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= 2.8, δEu = 0.96–1.00), with enrichment in LILEs and depletion in HFSEs. They also contain high Cr and Ni, and have Zr/Hf and Nb/Ta ratios similar to those of the primitive mantle. The syenites are alkaline in composition, with 8.67–8.88 wt.% Na2O + K2O, and show high total REE contents (543–854 ppm) and strong LREE-enriched patterns with minor Eu negative anomalies (La/YbN |
= 50–101, Gd/YbN |
= 5.2–5.3, δEu = 0.80–0.82). Trace element diagrams show strong LILE-enrichment relative to HFSE. Zr/Hf and Nb/Ta ratios are 47–49 and 26–76, respectively, which are much higher than those of primitive mantle and higher than the average Nb/Ta ratio of post-Archean continental crust. The petrological and geochemical features indicate that these dykes were derived from a deep subcontinental lithospheric mantle source, which implies that the NCC probably had continental crust of considerable thickness at this time. Combined with evidence for ∼2.5 Ga granite intrusion and metamorphism in the Eastern Hebei region and adjacent areas, we propose that the NCC has been a present scale craton at the end of Archean.The North China Craton (NCC) contains some of the oldest rocks on earth with crust up to 3.8 Ga () and has a complicated evolution history (As with other cratons, the Archean rocks in the NCC can be divided into high-grade region and greenstone-granite region, although nearly all rocks underwent metamorphism of granulite to amphibolite facies. shows the distribution of the greenstone belts in the NCC. According to rock associations, greenstone belts metamorphosed in amphibolite facies are the Yanlingguan in western Shandong, the Dengfeng in central Henan, the Dongwufenzi in Inner Mongolia, the Wutaishan in Shanxi and the Qingyuan (Hongtoushan) in NE China (). The Yanlingguan greenstone belt formed at 2600–2700 Ma, and is composed of bimodal volcanic rocks and sedimentary rocks metamorphosed (). Some hornblendites and pyroxenites are similar to komatiites in chemistry, but typical spinifex texture is rare, possibly because of metamorphic recrystallization (). The metamorphosed sedimentary rocks include banded iron formations (BIFs), metapelites, and marble. The other four greenstone belts formed at the end of Neoarchean (). Their volcanic rocks have compositions ranging from basalt, andesite to rhyolite, and show geochemical characteristics of an island arc association. The BIFs in the Wutaishan greenstone belt constitute industrial deposits, while the Qingyuan greenstone belt contains Cu–Zn massive sulfide deposit with a few BIFs. High-grade granulite gneisses are extensively developed in the NCC. The main high-grade regions include Baishanzhen and Anshan in NE China, Qian’an in East Hebei, Taishan in Shandong, Huai’an in the juncture area of Hebei–Shanxi–Inner Mongolia, and Lushan in central Henan. The greenstone belts and high-grade regions were generally intruded by gneissic granites and charnockites. The high-grade regions are composed of orthogneisses (80–90%), meta-gabbros (5–10%) and slabs of supracrustal rocks (10–15%), associated with strong and complicated deformation. The supracrustal rocks comprise mafic granulites or amphibolites, BIFs, and medium-grained biotite gneisses with chemistries of slate-graywacke and intermediate-acid volcanics (). The Qian’an complex at granulite facies and the Anshan complex at amphibolite facies are characterized by abundant BIFs. Geochemical characteristics with rock associations show that these BIF-bearing supracrustal rocks and related intrusions have been produced by subduction-related processes (). Early arcs and back-arc basins which were engulfed by later plutonic rocks developed at active continental margins () proposed that the NCC can be divided into several micro-blocks with >∼3.0–3.8 Ga old continental nuclei, which are surrounded by late Archean and Proterozoic rocks. The greenstone belts are interpreted as back-arc basin associations while the 3.0–2.5 Ga high-grade regions are thought to represent a continental margin, or island arc association. The suggested micro-blocks are outlined by the greenstone belts (), which are, in turn from east to west, Jiaoliao (JL), Qianhuai (QH), Fuping (FP), Ji’ning (JN), and Alashan (ALS) blocks, and Xuchang (XCH) block in the south. Recent studies have led to a consensus that the basement of the NCC was composed of different blocks/terranes which were finally amalgamated to form a coherent craton (The Archean Eastern Hebei region is a key area for understanding the early Precambrian evolution of the NCC (). Mainly based on the early Precambrian geology of Eastern Hebei and comparing it to other Archean terrenes, proposed a two-stage cratonization model for the NCC during Neoarchean, when several micro-blocks amalgamated together. suggested that the NCC existed at ∼3.0 Ga and evolved to a platform-style craton at the end of the Neoarchean, experienced sodium (TTG intrusive event), sodium–potassium (TTG and granitic intrusive event) and potassium (granitic intrusive event) cratonizations. The above-mentioned models are established on, respectively, the horizontal and vertical crustal growth.Extensive granitic intrusive bodies/sills and mafic dyke swarms are marks of cratonization (). Emplacement of ultramafic–mafic and alkaline dykes has long been considered to mark a post-orogenic or anorogenic event, and thus can be used to constrain the time of cratonization. The Neoarchean granitoids and mafic dykes in the Eastern Hebei region have been described in detail (). Recently, we have for the first time found coeval ultramafic–mafic dykes and syenitic dykes in Eastern Hebei, which intrude Archean rocks and are also unconformably covered by the Paleoproterozoic Changcheng System sediments. This paper discusses the age and petrogenesis of the dykes, constraining the Archean–Proterozoic boundary, and its significance for cratonization of the NCC.Archean rocks are well developed in the Eastern Hebei region, and include TTG and granitic gneisses, gabbroic intrusive rocks, BIF-bearing supercrustal rocks metamorphosed to granulite and high-grade amphibolite facies (). These rocks constitute three lithological-tectonic units, which are the Palaeoarchean Caozhuang complex (CZC), Meso-Neoarchean Shuichang complex (SCC) and Neoarchean Zunhua complex (ZHC) (). The CZC includes remnants of 3.8–2.5 Ga old sial crust in the NCC (), occupying ∼4 km2. A Quaternary sequence covers the complex in the east, and the Paleoproterozoic Changcheng System unconformably overlies the complex in the west and south. To the north, the CZC is in contact with the SCC along a ductile shear zone that has been multiply deformed, with the CZC finally thrust on to the SCC (). The CZC includes metamorphosed supracrustal rocks and tonalitic gneisses named Caozhuang Group and Huangboyu gneiss, respectively. The Caozhuang Group is composed of thin interlayered meta volcanic (30–53 vol.%) and sedimentary (65–70 vol.%) rocks, which are amphibolites, BIFs, serpentine marbles, fuchsite quartzite and local tremolite- and diopside-rich rocks. The protolith rocks of the amphibolites and tremolite-rich rocks are geochemically tholeiitic or komatiitic. The amphibolites contain little high REE abundance with slightly enriched LREE patterns; their contents of Cr (∼226 ppm), Ni (∼144 ppm) and MgO (up to 9.44%) are also slightly high (). It has been proposed that these basalts were derived from large-degree partial melting of the mantle (). The Huangboyu tonalitic gniesses underwent very complicated deformation. Their zircon U–Pb ages are 3.4–3.2 Ga (). Overall, the CZC is similar in its rock association and chemistry to other Meso-NeoArchean high-grade complexes in the NCC ( suggested that this early sialic crust was possibly an old island arc related to subduction of intraoceanic crust.The SCC occurs as a dome with an area of ∼700 km2, and has traditionally been termed the Qian’an migmatite–granitoid uplift terrain (). The U–Pb zircon ages of diorite and granodiorite of the Qian’an dome are 2499 Ma and 2494 Ma (). It is unconformably covered by the Paleoproterozoic Changcheng System and Mesozoic sediments at its western and eastern margins. Its northern boundary is a fault separating it from the NeoArchean ZHC. The meta-supracrustal rocks and some banded orthogneisses commonly occur as complicated folded slabs along the margins of the terrain, especially at the western and northern margins. The main supracrustal rocks are mafic granulites, pyroxene amphibolites, pyroxene-bearing biotite plagioclase gneisses, and some garnet–sillimanite gneisses and garnet-bearing fayalite peridotites (eulysite). Abundant BIFs constitute the most important iron deposits in China. The supracrustal rocks underwent metamorphism to granulite facies under moderate pressure. The supracrustal rocks and intrusive granitic sills have Sm–Nd and zircon U–Pb ages of 3280–3049 Ma (). The metamorphosed supracrustal rocks and banded gneisses of the SCC are considered to be a typical example of old island arc complex according to the rock association, deformation and geochemistry (). However, granitic and charnockitic bodies occurring along the northern margin yield much younger zircon U–Pb ages of 2647–2495 Ma than those of the supracrustal rocks () can be divided into two parts: the linear Zunhua unit at high-grade amphibolite facies (partially granulite facies) and the domal Taipingzhai unit at granulite facies. The supracrustal Zunhua unit trends NE to EW, and contains some granitoid sills. suggested that the Zunhua unit is a high-grade metamorphosed greenstone belt. The Taipingzhai unit occurs as domes with complicated fold patterns and mainly comprises TTG orthogneisses, gabbroic rocks and some small lenses of supracrustal rocks. The supracrustal rocks in the two units are almost the same in terms of their geochemistry, metamorphic history and geochronology. The main rock types include amphibolites/two pyroxene granulites, biotite felsic gneisses/intermediate-acid granulites and BIFs (). The granitic gneisses of the Zunhua unit have zircon SHRIMP ages of 2495–2536 Ma (). Meta-volcanic rocks demonstrate an evolving trend from basalt, andesite to rhyolite, and have similar geochemistry to modern island arc volcanic rocks (). The Taipingzhai unit comprises tonaltitc granulites and some meta-gabbros (mafic granulites). Their Rb–Sr and Sm–Nd isochron ages are 2470 ± 70 Ma and 2480 ± 125 Ma, respectively (), their single-grain zircon U–Pb ages are 2480–2530 Ma (), and their zircon SHRIMP U–Pb age is 2564 Ma (). The Sm–Nd mineral-rock isochron ages for mafic rocks from Zunhua and Taipingzhai are 2591 ± 142 Ma and 2644 ± 112 Ma (). The metamorphic history of the mafic granulites is characterized by a mineral reaction texture with clinopyroxene surrounded by small garnets, showing an anticlockwise PT path ( suggested that the Zunhua and the Taipingzhai units jointly constitute a Neoarchean island arc terrain, respectively representing the upper part and the root part. From the above, it can be seen that the Eastern Hebei high-grade region is mainly composed of three ancient island arc terrains that formed during the Paleoarchean, Mesoarchean and Neoarchean periods, respectively (). This seems to indicate a tectonic process of island arc terrain accretion achieved by arc–arc or arc-micro-continent collision (Extremely rare Archean ultramafic–mafic and syenitic dykes have been found in the CZC. is a geological sketch map of the CZC. The >3.0–3.3 Ga rocks form approximately half of the outcropping rocks and include BIF-bearing supracrustal rocks and TTG–granitic gneisses. The remaining 50% are Neoarchean granitic rocks, including hypersthene granite with an age of 2.52–2.56 Ga, granite formed at 2.53 Ga and monzodiorite at 2.60 Ga (). The direct country rocks of the ultramafic–mafic and syenitic dykes are gneissic monzodiorite and BIF-bearing supracrustal rocks. The intrusive boundaries are clear and the dykes cut the gneissosity of the country rocks and show spherical weathering in the field. They occur as subvertical intrusions with a NW310° strike, and are up to 300 m long and about 10 m wide.The ultramafic–mafic dykes are dark grey in color and consist mainly of clinopyroxene (40–70%), olivine (5–20%), orthopyroxene (5–20%), with minor hornblende (<5%), biotite (<2%) Fe–Ti oxides (<2%), spinel (<5%), with or without plagioclase (0–40%). The dykes can be subdivided into olivine pyroxenite and olivine gabbro, which have medium granular (c and d). A reaction rim of orthopyroxene and hornblende replacing olivine is common (e). Also observed is exsolution of orthopyroxene along cleavages of clinopyroxene (The syenitic dykes consist predominantly of orthoclase (>75%) and biotite (5–15%), and minor plagioclase (<7%), quartz (<5%) and Fe–Ti oxides, and without pyroxene (g and h). So we call them syenite. The rocks have hypidiomorphic-granular texture.The samples Nos. 04QA09, 05QA11, 05QA12 are of ultramafic–mafic dykes, and Nos. 04QA08, 05QA10 and 05QA13 are syenitic dykes. The mineral compositions are listed in Olivine gabbro sample 04QA09 and syenite sample 04QA08 selected for zircon SHRIMP dating were collected in the area at N 39°55′55″ and E 118°33′16″ (). The samples of olivine gabbro and syenite are fresh and more than 10 kg and 2 kg, respectively. Zircon grains from the samples were separated using standard heavy liquid and magnetic techniques, and then, zircons were extracted by hand-picking under a binocular microscope. The zircons, together with a zircon U–Pb standard TEM (417 Ma), were cast in a epoxy mount, which was then polished to section the crystals in half for analysis. Zircon U–Th–Pb analysis was conducted on the SHRIMP II at the Beijing SHRIMP Center. U–Th–Pb isotopic ratios and absolute abundances were determined relative to the SL13 standard zircon (206Pb/238U = 0.0928 corresponding to 572 Ma, 238 ppm 238U). Measured compositions were corrected for common Pb using the measured non-radiogenic 204Pb. The data were processed using the Squid and Isoplot programs ( are given at 1-sigma with weighted means at the 95% confidence level. Cathodoluminescence (CL) images of zircons were collected prior to analysis on an electron microprobe Cameca SX51 (EMP) at the State Key Laboratory of Lithospheric Tectonic Evolution, IGGCAS.Zircon grains from both samples are light brownish and translucent with stubby, prismatic and irregular crystal shapes, and with oscillatory zoning, typical of a magmatic origin (). The analyses of the olivine gabbro and syenite dykes (04QA08 and 04QA09) are listed in . The Th/U ratios range from 0.83–1.90 to 0.91–1.78 for zircons from the olivine gabbro and syenite dykes, respectively. Because of low zircon yield, only six zircon grains were determined from the olivine gabbro and they yielded a weighted mean 207Pb/206Pb age of 2516 ± 26 Ma (), interpreted as the crystallization age. Fifteen zircon grains from the syenite dyke yielded a weighted mean 207Pb/206Pb age of 2504 ± 11 Ma (b), interpreted as the crystallization age of the syenite.Zircon Hf isotopic compositions were conducted on the Neptune MC-ICPMS equipped with a 193 nm laser in the State Key Laboratory of Lithospheric Tectonic Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences (IGGCAS). The spot sizes were 31.5 or 63 μm with an ablation time of about 26 s during analysis. Zircon 91500 was used as the standard. The laser impulse was 8–10 Hz and the energy was 100 mJ. Detailed analytical procedures are described by . The weighted average 176Hf/177Hf ratios of zircon 91500 during the sample analysis of 04QA09 and 04QA08 were 0.282308 ± 10 and 0.281314 ± 11, consistent with the results, within errors by the solution method (), respectively. The analyses are listed in . 176Lu/177Hf ratios of zircons from the olivine gabbro and syenite samples are less than 0.002, with average ratios of 0.001 and 0.0009, respectively, indicating low radiogenetic growth of 176Hf. Zircons from the olivine gabbro have 176Hf/177Hf ratios varying from 0.281286 to 0.281368, yielding single-stage Hf model ages between 2668 Ma and 2740 Ma, with a mean age of 2705 Ma, and ɛHf(t) values between +1.9 and +4.2, with a weighted mean value of +3.13 ± 0.40. Zircons from the syenite have 176Hf/177Hf ratios varying from 0.281280 to 0.281382, yielding single-stage Hf model ages between 2646 Ma and 2705 Ma, with a mean value of 2677 Ma, and ɛHf(t) values between +2.7 and +4.4, with a weighted mean value of +3.56 ± 0.23.Major elements, trace elements and Rb–Sr, Sm–Nd isotopic compositions were also determined in order to constrain magma genesis of the ultramafic–mafic and syenitic dykes.All elements were analyzed at the IGGCAS. Major elements were analyzed by X-ray fluorescence (XRF) combined with wet chemical methods for FeO and LOI. Inductively Coupled Plasma Mass Spectrometry (ICP-MS) was used to analyze trace element concentrations. Analytical uncertainties are ±3–5% for major elements and better than 5–8% for trace elements. Rb, Sr, Sm and Nd were separated using conventional ion exchange procedures and measured using a Finnigan-MAT262 mass spectrometer. Samples were dissolved in Teflon bombs after being spiked with 84Sr, 87Rb, 150Nd and 147Sm tracers before HF + HNO3 (with a ratio of 2:1) dissolution. Procedural blanks were < 100 pg for Sm and Nd and < 500 pg for Rb and Sr. 143Nd/144Nd ratios were corrected for mass fractionation by normalization to 146Nd/144Nd = 0.7219, and 87Sr/86Sr ratios were normalized to 86Sr/88Sr = 0.1194. Typical within-run precision (2σ) for Sr and Nd isotopic ratios was estimated to be about 0.000015. The measured values for the Ames Nd standard and NBS987 Sr standard were 143Nd/144Nd = 0.512147 ± 10 (2σ, n |
= 1) and 87Sr/86Sr = 0.710247 ± 14 (2σ, n |
= 1), respectively, during the period of data acquisition. The analytical results for major-trace elements and Rb–Sr, Sm–Nb isotopic elements are shown in The Mg# of olivine gabbro ranges from 59 to 63 and is similar to high-magnesian tholeiitic basalt. The samples have relative LREE-enriched patterns without Eu anomalies (La/YbN |
= 9.28–9.78, Gd/YbN |
= 2.8, δEu = 0.96–1.00; . Their primitive mantle normalized trace element spidergrams show an enrichment in LILEs and a depletion in HFSEs (b). They also contain high Cr and Ni, and have Zr/Hf and Nb/Ta ratios similar to those of the primitive mantle. High MgO, Cr and Ni contents in the olivine gabbros indicate a mantle source for the magma, and Zr/Hf and Nb/Ta ratios also indicate that the magma of the olivine gabbros was not substantially modified en route to the crust (). The enriched LREE and LILE characteristics likely inherited from a mantle source.The syenites are alkaline in composition, with 8.67–8.88 wt.% Na2O + K2O, and show high total REE contents (543–854 ppm) and strong LREE-enriched patterns with minor negative Eu anomalies (La/YbN |
= 50–101, Gd/YbN |
= 5.2–5.3, δEu = 0.80–0.82; c). Spidergrams of trace elements show strong LILE-enrichment relative to HFSE (d). Zr/Hf and Nb/Ta ratios of the syenites are 47–49 and 26–76, respectively, which are much higher than those of primitive mantle and higher than the average Nb/Ta ratio of post-Archean continental crust (). High Nb/Ta and Zr/Hf ratios combined with very high Ba (up to 2423 ppm) and Sr (up to 1120 ppm) contents, which are much higher than those of continental crust (Ba 220 ppm, Sr 215 ppm) (), exclude the possibility of crustal assimilation. The enrichment of LREEs and HFSEs in the syenites can be interpreted as a feature of an enriched mantle.Initial 87Sr/86Sr ratios (ISr) and ɛHf(t) values (), calculated back to 2516 Ma and 2504 Ma for the olivine gabbro and syenite, respectively, range from 0.70053 to 0.70135 and from +2.04 to +2.08 for four olivine gabbro samples, and from 0.700311 to 0.700445 and from +1.08 to +1.18 for two syenite samples. The olivine gabbros have higher ɛNd(t) values that correlate with relatively less enrichment in LILEs and LREEs, while the syenites have lower ɛNd(t) values that correlate with relative enrichment in LILEs and LREEs. Similar Sr and Nd isotopic compositions of the olivine gabbros and syenites may imply that they share a common origin. When compared to the DMM (ɛNd(t) value of 4.5 and ɛHf(t) value of 8.2 at 2.5 Ga), and coupled with the geochemical characteristics mentioned above, Nd and Hf isotopic compositions of the olivine gabbros and syenites indicate a mantle source that must have been enriched by geological processes such as metasomatism from a subducted slab (Although it is difficult to estimate the depth of the magma source, we consider that the coeval ultramafic–mafic and syenitic dykes may be derived from the continental lithospheric mantle based on their petrology and geochemistry. In general, the thickness of the continental lithosphere varies with time from ancient to present, and it shows a positive correlation that the thickness of continental lithosphere are 200–300 km, >200–150 km and <150–80 km on average in the Archean, the early Proterozoic and the Paleozoic, respectively (). Seismological studies suggest that the lithospheric thickness of the Kaapvaal Craton, Zimbabwe Craton and the Limpopo Belt is 300–250 km (). The thickness of the Archean lithosphere of the NCC has been considered to be >200 km according to the studies of seismology and petrology of kimberlite and other volcanic rocks within the NCC (). A >200 km lithospheric thickness indicates the Eastern Hebei region and surrounding areas were geotectonically stable at the end of Archean.The coeval olivine gabbro and syenite dykes yield ∼2.5 Ga SHRIMP zircon U–Pb ages. It is worth to notice that 2.5 Ga is the formal boundary age between the Archean and Proterozoic eons. After this time there was a diapause in continental evolution in 2450–2350 Ma without extensive magmatic activity (The Archean and Proterozoic rocks demonstrate an enormous difference on rock association and geochemistry. The connotation of the Archean–Proterozoic boundary is global cratonization and formation of continents on present scale. suggested that there was a ∼2.5 Ga Neoarchean supercontinent, followed by continental break-up in the Paleoproterozoic. The late Archean cratonization of Eastern Hebei is indicated by extensive intrusion of granites and mafic-granulite and amphibolite dykes. shows the locations of the Late Neoarchean granites with SHRIMP zircon U–Pb ages, which are widely distributed in the Eastern Hebei region and intruded into various metamorphic supracrustal and magmatic rocks (; Yang, J.H., personal communication). The granites occur as sills and small bodies, accompanied by strong migmatization and pegmatite intrusion. As the youngest magmatic intrusions in the Archean, the coeval ultramafic–mafic and syenitic dykes were emplaced into ∼2.5–2.6 Ga granite sills, migmatite and pegmatite, indicating Archean cratonization was finalized.The main micro-continental blocks in the NCC are shown in . The rock types and their distribution in these micro-blocks display distinct differences. For example, old rocks up to 3.8 Ga and abundant Mesoarchean BIFs are only present in the Qianhuai (QH) block. Rocks older than Neoarchean are not exposed in the Jingning (JN) and Fuping (FP) blocks, although they may exist in the deep crust, based on geophysical data. Neoarchean magmatism in these blocks took place at 2.9–2.7 Ga and 2.6–2.45 Ga, but their intensity in different blocks varies greatly. Volcanic activity from 2.9 to 2.7 Ga was, in general, strong in all blocks, especially in the Jiaoliao (JL), Qianhuai (QH) and Xuchang (XCH) blocks, associated with abundant BIFs. However, BIFs are not common in the Alashan (ALS) block (). Volcanic activity at 2.5 Ga was weak in the JN block, however, it was intense in the JL, FP and XCH blocks. Basic-intermediate-acid volcanic rocks in the FP and XCH areas were closely associated with the BIFs. In the JL block, however, volcanic rocks contain massive sulfide Cu–Zn ores. All these differences indicate that these micro-blocks possibly developed in different tectonic settings, i.e. they had not been amalgamated into a coherent craton until at least ∼2.5 Ga. It is noteworthy that nearly all Archean rocks underwent ∼2.5–2.55 Ga metamorphism and voluminous granitic sills with an age of ∼2.5 Ga intruded into neighboring blocks, suggesting amalgamation prior to the intrusion. For example, a series of granite bodies are located along the contact zone between the JL and QH blocks (), indicating that the micro-blocks were assembled together and constituted a combined NCC by the end of Neoarchean (). More data have been published recently, which reveal that the granite sills and pegmatites with 2457–2570 Ma zircon U–Pb ages are extensively developed in all six micro-blocks (). For example, the Molihong high-potassium granite and Caiyu hypersthene-bearing granite in the JL block, the Angou granite and Shipaihe granodiorite in the XCH block, the Wanzi granite and Pingshan granite in the FP block, the Guyang granite in the JN block, and the Shanhaiguan granite and Qian’an granite in the QH block are representative intrusive bodies with ∼2.5 Ga zircon U–Pb ages, clearly marking the Neoarchean cratonization of the NCC (). Therefore, it is reasonable to suggest that the NCC formed at the end of the Archean. proposed an important tectonic unconformity between Archean basement and the Paleoproterozoic metamorphic sedimentary rocks (khondalite series). Although both underwent high-grade metamorphism and complex deformation, they show substantial differences in rock association, geochemistry and structural style. The khondalite series are, as a common Precambrian rock association, distributed widely in the NCC, and called the Fengzhen Formation in the JN block, the Lüliang Formation in the FP block, the Fenzishan Formation in the JL block, the Louzishan Formation in the Qianhuai (QH) block, the Huoshan Formation and the Lushan Formation in the Xuchang (XCH) block. Detailed geological and geochemical studies support that the khondalite series were mainly formed at Paleoproterozoic (). The khondalites are composed of argillo-arenaceous rocks, so need a relatively large-scale Archean cratonic basement (The Archean coeval ultramafic–mafic and syenitic dykes are rare, which provide important evidence with respect to early continental tectonic evolution. Our study indicates that the dykes represent the latest stage of Archean magma activity in the NCC and that their magma source was in the subcontinental lithosphere mantle. In other words, the coeval ultramafic–mafic and syenite dykes mark that the Eastern Hebei region formed a stable craton at the end of Archean. Our results support that the eastern part of the NCC, together with other areas of the NCC, formed a stable craton in the Neoarchean (Development of Mo‐Ni‐Si‐B metallic glass with high thermal stability and H versus E ratiosWe report a novel Mo‐Ni‐Si‐B metallic glass which can be solidified into fully amorphous state by melt-spinning process, with high crystallization onset temperature of over 1100 K, extremely high Vickers hardness of 27.5 ± 2.2 GPa and relatively low Young's modulus of 364.3 ± 6.6 GPa. The dense cluster-packing model suggests that the addition of boron up to 10 at.% can occupy vacant cluster-interstices of (Mo, Ni)-Si cluster arrays, which results in a more efficiently dense-packed cluster structure, destabilizes the formation of nanocrystalline phases, and systematically increases the glass-forming ability (GFA) in Mo‐Ni‐Si‐B alloys. The GFA parameters that do not directly rely on Tg, such as ΔT* and ε parameter, show greater reliability to evaluate GFA for Mo‐Ni‐Si‐B metallic glass exhibiting no clear Tg. The H/E and H2/(2E) ratios of the newly developed Mo‐Ni‐Si‐B metallic glass, which reflect wear resistance and resilience, exhibit the highest values among various hard ceramic materials as well as metallic glass-forming alloys developed up to now. These advantages of Mo‐Ni‐Si‐B metallic glass can be used more widely to form a high temperature wear-resistant coating layer on various substrates. Furthermore, the same idea might be used to form a metallic glass-nitride nanocomposite coating layer by reactive deposition in N2 ambient, with highly lubricative property and high wear-resistance, especially at high temperature.Metallic glasses have excellent mechanical properties, such as high strength, hardness, large elastic strain limit and low elastic modulus In this regard, efforts to develop thermally stable metallic glasses continued for a few decades. The metallic glasses based on the early transition metal (ETM) elements such as Zr and Ti, which are widely used for composing glass-forming systems, have relatively low thermal stability with Tx under 800 K despite their high glass-forming ability (GFA) High-temperature wear-resistant coatings have been widely used for materials under continuous frictional stress without extra cooling process, such as high-speed bearings, cutting tools and engines, and also have been continuously developed to endure extreme environments required in modern mechanical engineering technologies and industries. Although high hardness (H) has been regarded as a primary property for highly wear-resistant coating materials, a relatively low elastic modulus (e.g. Young's modulus, E) is also required for achieving high wear resistance with reasonable reliability by reducing elastic property mismatch between coating and substrate and by increasing elastic strain to failure which is related to the H/E ratio In this article, we report a novel Mo‐Ni‐Si‐B metallic glass which can be fabricated by melt-spinning process, with high thermal stability of Tx |
= 1112 K, extremely high Vickers hardness of 27.5 ± 2.2 GPa and relatively low Young's modulus of 364.3 ± 6.6 GPa. In order to enhance the GFA of Mo‐Ni‐Si ternary system, boron was selected as the fourth alloying element. The effect of boron addition to the Mo‐Ni‐Si system, (Mo45Ni45Si10)100-xBx (x |
= 0, 2, 5, 7, 10), on GFA and mechanical properties of as-spun ribbons was systematically evaluated using transmission electron microscopy (TEM) and nanoindentation tests. Furthermore, we fabricated thin film metallic glass using the developed (Mo45Ni45Si10)90B10 glass-forming alloy, which exhibits properties similar to fully amorphous ribbon samples. The dense cluster-packing model The structures of the samples were confirmed by X-ray diffraction (XRD: Rigaku CN2301) for the as-spun ribbon samples and grazing incidence X-ray diffraction (GI-XRD: Bruker D8 Advance) for the thin film sample, using monochromatic Cu Kα radiation. The crystallization behaviors of the as-cast ribbons were investigated by differential scanning calorimetry (DSC: Mettler Toledo TGA/DSC 1) at a heating rate of 20 K/min. The microstructures of the samples were examined by TEM (Jeol JEM-3010, Philips CM300FEG/UT) operated at 300 kV. The thin foil TEM specimens were prepared by ion milling (Gatan 695 PIPS II) with liquid nitrogen cooling after mechanical thinning process. In order to reduce ion-milling time and re-deposition effect, the ribbon samples were mechanically polished to a wedge shape with a wedge angle of 1° (Allied Multiprep polishing system) before ion-milling.The mechanical properties of the ribbon samples and the thin film sample were evaluated from instrumented nanoindentation tests. The nanoindentation tests were performed for the ribbon samples using a nanomechanical tester (Hysitron TI 750 TriboIndenter) and for the thin film sample using in-situ SEM indentation tester (Hysitron PI-85 SEM Picoindenter) for precise measurements in small indentation depth conditions. Indenting force was loaded up to peak force in 5 s with constant loading rate using Berkovich diamond tip, remained at the peak force for 2 s, and then was unloaded in 5 s. The peak force was 5 mN for the tests of the ribbon samples and the hardness measurement of the thin film. For Young's modulus estimation of the thin film, the peak forces of serial indentation tests were in the range of 200–5000 μN. The Vickers microhardness of the selected sample was also measured with 0.1 kgf load condition by the microhardness tester (EMCO-TEST DuraScan 70). Both the nanoindentation and microhardness tests were repeated 10 times to obtain average values, and standard deviations were used as error ranges.Since the liquidus projection and eutectic point of the Mo‐Ni‐Si ternary phase diagram have not been reported yet, the GFA variation in the ternary system was firstly investigated by experimental process. Although we could not find a glass-forming composition area in the Mo‐Ni‐Si ternary system, relatively broad peaks were observed in XRD patterns of the Mo100-i-jNiiSij as-spun ribbons with the composition range of 40 ≤ |
i |
≤ 60, 0 ≤ |
j |
≤ 20. In particular, at the composition of Mo45Ni45Si10, wide peak broadening which is related to nanocrystallization during solidification appears at two-theta range of 40–47° as shown in , indicating that the alloy exhibits relatively high liquid stability (= low Tl). As marked in , the Mo45Ni45Si10 ternary alloy has crystalline peaks which originate from nanocrystalline phases of Mo24Ni21Si7 (ICDD PDF No. 01-089-5106, Mo6Ni5.25Si1.75) and Mo31Ni19 (ICDD PDF No. 00-047-1129, Mo1.24Ni0.76). Then, the effect of boron as a fourth element on the structure and GFA was investigated in (Mo45Ni45Si10)100-xBx (x |
= 0, 2, 5, 7, 10) alloy. As shown in , the intensities of these sharp crystalline peaks clearly become lower with increasing boron contents, and the broad diffuse peak without clear crystalline peak in the range of 40–47° starts to appear with the addition of boron over 7 at.%, while a small Mo24Ni21Si7 peak at near 37° still remains. With further addition of boron, (Mo45Ni45Si10)90B10 shows a sole broad diffuse peak without any crystalline peaks, as a typical pattern of fully amorphous materials. shows a DSC thermogram of as-spun Mo‐Ni‐Si‐B alloy ribbons. (Mo45Ni45Si10)95B5 or the other samples with under 5 at.% of boron exhibit no clear characteristic transformation behavior of amorphous phase before melting. In contrast, (Mo45Ni45Si10)93B7 and (Mo45Ni45Si10)90B10 show clear exothermic peaks which correspond to crystallization reactions of the amorphous phase. The crystallization onset temperatures (Tx) of (Mo45Ni45Si10)93B7 and (Mo45Ni45Si10)90B10 were 1098 K and 1112 K, respectively, which are significantly higher than those of general transition metal-based glass-forming alloys such as Cu-, Zr-, Ni-, and Fe-based systems. (Mo45Ni45Si10)93B7 has lower enthalpy change of crystallization (20.4 J/g) compared to (Mo45Ni45Si10)90B10 (33.1 J/g) because of partially crystallized structure and low fraction of the amorphous phase in (Mo45Ni45Si10)93B7 as shown in XRD patterns.The microstructures of the as-spun ribbons were carefully investigated by TEM. The bright-field (BF) images and selective area diffraction patterns (SADPs) of (Mo45Ni45Si10)100-xBx (x |
= 0, 2, 5, 7, 10) ribbons are shown in . From x = 0 to 5 samples, fully nanocrystalline phases were formed in as-spun state, and the spot patterns from multiple nanograins of different orientations create ring-type patterns with irregular intensity variation, as shown in (a–c). Furthermore, the SADPs of as-spun ribbons were converted to diffraction profiles by azimuthal integration (a–e), which correspond to the XRD patterns of . The relatively sharp peaks from nanocrystalline phases appear in the diffraction profile of Mo45Ni45Si10 ternary alloy, while the peaks clearly broaden and profile intensities decrease with the addition of boron. The average grain sizes of the samples with x = 0, 2, and 5 were 63 nm, 43 nm, and 26 nm, respectively, which shows that the grain size of nanocrystalline samples decreases with increasing boron content ( (f–h)). With boron addition over 7 at.%, amorphous matrix was formed with embedded crystalline phases of the average sizes under 10 nm ((i)). In (Mo45Ni45Si10)90B10 sample, the homogeneous amorphous structure was confirmed by uniform contrast in the BF image of (j) and the broad diffuse halo ring pattern in (e). The random atomic arrangement in the high-resolution image and the broad ring pattern without any diffracted spot in the inset fast Fourier transformed (FFT) pattern of also demonstrate the fully amorphous structure of (Mo45Ni45Si10)90B10 sample. shows nanohardnesses and reduced elastic moduli (E′) of the (Mo45Ni45Si10)100-xBx (0 ≤ |
