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u) + (∇ |
u)− 1], and εf=1−∑i=1kcVi/∆V where μe is the fluid effective viscosity, ∆ |
V and Vi are the volume of a computational cell and the volume of particle i inside this cell, and kc is the number of particles in the cell. Note that the fluid effective viscosity μe is determined by k-ε turbulent model Note that in the CFD-DEM governing Eqs. , fpf is the particle-fluid interaction force acting on individual particles, including the drag force and the pressure gradient force. The drag force calculation is based the model proposed by Di Felice , where the pressure gradient force is also included.The modelling of the solid flow by DEM is at the individual particle level, while the fluid flow by CFD is at the computational cell level. Their coupling is numerically achieved as follows. At each time step, DEM will give information, such as the positions and velocities of individual particles, for the evaluation of porosity and fluid drag force in a computational cell. CFD will then use these data to determine the gas flow field which then yields the fluid drag forces acting on individual particles. Incorporation of the resulting forces into DEM will produce information about the motion of individual particles for the next time step. This coupling scheme has been well documented in the literature and used in our previous studies The BF geometry used in this work is shown in (a). It is a 2D slot model, and the inner thickness of this model between front and rear walls is set to 4 coke particle diameters. Note that as reported (b)), and the CFD size is roughly at 2 coke particle diameter. The particle properties and DEM parameters employed in the simulation are listed in . Note that in the present work, it is assumed that furnace wall and ore/coke particles have the same properties including particle size and shape, friction coefficients and Young's modulus.During the simulation, 120,000 coke particles are charged first from the top to fill to the BF throat, and remain at a static state. Then, the blast starts to be injected from tuyere at a constant rate. The simulation will stop after the packed bed reaches steady state. This model is referred to as “Model I” where all particles have the same properties such as size and density. (c) shows a model referred to as “Model II”, where two types of particles are used including ore particles (density at 3300 kg/m3) and coke particles (density at 920 kg/m3). Ore and coke are added into this model layer by layer. Note that under the condition of Model II, ore particles are extracted from the cohesive zone representing the melting process. Hence, in the raceway region and BF bottom, only coke particles exist.The coupled CFD-DEM approach have been used to study gas-solid flow behaviour in our past studies In an ironmaking BF, different operating settings could lead to different raceway features. Under the real BF geometry condition, the raceway size and shape are difficult to predict due to the complexity. Note that unless otherwise specified, the simulation conditions are mainly based on Model II with layer structure of ore and coke particles. shows the raceway formation process when gas velocity is 18 m/s. Initially, a small plumelike cavity enlarging towards the vertical direction is generated in front of the tuyere ((b)). When the kinetic energy of incoming blast reaches a dynamic balance with the bed weight, an elliptic circulating raceway can be observed in front of the tuyere tip. After that, the raceway will keep enlarging and reach a steady state ((d)). In addition, comparing with the cavity generated, the bed height increases drastically. The increased height is cause by the ascending gas flow which loosens the entire bed. That is why the simulation takes a long time to generate a steady raceway. Also note that particles at the bed top is partly fluidised ((c) and (d)). This is because of the higher gas velocity in the BF throat region. Note that compared with the BF geometry, the raceway formed is quite small. Hence, in the following, only local raceway region is shown for a good visualisation of raceway characteristics. The tuyere geometry is simplified and represented by fixed and motionless particles as indicated in red (). In the simulation, gas flowing through the tuyere cannot pass through the tuyere top and bottom boundaries. shows typical flow patterns of particles in the raceway region under blast velocities of 17 m/s, 18 m/s and 20 m/s, respectively. It can be observed that the raceway size expands with increasing lateral gas velocity, particularly in the vertical direction. The penetration depth also increases correspondingly in the horizontal direction. Some particles are moving along the raceway boundary. The simulated results generally agree with early work observed in cold models that the raceway has a much rapid growth in the vertical direction than horizontal direction The common anti-clockwise circulating raceways are generated in both Model I and Model II. shows the drag force and particle velocity distributions acting on particles and its corresponding gas streamline of a steady anti-clockwise raceway. From the left figure, it can be observed that the initial drag forces are mainly located inside the raceway where marked with red colour. Particles with large kinetic energy inside the raceway are circulating in anti-clockwise direction and pushed back to tuyere tip region. At the same time, some particles below the tuyere are doing clockwise motions. From the corresponding gas flow streamlines around raceway, it can be seen that a distinct gas vortex and a slight vortex located upon and below the tuyere are formed. Clearly, the strong gas vortex upon the tuyere determines the particle circulating direction; while the weak gas vortex has slight effect on particle motions. The weak gas vortex is the cause of the clockwise circulated particles.The common clockwise circulating raceways are mainly generated in Model I. The drag force and particle velocity distributions acting on particles and its corresponding gas streamline of a steady clockwise raceway are shown in (b). Obviously, particles are pushed into the packed bed in different circulating direction, and a clear cavity is formed in front of tuyere. Large drag forces can be observed inside the raceway, and small drag forces act on the particles around the cavity. During the formation of clockwise raceway, no plumelike cavity can be observed during the progress. Two gas vortexes can also be observed in the gas flow field. Clearly, the large gas vortex is located below the tuyere. Thus, it can be concluded that the magnitude of the two gas vortexes is the main reason for different circulating directions of particles.For the further increase of gas velocity in model II, a typical type of raceway is formed, called plumelike raceway, as shown in (c). During the generation of both anti-clockwise and plumelike raceways, a small plumelike cavity is formed initially (see (b)). When the particle-fluid interaction force cannot reach a balance with the bed weight, the small plumelike cavity will keep enlarging and forming the plumelike raceway. From (c), instead of circulating around the raceway, particles located at the raceway roof show peeling and pasting behaviour which means that the gas flow is penetrating into the packed bed. This phenomenon can be proved by the gas flow field where the gas is directly ascending towards the top before the tuyere tip. Also, it is obvious that the slightly small vortex still exists below the tuyere, but the top whirlpool has become disordered. When the velocity has a further increase, the ascending gas will break the roof and fluidize the packed bed. illustrates different raceway types as a function of gas velocity and tuyere length in both Model I and Model II. Some interesting findings can be found and summarized below.The anti-clockwise raceways are formed when gas velocity is in the medium range. The formation of anti-clockwise raceway is the result of the dynamic balance between incoming kinetic energy and the bed gravitational energy. The clockwise circulating raceways are formed for cases with low gas velocities.The plumelike raceways are generated for cases with high gas velocities in Model II. In these cases, gas flow is large enough to break the restriction of the packed bed. However, due to the increased bed weight, the raceway top cannot be fluidised easily. Thus, a slight peeling and pasting behaviour is formed.Tuyere length can affect the raceway types. For example, in model II, the increase of the tuyere length could change raceways from anti-clockwise to plumelike. Generally, for the longest tuyere length, the restriction from the tuyere side wall is increased. Gas flow tends to ascend towards the top, forming plumelike raceway. But note that there are some exceptions, e.g., for cases of gas velocity at 20 and 21 m/s. It may need further extensive investigation on the effect of tuyere length.It is concluded that by changing the simulation condition such as gas velocity and tuyere length, the magnitudes of gas vortexes upon and below the tuyere are changed significantly which largely determine the direction of circulating motion of particles and raceway characteristics.The effect of tuyere length on the raceway size is examined, and shown in . In this work, the tuyere lengths are adjusted by selecting different number of CFD cells (3, 5 and 7 CFD cells, and their corresponding tuyere length at 0.4 m, 0.7 m and 0.9 m, respectively). shows the particle flow patterns as a function of different tuyere lengths when the incoming gas velocity is 18 m/s. It can be observed that raceway height experiences a rapid growth while the penetration depth expands slightly. In addition, in (c), instead of penetrating into the packed bed, the incoming blast expands towards the BF side wall. Hence, this length may be not suitable for raceway formation. shows the variation tendency of the raceway penetration depth and height as a function of blast velocity for two different tuyere lengths. Generally, the raceway height shows an obvious increase with gas velocity; the raceway penetration depth rises slightly. Comparing the raceways for two different tuyere lengths, it can be observed that the raceway height does not change much, but the raceway depth is affected significantly. This indicates that narrow raceways are generated for smaller tuyere length. This is consistent with the discussion above that as the raceway depth increases slightly and the height rises drastically. The blast is mainly ascending towards the BF side wall for short tuyere lengths.Coke combustion is simulated by exacting particles from raceways. The solid extraction rate used here is 2000 particles per second. The removed particles are added back to the top of bed to keep the bed at a constant height. As reported in the literature, the effect of particle extraction is not significant at low loaded beds shows a comparison of raceway sizes for two conditions with extraction and without extraction. It can be observed that when particles are extracted, the minimum velocity to generate a void is much less than the case without particle extraction. The penetration depth with solid extraction experience a larger expansion. The raceway penetration height with solid extraction is larger at low gas velocity, but decreases and becomes smaller at a higher gas velocity. This is because of the fact that solid extraction provides a driving force for the movement of the bed, and particles tend to move towards to the raceway. When particles are discharged from raceways, the inter-particle locking around the cavity periphery is interrupted. Therefore, a loose moving bed cannot restrict the enlarging process of raceways in the horizontal direction. The gas can easily penetrate through the bed and generate a long and narrow cavity in front of tuyere.A CFD-DEM model has been carried out under full-scale BF conditions to investigate the raceway formation. The conclusions from the present work can be summarized below:Three kinds of typical raceways are observed: anti-clockwise circulating raceway, clockwise circulating raceway, and plumelike raceway. The anti-clockwise raceway is formed when the gas velocity is in medium range. The clockwise raceway can only be observed in the cases with low gas velocity. The mechanisms of such two different kinds of raceways are closely related to circulating gas vortexes upon and beyond the tuyere.The plumelike raceway is formed at high blast velocity. When the particle-fluid interaction force increases under loaded condition (model II), the gas flow will break the raceway roof easily and form a plumelike raceway.Effects of tuyere length and solid extraction are examined. It reveals that for short tuyere length, the gas flow tends to develop along the BF side wall, causing small penetration length; but if the length is too large, particles will receive strong force from the BF central bottom, preventing the increase of penetration depth. Solid extraction increases the raceway penetration depth significantly, but decreases the raceway height slightly at a higher gas velocity.Fretting fatigue behavior of Al7075-T6 at sub-zero temperatureIn some fretting fatigue applications, such as aero industry, the temperature may drop well below −50 °C Fretting fatigue behavior of aluminum alloy Al7075-T6 is investigated at temperatures of 24, 0, −25 and −50 °C in this work. The results show that (i) normal fatigue life increases considerably at sub-zero temperatures up to around 85% for low working stresses and reduces to about 40% for higher working stresses; (ii) fretting fatigue life at sub-zero temperatures rises significantly up to around 220% for low working stresses and reduces to about 50% for higher working stresses; (iii) ultimate strength of material changes from −15% to 15% under the fretting fatigue test conditions; and finally (iv) some parameters such as mechanical properties and fatigue behavior of material at low temperatures, contact load relaxation, crack closure, oxidation and some unknown sources can be thought to be responsible for fretting fatigue behavior of Al7075-T6 at sub-zero temperatures.► Fatigue behavior of Al7075-T6 at sub-zero temperature depends on stress level. ► Plain fatigue life increases and reduces for low and high stresses respectively. ► Fretting fatigue life also shows the same trend as plain fatigue life does. ► The change of behavior may be due to grain size, material properties and oxidation. ► Crack closure, contact load relaxation may also be effective.Fretting fatigue damage occurs in contacting components when they are subjected to oscillating loads and sliding movements at the same time. This phenomenon may occur in many applications such as bearings shafts, bolted and riveted connections, steel cables, steam and gas turbines shows the relation between two connected bodies in airplane structure that are subjected to oscillatory motion due to variety of cyclic loads. The load transfer to the structure takes place on a local scale, though, at the bolt/ plate interface. The remote global load causes shear loading of the bolt and normal force comes from tightening of the bolt. Under normal operational conditions, aircraft structural components may encounter a severe temperature variation. For example, normally a grounded aircraft may experience temperatures up to 40 °C in tropical locations; however, when flying at high altitudes these temperatures can decrease to as low as −60 °C The mechanism of fretting fatigue is schematically shown in . Two fretting pads are pushed against the component by a contact force, P. The component is then subjected to a cyclic load, Q. The elastic elongation, which occurs in the component along the contact zone, gives rise to fretting fatigue of the component. The fretting fatigue behavior of materials can be influenced by many parameters, including (i) loading and contact conditions, (ii) material behavior and (iii) environmental conditions. In terms of environmental condition many studies have been carried out to characterize the fretting fatigue at room temperature for aluminum alloys and in particular AL7075-T6. However, the operating temperature in the region, where this alloy is used in the bolted and riveted connections at aircrafts, can fall well below zero up to −50 °C. Despite broad investigations carried out over past several decades on various aspects of fretting fatigue, less attention has been paid to the fretting fatigue behavior at elevated temperatures The fretting fatigue behavior of aluminum alloy, Al7075-T6 at sub-zero temperatures is studied by experiment in this work. As stated earlier, this material is used in the components where the operating temperature can drop to below −50 °C. Failure mechanism of fretting fatigue is studied by SEM and optical microscopy. In order to study the effect of cooling the specimens on their mechanical properties, a number of tensile tests at different sub-zero temperatures for different durations are carried out. This is to examine the change of material's properties and structures under fretting fatigue test conditions.Aluminum alloy 7075-T6 was used in this investigation. Because of its low-specific weight and high strength to weight ratio and also its high electrical and thermal conductance, this alloy is widely used in industry and in particular in aircraft structure and pressure vessels. From a number of tensile tests (three tests) carried out on a universal tensile testing machine at a velocity of 0.05 mm/s (or at a strain rate of 7×10−3 |
