. Working cutting edge angle χ was set to 93°. For a fixed nose radius, cutting parameters and cutting force coefficients, the nominal radial back force Fx0 was first computed. A rectangular grid in the (ux,ux,τ) plane, centered around the equilibrium condition (0,0), was determined. Grid semi-amplitude was proportional to the static displacement estimated by Eq. . The radial back force values corresponding to the selected couples (ux,ux,τ) were computed. Eventually, the regenerative radial cutting force coefficient kτ was estimated by linear regression performed on Eq. The calculation was repeated for different combinations of input parameters, see . The behavior of regenerative radial cutting force coefficient kτ is illustrated in Analysis of variance was carried out in order to evaluate the influence of input factors on the output variable kτ, by only considering main effects of input factors, see . Although all factors had a significant effect on the regenerative cutting force coefficient, F-test values of depth of cut and feed were negligible with respect to the other factors. Accordingly, the effect of cutting parameters could be neglected at first approximation.The following model was obtained where, for the sake of simplicity, only the most significant factors were considered:where rε is expressed in mm, kns in N/mm2 and knp in N/mm. The model is capable of representing the behavior of kτ with a square correlation coefficient R2 equal to 0.74.In the perspective of developing a practical model for the selection of stable tooling system configurations, Eq. was further simplified by assuming thatwhere ks is the cutting pressure (ratio of the main cutting force component Fc to the uncut chip section area A). The relation between cutting pressure and S&P coefficients can be derived from cutting pressure definition, as follows:where hm is the average uncut chip thickness given byHowever, S&P coefficients do mostly depend on workpiece material, whereas their dependence on cutting insert geometry and cutting parameters is small. Besides, the first term on the right side of Eq. is dominant. Therefore, cutting pressure is approximately constant, independently of cutting insert geometry and cutting parameters.Another advantage of considering the cutting pressure ks instead of the more complicated S&P coefficients is that it can be easily derived from direct measurements or indirectly estimated from other mechanical properties of the workpiece material such as the tensile strength or Brinnel Hardness where Λ, p and w are constant coefficients.For a given machining system configuration, which can be represented by its modal parameters (G,ωn,ξ), chatter occurrence does in general depend on spindle speed n and on the regenerative cutting force coefficient kτ introduced in previous section. The (n,kτ) plane can be split in two distinct regions, one stable and one unstable. In the standard chatter theory, depth of cut ap is considered instead of the regenerative cutting force coefficient kτ, since they are linearly correlated. The change of perspective proposed here is necessary because of the strong non-linearities of the function kτ(ap).The borders separating the stable region from the unstable one are the so called stability lobes, see where ωc is the chatter pulsation associated to spindle speed n, yielding a negative real part of the frequency response (a positive real part would produce negative kτ,cr's, which have no physical sense).When the ratio of spindle rotation frequency (n/60) to the first natural frequency of the machining system fn=ωn/(2π) is relatively high (above 1/5, approximately), some stable cutting parameters can be found between adjacent lobes, which allow to enhance the material removal rate. On the contrary, for lower spindle speeds, stability lobes become too dense and the only robustly stable region is that below the stability lobes minima, which can be determined by searching the maximumand by substituting the result into Eq. is independent of the natural pulsation ωn and of spindle speed n.Tool tip static compliance G can be estimated by applying the classical Euler–Bernoulli beam modelwhere E is the Young modulus of the bar material and the formula refers to a full circular section (the small coaxial hole for internal lubricant supply was neglected since it does not considerably affect bar stiffness).Accordingly, stability can be expressed in terms of the L/D ratioLD<(LD)cr=[6π64ξ(1+ξ)EΛ]1/3D1/3ks−p/3rε−w/3It has to be pointed out that this inequality is independent of cutting parameters. Accordingly, the effect of feed was not experimentally investigated, since the aim of this work was to focus on the most important factors affecting stability, which already required extensive and demanding experimental tests. However, for further details about the effect of feed on stability see Landers and Ulsoy Except Young modulus of steel, Young modulus of high-damping carbide and damping coefficients ξ of both steel and carbide are generally unknown and difficult to estimate without performing specific experimental tests. Also, constant Λ requires experimental cutting tests to be determined. Therefore, for the sake of simplicity, the following model was proposedwhere Q, a, b, and c are empirical model coefficients that have to be derived from experimental data. Constant Q incorporates the effect of boring bar material (including Young modulus and damping coefficient), while the second term on the right represents the effect of bar geometry. The third term represents the effect of workpiece material, while the fourth and last term describes the effect of cutting insert geometry. From the outlined model structure, exponents a, b and c should be independent of boring bar material.Cutting tests were carried out on a multifunction CNC lathe OKUMA Multus B300W in dry conditions. The experimental tests were executed in three phases. In the first phase, cutting pressures of the selected workpiece materials were estimated. In the second phase, modal tests were executed on each tooling system configuration, in order to estimate the transfer function between the radial cutting force and the machine tool head acceleration, for calibrating the chatter detection algorithm. In the third and last phase several cutting tests were performed in order to investigate the stability of the cutting process for different machining system configurations (specified by boring bar material, bar diameter and overhang, workpiece material, tool nose radius) and cutting parameters combinations.A special turning dynamometer was applied in the first phase (a). For modal testing, some impulses were applied on tool tip in the radial direction by using an impact hammer Dytran type5800B4, with sensibility of 2.41 mV/N, connected to an amplifier Kistler type 5134B, while machine tool head vibrations were measured by applying piezoelectric accelerometers Kistler 8704B50 installed on the machine tool head along X and Y directions. Process stability was assessed by analyzing the accelerometer signals acquired during the cutting process, according to the criteria explained in Regarding data acquisition, all sensor signals were sampled at 20 kHz by using a National Instruments device (cDAQ-9178 with NI9215 modules) connected via USB to a PC. Data were elaborated in MathWorks MATLAB environment.In order to confirm the hypotheses outlined in , a Design of Experiments was carried out for each selected workpiece material, as summarized in . Two workpiece materials were considered in this research: C45 steel (213HB) and aluminum alloy Al7075 (ERGAL, 151HB). For each workpiece material, rhombic inserts with 11 mm side length and a tool included angle ε of 55° were selected. All cutting inserts were fixed on a special toolshank described in For a fixed workpiece material and nose radius, cutting force components were measured, see . By analyzing the experimental cutting force trends, it was observed that the feed force Ff and the main cutting force Fc depended almost linearly on depth of cut ap and feed f, while their dependence on cutting speed vc and nose radius rε was practically negligible. Specifically, main cutting force Fc was proportional to the uncut chip section area A (i.e. to the product apf ) with good approximation, independently from nose radius and cutting parameters, confirming the hypotheses of . On the contrary, the back force component Fp had a strong nonlinear behavior against depth of cut ap, a linear behavior against feed f, it was not considerably affected by cutting speed vc and it was very sensitive to nose radius rε. These experimental observations were in accordance with the assumptions of the cutting force model proposed in , as evidenced by the satisfactory model adequacy parameters listed in In internal turning, chatter occurrence is dependent on the dynamic compliance of the tooling system, whereas that of the workpiece is usually negligible. Tooling system dynamics derive from the dynamic interaction between boring bar overhang of length L and machine tool head receptance measured at boring bar–adapter interface, see . Since the latter was fixed, main factors influencing tool tip receptance were the boring bar diameter D, the L/D ratio, and the boring bar material. In this study, commercial (Sandvik) boring bars of different diameters and materials were tested. Specifically, A16RSDUCR07-R (D=16 mm, steel), E16RSDUCR07-ER (D=16 mm, high-damping carbide), A10KSDUCR07-ER (D=10 mm, steel) and E10MSDUCR07-ER (D=10 mm, high-damping carbide) were selected, see Finishing internal turning operations were performed on two workpiece materials considered in the previous phase: C45 and ERGAL.Due the great relevance of the tool geometry, tools with different nose radius rε were considered. However, local cutting edge geometries and insert grades were the same of cutting inserts applied for cutting pressure estimate (). Specifically, Sandvik DCMT070202PF and DCMT070204PF (rε equal to 0.2 and 0.4 mm, respectively), grade CT5015, were tested on C45; Sandvik DCGT070202UM and DCGT070208UM (rε equal to 0.2 and 0.8 mm, respectively), grade GC1125, were tested on ERGAL. Nose radius rε=0.8 mm was selected for ERGAL to enhance the effect of tool geometry. The effective Design of Experiments is reported in For each combination of boring bar type, cutting insert and workpiece material, different levels of the aspect ratio L/D were tested around the expected critical value (L/D)cr representing the transition from a completely stable to a completely unstable configuration. For a fixed L/D ratio, a dedicated Design of Experiments was carried out for evaluating process stability, involving different levels of depth of cut ap and spindle speed n, as illustrated in . In all cases, feed was 0.08 mm/rev, except the case of ERGAL with rε=0.8 mm, which required f=0.16 mm/rev for chip breakage. The influence of feed on stability boundaries can be neglected at first approximation in the light of the subjects discussed in . Workpiece internal diameter Dw was approximately 25 mm when machining C45, while it was about 46 mm when machining ERGAL, in order to guarantee adequate average cutting speeds (vc of about 350 m/min for C45 and vc of about 650 m/min for ERGAL), as recommended by tool manufacturer. Anyway, chatter vibrations mainly depend on spindle speed – which was indeed considered as an independent factor – rather than on cutting speed. Spindle speed levels were chosen in order to highlight the effect of stability lobes, if any.The considered L/D ratio was considered stable or unstable according to the stability criteria illustrated in . On the average, 96 cutting tests were performed for each machining system configuration for a total of about 1600 cutting tests.For each tooling system configuration and L/D ratio, modal tests were performed according to pulse testing procedure which represents the dynamic relation between the force Fx applied to tool tip in the radial direction and the acceleration AX of the machine tool head along the same direction, see . Resonance peaks were mainly located from 500 to 4000 Hz. There was usually one important resonance peak due to boring bar dynamics, which can be approximately predicted from the Euler–Bernoulli theory applied to a cantilever beam with circular cross section, yieldingwhere ρ is the boring bar material density. Such dominant peak ranged over the afore mentioned frequency interval by varying bar material, bar diameter and bar overhang. However, there were other relevant resonance peaks deriving from toolholder–machine tool head subsystem. In general, it was very difficult to forecast the position of the highest resonance peak, due to the complex interaction between boring bar and machine tool head dynamics.In any case, both theoretical and experimental resonance frequencies confirmed the hypothesis outlined in , i.e. robust stable cutting conditions could be found only below stability lobes minima, since it was not safe to consider stable cutting conditions between adjacent stability lobes, which were very dense in the spindle speed range of interest (corresponding to a lobe order greater than 6).Surface quality is usually considered as one fundamental chatter indicator in finish operations. According to some preliminary cutting tests performed both in stable and unstable conditions, roughness and waviness parameters obtained in stable conditions were in good accordance with theoretical expectations, whereas they were about one order of magnitude greater when chatter occurred, see Since it was unpractical and in some cases even impossible (due to the very bad surface state) to measure surface profile for characterizing the chatter level, an alternative quantitative parameter extracted from acceleration signal AX was used as primary chatter indicator. This approach was inspired by a recent research work In detail, the following frequency-based chatter indicator was computed:CIER=EcE=∫ωr(1−Δ)ωr(1+Δ)|AX(jω)|2dω∫ωminωmax|AX(jω)|2dω,where Ec is the spectral energy in a neighborhood of the maximum frequency peak of the spectrum located at ωr, Δ is the neighborhood amplitude (10%), E is the total spectral energy within the range of interest (ωmin=250·2π, ωmax=4500·2πrad/s). A more sophisticated CIER was introduced and validated by Kuljanic et al. in milling (b). In the last conditions, CIER tended to 100%.The threshold CIER=50% was selected for discriminating stable from unstable cutting conditions, as illustrated in . From the analysis of experimental points, it was not possible to distinguish classical stability borders depending on spindle speed n. On the contrary, two opposite situations did typically occur: most cutting parameters combinations were either stable or unstable, depending on the considered L/D ratio, as evidenced in . A machining system configuration was considered stable when at least 95% of the tested conditions were stable. Accordingly, the critical ratio (L/D)cr was defined as the greatest stable L/D ratio.Scatter plot diagrams of experimental (L/D)cr values against input factors are shown in . In general, (L/D)cr is higher when adopting high-damping carbide boring bar instead of steel boring bar. Moreover, (L/D)cr is higher when the diameter D is higher, when nose radius rε is smaller or when cutting pressure ks is smaller.According to the ANOVA tests, main effects of the investigated factors were proved to be all significant for both boring bar materials. Among 2-level interactions, the effect of the interaction between boring bar material and diameter was the strongest.In the light of theoretical assumptions of and the above experimental results, multiple linear regression was performed on the output and input factors expressed in logarithmic scale, according to Eq. Q={10.097forsteelboringbar12.402forhigh−dampingboringbar,Scatter diagrams of percent relative residuals against input factors and experimental points are shown in . Data dispersion is higher in the case of carbide boring bar in comparison with steel boring bar. No clear trends against input factors and output (L/D)cr are visible. Standard deviation σδLDcr of relative error was only 6%, while maximum relative error was smaller than 12%, confirming the good accuracy of the model.It should be pointed out that recommendations of boring bar manufacturer in terms of maximum admissible L/D ratio (smaller or equal to 4 for conventional alloy steel bars, smaller or equal to 6 for high-damping carbide bars) are generally rather conservative and inadequate in some cases. By applying the proposed model a better estimate of (L/D)cr can be obtained.Finally, some practical charts representing the behavior of (L/D)cr for different bar diameters and materials, workpiece materials and nose radii are illustrated in , showing the applicability of the proposed approach for the selection of stable machining system configurations.According to the considerations and experimental results presented in this work, we may draw the following conclusions.Regenerative radial cutting force coefficient kτ represents the strength of tool tip–workpiece dynamic interaction. It was numerically estimated from S&P cutting force coefficients derived experimentally. According to experimental and numerical results, this coefficient does mainly depend on cutting pressure ks and tool nose radius rε, whereas the sensitivity to cutting parameters (cutting speed vc, feed f, and depth of cut ap) is negligible at first approximation, when performing internal turning finish operations.Modal analysis highlighted that machining system natural frequencies were located in the range 500–4000 Hz. The dominant resonance peak ranged over this interval by varying bar type, diameter D and overhang L, but it could not be accurately predicted because of the complex interaction between boring bar and toolholder–machine tool head dynamics. However, the ratio of the spindle revolution frequency to the main natural frequency of the tooling system, i.e. the stability lobes order, was very high in this application. Accordingly, the only recommendable robust stable region was that below the stability lobes minima (denoted by kτ,cr min).Based on these preliminary observations, a mathematical model of the critical ratio (L/D)cr – maximum boring bar aspect ratio assuring a stable cutting process for almost all cutting conditions – was proposed, whose input factors were bar material, bar diameter D, cutting pressure ks, nose radius rε, whereas the influence of cutting parameters was considered negligible.The final cutting tests confirmed that a given machining system configuration (characterized by bar material and diameter D, aspect ratio L/D, workpiece material and nose radius) was either mostly stable or unstable, independently of cutting parameters, proving that the critical ratio (L/D)cr was well defined.Statistical analysis was carried out on the obtained experimental results, evidencing that main effects of all investigated factors had a significant influence on the experimental critical ratio (L/D)cr. Specifically, the critical ratio (L/D)cr was higher when considering special high-damping boring bars or higher bar diameters D, while it was smaller when considering higher cutting pressures ks or nose radii rε, by varying one factor at a time.Model coefficients were finally determined by performing multiple linear regression on the experimental data. Model accuracy was very high (relative standard deviation 6%). Also, no clear trends emerged from the analysis of residues.The obtained mathematical model and diagrams can be applied for a more accurate selection of the tooling system configuration, when compared to the data available in literature and technical publications.It would be of further interest to use the experimental results and the proposed empirical model as a starting point for developing new and robust chatter prediction methods for internal turning applications.Quantification and characterization of C-S-H in silica nanoparticles incorporated cementitious systemThis paper presents the quantification and nanomechanical properties of calcium silicate hydrate (C-S-H), formed at early stage hydration of tricalcium silicate (major cement phase) in presence of silica nanoparticles (SNPs). SNPs showed dominant nucleation effect at 8 h and pozzolanic effect at 24 h and accelerate the hydration rate (∼83% at 8 h and ∼51% at 24 h) due to the formation of additional C-S-H nuclei. Further, 29Si-NMR and FTIR techniques showed the acceleration in polymerization of silicate chain leading to the formation of tobermorite like structure. Formation of polymerized and crystalline C-S-H gel in presence of SNPs increases the percentage of high density C-S-H (∼40%) and lowers the low density C-S-H (∼52%) at 24 h of hydration, as observed in nanoindentation results.Cement hydration is a complex chemical phenomenon and despite the availability of vast amount of literature on cementitious materials, the structure of C-S-H is of scientific interest Nanoindentation technique has been widely used for the characterization of C-S-H in hydrated cement paste based on the colloidal model proposed by Jennings In blended cement, various supplementary materials are used to improve the performance of cementitious system For better understanding of hydration chemistry in cementitious system incorporating SNPs at early stage, the main ingredient of cement i.e. tricalcium silicate (C3S) was used for hydration studies. C3S was prepared and characterized in laboratory using calcium carbonate and silica in a molar ratio 3:1 and heated at ∼1500 °C, as reported elsewhere in detail For the hydration studies, 10% SNPs were added by the weight of C3S and mixed first in dry form. The mixture of C3S and SNPs was hydrated with a w/C3S ratio 0.4 and hydration process was stopped with acetone at different time intervals. Present research focus is to understand the role of SNPs during early stage kinetic of C3S, thus, the major studies were focus only up to 24 h only. However, the hydration process continued upto 1 year for the determination of hydrated products formed on complete hydration. After 24 h of hydration, the samples were cured in water at room temperature. For the determination of SNPs reactivity in lime paste, samples were prepared by mixing hydraulic lime (calcium hydroxide) (95% purity) procured by loba chemicals and SNPs in different molar C/S ratio (0.5, 1.0, 1.5 and 2.0) using water to solid ratio of 2.0. The samples were stirrer for 3 min using magnetic stirrer and then the hydrated mixture was stored in a plastic air tight bottle. All the samples were kept in vacuum desiccator to minimize the carbonation rate. For the TGA analysis the paste was washed with acetone and then oven dried at 105 °C.C3S paste were prepared by adding 10% SNPs by the weight of C3S using fixed w/C3S ratio of 0.4 and nanoindentation studied were performed at hydration ages of 24 h. All the paste specimens (typically 10 × 10 × 10 mm3; cubes) were kept in the lab (20 ± 3 °C) in a sealable mould until the targeted hydration age was reached. After demoulding the hydration was stopped by rinsing the paste specimens several times with isopropyl alcohol (as C3H8O replaces water in the paste).Nanoindentation has been recognised by many researches throughout the world as a very useful technique in the field of micro-structural investigation of materials. It is making contact between an indenter tip of known geometry and mechanical properties and a material sample of interest. This is followed by an application of an increasing load causing the penetration of the indenter into the investigated surface. After reaching a predefined maximum load and typically a short hold period at this value, the load is reduced and the penetration depth decreases due to the elastic recovery of the indented material. During the duration of the experiment the load, P, and depth, h, values are continuously recorded. The most common method to evaluate hardness and reduced modulus from the load-displacement data obtained with a Berkovich indenter tip was proposed by Oliver and Pharr in 1992 where Pmax is the maximum measured load applied on the indenter and Ac is the projected contact area of the indenter tip on the surface and is typically determined as a function of the measured maximum depth, hmax. S = dP/dh is the measured slope of the initial unloading part of the P-h curve. Young's modulus, E, has the following relationship with the determined reduced modulus Er:where Ei and νi are the elastic modulus and Poisson's ratio of the indenter (for diamond: Ei = 1141 GPa and νi = 0.07), respectively, andν is the Poisson's ratio of the indented material.Due to low degree of hydration it was opted for a rather large number of 640 indentation test points to assure a minimum of 300 results related to hydrate phases (E < 50 GPa). Progressive multistep indentation testing with two load-unload cycles and a maximum load of 1 mN was performed at each of the 640 test points, but only the unloading data of the second cycle (hp ∼250 nm) was used to determine the Young's modulus and hardness values (). Statistical analysis of the obtained bulky array of indentation tests and a subsequent statistical deconvolution of the indentation results is then carried out to determine for each material phase for the corresponding mechanical property values such as Young's modulus and hardness To determine the degree of reaction of SNPs in C3S and CH paste, selective dissolution method was used Degree of SNPs reaction was determined by the following equation X2 is the weight of residue of 1 g of C3S sample (LOI of C3S).X3 corresponds to residue of 1 g of SNPs (LOI of SNPs).Degree of hydration was calculated using Portlandite content formed in hydrated samples at different time of intervals. The amount of CH was calculated directly from the TG curves using the following equations where, WL(CH) corresponds to weight loss due to dehydration of CH and MW(CH), corresponds to molecular weight of CH, while MW(H) represents molecular weight of water. Further, degree of hydration was calculated using following equation:where CH(t) and CH(∞) corresponds to CH content at the time of hydration and CH content at the complete hydration, respectively.Influence of SNPs on hydration of C3S at early stage was studied using FTIR (model NEXUS (1100), Thermo Nicolet, FTIR, USA) and TGA (model: Diamond, Perkin Elmer; USA) studies were performed at a heating rate of 5 °C/min under nitrogen flow. Statistical nanoindentation testing was performed to determine the micro-mechanical property values, such as Young's modulus and hardness of the individual hydrated phases using an Agilent (now Keysight, USA) NanoIndenter® G200 system fitted with a Berkovich indenter tip.For a better understanding of the hydration process in cementitious materials, it is important to quantify the amount of hydration products formed as a function of time. There are no direct methods for the quantification of C-S-H in hydrated paste due to its variable stoichiometry. However, some methods may be used for the quantification of the hydrated products such as quantitative XRD by Rietveld refinement, optical microscopy using point counting, the Bogue method and degree of hydration Another extensively used method to determine the DOH is the content of portlandite (CH) formed during the hydration process . The amount of CH formed on complete hydration cannot be equal in control and SNPs incorporated samples because Ca2+ are consumed by SNPs and forms additional C-S-H through nucleation and pozzolanic reaction. It is reported that ∼70% C3S hydrates in 28 days and almost completely hydrate in 1 year 3CaO·SiO2+(3−x+y)H2O→CaO(x)·SiO·H2O(y)+(3−x)Ca(OH)2where, x should be close to 2, and experimentally it was found that the value of x varies from 1.5 to 2. The C/S ratio depends on the hydration conditions (bottle, paste), particle size, age and the analytical method employed 3CaO·SiO2+5.07H2O→CaO(1.86)·SiO·H2O(3.96)+1.14Ca(OH)2While for SNPs incorporated samples, the complete reaction may be as follows:3CaO·SiO2+5.07H2O+0.38SiO2→CaO(2.43)·SiO(1.38)·H2O(4.5)+0.57Ca(OH)2The value of y may vary from the theoretical value as the water amount calculated through the TGA is the only chemically bound water. The unreacted C3S was calculated from degree of hydration (1- α). In the case of the stoichiometry of C-S-H gel, the water content was experimentally measured from the differences obtained between the mass loss between 105 and 400 °C; the CaO and SiO2 were adjusted by mass balance between the initial and final products of the reactions. Hf represents the free water content which is not chemically bounded with hydrated compounds known as evaporable water.These results show that addition of SNPs results in the formation of C-S-H exhibiting low C/S ratio in the first hour of hydration. Formation of higher amount of C-S-H and lesser CH content at 1 h of hydration indicates the lower Ca2+ concentration in pore solution than the control, which accelerates the hydration rate of C3S. Reduction in Ca2+ concentration was also observed in our previous study, where we monitored the Ca2+ concentration using Inductive Couple Plasma (ICP), showing that Ca2+ concentration reduces in initial first few minutes of hydration due to formation of additional C-S-H nuclei, which further accelerates the hydration rate (). These results are in agreement with our earlier findings, where we observed that maximum Ca2+ concentration was observed at 4–6 h in SNPs incorporated samples, while in case of control sample maximum concentration of Ca2+ was appeared at 10–12 h of hydration ( (a and b) shows the mass percentage of hydrated and unhydrated products at different time intervals of hydration process. These results show that in control samples hydration rate increases gradually up to 15 h and then reaches to its steady state level, while in case of SNPs incorporated samples hydration rate increases rapidly up to 8 h and then steady state level is achieved, showing good agreement with our previous finding regarding shift in acceleration period ), respectively and water content in C-S-H was experimentally measured from the differences obtained from the mass loss between 105 and 400 °C. The CaO and SiO2 in C-S-H were adjusted by mass balance between the initial and final products of the reactions. These results show that SNPs reactivity at 1 h increases as the C/S ratio is increased due to the availability of Ca. At 1 h of reaction, only 20% SNPs is consumed in 0.5 C/S lime paste sample, while 50% SNPs reacted in the mixture having a C/S ratio 2.0. shows the reactivity of SNPs and CH at different time intervals of reaction in various lime paste samples. It clearly indicates that at 24 h of reaction, in the mixture having low C/S ratio (0.5 and 1.0), CH is almost completely consumed, while SNPs reacts more than 85%. However, with 1.5 C/S ratio mixture, SNPs reacted almost completely and ∼90% CH is consumed, while in higher C/S ratio mixture i.e. 2.0, SNPs completely reacted and 75% CH is consumed. Therefore, it may be concluded that almost all SNPs may react within 24 h if sufficient lime (∼1.5 times) is available. However, this condition may vary in cementitious system due it its heterogeneous nature as the presence of other mineral phases may alter/hinder the reaction kinetics.Structural changes occurred in C-S-H gel, during the early stage of hydration, in presence of SNPs were monitored by 29Si NMR technique. 29Si NMR spectrum of anhydrous C3S shows 3 distinct peaks of SiO4 tetrahedral in the range from −67 ppm to −78 ppm a(i) and 8a(ii)), while in SNPs incorporated samples, a broader resonance is observed at 1 h of hydration indicating the formation of hydrated layer having amorphous nature (a (iii) and (iv)), while in SNPs incorporated samples, intense Q2 and a small peak of Q3 is also observed (). While in SNPs incorporated samples, a sharp peak is observed at 968 cm−1 with a shoulder at 1100 cm−1 and a small bump just above 1200 cm−1(Q3 peak) (), which are the characteristic peaks of tobermorite (Ca5Si6O16(OH)2·7H2O) in Si-O stretching region Recognising the high heterogeneity of hydrated cementitious paste the application of the indentation technique is challenging as it is almost impossible to place indents on a specific material phase with sufficient repeatability. This challenge has been tackled by performing large number of indentation grids on the surface of a heterogeneous material. Statistical analysis of the obtained bulky array of indentation tests and a subsequent statistical deconvolution of the indentation results is then carried out to determine the mechanical properties for each material phase. From the obtained result histograms for Young's modulus and hardness the probability density functions are created. Through simultaneous curve-fitting of both types of experimental results with multimodal Gaussian distribution curves, with each curve representing a material phase, using nonlinear least squares method it is then possible to determine the corresponding mechanical property values and phase content (equation Where, μ is the mean value and σ is the standard deviation of the distribution curve that is related to the mechanical property of an individual material phase. This approach is known as statistical or grid nanoindentation technique and was first reported in 2004 For each sample, 640 results were obtained by nanoindentation. The specific mechanical properties for individual hydrated phases (LP C-S-H, LD C-S-H, HD C-S-H, and CH) were extracted by statistical analysis/deconvolution technique. In , the statistical histogram plots of the Young's modulus results, fitted with 4 Gaussian distribution curves are presented for control and SNPs incorporated C3S samples at 15 h and 24 h of hydration, respectively. For low density (2nd peak from the left) and high density C-S-H (3rd peak from the left), Young's modulus values of LD C-S-H ∼22 GPa and HD C-S-H ∼30 GPa, respectively were determined from the deconvolution of the statistical nanoindentation data.The extracted mechanical property values are in good agreement with the results reported in the literature, although those were mainly measured on cementitious systems hydrated for at least 28 days ) show large quantities of loose-packed (LP C-S-H) and low density C-S-H (LD C-S-H). In general, with progress of hydration a shift from the lower qualities of C-S-H towards higher quantities of high density C-S-H (HD C-S-H) was noticeable. Regarding C3S pastes with SNPs addition, the nanoindentation results on such systems show in comparison to their reference materials higher quantities of HD C-S-H. At the same time the contents of LP C-S-H and LD C-S-H were found to be significantly smaller. Additionally, the number of test results with a Young's modulus of less 50 GPa, which is expected to be the range for hydration products, was higher thus suggesting a higher degree of hydration. This appears to support well the findings made by TGA.Properties of concrete, such as strength, porosity, permeability, durability etc. depend on its main hydrated product i.e. C-S-H. In hydrated paste, it is present in the form of gel like network with variable stoichiometry. Incorporation SNPs not only affects the early stage hydration phenomenon but also the mineralogy and morphology of hydrated products. In the present paper we have quantified the C-S-H gel formed as well as the mineralogical changes occurring in C-S-H gel by the addition of SNPs at early stage of hydration. The major findings are:SNPs accelerates the hydration rate of C3S maximum during acceleration period (4–8 h) showing the nucleation effect of additional C-S-H seeds formed on the surface of SNPs during pre-induction period of hydration. Further, it was observed that C/S ratio reduces from 1.86 to 1.6 with the incorporation of SNPs at 24 h of hydration, showing higher polymerization in silicate chain.SNPs shows dominant nucleation effect at 8 h of hydration because at this time of hydration the amount of hydrated products was higher (∼85% additional C-S-H and ∼60% more CH) than the control. At 24 h of hydration, the amount of C-S-H was higher (∼43%) and CH content was lower (∼25%) than the control, indicating the pozzolanic reactivity of SNPs.Results of mass fraction distribution of hydrated and unhydrated products during early stage hydration process show that C3S hydration rate accelerate ∼80% at 8 h of hydration, while ∼51% at 24 h of hydration. Further, it was observed that in control sample steady state hydration rate achieve after 15 h of hydration, while in SNPs incorporated samples, this stage was observed after 8 h of hydration.Selective dissolution results indicate that SNPs completely reacted within 24 h of hydration and it was evaluated experimentally that 0.38 mol of SNPs consumed 0.57 mol of CH which are 1.5 times of SNPs content.Similar results were observed in SNPs and lime paste samples. These results show that SNPs reactivity increase with C/S ratio. At 24 h of reaction in lower C/S ratio (0.5 and 1.0) ∼83% SNPs is reacted while with high C/S ratio mixture i.e. 1.5, SNPs reacted almost completelySNPs accelerate the polymerization of silicate chain in C-S-H gel (presence of intense Q2 peak and small Q3 peak) which leads to the formation of tobermorite like structure (presence of four characteristics peak in Si-O stretching region) at 24 h of hydration.Nanoindentation results clearly show that SNPs not only accelerate the hydration rate but also improved the packing density of C-S-H particles. At 24 h of hydration, in SNPs incorporated samples LD C-S-H reduces ∼52% while HD C-S-H content is increased by ∼40% compare to pure C3S paste indicating the formation of more compact and dense microstructure.Therefore, it is evident from the experimental results that addition of SNPs accelerates the hydration rate at early age (within 24 h of hydration) and helps to promote the formation of high density (HD) C-S-H.Oberst and aging tests of damped CFRP materials: New fitting procedure and experimental resultsMaterials play a fundamental role in defining the vibrational and acoustic characteristics of structures and their importance is even increasing because of the continuing demand for lightweight products. Carbon Fibre Reinforced Plastics (CRFP) components are becoming more and more popular because of their excellent mechanical properties but are unfortunately almost unable to dissipate energy. This is one of the reasons why their usage is limited to structural components and does not directly affect acoustic and vibrational response, which are among the factors responsible for harshness and comfort. In vehicles, for example, large panels of CFRP are as noisy as metallic panels so that this kind of lightweight structures is only used when a limited mass is of paramount importance, e.g. in racing cars. The chance of incorporating a damping material in the stacking sequence of CF layers that define a composite seems to be a viable solution to ameliorate the vibrational behaviour of composite materials. This configuration permits to cure the damping layers together with the resins, in order to obtain both free and constrained layer solutions.In this paper, the Oberst beam method has been chosen to determine the elastic modulus and loss factor of such materials, as a function of both frequency and temperature. Three nominally identical samples for each configuration have been tested in a temperature controlled environment, according to the Oberst beam test method. The effects of aging have been simulated by an accelerated standard procedure, with cyclically varying temperature and humidity for a total of 792 h (3 cycles x 264 h). The analysis of experimental data has been performed in the frequency domain by a least square fitting procedure, aimed at outperforming the simple half-power point method. An open source version of the fitting technique has also been implemented and can be obtained from the authors under the CC-by license.Lightweight design and noise reduction are two of the hot spots of vehicle manufacturers as explained in Refs. []. These two critical topics are treated in this article starting with the analysis of CFRP mechanical behaviour and continuing with the integration of rubber-based compound to obtain a lightweight damped composite. The proposed target is the integration of damping material between CFRP layers, maintaining as constant as possible the mechanical and weight characteristics of composite while improving the NVH property. Nowadays the integration of the damping material in the stacking sequence is performed in two ways:external application on the surfaces of produced components (free layer formulation);integration between layers of CFRP (constrained layer formulation).A noticeable characteristic of damping material used in this research is the possibility of integration in the CFRP, before the cure procedure, whose effects can be analyzed in deep as performed by Ref. []. This characteristic is interesting because their application can be integrated into the production process maintaining under control the technology and final product costs.Material characterization is performed using Oberst test standard (following []), avoiding the use of destructive test as in Refs. []. The use of non-destructive Oberst test, to define Young modulus and loss factor of damping and structural materials, is preferred because of its capability to test exactly the same specimens at different environmental conditions. The use of vibrational and non-destructive test permits the repeatability and the immediate evaluation of damping characteristics as in Ref. [The effect of temperature and aging effect must be considered to verify if any unwanted damping decrement occurs, which could increase the vibration criticalities. In fact, the final use of these materials is on road vehicles where a vibration and noise increment gives the perception of quality decrement to the customer. For this reason, the aging tests have been integrated to the thermal Oberst tests taking under control the material performance degradation. Nowadays, the acoustic comfort is achieved by applying massive sound and vibration deadening materials on critical areas, such as the bonnet, door panel, roof and floor. Considering the new target of automotive weight reduction those solutions are not suitable for new applications, therefore innovative solutions and materials are analyzed in this article.The aim of the study is the characterization of a CFRP sandwich, with and without a damping layer, at different temperatures, and also the documentation of its variations (if any) under an accelerated aging cycle. The damping material is basically a rubber based compound which can be produced in thin, flexible, large and light sheets. It can very simply be included in the stacking sequence of any CFRP component, beams in the present examples but also in more complicated structures, and can undergo the same curing process as the resins. These qualities make it particularly suited to fulfill the current standard production process of multi-layered sandwiches, and also to drastically limit the detachment of layers in sandwiches.The Oberst beam test is a standard method to determine the elastic modulus and the loss factor of a damping material on the basis the frequency response of a multi-layered clamped-free beam (standardized by Refs. []). A summary of the procedure and some comments are given in this section, and the relevant expressions are reported in ) and weight is vibrated by a non-contact exciter () and the measured frequencies of the first few flexural modes, together with their analytical expression based on the Bernoulli-Euler model, allow to determine its Young's modulus – eq. . A layer (or two) of damping material is then bonded on the same beam, according to one of the configurations presented in . The composite beam is vibrated again, possibly at different temperatures, and from its dimensions, weight, resonant frequencies and damping ratios, the properties of the viscoelastic material (elastic modulus and loss factor) are inferred – eq. The base beam is supposed to be un-damped so that most often it is metallic but, in the present work, a CFRP material has been used as a support for the damping layer. The first aim was to measure the properties of the CFRP sandwich itself, and the second was to bond the damping layer on the same material as in the actual applications, in order to determine its effectiveness in terms of total damping. It is also worth noticing that in the Oberst model, the damping layer is required to be much more flexible than the supporting beam and this is one of the reasons why the damping layer thickness has to be limited.The important issue of simulating the interfacial behaviour between different layers, which is addressed by a number of papers with both static and dynamic applications, e.g. Refs. [], has not been investigated because of three main reasons. First of all, the procedure for manufacturing the composite beams does not require any additional adhesive layer, since the resins of the viscoelastic material and of the carbon fibre pre-preg undergo the same curing cycle and eventually form a unique component. Secondly, the accelerated aging process showed no detachment of the layers, as attested by both a visual check and the measured mechanical parameters, thus confirming the excellent junction of the layers. Finally, the fitting procedure described in Section does not rely on any specific model aimed at describing neither a sandwich beam nor a CFRP material, but only on a generic multi-degree-of-freedom system.The test rig used for the experiments is presented in gives the relevant characteristics of the tested specimens. The free length of the beam was fixed to 200 mm and an electromagnetic contactless exciter MM002 was placed at about 42 mm from the clamping, on the right side in , so to avoid the nodes of the first five flexural modes. The magnetic transducer MM0002 is a device produced by Brüel & Kjær and can be used as either a tachometer or an electromagnetic vibration exciter. Both its sensitivity (when used as a velocity sensor) and the applied force (when used as vibration exciter) largely depend on the mean distance from the tested ferromagnetic specimen (the beam in the present case). The producer declares 0.45 N at 0.2 mm and less than 0.15 N at 1.0 mm. The output, proportional to the displacement, has been recorded by a contactless capacitive sensor MM004 placed at the tip of the beam, on the left side in . Also this capacitive transducer is produced by Brüel & Kjær and is a displacement sensitive pickup. The distance between the specimen and the transducer is again of great importance because the sensitivity is inversely proportional to the squared distance. The producer declares a typical value of 0.9 V rms with a mean distance of 0.5 mm and a peak-to-peak displacement of 0.1 mm.It is worth saying that the actual applied force cannot be registered because there is no feedback from the MM0002 device. Nonetheless, the time history of the input force is not really necessary as far as its amplitude is constant in the frequency range of interest (Section ), which is actually below the 2000 Hz limit reported on the data sheet of the exciter. Also the exact amplitude of motion of the free end of the beam is not strictly necessary. In fact, the fitting procedure presented in Section , similarly to the well-established -3 dB method, manipulates the frequency response of the beam to extract the natural frequency and damping ratio, whatever the amplitude of oscillation is. In practice, the output voltage of the sensor is directly transformed in the frequency domain, without using the sensor sensitivity.A swept sine excitation was given in a frequency range covering the flexural natural frequencies two to five because the standards suggest neglecting the first resonance. As regards the number of modes to be analyzed, much depends on the distribution and the performances of the damping material. With a proportional damping configuration, as achieved by any of the three arrangements presented in , the damping ratio increases with frequency so that high frequency modes usually give rise to a very low amplitude response. As a direct consequence, it is often difficult to obtain reliable results for the damping ratio above the fifth mode of the beam, if the damping material is properly designed.The output (voltage, proportional to displacement) has been recorded by a National Instruments USB-4431 acquisition board, programmed with the dedicated LabView software. The system features a 24 bit δ−σ analogue-to-digital converter, with anti-aliasing filters and adjustable sampling frequency. The sampling frequency was at least four times larger than the fifth resonance frequency and the sweep duration set at 5 min. During this period the compressor and the fan of the climatic chamber (Angelantoni Challenge 250) were switched off so to limit the mechanical noise on the specimen, i.e. to ensure that the only input is due to the magnetic exciter. It is important to keep the sweep duration as long as possible in order to properly excite the specimens, especially in the highly damped sandwich configuration where the response of the beam is limited. On the other hand, the sweep duration has to be as short as possible to maintain a constant temperature within the climatic cell, whose control is switched off during the vibration measurement. Experience indicates that 5 min is a good compromise, producing a temperature variation limited to 1/2 °C and allowing for the application of a satisfactory excitation. Three specimens for each layout have been measured so that the results presented in this paper are to be considered the average values.Oberst tests have been performed in a thermally controlled environment with temperature rising from −20 °C to 60 °C, with 10 °C steps. The cycle is shown in : periods of 1.5 h at constant temperature were imposed in order to get the thermal equilibrium of the heavy test rig (14.6 kg) and also to complete the temperature progression overnight. The selected range is typical for many different applications, mainly in the automotive sector.To investigate the aging effect on the behaviour of the materials, the temperature and humidity cycle defined by Ref. [). Each specimen has been exposed to the aging cycle for 792 h, and the Oberst test has been repeated every 264 for a total of four tests for each specimen, simulating environmental exposure effects as reported in Ref. [The rationale for selecting the Oberst test is simple: the damping material is in the same configuration (free or constrained layer) as in the actual components (e.g. a door panel) and the same specimen can be repeatedly analyzed. The latter feature not only limits the number of samples to be prepared but also reduces the variability introduced on the results (elastic modulus and loss factor) by the sample characteristics (i.e. slightly changing dimensions and weight), as typical for every non-destructive procedure.In brief, the sequence of the testing procedure follows:set the desired temperature and humidity in the environmental test chamber and wait for their stabilisation;excite the beam and measure the displacement of its free end. This time domain output is used to compute the PSD Syy (see Section switch the chamber on and return to step a).Many standards, e.g. ISO 6721–1 and ASTM E756, suggest relying on the half-power method, also called -3 dB method, to determine the natural frequency and damping ratio of a single degree of freedom (SDOF) system. The method requires to plot the resonance curve of the system under forced vibrations and to determine the resonance frequency, which is assumed to be equal to the natural frequency fn. Two frequencies f1 and f2, where the amplitude of the response is 3 dB lower than its maximum value, give the width of the resonance peak and then the damping ratio.It is then usual to link the damping ratio ζ and the loss factor η by the relation η = 2 ζ.The procedure is very simple and very quick to apply but suffers from some drawbacks []. In the case of very lightly damped structures, it may be difficult to precisely estimate the value of the maximum amplitude (much depends on the frequency resolution) and, consequently, the values of f1 and f2. In the case of very highly damped structures, it may be difficult to get the -3 dB points. In any case, only three points of the frequency response are used, although many more spectral lines are usually available. Another very simple and well-known approach is the logarithmic decrement, which is nonetheless limited to the analysis of the free response of single degree of freedom systems [], which is not the case when a beam is studied.The method presented in this section is still based on the resonance curve but fits many measured spectral lines (and not only three, f1, f2 and fn) to give a least square evaluation of the natural frequency and the damping ratio. Some numerical examples are presented in Section to show the capabilities of the procedure.The issue of modal parameters identification has indeed interested a large number of scholars both in the linear and non-linear domains [[], just to mention a few]. Aim of the following section is to describe a simple method, specifically dedicated to the output-only estimation of frequency and damping ratio.The impulse response function h(t) of a linear and time invariant system with n degrees of freedom can be expressed in the formand the poles sr are linked to the natural angular frequencies ωr and damping ratios ζr by the expression sr=−ζrωr±iωr1−ζr2. The Fourier transform of h(t) gives the frequency response function (FRF) H(Ω)The problem is to identify the poles sr, and then ωr and ζr, given a measured time history h(t) or its correspondent FRF H(Ω). In the previous expressions (1) and (2), both time and frequency axes are continuous, which is not the case when data are recorded with a digital acquisition system. In practice, a limited (although possibly very large) number of samples is collected in the time domain, which in turn generate a discrete sequence of spectral lines Hk=H(Ωk).Here Ωk indicates the generic frequency given bywhere fs is the sampling frequency, Δf is the frequency resolution, N is the number of spectral lines and k = 1 …N.The plot of the modulus of the discrete FRF |Hk|, k = 1 …N, usually on a logarithmic scale, is the first step for obtaining an estimate of the damping ratio by the half-power method.The technique described in this section exploits the information of many spectral lines (at least four) around the resonance and takes advantage of expressing the FRF in the Z-domain. The Z transform of the sampled impulse response function iswhere zr=esrΔt and zk=ei(k−1)ΔΩΔt=eiπ(k−1)(N−1).zk indicates the spectral line at frequency Ωk, zr is linked to the natural frequency and the damping ratio through sr, Hk can simply be computed by the fast Fourier transform (FFT). The Z transform conveniently maps the frequency axis into a circle, thus limiting to one the modulus of zk.If the resonant frequencies are well separated, as also required by the half-power method, a SDOF model can be assumed and Eq. where the four unknown coefficients a0,a1, b1,b2 are real.The complex zk can also be written in the formThe squared modulus Mk of the FRF, after the introduction of (6) and (7), into Eq. where * indicates the complex conjugate. The four real coefficients are given by:A=p/qB=(1+a02+a12)/qC=2a1(1+a0)/qD=2a0/qp=2b1b2q=b12+b22which leads to the following linear system of equations[−cosxpMpMpcosxpMpcos2xp−cosxp+1Mp+1Mp+1cosxp+1Mp+1cos2xp+1⋮⋮⋮⋮−cosxqMqMqcosxqMqcos2xq]{ABCD}={1111}p and q respectively indicate the lowest and highest frequencies of interest around the resonance and K = q-p+1 is the number of spectral lines. When K > 4, eq. is an overdetermined system of equations that can be solved in a least square sense, for example with a singular value decomposition.With A, B, C and D it is then possible to determine a0 and a1 and finally, since a0=zrzr∗ and a1=zr+zr∗, to retrieve the natural frequency ωr and damping ratio ζr:The proposed method is not as easy as the half-power technique but offers at least three advantages:it is based on many spectral lines and gives a least square solution for both ωr and ζr;it can be applied also to highly damped structures; – can be plotted to visually verify if it correctly fits the original dataAn open source Matlab® implementation of the fitting procedure can be obtained from the authors under the CC-by license.The first two examples use a single degree of freedom system with natural frequency 1 Hz and damping ratio either very small (0.2%) or very large (40%). Every spectral line of the theoretical FRF of the model has been numerically corrupted with 3% random noise to simulate possible inaccuracies in the measuring apparatus. The resulting PSDs are presented in . In both cases the application of the 3 dB method would be very difficult: with ζ = 0.02%, the estimation of both the maximum amplitude and the width of the resonance peak can be largely inaccurate (in fact the spectral line at 1 Hz is not present); with ζ = 40%, the half power points are hard to find and it is not possible to assume that the natural (1 Hz) and resonance (about 0.8 Hz) frequencies are numerically equivalent.The results of the fitting procedure are graphically represented in where the original spectra, black solid lines with black dots, are overlaid on the synthesized curves (red dashed lines). The representation of the synthesized PSD gives also a qualitative estimation of the numerical results, which are indeed very satisfactory: 0.19% and 40.1%. When the peak is very sharp, i.e. the damping ratio is very small, a few spectral lines (less than ten in ) are sufficient to obtain accurate results, while larger values of damping require more spectral lines (about 100 in ). It is possible to conclude that the method is robust and can cope also with noisy data, as far as a SDOF system is concerned.In order to verify the effectiveness of the fitting procedure with a multi-degree of freedom (MDOF) system, a finite element model (FEM) of the Oberst beam has been prepared with dimensions 200 × 20 × 0.9 mm3 (length/width/thickness), in a clamped-free configuration. Convergence tests on the eigenvalues of the FEM suggested that a 100/10 mesh with shell elements (1000 in total) is appropriate to achieve correct results.Damping has been introduced according to the viscous proportional modelso that various levels of dissipation can simply be obtained just by changing α and β.The FRF has been computed between FE nodes located in positions similar to the input and output points of the actual test rig. The selected output node is not in the exact midline of the model, so to simulate a possible defect in the output sensor position, and consequently also the unwanted contribution of the torsional modes will be present in the FRF.Two examples with very small and very high damping ratios are proposed, and again with 3% noise on each spectral line. Also in this case the application of the -3 dB method would be complicated by either too low or too high damping ratios and this is the reason why a direct comparison with the -3 dB method is not reported., the method is instead validated by comparison with the theoretical results. The first flexural mode (, 17.1 Hz) is neglected, as suggested by the standard, as well as the torsional modes at about 170 and 500 Hz. In the low damping case, the fifth damping ratio is underestimated, both because of the noise introduced in the spectrum and the influence of non-resonant modes. Also the first estimation is lower than expected but its value is so low (0.2%) that the difference is negligible. When the high damping case is studied () Mode 4 at about 600 Hz is almost undetectable and largely modified by the other modes. The resulting fitting curve () is not very accurate because a SDOF model cannot correctly describe the shape of the MDOF system, and also because of the noise. Consequently, both frequency and damping estimations are far from the correct values. This conclusion is not unexpected, as also reported by Ref. []. Moreover, Mode 5 completely disappears from the resulting output (a resonance peak in the FRF cannot even be spotted) and cannot be detected, but the estimates of Mode 2 (110 Hz) and Mode 3 (310 Hz) are still very accurate.the proposed method is applicable to both high and low damped resonance curves;the least square solution can limit the influence of noise to a great extent;the SDOF approximation is not too restrictive, provided that modes are well separated;the synthesized PSD is a simple but effective tool to judge the quality of the results. is more complicated than computing the ratio η= (f2-f1)/fn. But, given a proper software, the end user just has to choose p and q in eq. This section presents the results obtained by analyzing the beams listed in . All the values are the average over three samples of the same type.The base beam has been named “T300” because it is formed by three layers of T300 (twill 200 gr/m2) carbon fabric in an epoxy matrix. The three samples under investigation have been cut from the same plate so that they underwent the same production process. shows Young's modulus and loss factor of T300 beam, as a function of temperature. The reported values, almost perfectly constant, are obtained as an average over modes from two to five. The loss factor is almost null and completely comparable with the values collected from a steel beam 1 mm thick, thus confirming the possibility of using T300 as a base beam for the damping materials.The aging cycle, at least up to 792 h, does not notably modify the material. Not only the external aspect does not change, but also the mechanical properties are invariant with only a slight increment of the elastic modulus. presents the elastic modulus of the damping material, as deduced by applying the ASTM expressions () to the experimental results of three beams damped on a single side (see ). At −10 °C two points only are plotted because at that temperature only modes two and three can correctly be fitted, due to the high level of dissipation introduced by the damping material. The figure makes it clear that large variations occur in the selected temperature range −20/60 °C while frequency, although not completely negligible, only exerts a low influence on the material in the 100–800 Hz range.Since the frequency variations are not so pronounced, and taking into account that in any actual installation the damping material is likely to be excited and to respond in a large frequency band, it has been decided to group the results. gives Young's modulus and loss factor of the damping material (KRAIBON® SUT9609), calculated as the mean value of many modes, from two to four depending on temperature. At each temperature the scatter about the mean is also plotted, for the four curves representing the aging progression. The loss factor largely depends on temperature, with some variance due to frequency, but exhibits almost no dependency on the aging cycles although in this configuration (one side damping) the damping layer is directly exposed to humidity and ice.The last example underlines the different effects that can be obtained by using the free (beam damped on one side) and constrained (sandwich beam) damping layer configurations. display the elastic modulus and the loss factor of two composites: the beam damped on one side (free damping layer) and the sandwich beam (constrained damping layer), as per . In this case, the specimens have been studied as if they were formed by a single homogeneous material and the plotted loss factors then have the effective values assumed by the specimens themselves.The influence of the stacking sequence (free or constrained layer) is of paramount importance in modifying the results: the damping properties of the sandwich beam not only are larger but also span a wider temperature range in comparison with the free layer configuration. The results presented in this section show that temperature largely modifies the behaviour of the composite and that, apart from the 0 h aging condition in the sandwich beam, the accelerated aging cycle does not evidently affect the properties of the tested specimen, at least up to 792 h. lists Young's modulus and loss factor of both beams, given as the mean value of four (0-264-528-792 h; free layer) and three (264-528-792 h; constrained layer) aging steps.Vehicles electrification and new targets concerning the fuel consumption impose a continuous research in weight reduction. Consequently, the use composite lightweight material with efficient mechanical characteristics will play a central role in future vehicle components. For this reason, the material used as a baseline for the research is a CFRP.The paper presents an accurate least squares fitting method to evaluate the natural frequency and the loss factor of a SDOF system from experimental data. The response is analyzed in the frequency range containing the resonance of the system and since the method relies on a large number of spectral lines, the limitations of the classical half-power points method are eliminated. Numerical examples show that the procedure is very accurate also for MDOFs systems, as far as the modes are uncoupled, and has successfully been applied to the analysis of the Oberst beam test recordings.Experimentation confirmed that the Oberst test is a reliable, fast and non-destructive procedure which permits a definition of materials database characteristics, that can be incorporated in FE analyses as done in Refs. []. The chosen damping material can very simply be added in the production process of any CFRP sandwich: it can be handled just like any other carbon fiber layer, it does not require the use of any specific tools and can be subjected to the same curing process of the epoxy resins. Experimentally obtained data have been averaged over three specimens and, although the number of samples is too low to allow for a correct statistical analysis, the scatter of the results from the mean value remains under 3% for each material. Each material has been tested in the −20/+60 °C temperature range, which is in line with SAE specifications for automotive components and proved to encompass the temperature of maximum damping effectiveness. The adopted aging cycle, combining the effects of temperature and humidity, did not yield any significant effect on the materials characteristics, neither on the external aspect nor on their mechanical properties. The only difference is showed by the first aging step of sandwich samples, which displays an altered behaviour from 20 °C to 60 °C.In summary, this paper presents a new fitting procedure that efficiently allows to determine the natural frequency and the damping ratio of an output-only frequency response function. These quantities, combined with the model of the Oberst beam test, yield the elastic modulus and the loss factor of the specimen. A particular damping material, whose formulation permits a simple inclusion in the stacking sequence of a common CFRP sandwich, has then been characterized as a function of both frequency and temperature. The stability of its mechanical properties during an accelerated aging cycle has finally been verified.Cn  = coefficient for mode n of clamped-free (uniform) beam,E = Young's modulus of beam material, Pa,fn = the resonance frequency for mode n, Hz,Δfn  = the half-power bandwidth of mode n, Hz,H = thickness of beam in vibration direction, m,η = loss factor of beam material, dimensionless,η1=ηc[(1+MT)(1+4MT+6MT2+4MT3+M2T4)(MT)(3+6T+4T2+2MT3+M2T4)]E = Young's modulus of beam material, Pa,E1 = Young's modulus of damping material, Pa,fn = the resonance frequency for mode n, Hz,fc = the resonance frequency for mode c of composite beam, Hz,Δfc  = the half-power bandwidth of mode c of composite beam, Hz,ηc = loss factor of composite beam, dimensionless,η1 = loss factor of damping material, dimensionless,ρ1 = density of damping material, kg/m3.Flow dynamics of grains in spinning bucket at high frequenciesA large-scale three-dimensional molecular dynamics type simulation study of dense granular media was performed to investigate the flow dynamics of grains in a spinning bucket at high frequencies. By utilizing the results obtained from simulations and using a continuum approach the hydrodynamic equations are presented and an expression for viscosity is obtained. The hydrodynamic equations were solved numerically to predict the flow dynamics of grains spinning at high frequencies in a cylindrical bucket. The model results were found to be consistent with experimentally observed surface phenomena across a wide range of rotation rates, including the development of a depression near the axis of rotation at high rotation rates and the formation of a cusp in the central section of the bucket at lower rotation rates.Cohesionless grains in a spinning bucket exhibit interesting flow dynamics, such as the existence of solid-like and fluid-like qualities side-by-side (), which may result in the formation of circular kinks on the surface of the granular material (). Although the slowly evolving surface shape of a bucket of sand experiencing vertical spinning motion at a fixed rotation rate cannot be completely explained using the Coulomb yield condition (), the formation of circular kinks, whose radius was reported in to be a function of the spinning speed and the tilting angle, remains a mystery. Several researchers () have proposed theories for the prediction of grain dynamic behavior in a spinning bucket. In particular, the model used by is based on the fundamental assumption of a thin flowing layer, and hence may be suitable for predicting the flow dynamics of the grains only at rotation rates lower than near the sidewalls as well as a very loose aggregate of grains in the central region. More evidence of ordering and even shear-induced crystallization has been reported by in their annular plane shear flow device. However, particle to wall friction as well as interparticle friction might delay ordering as suggested by In light of the above discussion, it is likely that the change in density of the granular material governs the dynamics at high rotational frequencies. In this case granular convection currents might form implying the presence of very complex flow dynamics for which the boundaries especially the bottom wall play a major role in initiating and sustaining relative particle movement.The dynamics of grains rotated deep down in a spinning bucket are much more complicated than those in rapid granular flows, for which the short-lived collisions between particles characterize the flow dynamics, even at high frequencies. In this case complex nonlinear elasticity exhibited collectively by an aggregate of grains which governs the flow properties of the system could result in chain formations in two dimensional granular systems (), which may result in an anisotropic stress tensor. Apparently, the structure of these force networks has a random transient character ( stated that it is not clear that contact forces or stresses would be nonhomogeneous in 3D cases. It is more likely that an isolated force perturbation or stresses concentration would have a smaller domain of influence. Therefore, the contact forces or stresses might be more homogeneous in 3D granular systems especially at time scales much larger than the average life time of chains where a hydrodynamic description might be relevant. In this light, within the frame of continuum mechanics an effective viscosity for a granular fluid may be introduced which decreases with granular temperature for low shear rate flows (). Savage argued that by assuming a viscous-like behavior for grains in a vertical channel flow plausible results can be found for stress and velocity distributions for a steady fully developed flow.This paper presents an investigation of rheology of aggregates of grains in a vertical bucket of sand rotating around its cylindrical axis at rotational frequencies higher than . The aim is to develop an approximate model to handle slow high concentration flows of granular material to predict phenomena such as the observed steep depression () around the center of a vertical bucket of sand rotating around its cylindrical axis at high rotational frequencies, namely . To this end, molecular dynamics type simulation results are presented in which a contact force model () is used to capture the key features of granular inelastic interactions. The results of molecular dynamics were used to develop a set of continuum equations for granular flows in an intermediate regime in which the granular aggregates are considered to be compressible. Numerical solutions are presented of the integral form of the governing equations for granular flow in the vertical spinning buckets at high rotational frequencies. To test the model, the numerical results are compared with the molecular simulation results as well as available experimental results. Finally, a summary of the findings and the direction of future investigation are presented.Collisions between particles, which have been studied since Newton's time, still pose many difficulties and unanswered questions. One of the simplest of these problems is the binary collision between two monosized, spherical grains which involves repulsive rigid elastic interactions as well as dissipative frictional contacts. Developing realistic models for the granular collisions by which slow collisions for rough as well as smooth grains can be described would be invaluable in understanding of the flow of granular materials especially in industrial systems.For this reason, a contact force model such as ) is often adopted to capture the key features of granular inelastic interactions when the impact velocity is much less than the speed of sound in the grain's material. have developed a model based on the classical harmonic crystal in which an expression for δ is given as is consistent with that found from Hertzian quasi-static force (). In this case, an expression of k for three-dimensional isotropic spheres is given as ( have suggested for colliding viscoelastic grains with radii R1 and R2, and masses m1 and m2 the coefficient c depends on the Young's modulus, the viscous constants and the Poisson's ratio of the material:, suggesting that c has the same form as k, namely , with E and ν replaced by the viscoelastic coefficients η1 and η2, respectively. These coefficients, however, are difficult to find in the literature.) it has been shown that using a Newton's Cradle the viscoelastic coefficients η1 and η2 can be measured. In this case a correlation has been developed for the viscous damping coefficient of glass balls whose density, chemical compositions, Poisson's ratio, and Young's modulus are , SiO2=66.0%, Na2O=16.0%, CaO=7.0%, Al2O3=5.0%, Bi2O3=3.0%, ν=0.244, E=6.3×1010Pa, respectively. The glass balls were manufactured by Sigmund Linder GmbH, Germany. It was found that . This correlation suggests the σ−5/2 dependence of the viscous damping coefficient, c, on particle diameter σ. illustrates velocity dependent coefficient of restitution for the aforementioned glass balls. The inset of depicts the numerical results obtained for the contact time, tc, by integrating . As can be seen, tc exhibits the Vimp−0.2 scaling consistent with the findings in argued that since the energy dissipated by plastic deformations of asperities is far smaller than for the typical systems found in nature, the present viscoelastic frictional model can describe slow collisions for rough granular systems satisfactorily. However, it appears that both the normal forces and tangential forces () whose reduced version was employed by must be considered to develop a realistic model for rough granular systems. In this case a particle i translates and spins, depending on the forces and torques acting on it. The governing equations for translational and rotational motion of the particle i in a granular assembly are presented in Using the above-mentioned nonlinear particle dynamic model the granular flow dynamics in a bucket as shown in spinning at high frequencies were investigated. More than 61 000 identical nonoverlapping spherical particles with diameter were placed randomly in the cylindrical computational box whose side and bottom walls were spinning at . The initial velocities of each particle in the x-, y- and z-direction are assigned with a magnitude according to a profile plus a small random number uniformly distributed over the interval represent the unit vectors in the x-, y- and z-direction.Using the correlation proposed earlier in this section for the viscous damping coefficient, the value of this coefficient for particles with which is a more realistic value compared to that used by . In fact, the contributions of inelastic collisions to the dynamics are replaced by normal velocity-dependent viscous damping forces.The other physical properties of spherical particles in the simulations such as density, normal elastic constant, and the coefficient of friction are given as , and μp=0.4, respectively. As discussed in , in the present model the effect of static friction is represented in a crude manner by a restoring force that counteracts mutual sliding motion at contact.Note that for Hertzian contacts, the ratio kn/kt, which depends on Poisson's ratio, is about no contribution of surface roughness in rotational velocity damping, namely ct=0, is considered in the present model.The importance of the wall friction coefficient on bulk flow fields due to the highly complex nature of the frictional forces that occur requires further discussions. In general, the walls are rough and tend to inhibit sliding motion. In the context of expanding flows, according to , for the flow of granular material on rough surfaces where the roughness of the wall is of the order of the particle size there seems a strong possibility that there is an immobilized granular layer at the wall. Such effects lead to irregularity of flow which is undesirable in bulk flow.) a cylindrical container was used made of polyvinyl chloride (PVC) plastic with density, Young's modulus, and Poisson's ratio, are given as , ν=0.33, respectively. In this case, the roughness of the wall is much smaller than the particles diameter which is of order of millimeter. Hence, a simplified representation of the relevant aspects of the particle wall contacts is chosen hoping that detailed comparisons between simulations and experiment can then be used to establish the quality of the approximation. In this case, the interaction between the particles and the surface is described by a simple friction law in which the coefficient of friction being a constant. The PVC-sand friction coefficient appears to be in the range of 0.5<μ<0.6. Hence, a constant particle-wall friction coefficient, namely μw=0.6, is chosen for the simulations with the anticipation of inhibiting sliding motion.It is likely that particle-wall frictional interaction will perturb the flow field. In fact, by decreasing the particle to wall friction the particle wall contact increases leading to denser and more ordered structures in the wall region. On the other hand, by increasing particle to wall friction ordering can be delayed which affects the ability of the particle to slide on the walls. Thus an important question is the degree to which the present model is able to reproduce the effects of the wall friction on the bulk flow field. This consideration will be discussed in a future paper in which attempts will be made to obtain finer resolutions of bulk flow fields.The proportional loading approximation of can be used as a simplified model of contacting particles with the bottom and side walls. To this end, ktw is set to , and an arbitrary but reasonable value is chosen for the viscous damping coefficient, namely . Also regardless of the rate of momentum exchange between the particles and the wall, the rotational rate of the bucket is assumed to remain constant.In this set of simulations two-fifths of a spinning bucket of radius is initially filled with monosized, spherical, glass particles. The apparent density of the system was are solved using the Verlet algorithm (. In the present simulations, the values of normal elastic constant are large enough to avoid grain interpenetration. In addition the simulation time step δt∼tc/100 is small enough to assure an accurate simulation. In addition, regardless momentum exchanged between the particle and the wall, the rotational rate of the bucket is assumed to be constant.The stress tensor Pαβ is calculated as the sum over all particles i within a sampling volume V, which is a sector of the cylinder, given by where V̄ is the time-averaged velocity of the particles within the sampling volume. If is the unit vector outer normal to the side wall of the bucket, then the normal stress acting on the sidewall is given by illustrates the time series of the dimensionless normal stress, , on a cylindrical strip of the side wall located at represents the dimensionless time defined as tω0.