x |
≤ 10) as-spun ribbons evaluated by nanoindentation test. The nanohardness values of the as-spun samples were over 20 GPa, which are much higher than that of nanocrystalline Mo (9.98 GPa shows grain size (D) variation depending on boron content (XB) and its exponential fitting line. The relation between grain size and nanohardness (H) is also fitted with Hall-Petch relation (H |
= |
H0 |
+ |
kHD− 0.5) . Interestingly, with formation of amorphous phase, the nanohardness values of (Mo45Ni45Si10)93B7 and (Mo45Ni45Si10)90B10 ribbons increased drastically as compared with the fully nanocrystalline samples (x = 0 to 5), and the nanohardness of fully amorphous (Mo45Ni45Si10)90B10 ribbon was 24.6 ± 0.4 GPa. Furthermore, the average Vickers hardness value from the measurements repeated 10 times was 27.5 ± 2.2 GPa, which is comparable with nanohardness value.From instrumented nanoindentation test, the Young's modulus (E) of a sample is determined using the relation E* is the “specimen and indenter” modulus, which can be directly obtained from a nanoindentation result using the unloading part of load-displacement curve and the projected area of the elastic contact. ν is Poisson's ratio, and the subscript i denotes indenter tip, where Ei |
= 1141 GPa and νi |
= 0.07 for diamond tip also shows reduced elastic moduli of the (Mo45Ni45Si10)100-xBx (0 ≤ |
x |
≤ 10) as-spun ribbons obtained from nanoindentation test. E′ of the fully nanocrystalline samples increased with the addition of boron or decrease in grain sizes (= increase in hardness), while the formation of amorphous phase does not lead to a meaningful increase in E′ despite drastic increase of nanohardness in (Mo45Ni45Si10)93B7 and (Mo45Ni45Si10)90B10 alloys. The Young's modulus of (Mo45Ni45Si10)90B10 metallic glass is 364.3 ± 6.6 GPa which is obtained by conversion from reduced elastic modulus (E′ = 407.6 GPa) under the assumption of 0.3 < |
ν |
< 0.35.A thin film sample was deposited using (Mo45Ni45Si10)90B10 alloy ingot as a source of e-beam evaporation process. The final thickness of the as-deposited film was around 100 nm. The GI-XRD pattern of the as-deposited film () includes a broad diffuse peak of an amorphous phase and a few sharp peaks from the stainless steel substrate underneath the thin film.In order to measure mechanical properties such as hardness and elastic modulus only from a thin film directly, the indentation depth is limited to < 1/10 of the film thickness where Hf, Hs, and Hc are the hardness of the film, the substrate and the composite, respectively. h is indentation depth (= 130 nm) and t is the film thickness (= 100 nm). C is a geometric constant determined from the semi-apical angle (δ) of indenter tip. For the Berkovich tip (δ |
= 65.3°), C is equal to 1 − sin δ (= 0.0915) for a hard brittle film on a soft substrate, and cos2δ (= 0.1746) for a plastically deformable film on a hard substrate Due to the same instrumental limitation of thin film indentation test, the Young's modulus of the deposited Mo‐Ni‐Si‐B thin film was estimated by serial nanoindentation tests with various indentation depths. shows the reduced elastic moduli of the composite (Ec′ = (1/E* − 1/Ei′)− 1 from Eq. ) depending on a/t values obtained from different indentation depths. a is the characteristic size of the contact area, which is a |
≒ 2.8 hc for Berkovich tip, where hc is the contact depth of indentation where α is an empirical constant, and the subscripts c, f and s denote composite, film and substrate, respectively. The red line of shows a fitting curve using Doerner and Nix function with α |
= 1.83 and the estimated E′ of Mo‐Ni‐Si‐B thin film (E′f) is 400.0 ± 10.1 GPa (Ef |
= 357.5 ± 6.5 GPa) under the assumption of 0.3 < |
ν |
< 0.35, which is comparable with that of (Mo45Ni45Si10)90B10 amorphous ribbon (E′ribbon |
= 407.6 ± 10.9 GPa and Eribbon |
= 364.3 ± 6.6 GPa).The GFA of refractory metal (including molybdenum)-based system is limited due to the high melting temperature of refractory metals and eutectic reactions at high temperature in refractory alloy systems ) and the existence of eutectic point at higher contents of Mo, 2293 K of Mo73.6Si26.4 composition and 2173 K of Mo46Si54 composition , which means the formation of fine nanocrystalline phases down to 100 nm as shown in In order to enhance GFA of Mo‐Ni‐Si alloy system, boron was chosen as an additional alloying element, because boron has large negative heat of mixing relation and also large atomic size difference over minimum 30% with the other three elements (). Chemical mixing enthalpy of an alloy based on the extended regular solution model (ΔHchem=∑Ωijcicj) can be calculated with the regular solution interaction parameter (Ωij |
= 4 × |
ΔHijmix) clearly show the dependence of GFA on the amount of boron addition. With increasing B contents the grain size in as-spun ribbon decreases and an amorphous phase starts to form with addition of boron over 7 at.%, and then (Mo45Ni45Si10)90B10 forms a fully amorphous ribbon.In order to explain how the boron addition enhances the GFA of the alloys, the atomic structure of amorphous Mo‐Ni‐Si‐B alloys was predicted using the dense cluster-packing model suggested by Miracle This model is potentially based upon a premise that glass-forming alloys have a single major element whose composition is far above 50 at.%, but the Mo‐Ni‐Si‐B alloys developed in this study have dual major elements of Mo and Ni with equivalent concentration (> 40 at.%) and similar atomic radius within 8% difference. In order to adapt this model to the developed alloy system, an assumption is introduced that both Mo and Ni act as a major solvent element from the equivalent composition and relatively small atomic size difference. By regarding both transition metals (Mo, Ni) as solvent atoms, their average atomic radius can be taken as the atomic radius of solvent (rMo |
= 1.39 Å, rNi |
= 1.28 Å shows the comparison of relative atomic size ratios (Rα |
= |
rsolute/rsolvent) and compositions for (Mo45Ni45Si10)100-xBx (x |
= 0, 2, 5, 7, 10) and the glass-forming composition range of Fe-metalloid (Fe‐(Si, P)‐(B, C)) metallic glasses . The atomic ratios of (Si, P) and (B, C) to solvent Fe in Fe‐(Si, P)‐(B, C) system are 0.797 and 0.609, respectively, which are very close to the ideal atomic ratios for the coordination number 10 and 8 (RN=10 |
= 0.799, RN=8 |
= 0.617). As shown in , the glass-forming range of Fe‐(Si, P)‐(B, C) system exists near the ideal composition of < 10 − 8 > γ vacant model, and this accordance shows that the dense cluster-packing model provides a good prediction on the favorable alloy compositions for glass formation in Fe‐(Si, P)‐(B, C) system . With increasing B addition in (Mo45Ni45Si10)100-xBx alloys, the alloy composition approaches the ideal composition in < 10 − 8 > γ vacant model. This means, according to the ideal dense cluster-packing model, the addition of boron can occupy vacant cluster-interstices of (Mo, Ni)‐Si cluster arrays, which results in more densely packed cluster structure. The slight difference in composition between (Mo45Ni45Si10)90B10 and ideal < 10 − 8 > γ vacant model can be due to difference of atomic size ratios of Mo‐Ni‐Si‐B system from the ideal ratio values for coordination numbers of 10 and 8, or the influence of pronounced covalent interatomic bonding of metalloid atoms , the GFA of (Mo45Ni45Si10)100-xBx alloys clearly increases with the addition of B and as the alloy composition approaches the ideal composition in < 10 − 8 > γ vacant model. Considering this, the < 10 − 8 > γ vacant model shows a good agreement with the favorable composition for glass formation in Mo‐Ni‐Si‐B alloy system, suggesting that the addition of boron results in more efficiently packed atomic structure, destabilizes the formation of nanocrystalline phases, and increases the GFA of the alloy The glass-forming alloy system can be categorized depending on the alloy components following Inoue's classification shows the classification diagram with five glass-forming alloy system groups slightly modified from reference To describe GFA in various alloys, many GFA parameters have been proposed on the basis of the characteristic transformation temperatures of metallic glasses such as Tg |
= glass transition temperature, Tx |
= crystallization onset temperature, Tl |
= liquidus temperature, and Tmmix=∑Xi⋅Tmi with Xi and Tmi being mole fraction and melting point, respectively, of the component i in a multi-component alloy Low thermal stability (or low Tx) is one of the main drawbacks which limit wide industrial applications of metallic glasses. A few LTM (Ni, Fe, Co)-based metallic glasses have crystallization temperatures near 1000 K, as listed in , while Tx over 1000 K can be obtained only in a few refractory metal (Mo, W, Ta)-based metallic glasses. Among the refractory metal-based systems, only a few alloys have GFA high enough to be fabricated to fully amorphous state even in ribbon-type samples (a few tens of micrometer thickness), and the others can be fabricated to amorphous state only by mechanical alloying, which may exhibit greater maximum departure from the equilibrium than rapid solidification process. However, (Mo45Ni45Si10)90B10 has relatively high GFA to form fully amorphous ribbon, and also has high thermal stability of Tx |
= 1112 K measured by DSC (). This novel alloy system does not include a precious metal such as Ru, the rare transition metal belonging to the platinum group, so it is more economical than W‐Ru‐B system Furthermore, the amorphous (Mo45Ni45Si10)90B10 alloy shows extremely high hardness (27.5 ± 2.2 GPa in Vickers hardness), similar to hard ceramic materials (VC: 28.4 GPa, W2B5: 26.5 GPa, SiC: 25.5 GPa, TiN: 20.6 GPa in Vickers hardness . The small difference in hardness and elastic modulus between the thin film and the as-spun ribbon originates from the error of the estimation model and a slight chemical composition shift due to evaporation rate difference among the components during deposition process.Based on these considerations, the possibility for a promising high temperature wear resistant coating material was evaluated by H/E and H2/(2E) parameters. High elastic moduli of hard ceramic coating materials well over 400 GPa cause extreme elastic property mismatch between coating and substrate shows H/E and H2/(2E) values of various metallic glasses according to their Tx. The Vickers hardness and the Young's modulus values of the metallic glasses except Mo‐Ni‐Si‐B alloy were taken from reference (a), Mo‐Ni‐Si‐B metallic glass has much higher H/E ratio (0.075) than other glass-forming alloys and hard ceramic materials such as VC, W2B5, SiC, and TiN (0.066, 0.035, 0.053, and 0.035, respectively, calculated from the data of (b). Thus, the novel Mo‐Ni‐Si‐B metallic glass is expected to have excellent wear resistance and high capability for elastic energy absorption among glass-forming alloy systems, which make it a promising high temperature wear resistant coating material.In addition, a combination of nitride-forming transition metal and transition metal with low elastic modulus (e.g., MoN‐Cu A novel Mo‐Ni‐Si‐B metallic glass was developed, which can be solidified into a fully amorphous ribbon by conventional melt-spinning process at (Mo45Ni45Si10)90B10 composition. The dense cluster-packing model suggests that Mo‐Ni‐Si‐B metallic glass is supposed to have < 10 − 8 > cluster with vacant γ position, which is an atomic configuration similar to that of Fe-metalloid-type metallic glasses in metal-metalloid glass-forming group (Group I). The addition of boron can occupy vacant cluster-interstices of (Mo, Ni)-Si cluster arrays, which results in a more efficiently dense-packed cluster structure, destabilizes the formation of nanocrystalline phases, and increases the GFA of the alloy. Although Zmax, ε |
= 1.54 mm is higher than Zmax. exp. |
= a few tens of micrometer, the GFA parameters that do not directly depend on Tg such as ΔT* and ε show greater reliability to evaluate GFA for Mo‐Ni‐Si‐B metallic glass with no clear Tg. The (Mo45Ni45Si10)90B10 metallic glass exhibits an exceptional thermal stability in metallic glass forming system (Tx |
= 1112 K), extremely high hardness (27.5 ± 2.2 GPa in Vickers hardness), and relatively low Young's modulus (364.3 ± 6.6 GPa). Furthermore, we carefully fabricate thin film metallic glass (t ~ 100 nm) using the (Mo45Ni45Si10)90B10 master alloy, which exhibits mechanical properties similar to fully amorphous (Mo45Ni45Si10)90B10 ribbon sample. Indeed, Mo‐Ni‐Si‐B metallic glass exhibits much higher H/E ratio (0.075) and H2/(2E) value (1.05), far above the values of other metallic glasses and hard ceramic materials, such as VC, W2B5, SiC, and TiN. These results suggest excellent wear resistance and high capability for elastic energy absorption (resilience) in Mo‐Ni‐Si‐B metallic glass.Empirical rule for predicting mechanical properties of Ti-6Al-4V bone implants with radial-gradient porosity bionic structuresThe focus of this study was the design of implants related to the tibia bone. Most of the pressure loads applied on the tibia bone by the human body are normal forces. An orthogonal structure has been introduced in porous implants because it can support higher normal stress than other porous structures. Human bone is composed of an outer cortical bone and an inner cancellous bone, varying in gradient. Based on the characteristics of human bone, the design in this study applied a radial-gradient structure. Samples were fabricated using additive manufacturing (3D printing) via selective laser melting. Two different structural design methods were proposed for the radial-gradient structure, namely same region thickness and same region volume. The relationship between the porosity-gradient structure designs and mechanical properties was systematically examined and analyzed in detail. The resulting porosity-gradient materials were demonstrated to exhibit similar Young’s moduli but higher strength in comparison with those of the human bone structure.Biomaterials are the materials used to assist or replace biological tissue and organ functions, and they come in direct contact with biological tissue, cells, and blood. Biomaterials must have appropriate mechanical properties, excellent biocompatibility, good corrosion resistance, etc. Metal and ceramic materials are used to replace the hard tissues of the human body, such as bone and teeth. Metal and alloy materials are commonly used in the biological implantation of bone tissue []. Currently, titanium and titanium alloys are the most popular biomaterials owing to their high specific strength, excellent corrosion resistance, high wear resistance, good biocompatibility, and good mechanical properties []. Among titanium alloys, Ti-6Al-4 V is the most popular and is commercially used for the application of orthopedic implants [However, the occurrence of stress shielding effects is an important issue, and is caused by the mismatch between the Young’s moduli of Ti-6Al-4 V (110 GPa) and human bone, including cortical and cancellous bones (4–30 GPa) []. Bone osteoporosis and adverse reactions, such as loose or broken implants after prolonged implantation, occur because the sustained loading energy is absorbed by the metal implants and not the bone tissue. According to the Gibson–Ashby model [], the mechanical properties of porous materials are related to the relative density (or porosity). In this study, a porous structure was introduced to reduce the Young’s modulus of Ti-6Al-4 V materials to solve the harmful disadvantage.The design of porous materials can refer to the bionic porous structures, such as bone trabeculae [], which have been discovered and proved to exhibit unique mechanical characteristics. These structures have been introduced in periodic cellular lattice structures to simultaneously achieve high strength, lightweight and thermal resistance characteristics []. Furthermore, due to the distribution of bone density is inhomogeneous, the design of a bionic structure should have a gradient-porosity structure to conform to the characteristics of human bone []. However, preparing porous structures or complicated gradient porosity materials using traditional processes, such as the space holder method is difficult []. In addition, to analyze mechanical properties more precisely, a uniform porous morphology is required to obtain a homogeneous mechanical strength. Additive manufacturing (AM) technology is introduced to overcome these obstacles. Additive manufacturing techniques are capable of manufacturing complex lightweight parts such as uniform and gradient lattice structures with variable densification and porosities, which results in different performances in mechanical behavior layer-by-layer compared to non-gradient lattice structures, and hence offer design freedom for engineers [At present, the application of AM technology, also called three-dimensional (3D) printing, is popular in fabricating porous materials []. AM has certain critical advantages over traditional manufacturing processes, such as customization and less consumption of materials []. The flexibility of AM enables the fabrication of extremely complex geometric structures applied in biomedical implants []. The gradient-porosity structure can be designed using computer-aided design (CAD) software. Powder bed fusion (PBF) is a common technology used in the AM of metal powder materials []. Currently, Ti-6Al-4 V powder is commonly used in biomedical implants []. One of the PBF technologies is selective laser melting (SLM) []. In this process, a product is manufactured using the energy source of a laser beam to melt a selective position of the metal powder layer by layer. SLM products exhibit excellent densities higher than 99 %, better mechanical strength than traditional casting workpieces, and non-oxidation owing to protective gas []. The microstructure and mechanical properties of solid Ti-6Al-4 V fabricated using SLM with various processing parameters have been widely reported [Over recent years, an increasing number of studies have focused on the discussion of different structures fabricated using SLM []. Different lattice structures result in different mechanical properties; for example, an orthogonal structure has higher strength []. In this study, we focused on the design of bionic implants related to the tibia bone. Most of the pressure applied to the tibia bone by the human body are normal forces. To satisfy the mechanical properties of the tibia bionic implant, an orthogonal structure was introduced in the porous structure as it can sustain higher stresses than other porous structures []. The human tibia bone consists of an outer cortical bone with a relatively higher density and an inner cancellous bone with a relatively lower density []. In other words, the mechanical strength of the bone structure is higher in the outer region and lower in the inner region. Consequently, a gradient-porosity structure should be applied to the bionic implant. However, research on the mechanical properties of gradient structures is still limited []. In our previous study, the characteristics of the longitudinal gradient porous structure and its mechanical properties were carefully examined and discussed [However, Gibson–Ashby models can only depict the mechanical behavior of “non-gradient” cellular materials; thus, the understanding and knowledge of various gradient cellular structures are indeed limited. To explore the relationship between the tibia bone-inspired radial-gradient porous materials and their mechanical properties, this paper focuses on the discussion of radial-gradient porous materials to satisfy the characteristics of a bionic structure for the tibia bone. The designs of the gradient-porosity structure are divided into two directions: the design of different region thicknesses and porosity variations. Meanwhile, the characteristics and mechanical properties of radial-gradient porous materials have been extensively investigated and discussed. In addition, the mechanical strength prediction of biomedical implants is important for further applications. Thus, an empirical rule derived from the experimental results is proposed.The porous structures were manufactured using CAD software. The stereolithography files (STL) of single-porosity foams and radial-gradient specimens with different designs were conducted using Design X and FlashPrint software. When describing the CAD model, all the compressive samples were designed as solid cylinders with a diameter of 24 mm and a height of 48 mm. To satisfy the mechanical properties of the tibia bionic implant, an orthogonal structure was introduced to the porous structure because it can sustain higher stresses than other porous structures. Therefore, the unit cell of the orthogonal porous structure, also known as the cubic structure, was introduced to transform the solid cylinders into porous ones. Three structural designs were adopted in this study.First, control specimens with single porosities of 70 %, 75 %, 77.5 %, 80 %, 82.5 %, 85 %, and 90 % were prepared and analyzed ((a)). Thus, the mechanical properties of single-porosity samples can be used to compare the radial-gradient porous samples and calculate the theoretical mechanical properties for the empirical rule.Furthermore, the human bone combines an outer cortical bone with a lower porosity and higher Young’s modulus and mechanical strength, and an inner cancellous bone with higher porosity and lower Young’s modulus and mechanical strength. A gradient porous structure is introduced to satisfy the mechanical properties of the bone tissue and avoid the stress shielding effect []. Thus, in this study, the tibia bone-inspired gradient porous structure was designed to consist of three regions, each region possessing a single porosity. To simulate the changes in bone density/mechanical properties of the tibia bone and simplify all the calculations to derive the empirical rule, the outer region had a lower porosity, the middle region was fixed at an 80 % porosity, and the inner region had a higher porosity. To satisfy the above requirements, the other two specimens were designed as radial-gradient porous materials with three regions ((b) and (c)). The radial-gradient porous structures had an outer region of lower porosity (green arrow), and an inner region of higher porosity (blue arrow), similar to the human bone. The middle region was fixed at an 80 % porosity. Three types of porosity variations were set as 5 % (77.5 %–80 %–82.5 %), 10 % (75 %–80 %–85 %), and 20 % (70 %–80 %–90 %) ((b) and (c)). The porosity transition area was simply a surface between the two different porosity regions. The outer region was first designed as a cylinder with lower porosity, and then the inner region was hollowed out and replaced with another cylinder with a higher porosity. Meanwhile, the unit cell sizes of these cylinders with different porosities were the same to ensure that no mismatch occurred at the border or interface.The key difference between the last two designs of radial-gradient porous materials was the region thickness (or volume fraction). The first was designed with the same region thickness (t1:t2:t3 = 1:1:1) and the thickness of each region was 4 mm ((b)). Moreover, the volume fractions in the first design were approximately 11.1 %, 33.3 %, and 55.5 % (V1:V2:V3 = 1:3:5) from the inner to the outer region. The other one was designed with the same region volume fraction (V1:V2:V3 = 1:1:1) and the thicknesses of each region were 6.93, 2.87, and 2.20 mm, respectively, (t1:t2:t3 = 1: 2-1: 3-2) from the inner to the outer region ((c)). The relevance of thickness and volume fraction in each region within these two radial-gradient porous structures were calculated and are summarized in . Such information is critical for the calculation of mechanical properties in the discussion section.The porous specimens were prepared using the SLM process. Pre-alloyed Ti-6Al-4 V powders purchased from Renishaw, England, were used in the SLM system. The pre-alloyed Ti-6Al-4 V powder is specified in ASTM F136 (Ti64 ELI Grade 23), which ensures that the product exhibits good biocompatibility, good corrosion resistance, and excellent ductility. The Ti-6Al-4 V powders are spherical, their fluidity is good, and the size distribution is near a normal Gaussian distribution. The D10, D50, and D90 of the powders are approximately 21, 32, and 47 μm, respectively.The SLM system was a Renishaw AM 400 system. The energy source was laser power, which had a maximum power of approximately 400 W. The parameters of the SLM were a power of 200 W, spot size of 70μm, scanning speed of 1500 mm/s, hatch distance of 65 μm, and layer thickness of 30 μm. Before the printing process, all the STL files were fixed in the Materialise Magics CAD software to ensure that the 3D data was correct, and then the 3D data were sliced into 2D data layer by layer. The building chamber was initially vacuumed to approximately 1 × 10−2 torr, and then filled with the high purity argon (approximately 1 atm) to avoid severe oxidation (oxygen content < 700 ppm) during the SLM process. After the process, the thermal residual stress was eliminated using a vacuum annealing furnace for all SLM specimens.All the porous specimens fabricated using SLM were prepared to analyze their mechanical properties through compression testing. Compression testing was conducted using an Instron 5582 universal testing machine with a 100-kN load cell. The mechanical testing was performed at a strain rate 1 × 10−4 s−1 at 25 °C. Additionally, an Instron 2601 linear variable differential transformer displacement transducer was used to measure displacement more accurately. All compression tests of porous materials were conducted at least three times, and the average measurements were presented using a compressive stress–strain curve.To understand the mechanical response affected by this radial gradient structure with the same region thickness in more detail, we calculated the mechanical properties using the rule of mixtures (ROM), which is described bywhere X may be Young’s modulus (E), yield stress (σys), maximum compression strength, or strain at failure; XROM is the calculated mechanical property of a radial-gradient porosity specimen; X1–3 are the mechanical properties of a single porosity in each region from the inner to outer region, and V1–3 are the volume fractions of each region from the inner to the outer region.Ti-6Al-4 V porous samples with single porosities from 70 % to 90 % were successfully fabricated using SLM equipment. Each of the single-porosity materials constructed with orthogonal unit cells was unbroken in appearance and their struts had normal surface morphology and no apparent defects ((a)). The Ti-6Al-4 V porous specimens with radial-gradient porosities were all designed from these single-porosity parts. Therefore, control samples with single porosities were crucial as references for the mechanical properties of the gradient materials. Furthermore, the actual porosity of each single-porosity specimen was required to result in a slight variation in the mechanical properties. The actual porosity (P) of the porous foams can be calculated using the formulaWhere ρ and ρs are the densities of the porous material and theoretical solid material, respectively. The density of the porous specimen was calculated using the weight and volume of the solid cylinder with a diameter of 24 mm and a height of 48 mm. The density of the theoretical solid Ti-6Al-4 V was measured as 4.37 g/cm−3. The actual porosity of each single-porosity specimen was measured at least three times, and the results are summarized in . The actual porosity of each single-porosity sample was approximate to the design value. Therefore, all subsequent research is discussed in terms of the design porosity, but the actual porosities are also listed in the Compression testing was conducted for the control specimens with single porosities from 70 % to 90 %. All the control porous specimens were tested at least three times until mechanical fracture occurred. The mechanical properties are summarized in , and the compressive stress–strain curves are shown in (a), which shows the stress–strain curves before the first apparent load drop. To simplify the observation, the stress–strain curves with porosities from 75 % to 90 % are shifted by different distances from 0 along the X axis. As shows, the mechanical properties exhibited identical tendencies. The Young’s modulus, yield stress (0.2 % offset), maximum compression stress, and strain at failure of the Ti-6Al-4 V porous materials from 70 % to 90 % decreased from 9.5 to 2.3 GPa, 116.4–23.8 MPa, 154.1–23.9 MPa, and 4.77 %–1.32 %, respectively. Thus, the mechanical properties all decreased as porosity increased from 70 % to 90 %.], the mechanical response depends on the relative density of the porous foams. The relationships between Young’s modulus, yield stress, and relative density are given bywhere E is the Young’s modulus of the porous material, Es is the Young’s modulus of the ligament material (raw materials fabricated using SLM), σ is the yield stress of the porous material, σs is the yield stress of the ligament material, ρ is the density of the porous material calculated using the actual porosity, ρs is the density of the ligament material, and ρ/ρs is the relative density. Additionally, C1 and C2 are constants that depend on some control variables, including structural design, process, and bonding strength. Frequently, n1 is a constant of approximately 2, and n2 is a constant of approximately 1.5 for open-cell porous materials [A lower relative density (or higher porosity) would result in a lower Young’s modulus and yield stress. In this study, the results of the mechanical properties were considerably consistent with this model ((b) and (c)). The Es and σs of dense Ti-6Al-4 V materials prepared using SLM are 110 GPa and 990 MPa, respectively [(b) and (c), the variations in the Young’s modulus and yield stress are normalized using ES and σs versus the relative density of the porous SLM Ti-6Al-4 V materials. The relationships of the fitting line between E/Es (or σ/σs) and relative density (ρ/ρs) arewith a fitting R-square value of 0.97257 and 0.99883, respectively. (b) and (c) indicate that the dependence of Young’s modulus and the yield stress can be fully predicted, although the Young’s modulus data slightly deviates from the fitting line. In a previous study, the constants C1 and C2 were experimentally reported to vary by approximately 1–4 and 0.1–1, respectively, using the Gibson–Ashby model for open-cell foams [ indicate the constants as C1 = 1.10 and C2 = 0.73. Compared with our previous studies, the constants C1 and C2 of the porous SLM samples were higher than those of the porous materials fabricated using the space holder technique (C1 = 0.8 and C2 = 0.4), which is one of the traditional powder metallurgy methods []. This result is primarily because the porous materials with orthogonal structures fabricated using AM technology are homogenous. In other words, the bonding strength of the SLM porous specimen is significantly greater because of the uniform mechanical properties.In this study, the elastic limit was the strain value at the yield point. The value of the elastic limit also decreased from 1.48 % to 1.23 % as porosity increased from 70 % to 90 %. In other words, a material with a higher porosity will enter the plastic region earlier under the same compression strain rate. shows that the deformation and failure positions of single-porosity samples occurred randomly within the entire porous structure, as indicated by the red arrows. The behavior of fractures in porous materials with orthogonal structures is characterized by destruction in the same horizontal region. When one of the struts breaks, the fracture position will be the stress concentration point because the other struts will sustain larger true stresses in the same horizontal region. In this study, the porous materials with single porosities from 70 % to 90 % were deformed in this fracture behavior. Furthermore, the response of strain at failure, which is the destructive localized deformation, in the plastic region is primarily related to the ligament width []. The ligament width decreased as porosity increased from 70 % to 90 %. Thus, the strain at failure decreases with increasing porosity. This indicates that the lower porosity has better fracture durability or deformation stability.Compared with the mechanical properties of human cortical and cancellous bones, the Young’s modulus and yield stress are approximately 4–30 GPa and 20–193 MPa, respectively []. In this study, the mechanical properties of control specimens with single porosities from 70 % to 90 % were nearly consistent with the human bone. Although the results are slightly lower, the lower porosity can predictably satisfy the level of cortical bone through the relationship equations of the Gibson–Ashby model above.Furthermore, the human bone is composed of an outer cortical bone with a higher bone density and an inner cancellous bone with a lower bone density. To conform to the characteristics of the human skeleton, we propose a bionic design of a radial-gradient porous structure. Therefore, the cylinders of the radial-gradient porous structure were designed to consist of an outer region with a lower porosity (70 %, 75 %, 77.5 %), an inner region with a higher porosity (90 %, 85 %, 82.5 %), and a middle region with average porosity (80 %), as shown in (b) and (c) for the CAD schematic diagram.Moreover, two different designs were created for the radial-gradient porous structure. One was designed with the same region thickness (4 mm – 4 mm – 4 mm). The other one was designed with the same volume fraction of any region (or different region thicknesses, 2.2 mm – 2.87 mm – 6.93 mm). These two designs had the following three porosity variations. The porosity variations were 5 % (77.5 %–80 %–82.5 %), 10 % (75 %–80 %–85 %) and 20 % (70 %–80 %–90 %), respectively. The two designs are shown in (b) and (c). Based on these experimental designs, we aimed to identify the relationship between the porosity differences and mechanical properties, and the relationship between different designs of gradient structure and mechanical response.All the Ti-6Al-4 V radial-gradient samples were successfully prepared using SLM (). In addition, all the gradient samples had no visible defects in their entire appearance. (d) shows the enlarged schematic illustrations of 3D printed radial-gradient porous specimens, and the struct size variation from the lower porosity region (outsize, larger strut diameter) to the higher porosity region (inside, smaller strut diameter) can be observed. Furthermore, the CAD model of the gradient structure was completely confirmed to avoid the effect of interface mismatch, which would result in a harmful mechanical response []. To investigate the mechanical properties of two different designs for radial-gradient porous materials, all gradient specimens were introduced to the compression test with at least three repeated experimental data. These aspects are discussed individually in the following. shows the compressive stress–strain curves of the radial-gradient porosity samples with the same region thickness. The Young’s modulus, yield stress (0.2 % offset), maximum compression strength, and strain at failure are tabulated in . The average porosity of each porosity variation is also shown in . As the table shows, the Young’s modulus, yield stress, and maximum compression strength for a porosity variation from 5 % (77.5 %–80 %–82.5 %) to 20 % (70 %–80 %–90 %) all increased from 8.3–10.1 GPa, 81.1–100.3 MPa, and 104.8–130.8 MPa, respectively, indicating increments of 22 %, 24 %, and 25 %, respectively. The strain at failure was similar regardless of the porosity variation in this structure. Because the region thickness was the same at 4 mm, the volume fractions of the regions were approximately 55.6 %, 33.3 %, and 11.1 % from the outer to the inner region, respectively. Moreover, the average porosities as porosity variation increased from 5 % to 20 % were 78.9 %, 77.8 %, and 75.6 %, respectively. The actual porosities calculated using Eq. were 78.2 %, 77.6 %, and 76.1 %, respectively (). Therefore, the increase in mechanical strength was primarily attributed to the decrease in average porosity. Based on the Gibson–Ashby model, a lower porosity (or higher relative density) results in higher Young’s modulus and yield strength.Compared with the control specimens with similar single porosities from 75 %, 77.5 %, and 80 % (), almost all radial-gradient porosities with the same region thickness had higher mechanical properties except for the strain at failure. The mechanical response affected by this radial gradient structure could be calculated using the rule of mixtures (ROM). All the calculated mechanical properties are listed in . The application of the ROM in this design is described in the following paragraph.For example, when XROM is the yield stress for the radial-gradient porosity samples with the same region thickness within a 5 % (77.5 %–80 %–82.5 %) porosity variation, the theoretical value is calculated by the yield stress (X1–3) of a single porosity within 77.5 %, 80 %, and 82.5 % (). In addition, the volume fractions (V1–3) in this design were 11.1 %, 33.3 %, and 55.5 % from the inner to the outer region. All the mechanical properties are listed in . We observe that the outer region with a lower porosity had a larger volume fraction in this structure of radial-gradient porosities with the same region thickness; therefore, the effect on the mechanical properties in the outer region was apparent., the mechanical properties of radial-gradient porosities with the same region thickness were higher than the values calculated using the ROM, except for the strain at failure. Therefore, this structure with radial porosity gradient, composed of an outer region with a lower porosity and an inner region with a higher porosity, had an enhanced effect on the mechanical strength. This structure induced stress is comprehensively discussed in a later section. Otherwise, although the elastic limit in this structural design with different porosity variations from 5 % to 20 % was slightly lower than that of the average 80 % porosity specimen, the response of the strain at failure was higher. Compared with the results calculated using the ROM, the elastic limit was also slightly lower, but the strain at failure was similar. This indicated that the radial-gradient porous materials with the same region thickness entered the plastic region earlier because of the higher porosity in the inner region. However, the outer region with a lower porosity protected the inner region to avoid the destructive localized deformation that occurs too early in porous specimens. In addition, shows that the fracture positions of radial-gradient porous materials with the same region thickness occurred randomly within the entire specimen, as marked by red arrows. The fracture behavior in the radial-gradient porous specimens was the same as that in the control samples with single porosities, which was characterized by the destruction in the same horizontal region.Overall, based on the above discussion, the mechanical properties of radial-gradient porosities with the same region thickness were enhanced as porosity variation increased from 5 % (77.5 %–80 %–82.5 %) to 20 % (70 %–80 %–90 %). This was governed primarily by the following two reasons: The average porosity decreased with increasing porosity variation owing to the larger volume fraction of the outer region with a lower porosity; a lower average porosity results in higher mechanical strength, as calculated using the ROM. The second reason is that the structure induced stress is proposed in this structure with radial gradient porosity. Furthermore, note that this structure of radial gradient porosity is provided with higher mechanical strength under a similar strain at failure compared with the control specimens with single porosities approaching the average porosity. This indicates that the work of fracture in this structure is better []. In other words, this structure has better fracture durability or deformation stability.The mechanical properties of the radial gradient porosity with the same region volume fraction are summarized in . The compressive stress–strain curves are shown in . The region thicknesses of each region from outside to inside were calculated to be approximately 2.2, 2.87, and 6.93 mm, respectively. Because the volume fraction of each region was the same, the average porosity was fixed at 80 % regardless of the porosity variation within 5 % (77.5 %–80 %–82.5 %), 10 % (75 %–80 %–85 %), or 20 % (70 %–80 %-90 %). Furthermore, the average experimental porosities of the porosity variation from 5 % to 20 % were 79.9 %, 79.4 %, and 79.4 %, respectively. The actual porosities calculated using the ROM were 79.8 %, 80.1 %, and 80.3 %, respectively. In this structure with the same region volume fraction, the actual porosities were approximately the same; therefore, the mechanical properties were primarily affected by the characteristics of each region with different single porosities rather than the average porosity. indicates that the Young’s moduli of a porosity variation from 5 % to 20 % were 7.9, 8.6, and 8.2 GPa, the yield stresses were 75, 76.2, and 77.8 MPa, the maximum compression stresses were 95.3, 97.1, and 98.7 MPa, and the strains at failure were 3.44, 3.52, and 3.72 %, respectively. The mechanical strengths were approximately the same or increased slightly, and the increment of strain at failure was approximately 8 %.Compared with the control specimen with 80 % porosity, also shown in , the Young’s modulus, yield stress, and maximum compression stress of the radial-gradient porosity with the same region volume fraction were higher. However, the strain at failure was observed to be slightly lower than that of the control 80 % sample. Additionally, the ROM (Eq. ) was used to realize the mechanical response of this radial gradient structure with the same region volume fraction. The mechanical properties calculated using the ROM are listed in , the mechanical properties of the radial gradient porosity with the same region volume fraction were higher than the calculated values. Moreover, the strain at failure was approximate to the calculated values, although it appeared to have a slightly opposite tendency. Therefore, a structure induced stress was significant in this structure with a radial gradient porosity, which was composed of an outer region with a lower porosity and an inner region with a higher porosity. Moreover, the elastic limit in the radial-gradient porous materials with the same volume fraction was lower than that of the control specimen with 80 % porosity, and the results calculated using the ROM because the inner region had a higher porosity. Although the strain at failure was also lower than that of the control specimen with 80 % porosity but similar to the results calculated using the ROM, the outer region with a lower porosity still protected the inner region because the strain at failure was also higher than that of the control specimens with higher porosities of 82.5 %, 85 %, and 90 %. Furthermore, the strain at failure in this structural design increased as porosity variation increased from 5 % to 20 %. In addition, the fracture positions of radial-gradient porous materials with the same volume fraction appeared randomly, as marked by red arrows in . Moreover, destruction in the same horizontal region was also observed in this structural design.Here, the mechanical properties of radial gradient porosity increased slightly as porosity variation increased from 5 % (77.5 %–80 %–82.5 %) to 20 % (70 %–80 %–90 %). Because the average porosity was fixed at 80 %, the increment was primarily caused by the larger porosity variation, similar to the tendency of the ROM calculation results. Moreover, note that the strain at failure improved when the porosity variation increased from 5 % to 20 %. Therefore, the work of fracture increased slightly with increasing porosity variation; thus, the fracture durability also increased with higher porosity variation. However, as mentioned earlier, the tendencies of the Young’s modulus and mechanical strength were similar to the values calculated using the ROM. However, all the experimental results for Young’s modulus and mechanical strength were higher than the calculated values. Therefore, an interesting observation was that there was a structure induced stress in this structure of radial gradient porosity with the same region volume fraction.Moreover, for comparison of the two different structural designs above, the elastic limit and the strain at failure were both lower in the structural design with the same volume fraction. The reason might be the volume fraction of each region. The elastic limit determined the strain value from the elastic region into the plastic region. This was primarily related to the inner region with a higher porosity. In addition, the volume fraction of the inner region was larger in the structural design with the same volume fraction (). Therefore, the elastic limit was lower in the structural design with the same volume fraction. Furthermore, the strain at failure in these two structural designs indicated that the outer region with a lower porosity protected the inner region to avoid destructive localized deformation. In addition, the volume fraction of the outer region was larger in the structural design with the same region thickness (). Consequently, the strain at failure was larger in the structural design with the same region thickness. In summary, as show, the mechanical properties of the radial gradient porosity with the same volume fraction were lower. However, the discussion on the mechanical strength is still insufficient. The structure induced stress is discussed in more detail in the next section.As mentioned earlier, porous materials with radial-gradient regions exhibited higher experimental mechanical strengths (including Young’s modulus, yield stress, and maximum compression stress) than both the control samples and the values using the ROM, which also represents the theoretical summation contribution of the mechanical response from each region. This scenario was also observed in a previous study on gradient porous materials []. To intuitively discuss the increments, shows the porosity variation dependence of Young’s modulus and yield stress for different structural designs. Both the experimental and calculated values are presented in . However, the maximum compression stress is not discussed despite the presence of structure induced stress because the deformation of porous materials has many complicated factors for the plastic region. (a) and (b) show the relationship between Young’s modulus and structural design, and (c) and (d) show the dependence of the yield stress. According to , each graph implies that the mechanical strength slightly increased with porosity variation from 5 % (77.5 %–80 %–82.5 %) to 20 % (70 %–80 %–90 %). The ROM-calculated results in show an identical tendency. The main reason was that the calculation value considered the volume fraction of each region. Therefore, the increment in the structural design with the same region thickness was relatively apparent because of the larger volume fraction in the outer region with a lower porosity and higher mechanical properties. Furthermore, the most important factor is that the considerable increment between the experimental and calculated values was defined as the structure induced stress (σs).These results demonstrated that the structure induced stress appeared in both elastic and plastic regions under axial compressive stress. In other words, in this study, the radial-gradient porous materials exhibited a normal stress (σN) and structure induced stress (σs) ((a)). Stress (σ) can be estimated using the following relationships:The normal stress (σN) is contributed by each region with different single porosities and the volume fraction affected the contribution level (σN = σ1V1 + σ2V2 + σ3V3). The normal stress was equal to the values calculated using the ROM. σs was induced by the interactions between two adjoining regions, including the inner–middle and middle–outer regions (σs = σ12V1 + σ23V2). The interactions between regions and the calculation of the structure induced stress are discussed in detail in a later paragraph.Additionally, for clarity and ease of discussion, (b) shows that σN and σs are indicated in the strain–stress curve of a radial-gradient porous specimen with the same region volume fraction within a 20 % (70 %–80 %–90 %) porosity variation, which is selected as an example. Simultaneously, the calculation curve using the ROM (red line) represents the part of the normal stress contributed by each region. The green line indicates the linear schematic following the Young’s modulus by the experimental value in this structure, and the stress at the end of the green line is considered the expected stress (σexpected). Because the structure induced stress is visualized in the elastic and plastic regions, two reference lines are obtained at Σ=0.5 % and Σys (Σ at the yield point, approximately 1.15 %) as the basis for discussions.In the elastic region (Σ=0.5 %), the actual stress (σ0.5 %) was 41 MPa, and the normal stress (σN,0.5 %) was 29 MPa. The structure induced stress (σs,0.5 %) was 12 MPa as the difference between the actual and normal stresses (σs,0.5 % = σ0.5 % - σN,0.5 %). Subsequently, to quantify the difference, the structure induced stress was considered to be an additional increment of the normal stress. Thus, the increment percentage was defined as (σs,0.5 %/σN,0.5 %), which was approximately 41.4 %. In addition, along the line through the yield point (Σys ∼ 1.15 %), the yield stress (σys) was 77.8 MPa, and normal stress (σN,ys) was 67.9 MPa. The structure induced stress (σs,ys) was calculated as 9.9 MPa (σs,ys = σys - σN,ys). Thus, the stress increment percentage (σs,ys/σN,ys) was approximately 14.6 %. Note that the proportion of structure induced stress decreased when the gradient porous structure deformed from the elastic region to the plastic region, sustaining an axial compressive stress ((b)). In other words, the expected structure induced stress (σs,expected) was approximately 26.4 MPa (σs,expected = σexpected - σN,ys) because the expected stress was 94.3 MPa while the normal stress (σN,ys) was 67.9 MPa. At the yield point, only a proportion of the structure induced stress occurred owing to permanent deformation. The structure induced stress at the yield point (σs,ys) could also be considered as the remaining structure induced stress by the expected structure induced stress (σs,expected) at the yield point. The remaining percentage (σs,ys/σs,expected) was approximately 37.5 %. The remaining percentage of structure induced stress at the yield point was important for the prediction of yield stress using the empirical formula, which is discussed in the final section. These calculations and quantifications in the different radial-gradient porous materials with porosity variations from 5 % to 20 % are summarized in , the following conclusions can be summarized. First, the structure induced stress was used in this study in the structural design of radial-gradient porous materials. This structural design was characterized by an outer region with a lower porosity and inner region with a higher porosity. Furthermore, the proportion of structure induced stress was higher than 30 % in the elastic region and higher than 10 % at the yield point. Second, the proportion of structure induced stress for the gradient porous specimens was approximately the same or had a slight increment under the identical structural design (the same region thickness or volume fraction) with porosity variation from 5 % to 20 %. However, the proportion of structure induced stress in the structural design with the same region volume fraction was larger than that with the same region thickness regardless of the elastic region or yield point. Therefore, the structure induced stress was primarily affected by the structural design, which was distributed to the ratio of the region thickness, instead of the porosity variation.From the summary of above section, the effect of structure induced stress was seemingly observed in the literature for gradient structures. Wu et al. [] proposed intrinsic synergetic strengthening in gradient structure materials. Although the design of the porous structure is not described in the literature, the gradient structure is combined with an outer region with a higher mechanical strength and an inner region with a lower mechanical strength. The synergetic strengthening is primarily caused by the mechanical incompatibility, which results from the mismatch of Poisson’s ratio between the two regions, and the mechanical incompatibility results in different dimensional stress states. Moreover, studies on the relationship between Poisson’s ratio and porosity for porous materials were conducted []. This indicates that the Poisson’s ratio increases with increasing porosity.Based on these studies, the structure induced stress induced by the interactions between regions is discussed below. The radial-gradient porous specimens were designed with three regions, including an outer region with a higher mechanical strength and an inner region with lower mechanical strength. In addition, the Poisson’s ratio of the inner region was larger than that of the outer region; thus, the adjacent regions might have been mechanically incompatible. When conducting the compression test, owing to simultaneous deformation under compressive load, the strain should be the same in each region of the radial-gradient porous structure materials. Furthermore, the inner region with higher porosity should buckle more than the adjacent region with a lower porosity because of the difference in Poisson’s ratio. However, the outer region retained a higher Young’s modulus and mechanical strength; therefore, the deformation in the inner region with a larger Poisson’s ratio was constrained by the outer region. Moreover, the outer region constrained the inner region and simultaneously applied a reaction force to the testing machine. Therefore, interaction occurred between two adjoining regions under the described scenario. To achieve the same strain value in each region, additional stress was essential to overcome the interaction in the radial-gradient porous materials. In this study, the additional stress was defined as the structure induced stress. The schematic illustration is shown in . Structure induced stress was induced by the mechanical incompatibility due to the difference in Poisson’s ratios between each region of the radial-gradient porous structure materials. Moreover, mechanical incompatibility resulted in different dimensional stress states. Moreover, the proportion of structure induced stress in the elastic region was higher than that at the yield point because the structure induced stress occurred as a consequence of the constraint between regions under elastic deformation. Thus, at the yield point, only a proportion of the structure induced stress occurred because of the elastic deformation occurring in the stronger region, and the weaker region permanently deformed.The above discussions demonstrate that the structure induced stress is primarily affected by the structural design. In addition, radial-gradient porous structures with the same region volume fraction can provide higher structure induced stress than a design with the same region thickness. In addition, the structure induced stress is related to the interaction between two adjacent regions. To better understand why the structure induced stress is higher in the structure with the same region volume fraction, the interaction between adjoining regions is discussed in detail in the following paragraph.For the convenience of discussion, only an inner region with 90 % porosity and a middle region with 80 % porosity are analyzed under the same-porosity variation to explain the reasons for the higher structure induced stress in the structural design with the same region volume fraction. shows the thickness of the inner region (t1) and middle region (t2) in two different structural designs. The thicknesses of the inner regions (t2) of these two designs are 4 and 6.93 mm, respectively. Therefore, the following two results are derived. First, the inner region with 90 % porosity possesses the same Poisson’s ratio in two different structural designs. In addition, when the axial strain is the same, the lateral strain will also be the same. However, the displacement of the horizontal expansion is larger in the porous structure with the same region volume fraction because the region thickness of the inner region with 90 % porosity is larger. Therefore, when the middle region with a higher mechanical strength constrains the inner region with a larger displacement of horizontal expansion, a larger reaction force will occur. Furthermore, the structure induced stress is positively correlated with the reaction force. Consequently, this should be one of the reasons that the structure induced stress is higher in the structure with the same region volume fraction. Second, we can assume that the force in each contact, defined as the junction or interface of each strut with 80 % and 90 % porosities, is the same. In addition, the region thickness of the inner region is larger in the porous structure with the same volume fraction, so the lateral surface area of the inner region is larger than that of the structural design with the same region thickness. Consequently, the structure induced stress increases with an increase in the number of contacts. This should be the other reason for the increase in structure induced stress.Overall, the structural design with three regions is more complicated. The factors mentioned above to enhance the structure induced stress occur together. The increase in contact quantity is seemingly more important because the surface area of the two interfaces in the three-region structure is higher in the structural design with the same region volume fraction. Finally, the most important thing is that the proportion of structure induced stress in the structural design with the same region volume fraction is greater than that with the same region thickness regardless of the elastic region or yield point, although the decrease in the structure induced stress is also larger in the structural design with the same region volume fraction. Finally, the mechanical strength is well known to contribute to σN and σs. The mechanical strength is larger in materials with a structural design with the same region thickness because of higher normal stress, but the effect of structure induced stress is greater in materials with the same region volume fraction (According to the discussion above, the structure induced stress is related to the structural design. Moreover, the stress increment percentage is larger when the outer region is thinner. The tendency of the structural design for structure induced stress in radial-gradient porous materials is seemingly similar to that of the thin-walled cylindrical pressure vessel []. The state of stress in the thin-walled cylindrical pressure vessel is higher when the wall is thinner. For the pressure vessel, a longitudinal stress occurs in the wall when internal pressure is present. In this paper, the inner region has a structure induced stress when the outer region constrains the inner region. Therefore, the structure induced stress can be calculated by referring to the stress formula of the thin-walled cylindrical pressure vessel. The following discussion is the calculation of the structure induced stress in radial-gradient porous materials.Moreover, the deviation of the structure between the design and the specimens is frequently considered owing to the SLM process []. All the specimens, including single-porosity and gradient-porosity specimens, were fabricated using SLM with the same parameters. Each region with the same porosity was designed using the same CAD model regardless of them being single-porosity or gradient-porosity ones. All samples for each design were tested more than three times to ensure repeatable results.To infer the relationship between the structure induced stress and the structural design, (a) shows a schematic illustration of the free body diagram for a gradient-porosity specimen with two adjacent regions. For the convenience of discussion, a two-regioned structure is discussed first. First, the thickness of the outer region (t) is assumed to be much smaller than the radius of the inner region (r) because the derivation of the theoretical stress is derived from the thin-walled structure. Thus, the axial compressive stress (P) applied to the outer region is a force equal to P×(2πrt) when the thickness of the outer region is much smaller than r. The σs induced in the inner region is a force equal to σs×(πr2). Hence, the equation of equilibrium is described asand the structure induced stress for the two-region structure within a very thin outer region can be expressed as follows:However, in this paper, the thickness of the outer region does not follow the premise. Thus, the force applied to the outer region should be Pπr+t2-r2. The equation is regulated to be the following formula according to Eq. thus the structure induced stress in the two-region structure can be calculated usingwhere the ratio between r and t is defined as X and (r/t)/[(r/t)+1/2] is defined as a constant C. The constant C represents the structural factor because the value is determined by X. If t is very thin, the constant C−1 is very close to 1, and the structure induced stress is equal to 2Pt/r. This model can adequately describe the result of the thin-walled structure. However, because t is not significantly thin, which follows the premise, this formula should be modified. To make the formula more precisely predict the structure induced stress of the radial-gradient porous structure in this paper, the constant C is modified by the exponent n. The modified formula is as follows:In this study, the radial-gradient porous materials were composed of three regions; thus, two structure induced stresses caused by inner–middle region (σ12) and middle–outer region (σ23) interactions existed ((a)). Because the structure induced stress was induced in the inner and middle regions, the volume fraction was considered when calculating the total structure induced stress (σs = σ12V1 + σ23V2). For clarity and ease of discussion, (b) shows that σN and σs were considered for the radial-gradient porous specimen with the same region volume fraction within a 20 % (70 %–80 %–90 %) porosity variation, which was selected as an example. The formula derivation for structure induced stress is discussed with respect to the elastic region. The calculations for the structure induced stress caused by the inner–middle region (σ12) and middle–outer region interactions (σ23) arewhere V1 is the volume fraction of the inner region (V1 = 33 %), X12 is the ratio of the radius of the inner region to the thickness of the middle region (X12 = t1t2=12-1), C12 is the constant depending on the structural design (C12 = X12X12+12 =22+1), and P is 41 MPa.where V2 is the volume fraction of the middle region (V2 = 33 %), X23 is the ratio of the radius of the inner–middle region to the thickness of the outer region (X23 = t1+t2t3=23-2), C23 is the constant depending on the structural design (C23 = X23X23+12 =223+2), and P is 41 MPa.According to the calculations of σ12 and σ23 above, the total σs measured by experimental data is 12 MPa; therefore, the exponent n can be solved using the following equation:σs= (22+1)n×82(2-1)×33%+ (223+2)n×82(3-2)2×33%.Thus, n is approximately 2.38. All the calculations for different radial-gradient porous materials with porosity variations from 5 % to 20 % are summarized in , n is indicated to be approximately 2.5. Therefore, the empirical rule for predicting the structure induced stress in radial-gradient porous materials can be expressed asThe constants C12 and C23 depend on the structural design with different ratios of radius and thickness in each region. The exponent n may depend on some factors, including the material nature, microstructure, and design of the porous structure. In summary, the structure induced stress of radial-gradient porous materials with different structural designs can be calculated using the empirical rule of Eq. . The exponent is approximately 2.5 when the Ti-6Al-4 V porous specimens with an orthogonal structure are fabricated using SLM and the constant C, which is considered as the structural factor, is modified as C2.5. Therefore, the relationship between the constant C2.5 and the ratio (r/t) is shown in . The structural factor C2.5 approaches 1 when the outer region is thin.Till now, all the derivations are discussed with respect to the elastic region because the calculation of the structure induced stress can be significantly complicated at the yield point. However, the calculation of the structure induced stress at the yield point can be easily estimated using the remaining percentage of the structure induced stress (). The average remaining percentage is approximately 36.5 %. Therefore, according to Eq. , the yield stress can be calculated using the following equation:σys,calculation= σN + σs,ys,calculation.). The structure induced stress at the yield point (σs, ys, calculation) can be calculated using Eq. and the remaining percentage (approximately 36.5 %). The parameters with different structural designs are shown in , and the axial compressive stress (P) should use the expected stress (σexpected) ((b)) because the calculated structure induced stress can only be defined under elastic deformation. Meanwhile, permanent deformation occurs at the yield point and thus only a proportion of structure induced stress remains; therefore, the calculated structure induced stress should be modified using the remaining percentage (approximately 36.5 %). All the experimental and calculated yield stresses are summarized in . The table indicates that the calculated yield stress is very close to the actual yield stress, but it seems to be slightly higher because the value of the remaining percentage here is an average value. For a convenient and conservative prediction, the remaining percentage of structure induced stress is suggested to be approximately 33 %. Therefore, the mechanical strength can be predicted regardless of the elastic region or yield point because the normal stress and structure induced stress can be calculated separately using the ROM and the empirical formula proposed in this paper.The empirical rule derived from the experimental results of the tibia bone-inspired radial-gradient porous orthogonal structure was fully developed in this study. Meanwhile, it can be validated using the two radial-gradient structures, which were designed using different design logics: same region thickness and same volume fraction. The difference between the experimental and calculated strengths was less than 3 %. Moreover, this method provides a reference for deriving similar empirical rules for other porous structures by optimizing the exponent. Meanwhile, the residual stress will affect the mechanical properties of 3D printed samples indeed. If the residual stress caused by SLM is not been eliminated, the yield stress of the 3D printed sample will be higher. However, the yield stress increasing trend of the samples with single porosity or gradient porosity should be the same. Therefore, the yield stress of the radial-gradient porous structure with residual stress can only be predicted by the empirical rule derived from the database of the samples with residual stress, and vice versa.In summary, the designs of radial-gradient porous structures for some bionic implants related to the tibia bone were established using a CAD model, and the Ti-6Al-4 V porous materials were successfully fabricated using SLM 3D printing. By comparing the different structural designs and mechanical responses, the following conclusions can be drawn.The mechanical properties of the control specimens with single porosities from 70 % to 90 % have been adequately analyzed as a reference for the gradient porous structures. The results of the Young’s modulus and yield stress are considerably consistent with those of the Gibson–Ashby model. The design of different porosities can satisfy the level of cortical bone using the relationship equations presented in this paper. Furthermore, the elastic limit and strain at failure decrease with increasing porosity. This indicates that the lower porosity has better fracture durability or deformation stability.The mechanical strength of the radial-gradient porosity with the same region thickness is reinforced by increasing the porosity variation from 5 % to 20 %. It is governed primarily by the reduction in average porosity because the volume fraction of the outer region is larger. In addition, the mechanical strength in the structural design of the same region volume fraction with porosity variation from 5 % to 20 % slightly increases under the same average porosity. The values calculated using the ROM indicates the same tendencies. Therefore, the ROM can be used to explain the results of compressive strength because the volume fraction of each region is considered. However, the most important aspect is that a structure induced stress, which is the increment between the experimental and calculated values, exists in the radial-gradient porous structures.In the comparison of two different structural designs, the elastic limit is higher in the structural design with the same region thickness because the volume fraction of the inner region is smaller. The inner region with higher porosity possesses poorer mechanical properties; thus, the strain at the yield point is primarily related to the inner region. In addition, the strain at failure is also higher in the structural design with the same region thickness because the volume fraction of the outer region is larger. It is worth mentioning that the outer region with lower porosity protects the inner region to avoid destructive localized deformation. Therefore, the radial-gradient porous structures retain better fracture durability or deformation stability than the average 80 % porosity control specimen.The structure induced stress (σs) has an important function in the radial-gradient-porosity bionic structure. The structure induced stress provides an increase in the normal stress (σN) up to more than 30 %, which is contributed by each region, in the elastic region, and more than a 10 % increase in the yield point. Furthermore, the structure induced stress is attributed to the difference in Poisson’s ratios. The effect of the structure induced stress is greater in the radial-gradient structure with the same volume fraction. This is attributed to the larger displacement of the horizontal expansion and increase in the contact quantity (or surface area of the interface).The structure induced stress can be calculated using the empirical formula in Eq. for the elastic region. The exponent is proposed to be approximately 2.5 for the Ti-6Al-4 V porous specimens with an orthogonal structure fabricated using SLM. Moreover, the yield stress can also be estimated using the empirical formula in Eq. , considering the remaining percentage of the structure induced stress. Thus, the mechanical strength can be easily predicted by the calculation of normal stress using the ROM and structure induced stress from the empirical formula.The empirical rule developed in this study can predict the mechanical strength and Young’s modulus of the radial-gradient porous orthogonal structure with any enclosed radial porosity variation. Moreover, although only the orthogonal structure is discussed in this paper, the method for deriving the empirical rule is an important reference for other derivations for different structural designs that satisfy the biomedical requirements of application scenarios.