s−1), ultimate strength and yield stress of the material were obtained as σult=590 MPa and σy=503 MPa, respectively. The tensile specimen's geometry is the same as that used for fatigue tests specimens. The material's composition obtained using EDXRF apparatus is given in , has a width of 14.1 mm, a thickness of 4.5 mm and a gage length of 70 mm.The fretting fatigue tests were carried out on a universal 200 kN Dynamic Servo fretting fatigue machine. Fractography of fractured surfaces and the change of wear zones were performed using optical microscopy. The experiments were conducted for the stress ratio of R=0, frequency of 60 Hz at a contact force of 1200 N and working stress amplitudes of 130, 180, 200 and 280 MPa. The pressure required to produce fretting was transmitted to the contact area between the specimen and two pads via a calibrated proving ring shown in . Each pad had two bases through which loads were applied to the specimen (). Each pad has two bases (contacting surfaces) through which the load is exerted on the specimen. The pad span, which is defined as the distance between the centers of the fretting pad feet, was chosen to be 16.5 mm. The pad's base had a width of 3 mm and were made of stainless steel 410 with σult=700 MPa and σy=420 Map. For more details on the device and test procedure see Refs. The pads were clamped to the specimen by the same normal loads as was to be used in real experiments. The specimen was then pulled by constant load using Dynamic Servo testing machine. The specimens were placed in a chamber to cool down at 0, −25 and −50 °C temperatures. Dynamic Servo test machine equipped with a chamber to generate sub-zero temperatures is shown in In order to study the effect of cooling the specimens on their mechanical properties, a number of tensile tests at sub-zero temperatures for different durations were carried out. This was to examine the change of material's properties and micro-structures under fretting fatigue test conditions. It must be mentioned that for low stress fretting fatigue tests, the specimens may remain at the test temperature for more than a day. The tensile specimens, prepared according to DIN 50 125, are cooled in the chamber at temperatures of 0, −25 and −50 °C for durations of 2, 6, 12 and 24 h, respectively. On the whole, three types of tests, including normal fatigue, fretting fatigue and tensile tests were carried out at sub-zero temperatures in this work.Variation of normal fatigue life versus working stress for normal and fretting fatigue at ambient temperature is shown in . The figure clearly illustrates a significant reduction in fretting fatigue life particularly for low stresses (high cycle fatigue, HCF) in comparison to the normal fatigue life. The results of normal fatigue tests at sub-zero temperatures for different stresses are given in . As the results suggest, normal fatigue life increases considerably as temperature decreases for stress levels of 130, 180 and 200 MPa but it slightly diminishes for the stress level of 280 MPa. For more clarity, the change in fatigue life at different temperatures with respect to the results at ambient temperature (20 °C) are shown in . The results indicate a remarkable increase of about 40% in the fatigue life at zero temperature and the stress level of 130 MPa and around 85% for −50 °C and the stress level of 200 MPa. However, at the stress level of 280 MPa, fatigue life decreases by nearly 38%. The reasons for this type of fatigue behavior of Al7075-T6 will be disused in The results of fretting fatigue tests at sub-zero temperatures for different stress levels are given in . As the results suggest, temperature decrease increases fretting fatigue life dramatically for the stress levels of 130, 180 and 200 MPa but decreases the life considerably for the stress levels of 200 and 280 MPa. For more clarity, the change in fretting fatigue life with respect to the results for ambient temperature (20 °C) are demonstrated in . The results indicate a tremendous increase of fatigue life ranging from about 96% at −25 °C for the stress level of 180 MPa, up to around 223% for −50 °C and the stress level of 130 MPa. However, fretting fatigue life reduces by 23% for 0 °C and the stress level of 280 MPa and up to about 55% for −50 °C. The reasons for this type of fretting fatigue behavior of Al7075-T6 will also been disused in Some fretting fatigue tests particularly those at low working stresses take more than a day to be accomplished. As so much as, the specimens may remain at the test temperature for more than 24 h. This may give rise to severe changes in the micro-structural and mechanical properties of material. The changes may improve the material behavior or deteriorate its characteristics (degradation). Hence, in order to examine the possibility of material gradation or degradation, a number of tensile tests were carried out under the fretting fatigue conditions considering the tests temperature, heating up and cooling down procedures and duration of the tests.The tensile tests were performed at temperatures of 24, 0, −25, and −50 °C for time durations of 2, 6, 12 and 24 h, respectively, and stress–strain curve for each case was captured. Typical stress–strain curves are illustrated in . Mechanical properties of the material including ultimate strength, yield stress and elongation were measured from the stress–strain curves. The results are given in . For more clarity, the increase in ultimate strength with respect to that for ambient temperature is shown in . Three quite different trends can be distinguished in the figure. For 0 °C, material undergoes the highest degradation as the ultimate strength decreases continuously regardless of the cooling duration. For −50 °C the situation is opposite and material's properties improves more as cooling time increases. The least change of ultimate strength fluctuating between −5% and 2% occurs for −25 °C, which is negligible. The interesting point is that the elongation or ductility of the material, as given in , is not significantly affected by temperature drop or by cooling duration. The mechanical properties of the material used in this work are quite close to those reported by Campbell Failure mechanism of fretting fatigue was studied by SEM and optical microscopy. Some typical results of fractography of the specimens are illustrated in for different temperatures and stresses. As the figures suggest, the fracture surfaces typically consist of two quite distinct regions; a fatigue zone created by crack propagation and a tensile region which gives rise to fracture of specimen when it is sufficiently weakened by the crack zone development. Furthermore, the micro-structural change of the specimens at different temperatures and for different cooling durations was examined by optical microscopy. The tensile specimens were sectioned after the test, polished and etched for the examination. Typical pictures are shown in . The figures clearly illustrate the differences between the micro-structures of the specimens. The grains look to have become finer at sub-zero temperatures.Some possibilities, by alone or by combination, may be thought to be responsible for the dramatic changes in fretting fatigue behavior of Al7075-T6 at sub-zero temperatures and various working stresses.Grain size: It is well known that mechanical properties of metals such as ductility, tensile strength and toughness increase when grain size is reduced. The effect of grain size on plain fatigue life has widely been investigated and the results mostly indicate that grain size refinement increases plain fatigue life. However, the influence of grain size on fretting fatigue has received less attention. At the beginning, the authors of this work believed that the increase of fretting fatigue life could partly be attributed to the effect of grain size which, as illustrated in , is finer for lower temperatures. However, the results found in the literature do not fully support this idea. Jayaprakash et al. support the idea proposed by Raman et al. suggests, the effect of temperature on fretting fatigue life gets more profound as stress level decreases. The authors of this work believe that on one hand, finer grains pave the ground for earlier crack nucleation, but on the other hand they give rise to the increase of plain fatigue life as reported in the most of the literature. The reason is that crack nucleation occurs within less than 10% of the total fretting fatigue life, for which the effect of grain size should not be so significant, while most of the crack growth (after crack nucleation and early stages of crack growth) occurs in the manner of plain fatigue. The increasing effect of the latter prevails the reducing effect of the former giving rise to the increase of fretting fatigue life at sub-zero temperatures.Mechanical properties at low temperature: The change in fretting fatigue life of aluminum 7075-T6 can be attributed to the intrinsic nature of material behavior at low temperatures, which is normally observed for most of materials. At the beginning, the most likely reason imagined to be the most effective source to the change in fretting fatigue behavior of the specimens, was the change in mechanical properties of the material that may occur during the process of long time fatigue tests. This possibility was also examined by performing tensile tests at different sub-zero temperatures and for various cooling duration to simulate the test conditions. The results were explained in . Numerous works on the effect of low temperature on fatigue behavior of materials can be found in the literature. However, range of the temperatures used in these works is mainly above room temperature. One of the pioneer works in this regard is the one reported by Cox et al. , all three alloys exhibit a slight increase in tensile strength while no significant variation was noted in the elongation. The results showed a major decrease in the apparent fracture toughness of the two 7000 series alloys. The 7000 series specimens exhibited a change in fracture mode from a dimple type at room temperature to a cleaved one at low temperatures. Campbell Fatigue and crack growth at low temperatures: Unfortunately, unlike the fatigue behavior at elevated temperatures, less attention has been paid to fatigue behavior of materials at sub-zero temperatures. One of the most extensive and comprehensive reports, is given by Stephens . An improvement of up to 650 percent was observed in the fatigue life of the low temperature tested plates Oxidation: Surely, oxide layer is formed on the contact area for aluminum as this material is so liable for being oxidized under humid environmental conditions. The coefficient of friction increases drastically during the early stages of fretting due to the oxide layer contact and breaking of the oxide layer. During the initial contact, presence of thin oxide layer in aluminum specimens reduces the friction and after few tens of cycle the oxide layer breaks down and a contact of aluminum to aluminum occurs leading to the increase in friction. Because of the oxidation, fretting is often classified with corrosion processes in the literature. The oxide debris is created as oxide layers are repeatedly formed and removed by the abrasive action of one surface sliding against the other. The effect of oxide layer depends on the applied load so that under light loads, the slip is spread over the entire contact area and causes oxidation assisted wear damage Crack closure: The competing effects of crack closure due to freezing conditions inside the chamber and crack initiation and propagation is due to the fretting fatigue conditions. Therefore, the reduction in fretting fatigue life is partly compensated for by freezing conditions and crack initiation and propagation are retarded, giving rise to the increase of fretting fatigue life. The crack closure was also noticed by McClung and Newman Contact load relaxation: One possibility could be the relaxation of the contact force due to contraction of the pads, the specimen and the components of the proving ring, such as tightening screws, at sub-zero temperatures. This possibility was examined by experiment and a reduction of 10–20% in the contact load was observed at temperature of −50 °C after 3–6 h. With regard to the fact that the stress components, including shear stress, which is the most effective stress component in fretting fatigue at the contact area, vary linearly with the contact force Contact load relaxation was also noticed by Oskouei and Ibrahim Removing the pads at some time intervals: This possibility is ruled out altogether because all fretting fatigue specimens were kept continuously in the chamber under a constant temperature without removing the pads until the complete fracture of the specimens.As explained above and as it is seen in the literature, it seems that a number of parameters can be responsible for tremendous changes in fretting fatigue life of the material described in . However, there is no consensus among the authors on the effect of these parameters. Rather, the reports are sometimes contradictory. Moreover, the effects of some parameters are conflicting. For instance, while grain size refinement may reduce the fretting fatigue resistance, oxidation may give rise to the increase in fretting fatigue life. The role of each parameter and perhaps its interaction with the other parameters must be explored precisely. However, this requires a vast research program as the parameters have individually been the subject of numerous investigations. The effects of some of these parameters are being investigated by the authors of this work the results of which will be published in due course.From the experimental results, the following conclusions can be derived for the material and the test conditions used in this work:Normal fatigue life increases considerably at sub-zero temperatures up to around 85%, depending on the temperature, for low working stresses and reduces to about 40% for higher working stresses.Fretting fatigue life at sub-zero temperatures rises significantly up to around 220%, depending on the temperature, for low working stresses and reduces to about 50% for higher working stresses.The results of tensile tests show a change of about −15% to 15% in ultimate strength of material under the fretting fatigue test conditions.It seems that a combined effects of grain size, mechanical properties of material, oxidation, crack closure, contact load relaxation and fatigue behavior of material at low temperature and perhaps some other unknown sources can be responsible for the tremendous changes in fretting fatigue behavior of Al7075-T6.Crack growth measurement can be very helpful for a more thorough investigation and interpretation of fretting fatigue behavior of Al7075-T6 at sub-zero temperatures. This is intended to be carried out in future works.Identification of material parameters by means of compliance moduli in spherical indentation testAn identification method of elastic and plastic hardening parameters is proposed by measuring compliance moduli in loading and unloading in the spherical indentation test. The loading program is composed of consecutive loading and unloading steps from which the compliance moduli are determined from the load–penetration (P–h) curve. The hardening parameters k and m occurring in the plastic hardening curve are then specified. Identification of materials described by a more complex three parameters constitutive law εp=((σ−σy)/k)′1/m′, where σy denotes the yield stress, is also analysed. The identification of Young’s modulus from the indentation test is also presented.The attempts to correlate spherical indentation parameters with stress–strain curves (tension curves) of materials has been considered in numerous papers by Tabor where α=3.07, β=0.32 are constants and P, a, D, h are indentation parameters defined in for the case of an elasto-plastic material. The value characterizes the degree of sinking-in or piling-up of the material around the impression and depends on the exponent m. Thus, for a rigid-plastic material we have a unique relation between the penetration curve and the stress–plastic strain curve of the material.In the case of elasto-plastic materials, an inconsistency appears in this approach, namely the contact radius a is measured in an unloaded configuration in which the actual radius of residual spherical cavity equals Dp and is greater than the indenter diameter D (). The aim of some authors was to eliminate the effect of elastic deformation on the measured residual imprint geometry by means of the corrections introduced in the formulas (2), see Field and Swain A characterization method based on the analysis of the loading penetration curve during the sphere indentation test was presented by Taljat et al. An extensive numerical study of sphere indentation in an elasto-plastic half-space is presented in the paper of Mesarovic and Fleck which corresponds to the familiar Ramberg–Osgood relation., the total strain is expressed by a power law and in (4) only the plastic strain is expressed by such a law. We note that the elasto-plastic constitutive laws (3) and (4) contain three independent constants σ0,ε0,n. The numerical simulations were performed for