(a) may suggest the release of energy due to a collision of a chain of particles with the wall. This type of anomalous energy release represents fast phenomena followed by a long waiting time. Here the waiting time τ is defined as the time difference between two successive maxima of the time series of dimensionless normal stress as shown in (c). The analysis of the data revealed a power law distribution P(τ)∝τα with α≈−4 over roughly 1.5 orders of magnitude as illustrated in (c). The observed scaling behavior might be unrelated to self-organized critical state of granular aggregates in the sand pile for which no correlation between the successive high energy releases would be expected. The observed behavior displays time intermittency in the high energy releases suggesting that the dynamics of grains might be identified as chaotic (Using the averaging procedure described in the mass and momentum balances for the particles may be derived (ignoring the interstitial gas) as follows:, constitutive equations are required for the stress tensor. The third term on the left-hand side of includes the divergence of the velocity which characterizes the compressibility of the granular assembly. For the stress tensor, using the plastic potential theory (), a yield function in the stress space may be introduced that can predict both dilation and contraction. The yield function, Y, can conveniently be expressed in terms of principal stresses σi, i=1,2,3, which are the eigenvalues of the stress tensor σij:The yield surface is convex, and its size grows with increasing φs. The boundary between the dilatancy and contractancy surfaces is the critical state locus.Using the principle of coaxiality, the strain rates may be derived from a simple plastic potential function. In the simplest case when the yield and plastic potential functions are identical, the strain rates may be given by for stress components in terms of the rate of strains and then substituting the results in the yield function, relations between stress and rate of strain tensors may be found asAt very low shear rates where the strain-rate fluctuations are very small, a rate-independent, plastic behavior of the granular assembly may be predicted by At higher shear rates fluctuations exist in σij due to fluctuations in the strain rate εij which may be even larger than the mean strain rates . Therefore, the effect of viscosity associated with the pseudo-thermal motion of grains cannot be neglected. By assuming isotropic strain rate fluctuations with a Gaussian distribution with a standard variation of ε, namely , a stress–strain rate relation can be developed. The variance of the strain rate fluctuations, ε2, characterizes the pseudo-thermal motion of the grains and thus is analogous to the granular temperature T.The mean value of stress can be calculated from the fluctuating strain rate by multiplying for σij by f(εij) and integrating over the strain rate space. It is convenient to evaluate the resulting integral over e1,e2,e3 which represent principal strain rates. That is, which is valid for a two-dimensional case, the right-hand side of which is a small parameter when the values of ε are large compared to the mean strain rates. Transforming to spherical coordinates by introducing the mean principal stresses as a linear function of the mean principal strain rates may be found as , where μ and ζ are the coefficients of viscosity, which have the form of μ=PA/ε,ζ=PB/ε. The coefficient A and the ratio of viscosities, ζ/μ, depend on the angle of repose θf as illustrated in In a straightforward way the expressions for the mean stress components may be given as . This expression resembles a viscous-like character for a liquid-like granular material in the sense that the viscosity decreases with increasing strain-rate fluctuations. suggested that for an intermediate regime, P is composed of a pressure density contribution for quasi-static deformation as well as a collisional stress contribution which depends on granular temperature:At high deformation rates where ε is very large, the second term on the right-hand side of is dominant and the stresses can be calculated using a kinetic theory approach. In this case, an approximate expression for ε may be obtained by equating the expression of shear viscosity, namely μ=PA/ε, with that of the kinetic theory results (For the solids fraction in the range 0.4<φs<0.62, no significant variations can be observed in the value of εσ/T1/2 which may be assumed as a constant, η, whose order of magnitude is unity. Thus, the complete form of the mean stress tensor of the solid phase for the intermediate regime (where both collisional and frictional interactions between particles should be taken into account) is given bySince ε∼T1/2, the constitutive equation suggests that for low shear rate frictional dominated regime, the effective viscosity decreases with increasing granular temperature. To simplify the notation, hereafter overbars which denote the mean quantities will be omitted.By introducing the link between ε and T in the above equation, an additional equation is required for calculation of the granular temperature. The conservation of fluctuation energy for the particles includes the work performed by σij, the divergence of a pseudo-energy flux owing to the fluctuating motion, Qi, as well as the dissipation of the fluctuation energy due to strain-rate fluctuations γ. That isHere, the rate of energy dissipation due to strain-rate fluctuations, γ, may be given as , where the prime denotes the fluctuation quantities. illustrates variations of γ/Pε with the angle of repose. The flux of the fluctuation energy is expressed using the kinetic theory type approach, namely Qi=−λ∂T/∂xi, where λ is the coefficient of the fluctuation energy transfer, defined as λ=αPA/ε where the parameter α is a function of the average solid volume fractions given asApplying the equations derived in the preceding sections, the flow of grains in a spinning bucket as schematically illustrated in is simulated to predict unexplained hydrodynamic phenomena such as the steep depression around the center observed by . To proceed, the numerical solutions for the hydrodynamic equations are sought using the appropriate boundary conditions at the side wall, bottom wall, free surface and axis of rotation in a rotating cylindrical coordinates system r,θ,z, with a constant angular velocity, is the unit vector in the z-direction. The boundary condition on the velocity at the side wall is simply Vr|r=R=0, and that at the bottom wall is given by Vz|z=0=0. The suitable boundary conditions at the side wall for Vθ and Vz may be sought by applying the law of sliding friction. By leaving the slip velocity at the side wall undetermined, it may be stated that at any point on the wall the magnitudes of the shear stresses σrθ and σrz are proportional to the magnitude of the normal stress σrr. Hence |σrθ|r=R=μw|σrr|r=R and |σrz|r=R=μw|σrr|r=R where μw is the coefficient of wall friction whose value is positive. Since P is the dominant term in the expression for the normal stress at the walls, the aforementioned boundary conditions may be approximated as r∂/∂r(Vθ/r)|r=R≈Pμw/μ and ∂Vz/∂r|r=R≈−Pμw/μ, respectively. Here, the axial variations of the radial velocity along the side wall are neglected.The solids fraction at the side wall may be stipulated to be equal to 0.62. Moreover, the boundary conditions at the axis of rotation are derivatives of radial, axial and tangential velocity, solids fraction and granular temperature with respect to r are all zero. observed a continuing evolution of the free surface in a spinning bucket of sand. This observation and the difficulties in obtaining plausible steady-state solutions suggest that considerable insight into the dynamics of grains in a spinning bucket at high frequencies may be obtained by analyzing the time-dependent solutions. A set of computations was performed to predict the free surface shape at high frequencies as well as the velocity profiles in the tangential, radial, and axial directions and the profile of the granular temperature. Note that at high frequencies, the assumption of a thin flowing layer near the free surface is not likely to be valid. In this set of simulations one half of a spinning bucket of radius is initially filled with monosized sand particles with diameter of , e=0.84 and θf=34.6°. The operational parameters are , φ0=0.49, and φ∞=0.63. Moreover, the constant P0, in , the surface shape after 4 full rotations of bucket, as shown in contains a cusp in the central section at rotation rate of (c), a steep depression is formed around the center whose diameter is about 0.1R. (d) represents a sharper version of the depression. Unfortunately, no comparison of the theoretical and experimental surface shapes associated with the depression can be made due to insufficient experimental resolution. However, reasonable agreement between theoretical predictions and experimental measurements can be found for the radial position at which no variation in the surface height due to rotation of bucket occurs. As illustrated in (c), the numerical results confirm the experimental observations that it is likely that near r/R≈0.7 there is little variation in the surface height due to rotation. Moreover, as predicted by the numerical results, it is reasonable to suggest that the surface height of the sand at r/R=0.88 is z/R≈0.3. Note that no information has been provided in for the cases for which the rotation rates are higher than The numerical results cannot predict a linear profile for the surface shape at r/R>0.9 most likely due to the wall effects. However, the obtained variation in the maximum surface height near the side walls agrees with that found from molecular dynamics type simulations of a spinning bucket.Grid independent numerical results were found using fewer than 104 elements. In this light, the numerical results may correctly represent solutions of the equations of hydrodynamics for a granular flow in the intermediate regime. illustrates the development of the surface shape of granular material in a rotating bucket as the rotation rate varies. As can be seen, the height of the cusp in the central region decreases with increasing rotation rate. However, there is an evolution from cusp to depression near the axis of rotation at rotation rates higher than . The exact rotation rate at which the transition occurs cannot be specified at the present. However, for the parameters used in the simulation, the transitional rotation rate is likely to be close to corresponding to dimensionless angular velocity of presents results of velocity field as well as color-coded three-dimensional solids fraction profiles at rotation rate of . In this case, a somewhat deep hole can be observed around the center of rotation, and the surface height of the sand at r/R=0.95 is found to be z/R≈0.4. The formation of a low density zone in the central region of the bucket is clearly presented in (c). This finding supports an earlier prediction that the change in density of the granular material governs the dynamics at high rotational frequencies.It is worth mentioning that the fluctuations in the angular velocity of the spinning buckets, which is regarded as an undesired phenomenon, could make it difficult to capture the essence of the relevant physics from the data. To minimize the fluctuations in the angular velocity, the container is designed to be much more massive than the sand within it. However, it appears that the fluctuations cannot be completely avoided and the surface shape could change due to undesired fluctuations and vibrations. In this light, the agreement between numerical results and the data (, implies that the present model based on the earlier work of could predict the basic features of experiments for which a sufficient experimental resolution may not be reached due to the aforementioned technical problems.In summary, a model developed to describe granular flow dynamic behavior in the intermediate regime (where both collisional and frictional interactions between particles may occur) was applied to examine the continuous flow of grains in a spinning bucket at rotational frequencies higher than . It is shown that by using a rate-dependent effective viscosity for a granular fluid, an evolution from cusp to depression near the axis of rotation can be predicted at rotation rates higher than to corresponding to dimensionless angular velocity of . The sample results are presented for the case in which the rotation rate is . In this case, a steep depression is formed around the center whose diameter is about 0.1R.It may be argued that the granular material might never exhibit the relaxation to a uniform equilibrium that is required in kinetic type derivations of hydrodynamic equations such as that presented in this paper. However, the present description of the granular material using a set of hydrodynamic equations with a local velocity, a density and a granular temperature as local variables appears to be useful for interpretation of unexplained phenomena such as the formation of steep depression observed experimentally (). The present results could be more precise if a full consideration of the effect of slip velocities and granular temperature jumps at the walls could be taken into account. Such considerations will be discussed in a future paper, in which the rolling resistances () between contacting particles or between a particle and the wall of the bucket will be taken into account (in molecular dynamics simulations) to improve the resolutions required for more realistic theoretical treatment of the problems such as flow dynamics of granular material rotating in a tilted spinning bucket.Note that the current understanding of the dynamics of granular flows comes from two rather disjoint models, namely continuum models such as those used in soil mechanics, and kinetic theory models. The present approach appears to provide greater insight toward the explanation of poorly understood hydrodynamic phenomena in the field of granular flows.In the presence of gravitational field, the equation of motion of spherical particle i having repulsive interactions with its neighbors, together with normal and tangential frictional damping forces, may be given aswhere Ni represents the number of particles in contact with particle i at time t, and represent the normal and tangential force per unit mass acting on particles i, respectively, which are given by ( represents the unit vector in the direction of relative impact velocity defined as In this approach the strains corresponding to a given tangential and normal contact force, which is caused either as a result of a collision or because one particle is resting upon the other, are determined by the specific history of loading leading to these forces. The contact force per unit mass on particle i from particle j is given by and the contact force on particle j from particle i is simply given by Newton's third law as , the underlying physics of the complex behavior at the contact zone for colliding rough particles might be explained by noting that when a normal contact is sheared by a tangential force which is insufficient to cause failure, a region of microslip () forms adjacent to the outer perimeter of the contact zone. By increasing the tangential force this region moves inwards and two surfaces slip with respect to one another while in the interior of the contact zone the surfaces remain stuck together. By further increasing the tangential force at which the failure occurs, there is no stick region in the interior of contact zone. represent in a crude manner the complex behavior at real contact. Here, Coulomb friction law describes friction between two colliding grains with a surface friction coefficient, μp, when there is mutual slipping at the point of contact. Following , the magnitude of χij, which represents the tangential displacement, is calculated as necessary to satisfy . Otherwise, the contact surfaces are considered as stuck while . Here, the rate of change of tangential displacement, χij, is given byThe displacement, χij, is set initially to zero when a new contact is established and once the contact is broken, all memory of the prior displacement is lost.Frictional forces induce torques on particle i which is defined by must be augmented by a torque equation for the rotational motion of particle i which can be written aswhere δiw is the amount of deformation occurring at the contact and kniw is normal elastic constant. Following where θ=1 and ϕ1 and ϕ2 are elliptic integrals given asThe quantities ϕ1 and ϕ2 are evaluated by means of Legendre polynomials. Thus kniw may be simplified asTo obtain an expression appropriate to spherical–spherical contact from In the case of contact between an isotropic sphere i and cylindrical side wall the area of contact is an ellipse whose eccentricity is defined by which is a function of (2R−σ)/2R. Since R and σ are known, θ can be evaluated solving the following equationSubstitution of value for θ in the expression for the normal elastic constant knic defined asresults in the value for the normal elastic constant between a spherical and the side wall used in the simulations.Effect of recycled tyre polymer fibre on engineering properties of sustainable strain hardening geopolymer compositesStrain hardening geopolymer composite (SHGC) processing superior tensile ductility and multiple cracking is a promising alternative to traditional ductile cementitious composites whereas the extremely high cost of polyvinyl alcohol (PVA) fibres limits its large-scale application. This paper presents a feasibility study of replacing PVA fibres with recycled tyre polymer (RTP) fibres to reduce the material cost of fly ash-slag based SHGC and ease the pressure on environmental impact induced by the vast amount of waste tyres, focusing on the influences of PVA fibre content (1.0–2.0% by volume) and RTP fibre replacement dosage (0.25–1.0% by volume) on the engineering properties especially uniaxial tensile behaviour, microstructure, material cost and environmental impact. Results indicate that the incorporation of RTP fibres into SHGC can lessen the loss in flowability and compressive strength due to the addition of PVA fibres. The drying shrinkage of SHGC containing RTP fibres is effectively reduced by about 35.69% and 17.33% as compared with the plain matrix and SHGC containing 2.0% PVA fibre, respectively. Although the presence of more RTP fibres diminishes the uniaxial tensile behaviour of SHGC, the cost and embodied energy of SHGC utilising RTP fibres are reduced by up to 34.52% and 16.23%, respectively. SHGC with 1.75% PVA fibre and 0.25% RTP fibre can be considered as the optimal mixture as it provides adequate engineering properties including a tensile strain capacity of around 2.5%, lower material cost and lower environmental impact compared to the typical SHGC with 2.0% PVA fibre.Conventional concrete is strong in compression but exhibits brittle failure under tension with a tensile strain capacity of only 0.01% [], which would considerably impair the long-term behaviour of concrete structures even when steel reinforcement is incorporated []. To mitigate these concerns, strain hardening cementitious composite (SHCC) is developed in the early 1990s [], which is a broad class of fibre reinforced concrete featuring strain hardening and multiple cracking under tension []. The main difference between SHCC and normal concrete or fibre reinforced concrete under tensile loading is that the tensile stress of SHCC continues to rise or remains steady with the increase of tensile strain after the initiation of the first crack, achieving superior tensile ductility. Typically, SHCC processes a tensile strain capacity over 2% and a crack width below 100 μm under the loading state []. However, SHCC requires a higher dosage of Portland cement resulting in higher material cost as well as lower greenness []. Owing to the increasing production of Portland cement, the cement industry is responsible for about 8% of the global emitted CO2 [], and the CO2 emission and energy consumption from the cement manufacture would be expected to increase by around 85–105 Gt and about 420–505 TJ by the year of 2050 []. Thus, it is vital to seek for a sustainable alternative binder material for SHCC.Strain hardening geopolymer composite (SHGC) with higher greenness is considered as a promising substitute to SHCC. As the binder of SHGC, geopolymer (also called alkali-activated material) is an inorganic polymer synthesised through the alkali-activation of industrial by-products such as fly ash (FA) that is the most commonly used one. For instance, Ohno and Li [] conducted a feasibility study of FA-based SHGC using two different kinds of FA and developed a FA-based SHGC with a tensile strain of up to 4.5%. Besides, they proposed an innovative design method of FA-based SHGC which integrates design of experiment, micromechanical modelling, and material sustainability indices [] studied the effect of four different types of activators on the fresh and mechanical properties of FA-based SHGC and found that the SHGC activated by a combination of sodium hydroxide (SH) and sodium silicate (SS) solutions can exhibit better material behaviour, especially under tensile and flexural loadings. In addition, Nematollahi et al. [] observed that the incorporation of excessive fine sand or the utilisation of coarse sand adversely influenced the strain hardening behaviour of the composites. Farooq et al. [] explored the tensile performance of FA-based SHGC reinforced with various micro-fibres and concluded that all mixtures reinforced with polyvinyl alcohol (PVA) fibres can present a clear strain hardening feature with a tensile strain of higher than 0.52%. However, FA-based SHGC requires elevated curing temperature to gain strength, where this curing regime is not suitable for cast-in-situ application [] showed that SHGC utilising ground granulated blast-furnace slag (GGBS) can attain a superior tensile ductility (up to 7.5%), the SHGC incorporating solely GGBS has poor workability, low setting time and high shrinkage strain [] that are not favourable for the engineering applications.Thus, an increasing number of studies have attempted to combine GGBS with FA to produce SHGC not only to address the above concerns but also to improve the overall engineering properties [] developed a FA-GGBS based one-part SHGC under either ambient temperature curing or heat curing, which can exhibit a tensile strength of 4.4–4.6 MPa and a tensile strain of 3.6–4.2%, respectively. Furthermore, Nematollahi et al. [] examined the feasibility of using polyethylene (PE) fibres in FA-GGBS based one-part SHGC, who found that a tensile strain of about 4.9% can be obtained for this type of SHGC under ambient temperature curing. Ling et al. [] studied the effect of FA/GGBS ratio on the mechanical properties of SHGC and revealed that incorporating a lower content of GGBS (20% by weight) can increase the strength properties of SHGC while maintaining the strain hardening feature. Zhang et al. [] explored the influence of silicate modulus of activator (0.8–1.5) on the tensile behaviour of FA-GGBS based SHGC and suggested that 1.2 can be considered as the optimal silica modulus for the sodium-based activator. Wang et al. [] found that the incorporation of fine sand up to 20% (by weight of binder) can improve the flexural behaviour of FA-GGBS based SHGC compared to that without sand. Although replacing Portland cement with a geopolymer binder can reduce the carbon footprint and environmental impact, the costs of commonly used PVA and PE fibres hinder the large-scale application of SHGC. For a typical M45 SHCC, the cost of PVA fibres accounts for about 80% of the total material cost []. Moreover, the cost of PE fibres is even higher than that of PVA fibres (about 5–8 times) []. Apart from the economic aspect, the increasing manufacture of virgin synthetic fibres may consume more non-renewable natural resources and generate more wastes [], implying that the increasing application of SHGC reinforced with PVA fibres or PE fibres would impede the sustainable development of the construction industry. As a result, to improve the cost-effectiveness of SHGC while reducing the environmental impacts associated with the virgin fibres, one possible solution is to replace the commonly used virgin fibres with recycled fibres [Until now, extremely limited studies have been reported on using recycled fibres to replace virgin PVA or PE fibres in either SHCC or SHGC. In SHCC, recycled polyethylene terephthalate (PET) fibres have been mainly used to replace virgin PVA fibres. Choi et al. [] reported that the tensile behaviour of SHCC with recycled PET fibres was diminished in comparison with SHCC containing 2.0% (by volume) PVA fibre. However, acceptable tensile properties could be still achieved for certain practical applications when a proper dosage of recycled PET fibre is incorporated (up to 1.0%). Besides, it is worth noting that the material cost and embodied energy of SHCC can be considerably decreased after the replacement of PVA fibres with recycled PET fibres. Lu et al. [] observed that the utilisation of recycled PET fibres can improve the impact resistance of SHCC. Apart from recycled synthetic fibres, recycled tyre steel (RTS) fibres extracted from end-of-life tyres were used to replace PVA fibres in SHCC to optimise its mechanical properties and reduce its material cost []. It was stated that combining 1.5% PVA fibre and 0.5% RTS fibre in SHCC can achieve the optimal engineering properties []. Regarding the usage of recycled fibres to replace PVA fibres in SHGC, only one relevant study [] can be found, which investigated the effect of RTS fibres on the engineering properties of SHGC and noted that RTS fibres are favourable for the improvements of drying shrinkage resistance and compressive strength although the flexural strength is weakened after the incorporation of RTS fibres. It is worth mentioning that besides the above-mentioned benefits, incorporating RTS fibres in SHCC or SHGC can also significantly enhance the sustainability of the composites. It was reported that approximately 1500 million end-of-life tyres are created yearly [], where the enormous amount of these waste tyres would induce several environmental problems and increase the burden on landfilled areas []. Recycling these waste tyres as shredded materials is an effective approach to mitigate the above issues and RTS fibre is the major output of the recycling process. Thus, successful applications of RTS fibres in the construction industry can greatly enhance its sustainability by reducing the environmental impact. In addition, recently, a growing emphasis has been placed on the use of another recycled tyre material, recycled tyre polymer (RTP) fibre, in cementitious material as fibre reinforcement. The motivation of introducing RTP fibres in the construction industry is to find a possible usage for them, as storing RTP fibres is a big challenge that may lead to several environmental problems []. The existing studies on the effect of RTP fibres in cementitious composites found that the presence of RTP fibres can improve the resistance of the resultant composites to fire spalling [], autogenous, plastic and drying shrinkage cracking [], and enhance their dynamic properties and fatigue behaviour []. Although RTP fibres in cementitious composites have several positive impacts, the feasibility of using RTP fibres in geopolymer has not been extensively studied, which would limit the widespread application of RTP fibres. From the economic and environmental perspectives, it is promising to develop a cost-effective and sustainable SHGC with acceptable engineering properties through the replacement of commonly used PVA fibres with RTP fibres. To verify this hypothesis, it is vital to explore the effect of RTP fibres on the engineering properties and sustainability of FA-GGBS based SHGC, which has not been addressed.The main purpose of this work is to investigate the feasibility of partially replacing PVA fibres with RTP fibres to produce sustainable SHGC with acceptable engineering properties. Firstly, a series of tests were carried out to study the influences of PVA fibre dosage (1.0%, 1.5% and 2.0% by volume) and RTP fibre replacement of PVA fibres (0.25%, 0.5%, 0.75% and 1.0% by volume) on the engineering properties of FA-GGBS based SHGC including flowability, drying shrinkage, compressive strength and uniaxial tensile behaviour. Special focus was placed on the uniaxial tensile behaviour of SHGC in terms of stress-strain response, tensile strength, tensile strain capacity, strain energy and fracture pattern as well as the micromechanical analysis in terms of stress-crack opening behaviour and strain hardening indices. Then, the fibre failure condition after the uniaxial tensile test was characterised using scanning electron microscopy (SEM) to get a comprehensive understanding of tensile behaviour and fracture mechanism of SHGC. Afterwards, the economic viability and sustainability of all mixtures in terms of material cost and life cycle inventory data were assessed and discussed. Finally, an optimal mixture of SHGC was proposed considering the material cost, environmental impact, and acceptable engineering properties.] and GGBS with a hydration modulus (i.e. the ratio of CaO + MgO + Al2O3 to SiO2) of 2.0 were used as binder materials in this study, the chemical composition of which is given in . It is worth noting that the hydration modulus of GGBS should be higher than 1.4 to ensure good hydration characteristics [a presents the particle size distribution of FA and GGBS, where the corresponding average particle sizes are summarised in b and c, the shape of FA particles is spherical while GGBS particles are mostly angular. It was found that the fracture toughness of the cementitious matrix increases with the size of aggregate [], which may impair the strain hardening behaviour of composites. To control the fracture toughness of the geopolymer matrix, fine silica sand (see a and d) with a maximum particle size of 250 μm and a mean particle size of 130 μm was utilised as fine aggregate. 10 M SH solution and SS solution with a silicate modulus (SiO2/Na2O ratio) of 3.15 (Na2O: 8.5 wt%, SiO2: 26.8 wt%, H2O: 64.7 wt%) were used as alkaline activator (AL). To enhance the workability of mixtures, a modified polycarboxylate-based superplasticiser (SP) (Sika®ViscoFlow®3000) was applied. lists the specific gravity of these raw materials.PVA fibres (Kuraray Co., Ltd., Japan) and RTP fibres obtained mainly from the truck tyres were used as fibre reinforcements in this study. Since many rubber particles attach the RTP fibres, a sieving/cleaning process based on a previous study [] proceeded on the as-received RTP fibres before usage. The detailed sieving/cleaning method was reported in Ref. [ illustrates the physical appearance of PVA and RTP fibres (after processed) using various image-capturing instruments including digital camera, digital microscope, SEM equipment. It is worth noting that the brightness of fibres shown in c and d is relatively higher due to the large exposure level used during the image capturing procedure. Given that RTP fibres may contain different organic compositions, attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) was applied as it is considered as a fast, suitable, non-destructive and inexpensive method for fibre identification [] found that the primary composition of RTP fibres is PET, the ATR-FTIR method was applied on both RTP and PET fibres using a Nicolet iS10 FT-IR spectrometer with an ATR accessory as per ASTM ] to investigate the primary composition of RTP fibres. presents the FTIR spectra of RTP and PET fibres, indicating that the spectrum of RTP fibre mostly matched that of PET fibre considering various characteristic peak positions within a range of wavenumber. The main peaks [] for PET fibre were highlighted and marked in . For instance, the peak at 2968.51 cm−1 was related to the stretching vibration of methylene group (-CH2) while the significant peak at 1713.17 cm−1 can be attributed to the stretching vibration of carbonyl group (CO). Besides, the peak at 722.92 cm−1 was corresponding to the out-of-plane bending vibration of the CH on benzene ring. As shown in , compared to PET fibre, the spectrum of RTP fibre presented similar peaks at 2917.85, 1712.89, 1245.26, 1096.69, 1018.30 and 722.56 cm−1, suggesting that the RTP fibres used in this study are mainly composed of PET. As seen in , the RTP fibres are not uniform in dimension. Thus, a group of RTP fibre samples were characterised in terms of length and diameter using a digital microscope and a fibre diameter tester (XGD-1 Fibre Diameter Tester), respectively. illustrates the distribution of length (in mm) and diameter (in μm) of RTP fibres. It can be found that around 86.67% of RTP fibres are shorter than 8 mm and 82.67% of them have a diameter of less than 26 μm. Besides, the elongation, tensile strength, and elastic modulus of RTP fibres were measured using a fibre tensile tester (XQ-1A Fibre Tensile Tester). The density of RTP fibres was measured using a gas displacement pycnometry system (AccuPyc II 1345, USA), where helium was used as the displacement medium. During the sieving/cleaning process of as-received RTP fibres, the percentages of RTP fibres and rubber particles (attached with very short RTP fibres) were determined, which were 39.81% and 60.19%, respectively. presents the main properties of PVA and RTP fibres. lists the mix proportions investigated in this study. Regarding the geopolymer matrix, the mass ratios of FA/GGBS, silica sand/binder, AL/binder, the molarity of SH solution, and SS/SH were selected as 4.0, 0.2, 0.45, 10 M, and 1.5 based on previous studies []. The mass ratio of SP/binder was set as 0.01 as it was reported that adding this content of SP can significantly enhance the workability of FA-GGBS based geopolymer paste []. These parameters were kept constant and the changing parameters were fibre type and dosage. For the meaning of mixture label given in , for instance, P1.75R0.25 denotes the geopolymer matrix reinforced with two types of fibres, where ‘P1.75’ stands for the dosage of PVA fibre (1.75% by volume) while ‘R0.25’ represents the dosage of RTP fibre (0.25% by volume). P0R0 is the reference mixture (no fibre addition). P1.0R0, P1.5R0 and P2.0R0 were designed to investigate the influence of PVA fibre dosage on the engineering properties of SHGC. These mixtures were also considered as references. P1.75R0.25, P1.5R0.5, P1.25R0.75 and P1.0R1.0 were designed and compared with P2.0R0 to explore the effect of RTP fibre replacement on the engineering properties of SHGC. The upper limit of RTP fibre replacement content was set as 1.0% considering that: (1) it would be difficult for SHGC to exhibit strain hardening behaviour when the content of PVA fibres is less than 1.0% []; (2) the addition of RTP fibres over 1.0% may dramatically weaken the hardened properties of the composites []. P1.5R0.5 and P1.0R1.0 were compared with P1.5R0 and P1.0R0, respectively, to estimate the effect of RTP fibre addition on the engineering properties of PVA fibre reinforced SHGC.Regarding the sample preparation, the SH solution was prepared by mixing SH pellets (>99% purity) with tap water, 24 h prior to the mixing process. Herein, 400 g of SH pellets were dissolved in the tap water to prepare 1 L of 10 M SH solution. All mixtures shown in were prepared using a 20 L planetary mixer with a constant mixing speed of 140 rpm. Firstly, FA, GGBS and silica sand were dry mixed for 90 s followed by the gradual addition of AL. Then, the mixing was continued for another 180 s before the addition of SP. Once a consistent mixture was obtained, the PVA fibres were slowly added. It should be mentioned that for the mixtures containing both PVA and RTP fibres, the RTP fibres were first mixed with a certain content of AL to avoid fibre clumping or balling []. The mixing process finished when the fibres were uniformly distributed in the mixtures. The total mixing time of all mixtures (except plain matrix mixture) was approximately 10 min. A proportion of the fresh mixtures was used for the fresh property test while the remaining was cast in various moulds with sufficient vibration. The samples were sealed by the plastic sheet at ambient temperature (20 ± 2 °C) to avoid moisture loss. After 24 h, the samples (except samples for drying shrinkage test) were de-moulded and cured in a standard curing room (20 ± 2 °C, 95% RH) until desired testing ages. presents the overall testing scheme of this study including the number of specimens and complied standard for each test. The methodology of each test will be described in detail below.], the flow table test was conducted to assess the flowability of fresh mixtures. Firstly, the fresh mixture was poured into a truncated conical mould with a height of 50 mm, a top diameter of 70 mm and a bottom diameter of 100 mm. The spread diameter of each fresh mixture was measured after two steps: (1) lifting the truncated conical mould; (2) tapping the flow table 25 times. For each mixture, three repeated tests were conducted.The drying shrinkage test was performed on the 25 mm × 25 mm × 280 mm prismatic specimen with a gauge length of 250 mm. Upon the de-moulding of the specimen, the initial comparator reading of the specimen was taken immediately. Subsequently, the specimen was cured under an environment with a temperature of 20 ± 2 °C and relative humidity of 50% ± 5%. The comparator readings at various curing ages were recorded. The drying shrinkage was determined by comparing the subsequent comparator readings with the initial comparator reading based on ASTM The compression test was conducted on the 50 mm × 50 mm × 50 mm cubic specimen at 28 d in accordance with ASTM ]. The loading speed of the compression testing machine was kept fixed for all mixtures as 0.3 MPa/s.The uniaxial direct tension test was carried out on the dog-bone shaped specimen at 28 d according to the recommendation of Japan Society of Civil Engineers (JSCE) [ shows the schematic illustration of the experimental setup and the dimension of the dog-bone shaped specimen. As seen in a, the dog-bone shaped specimen was loaded uniaxially with a loading rate of 0.5 mm/min and two linear variable displacement transducers (LVDTs) were installed to measure the tensile deformation at both sides of the specimen within a gauge length of 80 mm. Besides, the region of the gauge length was used for the crack analysis (b). Regarding the crack analysis, the residual crack number and crack width of each specimen were determined using a digital microscope (WM401WIFI, Shanghai) until the load removal. Although the residual crack width could not fully represent the crack width whilst the tensile loading of the specimen, the result can still be used to evaluate the effect of fibres on the crack-controlling ability of the composite. Besides, the fibre failure status across the fracture surface was captured using a digital microscope.SHCC with high tensile ductility and multiple cracking can be designed and tailored based on the micromechanics theory [], through the optimisation of synergistic interactions between microstructural components. According to the micromechanical design theory [], two criteria (strength-based and energy-based) need to be satisfied to achieve strain hardening and multiple cracking behaviour for the composite. presents a typical tensile stress-crack opening curve for the fibre bridging of SHCC, which will be used to explain how the two criteria can be fulfilled [Regarding the strength-based criterion, the following condition must be satisfied for the crack initiation:where σfc is the stress required to initiate the first crack, σc is the stress required to form another crack (multiple cracks are formed already), and σ0 is the fibre bridging stress. suggests that the capacity of bridging fibres must be higher than the tensile stresses needed to initiate the first crack and a new crack. When the first crack is initiated, the crack propagation mode of the composite is dependent on the bridging fibres []. It is worth mentioning that the crack propagation modes of SHCC and SHGC differ considerably from the Griffith crack propagation mode that is normally observed in ordinary fibre reinforced cementitious composites [where J'b is the maximum complementary energy, Jtip is the crack tip toughness, δ0 is the crack opening corresponding to the maximum fibre bridging stress (σ0), δss is the crack opening corresponding to the steady-state bridging stress (σss), Em is the elastic modulus of the matrix, and Km is the fracture toughness of the matrix.Thus, it is important to evaluate whether the studied mixtures () can meet the above criteria. In this study, two important indices, i.e., σ0/σfc and J'b/Jtip, were experimentally determined using a series of tests. The single crack direct tension was carried out to attain the tensile stress-crack opening curve of the composite () at 28 d and then to determine σ0 and δ0. A schematic illustration of the experimental configuration is given in . The dimension of the tested specimen here was the same as that used in the uniaxial direct tension test (see Section ) while notches were cut around the mid-height of the specimen. The dimensions of the notched area and the remained area are given in . The loading rate of the test was kept constant at 0.5 mm/min. Two LVDTs were mounted to measure the crack opening of the single crack. Through conducting the uniaxial direct tension test on the matrix mixture (P0R0) at 28 d, two parameters, σfc and Em, were subsequently evaluated. To obtain Km, three-point bending test was performed on the 40 mm × 40 mm × 160 mm prismatic specimen with a notch at 28 d under a constant loading rate of 1 mm/min according to RILEM FMC-50 [], the experimental configuration of which is presented in . The thickness, length and depth of the single notch were 1.0, 40 and 12 mm, respectively. Km can be calculated by Ref. [f(a)=1.99−a(1−a)(2.15−3.99a+2.7a2)(1+2a)(1−a)3/2where Fp is the peak load recorded during the three-point bending test, m is the mass of the tested specimen, S is the loading span, a0 is the depth of the notch, t is the thickness of the tested specimen, and h is the height of the tested specimen.For the microstructural characterisation, several pieces of samples were obtained from the fracture surface of the specimen after uniaxial tensile test and then characterised using SEM equipment (FEI, QUANTA FEG 250, USA). The objective was to explore the surface condition and failure mode of the fibres, which are important to the understanding of the fracture mechanism of SHGC. Regarding the SEM test, the acceleration voltage was set as 20 kV while the working distance was around 10 mm.a shows the spread diameters of all mixtures, which can reflect the workability of fresh mixtures. The mixture without any fibre reinforcement (P0R0) had the highest spread diameter of around 250 mm (b) while regardless of fibre type and dosage, the spread diameters of SHGC became lower when the fibres were incorporated, which can be mainly attributed to the contact network between the fibres inside the geopolymer matrix []. Thus, the movement of the fresh mixture is restricted, resulting in an increase in overall yield stress. Regarding the effect of PVA fibres, the reduction in spread diameter caused by the addition of 1.0% PVA fibre was limited, only 7.28% lower in comparison with P0R0. Nevertheless, the higher dosages of PVA fibre (1.5% and 2.0%) reduced the spread diameter of SHGC by 18.62–22.10%, which is in agreement with previous studies on FA-based [] SHGC. There exists a critical fibre dosage, where fibre clumping or balling tends to occur when the incorporated fibre dosage exceeds it []. It is suggested that the critical fibre dosage is affected by the fibre aspect ratio and varies between different fibres, ranging from 0.2 to 2.0% (by volume) for geopolymer and cementitious composites []. In this study, the critical fibre dosage of PVA fibres is likely in the interval between 1.0% and 1.5%.a indicates a slight decrease of 12.22% in spread diameter when 0.5% RTP fibre was added to the mono-PVA fibre reinforced SHGC (P1.5R0), while the presence of 1.0% RTP fibre in SHGC resulted in a more obvious loss in spread diameter. As mentioned in Section , part of the AL was used to mix with RTP fibres during the sample preparation, which may reduce the liquid content inside the mixture, leading to an increase in viscosity. Considering the effect of RTP fibres, replacing 0.25% PVA fibre with RTP fibre in SHGC exhibited slightly better workability (a), implying that a small dosage of RTP fibres would not considerably influence the workability of the composites. This could be ascribed to the smaller aspect ratio of RTP fibres []. However, the spread diameters of SHGC containing RTP fibres higher than 0.25% were 8.31–11.91% smaller than that of P2.0R0, revealing that the critical fibre dosage of RTP fibres may fall in the range of 0.25–0.5%. This needs to be further verified by investigating the mono-RTP fibre reinforced geopolymers with various RTP fibre dosages. Furthermore, as PVA fibres are stiffer than RTP fibres, combining PVA fibres with a larger content of RTP fibres (over 0.25%) would result in a congested fibre network. Therefore, the flowable geopolymer matrix may be difficult to pass through this network properly [], affecting the workability of SHGC adversely. As shown in a, P1.0R1.0 exhibited the lowest spread diameter of about 171 mm, and thus more vibration would be required for this mixture to increase its compactness inside the mould to avoid a conspicuous loss of hardened properties (c). It should be noted that no pronounced fibre clumping or balling was observed for all SHGC mixtures during the sample preparation.Due to the high dosage of cement and low volume fraction of fine aggregate, SHCC typically exhibits a very high drying shrinkage, which can promote the initiation of early-age cracking and thereby weakening the long-term durability of concrete structures []. It was found that geopolymer matrix generally presents higher shrinkage than cementitious matrix, which is dependent on binder type and AL characteristics [], suggesting that SHGC may pose a larger restraint to the enhancement of durability than SHCC although fibres are incorporated. depicts the drying shrinkage of all mixtures up to 28 d. It can be observed that the drying shrinkage of all mixtures developed rapidly up to 7 d, after which the development of drying shrinkage gradually slowed down. Increasing the PVA fibre dosage consistently decreased the drying shrinkage of SHGC, where the 28-d drying shrinkage strains of P1.0R0, P1.5R0 and P2.0R0 were 11.29%, 21.06% and 22.22% respectively lower than that of P0R0. It is noticed that P1.5R0 and P2.0R0 presented a comparable performance in restraining the drying shrinkage of SHGC, which is inconsistent with the findings reported in previous studies on geopolymer composites [, exceeding the critical fibre dosage may entrap more air during the mixing, which would result in a higher internal porosity around the fibres. Therefore, the internal moisture inside SHGC can move more easily through the formed pore network, impairing the shrinkage resistance [, the presence of 0.5% and 1.0% RTP fibre in SHGC improved the shrinkage resistance at different extents, where a reduction of 27.51% in drying shrinkage can be observed after incorporating 1.0% RTP fibre into P1.0R0. Excellent shrinkage-restraining behaviour was also reported for cementitious composites containing RTP fibres [], which can be attributed to the release of temporarily blocked liquid content at the surfaces of RTP fibres and attached rubber particles [, the drying shrinkage strain of P2.0R0 was approximately 11671 με, which was much higher than that of traditional SHCC (1200 με) [], confirming the higher drying shrinkage in SHGC. However, it is interesting to note that the increase of RTP fibre replacement ratio resulted in a general decreasing trend in drying shrinkage, where the reduction was more pronounced when 0.75% or 1.0% PVA fibre was replaced with RTP fibre. P1.25R0.75 and P1.0R1.0 presented a drying shrinkage of around 10751 με and 9649 με at 28 d, which is 7.88% and 17.33% lower than that of P2.0R0, respectively. As mentioned earlier, the released liquid content from the surfaces of RTP fibres can partially contribute to the reduction in drying shrinkage while the synergistic effect between PVA fibres and RTP fibres is also beneficial to restrain the drying shrinkage via the crack-controlling at two scales. As shown in ]. To further reduce the drying shrinkage of SHGC, several possible approaches can be applied such as incorporating shrinkage-reducing admixture [The presence of fibres can simultaneously exert both positive and negative impacts on the compressive strength of cementitious composites, which are associated with the fibre type and fibre properties, especially stiffness []. The compressive strength of all mixtures at 28 d is illustrated in a. The compressive strength of SHGC containing mono-PVA fibres presented a decreasing trend. In comparison with P0R0, the addition of 1.5% and 2.0% PVA fibre led to a reduction of 14.49% and 24.94%, respectively, suggesting that the negative influence caused by the addition of PVA fibres on compressive strength suppressed its positive influence. Regarding the negative influence, the composite has a higher tendency to entrap more air during the mixing after exceeding the critical fibre dosage, which may in turn decrease the compactness of the whole composite, as discussed in Section . Therefore, local fractures tend to occur around the fibres and ultimately weaken the composite's compressive strength []. The reduced compressive strength of SHCC caused by the fibre incorporation become more obvious with the reducing water-to-binder (w/b) ratio, as reported by Yu et al. [] who observed a reduction of 14.30% in compressive strength when 2.0% PVA fibre was added into the plain mixture with a w/b ratio of 0.2. Besides, Wang et al. [] found that the compressive strength of SHGC with 2.0% PVA fibre was about 9.70% and 7.30% lower than that containing 1.5% PVA fibre at 7 d and 28 d, respectively.a, the addition of RTP fibres also had a negative impact on compressive strength of SHGC. For instance, the 28-d compressive strength of P1.5R0.5 was around 45.7 MPa which was 10.43% lower than that of P1.5R0. Such weakening effect in compressive strength caused by RTP fibres was also found for cementitious composites [], which can be attributed to the weaker fibre-matrix interaction and lower stiffness of RTP fibres. In addition, the rubber granules attaching the RTP fibres may also contribute to the reduction in compressive strength. Nevertheless, in this study, the RTP fibres were pre-treated to remove most of the attached rubber granules, which would effectively minimise the negative effect due to the rubber granules. Therefore, SHGC containing hybrid PVA and RTP fibres (except P1.25R0.75) exhibited even higher compressive strength (3.96–9.21% higher) than SHGC with 2.0% PVA fibre, indicating that replacing a certain content of PVA fibres by RTP fibres can help mitigate the loss of compressive strength in SHGC due to the addition of PVA fibres. Regardless of incorporating mono PVA or hybrid fibres, the compressive failure of SHGC is not sudden as compared with the brittle failure of plain matrix mixture. As displayed in b, P0R0 exhibited a significant damage after being subjected to a compressive load, leading to a triangular failure pattern with oblique cracks. By contrast, only some vertical cracks can be observed on the failure surface of SHGC, remaining its original shape (c). A similar phenomenon was reported in Refs. [] that the original cubic shape of SHGC was maintained after the compressive failure owing to the bridging capacity of the fibres. Compared to the plain matrix mixture, the compressive strength of SHGC is lower while its ultimate compressive strain may be higher [] that needs to be confirmed by measuring the longitudinal strain of the specimen during the compressive loading. In summary, the compressive strength of SHGC containing both PVA and RTP fibres is acceptable for general construction purposes. depicts the tensile stress-strain curves of all mixtures. Typically, the tensile stress-strain curve consists of two distinct regions, an elastic region and a strain hardening or softening region. During the elastic region, the tensile stress of the tested sample increases rapidly and linearly with a small change of strain before reaching the elastic limit that is regarded as the transition point between the linearity region and non-linearity region, also known as first cracking strength (ffc) []. After that, the tested sample either experiences steady rising stress (strain hardening) or gradual decreasing stress (strain softening) with the increase of strain. The highest point of stress is tensile strength (ft) and the corresponding strain is tensile strain capacity (εt). As seen in , P0R0 had a very brittle tensile behaviour and failed immediately after reaching its tensile limit. Remarkably, P1.5R0, P2.0R0, P1.75R0.25 and P1.5R0.5 displayed an apparent strain hardening phenomenon while the strain hardening behaviour of P1.0R0 and P1.25R0.75 was not pronounced. P1.0R1.0 even lost the strain hardening feature but exhibited strain softening behaviour after reaching ffc. Regarding the effects of PVA (b), it can be found that with the increase of PVA fibre dosage, the strain hardening region was consistently prolonged whereas the strain hardening behaviour was weakened when more RTP fibres replaced PVA fibres. The tensile properties including ffc, ft, εt and strain energy derived from the stress-strain curves are discussed below to further estimate the effect of fibres on the tensile behaviour of SHGC. shows ffc and ft of all mixtures. ffc of the composite is mainly dependent on its matrix and no clear trend of change in ffc of SHGC can be found when the fibre dosage altered. All SHGC mixtures had ffc ranging from 1.28 MPa to 2.42 MPa, which mostly was higher than ffc of P0R0 because of the fibre bridging effect inside the composite []. P2.0R0 had the highest ffc of 2.42 MPa, which is consistent with the finding by Ohno and Li [a). Converse to compressive strength, the increase of PVA fibre dosage led to an increase in ft of SHGC by about 57.18–123.87% as compared with P0R0 (b). It is worth noting that ft of P2.0R0 (3.4 MPa) in this study was comparable to that of FA-GGBS based SHGC with a modulus of AL of 1.5 []. The significant enhancement in ft due to the increase of PVA fibre dosage can be associated with the fibre distribution and fibre bridging action. The fibres inside the dog-bone shaped specimen can be regarded as two-dimensional randomly distributed [], suggesting that when more PVA fibres are present, the number of efficient bridging fibres tends to increase, in turn, significantly improving ft of SHGC. By contrast, adding RTP fibres into SHGC decreased ft of the whole composites. More specifically, ft of P1.0R1.0 was only 1.68 MPa which was 29.58% lower than that of P1.0R0. However, the negative influence of 0.5% RTP fibre on ft of SHGC was limited, only 3.81% lower as compared with P1.5R0. The loss in ft due to the addition of recycled fibres is in consistence with previous studies about SHCC []. Following the same trend of ffc, a lower ft of SHGC can be found when SHGC contained more RTP fibres, which can be mainly ascribed to the lower bridging stress of RTP fibres in comparison with PVA fibres. Nevertheless, all SHGC specimens containing hybrid PVA and RTP fibres showed higher ft than P0R0. shows εt of all mixtures. It can be observed that the influence of fibres on εt is similar to that on ft. For instance, εt of SHGC was increased with the increasing PVA fibre dosage, where the values of P1.0R0, P1.5R0 and P2.0R0 were about 16–255 times larger than that of P0R0 (only 0.01%). P2.0R0 had εt of around 3.04% which is slightly higher than that of SHCC M45 (2.49%), reported by Wang and Li []. Although SHGC containing RTP fibres showed a lower εt than P2.0R0, they still outperformed P0R0 by 2–188 times. On the other hand, the strain energy can be also used to reflect the strain hardening degree of SHGC, which is defined as the energy dissipation capacity per unit volume during the strain hardening region and can be calculated by integrating the ascending branch of the tensile stress-strain curve, as illustrated in a. The calculated strain energy of all mixtures is shown in b, which agrees well with the results of ft and εt, as discussed above. P2.0R0 had the highest strain energy of about 89.94 kJ/m3, representing the best strain hardening performance.In summary, it can be suggested that replacing a certain content of PVA fibres in SHGC with RTP fibres can ensure adequate tensile performance for certain applications. For instance, P1.75R0.25 outperformed P1.5R0 and P1.0R0 in terms of all relevant tensile properties.The typical tensile fracture patterns of all mixtures are illustrated in . It should be noted that the image of P0R0 was taken after tensile failure while the images of SHGC specimens were captured before unloading. As mentioned in Section , only the cracks that appeared inside the gauge length were considered in this study and the dimension of the region for analysing the cracks was 30 mm × 80 mm (b–h). The cracking patterns here are consistent with the stress-strain curves shown in that obvious multiple cracking features can be observed for P1.5R0, P2.0R0, P1.75R0.25 and P1.5R0.5 (c–f) along with clear strain hardening features. Only several cracks can be observed for P1.0R0, P1.25R0.75 and P1.0R1.0. Independent of fibre type and fibre dosage, the presence of fibres improved the post-cracking behaviour of SHGC compared to the brittle failure of P0R0 (a). Besides, more uniformly distributed cracks can be found in P2.0R0, which are consistent with its best tensile properties, as discussed previously. lists the residual crack number and crack width of SHGC after the removal of tensile load. The actual crack widths should be smaller than the residual crack widths as many micro-cracks are closed upon the removal of tensile load []. There exists a similar trend of residual crack number with that of εt. A large standard deviation can be noticed for P1.5R0, mainly due to the random fibre distribution between each sample even from the same batch of mixing []. The performance of P2.0R0 was more stable as the coefficient of variation (COV) of the residual crack number is only 3.57%. On the other hand, the residual crack width of SHGC was smaller when more PVA fibres were present, where the crack-controlling behaviour was affected by the fibre-matrix interface. As seen in a, at the fracture surface of SHGC, most of PVA fibres were pulled out, implying that the bond strength between fibres and matrix is adequate to avoid fibre rupture. Such fibre-matrix interface behaviour is favourable for improving the tensile behaviour and restraining the crack width, given that the bridging fibre has high enough tensile strength []. However, some PVA fibres were ruptured due to their inherent large chemical bond. Although RTP fibres also experienced pull-out behaviour during the tensile loading (b), the short length and low tensile strength (see ) limit the crack-controlling behaviour of the whole composite. Thus, a larger crack width was found in SHGC when more RTP fibres were added. This regard will be further discussed in Section through the analysis of micromechanical and microstructural investigation.In summary, the average residual crack widths of P1.5R0, P2.0R0, P1.75R0.25 and P1.5R0.5 were in the range of 29.8–39.2 μm, similar to those reported in a typical SHCC (60 μm) []. These tight crack widths indicate a strong crack-controlling ability of SHGC and are beneficial for many engineering properties, e.g., durability and self-healing performance []. However, further studies need to be conducted to confirm these benefits. illustrates the representative tensile stress-crack opening curves of SHGC from the single crack direct tension tests. The experimental results of σ0 and δ0 are summarised in is affected by the dosage and properties of fibre and more importantly, the interface properties between fibre and matrix []. σ0 is largely affected by the chemical bond and frictional bond between fibres and matrix []. Thus, the increasing branch of the curve shown in represents the required stress to overcome the chemical bond and pull out or rupture the fibres. With the increase of PVA fibre dosage, σ0 of SHGC was consistently increased, which explains why P2.0R0 presented the best tensile performance as shown in Section . By contrast, increasing the RTP fibre replacement dosage led to a lower σ0 in SHGC ranging from 1.08 to 2.02 MPa, which indicates that the tensile behaviour was diminished. Regarding δ0, similar to σ0, P2.0R0 had the highest value of 0.308 mm while there exhibited a general decreasing trend in δ0 as the PVA fibre dosage in SHGC reduced. It was found that a higher δ0 would benefit εt as higher stress is required to pull the fibres out [To further interpret the results shown in Section and verify whether the proposed mixtures here achieve a saturated strain hardening phenomenon, two strain hardening indices related to strength-based and energy-based criteria were determined (see Section ], two following conditions need to be satisfied to achieve a saturated strain hardening behaviour: (1) σ0/σfc≥1.2; (2) Jb′/Jtip≥2.7. The results of fracture toughness for P0R0 are shown in lists the strain hardening indices of all SHGC mixtures. It can be found that P1.5R0, P2.0R0 and P1.75R0.25 satisfied the above two conditions, which are consistent with the stress-strain curves and cracking patterns shown in , respectively. P2.0R0 achieved the highest values in both indices, implying that it had a higher tendency to achieve a robust strain hardening feature along with a stable multiple cracking behaviour [, P1.5R0.5 did not satisfy the requirements for a saturated strain hardening although its stress-strain curve showed an obvious strain hardening region. This phenomenon was also reported by Nematollahi et al. [] that pronounced strain hardening and multiple cracking were observed but the energy-based indices were only around 2.0. It is interesting to note that the strength-based index here was positively correlated to εt shown in , where a higher strength-based index corresponded to a higher εt, while the energy-based index showed a slight inconsistency. For instance, εt of P1.5R0.5 was considerably larger than that of P1.0R0 (0.96% versus 0.01%) but P1.0R0 possessed a higher energy-based index than P1.5R0.5 (see ). This can be attributed to the deviations of the results, which are also reported in a previous study []. It is worth noting that the deviations tended to be higher when more RTP fibres were incorporated into SHGC, implying the important role of PVA fibres in tensile performance. Besides, this suggests that the tensile behaviour of SHGC containing hybrid fibre reinforcement may be less sensitive to the energy-based index. shows the SEM images of fibre morphology in mono-PVA fibre reinforced SHGC at the tensile fracture surfaces. Most of the PVA fibres experienced pull-out behaviour (a. However, the ruptured PVA fibre with a necking end and several scratches can also be observed in b. Under adequate frictional stress, PVA fibres tended to be pulled out, where typically matrix fragments were attached with the fibre (c). The sufficient frictional stress can be also seen in d that no obvious gap was found between the fibre and matrix (red dash circles). Overall, not only the number of effective bridging fibres increases when the PVA fibre dosage increases but also the number of pull-out fibres increases. These ultimately result in a higher ft and a larger εt in SHGC. On the other hand, displays the SEM images of fibre morphology in hybrid PVA-RTP fibre reinforced SHGC. The pull-out RTP fibre can be identified which coincides with that shown in b. As explained previously, RTP fibres have a weaker bond with the matrix because of the hydrophobic feature, which can be supported by b that a clear void space was observed between the RTP fibre and the matrix. Besides, no pronounced matrix fragments attached to the RTP fibre. Therefore, the pull-out process can be easily facilitated and terminated quickly. This explains why more RTP fibres in SHGC would result in lower tensile properties and larger crack widths. However, when the incorporated RTP fibre content is appropriate, PVA and RTP fibres can form a synergistic effect to improve the crack-controlling behaviour of the whole composite.As stated previously, the main objective of this work is to reduce the cost and improve the sustainability of SHGC through the partial replacement of PVA fibres. Thus, the effects of fibres on the total material cost, embodied carbon and embodied energy were analysed. lists the market price, embodied carbon and embodied energy of all ingredients needed for producing SHGC []. The estimated total material cost of all mixtures in USD/m3 is presented in . It can be found that the cost of PVA fibres constituted a considerably big part of the total material cost of mono-PVA fibre reinforced SHGC and it was about 70.30% of the total cost. Replacing a certain content of PVA fibres (0.25–1.0%) with RTP fibres in SHGC significantly reduced the total cost by 8.63–34.52%. This large reduction can be attributed to the extremely lower cost of RTP fibres, which is only 1.62% that of PVA fibres. Although some other costs may be required for processing RTP fibres [], the huge difference in material cost between RTP fibres and PVA fibres makes the SHGC containing RTP fibres promising and attractive for certain large-scale applications given the presence of adequate engineering properties.Embodied carbon and embodied energy are considered as the major material sustainability indicators [], which were considered to reflect the environmental impact of SHGC. illustrates the embodied carbon and embodied energy of all mixtures. The corresponding results obtained from a typical M45 SHCC were also included in the figure for comparisons [a, all mixtures presented a dramatically lower embodied carbon than a typical M45 SHCC as the matrix of SHCC containing a very high dosage of cement contributed significantly to the increase in embodied carbon. The embodied carbon of P2.0R0 was around 329 kg CO2. eq/m3, approximately 48.83% lower than that of a typical M45 SHCC. The embodied carbon gradually increased with the increase of PVA fibre dosage while no significant effect can be observed when PVA fibres were replaced with RTP fibres (purple trend line). On the other hand, as shown in b, the embodied energy of SHGC was comparable with that of SHCC. The embodied energy of SHGC presented a similar increasing trend as the PVA fibre dosage increased. By contrast, the embodied energy of SHGC reduced gradually with the rising RTP fibre replacement and the reduction was in the range of 4.06–16.23% compared to P2.0R0, which can be mainly ascribed to the lower embodied energy of recycled fibres, as given in . In addition, more solid wastes can be reduced when RTP fibres are incorporated. Overall, replacing PVA fibres with RTP fibres in SHGC can lead to an enhancement in the sustainability of construction materials considering the above results.To comprehensively evaluate the feasibility of RTP fibres in SHGC, the overall performance between mono-fibre reinforced SHGC (P2.0R0) and hybrid fibre reinforced SHGC was compared. A comparison in terms of key engineering properties, total material cost and environmental impact is presented in , where all values of P2.0R0 were set as 1.0 while the results of hybrid PVA-RTP fibre reinforced SHGC were regulated based on those of P2.0R0. It can be found that apart from the improved sustainability and the reduced material cost, the dosage of RTP fibres in SHGC should be limited to ensure its applicability, resilience, and long-term durability. Overall, the addition of RTP fibres in SHGC is beneficial for compressive strength and especially drying shrinkage whereas the tensile behaviour is significantly diminished. P1.75R0.25 can be regarded as the most cost-effective mixture as it processed adequate engineering properties, lower cost and better sustainability as compared with P2.0R0. In addition, P1.5R0.5 with a εt of around 1.0% and the improved shrinkage-resistance is also promising for certain applications, where better controlling of early-age cracking is required, e.g., repairing of existing structures.To improve the cost-effectiveness and sustainability of fly ash-slag based SHGC with PVA fibres, this paper presents an experimental study on the feasibility of partially replacing PVA fibres with RTP fibres, considering the effects of PVA fibre dosage (1.0–2.0%) and RTP fibre replacement dosage (0.25–1.0%) on the engineering properties, material cost and environmental impact of SHGC. Based on the results of this study, the main conclusions can be drawn as follows:The presence of RTP fibres in SHGC can effectively reduce the drying shrinkage by 17.33% compared to that of SHGC with 2.0% PVA fibre, although lower flowability is observed in SHGC when more than 0.25% PVA fibre is replaced with RTP fibres. The reduced compressive strength in SHGC due to the presence of PVA fibres can be mitigated by the incorporation of RTP fibres.The tensile properties of SHGC including ft, εtand strain energy are considerably improved with the increase of PVA fibre dosage while these properties are reduced when more PVA fibres are replaced with RTP fibres. SHGC mixtures with mono PVA fibre (1.5% and 2.0%) and hybrid fibres (1.75% PVA and 0.25% RTP) present robust tensile strain hardening and saturated multiple cracking features according to the results of stress-strain response, fracture pattern and strain hardening indices.SEM micrographs indicate more pull-out PVA fibres appear at the tensile fracture surface of SHGC, which is favourable for the improvement of tensile properties, while a weaker bond is observed at the interface between RTP fibre and matrix, resulting in poor tensile behaviour of SHGC.The presence of RTP fibres decreases the material cost and embodied energy of SHGC by 8.63–34.52% and 4.06–16.23%, respectively. A comparison of the overall composite performance between mono-PVA fibre reinforced SHGC and hybrid PVA-RTP fibre reinforced SHGC indicates that the most cost-effective combination for SHGC is 1.75% PVA fibre and 0.25% RTP fibre, as it exhibits adequate engineering properties, lower material cost and better sustainability in comparison with SHGC with 2.0% PVA fibre.This paper reveals a large potential of producing a cost-effective and sustainable fly ash-slag based SHGC via the replacement of PVA fibres with RTP fibres. Although the use of RTP fibres is not effective in improving the static mechanical properties of SHGC, it can greatly restrain the drying shrinkage. Satisfactory engineering properties (e.g. εt of 1.0% or above) are still achievable when 0.5% PVA fibre is replaced by RTP fibres in SHGC, which can be useful for certain practical applications. Besides, it is expected that the addition of RTP fibres can enhance the dynamic mechanical properties of SHGC []. Therefore, it is vital to investigate the effect of RTP fibre on the dynamic behaviour of SHGC with a wide range of strain rates. Moreover, the drying shrinkage of hybrid fibre reinforced SHGC is still a concern as compared with traditional SHCC and thus it is important to find an effective strategy to further reduce the drying shrinkage of SHGC. These are subjects of ongoing works and will be presented in future publications.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.B. Mechanical properties at high temperaturesC. Powder metallurgy, including consolidationMicrostructure and mechanical properties of Ni3Al base alloy reinforced with Cr particles produced by powder metallurgyThe microstructural evolution of a powder metallurgy (PM) Ni3Al–8Cr (at.%) alloy reinforced with Cr particles has been correlated with its mechanical properties. The material was synthesised using rapidly solidified Ni3Al–8Cr powders which were mixed with a Cr volume fraction of 10% and milled for 20 h. Consolidation by HIP was carried out at 150 MPa for 2 h at 1250 °C. For comparative purposes the unreinforced Ni3Al–8Cr alloy was processed following the same route. After consolidation by HIP both materials show a bimodal microstructure consisting of coarse and fine grain regions in which fine particles are heterogeneously distributed. Besides Cr reinforcement, the difference between the two materials is the presence of β phase and higher volume fractions of γ+γ′ regions and α-phase precipitates in the reinforced material. The reinforced material presents the highest hardness, yield stress and the ultimate tensile strength values. The yield stress and ultimate tensile strength of the reinforced material at room temperature is 1286 and 1335 MPa, respectively. The strength of the composite is determined by the strength of the Cr particles and the good bonding between the matrix and Cr reinforcement. Although the ductility loss as the temperature increases is not suppressed, an improvement in ductility is obtained at temperatures above 500 °C compared with the unreinforced material.B. Mechanical properties at high temperaturesC. Powder metallurgy, including consolidationAlloys based on Ni3Al have been extensively investigated for many years due to their potential for high-temperature applications. Different aspects of these alloys have been studied with a view to improving their properties using a variety of synthesis and processing techniques, the effect of alloying elements, mechanical properties, oxidation and corrosion behaviour. Moreover, a great deal of work has been performed on basic aspects of the physical metallurgy of this intermetallic. Much information is available on Ni3Al based alloys; for example, ‘Intermetallic Compounds, Principle and Practice’ The present work, continues on from previous studies carried out by the authors on powder metallurgy (PM) Ni3Al consolidated by hot isostatic pressing (HIP) The present work focuses on the effect of chromium reinforcement on the microstructure and mechanical properties of PM Ni3Al–8Cr alloy processed by a PM route which includes the milling of the powders before the consolidation stage. The milling step induces a grain size reduction and the formation of a bimodal microstructure in the consolidated material. Mechanical behaviour has been studied by tensile tests in the temperature range from room temperature to 1000 °C. For comparative purposes a similar study has been carried out on the same material without Cr-reinforcement.A Ni3Al–Cr alloy, reinforced with 10 vol% Cr particles (designated as NAC-10Cr) and without reinforcement (designated as NAC), was prepared by a powder metallurgical route. Rapidly solidified argon atomised powders (<100 μm) of Ni–20.9Al–8Cr–0.49B (at.%) alloy were supplied by TLS Technik (Germany). The powders were mechanically mixed with Cr particles (99.8% purity) of less than 10 μm in size in a planetary ball mill using stainless steels jars of 500 ml and 80 g of powder. The process was carried out in air for 1 h at 120 rpm using six balls. Then, powders were milled for 20 h at 200 rpm using 12 balls in order to break the oxide layers covering the particle surfaces and facilitate diffusion processes during the consolidation stage. The NAC material was processed by a similar route. After the milling stage the powders were canned in steel capsules, out-gassed under 2 Pa at 673 K, and consolidated by HIP. In both materials the consolidation stage was conducted at 150 MPa for 2 h at 1250 °C with cooling over 2.5 h. The microstructure of the materials and their fracture surfaces were studied using optical microscopy (OM), scanning (SEM) and transmission electron microscopy (TEM). Samples for OM and SEM observations were prepared by conventional methods of mechanical polishing and chemical etching with an acidic mixture (CH3COOH/HNO3/HCl=8:4:1). Samples for TEM were thinned by electropolishing using a 10% solution of HNO3 in methanol at 253 K and 15 V.Vickers hardness was measured in both materials with a 10 N load and 15 s indentation time, averaging at least five tests.Mechanical properties were studied by tensile tests. Flat specimens were electrospark machined from the steel capsules. The samples had a cross section of 4×2 mm2, a gauge length of 6.5 mm and a curvature radius rc of 3 mm. Tests were carried out in air at different temperatures, from room temperature up to 1000 °C, at an initial strain rate of 3×10−4