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.Prediction of damage formation in hip arthroplasties by finite element analysis using computed tomography imagesFemoral bone fracture is one of the main causes for the failure of hip arthroplasties (HA). Being subjected to abrupt and high impact forces in daily activities may lead to complex loading configuration such as bending and sideway falls. The objective of this study is to predict the risk of femoral bone fractures in total hip arthroplasty (THA) and resurfacing hip arthroplasty (RHA). A computed tomography (CT) based on finite element analysis was conducted to demonstrate damage formation in a three dimensional model of HAs. The inhomogeneous model of femoral bone was constructed from a 79 year old female patient with hip osteoarthritis complication. Two different femoral components were modeled with titanium alloy and cobalt chromium and inserted into the femoral bones to present THA and RHA models respectively. The analysis included six configurations, which exhibited various loading and boundary conditions, including axial compression, torsion, lateral bending, stance and two types of falling configurations. The applied hip loadings were normalized to body weight (BW) and accumulated from 1 BW to 3 BW. Predictions of damage formation in the femoral models were discussed as the resulting tensile failure as well as the compressive yielding and failure elements. The results indicate that loading directions can forecast the pattern and location of fractures at varying magnitudes of loading. Lateral bending configuration experienced the highest damage formation in both THA and RHA models. Femoral neck and trochanteric regions were in a common location in the RHA model in most configurations, while the predicted fracture locations in THA differed as per the Vancouver classification.Total hip arthroplasty (THA) and resurfacing hip arthroplasty (RHA) are common procedures for patients with progressive hip osteoarthritis. Continuous development and improvement of prosthesis engineering design and advanced surgical approaches have enabled the success of the procedures for many decades The prediction of loading direction, which is associated to the fracture type, was very challenging. The unique characteristics of femoral bone with its irregular and inhomogeneous structure Improvement in the engineering design and material selection in RHA has increased bone preservation and reduced incidence of dislocation As a consequence, the aim of the present study is to analyze the effects of different types of femoral components, namely THA and RHA, in predicting the risk of femoral fractures using finite element (FE) analysis. Different loading configurations were considered in the analysis to simulate isometric loading modes and sideway fall. The fracture risk was discussed in the resulting damage formation element of the inhomogeneous bone model. To the best of our knowledge, this approach has not yet been applied to HA model to evaluate the possibility of bone fractures.The geometry of the femoral bone was developed from a CT based image of a 79-year-old living female with hip osteoarthritis in the left joint. The data was provided by Kyushu University Hospital, Japan. The CT images were compiled and stacked into commercial biomedical software Mechanical Finder 6.1 (Research Center of Computational Mechanics Inc, Tokyo) to construct a three dimensional (3D) model using FE analysis. The total number of elements for the femoral bone in THA and RHA were 146,414 and 166,414 respectively. For femoral components, prosthesis and femoral ball were assigned with 23,349 elements while resurfacing implant had 37,484 elements. Automated mesh size of 2 mm was considered with tetrahedron elements for all models. In generating an inhomogeneous model, each element of the bone model was generated based on the basis of the linear relationship between ‘apparent density’ and gray value of the data in Hounsfield unit (HU). Material properties for the bone elements were computed based on the basis of the study by Keyak et al. ). The high values of Young modulus in outer part present cortical bones, while lower values indicate cancellous bones. The model was also assumed to be an isotropic material.HA models were constructed by replacing the hip joint with different femoral component models. The 3D models of femoral components or implants were imported into the biomedical software to develop the THA and RHA models. The THA model was developed by replacing the hip joint with Titanium Alloy prosthesis stem and Alumina femoral ball. The femoral head was cut off and the prosthesis stem was aligned properly into the femoral canal. The difference in the RHA model is that the femoral head was resurfaced by implanting the Cobalt Chromium prosthesis pin. Descriptions of both models are illustrated in , while the mechanical properties of the femoral components . The connection between the implant and the bone is assumed to be perfectly bonded at the interface.In this study, we examined different configurations to demonstrate the various loading directions and boundary conditions. Three types of isometric loadings were axial compression configuration (ACC), torsion configuration (TC) and lateral bending configuration (LBC). The consideration of loading was adapted from the well-established and validated testing protocol for periprosthetic femoral shaft fixation shows the orientation of loading direction and illustrates the loading and boundary conditions for each configuration. The loading magnitudes may vary in each individual and configuration. Therefore, the magnitude of the applied load was subjected to the patient's body weight (BW) at 60.0 kg and the load increments were ranged from 0.5 BW to 3 BW in predicting the fracture patterns and locations at different configurations. Experimental study conducted by Groen et al. Damage formation criterion was predicted using a dedicated sub-program installed in the Mechanical Finder (MF v6.1) software. The damage mechanism was performed corresponding to tensile failure, compressive yielding and failures in bones, which predict the possibility of bone fractures in the femur models. The judgment of the failure and yield elements of the inhomogeneous bone model was measured initially based on the resulting Drucker–Prager equivalent stress. The process of the measurement is summarized in If the equivalent stress exceeded the element yield stress, the process proceeds to (b). If not, it goes to (d).After an element underwent compressive yield, the Young's modulus was reduced to the post yield modulus. Each yielded element was judged whether the minimal principal strain exceeded −3000 micro-strains. If yes, the process continued to (c). If not, the element was still considered to be in yielding condition.The element was judged as compressive failure and the stress was set to zero.The measurement continued on the resulting maximum principal stress. If the principal stress exceeded the ultimate tensile stress (which was set as 80% of the compressive yield strength), the element was assumed to crack. If not, the element was assumed to maintain in elastic deformation and showed no change.The clinical fracture of long bones is proven when the outer cortical bone fails. A small damage in the trabecular bone does not necessarily lead to fracture if the cortical shell remains intact This study concentrated on computational analysis. The femoral bone model developed in this study was verified with a synthetic composite femur as reported by previous researchers. Simoes et al. . Our findings indicated that the pattern of strain distribution demonstrated in our study is similar to that reported by Simoes et al. Different configurations present different loading directions and boundary conditions. In this study, the accumulation of loading magnitude was considered in each configuration to predict the effects of damage formation in HA models. The findings were compared to those predicted in an intact femur. The magnitude was set up with a range 0.5 to 3.0 of the patients’ BW. Comparison between each configuration is presented in a–f for ACC, TC, LBC, SC, falling 1 (FC1), and falling 2 (FC2). The number of element failures was separated between tensile failure and compressive yielding/failure in the THA and RHA models.The patterns of the accumulated damage were different between HAs and each configuration. Findings in AC, TC and LBC showed that tensile failures were dominant in the respective isometric loading, respectively (a–c). In ACC, the number of failure elements in THA was significantly lower even with a higher magnitude loading. In the RHA model, the failure element increased exponentially when the loading reached 3 BW. TC and LBC indicated a greater number of failure elements in the THA and RHA models. The failure elements increased rapidly when the loading reached 1.5 BW. The total number of failure elements (tensile and compression) in TC drastically increased from 500 to 18,680 elements in the THA model and from 1298 to 29,442 elements in the RHA model between 1.5 BW and 3 BW. Sudden accumulated failure element suggested a critical loading magnitude in TC. In LBC, the number of failures was predicted to increase from 1067 to 35,682 elements in the THA model and from 4542 to 43,690 elements in the RHA model at the similar range of loading magnitude. The prediction of femoral fractures in all respective isometric configurations indicates that the RHA model exhibits higher failure elements and more risks of fractures than the THA model.The patterns of accumulated damage were slightly different in SC, FC1 and FC2 (). Compressive yielding and failures dominated both the THA and RHA models, particularly at a higher BW loading. In SC at 3 BW, total failure elements in THA and RHA were highly projected at 14,737 and 16,236 elements, respectively. This finding suggested that a greater risk was expected in RHA models, particularly at larger loading magnitudes. Observation of FC1 and FC2 revealed that the number of failure element was lower compared to SC. However, the estimation of higher compressive yielding and failure elements in the RHA model suggested a high fracture risk at lower loading magnitudes.The presence of stiffer femoral components had modified the mechanical environment of the femoral bone. The findings of damage accumulation suggested the importance of loading directions and boundary conditions in predicting the fracture risks at different activities. In addition, the loading magnitudes may contribute to the extent of the damage. The role of the femoral components in the accumulation of the damage in different arthroplasties is important and worth considering. However, estimating the real loading magnitude is a challenge due to the possibilities on the involvement of various isometric loadings during certain activities or accidents.Estimation of bone fractures in HA models was conducted on the resulting failure elements in femoral bones. The location of fractures in the THA model was discussed according to the Vancouver Classification The comparison between THA and RHA models was conducted on each configuration. The results of fracture prediction at 3 BW loading for ACC and SC are shown in a and b, respectively. In ACC, the THA model demonstrated a minimum number of failure elements, while in the RHA model, the failure elements were concentrated at the upper neck and distal end of the femur. ACC did not result in any risk for the THA model but exhibited tensile failure at the upper neck region and compressive failure at the distal end in a RHA femur. The load from the axial direction was believed to be equally distributed in the prosthesis stem and was well distributed towards the femoral shaft. However, the femoral components in the RHA model had created bending effects in the femoral neck, which led to tensile failure in the respective regions. Therefore, bone fractures at the upper neck region were predicted in the RHA model at high loading. In SC, the pattern of damage formation was similar in the THA and RHA models. Tensile failures were predominant in the distal medial region, while compressive yielding and failures were found mainly in the lateral distal region. The presence of femoral components in the femur did not appear to influence the fracture location. The loading angle of 160° with reference to the long axis of femur had created a bending effect to the femoral shaft itself. Thus, bone fractures were predicted at the distal end of the femur at high loading magnitudes for SC. For the THA model, the fracture pattern correlated to type C in the Vancouver classification. The effects of HA to the damage formation were not clearly identified in SC.The location of damage formation in falling configurations was mainly concentrated at the trochanteric region in both the THA and RHA models. The illustration of the damage formations for FC1 and FC2 is shown in . In the THA model, instead of damages in the greater trochanter, failure elements were also projected at the bone-implant interface at the proximal lateral region in both FC1 and FC2. The applied loading at the femoral ball had impacted the femur to the ground and contributed to the damage formation at the trochanteric region. Predicted fracture locations in the THA model during falls drew a parallel view to type AG in the Vancouver classification. In the RHA model, predicted damage formation suggested a fracture location at the greater trochanter and upper neck region in both configurations. Moreover, tensile failure elements were projected at the lesser trochanter and proximal medial region in FC2. The femoral component in the resurfacing hip had created a bending effect to the femoral head after loading. The chances of implant loosening were predicted to occur at the proximal medial region and around the cup rim.The pattern of the accumulated damage with the increase of BW loading was presented for both TC and LBC. Both situations demonstrated a high number of failure elements at high impact loading in the THA and RHA models. The predictions of bone fractures in the THA model at different loading magnitudes are illustrated in a and b for TC and LBC, respectively. Failure elements appeared at a minimum of 0.5 BW loading. In TC, the damage was initiated at the distal end of the prosthesis stem. As the loading magnitude increased, the middle region of the femoral shaft experienced tensile failure at its anterior plane and compressive yielding/failure at its posterior plane.Furthermore, damage elements were defined at the bone-implant interface at the proximal region and distal prosthesis stem. Failure elements at the interface may lead to stem loosening and instability. In the LBC, failure elements were predicted to initiate at the distal femoral shaft, which was close to the boundary fixation. The damage formation increased drastically when the load reached 1 BW. Tensile failure was observed primarily in the medial distal region, while compressive yielding was observed mainly in the lateral distal region of the femur. In addition, failure elements were defined at the distal end of the prosthesis-bone interface which may have contributed to stem loosening. As the loading magnitude increased, total damage was projected at the middle region of the femoral shaft. The pattern of the predicted bone fracture was associated with type B2 and C of the Vancouver classification for TC and LBC, respectively.The results of the RHA models in TC and LBC are presented in . The RHA model experienced more damage formation than the THA model. In TC, the failure elements were initiated at the middle shaft of the femur (a). As the loading magnitude increased to 1.5 BW, compressive yielding and failure elements were observed predominantly at the trochanteric region. The impact of torsion loading at the anterior direction had created a bending moment to the femoral shaft and contributed to the incident. A different pattern of damage formation was predicted for LBC (b). Failure elements were predicted at the distal femoral shaft at 1 BW loading. As the load increased, the damage formation was formed at the lesser trochanter and upper neck region. The loading direction applied to the configuration suggested the formation of damage in the femur. Tensile failures were observed at the medial plane, while compressive yielding and failure elements were gathered at the lateral plane. The high loading magnitude analyzed in the simulation may overestimate the real loading magnitude. However, the current findings suggested that both produced greater consequences to the femoral bone at lower impact loading.The presence of prosthesis stem in the THA model had modified the mechanical environment of the femoral shaft since it involved a large amount of bone removal. Griza et al. The predicted fracture location obtained in this study for RHA was found to be focused at the femoral neck and trochanteric region. The results of femoral neck fractures were consistent with a simulation study conducted by Little et al. The results of the study explained the importance of loading directions and boundary conditions to predict fracture locations in HAs. Different configurations demonstrated different locations of the fractures in the THA and RHA models. Different types of implants would lead to other consequences. Loading in the perpendicular direction of femoral shaft, such as TC and LBC, simulated the greatest risks of bone fractures. The influence of the loading direction to the strength of the femur was reported by Keyak et al. The risks of femoral fractures were also associated with gender, age, structure of bones and bone mineral density Computational analysis conducted in this study was limited to a basic biomechanical model and may not accurately replicate the behavior of the bone in vivo. Limitations of the studies included the identification of spongy cancellous bones by bone density and the absence of hip joint attachment. The ligament and soft tissue of the bone may function in shock absorption during high impact loading The biomechanical study demonstrated the capabilities of CT-based FE analysis to predict damage formulation of femoral fractures in HAs. The presence of different femoral components in the femur had influenced the predicted fracture locations. The RHA model demonstrated a greater risk of femoral fractures compared to the THA model in all configurations. Different configurations applied in the analysis suggested the importance of loading and boundary conditions in simulating and predicting the fracture locations. TC and LBC demonstrated a large number of damage formation in both models at lower impact loading. Predicted femoral fractures in the RHA model focused on the neck and trochanteric region. The projection of fracture location in the THA model ultimately correlates with the Vancouver classification.Modeling the high strain rate behavior of titanium undergoing ballistic impact and penetrationTitanium is an important candidate in the search for lighter weight armors. Increasingly, it is being considered as a replacement for steel components. It is also an important component in the application of ceramics to armor systems, especially in armor modules that are capable of defeating kinetic energy penetrators while sustaining little or no penetration of the ceramic element. The best alloy available today for ballistic applications is Ti-6Al-4V, an aerospace grade titanium alloy. The principal deterrent to widespread use of this alloy as an armor material is cost, and a significant portion of the cost is in processing. Consequently, the U.S. Army Research Laboratory undertook a program to study a particular lower cost processing technique [1].The objectives of this work are to characterize the low-cost titanium alloy by generating constants for the Johnson-Cook (JC) and Zerilli-Armstrong (ZA) strength models, and to use and compare these two models in simulations of ballistic experiments. High strain rate strength data for the low-cost titanium alloy are used to generate parameters for the two models. The approach to fitting the JC parameters follows one previously used successfully to model 2-in thick rolled homogeneous armor (RHA) [2]. The approach to fitting the ZA parameters is based on a method described by Gray et al. [3]. The resulting model parameters are used in the shock physics code CTH [4] to model a Ti-6Al-4V penetrator penetrating a Ti-6Al-4V semi-infinite block at impact velocities up to 2,000 m/s. Similar experiments are performed, and the predictions of the two models are compared to each other and to the experimental results.Effects of scaling and geometry on the performance of piezoelectric microphonesRecent advances in microfabrication and nanofabrication techniques have allowed for the construction of ever-smaller sensors for the measurement of acoustic signals. The physics of sensor transduction and acoustics however place fundamental constraints on performance and limit the benefits of continual reductions in size. Key operating parameters such as sensitivity, minimum detectable signal (MDS) and resonant frequency are directly affected by device scale. Besides overall scale, relative sensor geometry (e.g. thickness ratio) can drastically alter performance. Through finite element and lumped element modeling, we study the effects of sensor geometry and scale on the sensitivity and noise performance of a piezoelectric microphone. The results indicate optimal relative geometric parameters for maximum performance and demonstrate the strong dependence on device geometry.Continued improvements in microfabrication and nanofabrication methods have been enabling smaller physical sensors in recent years. Piezoelectric microphones are no exception to this trend. A number of piezoelectric MEMS-based microphones have been developed over the last few decades. One of the earliest efforts was by Royer et al. In this paper, we focus on the scaling laws and geometric effects that influence piezoelectric-based acoustic sensor performance, particularly in regards to sensitivity and noise. The intent is to provide a framework for performance optimization during sensor design. In Section , an overview of piezoelectric microphone architecture, fundamental noise mechanisms and system-level considerations is presented. In Section , theoretical models for piezoelectric transduction is presented and incorporated into an equivalent circuit for a microphone, providing a foundation for scaling arguments of key operating parameters. Finite element modeling is then used in combination with the equivalent circuit to predict sensor performance. Microphone sensitivity, noise and minimum detectable signal (MDS) are then analyzed as functions of relative geometric ratios.A piezoelectric microphone can loosely be described as a transducer for converting acoustic pressure and volume velocity into electrical voltage and current for the purposes of signal collection. It generally consists of a diaphragm (membrane or plate) for coupling pressure fluctuations into mechanical displacements and a piezoelectric material for transferring the diaphragm strain energy into an electrical charge separation (). There is typically also a vent and cavity structure attached to the diaphragm for maintaining a pressure differential across the diaphragm at non-zero frequencies while allowing for static pressure changes to equilibrate. The piezoelectric material is typically placed somewhere along either the top or bottom surfaces of the diaphragm.The dominant noise source for most piezoelectric sensors arises from thermal noise. Thermal noise exists wherever there is dissipation in a system, a phenomenon expressed in the Fluctuation–Dissipation Theorem These noise sources may occur at various functional stages of the transduction process. It is therefore useful to build an equivalent circuit of the sensor and convert each individual noise source into an equivalent voltage source at the output. The total noise can then be calculated. When multiple incoherent noise sources exist, the total power is the sum of the individual powers, therefore Powertot=Power1+Power2+Power3 or for example, Vtot=V12+V22+V32. We will demonstrate this process later in this paper after we introduce the piezoelectric transduction model and equivalent circuit.Piezoelectricity refers to a phenomenon in certain materials to exhibit a change in polarization in response to an applied stress, as well as the reverse effect of a mechanical deformation resulting from an applied electric field There are a variety of standard notations and forms for expressing the linear piezoelectric effect. For the purposes of this paper, we will introduce and use exclusively the “Strain-Charge” form where Sij, mechanical strain; sijklE, elastic compliance at constant electric field [m2/N]; Tkl, mechanical stress [N/m2]; dkij, piezoelectric coefficient [C/N or m/V]; Ek, electric field [V/m]; Di, electric displacement [C/m2]; εikT, electrical permittivity at constant stress [F/m].The subscripts denote the components of each variable in a particular direction. A variety of materials exhibit piezoelectricity (e.g. ZnO, PZT and AlN), each offering various tradeoffs in terms of performance and process compatibility where j=−1, ω is the angular frequency, da is the acoustic piezoelectric coefficient, Cas is the acoustic compliance, P is the pressure and V is the voltage. Additionally, the electrical current is given by I |
= |
jωq |
= |
jωDiA |
[A], the acoustic volume velocity is given by Q=jωδvol[m3/s], and the free (i.e. P |
= 0) electrical capacitance is Cef, where q is electrical charge and δvol is volumetric displacement.Using the piezoelectric transduction equations defined in , we can construct an equivalent circuit of a typical piezoelectric microphone consisting of lumped elements representing acoustic and electrical components, as shown in . The portion of the circuit enclosed in the dashed rectangle represents the piezoelectric transduction (modeled here as an electro-acoustic transformer) and the remainder of the lumped elements arise from the dynamics of the overall mechanical and electrical structure. Several new terms are introduced in this circuit. This representation of the piezoelectric transduction requires a transformer “turns ratio”, ϕ, that provides a conversion from acoustical to electrical energy and an electrical capacitance, Ceb under blocked (i.e. Q |
= 0) conditions. The blocked capacitance can be related to the free capacitance via the coupling factor, k, which represents the fraction of energy that is coupled between the acoustical and electrical energy domains.Additionally shown in the equivalent circuit are the acoustic compliance, Cas, and mass, Ma, of the diaphragm, the acoustic radiation resistance and mass, Rrad and Mrad, the acoustic cavity compliance, Cac, and the parallel dielectric loss resistance, Rp. defines all of these lumped elements and relevant supporting parameters. The acoustic compliance of the diaphragm stores potential energy associated with bending and thereby inciting an elastic strain in the diaphragm. The acoustic mass stores kinetic energy associated with the motion of the diaphragm. The acoustic compliance of the cavity stores potential energy associated with the compression of fluid within the cavity when the diaphragm bends. The dielectric loss resistance arises from several factors associated with dissipative mechanisms within the piezoelectric material. The reader is referred to Horowitz et al. The radiation resistance represents the energy that is acoustically radiated away from the structure and is therefore seen as a loss (i.e. resistance). The radiation mass represents the storage of kinetic energy in the inertial mass of fluid that is moving with the vibrating diaphragm. Typically, it is sufficient to model these components by approximating the bending diaphragm as a piston in an infinite baffle. The full expression for the acoustic impedance of a piston in an infinite baffle is given in Blackstock . In these expressions, the effective area, Aeff, represents an equivalent piston face area that displaces an equal volume as the spatially varying displacement of a bending diaphragm where the piston displacement equals the center deflection, w0.The basic physical structures that will be analyzed in this paper are shown in cross-section in for both an isotropic (a) and composite (b) diaphragm. The circular diaphragms are assumed to be clamped at the edges and axisymmetric.The lumped element calculations for the diaphragm depend on the actual mode shapes of the diaphragm. For a circular diaphragm, as described in , which we can then use to calculate the acoustic compliance and mass of the diaphragm, provided the deflection is known. We will now look at the vibrating mode shapes for some common and simple diaphragm structures. For a uniformly loaded plate with clamped edges and no in-plane stress, the transverse deflection, wplate, is given by . For large values of in-plane stress, σ, the deflection of a diaphragm follows more closely with an ideal membrane For an actual piezoelectric microphone, the diaphragm is typically constructed of a composite of several piezoelectric and non-piezoelectric materials. Additionally, in-plane stresses may vary throughout the structure as a result of residual stresses imposed by the fabrication process. These factors combine to produce a transverse deflection under uniform load that differs from both the basic plate and basic membrane equations. Under certain conditions, the composite diaphragm deflection may be calculated analytically The complexities of the material interactions in the piezoelectric composite diaphragm ultimately led us to a finite element analysis of the structure. COMSOL Multiphysics was used to implement the model and analyze the results. The model was implemented using an axisymmetric approach. Clamped boundary conditions were applied to the outer edge of the structure and a pressure load was applied to the bottom surface. Residual stresses were set to zero for each of the layers. A ground potential boundary condition was applied to the interface between the ring and the diaphragm and a floating potential boundary condition was applied to the top surface of the ring. Quadrilateral elements were used for the mesh, which was scaled by the aspect ratio to keep a sufficient number of vertical elements in the thin structure.For the modeling and analysis presented in this paper we will assume all nonpiezoelectric materials have the properties of single crystal silicon and all piezoelectric materials have the properties of lead zirconate titanate (PZT). All electrodes will be assumed thin enough to be ignored and residual stress is assumed to be negligible to simplify the analysis and highlight the general geometric effects. Residual stress will be significant in any real-world application but inclusion in the following analyses needlessly obfuscates the qualitative geometric dependencies we wish to highlight. Inclusion of electrodes and residual stress will modify the magnitude of the performance parameters and the optimal geometric values and must be considered carefully in any real-world application. The cavity depth was assumed large enough to cause negligible stiffening on the diaphragm motion (highly compliant) and was omitted from the FEM model. The material parameters and their values used in the following modeling are shown in To illustrate how the composite structure deflection compares to some simple baseline structures, the normalized deflection curve (mode shape) was calculated for the plate, membrane and a composite diaphragm (). For a piezoelectric microphone with a thin piezoelectric layer and no residual stress, the deflection approaches the analytical model for a clamped circular plate. Note that as the piezoelectric thickness decreases (TR = 0.3), the response approaches the plate solution.The finite element model was used to directly compute the composite plate deflection, wcomp(r), and voltage output, V, for an applied pressure, P. Integrating the plate deflection for a finite applied pressure and zero applied voltage, as described above, yields the acoustic compliance, Cas. Integrating the plate deflection for a finite applied voltage and zero applied pressure similarly yields the acoustic piezoelectric coefficient, dA. Both parameters are defined in The general expression for the open circuit sensitivity is frequency dependent, but can be written generally as Sens |
= |
V/P. We compute the open circuit static sensitivity via FEM analysis by applying a uniform static pressure to the composite plate and measuring the generated potential difference (voltage) between the top and bottom surfaces of the piezoelectric. The sensitivity was then calculated directly via this measurement.As discussed earlier, thermal noise arises wherever there is dissipation in the system. As a microphone vent is not included in the present analysis, the piezoelectric microphone has two main sources of dissipation, radiation resistance, Rrad, and dielectric loss resistance, Rp. Their individual contributions to the overall output thermal noise depends upon their individual magnitudes as well as the frequency dependent dynamics of the composite plate equivalent circuit. The reader is referred to Horowitz et al. is the equivalent circuit noise model for the microphone. Each resistive component contributes noise to the overall output noise. To model the contribution from each component, a voltage or current noise source is added in series or parallel to each resistor. The total output noise voltage power spectral density (PSD), SvOUT_p=SvRp_p+SvRd_p is the sum of the individual PSDs. The individual contributions to the total PSD are found by looking only at the output voltage PSD due to a single source, while removing the others from the circuit (i.e. short-circuiting voltage sources, and open-circuiting current sources). SvRp_p is the output voltage noise PSD due to the dielectric loss resistance, Rp, and SvRd_p is the output voltage noise PSD due to the radiation resistance, Rrad.Following the above procedures, the SvRp_p is found to bewhere Zp |
= (1/sCeb)//Rp |
= (Rp/sCeb)/(Rp |
+ 1/sCeb), Zd |
= |
Rrad |
+ |
s(Ma |
+ |
Mrad) + 1/sCas, ZaC |
= 1/sCac and SiRp |
= 4kBT/Rp. Similarly, SvRd_p is computed aswhere SvRd=4kBTRd. The equivalent output voltage noise for a measurement bandwidth, BW, can then be found simply as Vth_out=BWSvOUT_p.The two contributors to the noise floor are shown in as a function of plate radius. The contribution due to the dielectric loss of the piezoelectric material is found to be dominant under the assumed geometric and material conditions. For these calculations, the radiation resistance was calculated at 1 kHz using the piston in an infinite baffle approximation, the dielectric loss resistance was estimated using an assumed material loss factor of η = 0.05 and the bandwidth of integration, BW, for both noise sources was 1 Hz.Up to this point, we have considered only the noise generated by the sensor. In an actual implementation, the sensor will most likely be interfaced to some form of preamplifier. Best case noise floors of available low-noise preamplifiers are typically on the order of 1nV/Hz. Depending on the particular dielectric loss (material and geometry dependent), the sensor noise could easily be above or below the amplifier noise.The choice of amplifier depends highly on the sensor output impedance and application. For a high output impedance (low capacitance), as is typical with these small piezoelectric sensors, a charge amplifier will offer the best performance if the amplifier must be placed far from the sensor, due to large parasitic cable capacitance. The use of a voltage amplifier will lead to a large drop in sensitivity arising from a voltage divider among the sensor and cable capacitances. However, if the amplifier can be placed close to the sensor, the voltage amplifier will usually offer best performance due to a lower amplifier noise floor. The choice of a particular type of voltage amplifier can further minimize amplifier noise. For a high impedance sensor, amplifier current noise can easily dominate over voltage noise. A low current noise amplifier (such as provided by a JFET input instrumentation amp) will generally work best in this situation.We will not consider amplifier noise in our calculations of minimum detectable signal (MDS) and our further analysis of sensor performance, as inclusion deviates from the main focus of this paper. Nevertheless, consideration of currently available preamplifiers and/or concurrent development of a custom preamplifier architecture should be included early in the design of a piezoelectric microphone to achieve optimal system performance.The minimum detectable signal is defined here as the smallest signal that can reliably be detected by the microphone. Although it is possible, with sophisticated signal processing, to measure signals with output voltages smaller than the noise voltage, it will be calculated here as equal to the input-referred noise level, thus MDS |