two values of n: n→∞ and n = 3. The following relations were calculated for different values of E/σ0These quantities were compared with the values for α, c2 and the function P(h) which result from the similarity solution. The role of friction and pre-existing stress within the half-space was also considered.The authors conclude that the region of validity of the plastic similarity solution is limited by elastic effects for small contact loads and by finite deformation effect for large contact loads. Friction has a quantitative effect on the contact size only below the similarity regime and in this regime the pre-existing stress has a minor effect on the indentation response. It results from the analysis that the similarity solution cannot be used to identify material properties by means of simple indentation tests. The authors have also stated that extraction of material parameters may require more sophisticated indentation measurement than those strains, which is engulfed by an elasto-plastic regime and next appears an elastic region. The characteristic plastic strain which equals 0.29 separates the innermost plastic zone from the surroundings. In view of numerous numerical simulations relations have been proposed which connect material constants and indentation parameters. Using these relations one can determine the unknown material constants σy, σ0.29, E∗, where σy is the yield stress, σ0.29 is the stress corresponding to the characteristic plastic strain εp=0.29 and E∗ is the effective elastic modulus. Let us note that the method enables to determine only two parameters of the plastic stress–strain curve, i.e. σy and σ0.29, which specify linear plastic hardening moduli.The present paper is closely related to the previous publications of these writers cf. Kucharski and Mróz The proposed method is referred to the self-similar solution for rigid-plastic materials satisfying the power hardening law (1) in uniaxial tension by Storakers and Biwa where ε is the total strain and εe, εp denote elastic and plastic strain components and E denotes Young’s modulus. For materials characterized by the yield stress σy, the stress–strain relation can be presented as followsThe plastic hardening response depends on three parameters k′, σy and m′. Obviously relations (8) and (9) do not satisfy the homogeneity property of and, therefore, the solution (2) provides only an approximate relation when referred to constitutive relations (8) or (9), cf. The load–total penetration curve, P–ht, measured experimentally corresponds to the elasto-plastic deformation of the material and is composed of elastic and plastic parts (As the parameters k, m are specified in the identification , the experimental relation P–hp required in this equation can be obtained by subtraction of he(P) from ht(P), which are measured in the indentation test. The simple subtraction of two equationsin the entire range of loading (0–Pmax) cannot be applied, because loading and unloading are executed in different configurations of the material. This difference is evident if one compares the initiation of the loading process and the end of unloading. At the start, the spherical indenter remains in contact with the plane, however, at the end of unloading it is in contact with the residual spherical cavity (The whole P–hp curve is constructed from segments Δhpi(ΔPi) corresponding to different ascending values of force reversals Pi, The constants k, m are determined from the condition of the best fit of relation (2) to the determined points (hpi, Pi) of the plastic penetration curve. The detailed analysis of the unloading process and the procedure of generation of P–hp curve using cyclic loading–unloading–reloading penetration curve is presented in the paper of Kucharski and Mróz (segment subtraction method) are given in Instead of constructing the P–hp curve from consecutive segments, the identification procedure can be based on the measurement of compliance moduli. In fact, by differentiating (11) with respect to P, we have the plastic compliance modulusThe plastic compliance modulus Cp(P) is specified by using the sequential loading–partial unloading curves, similarly to the procedure illustrated in . Specifying the load and penetration increments near the partial unloading point, we haveand for small increments, the total and elastic compliance moduli are given by the derivatives evaluated at the unloading pointswhere Ct and Ce are the inclination angles of tangents to the loading and unloading curves at the points P1, P2, P3,…,Pn+1, . The parameters m and k are specified from the condition of the best fit of relation (14) to the points (dhp/dPi,Pi) determined from (16).The presented application examples are based on the data obtained from numerical experiments. In the examples, the verification is demonstrated of the proposed method and is compared with methods proposed previously. The validation of the method consists of the following steps:Determination of the cyclic loading–unloading–reloading curve for assumed material parameters (Eg, νg, kg, mg) by means of the Finite Element Method.Identification of the material parameters (Ec, νc, kc, mc) using the proposed identification procedures (elastic and plastic parameters are specified in separate procedures).Comparison of the assumed and identified material parameters (Eg, νg, kg, mg and Ec, νc, kc, mc).The details of the numerical analysis (finite element mesh, constitutive model) are described in the previous paper of Kucharski and Mróz We assume the following elastic parameters: E=74,500 MPa, ν=0.3 and the strain hardening relation. It is assumed that the plastic strain obeys (8). In actual materials the initial yield stress σy specifies the onset of plastic yielding, but now it is assumed that σy=0. The numerically calculated load–penetration curve for D=2.5 mm and σy=0 is presented in . To demonstrate the effect of yield stress value, the load–penetration curve for σy=150 MPa corresponding to the curve with an initial yield stress in The load reversal points are at the loads: P1=40, 54, 73, 98, 132, 180 N. The corresponding plastic indentation curve hp=hp(P) for 0<P<180 MPa obtained by subtracting penetration depths at consecutive loading–unloading segments is shown in The application of the method of compliance moduli provides a more reliable identification procedure. The differences of compliance moduli on the loading and unloading curves (), provide the compliance moduli dhp/dP. They are specified at the stress reversal points. presents the variation of elastic and plastic compliance moduli with the load value. In order to compare the measured moduli from (16) with the prediction of formula (14), the curve dhp/dP is plotted for the parameters m=0.24, k=800 MPa. The predicted curve corresponds to a stiffer response. The method of compliance moduli, therefore, provides the parameters m=0.27 and k=942 MPa. show the results of the identification carried out by the two methods. presents the load–plastic penetration curve and shows the identified stress–strain curves which are compared with the assumed (actual) stress–strain curve. Both load–plastic penetration (P–hp/D) and the stress–strain curves generated by the method of compliance moduli (method II), , are sufficiently close to the actual curves. In the case of the segment subtraction method, for lower values of loading, the generated P–hp/D curve, , is less stiff than the actual one and for greater values of P it becomes stiffer. This fact is also exhibited in where the predicted stress–strain curve is at the beginning characterized by lower tangent moduli and for larger values of strain by greater moduli than the actual values. The stress–strain curve obtained by the method I thus departs significantly from the actual σ–εp curve.Now the full range of loading is considered, that is 0≤a/D≤0.2. In the numerical experiment, the following load reversal points were assumed: P=242.83, 327.95, 442.25, 557.39, 805.74 N. Using the method I of subtraction of unloading segments, the curve P–hp was generated for the full loading range . Let us note that the data for the lower loading range (40–180 N) provide the input for curve generation at the higher loading range (242–806 N). Using the P–hp curve in the whole loading range the values of identified parameters are k=1234 MPa, m=0.354, however, when only the higher loading range P = (242–805 N) of the generated curve is used, then the identified values are k=793 MPa, m=0.234. On the other hand, using the compliance moduli, the identification can be based uniquely on data for the higher loading range, 0.09≤a/D≤0.2. The identification process is more reliable when the initial segments are neglected, the compliance moduli method (II) provides the parameter values k=830 MPa, m=0.246, which results in a very good reproduction of the stress–strain curve. The stress–strain curves identified by both methods using data corresponding to the higher loading range practically coincide with the assumed curve, σ=800εp0.24. The prediction based on the lower load range using method II is sufficient, but using method I is not as accurate. It should be noted that for the comparable accuracy level method II requires a smaller penetration depth than method I, and is therefore more convenient in the parameter identification procedure.In the examples presented we identify the stress–plastic strain curve which exactly fulfils the power law (8), thus its initial yield stress is equal to zero. The assumption of a finite value of the initial yield stress (9) (which occurs in actual materials) does not provide similar good predictions of the stress–strain curve and of the parameters k and m. This fact needs to be discussed in more detail.We note that the actual stress–strain curve does not satisfy the power law representation and is characterized by a linear, elastic response below the yield stress value. Let us consider the stress–plastic strain curve of the form σ=σy+k′εpm′, corresponding to (9). This curve can also be described by the expressionwhere k′=800 MPa, m′=0.24, εp0=0 (this corresponds to σy=0) and εp0=0.0015 (this corresponds to σy=150 MPa). These two curves are shown in . The difference between the curves occurs at the initial stage for strains 0≤εp≤0.0015 and for larger strains these two curves almost coincide. However, the penetration curves P–ht and P–hp for the two materials differ, see . The compliances dhe/dP and dhp/dP for the two materials are shown in . There the unloading moduli are the same, however the plastic compliance moduli differ for tests within the penetration range 0≤a/D≤0.09. In particular the values dhp/dP are lower for the material with the nonzero initial yield stress (σy=150 MPa). For larger penetration values (P = 242–806 N), the difference between the plastic moduli of the two materials is much smaller.The stress–strain curves identified by the two methods for the material characterized by the finite yield stress σy=150 MPa are shown in . The predicted curves are stiffer with respect to the actual curve at the initial stage of plastic deformation.Method I provides a slightly better identification of the parameters k, m in the lower range of strain (0–0.02), and the σ–ϵp curve is less stiff and closer to the actual one than that obtained by method II. This results from the fact that in method I the P–hp curve is generated from consecutive segments and thus the stiffness of the first segment has the greatest effect on the position of the total curve. As in method I the segment subtraction starts from a certain load level (40 N), the stiffness of the first segment and consequently of total P–hp curve can be slightly underestimated, similarly as for σy=0, cf. is also less stiff than that obtained from compliance method, where the compliance moduli in consecutive points are calculated independently. For the larger loading range, , the results of both methods are better.The identification method discussed in this paper is aimed to eliminate the effect of elastic stiffness moduli on the plastic compliance moduli. presents the variation of moduli dht/dP with penetration load for different values of Young’s modulus, E=E0, E=3E0, E=4E0, where E0=74,500 MPa.In the numerical calculations the plastic hardening curve (18) exhibiting a nonzero initial yield stress is assumed, and the loading range is (0, 180 MPa), that the evolution of the plastic compliance moduli calculated by (16) does not depend on the value of Young’s modulus. On the other hand, the moduli dhe/dP and dht/dP are dependent on the elastic stiffness moduli. In particular, it can be stated that and dhe/dP are calculated at the points of loading reversal. The parameter s is defined for materials characterized by the same plastic properties and different elastic moduli E∗, i.e. EI∗ and EII∗, then . Relation (19) follows from the fact that the contact configuration does not change at the initial unloading stage. A similar assumption for Vickers tests was made by Giannakopoulos in After each indentation test a residual imprint is generated having a shape of a spherical cavity of diameter Dp>DConsider the case of penetration of a rigid sphere of diameter D into an elastic semi space with the spherical penetration cavity of diameter Dp, Dp>D, induced by the permanent plastic deformation. Using the Hertz formula, the expression for elastic penetration depth isFor the specified value of P and different Young’s moduli one getsThe diameter Dp is related to the permanent penetration depth hp and the elastic unloading depth he by the formula, cf. Kucharski and Mróz The diameter ratio (23) can be expressed asIn view of (25) and (22), the ratio of elastic penetration depths expressed by (22) isBy numerical calculations the factor W in (26) can be evaluated. For E0<E<4E0 the permanent penetration depth hp is almost constant, so it can be assumed that hp1≈hp2=hp=the, where t>3. Then, W≈1 andFor example, when E1=E0, E2=4E0, he1/he2=3.78, W=0.92 and for E1=3E0, E2=4E0, there is he1/he2=1.33, W=0.99. The approximate assessment (27) is sufficiently accurate when E2 and E1 do not differ much, that is s=E2/E1 < 4. For fixed hp1, hp2 (i.e. fixed maximum P), the ratio (dhe1/dP)/(dhe2/dP) can be expressed by the same relation as he1/he2, cf. (26) and (27). Now, the elastic modulus can be identified by using the relations (19) or (27). As in the actual unloading process he1, he2 are affected by the residual stress, cf. Kucharski and Mróz is used, where Ec denotes Young’s modulus of the reference material, and (dhe/dP)ic are the compliance moduli of the reference material at the ith load reversal point, (dhe/dP)is are the compliance moduli of the tested material. The elastic properties can be specified (i.e. is accurate) even when the plastic hardening moduli are not determined precisely.Seismic performance of lightly shear reinforced RC columnsPrevious experimental studies on reinforced concrete columns subjected to cyclic loading simulating earthquake loading have shown that the columns with non-seismic details of transverse reinforcement are vulnerable to the cyclic loading. In this study, to investigate the behavioral characteristics of concrete columns with light transverse reinforcement, ten half-scale specimens were fabricated and tested under repeated cyclic loading together with axial loading. The main test parameters included axial load level, hook angle, longitudinal reinforcement ratio, transverse reinforcement ratio, and shear span to depth ratio. The performances and characteristics of the test specimens were analyzed in terms of load-drift relationship, dissipated energy, damping ratio, strain profile, drift capacity, effective stiffness, and ductility. The test results showed that the axial load level is the major parameter affecting seismic performance including the drift capacity. Based on the test results, the nonlinear modeling parameters for concrete columns presented in ASCE 41-13 were investigated using fragility analysis.Over the last several decades, a lot of concrete buildings have been constructed in developing countries (e.g., Korea), but many of the buildings do not satisfy the special requirements of current seismic design codes. When such buildings are subjected to a high level of seismic hazard (e.g., 10% or lower probability of exceedance in 50 years From the experimental studies mentioned above as well as a number of other studies Thus, in this study, ten half-scale reinforced concrete column specimens with light shear reinforcement were designed following the structural guidelines as the preceding building design code of Korea To investigate the seismic behaviors of the reinforced concrete columns in the existing buildings constructed based on the preceding Korea design code briefly introduces the history of seismic design codes for buildings in Korea.The geometries and reinforcement details of the test specimens could be classified into two series as shown in . The first series of the test specimens (NRC-1–6) had a transverse reinforcement spacing to depth ratio (s/d) equal to 1.2 and a lower longitudinal reinforcement ratio (1.06% or 1.51%), while the second series of test specimens (NRC-7–10) had s/d equal to 0.6 and a higher longitudinal reinforcement ratio (2.03%). The other test parameters included the applied axial load level, hook angle, longitudinal reinforcement ratio, transverse reinforcement ratio, and shear span to depth ratio. In the case of the first series, the main properties of the control specimen NRC-1 were as follows: column height (L) was 1660 mm; the shear span (=L/2) to depth ratio (a/d) was equal to 3.3; longitudinal reinforcing bars were D16 with a diameter of 16 mm with a longitudinal reinforcement ratio of ρl |