s−1. At least three tensile tests were performed for each material at each temperature.The cross sections of powder particles in as-solidified condition show a two-phase dendritic microstructure consisting of Ni3Al (γ′) dendrites and a NiAl (β) phase in the interdendritic regions ((a)). After milling for 20 h the particles exhibit the characteristic microstructure of metallic materials after severe plastic deformation, as can be seen in (b). Moreover, chemical analysis carried out in a Leco analyser equipped with an infrared detector, indicates a pick-up of oxygen during milling, with the oxygen content increasing from 0.0365 wt% in the as-received powders to 0.281 wt% after milling.The microstructure of both materials after consolidation by HIP is shown in . At low magnifications a bimodal microstructure consisting of coarse and fine grain areas with a heterogeneous distribution of fine particles is seen. The coarse grain size areas come from coarser original powder particles. Fine grain areas are constituted by grains of different sizes with small Al2O3 particles at the grain boundaries and within the grains. The origin of Al2O3 dispersoids is explained by either the fracture of the oxide layer covering the original powder particles or powder oxidation resulting from the reaction of the newly exposed oxide-free surfaces with the air during the milling process. The formation of Al2O3 dispersoids and their effect on the formation of a bimodal microstructure has been explained elsewhere shows the microstructure of the NAC material, in which the labels correspond to the microanalysed areas listed in . The coarse grain areas are constituted by γ′ phase and only a few grains exhibit a γ+γ′ microstructure. In fine grain areas, γ′ grains, Al2O3 particles and α-phase (Cr-rich solid solution) precipitates are visible.The NAC-10Cr material exhibits a more complex multiphase microstructure. The backscattered electron images and microanalysis results allow the identification of γ+γ′ phase regions and NiAl areas (β phase) within fine spherical precipitates. Moreover, a homogeneous distribution of α phase, Cr reinforcement and small aluminium oxide particles is also well resolved. It is interesting to note that the volume fraction of these phases is different in the coarse and fine grain areas. shows a detail of both coarse and fine grain areas and the microanalysis results identifying the phases are presented in . The coarse grain areas are constituted by γ+γ′ and β phase embedding spherical α precipitates. Moreover, a γ′ layer surrounding β is also present. On the other hand, γ+γ′ areas, Al2O3, Cr reinforcement and irregular α precipitates of about 1 μm in size are seen in fine grain areas.The volume fraction of Cr-reinforcement was measured by the linear intercept method and a value of approximately 2% was obtained. This decrease from 10 to 2% indicates that Cr particles are partially dissolved in the matrix during consolidation, and thus the estimated actual composition of the alloy will be Ni–19.4Al–14.9Cr–0.44 B (at.%). Therefore it can be concluded that during the consolidation stage at 1250 °C solid-state transformations consisting of recrystallisation processes, chemical readjustment of alloying elements and changes in the phases present take place.The most important differences compared with the NAC material are the higher volume fractions of γ+γ′ regions and α-phase precipitates and the presence of β phase.The differences between the two materials in terms of the nature and volume fraction of phases also give rise to differences in grain size. Although the high dispersion of grain sizes shown by the two materials prevents an accurate estimate of the average grain size, observation of the micrographs suggests that the grain size is somewhat coarser in the case of the NAC material. Thus the grain size in the fine grain areas of the NAC-10Cr material is finer than 1 μm, whereas it is two or three times coarser in the NAC material.The microstructure exhibited by the two materials, which is notably different to that of the original powders, especially in the case of NAC-10Cr, indicates that the alloy microstructures evolve during the processing step. Moreover, these microstructural differences between the materials will give rise to differences in their mechanical behaviour.Vickers hardness measurements were performed on both materials using a load of 10 N. Values of 318±6 and 498±7 were obtained for NAC and NAC-10Cr, respectively. Therefore, the reinforced material is 57% harder than the NAC material.Tensile true stress-true strain curves for both materials in the range from room temperature up to 900 °C are shown in lists the 0.2% proof stress, ultimate tensile strength and work hardening rate values from curves of . Vickers hardness values at room temperature are also included. The highest yield stress and ultimate tensile strength values, 1286 and 1335 MPa, respectively, are exhibited by the NAC-10Cr material at room temperature. The elongation to failure value, however, is low (2%), as can be observed in the tensile curve. In the temperature range between room temperature and 600 °C, both materials exhibit a nearly linear strain hardening behaviour. Therefore a constant work hardening rate equal to the average slope has been calculated at the different temperatures (). Although the work hardening rate values decrease with temperature in both materials, the decrease is smaller in the case of the reinforced material. Above 600 °C, the NAC material breaks in the elastic regime whereas the composite always shows some plastic deformation. Thus at 700 °C the NAC-10Cr material breaks after 5% of elongation and its ultimate tensile strength decreases strongly. Above this temperature the material exhibits no further work hardening and a steady stress is maintained until fracture takes place. The increase in ductility observed in the NAC-10Cr material above 600 °C indicates the beneficial effect of Cr powder additions.The fracture surfaces of samples tensile tested up to 400 °C were examined to elucidate the effect of Cr reinforcement. It was not possible to study the fracture surfaces of samples broken at higher temperatures due to the formation of oxide films covering the fracture surfaces during cooling.Observation of the external surfaces of all the samples shows a large area of the gauge length which had deformed plastically, and slip bands () are clearly seen in a wide region. Cracks perpendicular to the tensile axis are also observed, propagating in all cases by interparticle and intergranular mechanisms. Nevertheless, some transgranular cracks are observed in both coarse and fine grain areas, with the crack density decreasing the lower the elongation to fracture, e.g. as the testing temperature increases. Furthermore, as is shown in , cracks traversing reinforcing Cr particles are visible in the NAC-10Cr and cracked Cr reinforcing particles can be seen throughout the crack paths.The analysis of fracture surfaces in both materials indicates a brittle fracture mode. The fracture surface of the NAC material at room temperature is shown in . Zones of intergranular fracture correspond to coarse grain areas while dimple rupture seems to be associated with fine grain areas. Dimple rupture results from the coalescence of voids around aluminium oxides and Cr-rich second phase particles. Similar fracture surfaces are observed at 400 °C. At low magnifications, the fracture surfaces of the NAC-10Cr material are similar to the unreinforced material, although the area occupied by the dimple rupture network is greater (The addition of 10 vol% of Cr to the alloy as reinforcement causes compositional changes during the HIP consolidation stage which are associated with partial Cr dissolution into the matrix. This dissolution, calculated by the decrease in the volume fraction of Cr particles from 10 to 2%, changes the nominal composition of the alloy, and NAC and NAC-10Cr therefore, have different chemical compositions: Ni–20.9Al–7.9Cr–0.49B and Ni–19.4Al–14.9Cr–0.44 B(at.%), respectively. Rapidly solidified powders of Ni–20.9Al–7.9Cr–0.49B have a two-phase microstructure consisting of γ′ phase and a small fraction of β phase. The microstructural changes observed in the two materials take place during consolidation by HIP at 1250 °C and are assisted by the metastable structure of the powders (rapid solidification process) and the defects introduced during mechanical milling.The differences between the two materials consist of the different volume fractions of β, γ, γ′ phases and α precipitates and the presence of Cr reinforcing particles. Considering that cooling from 1250 °C to room temperature after HIP consolidation can be considered a quenching stage, and according to the isothermal section at 1150 °C of the ternary Ni–Al–Cr system proposed by Taylor and Floyd ), both alloys should be located in the γ+γ′ (NAC) and β+γ (NAC-10Cr) fields, but this is not seen in the observed microstructures. Moreover, the presence of α precipitates, not expected in the aforementioned isothermal section, proves that the two materials have not attained the equilibrium state after 2 h at 1250 °C. Longer times to attain complete equilibrium by diffusion in Ni3Al-based alloys have been observed by different authors ). It is interesting to note the coarser size of α precipitates in fine grain areas, which could result from the preferential distribution of the Cr reinforcement at the particle boundaries of Ni3Al powders, and so the Cr concentration in these areas should be higher. Since this feature is observed in both materials, Cr reinforcement cannot be the origin of this effect. A higher fraction of γ’ in fine grain areas could result from the decrease in Cr solubility in the γ′ phase as the temperature increases, in agreement with the phase diagram.On the other hand, the β+γ+γ′+α microstructure observed in the reinforced material may be explained by Cr dissolution in the γ′ matrix and by the different transformations that take place during HIP. Thus it can be assumed that for 2 h at 1250 °C the increase in the Cr content in the γ′ matrix causes its evolution to the γ phase and the diffusion of Al atoms towards the β phase, increasing the volume fraction of β phase. The γ′ layers separating β from γ ((a)) must be interpreted as an interaction between the two phases through a peritectoid transformation which was described by Taylor and Floyd Both materials exhibit high hardness and strength values compared with other advanced nickel aluminides from the literature ). Thus the hindering of the cross slip should be more efficient in NAC-10Cr due to the higher volume fraction of second phase particles. On the other hand, the fine grain size of these materials may also account for the non-increase in yield stress with the temperature, since it is well known that this phenomenon does not occur in fine grain Ni3Al alloys (<5 μm) The high yield stress and ultimate tensile strength values exhibited by the two materials must be related to a combined effect of the fine grain size and the presence of second phase particles and their interaction with dislocations. The higher values in the reinforced material at any temperature must be related with the Cr reinforcement. As has been discussed in the preceding section, partial dissolution of Cr in the matrix induces two main effects influencing the mechanical properties: (1) changes in the nature and volume fraction of the phases present; and (2) strong matrix-particle bonds. The greater volume fraction of β phase in the reinforced material contributes to strengthening the alloy since it is well known that Cr additions to Ni3Al promote β formation, substantially increasing the strength of the alloy but decreasing the elongation to failure On the other hand, Cr reinforcement must provide an additional increase in the yield stress of the composite due to the dislocations generated by thermal-mismatch stresses at the matrix-Cr reinforcement interface during the fast cooling step of the HIP process. Considering that the phases present in the matrix have a linear thermal expansion coefficient at least twice that of Cr (12.5, 13.2 and 16.3×10−6