= 20 log[(Vth_out/Sens)/20 μPa].The coupling between the circular diaphragm and piezoelectric circular ring leads to performance results that are dependent upon the absolute scale of the structure as well as the relative geometries of the components. First, we look at the dependence upon the radius ratio (RR). In the following sets of figures, we will look at sensitivity, noise floor and minimum detectable signal (MDS). The sensitivity is computed numerically via COMSOL, while the noise floor is found analytically from the expressions above. The MDS is then computed from these as described above., the sensitivity as a function of the radius ratio is plotted for several different values of thickness ratio (TR). We overlaid these different thickness ratios to highlight the interplay between both parameters. The common trend is for the sensitivity to increase as the radius ratio increases, with a maximum corresponding to a very narrow ring near the clamped edge of the circular diaphragm. Physically, this is the region of highest stress on the surface of the diaphragm., the noise voltage, Vth_out, is plotted as a function of the radius ratio (RR) for a selection of different thickness ratios (TR). As the voltage is dominated by the dielectric loss component, the voltage is proportional to the dielectric loss resistance, which is inversely proportional to the capacitance. Thus, the noise voltage is lower for small thickness (as TR → 0) and large surface area (as RR → 0).Combining the geometric effects of the sensitivity and the noise voltage yields the MDS shown in . The MDS is plotted (on a logarithmic scale) as a function of radius ratio (RR) for a selection of different thickness ratios (TR). The optimum MDS was found at a radius ratio of 0.75 and a thickness ratio of 0.3. Note from the previous two figures, that this combination is neither the highest sensitivity, nor the lowest noise, but instead offers the best combination of the two.Although the effects of varying the thickness ratio can be seen in the prior figures, it is useful to look directly at the sensitivity as a function of thickness ratio, as shown in . The figure plots the thickness ratio dependence for several values of radius ratio. As can be seen, there is a peak in the sensitivity that varies in magnitude and location depending on the radius ratio. In , the noise voltage is plotted as a function of the thickness ratio (TR) for a selection of different radius ratios (RR). The noise voltage is lower for small thickness (as TR → 0) and large surface area (as RR → 0). In , the minimum detectable signal is plotted as a function of the thickness ratio (TR) for a selection of different radius ratios (RR). As the thickness ratio is increased from 0.1, the MDS improves (decreases) as a result of increasing sensitivity. Above a certain, RR-dependent, point, however, the MDS begins to increase as the noise voltage rises while the sensitivity begins to drop.The remaining, unexplored, relative geometric parameter is the aspect ratio (AR), defined here as the ratio of diaphragm radius, R2, to thickness, tm. In , the sensitivity is plotted as a function of the aspect ratio, for several different size diaphragms, while the thickness and radius ratios are held constant at 0.6 and 0.9, respectively. The result is a distinctly linear dependence on the aspect ratio, where the slope is determined by the radius. A high aspect ratio is thus desirable from a sensitivity perspective. While the sensitivity increases with aspect ratio, the noise voltage was seen to decrease, as shown in . A high aspect ratio is thus desirable from a noise perspective as well. Combining the sensitivity and noise results, we obtain the plot in for the minimum detectable signal as a function of the aspect ratio. Clearly, the combined effect of sensitivity and noise leads to a lower MDS for high aspect ratios.The absolute scaling behavior of the composite structure is now explored through an analysis of the sensitivity as a function of the outer radius, R2, of the diaphragm. By keeping the relative parameters constant, the radius serves as a useful indicator of scale. Shown in is a plot of the sensitivity as a function of radius for a range of different aspect ratios. Note the linear dependence on scale. For this plot, thickness ratio (TR) and radius ratio (RR) were held constant at 0.6 and 0.9, respectively. Repeating this analysis for a different set of constant relative parameters would yield the same trends but with different magnitudes.The noise voltage is seen to decrease with increasing radius, as shown in , with the best MDS result obtained at the largest radius and aspect ratio.In summary, the modeling results demonstrated the following design considerations () for optimal performance of a piezoelectric microphone consisting of a ring-shaped PZT film on a circular silicon diaphragm. Note that a range of optimal RR and TR values are listed as they are interdependent (i.e. the optimal value for one depends on the choice of the other).Stephen B. Horowitz graduated in 2005 from the University of Florida with a Ph.D. in electrical engineering, focusing on the development of a MEMS-based electromechanical acoustic energy harvester. He is currently employed in the Emerging Technologies Group of Ducommun Miltec as program manager and lead engineer for MEMS and NEMS research. Stephen is the author of 25+ publications and 4 patents related to optical pressure and shear stress sensors, piezoelectric microphones, acoustic and mechanical energy harvesting, and tunable liners for aircraft noise control. He has 10+ years of experience in designing, modeling, fabricating and characterizing miniaturized sensors and systems based on emerging technologies, such as micro- and nanotechnology.Adam D. Mathias received a B.S.E. degree from the University of Alabama in Huntsville in the Department of Mechanical and Aerospace Engineering in 2008. He is currently finishing an aerospace M.S.E. degree at the University of Alabama in Huntsville with a focus on computational fluid dynamics. His thesis is a study of vibrational modes and acoustic transmission loss through offset-honeycomb core panels for aircraft noise reduction via the finite element method. He has worked at Ducommun Miltec as a MEMS engineer since 2008 and gained experience in the design, modeling, and testing of MEMS devices including acoustic sensors and micro-actuators.Jon R. Fox received his B.S. in physics, magna cum laude, from the University of Missouri – Rolla in May of 1993. He completed a Ph.D. in physics at Penn State University in August 2000. Beginning in 2000, he was employed with Research Support Instruments of Princeton, NJ working on MEMS device development and was a Visiting Professional Technical Staff Member at Princeton University. Since 2010, he has been employed by Ducommun Miltec in support of programs with the Weapons Sciences Directorate of the Aviation & Missile Research, Development, and Engineering Center (AMRDEC) of the U.S. Army.Jean P. Cortes received his B.S. in mechanical engineering from the University of North Carolina in Charlotte, NC. He has been working with MEMS and NEMS since 2008 and has helped the Emerging Technologies Group at Ducommun Miltec after his graduation. Before graduating, he achieved the second place on the University Alliance Competition (Sandia National Labs), and made a workable pressure sensor from thermal principles in his senior project. Currently, he is pursuing his Masters in Electrical Engineering at the University of Alabama in Huntsville with a focus on MEMS and nanotechnology.Mohan Sanghadasa received the B.Sc. degree from University of Colombo, Sri Lanka, the M.S. degree from Bowling Green State University and the Ph.D. degree from University of Alabama in Huntsville (UAH). He was senior research associate and asst. research professor of physics at UAH from 1993 to 2007. He is currently a Research Scientist in U.S. Army Aviation and Missile Research, Development, and Engineering Center (AMRDEC). His current research interests include micro- and nano-scale devices, acoustic sensors, supercapacitors, and high speed electro-optic polymer modulators. He is a member of IEEE, Optical Society of America and SPIE.Paul Ashley received a B.S. degree in physics from Baylor University, the M.A. degree in physics and M.S. and D.Sc. degrees in electrical engineering, all from Washington University, St. Louis. He was formerly the deputy director of Weapons Sciences Directorate at the U.S. Army Aviation and Missile Research Development and Engineering Center (AMRDEC) where he had been involved in integrated photonics, guided wave structures, electro-optical polymers, and micro/nano-devices for the past 30 years, before retiring in 2011. He has over 200 publications and numerous patents in micro- and nanotechnology. Previously, he was director of the Electro-Optics Laboratory, Science Applications Inc. He is a member of Sigma Xi, Eta Kappa Nu, Optical Society of America and SPIE.Effect of loading mode on fracture behavior of CrNiMoV steel welded joint in simulated environment of low pressure nuclear steam turbineStress corrosion cracking (SCC) behaviors of 30Cr2Ni4MoV welded joint in simulated environment of low pressure nuclear steam turbine were addressed with different fracture positions in the welded joint by constant loading test (CLT) and slow strain rate test (SSRT). The fracture of the welded joint happened near the fusion line which was ascribed to the interaction between stress and galvanic effect for CLT, while in welded metal with the weakest strength for SSRT. The mismatch between galvanic corrosion and strength of welded joint determined the fracture location and SCC sensitivity of the welded joint when the two different loading modes were applied.Stress corrosion cracking (SCC) is one potential risk of the environmental degradation for nuclear steam turbine rotor and their welded joints. It is well known that occurrence of SCC requires synergistic effects between mechanical, metallurgical and environmental factors. Slow strain rate test (SSRT) and constant loading test (CLT) are the most widely used methods to evaluate SCC susceptibility of structural materials in specific environment The most important reason for the above described limitation is the complexity of stress corrosion mechanism that involves the interaction between mechanical and electrochemical process. For smooth specimen of homogenous materials, cracking mostly primarily initiates and propagates at the position of the highest stresses and strains which may relate to electrochemical process In present paper, the SCC susceptibility of CrNiMoV steel welded joint in simulated environment of low pressure nuclear steam turbine were studied by both SSRT and CLT methods. In order to describe the SCC mechanism further, it is important to remark effect of loading mode on the fracture position of welded joint in tensile tests, furthermore, clarify the relationship between key mechanical parameter and galvanic effect.The welded joint of forging rotor steel 30Cr2Ni4MoV, fabricated by the narrow gap multilayer submerged arc welding (NG-SAW) combined with the narrow gap tungsten inert gas (NG-TIG) welding, was selected as the sample, as shown in (a) and (b). The Post-weld heat treatment was performed at 560 °C for 20 h to relieve residual stress. Chemical compositions and mechanical properties of 30Cr2Ni4MoV BM and WM are listed in , respectively. The location and geometry of the cylindrical tensile specimen for stress corrosion cracking tests are shown in (b) and (c) respectively. The fusion line is in the middle of the gauge section.The microstructures of BM, WM and HAZ of the welded joint were observed by optical microscope (OM), as shown in . It can be found that the BM is composed mainly by lathy tempered martensite ((a)), while the strip-like tempered bainite embedded on the martensite matrix was observed in the WM. The length of HAZ is approximately 2 mm. Owing to the temperature gradient during the weld process, the HAZ can be divided into three parts from fusion line to base metal, i.e., fully quenched-tempered zone (FQTZ), partially quenched-tempered zone (PQTZ) and tempered zone (TZ). The grain size of the HAZ declines from FQTZ to TZ, as shown in (c)–(e). The large block-like tempered martensite is surrounded by the tempered bainite in the FQTZ ((c)). The PQTZ is composed by smaller tempered martensite and tempered bainite ((d)), while fine granular martensite and tempered bainite dominates the TZ (The hardness measurement was conducted using the Vickers hardness tester with holding load of 4.9 N for 15 s. The hardness distribution is shown in . The fluctuation of hardness in WM is more severe than that in BM which ascribed to the difference of equiaxial crystal and columnar crystal in WM. According to numerous researches, the yield strength increases as the hardness grows. The average amount of hardness of WM (271HV) is lower than that of BM (280HV) which is corresponded to the yield strength of WM (781 MPa) and BM (803 MPa). The hardness of HAZ increases from BM to the fusion line (FL) and obtains the maximum value on the FL which declares that the yield strength gradient occurs in the HAZ and the yield strength reach the maximum value on the FL.Prior to stress corrosion cracking test, the electrochemical properties of each part of 30Cr2Ni4MoV welded joint, i.e. BM, WM and HAZ, were carried out in a 3.5 wt% NaCl solution at ambient temperature. A three-electrode system was used including a platinum wire electrode and a saturated calomel electrode (SCE) reference electrode. As working electrodes, the welded joints were sliced into three independent samples. The exposed surface size of BM and WM was 10 mm × 10 mm while it was 10 mm × 1 mm for HAZ. Prior to the electrochemical test, the surfaces of three samples were ground and polished to mirror finish, and then ultrasonically cleaned in deionized water, ethanol and acetone respectively. Three open circuit potential (OCP) and polarization curves were performed for BM, WM and HAZ specimens, respectively. The open circuit potential and polarization curves were also measured to observe galvanic effect on welded joint. All of the test specimens were immersed into the solution for 10 min before OCP measurements. The polarization curves were measured in the potential rage of ±0.4VSCEvs.Ecorr with the scan rate of 0.01 VSCE/s.The galvanic corrosion property of welded joint including BM, WM and HAZ was studied by scanning vibrating electrode technique (SVET) measurement. The specimen used in SVET was prepared with HAZ locating in the middle of the specimen with dimension of 15 mm × 15 mm. The scan microprobe was made of a platinum (Pt) wire with the diameter of 100 μm. The distance between the probe tip and specimen surface was maintained at 100 ± 10 μm which was monitored by a video camera system. Vibration amplitude and frequency were 30 μm and 80 Hz, respectively. The scan area was 12 mm × 10 mm, starting from the location approximatively 6 mm left side of fusion line. Since the 3.5% NaCl solution is too severe to catch the galvanic corrosion current, the micro-electrochemical measurement was conducted in corrosion cell with the 500 ppm NaCl solution at ambient temperature. Making the assumption that the electric field is constant around the probe, the current density is j (μA/cm2) is calculated by correlating the measured electric potential Δ∅V with kμScm-1 and the vibration amplitude dcm, as can be seen in Eq.Stress corrosion cracking tests were conducted in the aerated 3.5 wt% NaCl solution at 180 °C to simulate the environment of the liquid film on the surface of nuclear steam turbine welded rotor. Constant stress and slow strain rate were applied on the same geometry cylindrical tensile specimens (For constant loading test, various stresses which are less than the yield stress of BM and WM were applied, i.e., 715 MPa, 730 MPa, 745 MPa and 760 MPa. For slow strain rate test, various strain rates were applied, i.e., 1 × 10−5 s−1, 1 × 10−6 s−1, 1 × 10−7 s−1 and 1 × 10−8 s−1. Before the tests, all of the specimens were cleaned with deionized water, ethanol and acetone successively by ultrasonic cleaner. At the beginning of the experiment, the solution was heated to 180 °C and then loadings were applied to the specimens. The Stress and displacement were recorded before the fracture of the specimen. The solution was refreshed through a circulation system with the flow velocity of 1 ml/min. When the stress corrosion cracking tests were stopped, the fractured specimens were taken out and then cleaned with deionized water, ethanol and acetone using ultrasonic cleaner, successively. The reduction in area was measured and the morphology of the fracture surfaces were observed by scanning electron microscope (SEM). After that, the samples were cut from the tensile specimens through the longitudinal section and then were ground, polished and etched for the corrosion cracks observation.The distribution of stress and strain in the cylindrical specimens were analyzed by finite element analysis. A two-dimensional axisymmetric finite element model was built using ABAQUS software. The elastic and plastic parameters, Young's modulus (E), yield strength (σs) and slope of plastic deformation and stress (kp), used in the different regions (BM, WM, and HAZ) of the specimens were defined by the micro-sample tensile tests. The specimens were cut at the location of the BM, WM, CGHAZ and FGHAZ with the gauge section of 4 mm in length and 0.5 mm in thickness. The local mechanical properties of each regions are listed in . Since the geometry of micro-tensile specimen is different from standard specimen, the yield stress of BM and WM is significantly smaller than the value listed in , however, the tendency of yield strength is in accordance with micro-hardness distribution of welded joint. The 4-node bilinear quadrilateral element was used for mesh generation and the mesh was refined in the gage section. The specimen was fixed at one end and tensile stress or displacement was conducted at the other end.The potential dynamic polarization curves of various zones are shown in . Significant difference can be observed from the polarization curves, the WM showed the lowest corrosion potential. According to mixed-potential theory, galvanic effect exists among the welded joint because of the different corrosion potentials among BM, HAZ and WM. The electrochemical properties depend on different microstructures, the grain size and precipitations of carbides, etc. As can be seen in , the microstructures in HAZ and BM predominately consist of tempered martensite, while the tempered bainites embedded on the martensite matrix, which causes the obvious distinction of corrosion susceptibility between BM, HAZ and WM. In addition, the defects due to weld process and the heterogeneity of chemical elements in WM may also aggravate the corrosion susceptibility.In order to clarify the galvanic effect of the whole of the welded joint, the current density map in the welded joint was measured by using SVET which is shown in . The anodic and cathodic activities can be noticed over the WM and BM electrodes while HAZ acts as transition region from anodic to cathodic. Regarding both cathodic and anodic activities remain constant during the entire test, it is known that the presence of Cl− induces a breakdown of the passive film, resulting in a rapid average corrosion on WM. Anodic activity peaks referring to local dissolution for pit formation can be sometimes distinguished An elongation versus time curve up to failure under constant applied loadings for 30Cr2Ni4MoV welded joint in 3.5 wt% NaCl solution are shown in (a). The corrosion elongation curve consists of three typical regions with an initial sudden rise of elongation, steady of elongation and final fracture region, which corresponds to crack nucleation, steady crack propagation and terminal crack propagation respectively (b) shows the typical stress-strain curves of the SSRT tests applied with different strain rates. It can be seen that the elongation of the specimens in the solution are smaller than that of the specimen in the air which illustrates corrosion influences the fracture behavior in the solution. In the 3.5 wt% NaCl solution, the elongation of the specimens decreases with the strain rate decreases from 1 × 10−5 s−1 to 1 × 10−7 s−1, while the elongation of the specimens changed little when strain rate decreases from 1 × 10−7 s−1 to 1 × 10−8 s−1.The typical fracture morphologies of all the CLT and SSRT specimens are shown in . The fracture surfaces of both CLT and SSRT specimens in the 3.5 wt% NaCl solution are the combination of brittle fracture and ductile fracture which is distinguished by the black imaginary line in . This declares that the initiatory fracture of both CLT and SSRT specimens are due to the interaction between external environment and applied loading. When the stress concentration factor reaches to a critical value, the fracture surface turns from brittle fracture to ductile fracture. The magnifying pictures of location 1 and 2 show the detail of the morphology of the brittle and ductile fracture surface, respectively. The percentage of SCC area are summarized in . With the increasing of applied constant loading and strain rate, the percentage of SCC area decreased because the exposing time in environment is decreased., the fracture locations of the CLT specimens in 3.5 wt% NaCl solution at 180 °C were all in the HAZ near the FL. According to the hardness distribution in , the hardness of the HAZ near the FL is higher than BM and WM which corresponds to high stress corrosion cracking sensitivity. It can be seen that the crack initiation site of the SCC is in the FQTZ near the FL in displays the fracture locations of the SSRT specimens. It can be learnt from that the specimen conducted in air fractured in the WM, according to the hardness and yield strength value, the strength of WM is the weakest in the welded joint. What should be noted that all the SSRT specimens conducted in the 3.5 wt% NaCl solution at 180 °C fractured in the WM as well. The fracture locations which keep a distance from the FL are almost the same of the SSRT specimens in 3.5 wt%NaCl solution at 180 °C at the strain rate of 1 × 10−5 s−1–1 × 10−8 s−1. Consequently, the different loading modes alter the fracture locations of the specimens of the welded joint.The distribution of stress and strain in the cylindrical specimens were analyzed by finite element analysis. As shown in (a), a two-dimensional axisymmetric finite element model was built using ABAQUS software. When the model was built, the Mises stress and the distribution of the plastic strain were obtained through finite element analysis, as demonstrated in (b) and (c). The maximum stress of the specimen is in the HAZ near the FL i.e. CGHAZ, however the maximum plastic strain is in the WM away from the FL. The fracture locations of the CLT and SSRT specimens and the results of the finite element analysis are compared, as depicted in . It is clear that the fracture location of the CLT specimen is in the FQTZ near the FL which corresponds to the location of maximum stress ((b)), but the fracture location of the SSRT is in the WM which corresponds to the location of maximum plastic strain (As for the stress corrosion cracking of rotor steel, it is common that the cracks initiate preferentially from corrosion pits (a)). Due to the interaction of stress concentration and local corrosion environment, the microcrack initiated in the pit and propagated along the direction perpendicular to the loading direction. A corrosion pit inducing the main crack was observed in the FQTZ near the FL, as shown in . The pits near the FL are easy to be the crack initiation sites which results from the highest hardness/strength. When the cracks initiate in the HAZ near the FL, the crack which causes the fracture in HAZ propagate faster than that of the region of lower strength (b) shows the path of crack propagation, and it can be seen that most stress corrosion cracks are transgranular. In addition, the cracks prefer to propagate through the direction of martensite laths.(a) demonstrates the morphology of the gage section of SSRT specimens in the WM near the fracture location. There is no pit on the surface, that is to say, the cracks initiate on the surface directly. With applied the dynamic strain, the local strain disrupts the oxide films on the surface and then crevices form on the oxide film. The solution flow into the film through the crevices and then the base metal will be exposed to the local environment The strain rate not only influents the cracks initiation, but also have effect on cracks propagation. As for the SSRT specimens at 1 × 10−7 s−1 and 1 × 10−8 s−1, the micro-cracks on the specimen surfaces are shown in (a), transgranular crack path can be seen at the strain rate of 1 × 10−7 s−1 and the crack traverse the lathy martensite. However, as shown in (b), the crack propagates through the grain boundary or the lathy martensite. Totsuka et al. (b). The strain rate at the crack tip is identified as the promotion of crack growth The mechanisms of the crack initiation and propagation are different for corrosion cracking dominated by stress and strain which results in the difference of fracture location of the welded joint. The phenomenon also can be verified by EDS mapping of the oxides in the crack tip. As is illustrated in , the crack mouth of cracks for both CLT and SSRT specimens are filled with oxides. is the EDS maps of crack tip with applied constant loading and strain rate, it revealed that oxide in the crack mouth and crack tip are Fe-oxides. However, compared with SSRT crack tip, the inner surface of CLT crack tip was covered by continuous oxide film, the film would be broken by external applied loading due to stress concentration in the crack tip. These phenomena provided evidence that oxidation plays an important role at the crack initiation and propagation for CLT specimens. The oxide films ruptured due to slip bands intersecting the crack tip, fresh metal exposed to the local environment and then oxide formed along crack tip. The crack propagates with such a cyclic process of “slip-film rupture-oxidation”. While thin oxides can be observed for SSRT crack tip, although the solution permeated into crack tip, the crack propagation was mainly controlled by mechanical effect. Consequently, due to the corrosion properties of welded joint with inhomogeneous microstructure and strength, it is supposed to distinguish between the corrosion cracking dominated by stress and strain. On the condition of stable work of the steam turbine with steady load, the corrosion cracking is dominated by stress and the most sensitive fracture region is in HAZ near the FL. During the start and stop stage of the steam turbine or on the condition of increasing abnormal load, the dynamic load will form, then the corrosion cracking is dominated by strain and WM becomes the most dangerous region.It is known that SSRT is the most important and efficient method to rank the sensitivity and CLT is auxiliary method for more detailed SCC mechanism for different material in specific environment. The mechanical analysis and SCC sensitivities for SSRT and CLT are usually complicated when the cracks initiate due to the rate-dependent inelastic behavior and lack of suitable failure criteria. For SSRT, the SCC sensitivity is the mechanical change in corrosion environment over those in air environment. However, it is difficult to assess SCC sensitivity because it is imposable to fracture in air environment for CLT. A quantitative indication of SCC susceptibility in Lee’s study According to above mentioned SCC mechanism in , the SCC processes under CLT and SSRT were illustrated in . The typical different features of two loading modes are highlighted in the figure. Three stages can be divided both for CLT and SSRT, they are SCC initiation, transition process and SCC propagation. However, the dominated effects in SCC initiation process are totally different which affects the following crack initiation and propagation position. For CLT method, the galvanic corrosion near the fusion line is significant for SCC initiation because the stress distribution in the welded joint is uniform before pit formation, the local corrosion will be accelerated by local plastic stress in the pit bottom once the pit formed Since the fracture location of the two loading modes are different, the obtained SCC sensitivity of SSRT is essentially for WM rather than the integrated welded joint, while the SCC sensitivity assessment of CLT is more suitable for the welded joint. Furthermore, the brittle corrosion cracking surface ratios are similar when the constant loading transforms from 760 MPa to 745 MPa and the strain rate from 1 × 10−7 s−1 to 1 × 10−8 s−1. This is because when the applied stress increased to 745 MPa, the stress corrosion cracking is stress dominated while the stress corrosion cracking is corrosion dominated when the strain rated decreased from 1 × 10−7 s−1 to 1 × 10−8 s−1. When the constant loadings are 730–745 MPa, the strain rate are 1 × 10−6 s−1 to 1 × 10−5 s−1, the brittle corrosion cracking surface ratios are similar but the exposure time are totally different. Because specimen applied with the constant strain rate is more sensitive to film rapture than that applied with constant stress and dominate mechanical parameters are different and the galvanic effect changes the film formation rate under constant loading. Therefore, SSRT method cannot be used to assess the SCC sensitivity of welded joint. Multiple SCC test methods should be adopted for the SCC sensitivity assessment for welded joint.CLT and SSRT of the welded joint of 30Cr2Ni4MoV were conducted with cylindrical tensile specimen in 3.5 wt% NaCl solution at 180 °C. The different SCC behaviors in welded joint dominated by stress and strain due to the different loading modes were discussed and the main conclusions are summarized as follows:The difference of corrosion cracking dominated by stress and strain results in different mechanisms of cracks initiation. Dominated by stress, sever corrosive environment and stress concentration within the pits prompt the cracks initiation from pits for the CLT. However, there is no pit for SSRT which is dominated by strain. When applied constant strain rate, the local strain disrupts the oxide films on the surface and then crevices form on the oxide film. The solution flow into the film through the crevices and then the base metal will be exposed to the environment. The local solution is trapped in the interface of the oxide film and the base metal then the micro-cracks initiate under the effect of strain.The differences of corrosion cracking dominated by stress and strain result in different fracture location in welded joint. As for the corrosion cracking dominated by stress, the fracture location is in the FQTZ near the FL with the highest strength and highest stress. When dominated by strain, the specimens were disrupted in the WM whose strength is the lowest but the plastic deformation is the most sever.The mismatch between galvanic corrosion and strength of each part of welded joint determined the fracture location and SCC sensitivity of the welded joint when the two different loading modes were applied. Simplex SSRT method is not suitable to assess the SCC sensitivity of welded joint. Multiple SCC test methods should be adopted for the SCC sensitivity assessment of welded joint.High performance fibre reinforced cementitious composites (HPFRCC)Dynamic tensile behaviour of high performance fibre reinforced cementitious composites after high temperature exposure► We performed static and dynamics tests on HPFRCC material. ► We studied the influence of strain rate and high temperature on the HPFRCC material. ► HPFRCC show a high value of DIF up to 400 °C for all the strain rates investigated. ► Dissipated energy in damaged HPFRCC remains almost constant for growing strain rate. ► HPFRCC exposed to 600 °C fails due to fibre rupture and changes in matrix structure.The uniaxial tension behaviour of high performance cementitious composites subjected to high strain rates after high temperature exposure has never been investigated. The material investigated was a steel fibre reinforced mortar. Straight low carbon steel micro-fibres were used. The fibre content was 1.25% by volume and the mix design guaranteed a self compacting mixture. The main purpose of the research was to highlight the role of thermal damage in uniaxial tension at low and high strain rate loadings. Looking in particular at peak strength and post-peak toughness the results show that, in low strain rate tests after high temperature exposure up to 600 °C, the thermal damage progressively reduces the toughness and weakly increases the strength; at high strain rate the peak strength significantly increases in comparison with low strain rate one for all the temperature investigated, while the toughness for growing temperature progressively decreases.High performance fibre reinforced cementitious composites (HPFRCC)The interest for the mechanical behaviour of normal and advanced fibre cementitious composites subjected to severe loading is growing, since the strength and durability of these materials make them promising for important and social sensitive structure, as primary and secondary containment shells, waste burning plants, coaling gasification reactors, but also tunnel linings, runway slabs, bridge and high-rise building, where exceptional scenario like fire and blast cannot be ignored. This experimental research was instrumental in the designing of new multi-layered tunnel segments improved for blast and fire mitigation. Special equipments as the Hopkinson bar for very high strain rates (as in explosions) have shown significant increases in peak strength, but these increases provide a partial information on the dynamic material behaviour. Fibre cementitious composites are often used to improve the impact resistance, preventing scabbing and fragmentation problems, due to their ability in energy absorption, but if the link between the dynamic energy and the static energy absorption is object of discussion, the influence of thermal damage on strain rate sensitivity is completely unknown. While the behaviour of ordinary and high performance concrete at high temperature is well known (), scanty informations are available in literature on fibre cementitious composites (To the best knowledge of the author, no studies have been reported on the effect of high temperature on the pull-out behaviour of single fibre, but the researchers have focused their attention on the behaviour at the composite level ( studied the mechanical and the thermal properties of a concrete reinforced by steel hooked fibres (30 mm long and with an aspect ratio lf/df equal to 45) at high temperatures. The results highlight a significant reduction in the peak tensile strength at 400 °C and an expected increase of the ductility for high temperature. In fact, pull-out residual strength is less affected by thermal damage with respect to matrix tensile strength, as confirmed by , who studied the thermal and mechanical properties of a fibre reinforced concrete in tension. It is worth noting that fibres used by the author were macro fibres and hooked, hence the dominant pull-out mechanism was mechanical (). Moreover, these tests do not give any information on the influence of actual temperature on the residual strength, because the tests were carried out at room temperature after cooling. This means that the mechanical characterisation is only significant if the damage introduced by high temperature exposition is related to the maximum temperature reached. An interesting aspect concerns possible differences from the material response at high temperature (hot condition) or after cooling down to room temperature (residual condition); some promising comparison are available in the literature. studied the high-temperature mechanical behaviour of three different materials subjected to direct tension in hot and residual conditions. The materials investigated were: high-strength concrete (HSC, fc |