= 1.06%; and transverse reinforcing bars were D10 with a hook angle of 90° with a transverse reinforcement ratio of ρv |
= 0.17%. NRC-2 and NRC-3 differed from NRC-1 in the hook angle (135°) of transverse reinforcement and the ratio (ρl |
= 1.51%) of longitudinal reinforcement, respectively, while the other parameters were almost the same. NRC-4 and NRC-5 differed from NRC-1 in the applied axial load level (P/Agfc′), which was 0.06 and 0.38, respectively, and NRC-6 differed from NRC-1 in a/d (equal to 2.5).In the case of the second series (NRC-7 to NRC-10), the specimens had low s/d (equal to 0.6) and high longitudinal reinforcement ratio (ρl |
= 2.03%). NRC-7 was a control specimen in the second series. NRC-8 differed from NRC-7 in the hook angle (135°), and NRC-9 and NRC-10 differed from NRC-7 in the applied axial load level, which was 0.10 and 0.44, respectively. The top and bottom concrete beam studs of all specimens were designed to remain elastic during the loading time and were cast together with the columns. It is noted that the chord rotation of the columns is not significant since the beam studs are adequately stiff.In this study, all specimens were designed to be failed in flexure-shear mode based on the shear demand ratio (Vp/Vn), which was specified in ASCE 41-13 , the shear demand ratio (Vp/Vn) of all specimens ranged from 0.63 to 0.96. The presents the evaluation of the shear strength capacity, plastic shear demand, and shear demand ratio of the concrete columns.In this test, a low compressive strength (fc′≈20 |
MPa) of concrete and yield strength (fy |
≈ 300 MPa) of steel rebars was used to investigate the structural characteristics of the existing buildings constructed during the 1970s and 1980s in Korea based on the investigation results shown in a previous report a shows the typical stress-strain relationship of concrete acquired from the test. The longitudinal strain corresponding to the maximum compressive strength was 0.0018. In b, up to almost 60% of compressive strength, a constant value of Poisson’s ratio of 0.2 was maintained, but subsequently drastically increased due to the lateral expansion of concrete Tensile tests of longitudinal and transverse rebars were also performed according to the test standards of KS B 0802 c presents a typical stress-strain relationship of steel rebars acquired from the test. In the figure, the measured yield strengths of D16, D19, and D22 steel rebars were 327, 319, and 375 MPa, respectively, and the corresponding yield strains were 0.0019, 0.0017, and 0.0018, respectively. In contrast, the yield strength of D10, which was used in NRC-1–NRC-6, was 378 MPa, exceeding the specified yield strength of 300 MPa. In the evaluation of the test results hereafter, the material strengths measured from the test were used instead of the specified strength of concrete and steel rebars. shows a schematic drawing and photos of the test setup. The specimens were mounted vertically onto the loading steel frame. A guide frame was installed to maintain the loading steel frame to be horizontal and to prevent lateral instability of the specimens during loading. The top of the column specimens were axially loaded through the loading steel frame by using a hydraulic actuator of 1000 kN capacity. In addition, the top part of the columns was subjected to lateral cyclic loading by another hydraulic actuator with a capacity of 1000 kN, which was mounted to a strong wall.In this study, the cyclic loading history conforming to ACI 374.2R-13 . The lateral displacement cycles were repeated twice with amplitudes of 0.5Δy, 1.0Δy, 2.0Δy, 3.0Δy, 4.0Δy, 5.0Δy, and so on until failure, where Δy is the yield displacement evaluated assuming the effective stiffness of columns were evaluated considering the concrete strength measured from the test.Strain gauges were attached to the column concrete, and longitudinal and transverse rebars to measure concrete and steel strains, respectively. shows the arrangement of the concrete and steel strain gauges. The strain gauges were attached in the regions considered to be plastic hinge zones. Two linear variable displacement transducers (LVDTs) were installed at the top and bottom concrete beam stubs to measure the lateral deformations and slip of the specimens, respectively. shows the observed damage pattern at the end of testing. Most specimens, except for NRC-5, showed yielding of longitudinal steel rebars, concrete crushing, and final failure in flexure-shear mode. Before flexural cracking (approximately at the drift ratio of 0.25%), all column specimens showed elastic behavior. Immediately after flexural cracking, several thin inclined cracks occurred near the column ends. Then, the longitudinal rebars yielded at the drift ratio of approximately 0.8–1.6%, and the applied lateral load then began to decrease at the drift ratio of approximately 1.5–3%. With repeating loading cycles, inclined cracks significantly widened and the wide part of the concrete showed spalling. This impairment was concentrated in the plastic hinge regions. Specifically, for most specimens, the longitudinal rebars were buckled between the transverse rebars, and crushing and spalling of concrete cover followed. NRC-5 showed crushing and spalling of the concrete cover in the plastic hinge prior to yielding of longitudinal rebars, and failed in shear mode unlike the other specimens. In NRC-6–NRC-10, vertical cracks developed along longitudinal reinforcement, which is expected to cause significant loss of lateral load resistance. shows the measured load-drift hysteretic relationships of NRC-1–NRC-10 specimens. In this study, drift ratio (θ) was defined as Δ/L, where Δ is the lateral displacement and L is the column height. It is noted that the lateral deformation of the column causes a secondary moment (P-Δ effect) are the modified load – drift hysteretic curves after considering the P-Δ effect, which was determined based on the obtained test results.a shows the load – drift hysteretic relationship of a control specimen NRC-1. Under lateral load, initial cracks occurred at an early drift ratio of 0.25%, and the longitudinal rebars yielded at the drift ratio of 1.25%. Immediately after yielding of the rebars, the inclined cracks significantly widened and the lateral resistance of the column began to decrease. Concrete was crushed at the drift ratio of 2%, inducing obtrusive impairment of the column. The sequence of the failure in the NRC-1 specimen was in the order of initial crack development, longitudinal rebar yielding, and concrete crushing.d presents the load – drift hysteretic relationship of NRC-4 specimen subjected to low level of axial load (P=0.06Agfc′). The figure shows that the strength was almost halved, but the deformation capacity significantly increased in comparison with NRC-1. No significant concrete crushing was observed though the initial cracks occurred at the drift ratio of 0.25%. The longitudinal rebars yielded at the drift ratio of 1%, and then the specimen retained its strength almost up to the drift level of 4%.NRC-5 specimen was subjected to a high level of axial load (P=0.38Agfc′). e shows the load-drift hysteretic relationship of NRC-5 specimen. The initial inclined cracking occurred at a relatively high drift ratio of 0.5%. Then, the concrete crushing occurred at the drift ratio of 1%, and simultaneously the specimen reached its peak load with continuing loading cycles. The longitudinal rebars finally yielded at the drift ratio of 1.75%. The sequence of the failure in the NRC-5 specimen was in the order of initial crack development, concrete crushing, and longitudinal rebar yielding. NRC-2, NRC-3, and NRC-6 showed almost the same behaviors as that of NRC-1. This indicates that the hook angle, longitudinal reinforcement ratio, and shear span to depth ratio are parameters that do not significantly affect the load-drift behavior for the given test condition.In cases of the second series, for a control specimen NRC-7 (g), the sequence of the failure was almost the same as that of NRC-1 as follows: initial cracks appeared at the drift ratio of 0.4%, then longitudinal rebars were yielded at the drift ratio of 0.81%, and after that the concrete was crushed at the drift ratio of 1.23%. In addition, NRC-7 showed vertical cracks immediately before failure, which is expected to be due to the high ratio of longitudinal rebars causing concrete cracking between the rebars. NRC-8 and NRC-10 showed almost the same behaviors as that of NRC-7. In case of NRC-9 specimen, which was subjected to a low level of axial load (i), showed similar behaviors to that of NRC-4.Judging from the observed behaviors of the test specimens, most specimens, except for NRC-5, showed flexure-shear failure mode as designed because the longitudinal reinforcing bars were yielded before attaining the peak load. Unlike test plan, however, specimen NRC-5 was failed in shear due to the inclined cracks appeared in the plastic hinge before the longitudinal rebars were yielded (see ). The difference between the predicted failure mode and observed failure mode of specimen NRC-5 was attributed to the fact that the wide space of transverse reinforcement was not effective on confining the concrete and on resisting high applied axial load; thus, lowered ductility and shear failure might occur a shows a comparison of load-drift envelop curves for columns NRC-4, NRC-1, and NRC-5, which were subjected to different axial load levels of 0.06Agfc′, 0.27Agfc′, and 0.38Agfc′, respectively. In the figure, as the axial load increases, the peak load also increased; the strengths of NRC-4, NRC-1, and NRC-5 were 69.14, 109.3, and 128.09 kN, respectively. In contrast, the deformation capacity of the column showed the opposite results; as the axial load increased, the deformation capacity decreased. From the test results shown in b, the trend of the peak load and deformation capacity of these specimens matching with the level of axial load were almost the same as those of NRC-4, NRC-1, and NRC-5. In c and d, no significant difference was observed between the two different hook angles (90° for NRC-1 and NRC-7 specimens, and 135° for NRC-2 and NRC-8 specimens). This is because the stirrups were widely spaced and did not show significant strain (d). Thus, the difference between the transverse reinforcement hook angles did not considerably contribute to the shear capacity of the column for the given test condition.e presents the effect of longitudinal reinforcement ratio (ρl) on the lateral load-drift envelopes: NRC-1 with ρl |
= 1.06% and NRC-3 with ρl |
= 1.51%. Both the strength and deformation capacity of specimens increased with increasing longitudinal reinforcement ratio. f compares the effect of column height (or shear span to depth ratio) on the load-drift curves for NRC-1 and NRC-6 specimens. The figure shows that reducing the column height increased the strength by about 25.53%, which indicates that the flexural capacities for NRC-1 and NRC-6 were almost the same: Mn |
= 181.5 kN m for NRC-1 and Mn |
= 176.6 kN m for NRC-6.This section presents the investigations based on the test results in various factors: dissipated energy, damping ratio, strain profiles, drift capacity, stiffness, ductility, plastic rotation (a), and failure probabilities.Based on the hysteretic loops of the load-drift curves shown in , the dissipated energy of the columns was investigated. In this study, the dissipated energy was evaluated as the areas bounded by the hysteretic loops for each loading cycle. shows a comparison of dissipated energy for test specimens in accordance with test parameters.a shows the effect of the column height on the dissipated energy. As shown in the figure, the shorter column (NRC-6) showed greater dissipated energy than the longer column (NRC-1). The effect of the axial load level on dissipated energy is presented in b, showing that as the axial load increased, the dissipated energy also increased. However, e shows that NRC-10 specimen with a high level of axial load (44%) exhibited less dissipated energy than that of NRC-7 (31%).No significant effects of longitudinal reinforcement ratio and hook angles on the dissipated energy were observed as shown in c and d. The dissipated energy of NRC-3 and NRC-2 was almost the same as that of NRC-1. f shows that the dissipated energy of NRC-8 specimen with a hook angle of 135° was slightly less than that of NRC-7 specimen with a hook angle of 90°, but the difference was not considerable.In addition, the damping ratio (ξ), which is one of the important indices to represent the dynamic response of the structures, is also presented in . ξ is defined as Ed/4πEs, where Ed is the dissipated energy per cycle, and Es is the elastic strain energy. In the cases of NRC-1–NRC-6 specimens, the damping ratios were around 0.15 at elastic state, and decreased to 0.08–0.12 at the drift level of 1%. However, with accumulating inelastic damage, the damping ratio then increased up to almost 0.2. Nikbakht et al. a shows that the NRC-6 specimen with low shear span to depth ratio produced less damping ratio than that of NRC-1 specimen. In b, as the axial load increased, the damping ratio also increased. At the drift ratio of 1.65%, the NRC-5 specimen exhibited a damping ratio of 0.22, while the damping ratios of NRC-1 and NRC-4 were 0.14 and 0.11, respectively. On the other hand, e, which shows the damping ratio according to the axial load level, shows a different trend and complex fluctuation compared to that in c, d, and f shows that the use of high longitudinal reinforcement ratio and 135° hook angle reduced the damping ratio. This is mainly because the high longitudinal reinforcement ratio and 135° hook angle increased the elastic strain energy.Strain profiles for concrete, longitudinal rebars, and transverse rebars were obtained from the test (). At the start, the strain of the transverse rebars was zero (d); meanwhile the longitudinal rebars and concrete column were already in compressive deformation due to axial load (e and f). The initial strain of the longitudinal rebars did not exactly match that of the concrete column, which is assumed to be due to measurement error. In the lateral load-concrete strain curve (e), it can be seen that the concrete strain was non-symmetrical, which is attributed to the existence of the axial load. At the drift ratio of 2.5%, the concrete crushing developed in the compression side. Before the concrete crushing, the longitudinal rebars yielded in the tension side (d, the deformation of transverse rebar was relatively small in comparison with yield strain. Hence, the contribution of the transverse rebars to the seismic capacity was not considerable. shows the variation of the depth of the compression zone for NRC-1 specimen. In the figure, the neutral axis and the depth of the compression zone were simply determined by using two strain data at the tension and compression longitudinal reinforcement. Generally, with increasing load, the neutral axis shifted upwards and thus the depth of the compression zone reduced. The final depth of the compression zone was 140.5 mm. presents the variation of the depth of the compression zone in the specimens in response to different levels of axial load. In the case of NRC-4 subjected to the axial load level of 0.06Agfc′, the ratio cu/h decreased from 1.0–0.1 immediately after loading, but increased again up to 0.2 after the longitudinal rebars yielded at the drift ratio of 1.7%. As shown in the figure, the effect of the axial load on the depth of the compression zone of columns is significant; for example, the ratios of cu/h are 0.1 and 0.75 for the axial load levels of 0.06Agfc′ and 0.38Agfc′ at the drift ratio of 1.4%.In this study, to investigate the drift capacity of the test specimens, the drift capacity (θu) was defined at the point where the applied load dropped to below 80% of the peak load (refer to presents the drift capacity (θu) of the existing test specimens Based on the backbone curves acquired from the test results (see ), nonlinear load-deformation curves were established for the application of the nonlinear load-deformation curves to the performance-based design. shows the established nonlinear load-deformation curve of a control specimen, NRC-1. In the figure, the data of the backbone curve was linearly extended to 80% of the peak load to define the post failure behavior since the test was terminated before it reached the point of 0.8Vmax. The failure of specimens was defined at the point where the lateral load-carrying capacity dropped to below 80% of the peak load. Based on the nonlinear curve as shown in , Ke was defined as effective stiffness which was evaluated in the initial segment of the test backbone curve; θe [= 0.75Vmax/(KeL)] was defined as the drift ratio at 0.75Vmax according to ASCE 41-13 ). μ was defined as drift ductility factor at specimen failure , a (=θu |
− |