K−1 for γ′, β and γ, respectively, and 6.2×10−6

K−1 for Cr), dislocations at the interface may appear since the Cr particles are in compression. This assumption agrees with the bright field image of that shows a Cr reinforcement particle located in the γ+γ′ region. The selected area diffraction pattern corresponds to the γ+γ′ region. The high contrast at the Cr/matrix interface indicates a strong strain field.The decrease in the elongation to failure value with increasing temperature, as observed in , is explained not only by oxygen embrittlement but also by the combined effect of high yield stress values and the decrease in the work hardening rate with increasing temperature ). In the case of the NAC material the yield stress values are lower than in the reinforced material, which could therefore account for the higher elongation to failure values. However, the work hardening rate decreases more quickly with increasing temperature, and the ductility loss will therefore occur earlier than in the reinforced material. The low fracture strain shown by the composite material below 700 °C and the fracture studies that have been performed demonstrate the strong interfacial bonds between the matrix and the Cr reinforcement mentioned above. As is shown in (a), slip bands in the matrix close to broken Cr particles suggest that stresses are transferred from the matrix during testing. The dislocations piled up against the Cr particle, which is in compression, will interact with those present due to thermal stresses, producing an increase in the local stress, and crack nucleation in the particles will occur. Therefore, from the fracture surface observations it can be concluded that the strength of the composite is determined by the strength of the Cr particles, and thus failure occurs when a sufficient number of particles have broken so that the remaining material cannot withstand the increased stress and breaks. At this stage, fracture results from the linking of cracked particles by regions of matrix rupture as is shown in it can be deduced that although the decrease in ductility in these materials as the temperature increases seems to be due mainly to intrinsic characteristics, since the decrease starts at room temperature, reinforcement with Cr improves ductility above 500 °C. As has been seen on the surface of the tested samples, Cr reinforcing particles are present in the paths of the cracks that propagate mainly at the particle boundaries. Therefore it may be supposed that the particles act as a source of chromium supply, promoting the fast formation of oxide films that impede or delay the entry of oxygen. Nevertheless, the increase in ductility observed in the NAC-10Cr material has to be related not only with the reinforcing particles but also with changes in composition of the alloy due to the partial Cr dissolution into the matrix, as was commented previously.The reinforcing effect of 10 vol% chromium on the microstructure and mechanical properties of Ni3Al–8Cr alloy, processed by a PM route that includes the milling of the powders before the consolidation stage, has been studied. The most important conclusions may be summarised as follows:Cr particles are partially dissolved in the matrix during HIP at 1250 °C, with the composite material attaining a final volume fraction of 2%Cr. Moreover, during the consolidation stage recrystallisation process, chemical readjustment of the alloying elements and changes in the phases present take place.After consolidation by HIP, both materials show a bimodal microstructure consisting of coarse and fine grain regions in which fine particles are heterogeneously distributed. The most important differences between the two materials, besides the Cr reinforcement, consist of the formation in the reinforced material of β phase and higher volume fractions of γ+γ′ regions and α-phase precipitates.The highest hardness, yield stress and ultimate tensile strength values are exhibited by the NAC-10Cr material at room temperature. The composite is 57% harder than the unreinforced material. Moreover, it attains yield stress and ultimate tensile strength values of 1286 and 1335 MPa, respectively.A strong interfacial bond between the matrix and Cr reinforcement has been observed. The strength of the composite is determined by the strength of the Cr particles and failure occurs when a sufficient number of particles have broken so that the material cannot withstand the increased stress.Although the decrease in ductility observed in these materials as the temperature increases is mainly due to intrinsic characteristics, changes in the alloy composition as well as Cr reinforcement improve ductility at temperatures above 500 °C.Addressing the strength-ductility trade-off in a cast Al-Li-Cu alloy—Synergistic effect of Sc-alloying and optimized artificial ageing schemeA dramatic improvement of strength and ductility of cast Al-2.5Li-1.5Cu-1Zn-0.5Mg-0.15 Zr alloy was obtained by the collaboration of Sc-alloying and optimized ageing scheme. Joint and independent influence of Sc-alloying and different ageing temperatures were investigated. The results revealed that a substantial increase was realized in the hardness of Sc-containing alloy, and the ageing response time was only influenced by ageing temperature. Coarse and heterogeneous δ' (Al3Li), wide δ'-precipitation free zones (δ'-PFZs), and a large amount of T1 (Al2CuLi) precipitates were observed in Sc-containing alloy aged at 175 °C, which resulted in superior yield strength and poor elongation. The Sc-containing alloy obtained an excellent combination of ductility (elongation = 8.2 %) and tensile strength (ultimate strength =565 MPa) suffered to 150 °C ageing for 64 h. The increase in the elongation was mainly due to the combined effect of grain refining, much finer δ', and extremely narrow δ'-PFZs (<10 nm), while the higher strength was mainly attributed to the formation of Al3(Sc, Zr, Li) composite particles and a large amount of S' (Al2CuMg) phase. However, the enhancement of the different ageing temperature (150 °C and 175 °C) on the mechanical properties of the alloys without Sc addition was not obvious.Because of the ever-increasing requirement for stiffness in the aerospace industry and military fields, there has been a great deal of interest in the high lithium-containing (≥2 wt%, all compositions are in wt% hereafter unless noted otherwise) aluminium alloys []. However, the high anisotropy and a significant reduction of ductility resulted by high content of Li kept obsessing researchers over the past decades []. Cast method can be applied to overcome the high anisotropy by virtue of its particularity and obtain complex-shaped components with high stiffness (78−82 GPa), whilst the mutually exclusive relationship between the strength and ductility is still hard to be solved [A fundamental understanding of the mechanism of the negative influence on fracture toughness and ductility brought by a high content of Li is necessary before an effective solution can be achieved: On the one hand, as the Li content rise up to 1.7 wt.%, age-hardenable Al-Li alloys promote their strength mainly by the wide precipitation of coherent, ordered δ' (Al3Li) phase []. During plastic deformation, coplanar slip caused by δ' gives rise to inhomogeneous deformation and stress concentration at grain boundaries resulting in the intergranular cracks and brittle failure []; On the other hand, the weak δ'-precipitate free zones (δ'-PFZs) keep coarsening as ageing time prolongs [], which is also a common reason in reducing mechanical properties of many other aluminium alloys []. Thus, it could be recommended to reduce the inhomogeneous slip and convergence of dislocations by inhibiting the coarsening of δ' phase and δ'-PFZs.From the point of view of thermodynamics and kinetics, there exist two ways to modify the microstructure of cast alloy: optimizing heat treatment scheme and microalloying []. Our earlier study discovered that 1 % Zn addition to Al-2.5Li-1.5Cu-0.5Mg-0.15 Zr alloy could stimulate the precipitation of T1 (Al2CuLi) phase under ageing at 175 °C, leading to high tensile strength of 504 MPa []. However, as the main strengthening phase, δ' phase and its δ'-PFZs were not paid enough attention in the previous study, resulting in a little promotion of elongation. From the perspective of kinetics, decreasing ageing temperature would be the most effective way to inhibit the coarsening of δ' and δ'-PFZs for the diffusion is strongly temperature-depended []. However, the precipitation of key strengthening phase, T1 and S' (Al2CuMg), will be decreased simultaneously because of their high nucleation energy []. Therefore, it is necessary to find an effective alloying element to make up for the loss of strength caused by low-temperature ageing. In Al-Cu alloys, minor Sc addition can achieve the formation of numerous Al3Sc strengthening particles which are able to pin dislocations [] held the point of view that Al3(Sc, Zr) particles can serve as the preferential nucleation sites of the T1 and S' phases in Al-Li-Cu-Mg-Sc-Zr alloys. It was also found that the coarsening of δ'-PFZ growth could be precluded by Sc []. However, a kind of ternary phase named W (Al8-xCu4+xSc []) found in Al-Cu alloys with high Cu content could diminish the positive effect of Sc [], while there was no evidence for the presence of W phase in Sc-containing Al-Li-Cu alloys with relative low Cu content (< 2%) []. Further researches are demanded to confirm whether the formation of the W phase will be inhibited in aluminium alloys with low Cu contents.Given these facts, the present study explored the independent and combined influence of different ageing temperatures (150 and 175 °C) and 0.2 % Sc alloying on the microstructure evolutions and mechanical properties of the cast Al-2.5Li-1.5Cu-1Zn-0.5Mg-0.15 Zr alloy. The mechanisms of inhibiting δ' phase and δ'-PFZ and the precipitation behaviours of Cu-containing phases were compared in detail by microstructure characterization, based on which the contribution to mechanical properties was investigated.The studied alloys are prepared from commercial pure Al, Li, Zn, Mg ingots, and master alloys of Al-50 wt.% Cu, Al-10 wt.% Zr, and Al-2 wt.% Sc by an electronic resistance furnace. More detailed preparation procedure can be found in our previous work []. In this study, Al-2.5Li-1.5Cu-1Zn-0.5Mg-0.2Zr-(0.2Sc) alloys are selected. The alloy compositions were determined by Inductively Couple Plasma-Atomic Emission Spectroscopy (ICP-AES), which are listed in and hereafter denoted by Alloy A (with 0.2 % Sc addition) and Alloy B (without Sc addition). Following the two-stage solution heat treatments (485 °C × 24 h + 540 °C × 30 h for Alloy A, 480 °C × 24 h + 540 °C × 24 h for Alloy B) adapted to each alloy, the alloys were quenched into water at room temperature immediately. The two alloys were then subjected to isothermal artificial ageing at 150 °C and 175 °C up to 1000 h in the oil bath (hereafter denoted by 150/175-xh-A/B alloy).Microstructure analysis was carried out by optical microscope (OM, LEICA MEF4M, SDI Group Germany GmbH, Bielefeld, Germany) and scanning electron microscopy (SEM, Phenom XL). Energy Dispersive Spectrometer (EDS) was adopted for the elemental analysis. Vickers hardness tests were carried out on 10 mm × 20 mm × 20 mm cube samples using a load of 5 kg and a holding time of 15 s. Duplicate tensile tests were carried out at room temperature for all alloys after ageing for various time using Zwick/Roell Z100 testing machine with a strain rate of 0.5 mm/min. The schematic of the tensile tests of sheet specimens is shown in , whose sizes were 15 mm in gauge length, 2.2 mm in thickness, and 3.5 mm in width, respectively. Every mechanical property value is the average of four tests. Samples after ageing were mechanically ground to about 100 μm and punched into 3 mm diameter disks to prepare thin foils for transmission electron microscopy (TEM) observations. These thin foils were then twin-jet electropolished at the temperature range between -30 and −35 °C utilizing a Struers Tenupol-5 system jet electropolisher operating at 35 V in a solution of 4 vol.% perchloric acid and 96 vol.% ethanol. Conventional TEM images were taken using a JEOL 2100 TEM apparatus operating at 200 kV. For High-Resolution Transmission Electron Microscope (HRTEM) images, a 200 kV field-emission transmission electron microscope (Talos F200X G2) was applied.(a) and (b) presents the OM graphs of as-cast Alloy A and Alloy B, respectively. It is observed that the average grain size was much refined by Sc addition. The average grain size of Alloy A was about 33 μm, which was 64.5 % smaller than that of Alloy B. The morphology of the α-Al matrix was transformed from dendritic grains or cellular structures to equiaxed grains after the Sc addition. A large number of secondary phases were distributed along the grain boundaries. According to the XRD results of previous studies [], the secondary phases consisted of δ՛, Al2CuLi, δ (AlLi), Al2CuMg, Al6CuLi3, Al3Sc and Al2Cu phases.(c) displays the SEM images and the distribution of the corresponding elements acquired by EDS of as-cast Alloy A. Compared to SEM mapping analysis of Alloy B in our previous study [], the distribution of elements Cu, Zn and Mg were not affected by Sc addition. Cu kept enriching in the secondary phases along the grain boundaries or interdendritic regions and Zn atoms were still in the vicinity of grain boundaries. As arrowed in (c), some primary cubic-shaped containing Sc and Zr elements could be found sporadically. According to the previous researches [], the primary particles were Al3(Sc, Zr), of which the dominant morphology was dependent on the cooling rate and initial melt temperature.(a) presents the SEM microstructure of as-quenched Alloy A, indicating that almost all the Cu-containing secondary phases were dissolved into the matrix. Only a small amount of residual Al3(Zr, Sc) particles could be found as the spot scanning result shown in (a). After solution treatment, the average grain size of as-quenched Alloy A was about 38 μm, exhibiting an excellent grain growth resistance. In addition, some rod-shaped precipitates with a width of about 40 nm could be found to associate with the boundary, as shown in (b). The phenomenon was also found in some as-quenched binary alloys, such as Al-0.8 Zr [] alloys, and was named discontinuous precipitation []. The total content of Sc and Zr in this study is less than 0.4 wt.%, so this discontinuous precipitated Al3(Zr, Sc) phase rarely occurred in the studied alloys. Besides the rare coarse rod-shape Al3(Zr, Sc) precipitates, there were also extremely fine δ'(Al3Li) particles widely distributing in the matrix. The ordered precipitating δ' phase is cube/cube-oriented with the matrix, and the constrained lattice mismatch is less than 0.1 %, resulting in extremely low nucleation energy and forming quickly during the short natural ageing after quenched []. Both of δ′ phase and discontinuous precipitated Al3(Zr, Sc) phase are L12 structure [], so the superlattice-centered dark field (CDF) image could present them simultaneously.(a)-(d) are the OM graphs of Alloy A suffered to different ageing states after quenching: 150 °C -64 h, 150 °C -128 h, 175 °C -64 h and 175 °C-128 h, respectively. (e) and (f) are the OM graphs of Alloy B aged at 150 °C for 64 h and 175 °C for 64 h. The average grain sizes in these six OM graphs are about 39 μm, 38 μm, 39 μm, 37 μm, 75 μm and 71 μm. Compared with the grain sizes of as-quenched samples (the OM graph of as-quenched Alloy B can be referred to the previous study []), the grain sizes of the alloys are almost unchanged during ageing whether at 150 °C or 175 °C.(a)-(e) present the bright-field (BF) TEM micrographs of Alloy A after ageing at 150 °C for 32 h, 64 h, 128 h and 256 h. It is widely accepted that the T1 phase shows a hexagonal structure of symmetry P6/mmm with the lattice parameters of a=0.495 nm and c = 0.935 nm, growing on {111}α planes []. The bright-field micrographs were taken along the [1 1¯ 0]α or [11 2¯]α zone axis, from which T1 particles could be viewed edge-on and showed needle-like morphology. The lath-shaped S', whose orientation relationships are [100]S՛//<100>α and [010]S՛//<012>α [], could also be judged by the dihedral angle between T1 and S՛. The dihedral angle between {111} and {210} planes is 39.23°or 75.04°. It can be observed that the volume fraction of S' phases kept increasing during artificial ageing at 150 °C as ageing time prolonged and there were also some fine plates-like T1 particles distributing in the matrix. In order to show T1 phases more obviously, (e) presents its micrograph with a higher magnification taken along [11 2¯] zone axe. Some spherical Al3(Zr, Sc) precipitates were found in bright-field images (arrowed in (f) shows the Alloy A aged at 175 °C for 64 h. Compared with the samples aged at 150 °C, the Cu-containing phases in the samples aged at 175 °C showed another characteristic: a large number of T1 precipitates with the average diameter of ∼103 nm distributing in matrix uniformly, while the amount of S' phase decreased obviously.(a) presents the TEM micrograph (B= [11 2¯]) of the Alloy B aged at 150 °C for 64 h. The observation area containing a large number of Al3Zr particles was selected. It could be observed that the number of S' phases in the alloy without Sc was much lower than that in the alloys containing Sc under 150 °C ageing. But after being aged at 175 °C for 64 h, Alloy B was similar to Alloy A that there was also a large amount of T1 phases in the matrix as shown in exhibits δ' CDF images of the studied alloys with different ageing states. (a)-(d) shows the DF images of Alloy A aged at 150 °C, it can be observed that the volume fraction and coarsening of δ' phase were increased with the increasing ageing time. (a) shows Al3(Li, Zr, Sc) composite precipitates and the interaction between S' and δ' precipitates. In the previous studies, the lath-shaped S' precipitates were also observed to preferentially nucleate around the Al3(Li, Zr) particles []. Most of the δ' in the samples aged at 150 °C showed irregular morphology rather than more spherical δ' in samples aged at 175 °C referred to (e). And the spacing among the particles aged at 175 °C is obviously higher than that aged at 150 °C. The morphology of the δ' particles in Alloy B aged at 150 °C ((f)) and 175 °C (referred to the previous study []) for 64 h were similar to those of Alloy A.The TEM microstructure of the studied alloys aged at 150 °C for 512 h are presented in (a), the number density of T1 phases in both Alloy A and B ((a) and (c)) was much higher after ageing at 150 °C for a long time, and the plate diameter of T1 was bigger. There existed S' phase in the matrix of Alloy A, while the precipitation of S' phase was hardly to be found in Alloy B even after 150 °C for 512 h. (b) and (d) shows the δ'-centered dark field micrographs of Alloy A and B respectively. As ageing time prolonged, the δ' phase in Alloy A grew and coarsened, but kept irregular. The average size and spacing of the δ' particles in Alloy B was larger than that in Alloy A. Some spherical δ' particles appeared in Alloy B while most of them were irregular. In addition, the distribution of δ' in Alloy A was still homogeneous, but heterogeneous in Alloy B.In order to study the interactions of different precipitated phases in detail, TEM and HRTEM observations with higher magnification are performed (). All the micrographs were taken along the [11 2¯] zone axis. (a) represents the interaction state between the S' phase and spherical Al3(Zr, Sc) particle, and (b) gives an HRTEM image of the red box. There is a good coherent relationship between the S' phase and Al3(Zr, Sc) particle as illustrated by the magnified image in the white dotted box. It was reported that the composite particles could act as nuclei of the Cu-containing phases [] and the HRTEM image in this study shows that the atomic arrangement of the two precipitates remained stable. (c) exhibits some other Cu-containing phases (T1 and S') precipitating around Al3(Zr, Sc) particle. The area of the red box in (d). It can be found that there was a good semi-coherent relationship between T1 phase and matrix, while the arrangement of Al atoms around S' phase was distorted. exhibits the expansion of δ'-precipitate-free zones (PFZs) in Alloy A ageing at 150 °C with the increasing ageing time. The δ'-PFZs half widths were measured from the grain boundary to the nearest δ' particles. The δ'-PFZs of the sample aged for 32 h was nearly equal to the distance between δ' particles. The half-width of the δ'-PFZs after ageing for 64 h, 128 h, and 256 h was 9 nm, 24 nm, and 59 nm, respectively. shows the expansion of δ'- PFZs near the grain boundary of Alloy A ageing at 175 °C. It is noticeable that the widths of δ'-PFZs aged at 175 °C were much wider than those of the samples aged at 150 °C. The half width of the δ'-PFZs after ageing for 32 h, 64 h, 128 h, and 256 h was 51 nm, 76 nm, 115 nm, and 233 nm, respectively.(a) and (b) presents the δ'- PFZs of Alloy B ageing at 150 °C and 175 °C for 64 h. The half-widths of the two samples were 24 nm and 84 nm. Compared to the same state of Alloy A, the half-width was increased by 166.7 % and 10.5 %. shows the δ'- PFZs near the grain boundary of Alloy A and Alloy B ageing at 150 °C for 512 h. The half width of the δ'-PFZs was 96 nm and 108 nm, respectively. presents the macro-Vickers hardness curves of the investigated alloys aged at 150 °C and 175 °C as a function of the ageing time. The four groups of alloys showed obvious but different age-hardening responses, indicating their microstructural evolutions during the ageing treatment. The hardness of Sc-containing samples were higher than those of Sc-free samples in the same ageing condition. The ageing response speed was sensitive to ageing temperature, while the addition of Sc brings about little influence on that. As the ageing temperature is 150 °C and 175 °C, both the two studied alloys require 64 h and 512 h to reach peak ageing, respectively. The highest hardness was 209 HV obtained in Alloy A aged at 150 °C for 512 h.(a) represents the tensile engineering stress-strain curves of the selected samples in this study. The representative values are shown in (c). It is worth noticing that the 0.2 wt.% Sc-containing alloy was characterized by high strength and high ductility under 150 °C ageing at under-ageing state. Especially, an excellent combination of YS =401 MPa, UTS =565 MPa and EL = 8.2 % could be obtained by Alloy A suffered to ageing at 150 °C for 64 h. As a contrast, the YS, UTS and EL of Alloy A were 49 MPa, 111 MPa and 3.6 % higher than those of Alloy B after ageing at 150 °C for 64 h, respectively. Although Alloy A could obtain an extremely high YS of 466 MPa after ageing at 150 °C for 512 h, the elongation was only about 1.7 %. Generally, the strength of the alloy was improved while the EL decreased with the increase of the ageing time. When the ageing temperature was 175 °C, the YS of Alloy A increased significantly, accompanied by a great decrease in EL. After ageing at 175 °C for 64 h, the YS of Alloy A could reach 458 MPa, and the EL was only 3.9 %. The mechanical properties of alloy B without Sc were much lower than those of alloy A under a same ageing treatment. The trends of hardness were positively correlated with the trends of tensile strengths during ageing.A summary of tensile properties of the studied alloys and some other cast Al-Li alloys or Al-Cu alloys is exhibited in (b). It declares that Alloy A obtained a higher mechanical performance than other highly strengthened cast aluminum alloys []. Based on the previous study of Zn alloying in Al-2.5Li-1.5Cu [], the comprehensive action of Sc addition and the ageing treatment at 150 °C further overcame the mutual resistance between strength and ductility in Al-Li-Cu alloys with high Li content.In this section, improved microstructural characters and enhanced properties arising from Sc addition and optimized ageing treatment will be discussed and compared in detail. (a), it is noticeable that the addition of Sc greatly stimulated S' precipitation during ageing at 150 °C and the volume fraction of T1 was much lower than that of S'. The Cu-containing phases in both Alloys A and B were primarily T1 precipitates when the ageing temperature rose to 175 °C, as shown in A large amount of uniformly dispersed S' is beneficial to both strength and toughness [], which is one of the important reasons for Alloy A aged at 150 °C exhibiting excellent mechanical properties. It has been reported that the addition of Sc refined the size of the S' and boost the nucleating of δ', S', and T1 phases by nanoscale Al3(Sc, Zr) dispersoids serving as nuclei [(a), S' was still infrequent in the selected area of Alloy B where many Al3Zr particles existed. And there are still many S' phases that are independent on Al3(Zr, Sc) particles to precipitate in . Therefore, in addition to the improved nucleation site resulted from the Al3X particles, there must be some other reason for the increased amount of the S' phase in alloy A.It has been recognized that the vacancy mechanism is one of the dominant mechanisms for the diffusion of matrix atoms and substitutional solutes in metals. Based on recent DFT calculations [), Sc-Cu-Va (vacancy), Sc-Mg-Va, Mg-Cu-Va and Mg-Zn-Va clusters own intense binding energy. Vacancies have an overarching influence on stabilizing solute-solute clusters with a few exceptions: homoatomic pairs of Li, Sc and Zr (known to form L12-trialuminide) []. Thus, Sc tended to form Al3Sc particles and released Mg-Va or Cu-Va pairs. The diffusion of solutes strongly requires vacancy, for which these solute-vacancy pairs obtained high atomic migration energy and easily gathered together to form precursors of S' phases, resulting in a higher volume fraction of S' phases in Alloy A. From the point of view of thermodynamics [], the equilibrium concentration of vacancies increases with the ageing temperature, so the lower ageing temperature led to the decrease of Cu-Va and Mg-Va pairs. As for the Alloy B aged at 150 °C, there was neither the effect of Sc nor high ageing temperature, resulting in the extremely low content of S' phase even ageing for a long time of 512 h.After ageing to peak-aged state whether at 150 °C or 175 °C, T1 phase was found to widely distribute in the matrix of both alloys. According to Noble and Thompson [], the nucleation of T1 plates occur by the mechanism of dissociation of 1/2 < 110> dislocations into 1/6 < 112> Shockley partials bounding a region of intrinsic stacking fault, where T1 plates grow by a ledge mechanism on {111} planes. Since the number density of dislocation of cast alloy is far away from that of wrought alloys, the precipitation of T1 was likely depended on the helical dislocations or loops formed by annihilation of a large fraction of the vacancies retained by quenching []. In the previous study, a low density of dislocation loops and a few helical dislocations were observed in the as-quenched Al-Cu-Li alloys, but ageing at 40 °C or 100 °C for a period greatly increased the number of loops []. Besides the high stacking fault energy of the dissociation of dislocations required for T1 nucleation [], the decrease of the rate of loops formation under lower ageing temperature should be another important reason for the retarded precipitation. Thus, the precipitation rate of T1 phase at 175 °C is much higher than that at 150 °C.In addition, there was no evidence for the presence of W (Al8-xCu4+xSc) phase in this work. Insoluble W phases, which compete with Al3Sc particles for Sc atoms in some Al-Cu-Mg-Ag alloys with a high content of Cu, was harmful to the mechanical properties of the alloys []. On the contrary, the absence of the W phase was reported in the alloys with relatively low Cu content, such as Al-2Li-2Cu-0.5Mg-xSc [] series alloys. Although there is currently a lack of detailed explanation on the formation of W phase, the critical factor of the formation of W might be the high Cu content instead of the Sc content, ageing temperature, or Cu/Sc ratio.It can be found that from the results in ], the morphology of the δ' phase was sensitive to ageing temperature and ageing time. The size and spacing of δ' particles of the samples aged at 175 °C were larger, while the particle morphology turned to be irregular and their spacing became denser after ageing at 150 °C. In the process of ageing at 150 °C, due to the small distance between particles, the initial spherical δ' contacted with each other to form an irregular morphology. When ageing at 175 °C, the faster-growing of particles would cost the surrounding small ones, resulting in larger gaps between the particles, heterogeneous distribution and a smaller number density [] reported that the diameters (d) of the δ' precipitates follow a d3 law as ageing temperature above 200 °C, that is:where d¯0 and d¯ are the mean particle diameter at the start of ageing (t0) and after ageing for time t, respectively; σ is the interfacial free energy of the precipitate; D is the coefficient of diffusion of the solute in the matrix; Ce is the equilibrium solute concentration at temperature T; and Vm is the molar volume of the precipitate., d¯3 of δ' precipitates also has a nearly linear relationship with t, though the ageing temperatures are lower than 200 °C. The change of ageing temperature brings a significant effect on the parameters such as D and Ce, so the growth rate of the particles is strongly temperature-dependent. As for the effect of Sc, high Sc-vacancy binding energy resulted in increased activation energy for the coarsening of δ', leading to the reduction of diffusion coefficient D [] also hold the point of view that the coarsening of δ' could be retarded by Sc to some extent. In this study, the influence of Sc on inhibiting the coarsening of δ' was more obviously after ageing at 150 °C for a long time of 512 h as shown in Previous studies concluded that the fine, dense, and homogeneous δ' is beneficial to the ductility and toughness of the alloys []. It should be recognized that the elongation of Alloy B is not greatly improved though there are similar morphologies of the δ' in Alloy B and Alloy A after ageing at 150 °C for 64 h. Thus, the refinement of the δ' phase is among the factors that greatly increase the elongation of Alloy A aged at 150 °C.The presence of soft δ′-PFZs adjacent to grain boundaries will result in strain localization, which leads to the nucleation and propagation of micro-cracks at grain boundaries [] demonstrated that the growth of δ'-PFZs followed a parabolic growth law expressed by:where h is the δ'-PFZs half-width, t is the ageing time and Kp is the δ'-PFZs growth rate constant. That is to say, there is a linear relationship between h and the n th-power of t. The scatter diagram of h and t and corresponding linear fitting was performed based on the results of this study, as shown in (a). The value of the exponent n here was found to be close to 1/2. Sanders et al. [] reported an n value of 1/3 according to their limited experimental data. But Sanders et al interpreted the concept of activation energy for the formation of the PFZ as a simple algebraic summation of activation energies for multiple processes during the formation and growth of PFZs [] carried out isothermal ageing on serval Al-Li alloys and modified the n value as 1/2, which is consistent with this study.It is found that growth rate constant Kp of the δ′-PFZs in Alloy A aged at 150 °C is much lower than those of others. The formation of PFZs in aluminum alloys has been explained either by a vacancy depletion or a solute depletion mechanism []. In the case of Al-Li alloys, the formation and growth of δ'-PFZs have been interpreted as being the result of the growth of equilibrium phase δ (AlLi) in consume of δ' by the high diffusion coefficient of Li at grain boundaries []. The most common precipitation sequence of Al-Li alloy during artificial ageing is as follows: supersaturated solid solution→ δ'→ δ []. The B32(NaT1) bcc structured δ phase, whose habit plane is {111}α and lattice parameter is 0.637 nm [], usually discontinuously precipitates at grain boundaries or formed by the transformation of the δ' phase near the grain boundary for the high mismatch. The decrease of temperature brought about significant suppression on the diffusion ability of Li which is the pivotal factor of inhibiting δ'-PFZs coarsening. In addition, the strong binding energy of Sc-Va resulted in the reduction of effective vacancy concentration for the diffusion of Li atoms. In conclusion, the combined contribution of decreased ageing temperature and Sc alloying led to the retardation of Li diffusion towards grain boundaries, thus the half-width of δ'-PFZs was even narrower than 10 nm after ageing at 150 °C for 64 h.In the end, there is another interesting phenomenon: there is a good linear relationship (the correlation coefficient R2 = 0.92) between the half-widths of δ'-PFZs and related EL values of alloys aged at different temperatures, as shown in (b). Such result might imply the point that the plasticity of Al-Li alloy is effectively influenced by the width of δ'-PFZs.The joint and independent influence of ageing temperatures (150 and 175 °C) and 0.2 % Sc alloying on the microstructure evolutions and mechanical properties have been characterized in cast Al-2.5Li-1.5Cu-1Zn-0.5Mg-0.15 Zr alloy. The following conclusions can be drawn:Sc enhanced the combination of Cu-vacancy and Mg-vacancy, accompanied by Al3(Sc, Zr) particles serving as nuclei of S' phase, which could significantly increase the volume fraction of S' phases as the ageing temperature is 150 °C. A large amount of uniform S' is beneficial for strength and elongation.There is a significant influence of ageing temperature on the coarsening rate of δ' phase. The coarsening of δ' particles could be further inhibited by Sc for the diffusion of Li being retarded by the strong combined Sc-vacancy pairs. Under the joint influence of 150 °C ageing and Sc-alloying, a dense and irregular morphology of δ' could be obtained until peak-ageing state.The combination of Sc addition and 150 °C ageing obviously restrains the coarsening of δ'-PFZs, which is crucial for the improvement of ductility. There is a good linear relationship between half-widths of δ'-PFZs and EL as the EL is 4 %-9 %.Owning to the fine grain size, fine and dense δ' particles, high content of S' and narrow δ'-PFZs of Al-2.5Li-1.5Cu-1Zn-0.5Mg-0.2Sc-0.15 Zr alloy aged at 150 °C for 64 h, excellent mechanical properties of UTS=565 MPa, YS=401 MPa, and EL = 8.2 % can be obtained.The authors declare that they have no conflict of interest.Shot peening of TRIP780 steel: Experimental analysis and numerical simulationThis study aims at the experimental and numerical analysis of TRIP780 steel after conventional shot peening. TRIP steels exhibit a multiphase microstructure with martensitic transformation of the retained austenite during shot peening. In-depth experimental analysis are carried out with microhardness and X-ray diffraction. Residual stresses profiles are determined in the pseudo-ferritic phases (α + α′) and in the retained austenite γ. A representative finite element model of shot peening with a material behavior law describing the multiphase microstructure and the martensitic phase transformation during loading is proposed. The results are compared to experimental data and the effect of martensitic transformation is numerically investigated.The shot peening process is applied on many metallic structures to enhance their resistance and fatigue life. It is achieved through the generation of a compressive stress profile in the subsurface of a part with a controlled roughness of the surface. TRIP-aided steels are multiphased with ferrite, bainite and retained austenite where austenite transforms to martensite during a thermomechanical loading. TRIP steel sheets are mainly used in the automotive industry after a forming process. In order to enhance their fatigue properties, some automotive parts made of TRIP steels are shot peened. Shot-peening is generally the last step after metal forming and joining. Shot peening is mainly applied to local regions with stress concentration where fatigue failure may occur such as holes, cut-outs or welded regions. Those operations prior to shot peening provide inhomogeneous states with microstructural and mechanical gradients.The TRIP effect (TRansformation Induced Plasticity) accompanies the martensitic transformation with an additional irreversible strain resulting from the selection of the martensitic variants according to the local stress level (Magee effect) and, from the accommodation of the volume change and the shear components of the phase transformation in the austenitic phase (Greenwood-Johnson effect). have presented the different formalisms to take into account the Greenwood-Johnson effect and the Magee effect to derive the transformation kinetics and the thermomechanical behavior.Many thermomechanical models of strain induced martensitic transformation on shear bands intersections have been proposed in the literature based on the work of have investigated the effect of stress triaxiality. They have taken into account that a greater triaxiality would increase the formation of martensite. have proposed an improved model incorporating the strain rate effect and heat generation for describing martensitic transformation. have proposed a martensitic transformation model to take into account the deformation mode by incorporating the effect of the third stress invariant. Using the aforementionned model of (IT-model), the TRIP effect has been also investigated at the level of the structure. have modeled crashworthiness of a top-hat crush tube made of TRIP800 steel. Comparing to experimental data, they observed how different contents of residual austenite and bainite maximize the energy absorption capacity. implemented the IT-model in Abaqus for the simulation of the deep-drawing process of a cup. They have numerically investigated the effect of model parameters on the thinning of the material, the punch load vs displacement curves and the residual martensite content.Within a thermodynamically consistent framework, several constitutive models were proposed in the litterature to describe the thermodynamical driving force for martensitic transformation in TRIP steels. have proposed analogous expressions of the driving force for martensitic transformation. This force is compared to a critical force to derive the transformation kinetics in an elastoplastic material. Works have investigated the TRIP effect in steels at the level of the variants experimentally and with crystallographic models applied to representative polycrystals. have used a double scale transition in a polycrystal (self-consistent scheme) and inside each austenitic crystal () to obtain the stress in each martensitic variant. The inelastic behavior has been modeled using crystal plasticity and variant selection in austenitic grains to derive evolution equations for the internal variables from the Helmholtz free energy. have developped a crystal plasticity and phase transformation model in Abaqus that was used by to investigate the effect of the microstructural parameters such as crystallographic orientations, the initial volume of retained austenite and the elastoplastic properties of the ferritic matrix. They have shown that the crystallographic texture and the elastoplastic properties of ferrite have a strong effect on the transformation kinetics and on the mechanical behavior. have implemented in Abaqus, a finite transformation crystal plasticity and variant selection model based on thermodynamic principles to model the behavior of TRIP assisted steel. With a finite element representation, they have explicitly modeled the microstructure with austenitic grains embedded in a ferritic matrix. The model has been able to capture the TRIP effect under multiaxial loadings. Those microstructural models of TRIP steels are excellent tools to capture the effect of the microstructure on the global behavior of a representative homogenized material point. However, due to computational cost, they are not yet well suited to investigate directly the behavior of structures and of material processes. have developed a multiphase semi-phenomenological model at the scale of the microstructural components (ferrite, bainite, retained austenite, martensite) by describing the elastoplastic behavior of each component by a standard von-Mises approach, for the phase transformation, a mean instantaneous transformation strain that encompasses the different contribution of each variant forming at the same time has been introduced. Though less microstructural parameters than polycrystalline models are considered, this model is able to consider the transformation kinetics, multiaxial effects of the martensitic transformation and the Greenwood-Johnson and Magee effects. It has been implemented into Abaqus to model sheet metal forming of TRIP-aided steels (). The simulations have been correlated to experimental data of martensite volume fraction and strain field on a cross-stamped metal sheet.Shot peening and more generally mechanical surface treatments are also of great interest where the prediction of residual mechanical fields, the induced microgeometry and the study of their impact on fatigue life still remain a challenge. first proposed an analytical approach to predict the stabilized elastoplastic response of a structure under a cyclic load. They have applied this approach to predict the residual stresses profile after shot peening and their evolution during a cyclic behavior. The benefit of this model is its direct resolution with minimal computational cost. A drawback would be that it is not suited for material with non-standard behavior and that it relies on the assumption of an homogeneous surface treatment. Beside analytical approaches, the effect of shot peening is often modeled with multiple impacts of shots using finite element (FE) analysis that is sometimes coupled with other numerical approaches. The coupling of FE analysis for modeling the subsurface behavior with SPH (Smooth Particles Hydrodynamics) or DEM (Discrete Element Methods) allows to consider the description of the flow of shots and its interaction with any surface. relied on analogous DEM-FEM approaches to model coverage, roughness and residual stresses profiles. The positions and initial velocities of shots are output from a DEM software and applied as initial condition in a FE analysis. proposed a SPH-FEM approach, where the shots are modeled with SPH particles and the target material with finite element (FE) in a single model. Those models allow to link the process parameters of shot-peening to the residual state of the impacted surface. has linked the Almen intensity to the predicted residual stresses in a shot peened part made of 39NiCrMo3 steel and SAE 1070 steel. The residual stress profile generated by the simulation of multiple shots is inserted in a Almen strip to predict its bending. have modeled the surface layer characteristics on a AISI4140 steel with elastoviscoplastic model with a combined isotropickinematic behavior using finite element simulations of 121 rigid spheres impacting a surface. They have compared the surface topography with single and double impacts and the residual stress field after multiple impacts. A good correlation between their model and experimental data has been observed. have used a finite element to study the effect of different impact velocities and shot diameters and analyzed the effect of process-related impact velocity scatter on the scatter of the stress distribution. They used an isotropic-kinematic hardening formulation built into the Abaqus solver representing the cyclic hardening behavior of AA2024-T351 alloy. For their process parameters, reducing the number of impacts can be suitable to predict the residual stress distribution with a smaller computational cost.The effect of friction coefficient has been investigated by . They have shown that the residual stresses profiles are relatively insensitive to the friction coefficient between the shot and the target material for values between 0.1 and 0.5.To limit calculation costs, the FE models use generally a representative part of the impacted surface with given positions of the impacts representing the process parameters. Random or regular patterns are used and the realistic simulation of coverage rate is challenging and still needs to make some assumptions. have studied numerically the effect of random impacts to obtain 100% of coverage and proposed a method to obtain high coverage rates. have investigated the effect of coverage rate and impacting density on the residual stresses profile with FE analysis, comparing random and regular impact patterns. When the value of coverage is relatively great, the same coverage in random peening corresponds to slightly greater induced stresses. have presented different analytical and finite element approaches to model residual stress fields after shot peening of representative parts as well as on parts with complex geometries. They have linked analytically the process parameters to the obtained stress field using a dimensional analysis.Semi-analytical methods as developed by based on calculation of inelastic strain field embedded in a semi-infinite media submitted to contact have been adapted to shot-peening of elastoplastic materials. They have been able to predict the same fields as FE models with a drastic reduction of the computational cost.In the case of shot peening of steels exhibiting a TRIP effect, the effect of martensitic transformation was investigated in the literature. have determined the residual stresses profiles in austenite and martensite after shot peening of a 18CrNiMo7-6 austenitic steel, with a higher level of compressive stress in martensite due its higher yield stress. have investigated the microstructural evolution for a cryogenic SMAT process applied to 304L stainless steels. Beside nanostructuration, strain induced martensitic phase transformation has been observed in the depth of the specimen: the lower the temperature of shot peening, the greater the affected depth with martensitic transformation. have determined the martensitic volume fraction and residual stresses in martensite using Barkhausen noise technique in an AISI304L stainless steel after different shot-peening conditions. The greatest amount of phase transformation arises at the surface. have studied the effect of fatigue testing on the phase transformation and stress in BCC phase after shot peening. The volume fraction of martensite does not considerably change whereas the residual stresses relax after fatigue testing. To the authors knowledge, only have experimentally studied the stress state in both austenitic and martensitic constituents after shot-peening. For the modeling of surface treatment with phase transformation and the prediction of residual stresses, have presented a parametric numerical study of laser shock peening (LSP) on an AISI304 steel using the material model developed by implemented in an Abaqus UMAT subroutine. They have investigated the temperature effects in LSP, and have shown that, at lower temperatures, the phase transformation was the main cause for residual stresses generation, while plasticity dominates the residual state at higher temperatures. The resulting macroscopic residual stresses were not significantly affected by changing the temperature. It is important to note that for LSP, the maximal plastic strain is less than 0.5% whereas for conventional shot peening, plastic strain can reach several tens of percent.Shot peening has the objective to enhance fatigue life of TRIP steels widely used in the automotive industry. Without considering shot peening, have investigated the high cycle fatigue behavior of TRIP700 steel and the role of austenite stability. By comparing two TRIP steel grades with different austenite stability, the authors have concluded that the steel grade with higher austenite stability exhibit greater fatigue performances. As for metal forming, shot peening is a gradient straining process localized close to the surface where it is applied. have studied the effect of uniform pre-straining conditions in uniaxial tension on the low cycle fatigue (LCF) performances of TRIP780 steel. They have concluded that the LCF life was relatively independent of prior strain history with respect to the applied strain amplitude and that the amount of austenite transformed during fatigue was comparable or slightly larger than the amount formed at equivalent strains in tension.This work aims at the study of the shot peening effect on the residual stresses profile of a TRIP780 steel without initial in-depth gradient of microstructure. Experimental investigations were carried out after different shot peening conditions analyzing the gradient of microstructure and residual stresses profiles in the different components. The thermomechanical model for TRIP steels developed by was adapted to model the effect of shot peening of TRIP steels in terms of martensitic transformation and stress distributions in the different microstructural components. A representative finite element model of impacts of spheres on a plate using a multiphased behavior law with martensitic phase transformation has been developed and applied to predict the residual stresses profiles in the different constituents. The effect of martensitic phase transformation has been numerically investigated.The TRIP780 steel is a low alloy cold-rolled steel. Its name comes from its ability to undergo the TRansformation Induced Plasticity effect and its required ultimate tensile strength (YTS ≥ 780 MPa). This material is well suited for automotive structural and safety parts such as cross members, longitudinal beams, B-pillar reinforcements, sills and bumper reinforcements. It was provided by ArcelorMittal as 2 mm thickness sheets. Its chemical composition (in weight%) is the following: Base Fe – 0.209% C – 1.61% Si – 1.64% Mn. shows the microstructure of TRIP780 steel. It is composed of islands of hard retained austenite (15%) and carbide-free bainite (10–15%) dispersed in a soft ferritic matrix (70–75%). Austenite appears as island-like-grains of 2–3 μm diameter.Samples of 60 × 60 mm2 were cut from the rolled sheet. They were shot peened on one side in a turbine Wheelabrator shot-peening machine with steel shots (hardness 700 HV). Two shot peening conditions were applied: SP1 (shot diameter 400 μm, Almen intensity F19A, coverage rate 230%) and SP2 (shot diameter 600 μm, Almen intensity F31A, coverage rate 270%).Microhardness in-depth profiles were performed using a Shimadzu indenter. The initial hardness of the as-received material was measured to 270HV0.3 and was constant along the thickness of the material. Microhardness profiles were obtained for SP1 and SP2 conditions by cutting the samples and measuring along the edge.Texture analysis performed by X-ray diffraction showed that no significant crystallographic texture was present at the surface of the as-received material. X-ray diffraction analysis were performed using a PROTO iXRD portable goniometer, with a spot size of about 2 mm in the center of the plate. Indeed, preliminary measurements demonstrated that residual stresses were homogeneous at the surface of the shot peened plate until 20 mm from the center.The diffraction peaks of ferrite (α, BCC) and martensite (α′, QC) appearing more or less at the same position and since no peak separation has been performed in this study, residual stresses results thus matched to the pseudo-ferritic phases (α + α′). The residual stresses were also determined in the austenitic phase γ (FCC).Residual stresses analysis was conducted using the sin2(Ψ) method (α + α′: {211}α+α′ lattice planes, Cr Kα anode, −S1 = 1.28 × 10−6MPa−1, 1/2S2 = 5.92 × 10−6MPa−1;γ: {311}γ lattice planes, Mn Kα anode, −S1 = 1.20 × 10−6MPa−1, 1/2S2 = 7.18 × 10−6MPa−1;13 Ψ angles were used and peaks were localized with a gaussian fit at 30% height of the peak maximum.The full width at half maximum (FWHM) profiles were acquired for the pseudo-ferritic phases (α + α′) and the austenitic phase γ (FCC). The volume fraction of retained austenite was determined following ASTM standards () with a Cr anode and a V filter by measuring the corresponding intensities of the following peaks in both phases: {220}γ, {200}γ and {211}α+α′, {200}α+α′.Electrolytical polishing was used to remove locally a material layer and thus determine the retained austenite content and the residual stresses in both phases in the sub-surface. The layer removal was conducted gradually and was measured at each step by a dial indicator. The estimated measurement accuracy was about 5 μm.The layer removal can induce a stress relaxation, even greater as the reached depth is significant. Residual stresses results were thus corrected by a model suggested by σcorrectedz=σmeasuredz−4×σmeasuredz=0×Δzewhere z is the corresponding depth of the measurement, Δz the layer removal thickness, e the initial thickness of the specimen and σmeasuredz=0 the residual stresses obtained at the surface.A representative finite element modeling of the shot peening process was carried out in order to model the residual mechanical fields from the surface towards the core of the material. A specific material behavior law for multiphased TRIP steels has been adapted from the model developed by . The strain sensitivity effect is negligible for TRIP780 steels, therefore it was not considered in the model and the behavior is elastoplastic with time independent martensitic phase transformation. The simulation uses a user subroutine (VUMAT) for the material behavior implemented in Abaqus Explicit. The shot peening process was modeled using finite element method with multiple successive impacts of spheres on a semi-infinite body.The material behavior law for TRIP steels is a multiphased model where the elastoplastic behavior is predicted in each phase (ferrite, bainite, austenite and created martensite) and martensitic transformation is taken into account by a transformation kinetic law. presents the notations used to formulate the constitutive equations of the model.For multiphase steel grades containing ferrite (α), bainite (b) and metastable austenite (A) of respective volume fraction Fα, Fb and FA, the total strain rate is divided in each constituent, within a small strain assumption, such as:In the representation proposed by the model, the retained austenite A includes the non-transformed austenite γ and the created martensite α′ such as A ≡ γ + α′.With the thermo-elastoplastic behavior of ferrite and bainite, the total strain rate is:E˙__=Fαε˙__epα+ε˙__thα+Fbε˙__epb+ε˙__thb+FA1−fε˙__epγ+ε˙__thγ+f˙1−fξ¯__T+fε˙__epα′+ε˙__thα′The martensite α′ of volume fraction f=Vα′VA, is created from the transformation of austenite γ under a thermomechanical loading.ε˙__ep is the elastoplastic strain rate, ε˙__th is the thermal strain rate and ξ¯__T is the mean instantaneous transformation strain (MITS) describing a part of the induced plasticity (For the finite element implementation of the behavior law in a VUMAT subroutine, the total strain rate is localized in each constituent using Taylor's assumption: E˙__=ε˙__α=ε˙__b=ε˙__A.The macroscopic stress rate derives from the contribution of the stresses in each constituent such as:Σ˙__=Fασ˙__α+Fbσ˙__b+FA1−fσ˙__γ+fσ˙__α′+f˙σ__α′−σ__γThe constitutive behavior includes different contributions:The elastoplastic behavior is described in each constituent using von-Mises criterion with non-linear hardening.The linear elastic behavior is isotropic and is described with the shear modulus μ = 80 GPa and Poisson's ratio ν = 0.3. The yield surface is defined by the yield function Y as:where σy is the yield stress and the von-Mises stress is defined as:s__ is the deviatoric stress tensor. R and X__ representing the isotropic and the kinematical hardenings are defined as functions of the plastic strain ε__p and its equivalent value εeqp such as:where Q0, b, C and Γ are material parameters, and p˙ the accumulated plastic strain rate.The incremental elastoplastic behavior is defined by:Using the standard approach for associated plasticity (), the elastoplastic modulus l__ep of each constituent is derived as a function of the hardening parameters:l____ep=C____−α9μ2(H+3μ)σeq2s__−X__⊗s__−X__with C____ the tensor of elastic moduli and H defined as:Mean Instantaneous Transformation Strain (MITS):The MITS ξ¯T represents the mean contribution of transformation strain rate over all the activated variants of martensite. It is additively decomposed in a volumic part 13θδ and a deviatoric strain contribution eT:being the volume variation, resulting from the crystallographic transformation from the austenitic to the martensitic lattice. θ is independent of the stress level and considered as a material data.Including volume variation, the MITS is given as a function of the deviatoric stress in the non transformed austenite sγ by ξ¯ijT=θ3δij+d1′sijγ+d2′916sklγsklγδij−2716skiγskjγwhere d1′ (MPa−1) and d2′ (MPa−2) are two parameters.The martensitic transformation kinetics, i.e. evolution of the volume fraction of martensite f versus the control parameters, is defined within a thermodynamical time-independent framework. completed the transformation kinetics proposed by , where the transformation kinetics involves Patel-Cohen (f˙=1−fκσ__˙γ:ξ__¯T−B.T˙+α.β.n.exp(−α.εeqpγ).1−exp(−α.εeqpγ)ε˙eqpγwhere κ, α, β and n are material parameters.The calibration of the material parameters was carried out with mechanical tests in tension (monotonic and cyclic) at room temperature coupled with martensitic volume fraction determination vs strain on TRIP780 specimens obtained from a first steel cast. Results from the litterature () were also used for shear testing. The volume fractions of the initial constituents were Fα = 70%, Fb = 13% and FA = 17% (f = 0). The calibrated material parameters are presented in for the transformation kinetics. Only the kinematical hardening was considered in the calibration (i.e. Q0 = 0). The comparisons between experimental and simulation data are presented in for a monotonic loading. Though phase determination was not available in shear testing, simulations are in good agreement with experimental data. The model predicts more phase transformation in tension than in shear testing.For the TRIP780 steel grade that was used for shot peening, the initial value of retained austenite volume fraction was determined by XRD and was set in the simulation to FA = 13% with Fα = 70% and Fb = 17%. Before shot peening, the simulation considers a constant distribution of constituents in the depth of the modeled medium.The model is coded in FORTRAN and implemented in a VUMAT subroutine using ABAQUS Explicit.In order to link the finite element simulation to process parameters such as coverage rate and impact velocities, an a priori estimation of the coverage is needed. The case of a single shot of diameter D impacting at a velocity V is useful to obtain an analytical value of impact radius a using Hertz theory, as developed in A. The impact radius a is given by:where K is the impact efficiency ratio, ρs is the density of the material of the shot and E¯ is the equivalent Young modulus.The shot peening process is modeled by the impact of multiple spheres on a plate. Considering an homogeneous repartition of the shot peening flow, a representative volume element of the process can be modeled. A symmetry condition is also considered in order to model halfspace. The plate is restricted to a rectangular box of thickness P, length L and width L/2 as seen in . The spheres have only an elastic isotropic behavior (E = 210 GPa, ν = 0.3). The spheres in the plane of symmetry are cut in half and boundary conditions are applied according to the symmetry. The translations of each face of the box are blocked along their normal directions, except the top face. The cutting planes of the half spheres in the plane of symmetry are blocked in translation in direction y. The other spheres are free. In the presented study, the velocity of the shot is initialized on each node of the spheres in direction y (normal impact). The initial velocity for SP1 and SP2 are estimated from the turbine rotation velocity and its diameter, and are set to: V = 60 m/s.For multi-impact simulations, the spherical pebbles impact the plate according to an hexagonal pattern, where the distance between the center of the closest peebles is equal to e. The impact radius a representing the diameter of the dimple after impact is estimated using Eq. The coverage rate T defined as the ratio of the impacted area over the total area, is estimated with respect to the distance e (see ), the diameter D and the velocity V as:T=SimpactedStotal=2π3ae2=2π3De.K.πρsV242E¯1/52, the coverage rate T will give the distance between impacts e for a given media impacting with a velocity V.Two ranges (nR = 2) around the central impact are modeled allowing the simulation of a 19 shot peening process. The mesh consists of C3D8R elements in the impacted material close to the surface and in the shots. At a depth where the residual stresses become negligible, C3D4 elements are used. The mesh size close to the surface is 25 μm.The contact is defined between the impacted surface (slave surface) and and the shots (master surface) with the penalty method with a normal and tangential behavior and a constant friction coefficient of 0.4. The initial state is free of residual stresses and with an homogeneous composition (no gradients of behaviors or volume fractions). is used to set the size L of the rectangular box so that the closest sphere contacts the plate at a distance of the edge of the box. P is also set to obtain a semi-infinite body conditions. presents the adopted mesh. The shooting order has no effect on the averaged results if the results are averaged on a zone bigger than the first range. In this case, the results are averaged over an hexagonal zone corresponding to the last range of the impacted part (hexagon of radius 2e). The mechanical (residual stresses and plastic strain) and microstructural fields (martensitic volume fraction f) are averaged at a depth with respect to the undeformed mesh. presents the hardness profiles after shot peening SP1 and SP2 which was performed on the cross sections of shot peened samples; the dashed line represents the base material. Hardening is clearly observed for SP1 condition (respectively SP2 condition) for which the maximum value of 315HV (respectively, 410HV) is reached at the near-surface and decreases until the material hardness at a depth of roughly 50 μm (respectively, 150  μm). These results are in agreement with the literature [The retained austenite fraction was measured by XRD; the absolute accuracy is about ± 3%. Before shot peening, the austenite content is 5% at the surface; it increases up to 12% for depths larger than 50 μm. The lowest value at the surface is due to the processing route as the sheets were skin-passed; this has induced martensitic transformation in the near surface. presents the retained austenite content as a function of depth for both SP conditions. In the first fifty micrometers, it was too weak to be detected by XRD. Then the retained austenite content increases up to its initial value, 12%, at a depth of 100 μm for SP1 condition (respectively 200 μm for SP2). The TRIP effect induced by SP is maximum at the surface; an increase of the shot diameter and the intensity induces an increase of the affected depth (i.e. where the martensitic transformation occurred).Before SP, the residual stresses in ferritic phases and in austenite were quite low, less than 100 MPa in absolute value. presents the residual stresses profile for the ferritic phases for both SP conditions. As mentioned in Section 2.2, this is an average value over ferrite, bainitic ferrite and martensite phases as XRD do not allow to separate each contribution. Both profiles are quite similar to those commonly found in the literature. SP1 condition leads to a more intense surface and maximum compressive stresses than SP2, respectively -380 MPa and -420 MPa for SP1, and -490 and -510 MPa for SP2. Moreover, whereas the compressive stress is rather constant over the first hundred micrometers for SP2, it decreases from the first twenty micrometers for SP1: its value at 250 μm depth is almost null, compared to -200 MPa for the other peening condition.In austenite, due to its low fraction, stresses could not be determined in the first hundred micrometers as the accuracy was not sufficient. shows that austenite is also in compression; the values are larger than in the ferritic phases, of about 150–200 MPa. The highest compressive stresses are observed with the larger shot diameter (SP2) which are 100 MPa higher than the SP1 values. Moreover, the stress has returned to zero value at 250 μm for SP1 whereas it is still in high compression for SP2. An inflection point seems to be observed around 120 μm, resp. between 150 and 200 μm, for SP1, resp. SP2; these depths correspond to the point where the retained austenite fraction becomes equal to its initial value of 12%. In agreement with literature, increasing the shot diameter induces an increase of the maximum compressive stress and the stress peak is shifted towards larger depths. Stress analysis in the austenitic phase seems to show that the stress decrease is more important in the non martensitic transformation affected depth.The Full-Width at Half Maximum (FWHM) of diffraction peaks is an indicator of micro-strain and coherent domain size. In the following, only the FWHM corresponding to {211} crystallographic planes of the ferritic phases is presented; there is no austenite diffraction peak at the near surface, as it has been fully transformed into martensite. The FWHM evolution is plotted in as a function of depth. The maximum value, observed at the surface, is the same for both SP conditions. It decreases to a constant value, corresponding to the initial value (before SP), from 200 μm depth for SP1; for SP2, the stable state does not seem to be reached yet at 250 μm depth. From a qualitative point of view, the FWHM is increased compared to the initial value in the zone where compressive stresses are observed too.To summarize, all these measurements show an impact of martensitic transformation on stresses profiles and FWHM. The depth affected by SP can be defined as the one where the retained austenite fraction is lower than the initial one, that is 100 μm for SP1 and around 200 μm for SP2; it is also associated with the highest compressive stresses and hardness which differ from less than 10% from the maximum value. In the non affected zone, stresses, hardness and FWHM decrease. An increase of the shot diameter increases the zone size where the martensitic transformation occurs but it decreases the maximum stress value in the ferritic phases.The modeled mechanical and microstructural quantities are averaged in order to be compared to experimental profiles obtained from X-ray diffraction. After the sequence of impacts on the surface, the following quantities averaged on the elements located at a depth z, are analyzed:Volume fraction of retained austenite f × FA;Residual stresses in austenite σxxγ−σzzγ;Residual stresses in ferritic phases comprising ferrite α, bainite b and created martensite α′, σxxα+α′−σzzα+α′; presents the contours of residual stresses and martensitic volume fraction after impacts for SP1 condition. The averaging region is similar to the hexagonal pattern limited by the center of the impacts as shown in , it is shown that the average stress is axisymetrical since the σxx contours look like the σyy contours with a 90° rotation. All the quantities are compared to experimental data in the depth of the sample after shot peening. compares the predicted and the experimental profile of retained austenite after SP1 (a) and SP2 (b). The model predicts accurately the increase of the affected depth for SP2 compared to SP1. The predicted affected depth by martensitic transformation is 150 μm for SP1 (exp: 100 μm) and 250 μm for SP2 (exp: 200 μm). The profiles are in good agreement with respect to the experimental uncertainty.In the experimental work, it was not possible to measure the volume fraction of austenite at the surface. However, the model predicts a volume fraction of retained austenite of 6% at the surface. At the surface, where contact between the shots and the plate takes place, this may be attributed to a shear loading where less retained austenite is transformed compared to tension (see ). Let us also remind that the decrease of retained austenite content at the surface (< 50 μm) prior to shot peening was not considered in the model.