= 92 MPa), a compact fibre-reinforced concrete (CRC, fc |
= 158 MPa, steel fibres lf/df |
= 12/0.4 = 40 with a content equal to 6% by volume) and a reactive-powder cementitious mortar (RPC, fc |
= 165 MPa, steel microfibres lf/df |
= 16/0.16 = 100 with a content equal to 2% by volume, polymeric fibres with a content equal to 2% by volume). The authors reported that, up to high temperature (T |
= 600 °C) and after cooling, the direct tensile strengths measured at hot and residual conditions were close, particularly for the HSC and PRC but less for CRC. Considering the fracture energy (which was measured only in the residual tests), CRC exhibits a strong increase up to 250–300 °C, followed by a steep decrease. In contrast, the lower fracture energy of RPC is hardly affected by the temperature and the extremely reduced fracture energy of HSC (one order of magnitude) is scantly affected by the temperature. These different fracture energy trends point out the role played by steel fibres and suggest a change in the mechanical properties of the fibres and/or the matrix surrounding them with temperature growth as observed by in their physical analysis performed by the use of Mercury Intrusion Porosimetry (MIP) and microscopy observation (SME). In particular, the steel microfibres became weak and brittle and specimens showed a response not influenced by fibres. No fibre pullout was detected in the specimens treated at highest temperature. They observed, by means of SEM and EDS analysis on single steel fibre, that when the maximum temperature reached was equal to 750 °C, a fibre partial melting occurred and the internal core of fibres was clearly different from the external portion in terms of both morphology and composition. The steel fibres partially melted tended to fill the cracks formed in the concrete. An exchange of material between the external portion of steel fibres and concrete paste took place, as confirmed by the presence of calcium and silica in the fibres.Focusing the attention to the mechanical behaviour of fibre-reinforced cementitious composites when subjected to impact or blast it is possible to highlight many aspects open to investigation (). The current understanding of the dynamic response and impact resistance of cementitious composites, and especially of high-strength concrete, is very limited. There are also contradictory results in the literature. For example, while reported a reducing sensitivity to strain-rate with the growth of concrete static strength, High performance fibre cementitious composites are characterised by high toughness and a hardening behaviour in bending. Fibres enhance the ductility of brittle materials like concrete, and this improvement is strictly related to the process by which load is transfered from the matrix to the fibres and the bridging effect of fibres across the cracks. Hence fibre pull-out is the principal mechanism contributing to the high toughness of the material and it is the preferable failure mode rather than fracture failure mechanism. Many researchers studied the pull-out sensitivity to loading rates for different types of fibre (polypropylene, hooked, twisted and smooth steel fibres) (). They concluded that polypropylene and “deformed” steel fibres were sensitive to the loading rate while smooth steel fibres were insensitive to it. Since of the behaviour of the fibre, the cement matrix and the bond between them (or the pull-out mechanism) are likely dependent on strain rate, it is expected that strain rate sensitivity is translated at the composite level; however, the investigation on rate dependency based only on the pull-out mechanism is not sufficient.) analysed strain rate effects on the tensile properties of strain-softening fibre reinforced concrete. They observed a significant increase in tensile strength, strain at peak stress and fracture energy due to high strain rates. Very few studies reported the effect of strain rate on tensile behaviour of strain-hardening high performance fibre reinforced cementitious composites ( investigated the tensile responce of HPFRCC reinforced with twisted and hooked steel fibres with reference to strain rates. They reported that, in general, the HPFRCC specimen with twisted fibres are generally sensitive to strain rate, whereas their counterparts with hooked fibres are generally not. While focused their attention to a range of strain rate proper of the seismic problems (ε˙=0.1/s and lower), studied the behaviour of two HPFRCC (reinforced with two different types of fibre: polyvinyl-alcohol and steel) at high strain rates (ε˙=50/s and higher) by means of a modified Hopkinson bar (MHB). They observed, after the dynamic failure, that steel fibres were pulled-out from the matrix, while the majority of polyvinyl-alcohol fibres were subjected to tensile failure, this could originate the difference in terms of fracture energy reported by the authors. On the other hand, the tensile strength of the steel fibre composite increases with the strain rate growth, while the tensile strength of PVA composites seems to be less sensitive to strain-rates even though it is remarkably increased with respect to the static values.A high performance cementitious composite optimised with steel fibres has been taken into account. Following a methodology for mix optimization proposed by the mix tailoring is done step by step starting from cement paste and moving towards high performance fibre reinforced cementitious composites by adding growing fibre contents. The mix design of the HPFRCC material is specified in . Steel fibres were high carbon straight fibres, 13 mm long with a 0.16 mm diameter (aspect ratio lf/df equal to 80); their content was equal to 100 kg/m3.The sand used in the material was sieved up to 2 mm and its petrography is listed in . The petrography analysis was conducted by means of an optical microscope for mineralogy and a stereoscopic microscope. Mineralogic composition and the material structure were analysed and evaluated starting from the constituent optical properties obtained by the optical microscope. The stereoscopic microscope was used to define morphological characteristics as sphericity, color or materials which could alterate the surface. The sand used can be defined as quartz sand mixed. The mix procedure was composed by more phases. First cement and slag were mixed in dry condition for two minutes, after water and super plasticizer were added and the cement paste was mixed for five minutes. Then, the sand was introduced in the cement paste and mixed for five minutes. In the end, fibres were added while the mortar material was mixing. Small beam specimens were cast in order to identify the material behaviour in bending at room condition and after thermal treatment. Specimens were all extracted from a slab 1.6 m × 0.60 m in plane, 30 mm thick. The slab was cast by applying a unidirectional flow as shown in . In order to guarantee a certain fibre orientation, the properties of the self compacting material were used taking advantage of the flow direction. Three prismatic beam samples, 40 mm wide and 600 mm long, were sawed from the slab and tested at room temperature to perform a proper mechanical characterization of the material according to Italian Guidelines (). The high fibre content and the favourable orientation imposed by the casting flow control allow us to guarantee a small dispersion of the response before and after single-crack localization and a hardening behaviour in uniaxial tension (). Nine beam specimens, with the same geometry, were used to investigate the thermal decay of multi-localization and single-localization cracking phases and the change of residual strengths in bending after exposure to high temperatures (). The thermal treatment of the samples was carried out in an electric furnace ((b)) by performing thermal cycles up to different maximum temperatures. Three maximum temperatures thresholds (200, 400 and 600 °C) were reached. A heating rate equal to 50 °C/h was imposed up to the maximum thresholds, and after, two hours of stabilization were imposed in order to assure a homogeneous temperature distribution within the sample volume. Afterwards the temperature was reduced with a rate of 25 °C/h down to 100 °C and then a cooling process at room temperature was carried out ((a)). From the bent specimens, several small cylinders 20 mm long, objects of the present work, were cored in the direction of tensile stresses in the stressed-undamaged external zone (). Their diameter was nominally equal to 20 mm (). Each cylinders extracted from each prismatic specimen was notched (U-form notch with a depth = 1.5 mm), to be tested in uniaxial tension at different loading rates. No macro-cracks can be distinguished on the samples extracted from thermally undamaged material and material exposed up to 600 °C as In order to identify the influence of high temperature on the mechanical properties of high performance steel fibre reinforced cementitious composites under static and dynamic conditions an experimental programme was carried out. Two different mechanical testing machines were used to investigate the dynamic field: a hydro-pneumatic machine (HPM) was employed to investigate the strain rate equal to 1 s−1 (), while to carry out high strain rate tests (150 and 300 s−1) a modified Hopkinson bar (MHB) (Uniaxial tensile tests on notched cylindrical specimens (S0 series) were performed with an electro-mechanical testing machine INSTRON 5867, in the laboratory of Politecnico di Milano – Polo Regionale di Lecco. The samples were glued to the machine platens by means of an epoxy resin. Two aluminum cylinders connected to the press by a knuckled joint ((a)) were used as press platens. In both cylinders, a 5 mm deep cylindrical cavity with a 22 mm diameter was made in order to increase the glued sample surface. Stroke was considered as feedback parameter during the tests. The displacement rate imposed during the tests was equal to 5 × 10−5 |
mm/s up to 1.5 mm and it was progressively increased up to 10−3 |
mm/s. The reported crack opening displacement are computed eliminating the deformations of the glue.The HPM functioning is widely described in , here only a brief description of the device is reported. The HPM is presented in ; first the samples were glued on cylindrical alluminium supports and in a second step the supports were been screwed to the bars of HPM machine. At the beginning of the test, a sealed piston divides the cylindrical tank into two chambers, one being filled with gas at high pressure (viz. 150 bars), and the other with water. An equal pressure is initially established in the water and gas chambers so that the forces acting on the two faces of the piston are in equilibrium. The test starts when the second chamber discharges the water through a calibrated orifice that is activated by a fast electro-valve. The piston starts then to move, expelling the water. The specimen (S2 series) is connected on one side to the piston shaft and, on the other side, to the end of an elastic bar which is rigidly fixed to a supporting structure. When the piston shaft moves, the specimen is pulled at a fixed strain rate that depends on the velocity of expulsion of the gas from the chamber.Finally, the load P resisted by the specimen is measured by the dynamometric elastic bar, whereas specimen elongation ΔL is measured by the displacement transducers, sensing the displacement of the plate target fixed to both specimen ends.The Hopkinson pressure bar (HPB) is an experimental device widely used for intermediate and high strain rate testing (101÷104s-1). Several versions of this equipment were developed to derive the dynamic properties of a material under different stress conditions (tensile, compression, flexural, etc.) (In the present research program, to determine the mechanical properties of HPFRCC under high loading rates, a dynamic test campaign was conducted at the DynaMat Laboratory of the University of Applied Sciences of Southern Switzerland (SUPSI) of Lugano. A modified Hopkinson bar (MHB) was exploited. The MHB consists of two circular aluminium bars, called input and output bars (with a diameter of 20 mm and having length of 3 and 6 m, respectively) between which the HPFRCC specimen (S3 and S4 series) is glued using a bi-component epoxy resin. The input bar is connected to a high strength steel pretension bar (having 6 m length and 12 mm diameter), used as pulse generator. A test with the MHB is performed as follows:(a) first, a hydraulic actuator (of maximum loading capacity of 600 kN) pulls the high strength steel bar; the pretension stored in this bar is assured by the blocking device;(b) the second operation is the rupture of the fragile bolt in the blocking device, which gives rise to a tensile mechanical pulse of duration 2.4 ms and with a linear loading rate during the rise time. The pulse then propagates along the input and output bars, leading the specimen to failure.As for the classical Hopkinson bar apparatus the pulse propagates along the input bar characterized by a sound wave speed C0 equal to 5065 m/s, and constant shape. When the incident pulse (εI) reaches the HPFRCC sample, it is partly reflected by it (εR). The portion of pulse that is not reflected, passes through the specimen (εT) and propagates into the output bar, as shown in . The relative amplitudes of the incident, reflected and transmitted pulses, depend on the mechanical properties of the specimen. Strain-gauges glued on the input and output bars (800 mm from the specimen) are exploited to measure the elastic deformation over time generated by the incident/reflected and transmitted pulses. the raw signals measured on the input and output bars are shown. The clean resolution of the incident, reflected and transmitted pulses, the sharp rise time of the incident pulse (of the order of 30 |
μs), as the almost constant amplitude of the incident pulse can be observed. Since the signals (εI+εR) and εT are equal, the specimen is in equilibrium throughout the fracture process. Thereafter, the stress and strain in the sample can be derived by Eqs. , where L is the specimen length (20 mm).On the other hand, the history of the crack opening displacement (COD) can be calculated as:In the first phase of the tests at high strain rates, when the mechanical wave reaches the samples the equation εI+εR=εT is not valid. The duration of this phase depends on the wave velocity of the material and on the length of the sample: the shorter is the specimen, the lower time needed to reach the equilibrium is. In the tests reported a formal check of the equilibrium has been performed, samples length was equal to 20 mm this means that the unbalanced phase was limited to 100 |
μs or less. The stress in Eq. is computed with reference to the net cross section area. While strain and the strain rate are computed considering the total specimen length L because in the hardening branch the multi-localization takes place despite the notch due to the very high bond between fibres and matrix. In this situation the displacement field can be assumed continuous due to the reduced discontinuity shown in the closed micro-cracks which are smeared along the whole specimen. After the peak a macro-localization takes place therefore the length of the whole sample becomes a rough approximation of the material characteristic length and is used in favor of safety. The COD is computed as the relative displacement between the two sides of sample, hence the sample elastic elongation is included. As considered for the static test the contribution of the very thin glue layers placed between sample sides and aluminium bars was considered and subtracted from the global response in the dynamic test.(a) and (b) in terms of nominal stress (σN) versus crack opening displacement (COD) for the specimens exposed up to 20, 200, 400 and 600 °C respectively. Moreover, in (a) a detail of the peak zones are plotted to highlight the first linear elastic and the post peak behaviour, close to the peak. In this case the nominal stress is defined as follows:where P is the applied load while A is the area of the net cross section. Peak strengths and the corresponding crack opening displacements are listed in ; the values of peak strains could be calculated as follows:where L∗ is the clear span equal to 10 mm ((b)), and representing the equivalent specimen length, while wpeak is the crack opening displacement corresponding to the peak strength. According to this assumption, the cavity depth of the platens (5 mm for each side, where samples are glued, (b)) are approximately considered as a rigid zone. It is interesting to observe that steel fibres are able to favour stable propagation at room temperature up to a strain of about 2%, computed according to Eq. after this a slightly softening up to 4% takes place. The pre-peak behaviour is well described by a parabola rectangular model, where the plateau is very close to a value of 2% (). It is worth noting that, by increasing the temperature, the peak strength does not significantly change up to a maximum temperature of 400 °C. The slight slope of the softening at 200 °C increases; even though up to 400 °C the peak strength remains very close to 1%. At 600 °C the behaviour is significantly changed by a peak strength reduction of about 40% and a significant elastic modulus decrease, even though the material exhibits a stress plateau up to about 1.5% of strain. This means that, even if a notch depth ratio equal to 0.15 was used, the material can distribute over the whole length the cracking process. Of course, the geometrical defect introduced by the notch prevents a correct evaluation of the effective ductility measured in terms of strain of the peak plateau. New tests without any notch are in progress.The low values of the elastic stiffness obtained in these tests could be caused by the visco-elastic behaviour of the glue. In order to account for the contribution of the visco-elastic behaviour of the glue, results were compared with some preliminary tests aimed at evaluating the elastic modulus of the material. These tests showed an upper limit for the elastic modulus equal to 40 GPa. The elastic deformation for a stress level equal to the peak strength computed with an elastic modulus of 40 GPa was compared to that computed with the elastic modulus obtained in the tensile tests. It was then possible to estimate the maximum value of the error affecting the strain measures. The difference between the two strain values discussed above (Δεpeak) is equal to about 1%. The peak strains, for the undamaged material, could be thereafter overestimated as maximum of a 1%.According to the Italian guidelines, the material can be defined as a hardening material. The first cracking strength is close to 3 MPa, while the peak strength is about 10 MPa. This means that, even if a notch depth ratio equal to 0.15 is used, the cracking process is distributed over the entire length. Again the geometrical defect introduced by the notch and the gluing procedure prevent a correct evaluation of the actual ductility measured in terms of strain of the peak plateau.On the basis of the presented results, the energy absorbed up to a crack opening displacement equal to 5 mm was computed: if the residual stress was not nihil, a vertical cut-off was applied (Gf; ). Gf represents the energy involved in the fracture processes and it is computed as the area subtended by the stress-COD curve (see Eq. The energy Gf, computed according to Eq. , takes into account three different contributions: the energy required to create a new fracture surface in the matrix, the energy involved in a pull-out process and the energy required to fail steel fibres. These contributions could have different COD activation thresholds and different relative importance. The evolution of the fracture energy with respect to the crack opening displacement (COD) is shown in (a) and (b) for the specimens exposed up to 20, 200, 400 and 600 °C respectively. During tensile tests on undamaged specimens (at 20 °C), the generation of a new fracture surface in the matrix and the fibre pull-out are the main mechanisms involved, while the fracture energy associated to fibres failure is negligible. By increasing the maximum temperature exposure, pull-out energy decreases while the energy associated to the failure of fibres increases, this being justified by the change in the ratio between the number of fibres pulled-out and the fibres failed. In fact, the specimens exposed up to 600 °C have a brittle behaviour associated with fibre failure. Thermal treatment up to 600 °C seriously reduces the mechanical properties of steel fibres, as shown in (a) and (b), where fracture surfaces of bent specimen are presented. Some preliminary tensile tests conducted on wires used to produce fibre have highlighted a decay of about 75% of the tensile strength (passing from 3180 MPa to 500 MPa) when the samples are heated up to 600 °C. In order to enlighten the change in the wire microstructure, a microscope analysis was carried out. Transversal cross sections was investigated before and after the thermal treatment exploiting an optical microscope. (a) and (b) show an oxide film 20 |
μm thick, covering the external wire surface. The measure of the wire diameter, before and after the thermal treatment, detected an increase of about 0.02 mm, this being partly due to the developed oxide film. This increase in the sectional area, coupled with the decay in the tensile strength, compromises the effectiveness of the pull-out mechanism and explains the material embrittlement when exposed to high temperatures. The results of static fracture energy versus temperature are shown in (b), where a linear decay trend can be observed. Furthermore, in (b) from the average curves the fracture energies computed up to 0.1, 0.4, 1.0 mm and the peak strength are plotted; as (b) shows, these four energy values are less affected by the thermal damage than the total one. show clearly that a single macro crack was triggered in the notched section of samples tested.For a better understanding of the dynamic behaviour of the material, a series of tests at strain rate equal to 1 s−1 (specimens named T20/U-20-S2) were carried out exploiting the Hydro-pneumatic device. For each temperature (room condition, 200, 400, and 600 °C), at least three samples were tested. The results of tensile tests in terms of nominal stress (σN) versus crack opening displacement (COD) are shown in (a), (b) for maximum temperature equal to 20, 200, 400, and 600 °C, respectively. Also in this case, details of the peak zones are presented in (a) and (b). Peak strengths and corresponding crack opening displacements are listed in . It can be observed that steel fibres favour a stable propagation at room temperature up to a strain larger than 2.5% (computed according to Eq. where L is the specimen length (=20 mm), and wpeak is the crack opening displacement corresponding to the peak strength.The pre-peak behaviour is well described by a parabola rectangular model, where the plateau is activated at a value of 2% as observed in the static tests. The plastic plateau reaches a stress level equal to 15 MPa, being twice the value obtained in the static tests. The constant stress plateau becomes weakly softening at 200 °C, even though up to 400 °C the strain corresponding to the peak strength remains very close to 1%. It is worth noting that, by increasing the temperature, the peak strength does not significantly change up to a maximum temperature of 600 °C the energy dissipated up to a crack opening threshold of 5 mm is highlighted in (a), it is possible to observe that the dynamic peak strength is always greater than the static one. At 400 °C the post-peak behaviour significantly changes and an abrupt decay of the residual strength is shown. It is also worth analyzing how the energy involved in the fracture processes changes in the dynamic range with the increasing temperature. Gf represents the energy involved in the fracture processes computed as the subtended area in a stress – COD curve (Eq. ) following the criteria introduced in Section (b) shows not only the total energy involved in the fracture processes, but also the trend of the energy Gf computed up to different thresholds (0.1, 0.4, 1 mm and at the peak strength). The total energy Gf shows a significant decay starting from 200 °C as exhibited in (b). However, the energies computed from the average curves up to 0.1 mm and the peak strength are less sensitive to the temperature.The strain rates reached in the tests here reported were equal to 150 s−1 (specimens series T20/U-20-S3). The high strain rate results obtained on HPFRCC exposed to 20, 200, 400 and 600 °C are reported in in terms of peak strength, crack opening displacement at the peak and dissipated energy. In , the stress versus COD curves of the HPFRCC specimens tested with the same high strain rate are shown. A detail of the peak zones are plotted in (a) in order to highlight the first linear elastic branch and the post peak behaviour close to the peak. It can be observed that the behaviour changes as a function of the exposition to high temperature. After a remarkable peak strength, which is higher than the peak observed in static conditions and for a strain rate equal to 1 s−1, specimens cured at room condition show a small drop down to a post-peak stress plateau up to a COD of 0.4 mm, as highlighted in the static tests. The stress plateau reached a stress level equal to 15 MPa, as observed in the dynamic tests performed at ε˙=1s-1. The constant stress plateau decreases with temperature growth. At 600 °C, the behaviour is significantly changed, becoming softening in the post-peak region. By analysing the data listed in (a) where the average curves are plotted, two experimental evidence can be highlighted: at this velocity, the peak increases with the exposition to high temperature as well as the post-peak strength decreases till to disappear for higher temperatures. By observing the fracture surface of the specimen, it is evident as the failure type was changed ((a), the observable hole in the specimen demonstrates the fibre pullout process occurrence while in (b), all the fibres are broken; this means that, during the high temperature exposure, fibres became more brittle due to thermal damage as highlighted in the static test results presented above. In the evolution of fracture energy with respect to the crack opening displacement (COD) for each temperature is shown. As in static tests, fracture energy is computed by using Eq. . The same criteria mentioned in Section were followed: when the test curves were stopped due to the sudden drop induced by fibre failure, a vertical jump assumption was used and the energy absorbed was always computed up to a crack opening displacement equal to 5 mm, by applying a vertical cut-off. The total dissipated energy computed for the undamaged material shows a comparable value with respect to the tests carried out at lower strain rates and a significant decay starting from 200 °C, following a trend similar to what observed for specimen tested at medium strain rate ((b) shown. Moreover, it can be observed that the fracture energies computed from the average curves up to 0.1 mm and at the peak strength are less affected by the thermal damage with respect to the total one as reported for the tests at medium strain rate.In this section, the results from the tests carried out by means of MHB were reported. The strain rate imposed during the tests was equal to 300 s−1. (a), (b) show the results for specimens undamaged and exposed up to 200, 400, and 600 °C respectively. The results in terms of peak strength and crack opening displacement are reported in . Test results from the undamaged material showed a peak strength close to that observed at strain rate of 150 s−1. The post-peak behaviour is characterised by a stress plateau up to a crack opening displacement of 0.4 mm which represents a strain, computed according to Eq. , equal to 2%. As already observed in the dynamic material behaviour at 150 s−1 the stress plateau reached the stress value of 15 MPa after a small drop down from the peak. This quite constant stress plateau seems to be a dynamic material property linked to the debonding phase and partially to the first stage of pull-out mechanism. High strain rates mainly affect peak strength rather than fibre pullout strength. The peak strength in static condition and for medium strain rate is highly influenced by fibres which contribute to develop a multiple cracks. The stress plateau vanishes completely in the dynamic response of specimen treated up to 200 °C ((b)); this behaviour is different from what observed in the tests performed at 150 s−1, where a small plateau up to a COD of 0.15 mm was found (see (b)). At 400 °C, the behaviour highly changes, by becoming strongly softening in the post-peak region, as can be highlighted in (a) where the average curves and a detail of the peak zone are plotted for all the temperatures investigated. The peak strengths listed in do not change significantly with respect to results at 150 s−1 for the undamaged specimens and the specimens exposed up to 200 and 400 °C. On the other hand, at 600 °C a remarkable peak strength reduction can be observed with respect to the test at 150 s−1. (a), (b) show the fracture energy evolution with respect to crack opening displacement for specimens exposed up to 20, 200, 400 and 600 °C, respectively. The results are summarised in in terms of total fracture energy. The energy dissipated was computed according to Eq. , following the same criteria explained in Sections . As observed in the previous section, the thermal treatment up to 600°C seriously damages fibres inducing a reduction in the cross section and in the strength because of a change in the material micro structure. This fibre damage, coupled with the matrix damage, causes a change in the material behaviour in the static range undergo ductile to brittle and this trend is sharper in dynamic as can be pointed out analysing the dissipated energy involved in the fracture process (In order to have an overview of the global material behaviour, the average of the stress versus crack opening displacement curves are plotted. (a), (b) summarise the experimental results in terms of average curves for the material previously exposed up to 20, 200, 400 and 600 °C respectively. Each curve represents the material response for a different strain rate. Besides in (a) a detail of the peak zone is plotted in order to highlight the first elastic branch and the region close to the peak. It is worth observing the initial stiffness growth with the strain rate increase for all the temperatures investigated. This increase is much more evident when the strain rates are equal to 150 or 300 s−1.For a strain rate equal to 1 s−1, only the material exposed to 200 °C showed a remarkable increase of initial stiffness. A small increment was also expected for the undamaged material tested at 1 s−1. On the contrary, the material not exposed to high temperature showed in the pre-peak region a behaviour well described by a parabola-rectangular model with a initial stiffness close to the static one (see (a)). The behaviour described above could be attributed to a pre-cracking problem; nevertheless this explanation seems unlikely because all four samples tested at 1 s−1 showed a similar pre-peak behaviour. Moreover, it is important to highlight that the three test set-up used have small differences in the boundary conditions. Quasi-static tests were exploited with a rotating platens system, while the MHB is characterised by boundary conditions similar to a fixed end test. The boundary conditions of HPM can be considered in between the rotating and the fixed end set-up. These differences could slightly influence the tests results ((b) the DIF versus temperature for different strain rates are plotted. For a fixed strain rate a remarkable variation of DIF cannot be highlighted up to 400 °C. DIF was equal to about 1.75 for strain rate equal to 1 s−1 while a DIF equal to about 2.5 was observed for high strain rates. At 600 °C the DIF shows a marked increment much more pronounced for strain rate equal to 150 s−1 respect to 300 and 1 s−1. This increment could be associated to a change at the micro-structural level of the material. This micro-structural modification was caused by the thermal treatment as highlighted in the porosimetry tests (). Porosimetry tests pointed out an increase of the pore size for material exposed up to 600 °C even if the total amount of mercury volume intruded did not show a significant change. The increasing micro-defects induced by the thermal treatment affect significantly the material behaviour in the static regime, where a decreasing in the peak strength can be observed: crack propagation can follow the path with the lowest energy release. On the contrary, when the material exposed to high temperature is subjected to high strain/stress rates the path associated to the minimum energy release could not be followed, this leads to a higher dynamic increase factor (DIF) with respect to the one observed for the undamaged material. (a) shows the dynamic increase factor versus strain rate for each temperature investigated. DIF increases till strain rate equal to 150 s−1 for each temperature, but while the DIF for the undamaged material increased at 300 s−1 the material exposed at high temperature showed a decrease in the DIF. The decrement increases with the maximum temperature reached in the heat treatment. Obviously, both the micro-structural changes of the matrix and the changes of steel fibre properties influence the behaviour after the exposure at 600 °C. In particular, focusing the attention to the peak strength the micro-structural changes affect much more the peak response in the dynamic behaviour with respect the static one. In the static field the decreasing of peak strength can be associated prevalent to the decay of the steel fibre properties which cannot favor the stable crack propagation, hence the high peak strength reached by the thermal undamaged materials. If the fracture energy is considered, both the phenomena play a significant role in the behaviour of the material treated up to 600 °C in static as well as in dynamic conditions. (a) shows the average energy Gf5.0 computed in the previous chapter with respect to the temperature. The energy Gf5.0 decreased with the increase of temperature for each temperature investigated in the research. Gf energy decrease linearly for the static tests while it decreases exponentially for higher strain rates. The ratio between the dynamic fracture energy and the static one versus temperature is plotted in for each strain rate imposed. The undamaged material showed a ratio higher than 1 for each strain rate; the ratio first increases up to 1 s−1 and then decreases. For material, first heated, the trend could be affected by a certain scatter, but a clear trend highlights that at 600 °C matrix damage and steel fibre damage play a significant role, thus increasing both the stability of the cracking process (DIF) and the ratio (Gf,d/Gf,s) dynamic and static fracture energy. Finally, show clearly that a single macro crack was triggered in the notched section of samples tested at high strain rates, no other fracture plane can be detected. Some external micro- and nano-fracture planes could be present but their contribution to the total energy is negligible if it is compared to the energy involved in the pull out process which is several orders of magnitude higher even if they could play a key role in the pre-peak behavior.The behaviour of an advanced high performance fibre reinforced cementitious composite when subjected to different strain rates was investigated. An extensive experimental investigation was carried out by means of uniaxial tension tests. The quasi-static characterization (ε˙ |