θy) was defined as the flexural plastic hinge rotation of the columns at significant loss of lateral load-carrying capacity Detailed results of nonlinear modeling parameters (Ke, θy, θu, μ, and a) for all specimens are presented in . In the positive direction, the yield drift ratios of most specimens were around 0.5%, except for NRC-5 and NRC-9, of which the values were 0.33% and 0.9%, respectively; the ultimate drift ratios of most specimens were around 2.5%, except for NRC-4, NRC-5, and NRC-9, of which the values were 4.37%, 1.66%, and 0.9%, respectively. The drift ductility factor of most specimens was around 5, except for specimen NRC-4, of which the value was 11.64; similarly, the flexural plastic hinge rotation a was around 0.020 for most specimens except for NRC-4, NRC-5, and NRC-9 specimens, of which the values were 0.040, 0.013, and 0.043, respectively. Meanwhile, the effective stiffness showed variation from 4.49 to 16.48 kN/mm. In the negative direction, the yield drift ratio, the ultimate drift ratio, the drift ductility factor, and the flexural plastic hinge rotation a of most specimens showed almost the same trend as shown in the positive direction, while the effective stiffness showed a different trend.The applicability of the nonlinear modeling parameters presented by ASCE 41-13 shows the modeling parameters presented by ASCE 41-13 explaining the determination of the modeling parameters in this study). As can be seen in the Table, for low axial load level (P/Agfc′≈0.1), the modeling parameters (a and b) in this study were determined to be 0.022 and 0.022, respectively, which were greater than those specified in ASCE 41-13 Additional 54 EA test results obtained from PEER DB shows the geometries and material properties of the test results including PEER DB ). Therefore, the modeling parameter (in this study, a) should not be determined as a mean value; instead, the parameter needs to be investigated and determined based on column failure probability assessment.) is recommended to be 15% or 35% when concrete columns are in shear failure or flexure failure, respectively.In this study, the column failure probabilities (Pf) of the modeling parameter a were evaluated according to the plastic deformation capacity a (= |
θu |
− |
θy) from the test results. As presented in , the fragility curve was investigated by using a lognormal distribution curve, which was expressed as Eq. where β is the coefficient of variation, atest and aASCE are the plastic rotation values evaluated from the test results and proposed by ASCE 41-13 . This indicates that the failure probability of the concrete columns using the modeling parameters proposed by ASCE 41-13 In this study, ten half-scale concrete column specimens with light transverse reinforcement were fabricated and tested under cyclic loading using double curvature test setup. The main parameters of this test are the applied axial load level, hook angle, longitudinal reinforcement ratio, transverse reinforcement ratio, and shear span to depth ratio. Based on the test results, the primary findings are as follows:All specimens, except for NRC-5, were observed to be failed in flexure-shear mode as predicted based on the guidance specified in ASCE 41-13 Enlarging the hook angle of the transverse reinforcing hoops of concrete columns from 90° to 135° did not significantly improve the peak load and deformation capacity, but slightly lowered the dissipated energy and damping ratio. Specimen NRC-2 with the hook angle of 135° showed 8.2% and 13.3% reduction of the dissipated energy and damping ratio compared to those of specimen NRC-1 with the hook angle of 90°, at the drift ratio of 2%. In specimens NRC-7 and NRC-8, the hook angle presented almost the same trend of the dissipated energy and damping ratio as observed in the specimens NRC-1 and NRC-2. However, further research is necessary to make a general conclusion.In specimens NRC-1, NRC-4, and NRC-5, with increasing the axial load level, the peak load of the concrete columns subjected to lateral load increased up to approximately 63%, but their deformation capacity decreased up to approximately 62%. In specimens NRC-7, NRC-9, and NRC-10, the axial load level presented almost the same trend of the peak load and deformation capacity.In specimens NRC-1 and NRC-3, with increasing the longitudinal reinforcement ratio from 1.06% (NRC-1) to 1.51% (NRC-3), the peak load and deformation capacity increased up to 15.2% and 16.7%, respectively, but the damping ratio decreased up to 13.3% at the drift ratio of 2% while the dissipated energy did not show any significant difference.According to the results of fragility analysis using the existing and above test results, the nonlinear modeling parameter a, which is specified in ASCE 41-13 The history of seismic design codes for buildings in Korea can be briefly introduced as following:In Korea, the first seismic design code for buildings was established in 1988 by the Architectural Institute of Korea (AIK) based on ATC 3-06 In 2005, a new seismic design code, KBC 2005 The shear strength (Vn) of the reinforced concrete columns is evaluated as recommendation of ACI 318-14 where Vc is the shear strength provided by concrete (Eq. ) and Vs is the shear strength provided by transverse shear reinforcement (Eq. where P is the axial load, b and h are the width and depth of cross section of column, d is the effective depth, fc′ is the concrete compressive strength at the 28th day of concrete, Av is the area of transverse rebars, fyt is the yield strength of transverse rebars, and s is the space of transverse rebars.The plastic shear demand (Vp) of the reinforced concrete columns is evaluated as Eq. where As is the area of longitudinal rebars and fyl is the yield strength of longitudinal rebars.In concrete columns, most nonlinear deformations develop in the plastic hinge. Based on backbone curves acquired from the test, nonlinear modeling curves were recommended by ASCE 41-13 ). In the figure, the main parameters representing nonlinear behaviors are the modeling parameters a and b, where a is evaluated from the difference between the generalized deformations at points B and C in , and b is evaluated from the difference between the generalized deformations at points B and E in Thermo-coupled elastoplasticity models with asymptotic loss of the material strengthRate-independent finite elastoplastic equations with thermo-coupled effects are proposed to bypass the yield condition and loading–unloading conditions. These new equations are shown to be more realistic and of much simpler structure than classical equations. In a sense of thermodynamic consistency the strength property of elastoplastic solids is then studied from the standpoint of stress-bearing capacity. It is shown that asymptotic loss of the strength may be derived directly from elastoplastic equations, thus leading to the finding of a noticeable phenomenon, namely, asymptotic vanishing of the stress concurrent with developing elastoplastic flow. It is indicated that this finding may suggest a natural constitutive characterization of fatigue, fracture and failure as certain limiting cases of elastoplastic behavior. Simple models with asymptotic loss of the strength are constructed as examples of potential practical applications.the free energy per unit reference volumecomplementary thermo-elastic potential (see Eq. the plastic characteristic function (see Eq. the normalized plastic modulus (see Eq. the stress-rate loading function (see Eqs. the strain-rate loading function (see Eqs. increasing function characterizing free energy (see Eq. positive dimensionless constants (see Eq. the extremum point of the stress limit (see Eq. 2nd-order gradient tensor with Cartesian components ∂f∂Aij4th-order gradient tensor with Cartesian components ∂2W¯∂τij∂τklthe elastoplastic rigidity tensor (see Eqs. The load-bearing capacity of an engineering structure rests on the thermomechanical behavior of the applied materials in response to various loading conditions. Adequate and practical representations of thermomechanical behaviors of materials under various loading conditions are accordingly of central, substantial importance. In fact, it is at the heart of modern continuum mechanics and theory of materials as well as related engineering fields. In the framework of continuum mechanics, fundamental quantities representing thermomechanical responses of a deformable body include the deformation, the stress, the temperature and the heat flux, etc. Of them, the deformation quantity represents continuing shape changes of the material body from a kinematic standpoint, while the stress is the macroscopic characterization of the internal resistant reactions of the material body to experienced deformations due to the internal interactions characteristic of this material. Moreover, the temperature and the heat flux characterize thermal effects with dissipation in courses of motion and deformation. Then, the thermomechanical behavior of a material body is modeled by certain constitutive relations prescribing how the stress and the heat flux are related to deformation and temperature as well as their histories. Alongside certain universal physical laws common to all kinds of materials, constitutive relations of material behavior, also known as constitutive models of materials, play a central role in analyzing and assessing significant mechanical problems of materials and structures subjected to typical loadings and actions.Of particular interest is the assessment of reliability and safety problems associated with fatigue, fracture and failure, etc. In recent years, numerous studies have been made from various standpoints. Here, only certain representatives of most recent results are mentioned below. presented a general forming limit criterion for sheet metals with an ultimate split in the sheet and proposed a criterion for failure prediction in anisotropic sheet metals. A review in this respect is given by . Subsequent analyses and developments may be found, e.g., in for a study of the localization behavior of tantalum and stainless steel, for a model of small fatigue crack growth in metallic materials, for the path-dependence property of the forming limit and the fracture locus, for anisotropic materials under non-proportional loading and for path-independent forming limits etc., for an anisotropic stress-based criterion to predict the fracture mechanism etc., and, in particular, for latest advances concerning strain rate and temperature effects. On the other hand, studies have been made based on continuum damage mechanics. Recent results in this respect are presented, e.g., in for a ductile damage model with irreversible thermodynamics and for numerical treatment, for ductile damage evolution under multi-axial stress states, for a nonlocal model for anisotropically damaged metals, for a ductile damage criterion under multi-axial stress states, for test data for combined effects of stress magnitude and triaxiality on failure behavior etc., for damage evolution simulation under dynamic loading, for a modified damage model, as well as for a study of ductile fracture under various cases of triaxial stress. Furthermore, most recent results are given in for micro-mechanical studies in tri-axial stress cases and for a study of brittle to ductile damage based on viscoplastic models. Moreover, numerous studies have been devoted to understanding effects of microstructure on fatigue behavior etc. References in this significant respect seem immense. For samples of recent results, refer to It is noted that either additional criteria or augmented constitutive structures arising from additional variables should be introduced into the existing studies. In this contribution, an attempt will be made to treat fatigue, fracture and failure behavior of metals and alloys etc. from a fresh standpoint. The starting point is as follows. Since fatigue, fracture and failure manifest themselves as extreme aspects of thermomechanical behavior of materials, it may be natural that they should be incorporated as inherent features into constitutive models. As such, various complicated phenomena related to fatigue, fracture and failure may be derived and predicted as direct consequences of constitutive models of materials.The above idea appears to be attractive, considering the current state of investigations into problems concerning fatigue, fracture and failure (cf., e.g., in the respect of fatigue failure). However, a question arises as to whether it is feasible to develop and establish constitutive models incorporating fatigue, fracture and failure as inherent physical features in a realistic sense. It appears far from being simple to deal with this challenge, whenever the essential features of the extreme material behavior close to and even just at fracture and failure are taken into consideration. In fact, usually pronounced dissipation with thermal effects will be generated just at fracture and failure, displaying markedly irreversible feature. Moreover, usually large inelastic deformations will be induced with strong geometric and physical nonlinearities. In particular, large deformation may be coupled inextricably with pronounced thermal dissipation, leading to the four fully coupled fields of deformation, temperature, heat flux and stress in a material body. These features are typical of materials undergoing elastoplastic deformations, such as single- and polycrystalline metals, high-temperature superalloys in aircraft engines (cf., e.g., ), and shape memory alloys undergoing phase transitions (cf., e.g., The above suggests that large elastoplastic deformations coupled with thermal effects should be the very features of fracture and failure behavior. It seems that this fact has long been well established by experimental tests for metals undergoing plastic deformation, but it has received not so much attention. Usually, attention is directed to cases at small isothermal deformation. In general, however, finite elastoplastic deformations coupled with pronounced thermal effects should be brought into focus in further understanding and characterizing fatigue, fracture and failure behavior for metals and alloys, etc. Toward this purpose, the main effort will be devoted to the following three respects. Firstly, large deformation elastoplasticity models with strong heat flux should be established in an explicit, free sense of identically fulfilling the restrictions stipulated by the second law for intrinsic dissipation. Secondly, the meaning of fatigue, fracture and failure should be rendered clear and precise in a phenomenological sense without going into unduly complicated details at various microstructural levels, albeit the latter are evidently essential to the understanding of the failure mechanisms. Thirdly, it should be demonstrated how fatigue, fracture and failure behavior may be incorporated as inherent features into thermo-coupled elastoplasticity models.An initial study of the above respects will be made in this contribution. It is intended for a direct approach to modeling failure behavior of elastoplastic materials such as metals and alloys, etc. Toward this objective, elastoplastic constitutive relations of phenomenological nature will be established in a broad sense with no assumptions concerning microstructural details. Accordingly, such relations will be compatible with and adaptable to various microstructural mechanisms. The latter may play a basic role in explaining and even determining macroscopic constitutive quantities.The main contents of this article are arranged as follows. In Section , thermo-coupled elastoplasticity models of Eulerian rate type will be established in a broad sense. The thermodynamic restriction from the second law, i.e., the Clausius–Duhem inequality, will be identically satisfied by presenting the free energy function and the specific entropy function in explicit form. New results will be derived and shown to be not only much simpler than the previous results, but applicable to a much broader case. In Section , a new formulation of rate-independent flow rule will be suggested for the purpose of bypassing the yield condition and hence the non-smooth transition between the elastic and the plastic behavior, thus leading to free, smooth rate-independent elastoplastic equations without the extrinsically imposed conditions including the yield condition and the loading–unloading conditions. In Section , it will be shown that this new formulation will incorporate not only the essential features of the classical rate-independent elastoplastic formulation with the extrinsic loading–unloading conditions at yielding, but may be much simpler and more realistic as compared to the latter. In Section , a unified macroscopic characterization of fatigue, fracture and failure behavior will be introduced with a new understanding, namely, it is understood to be asymptotic loss of the strength based upon the stress-bearing capacity of solid materials. Then, this understanding will further be investigated in association with the hardening moduli introduced, and straightforward conditions for asymptotic loss of the strength of elastoplastic materials are presented. In Section , simple models with asymptotic loss of the strength will be constructed for potential practical applications. Discussions and remarks concerning relevant issues will be presented in Section that pronounced dissipation via thermal effects is the very essence of elastoplastic deformation, as mentioned before (footnote ). This suggests that elastoplastic behavior should be coupled inextricably with heat. In particular, this is left outstanding in cases without temperature change in surroundings. As a result, a sound, in-depth study of elastoplastic deformation