(a-b) presents the residual stresses profiles σ11α+α′ for SP1 and SP2 conditions. A good agreement is found between the model and experimental data. The residual stresses at the surface are identical for SP1 and SP2 conditions. When regarding the affected depth by the compressive residual stresses, the model predicts 300 μm for SP1 and more than 400 μm for SP2. In (c-d), the predicted residual stresses level in the non-transformed austenite σ11γ underestimates the experimental stress though the affected depth is well predicted. The predicted affected depth by the compressive residual stresses in austenite are identical to the one predicted in the pseudo-ferritic phases (α + α′).The adopted model for TRIP steels allows to investigate the effect of the martensitic transformation by canceling artificially the transformation. The same sequence of impacts was simulated with the extinction of the martensitic transformation, i.e. the impacted surface behaves as a multiphased elastoplastic steel. .a shows the effect of the martensitic transformation on the macroscopic stress profile. A beneficial effect is observed in the first 50 μm where the martensitic transformation generates more compressive residual stresses (Δσ = 50 MPa). In b, it is observed that with martensitic transformation the pseudo-ferritic phases are more in compression (Δσ = 100 MPa) on a depth of 180 μm corresponding to the depth affected by martensitic transformation. Martensitic transformation has a positive effect on the compressive stress generation. In the retained austenite, the stress profile is only slightly affected by the transformation (c). The martensitic transformation is accompanied by a transformation strain resulting from the Bain strain in each martensitic variant and the accommodation inelastic strain in the other phases. shows that the additional transformation strain is maximum at the surface with a value of 5% and decreases to zero until no martensitic transformation takes place at a depth greater than 150 μm. Compared to the total inelastic strain, the contribution of the transformation strain represents 10%.Shot peening was experimentally and numerically investigated in a TRIP780 steel with two shot peening conditions.The experimental X-ray diffraction analysis allows to distinguish the austenitic phase γ and the pseudo-ferritic phases (α + α′). The martensitic peaks have not been separated from the ferritic peaks in this study. However, in a future work it would be interesting to investigate the stress in ferrite and in martensite.Martensite appears in the first hundred micrometers and the martensitic transformation is greater when Almen intensity is higher;The stress level is determined in the pseudo-ferritic phases (α + α′) and in the austenitic phase γ in depth of the samples. Austenite appears more in compression than the pseudo-ferritic phases. Comparing two SP conditions, though the residual stresses in the pseudo-ferritic phases are similar at the surface, the affected depth is different. It is thus necessary to analyze the stress profiles;The affected depths by residual stresses in the pseudo-ferritic phases and in austenite are identical. Those affected depths by compressive residual stresses are greater than the affected depth by martensitic transformation.Numerical simulations by finite element analysis were carried out by representative dynamical shots on a TRIP780 steel medium, whose behavior is described by an elasto-plastic multiphase model with phase transformation. This model leads to the following conclusions:The martensitic transformation profile is well described by the model for two SP configurations;The stress profiles in the pseudo-ferritic phase are well predicted regarding the stress level and the affected depth. The stress in austenite is underestimated. A better model for strain partitioning between phases could help to improve the experimental-modeling agreement;By numerically canceling martensitic transformation in the studied TRIP780 steel, it is predicted that martensitic transformation has a beneficial effect on the level of compressive stress in the first 50 μm. An additional transformation strain of 5% contributes to this beneficial effect. In a stress fatigue life estimation, this would increase the fatigue life compared to steels without phase transformation.The presented finite element tool can be used to investigate the effect of other microstructural parameters (phase distribution, volume variation) and of different process parameters on the mechanical states after shot-peening. In future studies, the presented numerical tool could also be chained with other simulations of metal forming prior to shot-peening to take into account the initial gradients of microstructure and residual stress fields. Indeed, this could be performed by initializing in-depth profiles of internal variables (plastic strain, martensitic phase transformation) and of mechanical stress fields over which shot peening will be superimposed. Thus, understanding the loading history and their resulting mechanical and microstructural fields would benefit to the fatigue prediction of shot peened parts.The normal impact of a sphere of diameter D with a semi-infinite medium is considered.), the total compression δ is related to the contact size a by:In the Hertz theory, the load P, resulting from the pressure forces of the ball on the plate, is linked to δ by:with E¯ is the equivalent Young modulus defined as a function of the elastic material properties of the shot (subscript s) and of the impacted plate (subscript p):In order to obtain a relationship between the shot peening parameters and the resulting contact area of radius a, an equivalence between an elasto-plastic shock and an elastic one is made. The kinetic energy W of a shot is converted to an elasto-plastic energy Wep of the impacted material and a energy Wd dissipated in the form of temperature and oscillations such as:The efficiency of the impact is characterized by the ratio K between the elasto-plastic energy and the total kinetic energy.The elasto-plastic energy is thus defined as:where ρs is the density of the material of the shot, D its diameter and V its velocity.For a plastic impact at moderate velocities (up to 500 m/s), impact velocities are small compared to elastic wave speeds. Thus the impact behaviour can be investgated under static conditions. The kinetic energy W is absorbed in local deformation of the two colliding bodies, up to the instant of maximum compression, which is expressed by where the resulting load P is linked to the average dynamic pressure pd by:, the contact radius is linked to the shot peening parameters by:Topology-optimized design, construction and experimental evaluation of concrete beamsThis work presents topology-optimized design of plain concrete beams using a density-based approach and subsequent construction and experimental evaluation. Three elastic design cases are considered to allow investigation of the effect of using different topology optimization problem formulations and different safety factors on the material strengths. Specifically (i) the compliance is minimized under a limit on the material use, and (ii) stress limits are imposed with a Drucker-Prager criteria while the material use is minimized. Imposing stress limits on the design problem considered in this work is found to create solutions that require significant levels of post-processing prior to construction. This heuristic post-processing is demonstrated to have had a significant effect on the behavior of one of the design cases; leading to large variations in the experimental observations. In line with common design engineering practices, the most robust experimental behavior is found in the design with the highest safety factor on the concrete's tensile strength.Concrete is a complex material with a non-homogeneous composition that typically results in a drastically different behavior in tension and compression. As it generally has a high compressive strength it is most often reinforced to compensate for its weakness in tension. Reinforced Concrete (RC) is thus a composite with two distinct material phases; a concrete phase and a reinforcing phase. Most commonly the reinforcing phase consists of steel rebars. In current RC design frameworks both phases are assumed to interact and are therefore designed simultaneously. However, with emerging concrete construction technologies, such as CNC milled formwork, fabric forming and 3D printing, the classic reinforcement strategies are being revisited. Examples include using textile reinforcement for fabric formed concrete (see e.g. overview in []) and schemes for both interior and exterior reinforcement placement for concrete 3D printing [] designed and constructed a pure compression floor slab, eliminating entirely the need for the reinforcing phase. New design frameworks intended to leverage the possibilities afforded by novel construction technologies must thus be able to design for each phase of the RC separately.Topology optimization offers a means to leverage the new manufacturing possibilities. It is a freeform engineering design tool that can autonomously generate efficient forms within a design domain by ascribing fabrication material to key locations of a structure while removing it from underutilized areas. The design engineer is not required to have an initial notion of the final design layout. Therefore topology optimization has been known to lead to new design solutions that typically outperform conventional low-weight designs. This has made topology optimization a popular design tool for a wide range of applications, but the examples related to civil structures and components remain limited. This is partly because the resulting structures are often complex and with nonlinear features that impede manufacturability on a buildings-scale. However, this tendency suggests that concrete would be an excellent building material for topology-optimized civil structures, since its initial liquid phase makes it highly formable, and it's low cost and high strength make it an ubiquitous construction material.Several researchers have proposed topology optimization algorithms for RC design. Most have focused on generating Strut-and-Tie Models (STMs) for designing the reinforcing phase in complex structural regions. The first suggested approaches simplified the composite RC to an isotropic, linear elastic material and used either truss topology optimization [], continuum frameworks with heuristic ESO updating []. Topology optimization of STMs with different moduli in the two RC phases was later suggested []. Nonlinear formulations have also been proposed e.g. by Ali and White [] that use an elasto-plastic truss algorithm for generating STMs. Bogomolny and Amir [] proposed a continuum framework for the conceptual reinforcement phase design in which both RC phases have elasto-plastic behaviors. Several researchers have also proposed design frameworks for topology-optimized fiber distribution and orientation in fiber-reinforced RC []. In addition to only designing the reinforcing phase, topology optimization algorithms have been proposed for design of both phases to improve the damage strength [] of low weight elements. Recently, Amir and Shakour [] suggested a topology optimization algorithm for design of low weight post-tensioned RC.Few researchers have constructed RC structures with topology optimization informed designs. Dombernowsky and Søndergaard [] constructed a RC frame designed with a commercial software assuming the composite to behave isotropically in an initial design phase. The design solution was post-processed by adding steel reinforcement to compensate for tensile forces in the system. Jipa et al. [] designed and fabricated two floor slabs of fiber-reinforced ultra-high performance concrete. The slabs were designed with different topology optimization approaches; an ESO and a density-based formulation. However, no experimental testing was performed to evaluate the difference in performance. Recently, Oviedo et al. [] experimentally evaluated optimized STMs for a dapped beam, including specimens with topology-optimized STMs. However, in these designs significant post-processing was done to the continuum topology-optimized results. Still, an increased ultimate strength and better crack growth control was observed.The current lack of experimental validations poses a significant barrier for further development and use of topology optimization frameworks for RC design. As RC is a complex composite this work focuses on accurately designing for the concrete phase; an essential step in truly enabling freeform design of both RC phases. In this paper design, construction and experimental behavior of plain concrete topology-optimized structures will be compared. Three elastic design cases are considered and will be referred to as the (i) Compliance, (ii) High Tension and (iii) Low Tension designs. The aim of the Compliance design is to maximize the structural stiffness under a constraint on the allowable material. No limits are imposed on the stress field. The High Tension and Low Tension design cases aim at minimizing the structural volume (or mass) while constraining the stresses. Both cases have the same limit on the compressive stress, which is taken as the compressive strength fc′. To investigate influence on the tensile strength used in the design, two limits are taken as 11%fc′ (8fc′ in psi) and 8%fc′ (6fc′ in psi) for High Tension and Low Tension, respectively.This paper will first present the two topology optimization frameworks used in the design. Next the construction process will be detailed where digital CNC milling is used to cut the formwork. Finally, the experimental results will be presented and discussed.Several topology optimization approaches have been suggested (see overview in e.g. []). Within most approaches, the design engineer must define a design domain Ω with applied loads and boundary conditions on it. The design problem is formulated as a formal optimization problem and most rigorously solved using a mathematical program. This work uses the density-based approach [] and the Method of Moving Assymptotes (MMA) as the gradient-based optimizer []. To evaluate the performance of the design Ω is discretized with finite elements. In the density-based approach each element e is associated with a density ρe. The design goal is to find a 0–1 distribution of element densities that optimizes a given objective f while fulfilling structural equilibrium and some constraint c. However, to enable the use of gradient-based optimizers, the binary 0–1 restriction is relaxed and intermediate densities (0 ≤ ρe ≤ 1) are allowed as the design evolves. In turn, the intermediate densities are penalized to make them inefficient use of material such that the optimizer is guided from an initial smeared guess towards a discrete structural solution.The design domain Ω used in this work is the top beam of a 2D Hammerhead pier and shown in . Due to size and loading restrictions of used testing equipment, the length of the domain is taken as L = 0.91 m (36"), the depth is H = 0.23 m (9") and it is 7.6 cm (3") thick. Four point loads of P = 2.2 kN (500 lbs) are applied along the top of the beam and a fixed boundary condition is placed along a center section of the bottom. The domain is herein discretized with 2D quadrilateral, plane stress elements and symmetry is employed so only half the domain is designed. The plain concrete is assumed to be isotropic and linear elastic in all design cases. For the isotropic assumption to be somewhat sound for the experimental investigation, a minimum length scale requirement on the topological features is enforced as dmin = 5 cm (2"). The material properties used for the three design cases in this work are listed in In this work the Compliance design case seeks to maximize the structural stiffness using a predefined amount of material volume (or mass). For isotropic, linear elastic assumptions this is equivalent to minimizing the structural compliance f1. Minimizing compliance is a commonly used objective in topology optimization. The design problem is typically formulated as: minimizeϕf1=FTdsubject toK(ρ)d−F=0c1=∑e∈Ωρeve−Vmax≤0ϕmin≤ϕi≤ϕmax∀i∈Ω,where ϕ contains the design variables that control the element densities in ρ. The design variables are continuous and bounded by ϕmin and ϕmax that in this work are taken as 0 and 1. The volume constraint c1 is calculated as the sum over all elements e of the element density ρe times the element volume ve. The allowable volume of material is the user specified Vmax. Throughout the optimization the structure must fulfill the discretized static equilibrium where K(ρ) is the global stiffness matrix, F is the global load vector and d contains the free displacements.The High Tension and Low Tension design cases seeks to minimize the material volume f2 while respecting limits on the maximum and minimum stresses within the structure. The stress constraint c2 requires the stress tensor σ to be computed in all integration points ip of all finite elements e. The stress is calculated in the standard finite element manner by: where D is the constitutive tensor and ε is the strain tensor. The strain found as the multiplication of the strain-displacement matrix B and the element displacements de.Several researchers have proposed stress-based topology optimization frameworks (e.g. []) and a full review is beyond the scope of this paper. Often the objective of stress-constrained approaches is taken as minimizing the volume to ensure that the loaded design remains within the stress limits. The stress limits are often imposed using an equivalent stress measure such as the von Mises stress. However, a von Mises stress condition can only enforce equal strength limits in tension and compression. Therefore, a Drucker-Prager stress condition [] is herein preferred since it allows for different strength levels. shows the comparison of the von Mises and the Drucker-Prager yield criteria in the principal stress plane (σ1,σ2) with a compression to tension ratio of s = 2.5. All stress states on the interior of a criterion are allowed. It is clearly seen in the plot that the Drucker-Prager criterion allows for a larger stress in compression than in tension. However, the plot also reveals that the Drucker-Prager criterion allows for high biaxial compressive stress states. For concrete design where the s-value typically is around 5 times larger than that of (around 10), this tendency is further pronounced and can result in an inadequacy to capture failure in compression. As a remedy, a composite yield surface is commonly used for FEA of concrete. However, a composite yield surface introduces a discrete operation that complicates the sensitivity analysis. Therefore, this work is simplified by using a Drucker-Prager failure criterion in 2D plane stress defined as: The tensile and compressive stress limits, fc′ and ft′, are used to determine s=fc′/ft′. The stress invariants J1 and J2D are calculated by: ] suggested a topology optimization framework with a Drucker-Prager stress constraint applied locally to all elements within the design domain. This is used as the basis for the stress-constrained designs herein. However, instead of placing explicit stress limits on each element in the design domain, a P-norm formulation is used to globalize the constraint []. In this way a single explicit constraint is placed on the design problem. For the formulation of the globalized stress constraint c2, it is convenient to define the sum of the Drucker-Prager stress in all integration points as: where ngp is the number of integration points in each element and P is the P-norm factor. For the quadrilateral elements in this work ngp = 4.The design problem formulation used for the High Tension and Low Tension design cases is: minimizeϕf2=∑e∈Ωρevesubject toK(ρ)d−F=0fc'≤c2=σsum1/P≤ft'ϕmin≤ϕi≤ϕmax∀i∈Ω.The tensile and compressive stress limits are specified for both design cases in It should be noted that using a P-norm formulation is known to have limitations []. Since an averaging measure is taken, the limits on the stress constraints have no real-world correlation and must be chosen case-by-case at the discretion of the design engineer. This can especially pose a challenge when the design domain is prone to introduce stress concentrations. The design domain considered in this work does not have this tendency. To confirm this notion the maximum and minimum stress states occurring within the structure were closely monitored during the design. Using the P-norm on a Drucker-Prager criterion introduces additional complications due to the potential bias towards bi-axial compressive states as described above, and a limitation on the choice of the P value. Odd values allows for negative numbers within the radical, which produces imaginary sensitivities. Therefore P = 6 was used in this work. An even choice of P causes any negative Drucker-Prager stress states to be converted to positive. This could potentially lead to over-constraining the compressive stress limit. However, as will be discussed later, no issues with over-constraining the compressive regions were observed in the obtained designs.The Solid Intermediate Density Penalty method (SIMP) [] is used to connect the density of an element to its stiffness Ee: The stiffness of the pure solid material is denoted E0 and η is the SIMP exponent. An element with density ρe = 1 is therefore a solid concrete element where as elements with ρe = 0 has negligible stiffness and is void. A small positive number Emin is added in Eq. () to ensure positive definiteness of the global stiffness matrix. In this work Emin = 10−4 is used throughout.The stress in an element's integration points is similarly related to its density by: where ησ is the SIMP exponent for the stress penalization that herein is taken as ησ = 0.5.It is well established that most continuum topology optimization requires a filtering method to be used when relating the independent design variables to the element densities for numerical instabilities to be avoided. This work uses the Heaviside projection method (HPM) [] as it implicitly provides the design engineer with control of the minimum length scale dmin of the topological features. A complete explanation of the algorithmic steps in HPM is beyond the scope of this paper and the reader is referred to [In this work the optimization problems in Eqs. () are solved using gradient-based optimizers and objective and constraint sensitivities therefore guide the design evolution and must be computed. The sensitivities are commonly calculated as follows: The partial derivative of the objective function f with respect to the element density ρe is generally problem dependent and calculated using the adjoint method. For the minimum compliance objective f1 in Eq. (), the sensitivities take the well known form of the scaled elemental strain energies: The element stiffness matrix of a pure solid element is denoted Ke0. The sensitivity of the volume constraint c1 in Eq. (), the partial derivative of the constraint with respect to the element density is also calculated using the adjoint method. It can be shown that the adjoint variables λ can be found by solving the following: λTK=−Aeve(σsum)1/Pσsum∑ip=1ngp∂σDPip∂σipT(ρe)ησDB, is the standard global assembly operator used in finite element methods. Once the adjoint problem is solved, the sensitivity of the stress constraint can be calculated as: ∂ĉ2∂ρe=η(ρe)η−1(λe)TK0ede+ησ(ρe)ησ−1(σsum)1/Pσsum∑ip=1ngp∂σDPip∂σipT(Dε).), the partial derivative of the Drucker-Prager stress with respect to the stress components is: ∂σDPip∂σip=s+14s(3J2D)−1/22σxx−σyy2σyy−σxx6σxy+s−12s110.The partial derivative of the element density with respect to the design variables follows the chain rule. The reader is referred to [ give the results obtained for each of the three design cases and show: (a) the topology-optimized design, (b) the as-built digital fabrication model, and (c) an experimental sample. All designs are obtained on a 200 × 100 mesh. Continuation methods are used on the SIMP and Heaviside parameters. This is common practice in solving topology optimization problems. The SIMP parameter in Eq. () was initiated in an unpenalized state (η = 1) and raised till ηmax in increments of Δη = 0.5 every 50 iterations. For the compliance design ηmax was taken as ηmax = 5, whereas ηmax = 9 was used for the stress-based designs. The Heaviside parameter was initiated at β = 0 and applied with Δβ = 1 till βmax = 50.a is seen to have one compression strut originating from each point load, carrying forces to the clamp connection at the base of the beam. A single tension component runs along the top of the design domain. All structural elements are approximately sized equally. The High Tension design (a) is similar to the Compliance design in terms of material use (V = 49.3% and V = 50.0%, respectively). However, the High Tension beam has increased the cross-sectional area of the tension chord slightly. To do so with the same material use, the tension chord has been moved closer to the base of the system. The Low Tension beam in a has further increased the size of its tension chord to respect the lower tensile stress limit. The tensile structural element bifurcates at either end to lend further support and the total material use is higher than for the two other design cases (V = 52.0%). It should be here be noted that a single compliance design case with V = 50% was chosen rather than creating two compliance beams with the volume fractions obtained by the stress-based design cases. Two designs could potentially have offered a more direct comparison. However, since the stress-based cases resulted in very similar material uses, it was deemed that compliance beams with 49.3% and 51.0% volume factions would exhibit negligible difference in the experimental results following post-processing, fabrication and the inevitable variations in the local concrete composition.The dmin = 5 cm (2") minimum length scale is fulfilled everywhere for all designs. However, both stress-based topologies in a have many grey elements in the structures' compressive regions. The stress-based optimizer was thus not able to achieve a crisp 0–1 solution for either design case. This might be because the required minimum feature size dmin is relatively large compared to the dimensions of the design domain and therefore forces the compressive struts to be highly over-engineered. With a 5 × 7.6 cm2 (2” × 3”) minimum feature size, a compressive strut can approximately handle 133.5 kN (30,000 lbs) of direct compression force, but only a total of 8.8 kN (2000 lbs) was applied to the system. To evaluate the effect of the minimum length scale on the amount of grey elements in the solution, the High Tension case was redesigned with smaller length scale requirements. gives the topologies obtained with dmin = 2.5 cm (1") and dmin = 1.25 cm (0.5") and clearly shows how the design solutions become increasingly crisp and complex as the minimum length scale decreases. The obtained solutions in a and b reveal that reducing the minimum allowable feature size mainly affects the topology in the compressive zones of the structure, whereas the upper tensile chord has a similar dimension in both design cases. Additionally, the design objective of minimizing the mass is improved when implicitly imposing smaller length scale constraints. The volumes of the designs in are reduced to V = 33.8% and V = 30.0% for (a) and (b), respectively. However, as the quality of the concrete could not be assured for feature sizes smaller than dmin = 5 cm (2"), the densities from the obtained solutions in a were rounded. A rounding rule of ρe > 0.5 was used and the as-built digital models are shown in b shows, two small internal voids were removed from the Low Tension design in additional post-processing step as it would not have been possible to remove the molds here during construction. Although not employed herein, this additional step could have been avoided if a minimum length scale control has been imposed on the void features e.g. as in [c were cast into molds that were CNC cut from Styrofoam. Milling was done with a ONSRUD 3-axis mill using a 1.25 cm (0.5") diameter bit, with MasterCam software for generating the toolpath from the digital files (b). The molds were lined with a generous layer of white petroleum jelly to act as a release agent. Lined molds were filled with a 35 MPa (5000 psi) Quikrete ready-mix concrete with a maximum aggregate size of 1.25 cm (0.5") diameter. Slump tests were administered following ASTM standards [], and yielded a slump of approximately 2.5 cm (1") for each batch of concrete. A total of four concrete batches were mixed. Cylinder samples with a 10 cm (4") diameter were taken for strength testing. It was not possible to cast three cylinders of each concrete batch for both compressive and tensile testing. Since the tensile capacity was expected to govern the failure of the concrete beams, the tensile property tests were given priority and conducted for all batches whereas the compressive tests were performed only for batches 1 and 3.All experimental testing was performed by deflection control on a Baldwin Universal Testing Machine (UTM). For the concrete beam experiments, a test rig of square steel HSS tubes delivered the deflections to the four load points by balancing a tube at its midpoint on cylindrical steel rods. The rig was designed to deflect > 0.25 mm (0.01") at a load of 220 kN (50,000 lbs). To simulate the support conditions used in the design, steel plates were adhered to the bottom of the concrete with a high-strength 25 MPa (3500 psi) epoxy. Four linear variable differential transducers (LVDTs) were affixed to the concrete specimens to record the deflections at the load points. shows a Compliance beam in the test rig. Although the design herein was only concerned with the elastic behavior, the beams were tested until failure to observe the behavior in the nonlinear range.Compressive cylinder tests were performed with extensometers so the Young's modulus of the concrete could be determined. The tensile tests were conducted using the Brazilian split-cylinder method [The material properties obtained from the cylinder tests are listed in . The Young's modulus was found to be approx. 5–10% lower than assumed in the design. Both the compressive and tensile strengths are higher than enforced in any of the stress-based design cases. The compressive strength is on average around 36% higher than assumed and the tensile strength averages at 12% and 50% higher than imposed for the High Tension and Low Tension designs, respectively.The experimental behaviors of all beams are plotted in . The plot gives the sum of deflections at all load points on the x-axis and the sum of the forces on the y-axis. The dashed line indicates the design load. As assumed for the design, the samples appear to behave elastically at the design load. The effect of the choice of design algorithm on the experimental behavior of the design can be observed by comparing the beams with as-built material volumes of around 51% (Compliance with V = 51.3% and High Tension V = 50.9%). It is seen that the Compliance samples are stiff at the design load and have negligible ductility prior to failure whereas the High Tension samples are generally soft and ductile. Interestingly, however, the test specimens of these two designs appear to have a nearly identical initial stiffnesses and the Compliance design seems to exhibit a stress-stiffening effect as the loading is increased. The tendency is also evident for one of the High Tension specimens and could either indicate collapse of internal pores in the compressive regions or a geometric nonlinear effect occurring as the load path is distorted.The influence of the tensile strength limit on the stress-based design cases can be examined by comparing the High Tension and Low Tension performances. The Low Tension design, with the more conservative tensile strength limit and higher material volume (as-built V = 56.3%), exhibits a more uniform behavior across tested specimens. Generally the experimental behavior of the Low Tension design is stiffer, stronger and less ductile than observed for High Tension.For all tested specimens, the initial failure was observed in the upper structural features. The Compliance specimens all failed in the center tension chord orthogonal to the flow of forces, suggesting a tensile failure. By contrast, the High Tension samples all failed along an angled path just outside of one of the interior point loads signifying a typical shear failure. As opposed to the other designs, the Low Tension specimens failed at different locations. Two beams failed in shear just outside one of the interior point loads and one failed in the upper tension chord. Interestingly, the difference in failure location did not have a significant effect on the maximum applied load level or the overall behavior. The typical beam failure modes are shown in This work has focused on the elastic design of topology-optimized concrete beams. The considered design cases have either aimed at maximizing the elastic structural stiffness (Compliance design case using Eq. ()) or at ensuring the structure remains in the elastic range at the design load (High and Low Tensions design cases using Eq. ()). An important finding of this work is thus the observation that all experimental specimens appear to behave elastically at the design load. The current work has thereby demonstrated that plain concrete structures can be designed with topology optimization, constructed and their behavior experimentally validated. This constitutes an essential step in enabling high performing free-form design of both RC phases for novel construction technologies. the results of the experimental investigations are summarized. a compares the performance of all tested beams in the linear range by plotting the experimental compliance. The compliance is evaluated at the design load, grouped by the design case and plotted against the as-built volume. A comparison of the Compliance and High Tension specimens, that occupy roughly the same material volume, reveals that the Compliance beams have a lower compliance and thus a higher structural stiffness. This was to be expected since the Compliance design case directly aims at creating a stiff design, where as the stress-based cases have no incentive to do so. The variation of the compliance between tested specimens is also significantly lower for the Compliance design compared to High Tension. This suggests that an increased robustness with regards to the structural stiffness is achieved when it is the objective of the design. The Low Tension design, with about 8% higher structural volume, has similar stiffness and stiffness variation to the Compliance design. Although not the objective of the design case, this confirms standard engineering design intuition, where using higher safety factors should result in designs being less sensitive to imperfections and construction errors.For comparison, the expected behaviors from the design algorithms are indicated as stars in a. These are plotted against the un-rounded material volumes and are generally found to predict higher compliance values than observed in the experiments. To evaluate the effect of the post-processing, elastic 3D finite element analyses have been performed using the as-built digital models (b) and the commercial FE software ABAQUS 2017. These numerical analyses use the material properties and loading conditions from the design. The as-built predicted behaviors are indicated with circles in a. By comparison of the un-rounded and as-built (post-processed) compliances it is evident that the post-processing has more significantly affected the stress-based design cases. The effect of rounding is negligible for the Compliance design. This trend was expected since more post-processing was performed on the High Tension and Low Tension designs. Both of the stress-based designs' un-rounded compliances had notable amounts grey elements which the SIMP penalization gives negligible stiffness. In a the experimentally obtained compliance for the Compliance design case is seen to fit relatively well with both un-rounded and the as-built expectations. For High Tension, the experimental compliance is overestimated by both the numerical models. The Low Tension design is also overestimated by the numerical results, however, the as-built prediction is close to the experimental average. As described above, the Young's modulus obtained from the cylinder tests was lower than what had been assumed for the design and cannot account for this discrepancy. To investigate this inconsistency further, gives the maximum principal stress distributions from the numerical analyses of the un-rounded and as-built beams at the design load. The un-rounded and post-processed stress distributions for the Compliance design (a–b) are reasonably similar. In both, the maximum stress is located in the tensile chord which correlates well with the observed experimental failures. The stress distribution in the Low Tension design (e–f) is generally seen to be reduced by the post-processing but the location of the maximum stress has not been altered. However, in f a small peak in the stress distribution is introduced on the exterior of the internal point load. As mentioned, two samples failed here as shown in c and one failed in the upper tensile chord, corresponding well to peak locations in the as-built stress distributions. Notably, the difference in failure location did not have an effect on the ultimate load.By contrast, the rounding is seen to have a significant effect on the location of the maximum stress in the High Tension design (c–d). Rounding has here moved the maximum principal stress from the top chord to a stress concentration just outside the interior point load, identical to the failure observed in all specimens. The stiffness of the High Tension design is clearly sensitive to the local composition of the concrete mix at this location that is believed to cause the large variation between specimens. The dramatic change of behavior suggests that heuristic post-processing steps should be limited as much as possible, since these can significantly alter the performance of an optimized design. This underlines the need for implementing construction and manufacturing consideration into topology optimization frameworks and thereby eliminate the need for post-processing.As all constructed beams were tested till failure, it is possible to discuss the effects of the different design cases in the nonlinear range. However, it should be remembered that nonlinear performance was not considered in the design. b gives the maximum load capacities observed during testing, grouped by the design case and plotted against the as-built volume. For the domain, loads and boundary conditions in this work, a Compliance beam specimen reached the overall highest applied load. The Compliance design case also have the highest averaged load capacity with 51.4% higher than the High Tension average. For the two stress-based cases a higher load capacity was expected for the Low Tension design since it has a higher volume. However, the elevation of the maximum load is seen to be disproportional to the volume increase with 43% by using only 10.8% more material. As seen in , all the tested Compliance beams have negligible ductility. The decrease of ductility with increasing stiffness has previously been documented for RC e.g. by Kuchma et al. []. A far more pronounced variation in the maximum load between samples is observed for this design case compared to the stress-based designs. The local concrete composition and negligible ductility can possibly explain the large variation in observed failure loads between the Compliance specimens in this work. The High Tension beams were opposite seen to exhibit significant ductility in most tests and the difference in observed load capacity is low. As the Low Tension beams have a small difference in failure loads and all specimens exhibit ductility, the agreement in failure loads can be an interesting artifact of imposing limits on the stress field.It is worth noting that since no limits are imposed on the structures' stress field in the Compliance design case, the used algorithm cannot guarantee that the structure remains in the elastic range at the design load. In linear design, a guarantee can only be warranted if conservative stress limits are included in the design problem formulation such as in the stress-based design cases herein. The cylinder tests showed () that all imposed stress limits in this work underestimated the used concrete's compressive and tensile strengths. However, this underestimation can be speculated to have resulted in the reduced maximum load capacity compared to the Compliance beams. As an example, the lower than actual stress limits imposed on the High Tension design forced the top chord closer to the support so that the chord could be thickened with a low material use. As the actual tensile strength of the concrete was higher than the imposed limit, the thickening of the chord might have been a less efficient material use than having the chord placed at the top of the domain. In this context it should be kept in mind that only local optimality is assured in continuum topology optimization. As a result, better performing globally optimum solutions may exist for all design cases. It is therefore possible that the Compliance design in this work is a local solution to the stress-constrained design problem (Eq. ()). The stress-constrained problem is known to introduce more nonlinearity to the design space than the compliance problem in Eq. (). The optimizer can therefore have had more difficulty in obtaining quality solutions for both the High Tension and Low Tension cases. For the structures in this work, the additional nonlinearity can have contributed to the large amounts of grey elements in the design solutions and hence a greater need for post-processing. Although the post-processing herein did not significantly alter the structural volume (50.0% vs 51.3% for Compliance, 49.3% vs 50.9% for High Tension and 52.0% vs 56.3% for Low Tension), it did alter the optimality of the obtained solution by introducing concentrations to the stress distributions (This paper has demonstrated that topology optimization can be used to design plain concrete structures and that the designs can be constructed and their behavior experimentally validated. This constitutes a first important step in enabling freeform design of both RC phases and thus efforts to leverage the possibilities afforded by emerging digital construction technologies. As such, a natural next research step is to include design of the reinforcing phase and conduct an experimental validation of the performance. Once the performance is validated, topology-optimized RC components can be widely used to improve performance and/or save construction material within the built environment.The focus of this work has been on the design of plain concrete structures with improved performance in the elastic range. Two design frameworks have been used; one aiming at creating a stiff structural design with a fixed amount of material and one aiming at creating a light weight structure in which the stress field is constrained. The comparison between the experimental performances of the different design frameworks suggests that the considered objective typically will have a small sensitivity to the local concrete composition. All other performance properties cannot be controlled in the design and have been seen to vary significantly between tested specimens in the same design case. It is worth emphasizing that the trends observed for these properties may not be extendable to all possible design domains. Within the stress-constrained design framework the robustness of the experimental performance has additionally been seen to be influenced by the safety factors associated with the material properties used in the design. In line with common engineering design practices the smallest experimentally observed variations in both the linear and nonlinear ranges were observed in the most conservative design case. However, since most civil construction components and structures have multiple performance requirements there is a need for including multiple considerations in the design formulation. This future research could e.g. look at constraining the structural stiffness while minimizing the material use under stress constraints.The stress-based design framework used in this work was not capable of achieving a 0–1 design that fulfills the minimum feature size requirement. Significant heuristic post-processing was needed for the design to be constructed. The post-processing was shown to have detrimental effects on the behavior of the experimental samples. This emphasizes the need for research and development of design algorithms that does not require modifications of the results prior to construction.Evaluation of the mechanical properties of powder metallurgy Ti-6Al-7Nb alloyTitanium and its alloys are common biomedical materials owing to their combination of mechanical properties, corrosion resistance and biocompatibility. Powder metallurgy (PM) techniques can be used to fabricate biomaterials with tailored properties because changing the processing parameters, such as the sintering temperature, products with different level of porosity and mechanical performances can be obtained. This study addresses the production of the biomedical Ti-6Al-7Nb alloy by means of the master alloy addition variant of the PM blending elemental approach. The sintering parameters investigated guarantee that the complete diffusion of the alloying elements and the homogenization of the microstructure is achieved. The sintering of the Ti-6Al-7Nb alloy induces a total shrinkage between 7.4% and 10.7% and the level of porosity decreases from 6.2% to 4.7% with the increment of the sintering temperature. Vickers hardness (280–300 HV30) and tensile properties (different combination of strength and elongation around 900 MPa and 3%) are achieved.Biomaterials are commonly classified as a function of their intrinsic nature as polymeric, ceramics/glasses and metallic biomaterials and, thus, employed to fabricate specific surgical, orthopaedics and dentistry products and prostheses. Specifically, polymeric-based materials are characterised by a high degree of flexibility which permits to tailor their property for particular applications. High compressive strength and wear resistance combined with inert behaviour and pleasing aesthetic appearance are the properties for which biomedical ceramics and glasses are renowned. Relative ease of fabrication as well as high strength and resistance to fracture are the main reasons for which metals continue to be used in biomedical applications (). Titanium is generally preferred to other metallic biomaterials due to the combination of properties (i.e. low density, relatively low Young modulus, superior biocompatibility and corrosion resistance) that can provide (). When it comes to the introduction of new orthopaedic materials, until recently the adaptation of existing materials was the mainstream approach taken (). Therefore, concerning titanium-based materials, elemental titanium and the most well-known Ti-6Al-4V alloy were the first to be introduced and used for biomedical applications. Nevertheless, because of the concerns about the effect of the dissolution of the chemical elements, especially the formation of vanadium ions, and the possible toxic effect () alternatives were proposed. In particular, the Ti-6Al-7Nb alloy was developed with the aim of replacing the Ti-6Al-4V alloy due to its potential cytotoxicity and adverse reaction with the body tissues. Ti-6Al-7Nb alloy has equivalent mechanical performances to the Ti-6Al-4V alloy but improved biocompatibility (). The Ti-6Al-7Nb alloy was developed primarily for the production of cementless anchored hip prosthesis stems and elastic deformable cup shells () and it was primarily produced by ingot metallurgy plus forging (). In recent years, a new class of titanium alloys, known as beta titanium alloys, targeting the reduction of the intrinsic stiffness of the material has also been developed by primarily adding biocompatible beta stabilisers such as zirconium and tantalum. A comprehensive description can be found in the literature (The processing of titanium and its alloys by means of powder metallurgy (PM) techniques is claimed to be a suitable way to reduce the fabrication cost of titanium products where the master alloy (MA) addition variant of the blending elemental approach has been identified has the cheapest way to obtain titanium alloys with the desired composition (). The production of the Ti-6Al-7Nb alloy by PM techniques has been done considering different methods like hot-press and injection moulding (). The aim of this work is to study the suitability of the production of the Ti-6Al-7Nb alloy by combining the MA approach and the cheapest PM route (i.e. press and sinter) and evaluate its tensile behaviour. In particular, the microstructural features, physical, chemical and mechanical properties achievable by changing the sintering temperature are studied and correlated with the processing parameters and among themselves.The starting materials bought for the development of the study are a hydride-dehydride (HDH) elemental titanium powder and a niobium:aluminium:titanium (Nb:Al:Ti) master alloy, both supplied by GfE Gesellschaft für Elektrometallurgie mbH. The Nb:Al:Ti master alloy was in the form of granules (maximum particle size < 800 µm) and had a ratio between the elements of 60:35:5 (percentages in weight). Because, as delivered, the master alloy was not suitable for its mixing with elemental titanium, the particle size was reduced by high energy ball milling and the ratio of the alloying elements adjusted to the desired composition by adding an elemental aluminium spherical powder bought from Sulzer Metco Ltd. The detailed route employed to obtain the Ti-6Al-7Nb powder is available in the literature (Basic characteristics of the produced Ti-6Al-7Nb powder were analysed and they included particle size, contents of interstitial elements and morphology/composition. Specifically, the particle size distribution and, hence, the maximum particle size (Dmax) was determined by means of a laser beam Mastersizer 2000 particle size analyser. Concerning the interstitials, oxygen and nitrogen contents were measured following the specifications of the ASTM: E1409 standard using a LECO TC500 equipment. The morphology/composition of the powder was checked using a Philips XL–30 SEM in backscattered mode.The consolidation of the powder was done by means of a uniaxial press combined with a floating die whose walls were lubricated using zinc stearate. It is worth mentioning that, intentionally, no lubricant was added directly to the powder in order to prevent or, at least, limit as much as possible the contamination of the powder. Dogbones samples with standardised dimensions (ASTM: B925) for tensile tests were cold uniaxial pressed setting the compaction pressure to 700 MPa. The green components were sintered in a high vacuum tubular furnace (approximately 10-5 mbar) while laid on zirconia balls once again to prevent/limit interaction with the sintering substrate. The processing parameters to sinter the components were: sintering temperature range between 1250 °C and 1350 °C, dwell time at maximum temperature of 120 min and heating/cooling rates of 5 °C/min.The metallographic route used to prepare the samples for the microstructural analysis included grinding with SiC papers of different granulometry, polishing with an alumina-based solution (1 μm) and fine polishing with silica gel. The microconstituents were revealed by means of chemical etching using Kroll reactant (3 ml HF+6 ml HNO3+100 ml H2O). Microstructural analysis was carried out on an Olympus GX71 light optical microscope whilst the homogeneous distribution of the alloying elements and the fractographic study were done on the Philips XL-30 SEM.The variation of the dimensions experienced by the samples during the sintering step was considered and estimated because they are important industrial factors to take into account when designing a new component to be produced by means of PM techniques. The values of the density of the sintered samples was measured by means of the water displacement method. The total residual porosity (Pres) was calculated as a difference between the density measured and the nominal value of the density of the Ti-6Al-7Nb alloy, that is 4.52 g/cm3 (It is well known that the amount of interstitials dissolved greatly influence the mechanical properties of titanium (), therefore, oxygen and nitrogen contents of the sintered samples were measured using the same equipments and conditions previously specified for the starting powder.Regarding to the mechanical characterisation, Vickers hardness measurements were done on the cross section of the samples by means of a Wilson Wolpert Universal Hardness DIGI-TESTOR 930 tester performing HV30 measurements. Ultimate tensile strength (UTS) and elongation at fracture values were obtained using a MicroTest universal machine equipped with a load cell of 50kN and a Hottinger Baldwin Messtechnik, type DD1 extensometer. Tensile tests were performed following the ASTM: E8 standard applying a crosshead speed of 1 mm/min. In order to limit the experimental error, the (dynamics) elastic modulus was determined using the equation v=E/ρ which correlates the Young modulus (E) with the speed of sound in the material (ν) and the density (ρ). In particular, the speed of sound was measured by means of an ultrasonic transducer (Grindosonic) having a frequency range in between 20 Hz and 100 kHz and an accuracy better than 0.005%.Some basic characteristics (i.e. particle size distribution and contents of interstitials) of the powders used in this study are shown in whilst the morphology/composition can be seen in the micrographs shown in From the particle size distribution data shown in , it can be noticed that the produced Ti-6Al-7Nb powder is characterised by a D90 parameter of 81.94 µm and, thus, the powder can be classified as a 170 mesh powder (D<90 µm). Oxygen and nitrogen contents are slightly lower than 0.40 wt.% and 0.02 wt.%, respectively. In comparison to the typical interstitials contents of the wrought Ti-6Al-7Nb alloy (ASTM: F1295 or IMI 367) (), on the one side the produced Ti-6Al-7Nb powder has higher oxygen content and this will affect the mechanical behaviour of the sintered components. On the other side, the amount of nitrogen is lower than the limit specified for the wrought material.a) confirms that the Ti-6Al-7Nb powder is actually characterised by an irregular morphology due to the fact that it was produced by means of the HDH comminution process. The irregular morphology is paramount because the powder is consolidated by means of cold uniaxial pressing and, thus, undergoes particles rearrangement as well as elastic and plastic deformation. This results into mechanical interlocking between the powder particles (i. e. green strength) () and guarantees the handling of the shaped components. From b) it can be seen that the three powders used to produce the Ti-6Al-7Nb alloy could be clearly identified using the BSE mode due to the different atomic number of the elements. From the micrograph shown in b), it can also be seen that the shape of the elemental aluminium powder added to adjust the composition is not perfectly spherical but slightly deformed due to the fact that the powder was milled altogether with the Nb:Al:Ti master alloy. Moreover, the particle size of the Nb:Al:Ti master alloy is approximately 50 µm, which means that was effectively reduced by the high energy ball milling step, and its morphology is mainly angular.The evolution of the microstructure and porosity with the sintering temperature was studied by analysing the microstructural features at the optical microscope. Representative examples of the microstructure of the sintered Ti-6Al-7Nb alloy are shown in where it can be seen that the microconstituents that compose the microstructure of the sintered Ti-6Al-7Nb component are elongated α grains and α+β lamellae distributed throughout the microstructure. This is the typical lamellar microstructure of α+β titanium alloys slow cooled from a temperature above their β transus.Generally, there is a coarsening of the microconstituents with the increment of the sintering temperature due to the higher thermal energy available in the system for grain growth, resulting in an increase in grain size of the sintered Ti-6Al-7Nb alloy. Specifically, the size of the α grains becomes larger as the higher sintering temperature leads to the formation of coarser prior β grains during sintering, β grains from which α grains nucleate (134±17, 147±14 and 165±20 for the materials sintered at 1250 °C, 1300 °C and 1350 °C, respectively). Simultaneously, there is an increment in size of the α+β lamellae (11±3, 17±10 and 20±8 for he materials sintered at 1250 °C, 1300 °C and 1350 °C, respectively). From , the other feature characterising the microstructure of the sintered Ti-6Al-7Nb alloy is the residual porosity and it can be seen that it is closed and isolated porosity. The total volume percentage of residual porosity decreases with the increment of the sintering temperature. Besides, the pores are mainly spherical, even though some relatively large elongated pores are still present. Furthermore, the average pore size increases with the processing temperature. The presence of irregular pores and the increment of the pore size is because during the second stage of sintering, after that the interparticle boundaries had disappeared, the pores tend to coalesce reducing their percentage but increasing the size of the remaining pores. Summarising, the prior β grain size increases and the volumetric percentage decreases with the increment of the sintering temperature.Although the residual porosity could affect negatively the mechanical response of the sintered Ti-6Al-7Nb alloy, these pores are actually beneficial for osteoconduction and the ability to form apatite () where the optimal pore diameter distribution lies between 150 μm and 500 μm (). The microstructure of the sintered samples was also analysed at the SEM in order to check the homogeneity of the materials, which is paramount because the alloying elements are added by means of a master alloy and the sintering temperature has to be high enough to guarantee their diffusion. A possible presence of undissolved aluminium and niobium will affect considerably the biological response () such as inhibition of apatite formation and/or formation of debris leading to loosening of the implants due to osteolysis. Because no significant difference were found during this analysis, the micrograph of the samples sintered at 1300 °C is shown as representative example in d). The backscattered mode of the SEM permits to differentiate the elements present in a materials as a function of their atomic number which, therefore, will appear in a micrograph with different brightness. From the micrographs shown in d) it can be noticed that the microstructure of the Ti-6Al-7Nb components is composed of a grey phase, which is α, and a bright phase (i.e. β phase) due to the presence of the niobium as β stabiliser. Furthermore, the distribution of these two phases is homogeneous throughout the whole microstructure and not undissolved master alloy particles could be found. This indicates that, actually, with the sintering temperatures employed the complete diffusion and homogeneous distribution of the alloying elements is reached. From the EDS analysis carried out on the samples, it was found that the mean atomic percentage of aluminium is 10.2 at.% whilst that of niobium is 3.6 at.%, and titanium is the base. Moreover, it can be stated that the pressed and sintered components respect the limits of the alloying elements specified for the ASTM: F1295 alloy () and are, therefore, comparable to the wrought material in terms of chemical composition. On average, the chemical composition of the α-Ti and β-Ti phases of the sintered Ti-6Al-7Nb components is 87.7Ti-10.4Al-1.9 Nb and 81.3Ti-5.4Al-13.3 Nb in atomic percentage, respectively. The α-Ti and β-Ti phases are, respectively, Al and Nb-rich as aluminium and niobium are alpha and beta stabilisers. These results are in agreement with the Ti-Nb binary phase diagram which indicates that the maximum solubility of niobium in α-Ti is 2.2±0.5 at.% (After the shaping of the powder, the components are characterised by a green density of approximately 86.0±1.2%. The variation of the physical properties (i.e. shrinkage, density and residual porosity) of the sintered Ti-6Al-7Nb alloy with the sintering temperature are shown in The sintering of the green components induces a reduction of their dimension and, therefore, the samples undergo shrinkage (a). In particular, the contraction of the dimensions (length, width and thickness) increases with the increment of the processing temperature ranging from 2% to 4% as a function of the sintering temperature selected. Moreover, it can be noticed that the shrinkage of the dimensions of the components is quite homogeneous with the exception of the variation of the width which is somewhat lower. The absolute values of these variations are useful when design a new components. In particular, from the results shown in can be estimated that the dimensions of the prosthesis produced by PM should be 10% bigger than the required because the component will shrink during its sintering. From b) it can be seen that the density of the Ti-6Al7Nb alloy increases with the increment of the processing temperature and, conversely, the total volumetric percentage of residual porosity decreases. The value of the corresponding relative density (i.e. 94–96%) are common values for titanium alloys obtained by pressing and sintering ( shows the results of the chemical analysis carried out on sintered Ti-6Al-7Nb components where it can be noticed that there is some oxygen and nitrogen pick-up with respect to the initial powder () and the nitrogen pick-up is somewhat more pronounced. Nonetheless, the oxygen content is approximately 0.40 wt.% whereas that of nitrogen is as maximum 0.035 wt.%. The interstitials pick-up can be attributed to the handling of the powder and the air trapped into the green samples and, therefore, the contaminants adsorbed on the surface or trapped in the green body diffuse inside the material during the sintering step. It is expected that the total amount of oxygen dissolved inside the titanium lattice (0.4%) shifts the actual β transus of the Ti-6Al-7Nb alloy by about 20 °C and therefore influences the initial nucleation of the α grains from the prior β grains with respect to the wrought Ti-6Al-7Nb alloy. In the study, as the sintered materials have comparable oxygen content (), the coarsening of the microconstituents is dictated by the sintering temperature rather than by the oxygen content.The results of the Vickers hardness measurements of the sintered Ti-6Al-7Nb alloys are shown in where, as for the relative density, the hardness of the Ti-6Al-7Nb components increases with the processing temperature. This is mainly due to the reduction of the residual porosity present in the microstructure. However, it is well known that the higher the amount of interstitials dissolved into titanium the higher its hardness (). Thus, there is also a contribution from the slight differences in chemical composition because the samples sintered at 1300 °C have somewhat higher oxygen than those processed at 1250 °C. The values of hardness obtained for the sintered Ti-6Al-7Nb components are lower than that found by Semlitsch et al. (350 HV) in the wrought alloy () but comparable to the value specified for IMI 367 medical devices (290 HV) (From the tensile stress-strain curves presented in a), it can be seen that the Ti-6Al-7Nb sintered components show similar mechanical behaviour independently of the sintering temperature employed and, thus, they are characterised by similar elastic modulus. Furthermore, the sintered components undergo an elastic deformation up to approximately 700 MPa and then start to deform plastically.The ultimate tensile strength on the sintered components (b) does not seem to be greatly influenced by the sintering temperature because the strength is about 900±14 MPa (measured in, at least, three samples for each condition) for all the sintering temperatures studied. This seems to indicate that the positive effect of the reduction of the residual porosity and of the strengthening effect of the interstitials is balanced by the grain growth and the coarsening of the residual porosity induced by the higher processing temperature. As indicated in b), the strength of the sintered Ti-6Al-7Nb components is similar to that of the wrought (ASTM: F1295 or IMI 367) alloy, that is 900 MPa, and higher than that obtained by Itoh et al. () (approximately 850 MPa) when processing a spherical elemental titanium powder mixed with an Al:Nb master alloy by metal injection moulding and using a similar sintering temperature range. The sintered Ti-6Al-7Nb components have comparable strength to the wrought alloy even though of the presence of the residual porosity. This is because of the high amount of oxygen of the sintered alloy with respect to the wrought material. The elongation at fracture (c) of the alloy slightly decreases with the sintering temperature although the samples processed at 1300 °C (i.e. 2.7±0.5%) have somewhat lower strain than those sintered at 1350 °C (i.e. 3.1±0.9%) and 1250 °C (i.e. 3.8±1.0%). This behaviour is due to the higher oxygen content found in the components sintered at 1300 °C () in comparison to the other sintering conditions because oxygen decreases the ductility of titanium (). The strain of the sintered Ti-6Al-7Nb components is lower with respect to the wrought alloy (10%). This is due to the presence of the residual pores which act as stress concentration sites and to the higher oxygen content of the sintered Ti-6Al-7Nb components in comparison to the wrought Ti-6Al-7Nb alloy. Nonetheless, similar results in terms of strain (1–3%) were obtained when casting the Ti-6Al-7Nb alloy in a silica-based mould () indicate that the sintered Ti-6Al-7Nb alloy failed in a ductile way via the mechanism of microvoids coalescence as the fracture surfaces are composed by dimples. This is in agreement with the stress-strain curves shown in a). From the shape of dimples found in the fracture surface, dimples which are either conical or elongated, it is inferred that they were generated from the residual porosity leading to the pore-assisted fracture of the sintered alloys. During the analysis, no cleavage zones could be found in the fracture surfaces. The shape of the dimples becomes more spherical/conical or less elongated and their size slightly bigger with the increment of the sintering temperature as the residual porosity was found to decrease in amount and growth in size. As per the fractographic analysis, the elongation at fracture should continuously increase with the reduction of the residual porosity. Nevertheless, the elongation at fracture is negatively affected by the slight increase in oxygen content as discussed earlier.The study of the mechanical properties of the sintered Ti-6Al-7Nb alloys via quasi-static tensile tests showed that the strength and the fracture mode are similar to those of the wrought Ti-6Al-7Nb alloy but affected by the presence of the residual porosity. Dynamic properties such as fatigue strength of the sintered Ti-6Al-7Nb alloys, which are important for some structural biomedical applications, will also be lowered by the presence of the residual porosity.As indicated in the experimental procedure, the dynamic elastic modulus was considered and measured by means of an ultrasonic transducer. The dynamic elastic modulus measurements carried out on the sintered Ti-6Al-7Nb tensile samples results to be quite similar for the three sintering temperatures. The individual values obtained are in the order of 100 MPa giving a mean value of 101±5 GPa which is very similar to the typical value of 105 GPa of wrought Ti-6Al-7Nb alloy (). This result indicates that there is not a great influence from the level of relative density obtained and this is because, as shown in , with the processing parameters employed in this study, the pore structure is mainly composed by relatively small, spherical and isolated pores.From this study about the production and evaluation of the mechanical properties of powder metallurgy Ti-6Al-7Nb alloy obtained means of the press and sinter route, the following conclusions can be drawn:Irregular hydride-dehydride powders can successfully be shaped into pressed components which can be handled without fracture;The sintering temperatures studied permitted to obtain fully homogeneous microstructures that is paramount as the presence of undissolved particles would affect the biological response of the material;The total shrinkage increases from 7.4% to 10.7% and the porosity levels decreases from 6.2% to 4.7% with the increment of the temperature. The pores left after sintering would be beneficial to promote bone osteointegration;The mechanical behaviour of the sintered alloys is mainly comparable to that of the wrought alloy as Vickers hardness values of 280–300 HV30, elastic modulus of 101 GPa, ultimate tensile strength around 900 MPa and ductile fracture are achieved. Nevertheless, the elongation at fracture (3%) is affected by the presence of the residual porosity and the high oxygen content of the sintered materials;The powder metallurgy master alloy addition approach can successfully be used to process wrought-equivalent titanium biomaterials and therefore is a promising alternative for the manufacturing of non-critical and structural biomedical applications.Characterization of free-standing nanocrystalline Ni55.2Mn24.7Ga19.9Gd0.2 high temperature shape memory thin filmNanocrystalline Ni55.2Mn24.7Ga19.9Gd0.2 high temperature shape memory thin films had been prepared by the DC magnetron sputtering followed by rapid thermal annealing (RTA). Surface morphology, crystal structure, martensitic transformation behavior and shape memory effect (SME) were systematically investigated. The results showed that as-deposited film displayed a coexistence of amorphous and nanocrystal, while the annealed film was a single phase of seven-layered modulated martensite structure with the grain size about 200–500 nm at room temperature. The annealed film showed one step reversible martensitic transformation with martensitic transformation start temperature of 283 °C. Adjacent lamellar variants exhibited a (202) type Ι twin relationship and well coherent interlamellar interfaces. The annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin film displayed a stable SME above 200 °C, which could be used in high temperature field as micro-electro-mechanical-system (MEMS) devices.Besides the unique SME (shape memory effect) and superelasticity, small volume, high work output, rapid response frequency and batch fabrication of shape memory films make it attractive to become promising candidate materials for micro-actuators and micro-sensors in MEMS With giant magnetic-field-induced strain up to 10% Ni–Mn–Ga–Gd thin films with a thickness of about 5 μm were deposited onto (111)-Si substrate by DC magnetron sputtering technique at room temperature. The nominal composition of the target was Ni56Mn25Ga18.8Gd0.2 (at. %). The distance between substrate and target was fixed at 75 mm. The base pressure and working pressure were 9.0 × 10−5 Pa and 0.15 Pa, respectively. The sputtering process lasted for 2 h with sputtering power of 200 W. After sputtering, Ni–Mn–Ga–Gd thin films were mechanically removed from the substrate and then annealed at 650 °C for 60s in a rapid annealed furnace with 30 °C/s heating rate under a vacuum condition of 2.2 × 10−3 Pa.The in-plane views of Ni–Mn–Ga–Gd thin films were observed by scanning electron microscope (SEM, Quanta 200FEG). The composition of the as-deposited thin films was carefully evaluated to be Ni55.2Mn24.7Ga19.9Gd0.2 (at. %) by energy dispersive spectroscopy. Phase composition of Ni55.2Mn24.7Ga19.9Gd0.2 thin films was characterized by X-ray diffractometer with Cu Kα radiation. The phase transformation temperatures of the annealed thin films were measured using a differential scanning calorimeter (DSC) with a swap rate of 20 °C/min. Microstructure of the annealed thin films was observed by transmission electron microscopy (TEM, Tecnai G2 F30, 300 kV). Thin-foil specimens for TEM observation were prepared by twin-jet electro-polished with the solution of 30% HNO3 by volume in CH3OH at around −20 °C. Shape memory behaviors of Ni55.2Mn24.7Ga18.8Gd0.2 thin films were observed on a heating platform. shows the in-plane views of the as-deposited and annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin films. It is clear from (a) that the as-deposited thin film consists of island-like particles and the boundaries between particles are clearly visible. After annealing at 650 °C, the surface morphology is changed. The annealed film is composed of different orientated twin lamellas as shown in (b), indicating the annealed film is the state of martensite at room temperature. In addition, the grain size of the annealed films is ranged from 200 to 500 nm, which is about two orders of magnitude smaller than that of Ni–Mn–Ga bulk materials The XRD patterns of both as-deposited and annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin films were recorded as shown in . The as-deposited thin film shows a single broad diffraction peak at 2θ = 43.2°, which is also observed by A. Annadurai et al. . The selected area electron diffraction (SAED) result in the inset of shows an amorphous halo and some polycrystalline diffraction rings, indicating a coexistence of amorphous and nanocrystalline grains. The bright-field (BF) image shows that the nanocrystal is distributed randomly in the amorphous matrix for the as-deposited films. The annealed film shows three well defined diffraction peaks split from the broad diffraction peak in the as-deposited thin film, which means the Ni55.2Mn24.7Ga19.9Gd0.2 films crystallize completely after annealed at 650 °C for 60s. Base on the splitting of the diffraction peak at 2Theta = 43.2°, We can only suppose the formation of seven-layered modulated (7M) or five-layered modulated (5M) martensite in the annealed films. At the same time, combined with the TEM result on (d), the formation of 7M martensite can be confirmed. The three typical peaks at 43.0° 44.3° and 45.8° can be indexed as the plane of (220), (202) and (022) of 7M orthorhombic martensitic structure, respectively. Compared with the XRD pattern of 7M martensite in bulk Ni–Mn–Ga alloy It is known that the solubility of Gd in Ni–Mn–Ga bulk alloys is 0.1 at%, otherwise a Gd-rich brittle phase will be precipitated above the solubility limit, which is harmful to ductility and SME shows the evolution of crystal structure obtained from XRD patterns of annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin films as a function of temperature. In order to observe fine change in XRD spectra with temperature, log scale for XRD intensity was adopted as y-axis for (a) that the intensity of the diffraction peaks of 7M martensite become weaker and the (202) and (044) austenite diffraction peaks emerge when heating from room temperature to 220 °C, indicating the reverse martensitic transformation had started. When the temperature is further increased to 240 °C, the intensity of 7M martensite diffraction peaks continually reduces; while the peaks of austensite peaks display an opposite tendency. When the temperature is heated up to 260 °C, the diffraction peaks of 7M martensite are completely disappeared and only austensite peaks are observed, which means the reverse martensitic transformation finished. Compared with (a), the change of diffraction peaks for martensite and austensite is inverse as shown in (b) during cooling from high temperature to room temperature. When cooling from 260 °C to 240 °C, the martensite diffraction peak of (220) emerges, which indicates the martensitic transformation had started. With decreasing the temperature, the intensity of austensite diffraction peaks reduces, while the intensity of 7M martensite increases, indicating the phase transformation is under progress. When cooling to 200 °C, austensite diffraction peaks are not observed, which means the phase transformation had finished. All diffraction peaks achieve reversible change during one thermal cycling, which means no Gd-rich phase is observed in the Ni55.2Mn24.7Ga19.9Gd0.2 thin film. The increase of Gd solubility in the films could be attributed to the non-equilibrium process of magnetron sputtering which will be beneficial to the mechanical properties and SME. The lattice parameters of 7M martensite and austensite were determined to be a = 0.6220 nm, b = 0.5679 nm, c = 0.5459 nm and a = 0.5827 nm, respectively. shows the DSC curves of free-standing Ni55.2Mn24.7Ga19.9Gd0.2 thin films annealed at 650 °C for 60 s. It is obvious that an exothermic peak and an endothermic peak occur upon cooling and heating for the annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin films. That is the typical characteristic of one-step thermoelastic martenstic transformation, which is also observed in the bulk Ni–Mn–Ga–Gd alloy with similar composition shows TEM images and corresponding selected area electron diffraction (SAED) patterns of the annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin film. It can be found from the BF image shown in (a) that two parallel coarse lamellas with the width of 20–40 nm extending through the whole grain. The SAED from area A in (a) collected in the [11¯1] direction reveals the adjacent lamellas is a (202) type-Ι twin relationship as shown in (b). The twin boundary presents a typical self-accommodated morphology which means a high thermal stability according to previous reports (c) which is the enlarged image of area A in (c) displays that six extra diffraction spots are averagely distributed between two main spots along [110] direction as shown in (d). It is the characteristic diffraction pattern for 7M martensite structure, which is in consistent with the XRD results shown in . Recently, S. Kaufmann proposed that 7M modulated martensite can be regarded as a nanotwinned (52¯) sequence stacked structure composed from the non-modulated unit cells SME of the annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin film was investigated on a heating platform as shown in . An initially straight film was mechanically curled at room temperature. Then the film was placed on a heating platform. When heating up to 200 °C, the curled film begins to spread toward the original shape. Shape recovery process continues as the temperature increases. At about 280 °C, the thin film spreads completely and returns its original shape again. It is clarified that the annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin film possesses good SME. It should be noted that there is no any change about the above phenomenon after 500 thermal cycles, which means the Ni55.2Mn24.7Ga19.9Gd0.2 thin film has good thermal stability.A free-standing Ni55.2Mn24.7Ga19.9Gd0.2 thin film was successfully deposited by DC magnetron sputtering deposition. After rapid thermal annealing, seven-layered modulated martensite structure was obtained in the annealed thin film at room temperature.The observation of TEM confirmed the 7M martensite variants were (202) Ι type twin relationship with clear and straight intervariant boundaries.Stable SME was observed in the annealed Ni55.2Mn24.7Ga19.9Gd0.2 thin film with martensitic transformation start temperature of 238 °C, indicating Ni–Mn–Ga–Gd thin films is a potential candidate for MEMS devices in the high temperature field.A-type magmatism in the sierras of Maz and Espinal: A new record of Rodinia break-up in the Western Sierras Pampeanas of ArgentinaTwo orthogneisses have been recognized in the sierras of Espinal and Maz (Western Sierras Pampeanas, NW Argentina) that were emplaced within a Grenvillian metasedimentary sequence. Microcline, plagioclase and quartz are the main rock-forming minerals, with accessory zircon, apatite-(CaF), magnetite, biotite (Fe/(Fe + Mg) = 0.88–0.91), ferropargasite (Fetotal/(Fetotal