= 10−6 |
s−1; δ˙ |
= 10−6 |
mm/s) was carried out by means of an electromechanical press while for the dynamic characterisation a Hydropneumatic machine and a modified Hopkinson bar were used.From the experimental results presented in this research work some important conclusions can be drawn:thanks to the material self compacting properties, a good fibre alignment was obtained by imposing a unidirectional casting flow. This result is confirmed by the low scatter observed in the material response. A quite low scatter was observed in the overall test series carried out, and at all the strain rates investigated. These considerations were supported by who showed that samples obtained with different casting procedure and characterized by a diameter of 20 mm and 60 mm cannot be considered as representative due to the random fibre distribution, this means that the results reported are strictly related to the good fibre orientation highlighted in the samples. The material cast by imposing a flow direction, and thus characterised by a good fibre alignment, showed a very high performance compared with other cementitious composites at comparable costs.The good fibre orientation, the relative high number of fibre expected and measured, the limited maximum aggregate size used, as well as the acceptable scattering in the tests allowed us to look at sample 20 mm high, with a diameter equal to 20 mm, as a representative volume for this material. stress plateau shown in the static tests carried out on the undamaged material, was obtained also at different strain rates. Increasing the strain rate from 10−6 to 1 s−1 the stress plateau grows from 8.5 to 15 MPa. For higher strain rates (from ε˙ |
= 150 s−1 to ε˙ |
= 300 s−1) the peak in strength considerably increases. However, in the post peak region, after a drop, the stresses reach the stress plateau at 15 MPa up to a crack opening displacement of 0.8 mm. This value of stress plateau (15 MPa) appears to be a upper bound limit and a dynamic property for the investigated material.The material exposed to 600 °C fails due to steel fibre rupture, this behaviour being prevailingly due to the damage caused to the fibres by the high temperature leading to an abrupt decay of the fracture energy involved in the failure process.For the material exposed to high temperatures the DIF increases with the increasing strain rate at least up to a value close to 150 s−1. In particular, the material treated up to 600 °C showed a DIF equal to 5.5 when it was tested at 150 s−1. At a strain rate equal to 300 s−1 the DIF does not grow, on the contrary, it decreases. The higher the maximum temperature reached in the thermal cycles, the more evident is the decrease in the DIF.High performance fibre reinforced cementitious composites show a high value of DIF up to 400 °C for all the displacement rates investigated (ranging from 1.5 to 2.5 passing from 0.02 to 3–6 m/s), and even higher for higher temperatures;The dissipated energy up to a large crack opening (5 mm) in the material exposed to high temperatures remains almost constant for growing strain rates up to a value of 150 s−1 and scantly decreases at 300 s−1. Moreover, the dissipated energy at increasing exposure temperature shows a remarkable decrease at all the strain rates investigated, this trend being emphasised at high strain rates.The dissipated energies computed up to 0.1 mm and at the peak strength are less affected by the thermal damage with respect to the total one.The DIF and the ratio between high strain rate and quasi-static fracture energies grow for exposure to 600 °C. The reason is related to the damage of matrix exhibited by the specimens.Static behaviour of a full-scale steel–concrete beam with epoxy-bonding connectionBonding connection in steel–concrete composite beams is investigated in the case of static loading and high-strength concrete. The 3-point bending test performed on a large beam confirms that bonding is very efficient: the elastic domain is followed by a non-linear behaviour with noticeable ductility. The measurements are generally close to the numerical results provided by beam models or the FE model. The composite beam model which does not take into account slip and shear deflection could be used for engineering design purposes. However all the studied beam models do not allow a very accurate prediction of the behaviour close to the interface and the behaviour at failure in the case of shear failure. Non-linear FE approach may be more suitable but requires realistic failure criterion for all the materials.Steel–concrete composite structures combine the high strength of steel with the stiffness and the compressive strength of concrete to form a very economical system. The use of steel–concrete solution may even increase more in the future if it is possible to improve the control of the cracking of a concrete slab, especially at an early age.Composite action between a slab and a girder is generally achieved by means of mechanical connectors such as headed studs. Initially placed in fresh concrete, they act as vertical or horizontal stops as concrete hardens. Two main weaknesses of such a connection may be pointed out: on the one hand, the behaviour under cycling loading of the welding between the connectors and the girder; on the other hand, connectors induce cracking in concrete because of concentrated stresses and restrained shrinkage, especially at an early age The first attempts to bond concrete slab to steel girder took place in the sixties using ordinary concrete (fc=30–40MPa) and epoxy adhesive. The slab was concreted either on fresh resin Thanks to the development of materials, high-strength material was selected in recent studies as bonding connection requires a sufficient tensile/shear strength High-strength concrete was recently used in epoxy-bonding composite beam tested in bending in the case of small span elements (about 3 m.): either for steel–concrete composite beams The present paper investigates the connection by bonding in steel–concrete flexural members and focuses on static and instantaneous behaviour. The high-strength concrete slab is precast as this process allows limiting the risk of cracking and may thus increase the durability. Construction costs could also be reduced. The behaviour of a full-scale beam is examined. In the first part of this paper, an experimental study is presented. Material properties are given and the experimental set-up is described. Experimental results obtained on an 8.50 m-span beam are finally analysed. This steel–concrete composite beam is then modelled in the second part of this paper by means of a refined composite beam theory and finite elements method. Numerical results are discussed and compared with experimental results through deflection, slip, strain and stress.All high performance concrete specimens were cast at the same time and stored in the same ambient conditions. The mechanical characteristics were determined by means of standard tests 28 days and 125 days after concreting which corresponds in the latter case to the day of the bending test. Compressive properties and tensile strength were measured on Φ 16 × 32 cm cylindrical and on 7×7×28 cm samples respectively, they are presented in The passive reinforcements of the concrete slab are ribbed bars with a guaranteed yield strength of 500 MPa.The resin used is epoxy mixed with silica sand as it suits the conditions relative to bridges. The properties of the resin were determined by Si-Larbi et al. The tested beam was designed in order to account for local technical requirements such as maximum weight or maximum capacity of the loading system and to reach an average shear stress in the bonding joint about 3 MPa within the elastic domain. This latter limit value is recommended by resin manufacturer to meet satisfactorily the working conditions of bridges such as outside atmosphere, lifespan of more than 50 years and creep under sustained dead loads.It may be noticed that the concrete slab was precast in five identical pieces 1800 mm in length (). Each piece was bonded separately using a steel frame specially designed for this purpose as illustrated in . This tool allows spreading easily the resin on the concrete surface and turning securely the slab upside down in final position ready for bonding. The vertical interface between two pieces of slab was also bonded.The beam was subjected to a 3-point bending test and was simply supported on rollers. During the test, the vertical displacement of the jack was servo-controlled with a speed of 62.5 μm/s. The load was thus slowly applied and increased up to failure after some unloading–reloading cycles at the beginning of the test (within the elastic domain of the beam) as shown in The measurements carried out during the test were the following: applied load, vertical displacement, longitudinal strain in the concrete slab and in the steel profile, slip and uplift at the steel–concrete interface. Load cell, gauges and LVDT sensors were used with numerical recording. Locations of the whole measurements are detailed in The test was performed up to failure since the concrete was 125 days old. It may be noticed that in order to check the experimental device, the beam was loaded twice up 100 kN before the final loading up to failure.It may be first noticed that the behaviour and the measurements obtained during both preliminary loadings are close to those of the final loading up to failure. In addition, symmetrical measurements carried out are also very similar. This may point out the repetition and thus the reliability of the whole experimental set-up and the results presented below.) shows a linear elastic domain followed by a non-linear behaviour. The failure occurred for 401 kN after noticeable ductility but was very sudden: it corresponds to a failure of the adhesive joint which induced a division of concrete slab into four pieces and very large slipping as illustrated in . The strain in the top concrete fiber is about 0.9‰ (see ), no crushing was observed. The strain in the bottom steel fiber is greater than 1.4‰ but may not be known precisely in that section as the strain gauge stops before beam failure. Yet, yielding may occur in bottom fiber of steel girder in the central zone of the beam.The limit between elastic domain and non-linear domain may correspond to a load of about 150 kN/200 kN. At this stage of loading, the strain in the central zone of the beam (see ) is about 0.35‰ and 0.9‰ in the upper concrete fiber and lower steel fiber respectively. As these strains are lower than linear elastic strains of materials (1.6‰ measured in the case of steel girder and 0.5‰ estimated for concrete), this confirms that the beginning of the non-linear domain of the beam is not due to yielding of girder or slab but may originate from the behaviour of adhesive joint. The evolution of slip close to the central zone () show that the failure in adhesive joint might begin in the mid-span of the beam.Moreover, the vertical distribution of strain in S2N, S2S, S3N and S3S for different stages of loading is shown in . Navier’s assumption is therefore checked within the linear domain of the beam and becomes more and more inaccurate up to failure.The tested beam presented above is analysed using two different approaches: beam modelling and finite elements method. Both are briefly described hereafter.Many models suitable for steel–concrete composite beams have been proposed since the 50s. They account for both materials with their actual position through the composite section. The slip occurring at the steel–concrete interface and resulting from the flexibility of the connection device is either neglected (perfect bond) Within the elastic domain, steel and concrete constitutive laws are assumed to be linearly elastic for tension and compression stresses, the tension stress in concrete is therefore assumed to be lower than the tension strength.A linear distribution of longitudinal strain is assumed throughout the whole composite cross-section. The response of the composite beam is then governed by the following equations: where M is the bending moment, Hm=EcΩc+EsΩs, Hmf=dEcΩc, Hf=EcIc+EsIs, the subscript refers either to the steel girder (s) or to the concrete slab (c), Ω denotes the area of each part, d is the distance between the reference axis (which generally corresponds to the centroid of the steel section) and the centroid of the slab, I denotes the moment of inertia with respect to the reference axis, e is the strain at the reference axis and χ denotes the beam curvature (). Longitudinal passive reinforcements, commonly neglected, may be accounted for by completing the terms Hm, Hmf and Hf as follows: where subscript p refers to each bar or to each layer of bars and dpk denotes the distance between the layer k and Gs.The slip at the steel–concrete interface due to shear strain of the glue joint is accounted for. A linear distribution of longitudinal strain is then assumed throughout each homogeneous part with a discontinuity at the steel–concrete interface (). The governing equations are detailed in − in the steel girder: ε(x,z)=e(x)+zχ(x)− in the concrete slab: ε(x,z)=e(x)+zχ(x)+s′(x). Thus generalised stresses may be expressed as follows: Npk=−EpkΩpk(e+s′)−EpkSpkχ=−EpkΩpk(e+s′+dpkχ)=−EpkΩpkεpk−χ=M+Ns(d−1EsΩs∑kEpkΩpk(dpk−d))+s′∑kEpkΩpk(dpk−d)EcIGc+EsIs+∑kEpkΩpkdpk(dpk−d).Furthermore, the local equilibrium conditions of a small segment of the composite beam requires: where v denotes the horizontal shear stress per unit length and is related to s as follows: The term k (N/m2) is the stiffness of the lap joint determined from the push-out tests. Eq. α2=kEsΩs+EcΩc+∑kEpkΩpkEcΩcEsΩs+[d+∑kEpkSpkEcΩc][d−∑k(dpk−d)EpkΩpkEsAs]EsIs+EcIGc+∑k(dpk−d)EpkSpk1−[d+∑kEpkSpkEcΩc][∑k(dpk−d)EpkΩpk]EsIs+EcIGc+∑k(dpk−d)EpkSpk+∑kEpkSpkEcΩcβ=[d+∑kEpkSpkEcΩc]EsIs+EcIGc+∑k(dpk−d)EpkSpk1−[d+∑kEpkSpkEcΩc][∑k(dpk−d)EpkΩpk]EsIs+EcIGc+∑k(dpk−d)EpkSpk+∑kEpkSpkEcΩc is the characteristic differential equation of the continuously connected steel–concrete composite beam accounting for passive reinforcements. This equation is similar to that of a beam without passive reinforcements and may be solved in a similar manner: Ch and sh denote the hyperbolic cosine and the hyperbolic sine respectively, bM is constant depending on the load applied. The integration constants (AN, BN) and (As, Bs) are determined by assuming that the axial stress is zero at any point of the cross-sections located at the ends of beam.According to the perfect bond model and the slipping model, longitudinal strain and stress are calculated from the strain diagram in each part of the beam. Furthermore, deflection is generally determined neglecting the shear effect either by integrating the curvature twice and accounting for boundary conditions at supports or by means of the virtual work principle. The part of deflection due to shear may be determined also using the virtual work concept and assuming that the shear strain is only located in the web of the steel girder. As a consequence, the mid-span deflection vT due to shear of a beam subjected to a 3-point bending is given by vT=FL4GAw where Aw is the web area of the steel beam and G=E2(1+ν) with ν the Poisson’s ratio assumed to be 0.3 in the case of steel.Geometrical characteristics are determined from neglecting welding. Elastic moduli of steel profile and concrete were measured (see Section ): Ec=36600 MPa and Es=205000 MPa. Epk are assumed to be 200 000 MPa. The stiffness k is determined from push-out test results The ultimate behaviour of the beam is approached with a plastic model suggested in Eurocodes provisions ) and the ultimate material characteristics (see Section Analyses were carried out using the finite element system ANSYS. The mesh was determined from the geometry of the beam specimen () but passive reinforcements were not taken into account. A 3D FE model was used with 10 node tetrahedral structural solid elements (named solid 92) for each part of the structure. The materials are assumed to be elastic, isotropic and linear. The elastic constants E and ν of the materials are presented in and were those determined by means of tests (see Section ) or selected from realistic values. Perfect connection is assumed between the different parts of the beam. The boundary conditions were chosen in accordance with experimental conditions.The size element was chosen regarding the geometry of the cross-section and then accounting for the possible high variation of stress. The size of FE was small close to the bonding zone and increased in the slab and in the steel girder. In order to ensure accuracy and convergence, the final mesh was obtained from an optimization procedure as follows: the size of elements was progressively reduced until the mid-span deflection and the longitudinal strain in upper and lower fibers did not vary anymore. Finally, the thickness of elements was about 2 mm close to bonding joint and increased up to about 70 mm at the top surface of concrete slab. The total number of FE was about 60 000.Numerical simulations have been carried out in order to appreciate the accuracy of the different models within the elastic domain and to attempt to understand and to localize the failure.Measurements and numerical results are presented in for a load of 150 kN. It may firstly be noticed that the three studied models provide very similar results. The largest discrepancy is observed at the steel–concrete interface in the central zone of the beam between beam model results and FEM results. That may be explained as follows: beam models do not allow predicting accurately behaviour close to the loading area. Furthermore, models satisfactorily predict the real behaviour of the beam as small discrepancies may generally be observed. A large difference may be noticed in the steel beam bottom fiber of the S3N section. The strains measured close to the interface are also slightly different from simulations.The theoretical ultimate load is determined, according to Eurocodes provisions, from the plastic analysis of the central cross-section driven without any passive reinforcement and accounting for geometrical and mechanical characteristics (see Sections ). The plastic neutral axis is thus located in the concrete slab 7 cm from the upper surface of the beam. The plastic moment capacity is then Mpl, Rd = 1324 m kN and the predicted ultimate load is about 623 kN. This value is logically higher than the experimental ultimate load (401 kN) as failure did not correspond to a plastic hinge but to a brittle shear failure at the steel–concrete interface.In order to localize the beginning of this shear failure, FE simulations have been carried out for the experimental failure load (401 kN) assuming that materials remain elastic. show respectively shear stress and perpendicular normal stress–namely peeling stress–close to the interface along the beam and at different locations. It may be noticed that the shear stress is almost constant along the whole half beam (except close to extremity and loading area) and reaches about 4–5 MPa and 3–4 MPa in the bonding joint and in the first ten millimeters of the concrete slab respectively. The variation of shear stress close to steel corresponds to small numerical instabilities due to the high difference between steel elastic modulus (210 000 MPa) and that of epoxy (12 600 MPa). The peeling stress is very low (lower than 1 MPa) except close to extremity and loading area and does not exhibit significant variation with respect to the vertical position (close to interface).The failure along the interface has to be studied taking into account the shear stress and also the peeling stress. In order to illustrate this approach, the case of a failure in the concrete layer is presented. shows the theoretical shear limit stress τxz,u determined in the concrete slab from the 2D-Chalos–Beteille failure Criterion 10 mm far from the bonding joint: τxz,u(x)=σt,u(1−σzz(x)σc,u)(1+σzz(x)σt,u). In this equation, σc,u is the concrete compressive strength (σc,u=67 MPa), σt,u is the concrete tensile strength estimated by means of 0.6+0.06σc,u and σzz is the perpendicular stress negative in the case of tension. The shear stress τxz,u is compared to the numerical value τxz for the failure load. This graph shows that τxz,u is slightly greater than τxz except at extremity and close to loading area: in these zones, a risk of failure could be noticed as brittle shear behaviour of epoxy and concrete do not allow high redistribution along the bonding joint. However, these results do not allow one to permanently conclude about the localization of failure: the difference between τxz,u and τxz is not large enough regarding the natural variability of concrete behaviour and τxz should be determined accounting for the possibility of non-linear behaviour of materials at failure.This paper investigates the connection by bonding in steel–concrete composite beams and focuses on static and instantaneous behaviour. High-strength concrete was used in order to improve the mechanical characteristics of such a connection process previously studied with ordinary concrete.Results obtained from an 8.5 m-span beam show that the behaviour of such a beam is similar to that of a composite beam connected by studs: it exhibits a linear domain followed by a non-linear domain with a noticeable ductility. In this test, the shear failure at steel–concrete interface occurred before the central plastic hinge was complete. Measurements also show that the connection could be considered to be perfect as the slip remains very low during the test (except at failure). Navier’s assumption is also verified on the whole elastic domain and also at the beginning of the plastic domain. Therefore, the test performed on a full-scale composite beam confirms that bonding could efficiently replace ordinary connectors.The measurements are generally close to the numerical results provided by beam models or the FE model. The composite beam model which does not take into account slip and shear deflection could be used for engineering design purposes. However beam models presented above do not allow very accurate prediction of the behaviour close to the interface and the behaviour at failure in the case of shear failure. Non-linear FE approach may be more suitable but requires realistic failure criterion for all the materials and particularly for glue.Discrete element modelling of top soil burial using a full scale mouldboard plough under field conditionsIn order to improve the grain crop yield of non-wetting sandy soils, mouldboard ploughs are again being used in Australia. To improve the effectiveness of top soil burial from ploughing the most suitable operating parameters need to be determined. The discrete element method (DEM) has the potential to model soil–mouldboard plough interactions relating to both soil movement and tillage forces. A full scale mouldboard plough was tested in the field and then simulated using DEM. The draught forces predicted by DEM were of similar magnitude to those calculated using ASABE's Agricultural Machinery Management Data (D497.7 R2015). The DEM model predicted top soil burial to a similar depth in the soil profile as was measured in the field. However, DEM predictions of lateral and forward soil movements of the buried top soil were greater than that measured in the field. The DEM predictions showed that increasing speed from 5 to 15 km h−1 gave a 40% increase in draught and a significant reduction in the depth of top soil burial. Increasing the tillage depth from 200 to 350 mm gave a 270% increase in draught but very little change in depth of burial of the top soil. The use of a skimmer was predicted to increase the draught by 4% and increase the amount of top soil buried below 100 mm depth.Dimensionless soil texture adjustment parameterStiffness for unloading/reloading, (N m−1)Perpendicular distance of contact point from the centre of mass, (m)Normal component of the relative displacement, (m)Tangential component of the relative displacement, (m)Normal component of the relative velocity, (m s−1)Tangential component of the relative velocity, (m s−1)The mouldboard plough is a primary tillage tool and is often used to: 1) provide soil inversion that helps to bury trash, weeds and crop residue; 2) create the basis for a seedbed; and 3) loosen and aerate the soil. In Australia there is renewed interest in mouldboard ploughing to improve the potential yield of non-wetting sandy soils by burying the top layer of non-wetting soil and bringing to the surface soil that is more suitable for plant growth (). In order to improve the effectiveness of soil burial through ploughing, understanding the soil movement process is essential.Investigations of mouldboard ploughs, in terms of soil movement, have generally relied on empirical and semi-empirical methods (e.g. ). Although the effect of different operating conditions, mouldboard geometries and configurations (mouldboard plough + components such as a skimmer) on soil movement can accurately be investigated using experimental studies, only a small number of mouldboard geometries can be tested due to this resource intensive and costly procedure. If, however, the interaction between soil and mouldboard plough could be modelled using computational techniques, it would allow for optimisation of different mouldboard shapes and configurations without limiting the amount of geometric features and soil conditions that could be investigated.Modelling of the soil–tool interaction is a highly complex process due to the variability of the soil structure and its non-linear behaviour. In order to simulate the soil–mouldboard plough interaction, the discrete element method (DEM), which is a dis-continuum numerical method can be used. In DEM, the bulk system is assumed to consist of distinct particles with interactions between particles applied by using contact models that are governed by physical laws. Granular soil, which is ideal for planting, comprises of distinct particles which interact only at contact points and displace independently. Hence, DEM can be used to give both force and soil movement predictions. In order to achieve realistic simulations accurate determination of pertinent DEM parameters is essential. Although there is an emerging body of knowledge in the literature regarding to the DEM modelling of soil–tool interactions (e.g. ) nothing yet examines full-size soil–mouldboard plough interactions. In their research, used DEM to validate tillage forces and top soil burial for a one third scale mouldboard plough under controlled indoor laboratory conditions using a small soil bin (900 long × 500 wide × 170 mm deep).This paper now extends the applicability of DEM to a full size mouldboard plough operating under field conditions. A field test was undertaken to measure top soil burial by a full size mouldboard plough and was then replicated using DEM. The DEM model was also used to predict top soil burial and tillage forces with respect to the effects of depth, speed, and with/without skimmer. To validate the force prediction of the DEM simulation, the ASABE's Agricultural Machinery Management Data Standard (D497.7 R2015) was used to estimate the draught requirements of a mouldboard plough for a range of operating parameters.An experiment was undertaken at Nairne (35.0296° S, 138.9079° E), South Australia in September 2015 to measure top soil burial created by a mouldboard plough. The soil was a sandy loam (59% sand, 26% silt, 15% clay) with a bulk density of 1305 kg m−3 and 9.3% moisture content (dry basis). The field had been used for growing Brussel sprouts for the last 3 years. A location with minimal surface residue and roots in the soil was selected for the field tests.The field tests were conducted using a three furrow commercial plough (Kverneland™ ED85) fitted with standard manure skimmers, that were pulled by a 70.8 kW tractor. The experiment was performed at 300 mm tillage depth and 5 km h−1 ploughing speed. The skimmer was set to 250 mm above the tillage depth giving it a 50 mm depth of operation.The burial of the top 40 mm of soil by ploughing was measured by tracking the soil translocation before and after ploughing. To achieve this, a 3000 mm wide × 200 mm long × 40 mm deep trench was dug across the path of the plough using a hand shovel. Subsequently, this empty trench was filled with blue coloured sand (). After ploughing, nine cross sectional profiles, across the direction of travel, were excavated at 250 mm increments, in the direction of travel, starting 250 mm after the blue sand trench. Excavations were made manually using a shovel (a). After excavation of each vertical soil face a digital photo of the slice was taken (as per ). A metal frame was used to ensure the camera was always the same distance from the slice when taking the photos to assist in the accuracy of the image processing (b). The images were digitally analysed using MATLAB™ 2015a (MathWorks, Natick, MA, USA). An HSV (hue, saturation and value) algorithm was developed to locate the pixel locations of the blue coloured sand particles. Hue indicates true colour perceived by a human. Saturation describes how pure the colour is and describes the amount by which colour has been diluted with white. Value represents the degree of brightness. The images taken during the experiment were firstly cropped to remove undesired features such as excessive background and shadows. The HSV model with hue value limits between 0.3 and 0.5 highlighted the location of the blue coloured sand and was used to produce a binary plot of the blue pixels. The pixel coordinates were transferred into Microsoft Excel for analysis.The DEM simulations were carried out using EDEM™ 2.7 software operating on a DELL Precision T7910 Dual Xeon E5-2680 v3 @ 2.5 GHz and 128 GB RAM computer. Simulations took between about 9 h (for 15 km h−1) to 44 h (for 5 km h−1) to run. The simulations were run using a linear cohesion model integrated into a hysteretic spring contact model, as suggested by . Compressible materials such as soil can be modelled by using hysteretic spring contact model. The model allowed the particles to behave in a linear elastic manner up to a predefined stress and when the total stress on the contact area exceeds the predefined stress (which is the yield strength) in the model, the particles behave as though undergoing plastic deformation. The cohesion between the particles was defined by directly adding a cohesion force to the normal contact forces.In the hysteretic spring contact model the total normal (Fn) and tangential (Ft) forces were calculated as;where Fns, Fnd, Fts and Ftd are the normal contact force, normal damping force, tangential contact force and tangential damping force, respectively. Normal contact force was calculated as per Fns={K1UabnloadingK2(Uabn−U0)unloading/loading0unloadingwhere Uabn is the normal component of the relative displacement, Uo is the residual overlap. K1 and K2 are the loading and the unloading stiffnesses, respectively. As per where Y is the yield strength and req is the equivalent radius and defined as where r is the radius for the individual particles a and b. Following where e is the coefficient of restitution. The residual overlap was updated in each time step as;U0={Uabn(1−(K1/K2))loadingU0unloading/loadingUabnunloadingThe tangential contact force was calculated as per where Uabt is the tangential component of the relative displacement. nk is the stiffness factor which was defined as the ratio of tangential stiffness to normal loading stiffness. The normal and the tangential damping forces were calculated using;where Ůabn and Ůabt are the normal and tangential components of the relative velocity, respectively. nc is the damping factor which controls the amount of velocity dependent damping. meq is the equivalent mass and defined in where m is the mass for the individual particles a and b. The total tangential force was limited to the lessor of either the calculated tangential force or the sliding friction force;The magnitude of the moments caused by total tangential force (M) and the rolling resistance (Mr) were calculated following where rcon is the perpendicular distance of the contact point from the centre of mass, μr is the coefficient of rolling friction and λθ, is the unit vector of angular velocity at the contact point. After interacting with other particles, the new position of a particle was calculated by integrating Eqs To model soil cohesion, a cohesive force was added to the total normal forces. The inter-particle friction was assumed to restrict the tangential element motion in the governing equations, thus the cohesion force was not added in the tangential direction. The magnitude of the cohesion force was calculated as (where ξ is the cohesion energy density which is defined as the energy needed to remove a particle from its nearest neighbours divided by the total volume of the removed particle and Ac is the contact area. After adding the cohesion force, Eq. Randomly generated 10 mm nominal radii spherical particles (within the range of 0.95–1.05 times the nominal size) were used in the simulations. The DEM parameters were obtained from a combination of measurements and available data from literature, as shown in . The coefficient of rolling friction and cohesive energy density between soil particles were calibrated by means of an angle of repose test. This calibration process was based on matching simulation results to measured results using a soil sample taken from the field and held at its 9.3% moisture content. The blue sand used for experimental comparison had similar simulation characteristics as the soil and was at a similar moisture content. Using the known parameters () and varying coefficient of rolling friction of soil–soil and cohesive energy density, an angle of repose of 28.5° was achieved in the simulation () using a trial and error process (with an error margin of ±0.5°) for values of 0.225 and 30,000 J m−3, respectively. Due to field observations that no soil adhered to the mouldboard's surface during the experiment, the cohesive energy density between soil and steel was taken as zero.To simulate the field experiment a virtual soil bin whose dimensions were 20,000 mm long × 3000 mm wide × 600 mm deep was used. The DEM soil bulk density was set to match the value of 1305 kg m−3 of the field test. In order to provide an accurate model of the plough's working components (a) the surface of the mouldboard and skimmer were digitised using a (FaroArm™ (Faro Technologies, Lake Mary, Florida, USA)) portable coordinate measuring device. After taking the dimensions, a 3D digital surface model of the mouldboard, skimmer and the plough assembly was created (b). Under field ploughing conditions the first furrow moves soil into an empty furrow that was created by the previous plough pass. To represent this in the virtual soil bin a single furrow mouldboard was run through the soil (at 300 mm depth) to create a pre-furrow. It was found that due to the limited width of the virtual soil bin some of the particles thrown by this first pass hit the side of the soil bin and rolled back into the furrow. Therefore, in order to study top soil burial using a 3 furrow plough in the field, a four furrow plough was modelled and run in the simulation after the initial pre-furrow pass. Only the 3rd, 4th and 5th furrows were used for DEM top soil burial comparisons with the field test.The DEM simulations were run for the conditions matching the