may in no way be separated from the principles of thermodynamics, but has to be placed on the ground of thermodynamics within a broader scope. To this end, this has been done from various standpoints; see, e.g., , and many others. In a newest development within a thermodynamic framework based on Lagrangian formalism, ) have derived significant results for the constitutive structure revealed by continuous symmetries.Most recently, an explicit thermodynamic treatment for a general formulation of Eulerian thermo-elastoplasticity has been proposed in . In this treatment, both the free energy and the specific entroy in explicit form are worked out in the sense that the restriction from the second law may be identically fulfilled for arbitrary forms of constitutive functions introduced.Below we shall present a new development of the studies in . We shall give only a short account of relevant results from these studies and focus on new results.Consider a deforming material body. Let F and L be the deformation gradient and the velocity gradient. The symmetric part of L yields the stretching D. Moreover, let σ be the Cauchy stress (true stress). The Kirchhoff stress τ is given byThe absolute temperature is designated by T and always positive, i.e. T>0. The heat flux per unit current area is denoted q. The divergence of q, i.e. ∇·q, provides the heat flowing out of the unit current volume.Let ψ and η be the Holmholtz free energy and the specific entropy per unit reference volume. Then, the energy balance (i.e., the first law) and the Clausius–Duhem inequality (the second law) may be written in the forms:In the above, ζ is the heat supply per unit reference volume.An enhanced form of the Clausius–Duhem inequality equation requires that the intrinsic dissipation should always be non-negative, namely,for every possible thermodynamic process.The heat flux q may be related to the temperature gradient ∇T by an generalized Fourier’s law of the form:where the 2nd-order tensor H is the heat conductivity tensor. It may be clear that the second term in Eq. is positive, whenever H is positive definite. In this case, Eq. The two thermodynamic laws in the above are universal for all kinds of materials. Constitutive relations for thermo-coupled elastoplastic behavior and the interplay between them and the thermodynamic laws will be presented in the succeeding subsections.In the past decades, many formulations of finite elastoplasticity have been proposed from various standpoints (see ). Here we direct our attention to the objective Eulerian rate formulation (cf., e.g., The starting point of the Eulerian rate formulation is the separation of the total stretching D into an elastic and a plastic part, as shown below:where the De represents the contribution from recoverable elastic behavior, referred to as the elastic stretching, and the Dp the contribution from irreversible plastic behavior, referred to as the plastic stretching. Toward a consistent combination of elastic and plastic behavior, objective Eulerian rate constitutive equations should be established for the elastic and the plastic stretching De and Dp in a consistent sense. This will be done separately.is a complementary thermo-elastic potential and the τolog is the corotational logarithmic rate of the Kirchhoff stress τ. Detail may be found in, e.g., The next step is to establish a flow rule for the plastic stretching Dp. Usually, it is concerned with a few respects including formulations of yield function, hardening behavior and loading–unloading criteria, etc., as will be done below, separately.As is commonly known, a central concept for plastic behavior is the yielding state. The plastic flow, i.e. Dp, is induced only in the case when the yielding state is attained and maintained. The yielding state is formulated in terms of a yield function f. The yield surface f=0 in stress–temperature space changes itself both in size and in shape, known as hardening behavior. To characterize the hardening behavior, we introduce a scalar quantity, ϑ, and a stress-like tensor quantity, known as the back stress and denoted α, both evolving with the development of plastic flow. Then, generally the yield function f is formulated as follows:A normality rule for Dp is given as followsIn the above, ρ is the plastic indicator associated with the loading–unloading criteria (see Here and henceforward, the pair (fˆ,f̆), called the stress-rate loading function and the strain-rate loading function, is given by (cf. fˆ=∂f∂τ:τolog+∂f∂TṪ,f̆=∂f∂τ:S:D+∂f∂T-∂f∂τ:S:∂2W¯∂τ∂TṪ.Throughout, S is used to denote the thermo-elastic stiffness tensor, namely,The plastic modulus hˆ in the flow rule Eq. Now we are going to formulate the evolution equations for the two hardening variables ϑ and α. The hardening variable ϑ is taken to be the effective plastic work specified bywith the deviatoric stress τ̃, while the back stress α is governed bywhere the 4th-order hardening tensor H may rely on the variable set (τ,α,ϑ,T) and the αolog is the logarithmic rate, from the plastic consistency condition, namely, ḟ=0, we derive the plastic modulus hˆ in Eq. It should be pointed out that the previous study () is based on the usual plastic work θ (see Eq. given later), instead of the effective plastic work ϑ. Here, use of the effective plastic work given by Eq. represents a new development. The main reason lies in the fact that the latter is always non-negative for a convex yield function and accordingly most appropriate to the role of a time-like thermodynamic variable. Furthermore, this will result in considerable reduction in thermodynamic treatment, as will be shown in the next subsection.The constitutive relations given above constitute a complete formulation of thermo-coupled elastoplastic behavior. Of them, the plastic indicator ρ represents the typical feature of rate-independent elastoplasticity. In fact, it prescribes the loading–unloading transition at yielding and gives a switching rule between elastic and plastic behavior. A noticeable fact is that this transition is not smooth. As a consequence, there always emerges a jump at this transition. A further study in this respect will be presented in the next section., the intrinsic dissipation should be non-negative for every thermodynamic process, since pronounced dissipation is always induced in every process of elastoplastic deformation, as has been known from experience and observed in experiments. In a most recent study (), it has been shown that it is possible to find out the free energy ψ and the specific entropy η in explicit form which identically fulfil the second law with non-negative intrinsic dissipation for arbitrary forms of constitutive functions introduced. For our purpose here, following the explicit approach in the just-mentioned reference we treat a broad case with a general form of yield function f as shown in Eq. and with a general form of nonlinear anisotropic hardening equation. Reformulating the hardening tensor H in Eq. rely on the effective plastic work ϑ, the temperature T, the Kirchhoff stress τ and the back stress α, in general, and are referred to as Prager’s modulus and hysteresis modulus (the origin of these names will be explained below), respectively, and the hardening tensor H0 is a dimensionless 4th-order constitutive tensor that may rely also on the variable set (ϑ,T,τ,α).In usual forms of anisotropic hardening, the simplest case with a constant c and ω=0 as well as the H0 given by the 4th-order identity tensor I was proposed earlier by and a development with a non-vanishing constant ω≠0 was suggested later by plays a role in introducing a hysteresis effect on the evolution of the back stress α. The foregoing names of c and ω are derived from these facts.For arbitrary forms of the constitutive functions introduced, a free energy function ψ and a specific entropy function η in explicit form may be constructed by following the procedure in , which identically satisfies Clausius–Duhem inequality with non-negative intrinsic dissipation. Here, these two explicit functions with the new development are of the forms:where the ψ0(T) is the specific heat capacity of the material at issue, the θ is the plastic work given byand the φ=φ(ϑ,T) is a monotonically increasing function of the effective plastic work ϑ, namely,Then, the intrinsic dissipation is given byThus, for a convex yield surface f=0 containing the back stress point α, we have it follows that the intrinsic dissipation is always non-negative. Thus, the inequality equation is identically fulfilled. Moreover, Clausius–Duhem inequality is also identically fulfilled for a positive definite heat conductivity tensor H.It turns out that the new development presented here not only applies to a fully general case but leads to much simpler results for both the free energy function and the specific entropy. This becomes clear by comparing Eqs. with the corresponding results given in the previous works (). Moreover, it may be noted that here the constitutive tensor H0 in the hardening equation is allowed to be fully general, whereas in the previous works just mentioned this tensor should be derived from a scalar potential of limited form.Eventually, the two thermodynamic laws together yield an explicit equation below (cf. Eq. with the specific entropy η given by Eq. and the positive intrinsic dissipation D by Eq. It should be pointed out that each constitutive function should fulfil the joint invariance restrictions from the objectivity principle and the material symmetry principle. For initially isotropic materials, each of them is an isotropic function. Details for the treatment for any given type of initial anisotropy, such as crystallographic symmetry etc., may be found in In the structure of the theory of rate-independent elastoplasticity, the yield condition and the loading–unloading conditions are introduced as extrinsic restrictive conditions into the constitutive formulation, as can be seen from the expression for the plastic indicator ρ given by Eq. . This is the unavoidable consequence of the idealization of the realistic inelastic deformation behavior of materials such as metals etc. It is commonly known that as one of the typical feature of rate-independent elastoplastic formulations there is always a non-smooth transition between elastic and plastic behavior. Indeed, according to the loading–unloading criteria, only recoverable elastic deformation is induced in the unloading case, while irrecoverable plastic deformation is generated only in the loading case. The non-smooth transition implies that there are always discontinuous changes from larger elastic moduli to much smaller elastoplastic moduli. It is known that such discontinuities have been the source of tedious calculations as well as numerical error and instability in large-scale numerical treatment. Considerable effort should be made in coping with such discontinuities and, in particular, the yield condition.On the other hand, it may be evident that, according to classical elastoplastic equations, the high cycle fatigue phenomenon under cyclic stresses below the yield limit could in no way be induced. In fact, in every process of cyclic stresses below the yield limit, an elastoplastic material in classical sense would experience only reversible elastic deformations and then invariably return to the same state.In addition to the above issues, the flow rule with the extrinsic restrictive loading–unloading criteria as given by Eq. is not merely an approximation of realistic inelastic behavior in an idealized limiting case, but renders the constitutive structure overloaded and complicated. On account of all these issues and others, it may be meaningful to find out a new, simpler and yet more realistic formulation of rate-independent elastoplastic behavior free from the foregoing issues. However, it appears that any development in the just-mentioned sense could not be made within the scope of the current formulation of rate-independent elastoplasticity. Beyond the scope of rate-independent behavior, development may be made within the scope of rate-dependent behavior, treating the rate-independent behavior as a limiting case. Comments and references in this respect may be found in However, rate-dependent equations beyond the scope of rate-independent behavior could not be formulated without substantial changes in constitutive structure. Because of the time-dependence property of rate-dependent behavior, numerical implementation of rate-dependent equations entails discretization of the time domain and, consequently, the computational effort would constantly grow as the time is progressing. Moreover, the transition to the rate-independent case is not given by a continuous but, instead, a singular limit. Thus, for elastoplastic behavior without appreciable rate effects, it may be substantial to stay within the scope of rate-independent formulation. For a detailed account of the background and motivation, refer to the foregoing reference.It should be pointed out that unconventional elastoplasticity models have been established in treating issues concerning discontinuous tangential moduli as well as cyclic loading behavior etc., such as two-surface models and multi-surface models and many others. For details in these respects, refer to, e.g. the monograph by . In particular, significant studies have been made with no reference to the loading–unloading criteria, leading to the endochronic model by for the subsequent developments), etc. The former is of integral type and formulated in terms of an intrinsic time measure, while the latter is of rate type and presented with a normal-yield surface and a subloading surface.Considerable changes both in formulation and in structure should be introduced, as evidenced in the previous developments. Here we would like to propose a new idea to resolve the aforementioned issues. The starting point is as follows. In accord with realistic inelastic behavior, irrecoverable plastic deformation should always be concomitant with recoverable elastic deformation, but the former becomes appreciable only when the yielding state in the classical sense is approached, and otherwise the former is negligibly small as compared with the latter, and eventually plastic flow becomes dominant at yielding.), it has been shown that, in the absence of thermal effects, it is possible to establish a new flow rule based on the above idea, in which the yield condition is not involved at all. Instead, the yield function in the usual sense will manifest itself with a new, perhaps more far-reaching role in the new formulation. Accordingly, new rate-independent elastoplastic equations in this sense are free from the usual yield condition and loading–unloading conditions and, accordingly, more realistic and of much simpler structure than the classical equations. In what follows we are going to show that it may be possible to do so in a broader sense with thermal effects.Toward formulating a new flow rule, we need a new formulation of the function f as shown in Eq. . From now on, we reformulate f in a new form below:It is required that the physical dimensionality of either g or r is the same as that of stress. Besides, the function g is of the following properties:A non-negative function g of the above properties is referred to as an effective stress norm. Besides, the r is just the yield strength in the usual sense. Since the concept of yielding will not be involved in the ensuing development, here the r will be rephrased as the stress limit, corresponding with the fact that it provides a limit for the magnitude of the effective stress (τ̃-α) and hence τ̃, as will be seen in In the subsequent development, the function f introduced in the above will not be used for the purpose of formulating the yield criterion. Instead, it will be endowed with a perhaps more far-reaching role in the new development, as will be shown in the next section. On account of this, the function f is referred to as plastic characteristic function.To see the meaning of the plastic characteristic function f, as an illustrative example we take von Mises function into consideration. In this case, we haveHere, the effective stress norm g is just the magnitude of the effective stress (τ̃-α).With the aforementioned idea in mind, by replacing the discontinuous plastic indicator ρ specified by Eq. given later) we propose a new rate-independent flow rule as followsIn the above, β⩾0 is a non-negative dimensionless parameter and will be referred to as the plastic index. Generally, this index may rely on the variable set (ϑ,T,τ̃,α), namely,Moreover, at this stage the quantity ϒ, called the loading factor, may be given either byIn the above, the two pairs (fˆ,f̆) and (hˆ,h̆) may be recast in new forms by the plastic characteristic function f given by Eq. hˆ=∂r∂ϑ-∂g∂ϑ(τ̃-α):∂g∂τ+∂g∂τ+∂r∂α:H:∂g∂τ,The loading factor ϒ is already given in Eq. . According to the classical formulation, Eqs. ). Hence, the loading may be formulated in terms of either the stress rate or the strain rate, as shown in Eqs. . In addition, the modulus h̆ is referred to as the normalized plastic modulus. As will be seen in Eqs. given later, the plastic modulus hˆ and the normalized plastic modulus h̆ play a basic role in the elastoplastic compliance and rigidity tensors, respectively.is a smooth function and still referred to as the plastic indicator. This factor is introduced just in the spirit of the idea at the outset of this section. The