+ Mg) = 0.88–0.89), titanite (with up to 1.61 wt% Y2O3) and an REE-rich epidote. REE-poor epidote and zoned garnet (Ca and Fe3+-rich) are metamorphic minerals, while muscovite, carbonates and chlorite are secondary phases. Texture is mylonitic. Two representative samples are classified as granite (from Sierra de Espinal) and granodiorite/tonalite (from Sierra de Maz) on the grounds of immobile trace elements. Some trace element contents are rather high (Zr: 603 and 891 ppm, Y: 44 and 76 ppm, 10,000 × Ga/Al: 2.39–3.89) and indicate an affiliation with A-type granites (more specifically, the A2 group). Both samples plot in the field of within-plate granites according to their Y and Nb contents.Concordant crystallization ages (zircon U–Pb SHRIMP) are 842 ± 5 and 846 ± 6 Ma, respectively. 87Sr/86Sri (845) ratios are 0.70681 and 0.70666; ɛNdi (845) values are −1.5 and +0.3 and depleted-mantle Nd model ages (2TDM*) are 1.59 and 1.45 Ga, respectively. These values indicate the involvement of an isotopically evolved source. 2TDM* values are compatible with the presence of inherited zircon crystals of up to 1480 Ma in one of the rocks, thus implying that magmas incorporated material from Mesoproterozoic continental source. This is also indicated by the relatively high contents of Y, Ga, Nb and Ce compared to magmas derived from sources similar to those of oceanic-island basalts.These orthogneisses represent a period of extension at ca. 845 Ma affecting the Western Sierras Pampeanas continental crust that was already consolidated after the Grenvillian orogeny (1.2–1.0 Ga). They are thus a record of the early stages of Rodinia break-up. Metamorphic conditions during the subsequent Famatinian orogenic cycle (ca. 420 Ma, SHRIMP U-Pb on zircon) attained 7.7 ± 1.2 kbar and 664 ± 70 °C.The Sierras Pampeanas in northwestern Argentina constitute large exposures of pre-Mesozoic crystalline basement in the foreland of the Central Andes (). They record a complex tectonomagmatic history from the Mesoproterozoic to the Late Paleozoic that has not yet been completely deciphered. In the Western Sierras Pampeanas evidence for a reworked Grenville-age basement was firmly demonstrated by . This basement has since been considered the counterpart of the Grenville orogen along the southern Appalachian margin of Laurentia, which drifted away in the late Neoproterozoic to early Paleozoic to finally dock against the proto-Andean margin of Gondwana in the Ordovician. Whether this process involved an allochthonous exotic terrane, i.e., the Precordillera terrane hypothesis (for a review see ), or para-authoctonous translation along the proto-Andean margin of Gondwana (e.g., ), remains a matter of dispute. However all authors agree that the Western Sierras Pampeanas Grenville-age terranes were contiguous to Laurentia by the end of Rodinia amalgamation at ca. 1.0 Ga. Moreover raised the hypothesis that, at the onset of the Grenvillian orogeny, the Western Sierras Pampeanas Grenvillian terranes were part of a larger continental mass that embraced other Meso- to Paleoproterozoic outcrops such as the Arequipa block in southern Peru and northern Chile. This view opens new ways to interpret the Proterozoic history of southern South America (Rodinia is the name given to a hypothetical supercontinent that comprised almost all continental masses on Earth during the late Mesoproterozoic. Geological evidence for the existence and evolution of such supercontinent has been growing since the early 1990s (e.g., for a review), but consensus is still lacking on issues such as the number of participating cratons, their relative positions and the chronology of the assembly and subsequent break-up of Rodinia. Rodinia break-up and dispersal began around 900 Ma ago or even earlier (e.g., ), but evidence of widespread rifting associated with mantle plumes occurred much later, spanning the time interval between 825 and 740 Ma (Evidence for Rodinia break-up in the Western Sierras Pampeanas was first recognized in the Sierra de Pie de Palo (A). Here A-type orthogneisses hosted by reworked Grenvillian basement yielded a zircon U–Pb SHRIMP age of ca. 774 Ma. Protoliths were interpreted as resulting from an anorogenic magmatic event during early rifting of Rodinia (This contribution deals with a newly recognized anorogenic magmatic event at ca. 845 Ma in the sierras of Maz and Espinal (A) which records a still earlier event of Rodinia break-up. It thus adds to understanding of the Rodina break-up process in this part of Western Gondwana both in time and paleogeography.. Basement outcrops in the area, including those of the adjacent Sierra de Ramaditas and Villa Castelli massif, consist of metamorphic rocks with sedimentary and igneous protoliths intruded by a Lower Ordovician suite of metaluminous and peraluminous granites that occurs east of the sierras, near Villa Castelli (). The basement outcrops are covered by Late and post-Paleozoic sedimentary rocks in angular unconformity. Westward high-angle thrusting during the Andean orogeny led to superposition of the basement blocks over the sedimentary cover (In the basement of the sierras of Maz and Espinal three domains separated by first order shear zones and faults (B) were distinguished on the basis of field, geochronology and isotope composition evidence (). The Eastern Domain, consisting for the most part of high-grade rocks, i.e., garnet-sillimanite migmatitic gneisses with subordinate marbles and amphibolites, is younger than 1.0 Ga. Metamorphism took place during the Ordovician-Silurian Famatinian orogeny at ca. 440 Ma (see also ). The Central Domain (also known as the Maz terrane) consists of medium-grade (kyanite-sillimanite-garnet-staurolite schists, quartzites, amphibolites and marbles) to high-grade intermediate-to-ultrabasic meta-igneous rocks and metasedimentary rocks that underwent a Grenvillian-age orogeny starting at ca. 1.2 Ga (). Massif-type anorthosites of ca. 1070 Ma are restricted to the Maz terrane. Anorthosites also show evidence for Famatinian metamorphic rejuvenation (431 ± 40 Ma) throughout the Maz terrane (). Moreover, metamorphic and geochronological discontinuities within the Maz terrane suggest that it is in fact composed of a number of slivers separated by shear zones of unknown age, probably Famatinian. The Western Domain consists again of metasedimentary rocks younger than ca. 1.0 Ga that underwent Famatinian metamorphism. One sequence of rocks composed of thick marble beds, calcic semipelitic schists and quartzites is probably equivalent to the late Neoproterozoic Difunta Correa metasedimentary sequence of the Sierra de Pie de Palo, and to isotopically equivalent rocks of the Sierra de Umango (). Most rocks within this domain are low-grade but high-grade rocks are locally found. A recently described ca. 0.57 Ga alkaline syenite–carbonatite complex () occurs in the eastern margin of the Sierra of Maz.Two orthogneisses have been found that have provided almost the same crystallization age of ca. 845 Ma (see below). Both are foliated sheeted bodies concordant with the external foliation and bedding. Field evidence suggests that the protoliths were intrusive and not tectonically emplaced. The first, in the Sierra of Maz (), is a ca. 100 m thick body of leucocratic mylonitic augen-gneiss with streaks of mafic minerals and concordant stretched pegmatites; the fabric is S = L. It is hosted by whitish quartzites, sillimanite-garnet gneisses and garnet amphibolites that are assigned on the basis of Nd model ages () to the Western Domain referred to above. This domain underwent Famatinian metamorphism only. The second, in the Sierra del Espinal (B), is a mylonitic augen-gneiss hosted by a sequence of kyanite-staurolite-garnet schists, amphibolites, marbles and quartzites belonging to the Maz terrane (). The extent of this body is unknown, as only a section some 20 m thick is visible along one creek. This sequence underwent medium-grade Grenvillian metamorphism and a low-grade rejuvenation attributed here to the Famatinian orogeny (see below).Two samples were collected that are representative of the two orthogneisses: MAZ-6037 was taken from an outcrop along the Maz Creek (29°11′20″W to 68°28′48″S). ESP-7066 was collected on the western slopes of the Sierra del Espinal, close to Puesto Villalba (29°05′23″W to 68°31′40″S) (Electron-microprobe analyses were performed on sample MAZ-6037 and on a host amphibolite (MAZ-12046), the latter for estimation of metamorphic conditions, at the Complutense University, Madrid (Whole-rock powders of ESP-7066 and of a further sample of the MAZ orthogneiss (MAZ-12040) were analysed by ActLabs (Canada) for major elements (ICP) and trace elements (ICP-MS) (4-Lithoresearch code) (Rb–Sr and Sm–Nd isotope determinations were carried out at the Geochronology and Isotope Geochemistry Center of the Complutense University (Madrid, Spain) on an automated multicollector VG® SECTOR 54 mass spectrometer. Analytical uncertainties are estimated to be 0.01% for 87Sr/86Sr, 0.006% for 143Nd/144Nd, 1% for 87Rb/86Sr, and 0.1% for 147Sm/144Nd. Replicate analyses of the NBS-987 Sr-isotope standard yielded an average 87Sr/86Sr ratio of 0.710227 ± 0.00004 (n