field test of 5 km h−1, 300 mm operating depth, and skimmer set 250 mm above the plough depth.A 20,000 mm long soil bin was chosen so it would provide stable forces () and soil flows at speeds up to 15 km h−1. A width of 3000 mm was chosen so that the virtual soil bin would contain the soil throw. A typical force graph from the DEM for 15 km h−1 is shown in In order to compare the predicted top soil burial with the field experiment, the colour of the DEM particles in a 3000 mm wide × 200 mm long × 40 mm deep trench were changed from brown to blue (a). After the mouldboard plough simulation was complete, the brown coloured particles were removed from the simulation space and the coordinates of each of the blue coloured particles were exported to Microsoft Excel (As tillage force measurements were not taken during the field test, the ASABE's Agricultural Machinery Management Data Standard document (D497.7 R2015) was used to provide an estimation of typical draught requirements of a mouldboard plough. Its draught estimation equation is shown as Eq. . It is quoted as having an error margin of ±40%, (In the equation, dimensionless machine specific parameters of A, B and C were taken as being 652, 0 and 5.1, respectively as given in . The dimensionless soil texture adjustment parameter of Fi was taken as 0.45 as the field soil was a course textured soil. Modelled speed (S) and depth (T) were used for the calculations. The cutting width of one mouldboard plough was measured as 405 mm. Hence, to calculate the draught of the four furrow plough (as used in the DEM simulation) the cutting width (W) for the implement was taken as 4 × 405 mm = 1620 mm.In addition to the field plough settings, the same virtual soil bin was used to run further simulations to investigate effects on top soil burial and tillage forces using different plough speeds, different operating depths and ploughing with/without the skimmer.In order to measure the top soil burial for the field tests, nine excavations were made at 250 mm intervals starting from the trench of blue coloured sand. The 9th excavation did not show any blue coloured sand thus indicating the limit to forward top soil movement. Hence, the top soil burial analysis was undertaken only for the first eight excavations. shows the steps undertaken in the analysis of the eight excavations where blue sand was observed. The aggregated cross sectional locations of the buried blue sand observed in the excavated field profiles (sum of 8 images) are shown in . These field results showed clear cross sectional groupings of the buried top soil created by each plough body. also includes an overlay of the positions of all of the buried blue sand particles from the DEM simulation along with the DEM's profile of the soil after ploughing. As with field observations, the DEM also showed each plough body gave a distinct cross sectional grouping of buried top soil. On the right of the image in the DEM simulation shows a slumping of the un-tilled particles as they rolled down into the open furrow and no longer stayed at the original soil height. This shows a limitation of the chosen soil model that used larger than actual spherical particles. shows that the top soil burial at below 150 mm depth was quite similar in cross sectional locations for the DEM and field results. However, at the upper levels the DEM moved the soil with greater lateral throw (further to the left of the image).To quantify the proportion of particles buried at different depths, the tillage depth was divided into three horizontal layers (100 mm each) and the percentage of particles (DEM) and pixels (field test) in each layer were calculated for the DEM and field test, respectively. A comparison of proportions, shown in , shows that the percentage of the top soil buried in the various tillage depth layers predicted by DEM was similar to that measured in the field. Both the field results and the DEM simulations showed the mouldboard plough to be effective at burying the top 40 mm of soil at depths between 100 and 300 mm.), when using a 1/3 scale model plough operating in an indoor laboratory soil bin, there was a good match between measured top soil burial depths and DEM predictions. Whilst burial percentages differed between plough bodies, comparative experimental results and DEM simulations in showed good validation of the methods used.The main factors that explained the difference in soil burial included: experimental error due to excavating the vertical faces to capture digital images; along with errors in the image capture, post processing and digital image analysis. Additionally, 10 mm radii spherical particles were used in the DEM simulations instead of small (<2 mm) irregular shaped soil grains used in the field experiment. As a result some of the DEM particles were pushed below the tillage depth.A quantitative comparison of forward soil movement was also carried out by comparing particle densities in the direction of travel. The field experiment () had the blue coloured sand in the profiles excavated at 250–2000 mm from the end of the trench. shows the DEM simulated resultant top soil particles ending up at 500–4200 mm from the trench. As shown in , the majority of top soil particles in the DEM simulations were carried further forward than what was measured in the field, but in both cases most particles moved forward less than 2000 mm. The greater forward movement for the DEM simulations can be explained by the DEM using larger rather than realistically sized spherical particles to represent the soil and errors in estimating the values for the coefficient of rolling friction and coefficient of restitution. With likely improvements in computational power occurring in the future, the use of smaller particles and more accurate parameters could give better predictions.Following the validation that the DEM simulations can provide a good representation of top soil burial (with 5 km h−1 tool speed), the DEM procedure was then used to predict the effect of increasing speed on top soil burial and tillage forces. To do so, the same simulation that matched the field test at 300 mm operation and 50 mm skimmer depths was repeated using 7.5, 10 and 15 km h−1 speeds. The top soil burial results for the increase in speed on top soil burial, lateral movement and forward movement are shown in DEM predictions showed that as speed increased the depth of top soil burial reduced, as shown by the 43% difference in the 0–100 layer. Hence, to improve top soil burial a slow speed must be used. As speed increased, the soil was pushed further away from the plough (). The force prediction results for the four furrow plough are shown in . Both the ASABE draught estimations and the DEM predictions showed draught to increase with speed with the DEM results being within the ASABE's ±40% range. The DEM predictions showed that speed had no significant effect on the downward vertical force of the plough.Although at lower speeds there would be better top soil burial plus lower draught force, and hence lower fuel consumption, the time required to complete the ploughing operation would proportionally increases. Hence, choosing the best operating speed is a compromise between cost and performance which can only be answered by site and machine specific optimisation studies.In order to investigate the effect of operation depth on top soil burial and tillage forces, simulations were conducted using 200, 250 and 350 mm depths (with a fixed 50 mm skimmer depth) at a speed of 7.5 km h−1. Top soil burial results are shown in show that ploughing at a depth of 200 mm does not bury the top soil as well as when ploughing at depths in the range 250–350 mm. shows that as the depth increases the top soil is moved further away from the plough and further along from the trench (). The DEM predictions showed that draught force quadratically increased with increasing depth with a 270% increase in draught from 200 to 350 mm depth (). The DEM draught predictions were all within the draught estimations. With regards to vertical force, the DEM simulation showed no real effect of depth on downward vertical force. The results indicate that if it would be acceptable for 32.5% of the top soil to remain in the top 100 mm of the soil profile then a shallow 200 mm plough depth would be best as it uses least draught. However, if the top soil needs to be buried deeper, a deeper depth of operation is required at the expense of greater draught. However, it must also be noted that mouldboards are designed for different working conditions so findings related to using different operating depths would be a function of the mouldboard design and would change for differently shaped mouldboards.To investigate the effect of the skimmer (which is known to assist trash burial), the simulations were run again without skimmers at 7.5 km h−1 plough speed and 300 mm working depth. DEM predictions for with and without a skimmer are shown in , the skimmer helped move the top soil particles from the top 100 mm of the soil profile and place them into the 100–200 mm depth layer. The use of the skimmer did not help bury any more of the top soil in the 200–300 mm depth. As shown in , for the tillage forces, adding the skimmer required a small 4% increase in overall draught force. Adding the skimmer caused a decrease in the downward vertical force which suggests upward soil forces acting on the skimmer. The use of a skimmer was therefore shown to be a worthwhile addition to aid top soil burial with it only adding a small increase to the draught force.A field experiment was conducted to measure the depth of burial of the top 40 mm of soil after a pass of a mouldboard plough. The field test measured the movement of blue coloured sand placed in the top 40 mm of the soil and showed that when ploughing to a depth of 300 mm that only 4% of the top soil remained in the top 100 mm and 53% of the top soil was buried at a depth of 200–300 mm. Thus, the mouldboard plough was shown to be a very effective tool for top soil burial.DEM simulations were undertaken to replicate the field test using 10 mm radius particles. Such large particles were required to keep the computational times required manageable. Analysis of the depth of top soil burial predicted by the DEM was very comparable to the field measurements. However, the DEM simulations did show that the soil buried at a shallower depth was thrown further sideways than that measured in the field test. With regards to forward soil movement both the field and DEM simulations showed most of the forward soil movement to be less than 2000 mm but the intensity of forward soil movement (more particles moved further forward) was greater for the DEM results. This greater lateral and forward soil movement is likely to have been a result of (1) using larger than actual particles that have to move around the plough and (2) errors in determining the dynamic interaction properties (such as coefficient of rolling friction, coefficient of restitution).The good correlation of soil burial for a full-sized plough in the field with DEM simulations supports the use of the method, confirms the previous results of the authors and extends the knowledge of how top soil burial as well as lateral and along the furrow soil movement changes with mouldboard plough settings and operating parameters.The DEM predicted that slower speeds will give better soil burial and lower draught force but there is a compromise with work rate. The DEM simulations predicted that if 32.5% top soil remaining in the top 100 mm depth is satisfactory, then a 200 mm ploughing depth is suitable but if more top soil burial is required then a ploughing depth of 250 mm or greater is needed. Ploughing deeper than 250 mm did not give any more burial at depths below 200 mm but it did increase the draught force. DEM also showed that the use of the manufacturer's standard manure skimmer at 50 mm depth improved the burial of the top soil by 8.2% with only a small (4%) increase in draught.Whilst draught force was not measured during the field test, the DEM simulations predicted draught forces in the range of draught estimates from the widely accepted ASABE Agricultural Machinery Management Data (D497.7 R2015) for a range of operating speeds and depths. Thus, giving confidence that the DEM draught force predictions are of the right order of magnitude.In order to improve future results more work is being carried out on the procedures for image capture, post processing and image analysis as used in the field experiment. As computing capabilities improve, smaller size and irregular shape particles should be able to be used in the DEM simulations to obtain more precise results. In addition, further investigation are being undertaken to calibrate the dynamic interaction properties more accurately. It is intended that the modelling approach proposed here will be extended to compare the performance of other styles of machines (e.g. spaders and disc ploughs) for energy efficient and effective burial of non-wetting top soils.Sulfonated polyimides bearing benzimidazole groups for direct methanol fuel cell applicationsSulfonated polyimides (SPIs) bearing benzimidazole groups in the main chains were synthesized from 1,4,5,8-naphthalenetetracarboxiylic dianhydride, 4,4′-bis(4-aminophenoxy)biphenyl-3,3′-disulfonic acid and 2-(p- or m-aminophenyl)-5-aminobenzimidazole in m-cresol. The resulting polymer solutions were not precipitated to gain the solid polymers but directly cast into films because the precipitated SPIs became insoluble in common organic solvents. The strong interaction between sulfonic acid and benzimidazole groups reduced the water uptake and methanol uptake. The SPI membranes with ion exchange capacities (IECs) of 1.9–2.0 mequiv./g displayed reasonably high mechanical strength, thermal stability, water stability and proton conductivity. They showed anisotropic membrane swelling in water with 2.8 times larger swelling in thickness direction than in plane one and anisotropic proton conductivity with 25% smaller conductivity in thickness direction than in plane one. They suppressed methanol crossover in direct methanol fuel cell (DMFC) operation and displayed fairly high DMFC performances even at high methanol concentrations. The Faraday's efficiency and overall DMFC efficiency at 60 °C and 200 mA/cm2 for SPI membrane with IEC of 1.9 mequiv./g were 75 and 23%, respectively, at 5 wt% methanol feed concentration and 39 and 10.2%, respectively, at 20 wt%. The SPI membranes have high potential for DMFC applications at mediate temperatures (40–80 °C).Direct methanol fuel cells (DMFCs) have been attracting great attention as energy conversion devices for portable and transportation applications, because of their potential advantages of high energy density, simple structural design and ease in handling of liquid methanol Several methods have been reported to reduce the methanol crossover of membranes. The typical examples of thus-obtained PEMs are composite (hybrid) membranes with inorganic ionomers Acid–base polymer blend membranes were prepared by blending a polymer bearing sulfonic acid groups with a polymer bearing N-base groups In this paper, SPIs are synthesized from NTDA, BAPBDS and diamines bearing benzimidazole groups, and their physical properties and DMFC performances are investigated in comparison with the SPIs from a common non-base diamine.2-(p- and m-Aminophenyl)-5-aminobenzimidazole (p- and m-DABI, respectively) were prepared according to literatures SPIs, of which the chemical structures are shown in , were synthesized from NTDA, BAPBDS and p-DABI or m-DABI. As an example, the synthetic procedure of NTDA–BAPBDS/p-DABI(2/1) is described below, where the data in the parenthesis refer to the molar ratio of BAPBDS to p-DABI.1H NMR spectra were recorded on a JEOL EX270 (270 MHz) instrument with DMSO-d6. FTIR spectra were recorded on a Horiba FT-200 Spectrometer as polymer membranes. Thermogravimetric analysis (TGA) was performed on Rigaku TG-8120 in helium (flow rate: 100 cm3/min) at a heating rate of 10 °C/min. Mechanical tensile tests were performed on a universal testing machine (Orientic, TENSILON TRC-1150A) at 25 °C and about 60% RH at a crosshead speed of 5 mm/min.Water vapor sorption isotherms were measured at 60 °C and water vapor activities aw less than 0.93 using a sorption apparatus (BEL-18SP) by means of a volumetric method. The weight of membrane sample used was 80–100 mg. Water uptake (WU) or methanol uptake (MU) was measured by immersing a SPI membrane sample into water or methanol at 30 °C for 24 h, respectively. Then the membrane was taken out, wiped with tissue paper very quickly, and weighed on a microbalance. Water uptake or methanol uptake was calculated from Eq. where Wd and Ws are the weights of dry and corresponding water- or methanol-swollen membranes, respectively.Dimensional change in membrane thickness (Δtc) and length (Δlc) were measured by immersing more than two samples in water at 30 °C for 10 h. The changes of thickness and length and anisotropic dimensional change ratio (Δt/l) were calculated from:where td and ld are the thickness and length of the dry membrane, respectively; t and l refer to those of the membrane swollen in water.Ion exchange capacity (IEC) of membrane was determined by a titration method. A sample membrane in proton form was soaked in a 15 wt% NaCl solution at 40 °C for 72 h to exchange the H+ ion with Na+ ion. The solution, with keeping the sample membrane In-plane and through-plane proton conductivity (σ|| and σ⊥, respectively) of membrane were determined using an electrochemical impedance spectroscopy technique over the frequency from 100 Hz to 100 kHz (Hioki 3532-80). For σ||, a single cell with two platinum plate electrodes was mounted on a Teflon plate at 0.5 cm distance. The cell was placed under either in a thermo-controlled humidic chamber or in liquid water. For σ⊥, a membrane sample was set between two platinum plate electrodes of 1 cm2 area, and mounted on two Teflon blocks. The cell was placed in liquid water. Proton conductivity (σ|| and σ⊥) and anisotropic proton conductivity ratio (σ⊥/||) were calculated from Eq. where d is the distance between the two electrodes, ts and ws are the thickness and width of the membrane at a standard condition of 70% RH, respectively, A is the electrode area, R is the resistance value measured. For the measurements in liquid water, the swollen membrane thickness was used in the calculation of σ.Water stability tests were carried out by immersing SPI membrane sheets (150–200 mg of dry weight, in proton form) into ultra-pure water (90 ml) at 130 °C in an autoclave, which was set in the thermo-controlled oven for a given time (192 h).Pt/Ru (30%)/C (54%, TEC61E54, Tanaka Kikinzoku Gr.) and Pt/C (45.5%, TEC10E50E, Tanaka Kikinzoku Gr.) were used as anode and cathode catalysts, respectively. The catalyst was dispersed uniformly into the mixture of appropriate amount of water, 1-propanol, 2-propanol, and Nafion® dispersion solution (21 wt%, Aldrich) through ball-milling and degassing. The catalyst ink prepared thus was coated onto a carbon paper (Toray Indus. Inc., TGP-H-090, 0.28 mm) using a bar-coater, and dried to obtain a catalyst-coated electrode. The catalyst loadings for the anode and cathode were 2.2 mg Pt/Ru/cm2 and 1.67 mg Pt/cm2, respectively. Both sides of the PEM surface were impregnated uniformly with 1.0 mg/cm2 of Nafion by applying 0.02 ml/cm2 of 5 wt% Nafion solution as a binder. A PEM was sandwiched between two catalyst electrodes and hot-pressed at 150 °C at 30 kg/cm2 for 3 min. The effective electrode area was 5 cm2. The prepared MEA was positioned into a single cell test fixture (JARI).DMFC measurements were carried out in a DMFC test station (KIKUSUI KFM2030, EIWA) at 40–80 °C. An aqueous methanol solution (5–50 wt%) was supplied into the anode at a flow rate of 1.0 ml/min, air or oxygen was supplied into the cathode at 150–750 or 150 N cm3/min, respectively, under air atmosphere. The cathode gas was passed through a humidifier at 25 °C.The AC impedance analysis was performed under steady-state conditions. The frequency was from 0.1 Hz to 10 kHz and the load current was set at 0.25, 0.5, 1.0 and 1.5 A. The cell resistance (Rc) and electrode reaction resistance (Rel) were determined by the AC impedance cole–cole plots. The through-plane proton conductivity in DMFC operation (σ⊥FC) was evaluated by assuming that the membrane resistance is approximately equal to the cell resistance.Most of the methanol permeated through a membrane was oxidized into CO2 and water at the cathode. A small part of the methanol was not oxidized and flowed into the cathode outlet stream. The cathode effluent was conducted to a cold trap (<−60 °C) to condense the water and methanol vapor and then the dried gas was conducted to a gas sampler for the gas chromatography to measure the CO2 content. The condensed liquid was weighed and the subjected to the gas chromatography to determine the methanol content. The methanol permeation flux (qM) was calculated from Eq. where MCO2 (mol) and MMeOH (mol) are the CO2 amount and the methanol amount, respectively, flowed into the cathode outlet stream for the measurement time, tmea, and A is the effective area of MEA. The methanol permeation coefficient (pM) was evaluated from Eq. , assuming that the membrane was in contact with the feed methanol solution and feed gas:where CM is a methanol concentration in feed and t50% RH is the thickness of membrane under 50% RH.Preparation of NTDA–BAPBDS/DABI SPIs was carried out through the one-pot high temperature polymerization method in m-cresol in the presence of TEA, benzoic acid, and isoquinoline. The addition of isoquinoline was reported to have positive effects on the imidization and molecular weight The physical properties of NTDA–BAPBDS/DABI membranes (Code No. M1–M4) are listed in . For comparison, the data for NTDA–BAPBDS/BAPB ones (R1 and R2) and Nafion 112 are also listed in this table. The IEC was measured by the titration method. The titration was carried out for the solutions containing the sample membranes to complete the ion exchange shows the IR spectra of the SPI membranes in proton form. The spectra displayed the absorption bands of naphthalene imide rings at 1712 (CO asymmetric) and 1347 cm−1 (C–N asymmetric). The stretch vibration (OO) of sulfonic acid group was detected at 1200, 1090 and 1017 cm−1. The characteristic peak of polyamic acid at 1780 cm−1 was not detected, indicating the complete imidization. The characteristic vibration bands of benzimidazole groups of 1630, 1586 and 1286 cm−1The thermal stability of SPIs in proton form was investigated by TGA. Above 150 °C, the two-step degradation profile was observed for all of the SPIs. The weight loss below 400 °C was attributed to the cleavage of sulfonic acid group, whereas the weight loss above 500 °C was attributed to the decomposition of polymer backbone. The first decomposition (desulfonation) temperature (Td1) was 315 °C for M1 and M3, which was similar to that (309 °C) for R1 and R2. shows the tensile strain–stress curves of SPI membranes. The mechanical property was characterized by Young's modulus (M), maximum stress (S) and elongation at break (E). The data are listed in . All the SPI membranes had much higher Young's modulus, yield point and maximum stress than Nafion 112, and reasonably large elongation at break point, indicating their excellent mechanical properties. Compared to the BAPB-based SPI (R1), the DABI-based SPIs (M1–M4) showed the higher Young's modulus and yield point, but the smaller elongation after the yield point to the break point, and as a result the maximum stress was slightly smaller. This indicates that the DABI-based SPI membranes were slightly stiffer than the BAPB-based ones, because of the rigid structure of benzimidazole moiety in main chain and the ionic interaction between sulfonic acid groups and benzimidazole groups.Water vapor sorption and water uptake mainly depend on IEC of membrane, and number of sorbed water molecules per sulfonic acid group (λ) is usually used for comparison between membranes with different IECs. In this study, the λ values were calculated using the calculated IEC values. shows the water vapor sorption isotherms of SPI membranes at 60 °C in a form of λ versus water vapor activity, aw. The water vapor sorption increased sigmoidally with an increase in aw. At the low activities below 0.5, the λ values of M1 were comparable to those of R1 and Nafion 112, whereas at the high activities above 0.6, the λ values were smaller for M1 than for R1 and Nafion 112., the λ values in water at 30 °C of M1–M4 were 12–14, which were smaller than that (17) of R1 and R2. When compared to R1, M1 and M4 showed the smaller values of WU, MU and size change in water, in spite of the larger IEC value. Compared to R2, M2 showed the similar values of WU, MU and size change, in spite of the much larger IEC value. On the other hand, M3 showed much lower water uptake and membrane swelling than R2. These results were attributed to the effect of ionic cross-linking for M1–M4. All the SPIs showed anisotropic membrane swelling with 2.7–3.0 times larger swelling in thickness direction than in plane one, whereas Nafion 112 showed the isotropic membrane swelling.For all the SPI membranes, the MU was smaller than the WU, whereas, for Nafion 112, the MU was two times larger than the WU. shows the relative humidity dependence of in-plane proton conductivity (σ||) at 60 °C. also lists the σ|| values at 50% RH, 70% RH and in water at 60 °C. The SPI membranes displayed larger relative humidity dependence of in-plane conductivity than Nafion 112. For example, compared to Nafion 112, M1 and M4 showed 27% smaller σ|| values in water but 85% smaller σ|| values at 50% RH. M1 and M4 showed the smaller σ|| values than R1 in spite of the larger calculated IEC value and the similar measured one. M2 showed the slightly smaller σ|| values than R2, in spite of the much larger calculated IEC value. M3 showed the much smaller σ|| values than the other membranes because of the extremely low measured IEC value and low water uptake. This smaller proton conductivity for the DABI-based SPIs was attributed to the effect of ionic cross-linking as in the case of the smaller water uptake. The similar behavior has been reported for the sulfonated PEMs containing N-base groups The through-plane proton conductivity (σ⊥) and the anisotropic proton conductivity ratio (σ⊥/||) in water at 60 °C are summarized in . All the SPI membranes showed the anisotropic proton conductivity with larger σ|| than σ⊥. The σ⊥/|| values were in the range of 0.73–0.77, independent of the nonsulfonated diamine moieties, as in the anisotropy of membrane swelling. shows the temperature dependence of σ⊥ and σ|| in water for SPI membranes. The activation energies of σ⊥ and σ|| for M1, M2 and R1 were in range of 11–13 kJ/mol.The water stability of SPI membranes was evaluated by immersing the membranes in water at 130 °C for 192 h followed by investigation of weight loss, changes in proton conductivity and mechanical properties. M1 showed a weight loss of 6%, no appreciable decrease in conductivity and reasonably high mechanical properties (M, S and E) of 1.6 GPa, 45 MPa and 5%, respectively, after the aging. Thus, M1 showed the fairly high water stability in water at 130 °C, which were comparable to that of R1 Effect of cell temperature on DMFC performance was investigated for M1 with supplying 5 wt% methanol solution (1 ml/min) and air (450 N cm3/min). With increasing cell temperature from 40 to 80 °C, the DMFC performance significantly increased. The open circuit voltage (OCV) increased from 0.64 V at 40 °C to 0.67 V at 80 °C, the cell voltage at current density of 200 mA/cm2 (V200) increased from 0.24 to 0.37 V, and the maximum output (Wmax) increased from 50 mW/cm2 to more than 115 mW/cm2. This was due to the predominant effect of enhanced electrode reaction rate at the higher temperature rather than the negative effect of increased methanol crossover. In this study, the fuel cell properties at 60 °C were investigated in detail.Preliminary experiments were carried out for M2 at a methanol concentration of 5 wt%, varying flow rates and humidification conditions of air. Air flow rates of 450 and 750 N cm3/min hardly affected the DMFC performance up to the current density of 500 mA/cm2. The humidification at 45 and 25 °C (corresponding to 48 and 16% RH, respectively) gave the similar cell performances, which were slightly better than that without the humidification. For example, the Wmax values were 96, 97 and 87 mW/cm2 for 48, 16 and 0% RH, respectively. In the following experiments, the air humidified at 25 °C was supplied at a flow rate of 450 N cm3/min, unless noted otherwise. shows the effects of methanol feed concentration on the DMFC performance for M1 with O2 and air supply at 60 °C. The DMFC performance decreased with increasing methanol concentration. The reduction in the performance was larger for the higher methanol concentration and also larger for air than for oxygen. With oxygen supply, the cell performance for 50 wt% methanol was still kept in a fairly high level, namely, OCV of 0.60 V, V200 of 0.28 V and Wmax of 64 mW/cm2. On the other hand, with air supply, the cell performance for 50 wt% methanol reduced to a low level of V200 and Wmax of 0.16 V and 29 mW/cm2, respectively, which were about a half of those with oxygen supply. shows comparison of DMFC performances at a methanol concentration of 20 wt% methanol among SPI and Nafion 112 membranes. The cell performance data (OCV, V200, σ⊥FC and Wmax) for different methanol concentrations are also listed in . The DMFC performance of M3 was not measured because of the extremely low proton conductivity. Nafion 112 membrane showed the much lower cell performance at 20 wt% methanol concentration than the SPI membranes due to the much larger methanol crossover, although having the much larger σ⊥FC value of 63 mS/cm. In the range of the lower current density below 200 mA/cm2, the SPI membranes (R1, R2, M1 and M2) showed the similar cell performances, whereas in the range of the higher current density above 250 mA/cm2 up to 500 mA/cm2, M1 and M2 showed the higher cell performances than R1 and R2 due to the smaller effect of mass transfer resistance. This might be due to the difference in methanol crossover between the two types of membranes in the higher current density range or in the more hydrated state at 60 °C. M1 and M2 seemed to keep the methanol crossover in a lower level because of the ionic cross-linking effect and to reduce the mass transfer resistance of oxygen molecules in cathode compared to R1 and R2.The σ⊥FC values of Nafion 112, M1, M2 and R2 at 60 °C with supply of 5 wt% methanol and 16% RH air were less than a half of the corresponding values of σ|| in water at 60 °C, indicating that the membranes in DMFC operation were not so wet as in water. With increasing methanol concentration, the σ⊥FC decreased, for example, from 27 mS/cm at 5 wt% to 11 mS/cm at 50 wt% for M1, because of a decrease in the water content in membrane.The methanol permeation flux (qM) and coefficient (pM) values measured in situ during DMFC operation at a current density of 200 mA/cm2 are summarized in . For SPI membranes, the qM varied inversely as membrane thickness and the pM hardly depended on the thickness The methanol permeability coefficients determined by the liquid–liquid permeation measurements have been reported to be about 0.25 × 10−6 |
cm2/s at room temperature and 3.2–6.4 wt% for the sulfonated polyimides and polyisoquinolines bearing N-base groups The Faraday's efficiency (ηF) is defined as the ratio of the methanol consumed for electrochemical reaction to the total methanol consumption including the methanol consumed for electrochemical reaction and wasted by crossover. The potential efficiency (ηE) is defined as the ratio of cell voltage to the standard cell voltage (Eo |
= 1.214 V). The overall DMFC efficiency (ηDMFC) is defined as the product of ηF and ηE. These are effective factors to evaluate the PEM performance in the DMFC operation. summarizes the ηF, ηE and ηDMFC at a current density of 200 mA cm−2.At a low methanol concentration of 5 wt%, the ηDMFC values were 21% for M1 and R2 and 23% for M2, which were two times higher than that for Nafion 112. With increasing methanol concentration, the ηDMFC decreased largely, especially for Nafion 112. At a fairly high methanol concentration of 20 wt%, Nafion 112 showed the extremely low ηDMFC value of 1.9, whereas the SPI membranes except for R1 showed the five times higher ηDMFC values of 9.2–10.2. In the case of Nafion 112, the very high methanol crossover (qM of 2.5 μmol/cm2) largely reduced both the ηE and ηF. On the other hand, in the case of the SPI membranes, the relatively low methanol crossover (qM of 0.6 μmol/cm2) reduced the ηF fairly largely but the ηE slightly. At a high methanol concentration of 30 wt%, the ηDMFC further decreased to 6% for M1 and M2 and to 5% for R2.A short-term durability test was performed for M2 at 60 °C for 300 h, varying the methanol concentrations (5–20 wt%) and the load current density (100–500 mA/cm2). After the test for 300 h, the DMFC performance hardly changed, suggesting the good durability of this kind of SPI membranes for DMFC application at relatively low temperatures.NTDA–BAPBDS/DABI membranes had the strong interaction between sulfonic acid and benzimidazole groups, which made the membranes insoluble and reduced the water uptake, λ and proton conductivity. M3 with low IEC of 1.64 mequiv./g showed extremely low measured IEC value and very low proton conductivity. M1, M2 and M4 with relatively high IECs of 2.02 and 1.88 mequiv./g, respectively, showed the reasonably high proton conductivity and low methanol crossover as well as the high mechanical strength, thermal stability and water stability. They showed the anisotropic membrane swelling and proton conductivity similar to those for NTDA–BAPBDS/BAPB membranes. Compared to NTDA–BAPBDS/BAPB membrane (R2) with IEC of 1.51 mequiv./g, M2 showed the slightly smaller proton conductivity and slightly smaller methanol crossover and as a result slightly higher DMFC performances. For example, at 60 °C and a methanol concentration of 20 wt%, the σ⊥FC, qM and ηDMFC at 200 mA/cm2 and the Wmax were 18 mS/cm, 0.56 μmol/cm2, 10.2% and 79 mW/cm2, respectively for M2, whereas 23 mS/cm, 0.63 μmol/cm2, 9.2% and 70 mW/cm2, respectively for R2. The SPI membranes have high potential for DMFC applications at mediate temperatures (40–80 °C).Acoustic resonances of relaxation nature in CsI single crystals in the temperature range 2–20 KAcoustic relaxations in CsI single crystals are investigated in the temperature range 2–20 K at frequencies (1–7) × 105 |
Hz. The absorption peak found earlier at temperatures 3–5 K, which is caused by preliminary plastic deformation at room temperature, is studied in detail. A new relaxation resonance that corresponds to a thermally activated process with the activation energy U |
≈ (6.1–8.9) × 10−3 |
eV and the attempt frequency ν0 |
≈ 2 × 109 to 8 × 1010 |
s−1 is revealed in the temperature interval 8–10 K.Acoustic spectroscopy methods at liquid helium temperatures allow studying some local structural rearrangements in crystals which are controlled by overcoming very small potential barriers of about 10−2 to 10−3 |
eV. Low-temperature relaxation resonances (internal friction peaks and modulus defects in the acoustic susceptibility) may be regarded as experimental evidence of existence of such rearrangements. In some cases, when interpreting concrete experimental data, it is possible to attribute a certain microscopic mechanism for low-energy structural rearrangements using, for instance, the concept of geometrical kink motion along dislocation lines and overcoming of the second order Peierls relief When studying low-temperature acoustic properties in CsI single crystals, it has been established that the plastic deformation ɛpl |
≈ 3% at room temperature initiates an acoustic relaxation peak that is localized in the temperature interval 3–5 K at elastic waves frequencies f |
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