property of this plastic indicator is shown in for a few constant values of the plastic index β. It may be seen that, for a fairly large β, say 10, the smooth plastic indicator ρ approaches 1 very rapidly when f=g-r is going very close to 0, and it goes sharply down to 0 as f=g-r becomes slightly smaller than 0. Then, it is clear that, whenever ϒ>0, plastic flow is always induced concomitantly with elastic deformation, but becomes appreciable only on the verge of the yielding state f=0 in the classical sense and identical to the classical case at the yielding state f=0. The elastic deformation dominates whenever f<0, whereas the plastic deformation prevails whenever f is going very close to 0.The hardening equations are still given by Eqs. . Besides, the free energy and the specific entropy are still given by Eqs. . Now the intrinsic dissipation D (cf. Eq. with the plastic indicator ρ given by Eq. , we obtain a direct Eulerian rate equations for thermo-coupled elastoplastic behavior as follows:On the other hand, utilizing the equationh̆>0 we obtain another form of direct Eulerian rate equation below:τolog=S:D-S:∂2W¯∂τ∂TṪ-12ρh̆f̆+f̆S:∂g∂τ,Θ¯=-S:∂2W¯∂τ∂T+12(1+sgn(f̆))ρh̆∂g∂τ:S:∂2W¯∂τ∂TS:∂g∂τ., the sgn(x) is used to denote the sign function. is free from the yield condition and the loading–unloading conditions. The new formulation is simpler in structure and more realistic as compared to the usual formulation based on the yield condition and the loading–unloading conditions. Now, both the new rate Eqs. are continuous with respect to either the stretching D or the stress rate τolog, thus bypassing the discontinuity issue at the transition between elastic and plastic behavior, as encountered in the usual formulation.It should be noted that, unless ρ=1, the plastic flow Eq. . Usually, given the deformation, it is required to find out the responses for the stress, the temperature and heat flux. On the other hand, the normalized plastic modulus h̆ in Eqs. , will never become vanishing, whereas the plastic modulus hˆ in Eqs. , may become vanishing in the case of perfect elastoplasticity without hardening. On account of these facts, the plastic flow equation given by Eqs. is most suitable and will be taken into account.The plastic index β in the new flow rule Eq. plays a significant role. It prescribes under what circumstances and to what extent the plastic flow becomes appreciable and even dominant, as shown in . For a fairly large β, the plastic flow prevails only when the stress point stays in the vicinity of the surface f=f-g=0, and otherwise the plastic flow is negligible. For the sake of simplicity, the β at isothermal case may be taken to be a constant. In this case, it may be evaluated by fitting the almost linear part of a realistic uniaxial stress–strain curve with smooth transition.In the free elastoplastic equations proposed, the surface f=0 serves no longer as a yield surface as in the usual theory, but it is endowed with a perhaps more far-reaching property in the new theory, as will be indicated in the next section.The smooth elastoplastic equations proposed in the last section are free from the extrinsic restrictive conditions introduced into the current theory of rate-independent elastoplasticity, such as the yield condition and the loading–unloading conditions etc. As is commonly known, these conditions, in particular the yield condition, are among the representative features of classical formulation. It may be of interest to know what the usual yield condition implies in the new formulation. The study in this respect will be the main objective of this section.In the following development, it will prove helpful to take a geometric viewpoint. A given pair (τ,T) is regarded to be a point in the Kirchhoff stress–temperature space. A function f=g-r determines a surface in this space via the equationfor any given values of the effective plastic work ϑ and the back stress α. During a process of elastoplastic deformations, the two hardening variables ϑ and α are changing with the development of plastic flow and, accordingly, Eq. represents a continuous family of surfaces moving in the foregoing space. In the conventional theory of elastoplasticity, the function f is known as the yield function and the moving surface f=0 as the yield surface. The implications of the classical notions in the new theory are disclosed below.Let(τ,T,α,ϑ)be the stress, the temperature, the back stress and the effective plastic work in a process of elastoplastic deformation with. Then, the point(τ,T)in the stress–temperature space is always moving toward and approaching the surfacef=g-r=0, no matter where initially the point(τ,T)stays inside or outside or on this surface. When the point(τ,T)is on the surfacef=0, it keeps staying on this surface.The proof is as follows. In a process of elastoplastic deformation with ϒ>0, the changing rate of the function f is given by (cf., Section 4 in into this equality and then using Eqs. with f̆=ϒh̆. From this and ϒ>0 and h̆>0 (see footnote ), we deduce that the rate ḟ is always positive for ρ<1 and always negative for ρ>1. Thus, we may infer that, in every process of elastoplastic deformation with ϒ>0, the function f is monotonically increasing for ρ<1 and decreasing for ρ>1. Since ρ<1 and ρ>1 (cf., Eq. ) imply gr<1 (i.e., f<0) and gr>1 (i.e., f<0), respectively, we further infer that the value of the function f is always approaching 0, no matter what its initial value may be. Moreover, ρ=1 yields rr=0, i.e., f=0. This concludes the proof.Noticeable consequences may be derived from . It turns out that the yield condition and the yield surface in the classical elastoplasticity now become a stable limit for the stress and a stable limit surface for the stress–temperature point, respectively. In every process of elastoplastic deformation with ϒ>0, the moving point (τ,T) in the stress–temperature space is always moving toward and approaching this limit surface. In particular, that is the case no matter where the point(τ,T)stays inside or outside this surface at any time. This limiting process looks as if the point (τ,T) would always be drawn toward the limit surface by a strong “attraction”. This fact leads to consequences in two respects. One is that the magnitude of the stress is always bounded by a limit, and the other is that not only the yield condition in the classical sense need not be treated in both analytical and numerical treatment, but also possible numerical errors and instabilities will not be accumulated and, instead, will be suppressed automatically. It is known (see, e.g., ) that the enforcement of the yield condition entails considerable effort in large-scale FE computations and has been the source of error and instability. Thus, the new formulation with the far-reaching property just disclosed not only simplifies numerical procedures considerably, but renders computations more efficient and stable.In the new formulation with smooth elastoplastic equations, the yield function f=g-r in the classical sense plays a significant role in charaterizing the essential features of elastoplastic behavior with novel physical meanings, as indicated in the foregoing. A point of departure here is that the function f=g-r is no longer introduced to enforce an extrinsic restrictive condition, i.e. the yield condition in association with the non-smooth transition between elastic and plastic behavior. On account of the new meaning just explained, the function f=g-r has been referred to as the plastic characteristic function and, accordingly, the surface f=0 is referred to as the plastic characteristic surface.It follows from the foregoing facts that, in the free elastoplasticity model proposed, the classical yield function turns out to manifest itself with a perhaps more far-reaching role in characterizing the strength features of elastoplastic solids. Namely, it serves as a stable limit for the stress. In the extreme case, it is expected that constant reduction in the material strength will eventually result in the loss of stress-bearing capacity and, then, fracture and failure may be incurred. As will be shown in the next section, the strength loss of an elasoplastic material accompanying fatigue, fracture and failure, etc. may be modeled as certain limiting cases derived straightforwardly from the smooth elastoplastic equations proposed.As indicated in the introduction, fatigue, fracture and failure of elastoplastic solids should pertain to inherent aspects of thermo-mechanical constitutive behavior of elastoplastic solids, albeit they may be regarded as extreme aspects. These aspects should be incorporated as intrinsic constitutive features into thermo-coupled elastoplasticity models. On account of significance in numerous related fields, it may be of particular interest to explore how this will really be achieved. The consequence may be evident: Whenever suitable constitutive models are well established, fatigue, fracture and failure etc. under various circumstances will automatically be derived as limiting cases from these models under loading processes as well as well-posed initial and boundary conditions, with no reference to any additional extrinsic criteria or assumptions. In this section we are going to explain that it is possible to achieve this goal in the framework of the free elastoplastic equations proposed.As indicated in the introduction, high cycle fatigue would be excluded from usual elastoplastic models. This exclusion arises from the idealized notion of yielding, namely, yielding emerges only when the stress reaches a threshold, i.e., a yield limit, and, prior to this threshold, only elastic deformation may be induced.According to the free elastoplastic equations proposed, plastic deformation is always induced concurrently with elastic deformation, albeit the former becomes appreciable only when the stress level is close to the classical yield limit. Now, high cycle fatigue under cyclic stresses below the yield limit may indeed be derived from the new elastoplastic equations. For instance, consider uniaxial tensile stresses repeatedly changing from 0 to a certain level, say τm<τ0. Here, τ0 is the initial yield limit. Then, in the idealized case of perfect elastoplasticity, the accumulated plastic work after N cycles may be derived following the procedure in ϑ(N)=23N(1+ν)τ02E∫0τm/τ0x3dxeβ(1-x2)-x2.Here, the compliance tensor ∂2W¯/∂τ2 is given by the isotropic elastic compliance tensor at infinitesimal strain. As such, E and ν are the Young’s modulus and the Poison ratio.In the case of high cycle fatigue, the stress amplitude τm is below the yield limit. It may be expected that, in the case of low cycle fatigue with the stress amplitude close to or even equal to the yield limit, the accumulation of the plastic work will become more rapid.Furthermore, we explain that thermal fatigue under cyclic temperature changes may also be derived as an inherent feature of the proposed model. In a thermal process in the absence of the stress, the changing of the stress limit r is induced by changing temperature. Usually, the stress limit r should go down as the temperature T goes up. In this case, we infer that the loading function f̆ (cf., for ∂r∂T<0 and Ṫ>0. Since the gradient ∂g∂τ does not vanish for τ=0, we deduce that both the plastic stretching Dp (see Eq. ) will be induced at a process of pure heating. Accordingly, the effective plastic work ϑ will also be accumulated in a process of cyclic temperature changes.It may be expected that the accumulation of the effective plastic work may become more appreciable for cyclic thermomechanical changes both in stress and in temperature.After accumulation of the effective plastic work exceeds a certain level, the material strength will undergo a process of continuing reduction and may eventually be lost, as will be seen in the next subsection.From a phenomenological standpoint, fatigue implies continuing reduction in the material strength with accumulation of the effective plastic work, while fracture and failure may follow as consequences of eventual loss of the material strength. Here, the essential point may be as follows: From a thermo-mechanical standpoint, what the loss in the material strength really means and how it can be characterized. It appears that a unified, direct characterization of fatigue, fracture and failure behaviors accompanying such loss in the material strength has long been inaccessible for general multi-axial cases coupled with thermal effects. Since the stress just represents the resistant reaction of a solid to the experienced deformation, as indicated in the introduction, here the following understanding may be pertinent and perhaps substantial, namely, there will emerge asymptotic vanishing of the stress concurrent with continuing development of plastic flow. Indeed, the just-mentioned fact implies asymptotic loss of the resistance of a material to continuing deformation, namely, asymptotic loss of the stress-bearing capacity of a material.The above understanding leads to a thermo-mechanical characterization of the strength loss of an elastoplastic solid. Namely, the strength loss of an elastoplastic solid may be understood as the following asymptotic limit:The central result of this section is the following finding: In a broad sense the just-mentioned understanding may really be derived as limiting cases from the thermo-coupled elastoplasticity model proposed. The main result of this subsection is below.Consider the thermo-coupled elastoplastic model governed by Eqs.. Let the stress limit r, Prager’s modulus c and the hysteresis modulusωbe of the following limiting properties:Both the stress limit r and Prager’s modulus c tend to vanish as the effective plastic workϑgoes to infinity, viz.Asϑ→+∞, the limit of the hysteresis modulusωis no less than a positive constantω0, i.e.Then, in every process of elastoplastic deformation with unlimitedly growing effective plastic workϑ, both the back stress and the deviatoric stress are asymptotically going to vanish, namely,Toward the proof of the above Theorem, we first study the limit of the back stress α as t→+∞, i.e., ϑ→+∞. As ϑ becomes sufficiently large, Prager’s modulus c is vanishingly small (cf. Eq. ). In this case, the evolution equation for sufficiently large ϑ>0. This leads towhere the α0 is an initial value of the back stress at a sufficiently large ϑ0 and the Rlog is the logarithmic rotation (cf., we deduce that the value of the function f=g-r is always approaching 0 as ϑ→+∞. Hence, we infer that g should go to vanish as r goes to vanish (cf., Eq. , asymptotic loss of the strength of an elastoplastic solid is disclosed as an inevitable consequence of the free elastoplastic equations proposed. If the stress limit r, Prager’s modulus c and the hysteresis modulus ω introduced in the proposed equations are of the limiting properties shown by Eqs. , then follows asymptotic vanishing of the stress concurrent with unlimited development of elastoplastic flow. Since the stress represents just the resistant reaction of a solid material to experienced deformation, as indicated at the outset of the introduction, the asymptotic limit disclosed in suggests that a solid material at this limiting state is asymptotically losing its stress-bearing capacity. Consequences attendant with this limiting process may be various phenomena and effects at fracture and failure, etc.Here the essential point may be the following: Fracture and failure behaviors may be derived as limiting cases from thermo-coupled elastoplastic models in a sense of thermodynamic consistency and that may also be the case for fatigue behavior. Indeed, it may be concluded that asymptotic vanishing of the stress concurrent with constant development of highly dissipated thermo-coupled elastoplastic flow is just the thermomechanical essence of such extreme behaviors as fatigue, fracture and failure, etc. It may be noted that the just-mentioned thermomechanical characterization of fracture and failure at the macroscopic level of a material body in its own right is universal and straightforward, albeit unduly complicated, varied mechanisms may be involved at various levels of microstructures.The physical meanings of the conditions given in may be clear. The strength property of an elastoplastic solid is represented by the stress limit r and Prager’s modulus c as well as the hysteresis modulus ω, etc. Note that these three quantities characterize the hardening behavior of the solid at issue. The strength would be lost when both the stress limit r and Prager’ modulus c become vanishing with unlimited development of the effective plastic work. It may readily be understood that these conditions are not only sufficient, but necessary. In fact, the asymptotic limit representing asymptotic loss of the stress-bearing capacity could not be derived, whenever either of the r and c never becomes vanishing.Different cases of fracture and failure may be induced under various circumstances. Significant examples are necking of a cylindrical sample under growing tensile loads, fatigue failure under cyclic loadings, adiabatic shear banding and fragmentation at high strain rate, in particular under dynamic impact loadings such as ballistic assaults, initiation and development of cracks, formation and propagation of giant faulting zones at earthquakes, etc. Of them, the fatigue failure is concerned with gradual reduction in the material strength due to accumulation of the effective plastic