= 10) and La Jolla Nd isotope standard yielded an average 143Nd/144Nd of 0.511844 ± 0.00002 (n

= 10). Errors are quoted throughout as two standard deviations from measured or calculated values (U–Th–Pb zircon dating was performed on the two samples at the Research School of Earth Sciences, The Australian National University, Canberra, Australia, using SHRIMP RG (MAZ-6037) and SHRIMP II (ESP-7066). Separated zircons were mounted in epoxy resin together with chips of the FC1 Duluth Gabbro reference zircon. Reflected and transmitted light photomicrographs and cathodo-luminescence (CL) SEM images were used to decipher the internal structures and to target specific areas within the zircons. Analytical methods followed . U/Pb ratios were normalized relative to a value of 0.01859 for the FC1 reference zircon, equivalent to an age of 1099 Ma (see ) and data were reduced using the SQUID Excel macro of ). Uncertainties are quoted at the 1-sigma level. 204Pb-corrected data are presented, but it should be noted that this is not optimal for some of the low-U areas analysed, giving rise to large uncertainties in the radiogenic 207Pb/206Pb ratios and ages. All age calculations were carried out using Isoplot/Ex () and the resulting ages quoted in the text and figures are quoted with 95% confidence limits, including propagation of the uncertainties in the calibration of the U/Pb ratio of the reference zircons (0.40% for sample MAZ-6037 and 0.16% for ESP-7066).The Sierra del Espinal orthogneiss consists of quartz and microcline, with lesser amounts of plagioclase, opaque phases and very abundant muscovite and chlorite as alteration products after biotite (). Titanite and scarce zircon are the main accessory minerals. Because of the strong low-grade retrogression this rock was not further considered for electron-microprobe analyses.The orthogneiss from the Sierra de Maz shows a mylonitic texture; microcline and plagioclase constitute rounded porphyroclasts, while quartz forms recrystallized ribbons (C and D). Microcline, plagioclase and quartz are the main rock-forming minerals and are inherited from the igneous paragenesis. Zircon, apatite, magnetite, biotite, amphibole (ferropargasite), titanite and an REE-rich epidote are accessory and except for some biotite and titanite are probably also inherited. However, garnet and an REE-poor epidote forming mantles around REE-rich epidote grains are metamorphic minerals, as are some biotite and titanite, and muscovite. The low Mn (7.87–1.74 wt% MnO) and high Ca (13.67–11.02 wt% CaO) contents are not characteristic of garnets of magmatic origin and are instead similar to metamorphic garnets from meta-granites (). Biotite and amphibole have high Fe/(Fe + Mg) ratios (0.88–0.91 and 0.88–0.89, respectively). Muscovite is of secondary origin (after biotite and feldspars) and is locally associated with opaque minerals. Irregular carbonate concentrations are locally observed.The two rocks are chemically different (). Unfortunately, identification of the gneiss protolith in terms of major element chemistry is subject to uncertainty because of the strong metamorphic overprint. A more realistic classification should be based on immobile elements such as HFS elements. On the Zr/TiO2

× 0.0001 vs. Nb/Y plot (), ESP-7066 is a rhyolite, i.e., granite, whereas MAZ-12040 plots in the field of rhyodacites/dacites, i.e., granodiorite to tonalite.Relying on HFS elements only, contents of Zr and Y are high in both rocks (603, 891 and 44, 76 ppm, respectively). However, Nb and Ce are not so notably enriched (24, 27 ppm; 180, 97 ppm; respectively), although their values exceed those considered usual for fractionated I- and S-type granites (as compiled by ) and are more typical of A-type granitoids. In fact values of 10,000 × Ga/Al are 2.39 and 3.89, respectively, i.e., close to or above the value of 2.6 recommended by to distinguish A-type granitoids. On a Zr + Nb + Ce + Y diagram () the two rocks plot in the field of A-type granitoids (). On the other hand, contents of mobile elements such as Rb (low: 54–74 ppm), Sr (moderate: 97–232 ppm) and Ba (high: 1051–1787 ppm) are more typical of non-evolved granitoids. Normalized REE patterns are slightly fractionated (LaN/LuN

= 13 and 4, respectively), with REE concentrations close to 100 times chondritic values (B). The Eu anomaly is negative and moderate (0.64) in ESP-7066 and slightly positive (1.09) in MAZ-12040.Both samples plot in the field of within-plate granites close to the field of volcanic-arc granites on discriminant diagrams based on relative abundances of Ta, Y, Yb, Nb, Hf and Rb (). Moreover, the two samples belong to the A2 group as defined by , which represents magmas derived from continental crust that has been through a cycle of subduction-zone or continent–continent collision magmatism (87Sr/86Sri ratios at 845 Ma – the probable crystallization age (see below) – are 0.70681 and 0.70666 for MAZ 12040 and ESP-7066 respectively (). ɛNdi values at the age of 845 Ma are +0.32 to −1.5. Depleted-mantle 2-stage Nd model ages (2TDM) (). Sr and Nd isotope initial ratios are evidence that an isotopically moderately evolved source contributed to the magma composition. Moreover, Nd model ages suggest that this source might be sought in underlying Mesoproterozoic continental crust. This interpretation is reinforced by zircon data below. Whether a juvenile component was also involved in the magma composition cannot be confirmed with the available information.Zircons from MAZ-6037 are elongate to sub-equant, euhedral to sub-round grains or fragments that are generally between 200 and 300 μm in length. The CL images show a dominantly oscillatory-zoned internal structure, with many grains having a thin, <10 μm bright CL rim (). Some grains show a more complex internal structure, with central areas of oscillatory zonation overgrown by a less clearly oscillatory-zoned zircon, in turn overgrown by the very thin bright CL outermost rim for which no reliable analyses could be obtained. Thirty areas were analysed on 27 zircon grains (data obtainable from the Precambrian Research Data Repository). The Pb peaks were not correctly centred during the analyses of grains 5 and 6 and so no data is presented for these. The outer rim and core areas were analysed on grain 1 and both yield 207Pb/206Pb ages that are within uncertainty. The 28 analyses presented in the Data Repository are a mixture of both the inner and outer areas of grains, both types yielding Th/U ratios that are in the usual range recorded by igneous zircon (0.3–0.7). Furthermore, on the Wetherill concordia plot (B) it can be seen that the majority of data lie within uncertainty of concordia and there is no consistent difference between analyses of these two zircon types. Some dispersion is evident and this probably results from correction errors associated with very small amount of radiogenic Pb. Twenty-two of the 28 analyses yield a self-consistent Concordia age (as in ) of 846 ± 6 Ma (MSWD = 1.4) and this constrains the crystallisation age of the dominant zoned igneous zircon. The fact that both inner and outer-zoned components are within uncertainty at ca. 846 Ma indicates that they are coeval to within the uncertainty of SHRIMP analysis.The zircons from sample ESP-7066 constitute a more heterogeneous population than those described above. The grains are mostly ∼200 μm in length, but are more clearly sub-round, with a few subhedral, and under transmitted light they have clearly been more affected by a metamorphic event. The CL images show a range of complex structures. While many show oscillatory zonation, there are older central cores to some grains, and more homogeneous embayments of low-luminescence metamorphic zircon in others (C). This complexity is highlighted in the U–Pb data, with 17 analyses on 14 zircon grains (see table in ). Two analyses of the presumed metamorphic embayments on grains 4 and 7 yield 206Pb/238U ages of ca. 420 Ma, consistent with Paleozoic metamorphism. Older inherited cores and whole grains give ages of ∼1480, ∼1200 and ∼1000 Ma (C). The dominant oscillatory-zoned zircons yield a concordant group of analyses with a Concordia age of 842 ± 5 Ma (MSWD = 2.0, nine analyses, D). This ca. 842 Ma igneous zircon can be seen to enclose older components (both igneous and metamorphic), and in turn is itself rimmed and embayed by the ca. 420 Ma metamorphic zircon.The two samples thus provide crystallization ages that are coincident within error at ca. 845 Ma, i.e., Early Cryogenian, according to the International Stratigraphic Chart (). Both have been affected by metamorphism which, at least in the case of ESP-7066, is shown to be Silurian.Peak metamorphic P–T conditions were assessed for the Maz site to contribute to a better knowledge of the orthogneisses petrology. Using of multivariate equilibria procedure was however hampered by the garnet composition, which is very rich in Ca and Fe, and outside the range of thermodynamic models. Therefore, the best estimate of metamorphic P–T conditions is obtained from the host rocks.Calculations were made on a para-amphibolite close to the orthogneiss body (sample MAZ-12046) using THERMOCALC 3.1 (). Garnet, amphibole, biotite, quartz, plagioclase and ilmenite constitute the dominant assemblage, while calcite, epidote and chlorite were formed on the retrograde path. Other minor phases include apatite, allanite and zircon. Syntectonic garnet displays a very slight zonation, with decreasing Mg (XPy from 0.12 to 0.117-0.105) and Fe (XAlm from 0.654 to 0.645–0.647) and increasing Ca (XGro from 0.177 to 0.182–0.190) and Mn (XSps from 0.048 to 0.053–0.059) from core to rim. Neither biotite nor amphibole is significantly zoned. Biotite has an average Mg# of 0.44. Amphibole (ferropargasite according to the classification of ) has AlTotal between 2.668 and 2.875 apfu and #Mg = 0.43. The average Fe3+/(Fe2+

+ Fe3+) ratio is 0.10. Plagioclase ranges from An54 to An67 (mineral compositions are obtainable from the Data Repository). Peak metamorphic conditions were: P

= 7.7 ± 1.2 kbar and T

= 664 ± 70 °C.A-type magmatism is indicative of largely continental within-plate extensional settings (e.g., ). Thus we infer that the A-type granitoids described here represent a period of extension at ca. 845 Ma (early Cryogenian) affecting the continental crust of the Western Sierras Pampeanas that was already consolidated after the Grenvillian orogeny. This magmatic event implies that rifting of the Western Sierras Pampeanas Grenvillian basement started earlier than previously established. The oldest crystallization age yet reported for anorogenic A-type granitoids in the Western Sierras Pampeanas is ca. 774 Ma (middle Cryogenian; ). Compared to the juvenile isotope composition of the ca. 774 Ma Sierra de Pie de Palo orthogneisses (Sri

= 0.7005–0.7030, ɛNd = +4.1 to +4.9; ), those of Maz and Espinal orthogneisses resulted from the involvement of an isotopically more evolved source. Moreover, depleted-mantle Nd model ages of up to 1.46 Ga and inherited zircon crystals of up to 1.48 Ga in sample ESP-7066 lead us to speculate that the ca. 845 Ma A-type magmatism at Maz, largely involved a Mesoproterozoic continental source. The latter is also indicated by the relatively high contents of Y, Ga, Nb and Ce compared to those of magmas directly derived from mantle sources (Igneous rocks of uncertain chemical signature that might likewise correspond to the same anorogenic event referred to here have been recorded from other locations in the Western Sierras Pampeanas. reported a U–Pb SHRIMP zircon age of 839 ± 10 Ma for an orthogneiss from the Sierra de la Huerta, southeast of the Sierra de Pie de Palo ( reported depleted-mantle Nd model ages between 782 and 806 Ma for ortho-amphibolites from the Sierra de Umango, west of the Sierras of Maz and Espinal (). However, these rocks are more probably related to the second extensional event.The Western Sierras Pampeanas Grenvillian basement has been correlated with other outcrops of Proterozoic basement in South America, i.e., the Arequipa-Antofalla block and Amazonia, on the basis of geochronology of detrital zircons and Nd and Pb isotope geochemistry (). It is probable that these continental masses were accreted to Laurentia through the Grenville-Sunsás orogeny between 1.2 and 1.05 Ga and thus amalgamated to the Rodinia supercontinent, with Laurentia in a central position. The process involved a still highly conjectural history of collision and further protracted lateral displacement of Amazonia along the boundary between the two continents (e.g., , among others). In the Neoproterozoic and Early Paleozoic, the continental masses mentioned above, i.e., Laurentia, Amazonia, Western Sierras Pampeanas, Arequipa-Antofalla and other minor cratons such as Rio Apa () remained attached, forming a large continent that was involved in the Pampean orogeny between 535 and 520 Ma (). This orogeny resulted from collision with other Gondwanan cratons to the east (present coordinates), probably Kalahari, and led to closure of the intervening Clymene Ocean () and the final amalgamation of SW Gondwana (A-type orthogneisses in the Western Sierras Pampeanas are thus a record of Rodinia break-up that took place through a sequence of events in the Neoproterozoic. Allegedly mantle-plume related break-up pulses that affected large areas of the Earth have been recognized in different continents at ca. 825, 780 and 750 Ma ( (ca. 774 Ma) matches well one of the pulses mentioned above, whereas the age of the meta-granitoids reported in this contribution is the oldest yet. In the case of the Western Sierras Pampeanas Grenvillian basement these events resulted only in aborted rifts, inasmuch as no evidence for oceanic crust of Neoproterozoic age has been reported so far. Of relevance to our case is the opening of the Iapetus Ocean between Laurentia and Amazonia that took place near the Neoproterozoic-to-Cambrian transition after a long rifting initiated as early as 765 Ma (). Drifting apart from Laurentia led to development of passive margin sedimentary sequences on both sides of the Iapetus Ocean almost coeval with the Pampean collision (). A record of this process is represented by the Argentine Precordillera carbonate platform, located west of the Sierras Pampeanas (e.g., ). Regardless of whether this platform is an exotic terrane travelled from the western margin of the Iapetus and accreted to western Gondwana in the early Paleozoic (reviews in ) or a para-autochthonous terrane (e.g., ), it provides evidence that the Western Sierras Pampeanas Grenvillian basement was also part of the drifted conjugate margin of Iapetus.From the above discussion we infer that break-up of Rodinia along the Grenvillian boundary between Amazonia (+Western Sierras Pampeanas + Arequipa-Antofalla) and Laurentia was protracted, starting at least at ca. 845 Ma and ending through drifting and ocean opening in the early Cambrian.A few examples of A-type granitoids from elsewhere in South America coeval with those described here were recognized by in the reworked basement of the Brasiliano – Panafricano Dom Feliciano Belt, southern Brazil. Ages of 835 ± 9 Ma (IDTIMS) and 843 ± 12 Ma (SHRIMP) were obtained that are within error of those found here. Whether this rifting event in southern Brazil was spatially connected through the continental hinterland with that in the Western Sierras Pampeanas, or alternatively records coeval but independent extensional processes in a separate craton (such as the Rio de la Plata craton, ), remains conjectural. Recent geochronological, paleomagnetic and geological evidence for southern South American cratons in the Neoproterozoic () seem to favour the second interpretation.It is notable that the rifting event at ca. 845 Ma was almost coeval with consumption of the Brasiliano Ocean between the São Francisco/Congo and the Amazonia and Paraná cratons in the early Neoproterozoic (). An intra-oceanic magmatic arc, the juvenile Goiás magmatic arc in Central Brazil, existed between ca. 890 and 800 Ma (). Complete consumption of the Brasiliano Ocean took probably place at ca. 600 Ma (). This evidence of subduction in the early Neoproterozoic has been taken as a proof that some large cratons such as São Francisco/Congo and others were not part of the Rodinia supercontinent (). We can only state that the rifting events at ca. 845 Ma and ca. 774 Ma were comparatively very short and took place while subduction of the Brasiliano Ocean was underway.The age of the metamorphic rims in zircon grains from ESP-7066 (ca. 420 Ma, i.e., Silurian) confirms that a strong metamorphic overprint took place during the Ordovician–Silurian Famatinian orogeny. Although still poorly known in detail (time and P–T conditions) the Famatinian overprint in the sierras of Maz and Espinal was widespread, varying from greenschist to upper garnet-amphibolite facies conditions (). Because no conclusive evidence exists in the sierras of Maz and Espinal of orogeny between ca. 840 Ma and the Famatinian orogeny (however, see ), high-grade metamorphism (664 ± 70 °C) at the site of MAZ-6037 was probably Famatinian. The thin low-U zircon rims in sample MAZ-6037 were unfortunately undatable. Since sample ESP-7066 underwent metamorphism at much lower grade than MAZ-6037, it is suggested that zircon overgrowths in this case might be related to the pervasive influx of fluids leading to retrogression of the igneous association. Zircon crystallization seems possible from aqueous fluids under low P and T conditions (<500 °C) and high water/rock ratios (Supplementary data associated with this article can be found, in the online version, at Effects of cooling method after intercritical heat treatment on microstructural characteristics and mechanical properties of as-cast high-strength low-alloy steelThe effect of cooling method after intercritical heat treatment on the microstructures and mechanical properties of as-cast steel produced by electroslag casting was investigated. The microstructure characteristics were analyzed by optical microscope (OM), scanning electron microscope (SEM), transmission electron microscopy (TEM) and electron back scatter diffraction (EBSD). The mechanical performance was evaluated by tensile testing at ambient temperature and Charp V-notch impact tests at various temperatures (−40 °C, −20 °C, 20 °C). The tensile and impact fracture micromechanisms were discussed in details. The results of microstructure investigation indicated that water cooling after intercritical heat treatment led to a mixed microstructure of ferrite and tempered martensite, while a composite microstructure of ferrite and tempered bainite was obtained after air cooling. The carbides of Cr, Mo and Nb in matrix after water quenching were finer than the ones after air cooling. Compared with water cooling, a good balance of strength and toughness was obtained after air cooling. The crack propagation path in the steel after water cooling can propagate along the long axis direction of ferrite bands, directly across the intersecting banded ferrite and martensite as well as along the interfaces between ferrite and martensite. However, the crack propagation path in the steel after air cooling depends on the shape, size and distribution of M/A islands.High-strength low-alloy (HSLA) steels have been widely applied in various industries, such as automobile making The electroslag casting (ESC) is a kind of special casting process combining remelting and refining with casting process together. By controlling the ESC process parameters, complex-shaped castings with finer solidification structure, higher degree of purity, lower degree of segregation, lower micro-porosity as well as better surface quality can be achieved, compared with conventional casting procedure Intercritical heat treatment (IHT) is a new method to obtain duplex microstructure The cooling condition after thermomechanical processing and heat treatment is critical to the microstructures and properties of the final products. The present work aims at investigating the effect of cooling method after intercritical heat treatment on microstructure evolution and mechanical properties of as-cast steel produced by electroslag casting. More interests are paid to the effect of microstructures obtained by different heat treatment procedures on tensile and impact fracture behavior.An ingot about 165 kg weight with proper chemical composition was prepared by vacuum melting technique followed by die casting. The ingot was homogenized at about 900 °C and then forged into a rod with diameter of about 80 mm. The rod was subsequently used as an electroslag casting consumable electrode. The electrode connecting with alternating current (AC) power of 40 V, which was converted from 380 V AC, was remelted in a water-cooled copper mould with diameter of 100 mm. The current and voltage during the remelting process were 2100 A and 40 V respectively. The components of remelting slag were 70% CaF2 and 30% Al2O3. The inlet water temperature was about 25 °C. In order to keep suitable cooling condition, the temperature of outlet water was controlled below 50 °C. About several minutes later after the electroslag casting process (ESC), the as-cast ingot was taken out from the mould and cooled in the air.The chemical composition of the as-cast ingot after ESC is shown in . The critical transition temperatures were measured by differential scanning calorimetry (DSC) with a heating rate of 10 °C/min. The results indicated that the Ac3 and Ac1 temperatures were 856 °C and 747 °C respectively. The specimens with the size of 11 mm × 11 mm × 70 mm for heat treatments were obtained from the radius in half of the as-cast ingot. All the specimens were heated in a box-type electric resistance furnace at 950 °C, followed by water quenching. After that, the specimens were reheated to 800 °C and then quenched to water or cooled in the air, and finally tempered at 500 °C. The processes of common quenching-intercritical quenching/normalizing–tempering were abbreviated to QQT and QNT respectively below. The details of heat treatment processes used in this investigation are described in Samples for metallographic analysis were prepared by mechanically grinding, polishing and then etched with 4% nital solution. The microstructures before and after heat treatments were investigated by optical microscope (OM) and scanning electron microscopy (SEM, model: LEO-1450). To evaluate the microstructural characteristics of the metallographic samples, the samples were also etched with LePera reagent, which was obtained by mixing 4% picric acid in ethanol and 1% sodium metabisulfite in water at the ratio of 1:1. The volume fractions of all the microstructural constituents were determined by the Image Pro-Plus 6.0 software. Fractographic examination of tensile and impact specimens was performed to obtain a better understanding of the microscopic fracture mechanism of different microstructures. For further microstructural analysis, several slices about 0.35 mm thickness were cut by wire-electrode cutting, followed by thinning to a thickness of about 0.04–0.05 mm through mechanical method. Discs of about 3 mm diameter were punched from the thinned wafers and prepared in a twin-jet electro-polisher using a solution of 5% perchloric acid in alcohol kept below −20 °C by liquid nitrogen. These foils were analyzed by a field-emission transmission electron microscope (TEM, model: TECNAI G2 F30 S-TWIN). Electron-backscattering diffraction (EBSD) analysis was conducted for the investigation of the effect of microstructures on the crack propagation of impact cracks. X-ray diffraction (XRD) analysis was carried out to determine the residual austenite content.In order to assess mechanical properties, tensile and impact tests were performed. For tensile tests, three tensile specimens with round cross-section of 5 mm diameter and 25 mm original gauge length were machined, according to GB/T 228-2002 are the optical and scanning microscope photographs revealing the microstructural evolution during heat treatments. The original as-cast microstructure before heat treatments was a mixed microstructure consisting of granular bainite and upper bainite, which resulted from the special cooling condition in the electroslag remelting process, as presented in A revealed that the microstructure after water quenching was lath martensite, typical microstructure of low-carbon low-alloyed steel after conventional quenching. The microstructure after conventional quenching and intercritical quenching was a duplex ferrite–martensite structure characterized by block and lamellar ferrite as well as globular, acicular and irregular martensite as shown in B. The dual-phase (DP) microstructure contained about 54.32 vol.% ferrite and 45.68 vol.% martensite or martensite and retained austenite, which was obtained by averaging the statistical data of 10 different areas. The microstructure after water quenching and intercritical normalizing was a mixed microstructure comprised of lamellar ferrite and granular bainite contained much more M/A islands with the size range of 0.54–2.12 μm distributed in the bainitic ferrite along the long axis direction as described in . The austenite could nucleate either at the prior austenite grain boundaries (PAGBs) or martensite lath boundaries (MLBs) during the reversion of martensite to austenite. The austenite that nucleated at the PGABs grew to be globular or network austenite. The austenite that nucleated at the MLBs grew along the lath boundary and formed fibrous acicular austenite . After QNT treatment, the microstructure was ferrite and tempered bainite comprised of blocky, round, elliptoid, stringer M/A constituents or martensite as presented in The transmission electron micrographs further revealing the substructure of QQT and QNT steels are presented in respectively. TEM investigation indicated that the substructure of QQT specimens embodied banded ferrite, with the width range of 0.52–0.84 μm, and lath tempered martensite as shown in A showed the dispersed martensite or M/A constituents, blocky and banded ferrite in the QNT steels. Large amount of dislocations as revealed in B was observed near the ferrite boundaries, which resulted in the continuous yielding behavior of QNT and QQT steels in the early stage of plastic deformation as discussed in Section . The fine carbides of Cr, Mo, and Nb in ferrite matrix were found both in QQT steels and QNT steels as presented in C, which contributed to the strengthening of ferrite matrix. The precipitated phases in C were about 2.85–21.6 nm in diameter larger than the size in C (around 3.45–12.9 nm), which could probably originate from different cooling rates in the intercritical heat treatment step.The electron backscattered diffraction (EBSD) investigation results of QQT and QNT steels are showed in , depicting the misorientation angle distribution of grain boundaries including the low-angle grain boundaries (LABs) (the boundary angle: 2–5° in green lines, 5–15° in red lines) and the high-angle grain boundaries (HABs) in black lines (the boundary angle higher than 15°). The relative frequency of LABs and HABs in QQT and QNT steels was compared with each other. There were about 61.5% HABs in QQT specimens, a little more than QNT steels. In QNT specimens, the high angle boundaries included the interfaces between martensite islands and ferrite matrix as well as the boundaries of ferrite and bainite. The boundaries of ferrite and martensite were high-angled in QQT steels. Low angle boundaries mainly distributed in ferrite phases in both QQT and QNT steels. Previous studies A could be the interface between ferrite and martensite, which was retained after tempering treatment.The engineering stress–strain curves of the specimens processed under different heat treatments are presented in . It could be seen that the stress–strain curves of the specimens under QQT and QNT processes both exhibited continuous yielding behavior during the transition from elastic to plastic deformation, which was one of the typical characteristics of dual phase steels. For DP steels, it has been clearly known that the austenite to bainite or martensite transformation generates a larger number of dislocations in the adjacent ferrite phases due to transformation stress, most of which remain unlocked and mobile, even after tempering treatment The results of tensile mechanical properties are listed in shows the curves of Charp impact energy with temperature for QQT and QNT steels. Compared with QNT steels, the QQT steels had higher strength but lower plasticity and toughness, which was mainly attributed to the differences in microstructures. The strength and ductility of ferrite–martensite or ferrite–bainite dual phase steels were functions of a great number of variables such as the content and morphology of soft phases and hard phases, the precipitation behavior in the ferrite and so on The tough ferrite could hinder the propagation of microcracks and augment the resistance to brittle fracture. After air cooling, the austenite changed into granular bainite. The formation of granular bainite included two stages: in the first stage, the carbon-poor areas in the austenite transformed into bainitic ferrite with alloy elements further enriched in the retained austenite; in the second stage, the carbon-rich areas transformed into M/A islands A and did harm to the toughness. Compared with QQT steels, it was expected that the QNT steels had better elongation and toughness.To evaluate the microfracture mechanism, the Charp impact and uniaxial tensile fractography were examined as shown in B) steels were both characterized by tremendous small dimples and a few of large ones (large dimples about 6.94–27.74 μm in the QQT specimens, around 6.64–25.42 μm in the QNT specimens), a typical feature of a ductile fracture mechanism. In the fracture surface, dimples with different sizes can correspond to different void-nucleating particles. The small dimples mainly originated from the fine carbide particles precipitated in the matrix during tempering heat treatment. Because of the weak bond force between precipitated phases and matrix, the microvoids in the interfaces between matrix and precipitated phases were easily formed during tensile deformation. For the big dimples, previous investigation The observation of the radial zone of −40 °C impact fracture faces of QQT (B) steels indicated that the fracture mechanisms of QQT and QNT steels were both quasi-cleavage fracture, which was a kind of fracture type comprised of dimples and cleavage facets together. Not only the tearing ridges but also the river pattern could be observed. River patterns stemmed from the propagation of the crack across numbers of cleavage planes of various levels.To study the correlation between microcrack initiation as well as crack propagation and microstructure, the cross-sectional area beneath the impact fracture surface of the Charp impact specimens fractured at −40 °C was investigated as illustrated in A and B, it was seen that the cracks could propagate either along long axis direction of banded ferrite or directly cross the ferrite and tempered martensite. Kang et al. Additionally, the cracks could also propagate along the interfaces between ferrite and tempered martensite as indicated by arrows in B. As EBSD analysis indicated, the martensite–ferrite boundaries were high-angled, which were preferential positions for microvoid nucleation. The microcrack occurred by the joining up of microvoids as indicated by arrows in A. Large numbers of low-angled boundaries distributed inside the ferrite grains, which had low interfacial energy, so that cracks could cut through them straightly without consuming much more energy. The high angle boundaries, as obstacles and barriers of crack propagation, could slow down the propagation rate of cracks. While crossing the high energy interfaces, the crack propagation direction could be deflected and the crack narrowed down progressively until it was stopped.C were observed in the area marked with a circle in B. Although the crack propagation path in the QQT steels was also tortuous and bending, obvious plastic deformation was observed in C, which meant large amounts of energy consumption in the final fracture process of QNT specimens. This phenomenon was consistent with the results of impact test as presented in In contrast to QQT specimens, the mechanism of crack initiation and propagation in QNT steels was distinct. With respect to the soft ferrite matrix, M/A islands were hard phases. High stress concentration could emerge on the interfaces between M/A islands and ferrite. The microcracks could nucleate at martensite islands-matrix interfaces once the concentration stress in the interfaces between M/A islands and ferrite was higher than the binding force of phase interfaces. M/A islands were also brittle phases. While the concentration and triaxiality of stress around the boundary on the side of ferrite was higher than its binding force of martensite, the martensite islands could be induced to cleavage crack as shown in The crack propagation path had connection to the size of M/A islands. Wang et al. D. For large blocky M/A islands, during the propagation of crack, when the concentration stress in the crack tip was higher than the binding force of hard phase, the M/A islands could be cut through by the crack directly. For small blocky M/A islands, while the concentration stress fell in between the binding force of M/A islands and the interface binding force between M/A islands and matrix, the cracks could propagate along the interfaces and change the direction of crack propagation.A and B occurred due to the brittleness of martensite. The brittle of martensite initiated two microcracks. The crack propagation directions were almost parallel in A. But there was a certain angle between two crack propagation directions in B. It could be related to the shape of brittle martensite. Due to complex shape of M/A islands, the stress state around M/A islands was complicated. Once the cleavage cracks formed in the martensite, it was prone to propagate along the channel which could release impact energy easily.A was comparatively dispersed, which reduced the opportunity to meet with cracks. However, large and small M/A islands arranged along the long axis of bainitic ferrites in E. While the cracks went through the areas with M/A islands regularly distributed, the crack propagation path was curved with many corners as presented by arrows.In the present work, the effect of cooling method after intercritical heat treatment on the microstructures and mechanical properties of a low-alloyed high strength as-cast steel by electroslag casting was studied. Air cooling after intercritical heat treatment led to a final microstructure consisting of ferrite and tempered bainite and coarser carbides precipitated in the matrix, characterized by good elongation and toughness but lower yielding and tensile strength. On the contrast, a final microstructure was ferrite and tempered martensite after water cooling, characterized by low elongation and toughness to facture with higher yielding and tensile strength.SEM investigation of the tensile facture surfaces of QQT and QNT specimens was characterized by large and small dimples. A microcrack was found in the fracture surfaces of QQT specimens. The impact facture types of QQT and QNT specimens were both quasi-cleavage fracture characterized by dimples and cleavage facets. The microcracks in QQT steels initiated mainly at the high energy boundaries (the boundaries of ferrite and tempered martensite) and could propagate along the long axis direction of ferrite bands, directly across the intersecting banded ferrite and martensite as well as along the interfaces between ferrite and martensite. The microcracks in QNT steels initiated by decohension of the interfaces between ferrite and hard phase or brittle of martensite islands or at the high angle boundaries. The crack propagation path depended on the shape, size and distribution of M/A islands.Axisymmetric dynamic instability of rotating polar orthotropic sandwich annular plates with a constrained damping layerA sandwich annular plate built with two constrained layers of polar orthotropic material and a viscoelastic core layer is subjected to a periodic uniform radial stress while rotating. The axisymmetric dynamic instability of such a rotating sandwich plate is analyzed using finite elements. By employing a discrete layer axisymmetric annular element and Hamilton’s principle, the finite element equations of motion that facilitate considerations of transverse shear effect shear effect are derived. The viscoelastic material in the core layer is assumed to be incompressible, and its extensional and shear moduli are described by complex quantities. The regions of dynamic instability are determined by Bolotin’s method. Numerical results show that the constrained viscoelastic core layer tends to stabilize the sandwich annular plate system. In addition, the widths of instability regions decrease as the rotation speed increases.Circular plates are among the most critical parts of turbines, circular saws, and optical and hard disks of computer memory systems and their dynamic behavior has received considerable attention. Under periodic in-plane loads, the circular plate may suffer dynamic instability, also referred to as parametric resonance, and consequently violent vibrations are observed increasing the risk of structure failure. The parametric resonance of plates under axial loads had been extensively studied, and books by Bolotin Previously, free vibration of layered circular plates with or without a viscoelastic layer was extensively investigated, e.g., Constrained layer damping (CLD) treatment provides an effective way to suppress vibration and noise in structures. The works on sandwich plates with viscoelastic cores were given by Chen and Huang The dynamic stability of an initially straight, simply supported, viscoelastic column subjected to a harmonically varying axial load was studied by Stevens Let a sandwich annular plate consist of two constrained layers of polar orthotropic material and a viscoelastic core layer. While rotating, let the sandwich plate be subjected to a uniform radial stress along the outer edge of the annular plate. In this paper, the axisymmetric dynamic instability problem of such a rotating sandwich plate is studied. The balance consists of three sections. In Section , annular elements of the discrete layer are adopted to obtain the finite element equations of motion for the sandwich plate. The extensional and shear moduli of the linear isotropic viscoelastic material core layer are described by complex quantities. The regions of dynamic instability are determined using Bolotin’s first approximation. Thereby, influences of various parameters on the dynamic stability behaviors of rotating polar orthotropic sandwich viscoelastic annular plates are investigated in Section A finite element method that calculates dynamic instability regions of a sandwich annular plate with constrained surface layers of polar orthotropic material and a viscoelastic core layer is derived. First, the strain–displacement and stress–strain relations are given in Section , which is followed by the presentation of kinetic and strain energies in Section . The annular finite element of a discrete layer described in Section and is employed to facilitate the derivation of equations of motion in Section . Then, free vibration is investigated in Section the Bolotin’s method is adopted to derive the method that calculates the dynamic instability region.To analyze the axisymmetric parametric resonance of polar orthotropic sandwich annular plates, a modified axisymmetric finite element is employed. Let the displacement field of the layer i beThe linear strains in the layer i of the annular plate are written in terms of the displacement as follows:where the strain vector {εi} = {εr,iεθ,iγrz,i}T and the differential operator matrix [Let {σi} = {σr,iσθ,iγrz,i}T be the stress vector of layer i. Letbe the elasticity matrix. Then the stress–strain relations for the layer iis expressed asFor the polar orthotropic material, the components of the elasticity matrix are written as follows C11,i=Er,i1-νrθ,iνθr,i,C12,i=C21,i=νθr,iEr,i1-νrθ,iνθr,i,C22,i=Eθ,i1-νrθ,iνθr,i,where E is Young’s modulus, ν is Poisson’s ratio, and κ2 is the shear correction factor. The shear correction factor takes values of π2/12, 1, and π2/12 for layers 1, 2, and 3, respectively. Assume that the viscoelastic material of the core layer is almost incompressible C11,2=C22,2=E21-ν22,C12,2=C21,2=ν2E21-ν22,C44,2=E2(1+ν2),where the real and virtual parts of E2 are the storage and loss moduli of the viscoelastic material, respectively, ηv is the loss factor of the viscoelastic material, and j=-1.Let element e be on the layer i. Then the kinetic energy Tie=12∫Veρi{{u˙}2+[({r}+{u})Ω]2+{w˙}2}dV,Tie=12∫Veρi[{u˙i}T{u˙i}+Ω2([L3]{r(0)})T([L3]{r(0)})+Ω2([L3]{ui})T([L3]{ui})+Ω2([L3]{ui})T([L3]{r(0)})]dV,where {r(0)} is the position vector, ρi is the mass density, and ∫Ve represents a volume integral. In Eq. , the first term represents the kinetic energy contributed by the plate vibratory motions. The second term is contributed by the rigid body motion. The third term is the supplementary strain energy due to displacement dependent centrifugal force. The fourth term results from the initial in-plane stresses that are developed by the centrifugal force. It is noted that for an axisymmetric annular plate the second term of rigid body motion kinetic energy actually has null contribution to the equations of motion.Let Uie be the strain energy of element e on the layer i. ThenUie=12∫Ve{σi}T{εi}dV+∫Ve{σ¯ir}T{εiN}dV+∫Ve{σ¯il}T{εiN}dV. are the additional strain energies contributed by the rotation induced stresses and the external in-plane load, respectively. Let {σ¯ir} be the rotation-induced stress vector. Let {σ¯il} be the external in-plane load induced stress vector. Let {ε¯iN} be the nonlinear strain vector. Then{σ¯ir}=σ¯r,irσ¯θ,irτ¯rz,irT=[Ci][D]([L1,i][L2]){U¯ie,r},{σ¯il}=σ¯r,ilσ¯θ,ilτ¯rz,ilT=[Ci][D]([L1,i][L2]){U¯ie,l},{εiN}=12∂ui∂r2+12∂wi∂r212uir2∂ui∂r∂ui∂z,where {U¯ie,r} is the equilibrium nodal displacement vectors corresponding to the centrifugal force, and {U¯ie,l} is the external in-plane load. Both are evaluated using solutions of static problems. Details are given below.The value of {U¯r} is resolved using the following equation, where only the centrifugal force is applied:where [K] is the stiffness matrix that will be derived latter and presented in Eq. , and {Fr} is the global centrifugal force vector,The above elemental centrifugal force vector {Fe,r} derived form the fourth term of Eq. {Fie,r}=∫Ve[ρiΩ2([L3][L1,i][L2])T([L3]{r(0)})]dV.Assume that the layers are all linear, and the global nodal displacement vector {U¯l} is obtained using the following relations:is the global external force vector, andThe discrete layer annular finite element (a). Let the layer i be an axisymmetric annular plate with inner radius ri and outer radius ro. Then a finite element e of layer i has eight degrees of freedom, namely the displacements in the r-direction, UiA, Ui+1A, UiB and Ui+1B, the transverse displacements, WiA and WiB, and the rotational angles, ΘA and ΘB. Assume that the transverse displacements are constant throughout the thickness of the plate. Then, the transverse normal strain is zero. As a consequence, ϑiκ=ϑκ for i

= 1, 2, 3, ϑ

=

W,

Θ, and κ

=

A,

B, and the three-layered annular finite element as shown in (b) has 12 nodal degrees of freedom corresponding to Uiκ and ϑκ, where i

= 1, 2, 3, 4, ϑ

=

W,

Θ, and κ

=

A,

B.Express the displacement field of the layer i, i.e., {di} = {uiwi}T, in terms of the in-plane displacements of adjacent layer interfaces and transverse displacement, and we obtain{di}=ui(r,z,t)wi(r,t)=[L1,i(z)]Ui(r,t)Ui+1(r,t)W(r,t),where [L1,i] is the transverse thickness interpolation matrix for the layer i. Further interpolation in the r-direction produces the displacements of the two layer interfaces as follows:[L2(r)]=nuA000nuB0000nuA000nuB0000nwAnΘA00nwBnΘB,nuA=(1-ξ),nuB=ξ,nwA=(1-3ξ2+2ξ3),nwB=(3ξ2-2ξ3),nΘA=(ξ-2ξ2+ξ3),nΘB=(-ξ2+ξ3),andξ=r-riro-ri,where [L2] is the interpolation matrix, {Uie} is the vector of nodal displacements of the element, and the interpolation functions are given in the above Eq. and applying Hamilton’s principle, i.e.,we obtained element dynamic equilibrium equations as follows:[Mie]{U¨ie}+([Kie]+[Gie,r]+[Gie,l]){Uie}={0},where the elemental mass matrix [Mie], stiffness matrices [Kie], [Gie,r], and [Gie,l] of the layer i are given below:[Mie]=∫Ve[ρi([L1,i][L2])T([L1,i][L2])]dV,[Kie]=∫Ve[([D][L1,i][L2])T[Ci]T([D][L1,i][L2])]dV,[Gie,r]=2∫Ve[({D1}[L4][L1,i][L2])T[σˆir]({D2}[L4][L1,i][L2])+({D1}[L5][L1,i][L2])T[σˆir]({D2}[L5][L1,i][L2])+12({D3}[L5][L1,i][L2])T[σˆir]({D3}[L5][L1,i][L2])]dV,[Gie,l]=2∫Ve[({D1}[L4][L1,i][L2])T[σˆil]({D2}[L4][L1,i][L2])+({D1}[L5][L1,i][L2])T[σˆil]({D2}[L5][L1,i][L2])+12({D3}[L5][L1,i][L2])T[σˆil]({D3}[L5][L1,i][L2])]dV,{D1}=12∂∂r0∂∂r,{D2}=∂∂r0∂∂z,{D3}=01r0,[σˆir]=σ¯r,ir000σ¯θ,ir000τ¯rz,ir,[σˆil]=σ¯r,il000σ¯θ,il000τ¯rz,il,[L4]=[10],and[L5]=[01],where [Gie,r] is the rotation-induced elemental geometric stiffness matrix, and [Gie,l] is the elemental geometric stiffness matrix due to the external in-plane load. It is noted that the rotation-induced elemental geometric stiffness matrix [Gie,r] increases the plate stiffness.By assembling the contribution of all elements, the global finite element equations of motion is obtained as follows:where [M] is the global mass matrix, and [K], [Gr] and [Gl] are global stiffness matrices.By substituting {U(t)} = {U0}ejλt into Eq. , we obtain the following eigenvalue equation:where λ is a complex number because of complex-valued terms of the stiffness matrices. The natural frequency of the sandwich circular plate system is then given byLet the external in-plane load P be a periodic radial stress, i.e.,where Po and Pt are constants, and Θ is the frequency of the external load. Then, the external load-induced geometric stiffness matrix is expressed as follows:where [Go] and [Gt] are the static and dynamic geometric stiffness matrices, respectively. By substituting Eq. [M]{U¨}+([K]+[Gr]+[Gol]+[Gtl]cosΘt){U}=0. is a Mathieu equation with complex coefficients, and Bolotin’s method have a period 2T (4π/Θ) and the secondary periodic solutions share the same period T. They are given in the stated order below:where the components of {a1}, {a2}, {b0}, {b1} and {b2} are constants., equate the coefficients of identical sin(kΘt/2) and cos(kΘt/2) terms, and use complex notation as indicated by Evan-Iwanowski [K,r]+[Gr,r]+[Gol,r]-12[Gtl,r]-Θ24[M]-[K,i]-[Gr,i]-[Gol,i]-12[Gtl,i][K,i]+[Gr,i]+[Gol,i]-12[Gtl,i][K,r]+[Gr,r]+[Gol,r]+12[Gtl,r]-Θ24[M]{a1}{b1}={0}{0}[K,r]+[Gr,r]+[Gol,r][0]12[Gtl,r]-[Gtl,i][K,r]+[Gr,r]+[Gol,r]-Θ2[M]-[K,i]-[Gr,i]-[Gol,i][Gtl,r][K,i]+[Gr,i]+[Gol,i][K,r]+[Gr,r]+[Gol,r]-Θ2[M]{b0}{a2}{b2}={0}{0}{0},where the second superscripts r and i of the stiffness matrices denote the real and imaginary part of matrices, respectively. It is noted that the complex-valued terms of stiffness matrices are due to the strain energy terms of the viscoelastic material layer. For the above two sets of equations, i.e., Eqs. , non-trivial solutions does not exist unless determinants of both coefficients matrix equal zero. That is,[K,r]+[Gr,r]+[Gol,r]-12[Gtl,r]-Θ24[M]-[K,i]-[Gr,i]-[Gol,i]-12[Gtl,i][K,i]+[Gr,i]+[Gol,i]-12[Gtl,i][K,r]+[Gr,r]+[Gol,r]+12[Gtl,r]-Θ24[M]=0[K,r]+[Gr,r]+[Gol,r][0]12[Gtl,r]-[Gtl,i][K,r]+[Gr,r]+[Gol,r]-Θ2[M]-[K,i]-[Gr,i]-[Gol,i][Gtl,r][K,i]+[Gr,i]+[Gol,i][K,r]+[Gr,r]+[Gol,r]-Θ2[M]=0., where Θpu⩾Θpl. Then, Θpu and Θpl resolves the following quadratic equation 116(-4([K,i]+[Gr,i]+[Gol,i])2+[Gtl,r]2+[Gtl,i]2)+(-4([K,r]+[Gr,r]+[Gol,r])2+[M]Θ2)2=0., where Θsu⩾Θsl. Then, Θsu and Θsl resolves the following equation -12[Gtl,i][Gtl,r]([K,i]+[Gr,i]+[Gol,i])+([K,r]+[Gr,r]+[Gol,r])([K,i]+[Gr,i]+[Gol,i])212[Gtl,r]2+[K,r]+[Gr,r]+[Gol,r]([K,r]+[Gr,r]+[Gol,r]-Θ2[M])=0.Note that the instability region for the primary frequency lies between Θpu and Θpl, and the instability region for the secondary frequency does between Θsu and Θsl.The finite element method described in the previous section is employed to calculate the dynamic instability regions of rotating polar orthotropic sandwich annular plates with a viscoelastic core layer. Consider the sandwich annular plate as shown in that has an inner radius a, an outer radius b, and three layers in thicknesses of h1, h2 and h3, respectively. Let the sandwich plate be composed of two polar orthotropic face layers and a viscoelastic core layer. The following assumptions are made:The polar orthotropic face layers, designated as the layer 1 (top) and the layer 3 (bottom), respectively, are both pure elastic and homogeneous (e.g., high-modulus graphite, high-strength graphite epoxy, and ultra-high modulus graphite epoxy In comparison to those of the high damping viscoelastic materials in the middle layer, the loss factors for epoxy matrix of the face layers are very small The middle layer, designated as the layer 2 and assumed a linear viscoelastic material layer, is capable of adhesively dissipating vibratory motions.Perfect bonding is assumed for interfaces between layers.The thicknesses of three layers remain constant during deformation since changes in the layer thickness have negligible influences on natural frequencies and modal loss factors of the system The above assumption 5 was further justified by results obtained by Huang et al. In addition to the above assumptions, the following non-dimensional parameters in the finite element analysis are employed:ξ˜=ab,b˜=bh1,h˜2=h2h1,h˜3=h3h1,ρ˜2=ρ2ρ1,ρ˜3=ρ3ρ1,E∼θ,1=Eθ,1Er,1,G∼rz,1=Grz,1Er,1,E∼2=Re(E2)Er,1,E∼r,3=Er,3Er,1,E∼θ,3=Eθ,3Er,1,G∼rz,3=Grz,3Er,1,D1=E1h1312(1-ν12),Ω∼=Ωb2ρ1h18D1,Θ∼=Θb2ρ1h1D1,ω˜=ωb2ρ1h1D1,where meanings of symbols displayed in the above equations are given in The balance of this section applies the finite element model presented in the previous section using the above assumptions and non-dimensional parameters. First, supporting results for verification of the proposed finite element model are presented. Then, the proposed method is employed to investigate the dynamic stability behavior of annular plates.Three verification cases are presented. First, the non-dimensional fundamental natural frequencies of polar orthotropic laminated annular plates are calculated and compared to published results. Then, the non-dimensional natural frequencies of rotating annular plates without external loads in various rotational speeds are evaluated, which is followed by the comparisons for dynamic stability regions of a stationary annular plates.Let the polar orthotropic laminated annular plates be free at the inner radius r

=

a and clamped at the outer radius r

=

b. Let the grids of the finite element meshes be equally spaced, and the non-dimensional fundamental natural frequencies are predicted for the stationary circular plates without external load and constrained damping layer treatment where, ξ˜=0.001, Ko

= 0, Kt

= 0, ν

= 0.3. The results are listed in , where (b˜,Eθ,1/Er,1)=(100,0.5), (100, 1), (100, 2), (20, 1), (10, 1), (5, 1), and (4, 1). Let Nr be the number of elements in the r-direction and Nz the number of elements in the z-direction. For each of the aforementioned (b˜,Eθ,1/Er,1) case, the non-dimensional fundamental natural frequencies are predicted for (Nr

∗

Nz) = (4 ∗ 3),(8 ∗ 3),(16 ∗ 3) and (32 ∗ 3). As shown in , good monotonic convergence is achieved for all cases by the proposed method as the number of elements Nr increases from 4 to 32 while the value of Nz remains the same. Furthermore, results obtained for (Nr

∗

Nz) = (32 ∗ 3) are compared to those published by Woo . Good agreements are observed as revealed by the trivial percentages of disagreement given in the last column of Let the polar orthotropic laminated annular plates be clamped at the inner radius r

=

a and free at the outer radius r

=

b. Let the number of elements in the r- and z-direction be 32 and 1, respectively, where the grids of the finite element meshes in the r-direction are equally spaced. The non-dimensional fundamental natural frequencies of rotating annular plates without external loads in various rotational speeds are predicted. Results are listed in , where Ω∼=0,2,4,8,1216, b˜=10,50, and ξ˜=0.1, Ko

= 0, Kt

= 0, ν

= 0.3. (a) contains results for b˜=10, the thick plate case, while (b) does results for b˜=50, the thin plate case. In comparison to published results obtained by Liu using the 3D finite element method also reveals the following tendencies: (1) with the exception of Ω∼=12 and 16, results obtained by the proposed method are consistently smaller than the previously reported results for the thick plate case (b˜=10); (2) for the thin plate case (b˜=50), results obtained by the proposed method are larger than the previously reported results. It is noted that the good agreement observed for Ω˜=0 reinforces the previous verification where stationary circular plates were considered.Let a uniform radial stress P be applied along the outer edge of a stationary annular plate. Then, employ the proposed method to solve for the dynamic instability region. Results obtained for Ko

= 1 and 0 ⩽

Kt

⩽ 2 are shown in , where the solid line displays present results and the dots are results previously obtained by Chen and Hwang shows hatched dynamic instability regions for varying dynamic in-plane loading Kt, where (a)–(c) displays results obtained for the thicknesses b˜=10 and (a)–(f) contains two sets of results, one set for Eθ,1/Er,1

=

Eθ,3/Er,1

=

Eθ/Er

= 0.5 and the other set for Eθ/Er

= 2. (a) shows instability regions obtained for Ω∼=0, where it is observed that the primary instability region occurs in the vicinity of twice the value of the flexural natural frequency and the second instability region does in the vicinity of the flexural natural frequency. By comparing results obtained for Eθ/Er

= 2 and Eθ/Er

= 0.5, it reveals that the instability regions of Eθ/Er

= 2 occupy regions of higher Θ∼ values than those of Eθ/Er

= 0.5 do. In addition, the sizes of instability regions for Eθ/Er

= 2 are smaller. While (a) shows instability regions obtained for Ω∼=0, (b) does instability regions of Ω∼=1 and (c) of Ω∼=2. It is observed that the instability regions of Eθ/Er

= 2 still occupy regions of higher Θ∼ values than those of Eθ/Er

= 0.5 do in (b) and (c), and the sizes of instability regions for Eθ/Er

= 2 are smaller than those of Eθ/Er

= 0.5. In addition, it is also observed that increasing the value of Ω∼ makes the instability regions shift toward regions of higher Θ∼ values. Also, the size of instability region shrinks as the value of Ω∼ increases from 0 to 1 and 2. While (a)–(c) displays instability regions obtained for thicknesses b˜=10, (d)–(f) do for a thinner plate of b˜=100. By comparing (a)–(c), it is observed that the instability regions not only shift in the positive Kt direction but also shrink and move toward the positive Θ∼ direction. In addition, the characteristic shark points of the instability regions of (a)–(c) disappear. The shift of instability region in Kt and Θ∼, along with the accompanying shrinking in the size of instability region size, reveals that damping effects increase with thicker b˜.(a)–(c) and (d)–(f), it is again observed that increasing Ω∼ makes the instability regions shift toward regions of higher Θ∼ values and the size of instability region shrinks as the value of Ω∼ increases from 0 to 1 and 2. By comparing (a)–(c) with (d)–(f), it is observed that the instability regions of Eθ/Er