work during a process of cyclic or repeated loadings. Usually, each cycle just produces small and even very small amount of the effective plastic work, leading to two well-known cases of fatigue, namely, low cycle fatigue and high cycle fatigue. Here it is noted that both cases may be explained to be natural consequences of the new, smooth elastoplasticity model proposed and, in particular, this is true for the high cycle fatigue. Indeed, according to the new model, plastic deformation may be induced at any level of stress, no matter how small it may be., it turns out that fracture and failure as limiting cases may just be intrinsic constitutive features incorporated into thermo-coupled elastoplastic models at finite deformation. It should be indicated that the strength loss may actually be induced at a certain value ϑ=ϑ0, since the magnitude ||τ̃|| may become vanishingly small for ϑ>ϑ0. Whenever realistic thermo-coupled elastoplastic models with asymptotic loss of the material strength as indicated in are established, fracture and failure will be derived automatically as various asymptotic limits for continuing development of thermo-coupled elastoplastic flow. Examples will be given in the next section.Two examples for elastoplasticity models with asymptotic loss of the material strength will be presented in this section. One is for isotropic hardening and softening, and the other for combined hardening and softening.For the sake of simplicity, we first consider the simplified case of neglecting the anisotropic hardening effect. The plastic characteristic function f=g-r is taken to be of von Mises form, namely,We present a stress limit r that goes up prior to a certain value of the plastic work and goes down to vanish beyond this value. With this in mind, the stress limit r is taken to be of the form:In the above, r0,s,a and ϑm are constitutive parameters. Of them, s and a are dimensionless quantities. The constant a/(s-a) therein is introduced to ensure that ϑ=ϑm is the extremum point at which the stress limit r attains its maximum. is of the following properties: Its initial value at ϑ=0 is given by r0; it goes steadily up from ϑ=0 to ϑ=ϑm; at ϑ=ϑm it attains the maximum rm; and as from ϑ=ϑm it goes invariably down to vanish. The maximum rm, i.e. the highest stress limit, is given by is described by the initial value r0, the maximal point ϑm as well as the two dimensionless quantities s and a. When the plastic work ϑ goes beyond ϑm, the slope of the stress limit r is controlled by a. With the same s, the greater the a, the steeper the slope, as may be seen in Here and henceforth, q=a/(s-a)>0. Thus, it is evident that the strain-hardening behavior with hˆ>0 is expected for 0⩽ϑ<ϑm, while the strain-softening behavior with hˆ<0 is anticipated for ϑ>ϑm. The critical case hˆ=0 is given at ϑ=ϑm.The constitutive parameters ϑm and a represent significant features of material failure. Brittle behavior may be expected for small ϑm and large a, while ductile behavior with a mild falling slope with growing plastic work may be anticipated for modest a. Generally, the four parameters r0,rm,ϑm and a are temperature-dependent. How the stress limit r is related to the temperature will be described by the temperature-dependence properties of these parameters. Usually, the initial value r0 and the maximum rm may decrease with growing temperature, while ϑm and a may increase with growing temperature. As such, at elevated temperature, the stress limit may be weakened and the ductility may become more appreciable. Further study in this respect will be done elsewhere.The plastic characteristic function f=g-r is given by Eqs. is given by the 4th-order identity tensor I, namely, the hardening equation Moreover, Prager’s modulus c and the hysteresis modulus ω are given bywith c0>0,ω0>0 and λ>0 . Here, λ>0 is dimensionless and fairly large, such that the value of the hyperbolic tangent function in Eqs. is almost equal to −1 and +1, separately, for ϑ<ϑ-δ and ϑ>θ+δ. Here δ/ϑm≪1 is fairly small. As such, Prager’s modulus c given by Eq. is given nearly by c0 for ϑ<ϑm-δ and goes down to vanish for ϑ>ϑm+δ, whereas the hysteresis modulus ω is nearly vanishing for ϑ<ϑm-δ and is given nearly by ω0 for ϑ>ϑm+δ.Evidently, the r,c,ω given meet the conditions given by Eqs. . Note here that the plastic modulus hˆ is of the form:hˆ=1.5c0+r′|τ̃-α||,0⩽ϑ<ϑm-δ,1.5r′||τ̃-α||-ω0(τ̃-α):α,ϑ>ϑm+δ.Here, r′=∂r∂ϑ. It may be clear that the strain hardening, i.e., hˆ>0, takes place for ϑ<ϑm-δ.In general, both c0 and ω0 may be of general form. For the sake of simplicity, both may be taken to be constant.In the preceding sections, thermo-coupled elastoplastic models have been proposed in a broader, more realistic sense. Free, smooth Eulerian rate equations for rate-independent elastoplastic behavior with thermo-coupled effects have been introduced without reference to the commonly assumed extrinsic restrictive conditions as formulated by the loading–unloading conditions based on a yield criterion in the usual rate-independent theory of elastoplasticity. The proposed models have been shown to identically fulfil the second law with positive intrinsic dissipation. The yield function in the usual theory has been found to play a more far-reaching role in characterizing the strength property in the new models, as indicated in . Furthermore, it has been found that asymptotic vanishing of the stress concurrent with constant development of elastoplastic flow may be derived as a natural, inevitable consequence from the proposed models. This leads to a unified, straightforward thermomechanical characterization of fatigue, fracture and failure, as summarized in The above fact suggests that extreme material behaviors such as fatigue, fracture and failure etc. may be incorporated as limiting cases into thermo-coupled elastoplasticity models. Accordingly, whenever thermo-coupled elastoplasticity models with asymptotic loss of strength are established, as illustrated in Section , fatigue, fracture and failure may automatically be derived as limiting cases under various circumstances. In analyses and studies of safety problems of materials and structures concerning fatigue, fracture and failure, such models are of the following features:Fatigue behavior including both low and high cycle fatigue may be explained and evaluated in a natural, direct way.Fracture and failure with pronounced thermal effects may be investigated by the thermo-coupled models with explicit forms of thermomechanical equations derived.No singularities in stress and strain at fracture and failure may be involved, but, to the contrary, asymptotically vanishing stress concurrent with continuing elastoplastic flow will be treated. No additional assumptions and criteria need be introduced for initiation and development of fatigue, fracture and failure.Small localized zones with asymptotic loss of the material strength may emerge at crack tips, which from a fresh standpoint explains the notion of the embedded process zone (EPZ) initiated by Barenblatt–Dugdale models (cf. for details). Note here that the former may directly be derived as inherent consequences from the proposed model, whereas the latter should be introduced on an ad hoc basis.Cumbersome numerical issues may be rendered irrelevant, such as the treatment of the restrictive conditions arising from yield criteria, discontinuities and singularities, etc.Applications of the proposed models in assessing various problems concerning reliability and safety of significant engineering materials and structures at failure and fracture are expected, for which experimental tests for characteristics of material behavior and computer codes for numerical implementation need be integrated. Results will be presented elsewhere.Influence of thermal treatment time on structural and physical properties of polyimide films at beginning of carbonizationPoly(4,4′-oxydiphenylene-oxydiphthalimide) (POO) was thermally treated at 773 K for 1, 15 and 60 min under argon atmosphere resulting in free-standing films with intermingled characteristics between polymer and carbon-rich derivatives. Degradative thermal analysis performed by pyrolysis-gas chromatography/mass spectroscopy (Py-GC/MS) revealed CO2 among the major products of thermal decomposition which according to electron paramagnetic resonance (EPR) passed through a radical process. X-ray diffraction (XRD) revealed thermal treated samples with semicrystalline organization that was attributed to the development of lamellae structure. Moreover, Atomic force microscopy (AFM) showed an increase in the roughness of the samples that acquired pronounced roughcast-like surface. Hence, there was an enhancement of mechanical strength and dielectric permittivity. From the data collected a mechanism of thermal decomposition was proposed.A good understanding of the carbonization mechanism of polyimides (PI) is critical for the development of improved carbon materials for gas separation, and electrically conducting surfaces for microelectronics devices POO was synthesized from 4,4′-Oxydiphthalic anhydride (ODPA, Sigma-Aldrich, 97%) and 4,4′-oxydianiline (ODA, Sigma-Aldrich, 98%), using N,N-Dimethylacetamide (DMAc, VETEC, 98%) as solvent. DMAc was treated overnight with molecular sieves with 3 Å pores, and under nitrogen (N2, White Martins 99.99%) to provide inert atmosphere. Argon (Ar, White Martins, 99.99%) was used in the thermal treatment.POO films were cut in pieces, supported on alumina plates and thermally treated in different times from room temperature to 773 K in tubular furnace under argon atmosphere. The heating rate applied was of 3 K min−1. The pre-determined time used and the respective code of the thermally treated POO samples are shown in Fourier transform middle infrared in attenuated total reflectance mode (ATR-FTMIR) was carried out in a SHIMADZU spectrophotometer model IRAaffinity-1, in the range of 4000 to 650 cm−1 with spectral resolution of 4 cm−1.Thermal analysis (TGA) was carried out in a SHIMADZU instrument, model TG-50A in the range of 298–1253 K, heating rate of 10 K min−1, under argon atmosphere, using a platinum pan with ca. 8 mg of sample mass.Pyrolysis-gas chromatography/mass spectroscopy (Py-GC/MS) using a CDS Analytical 5150 Pyro-probe coupled to an Agilent 7890 gas chromatograph (GC) with an Agilent 5973 N quadrupole mass spectrometer (MS) for detection of analytes. The samples (ca. 0.5 mg) were measured into quartz sample tubes loaded into the Pt filament coil of the pyro-probe apparatus for pyrolysis. For the determination of the products of degradation, the sample was held at an initial temperature of 333 K for 0.5 min, and then pyrolyzed at a ballistic heating rate from 333 to 1273 K under a purge flow of helium (He) gas for a total pyrolysis time of 2.0 min. The degradation products were continually transferred from the pyro-probe apparatus to the GC inlet using an inert transfer line (both at 573 K) with a 10:1 split flow for the total pyrolysis runtime. An Agilent DB-1 (30 m × 0.25 mm i. d. 0.25 μm) analytical column under constant flow of 2.0 ml min−1 with He used as carrier gas. The initial GC oven temperature was set at 313 K for 2.0 min and then ramped at 10 K min−1 to 573 K and held for 10 min at the final temperature for a total analysis time of 38.0 min. The MS ion source and quadrupole temperatures were 503 K and 423 K, respectively. Total ion chromatograms (TIC) of the pyrolysis products were collected for each run, disposed in TIC plots, normalized to sample mass, baselined and individual identified product peaks were integrated to yield a relative assessment of the abundance of degradation products.X-ray diffraction (XRD) experiments were performed on a Rigaku diffractometer, model Rotaflex RU-200, with Kα radiation from copper (Cu Kα 1.54 Å) in the range of 3°–60° and acquisition rate 0.03° min−1, operating in grazing mode. Wide-angle x-ray scattering (WAXS) was performed in the National Laboratory of Synchrotron Light (LNLS) at Campinas, SP, Brazil, in a machine bench of rotating anode operating at 0° with the normal, with Cu Kα 1.54 Å, detector of Si(Li) at 150 mm from the samples and collection time of 120 s. The obtained images were processed using the calibration algorithm of FIT2D software.Scanning electron microscopy (SEM) was performed in a JEOL microscope model JSM-6390 LV operating with electron beam of 10 kV. The samples were previously gold and palladium coated by sputtering using a BAL-TEC metallizer model 020 instrument (Balzers).Atomic force microscopy (AFM) was acquired in a Bruker microscope, model Dimension Icon® in intermittent contact mode, in air, using a silicon probe, spring constant about 40 N/m, oscillating frequency 320 kHz, and scan speed 1 Hz. Roughness parameters Nanoindentation (NI) was carried out in a MTS Instruments equipment, model Nanoindenter®XP. In the analysis, 10 loads of 0.05 N were applied using a diamond Berkovich tip from Micro Star of order of 50–100 nm in three-faced pyramid shape.Electrical permittivity measurements were performed with a Solartron SI impedance analyzer, model 1260, coupled to a furnace. The samples were coated with gold electrodes, by sputtering, and analyzed in the range of frequency from 0.1 Hz to 1 MHz, with alternating voltage of 1 V, in temperature range of 298–423 K. The whole process was controlled by a computer using Smart software for data collection. To avoid water interference in the results, previously to the experiments the samples were heated up until 423 K and cooled down until the room temperature around 298 K.The conversion of OO into POO was evaluated by ATR-FTMIR and the spectra are presented in a. The bands assigned to the amide group at 1652 cm−1 (axial deformation of CO bond), and in the range of 1560–1520 cm−1 assigned as angular deformation of CH bonds were no longer observed after imidization. Instead, the characteristic absorption bands from the imide group emerged at 1778 and 1711 cm−1 assigned to the asymmetric and symmetric axial deformation of CO bond from carbonyl groups, and at 1364 cm−1 assigned to the axial deformation of CN bond from imide ring. Characteristic bands from aromatic rings in the range of 1520–1420 cm−1 and at 1596 cm−1 corresponding to the breathing mode vibration and the axial deformation of CC bond, respectively, were also observed both in OO and POO. All of these assignments are consistent with previous detailed work b. No significant mass lost was detected below 803 K, only 5 wt%. The largest weight loss in the analyzed range was detected at 830 K and at 1253 K significant residual mass still remained (ca. 50%).After thermal treatment, most of the PI still remained, preserving the polymer properties such as flexibility, as already pointed out by Barsema et al. shows the relative abundances of the degradation products identified from POO to PI-60 samples. Note that there are significant changes in the relative distributions of all degradation products and the product yield and release of chemical compounds decrease from POO to PI-60 as a function of thermal treatment time. While the individual trends are quite complex to evaluate, due to multiple sources of products driven by the thermal energy provided, there is clearly a global trend described following.It can be observed that POO series share common degradation chemistry, such as depolymerization, pyrolytic reformation and progressive loss of organic functionality through radical scission (see EPR data in supplementary material). Thus, based on the experimental data and mainly on the mechanism proposed by Sazanov et al. . Basically, the thermal decomposition of POO undergoes successive homolytical and hydrolytic cleavages (due to absorbed water or hydroxyl ions), followed by hydrogen ablation, intermolecular coupling and molecular rearrangements. In is the pathway in which the BSU are likely to form. Both pathways lead mainly to CO2 evolution.The structural characteristics of the POO samples were evaluated by XRD, and their respective diffractograms are presented in . Three broad peaks were identified centered at 2θ = 11.8°, 20.5° (22° for thermally treated films), and at 43.8°. Such a pattern found for POO-series revealed an ordered intermolecular packing typical of semi-crystalline polyimides indicating that the thermal treatment led to formation of lamellae structure A representation of the molecular arrangements displayed by the polymeric chains in the POO series is shown in . The possible formation of the BSU represented in was assumed to start in the ordered regions.d), the films acquired a roughcast-like appearance that became more pronounced as the time of thermal treatment increased. This is due to weight loss from gas evolution during thermal decomposition, causing the material to shrink and become wrinkled. From the evaluation of the roughness parameters, both the arithmetic average (Ra) and root mean square (Rq) average of height showed significant deviations from the mean line/plane between POO and its thermal treated samples, resulting in a decrease in the peak-to-valley height difference. Additionally, theory of statistics shows a ratio Rq/Ra ≈ 1.25 implying in a Gaussian distribution of the heights from the mean line Further morphological information was obtained by SEM analysis, . Despite the gas evolution, no significant differences were detected on the cross-section surface of the materials, so that even after 60 min of thermal treatment no pores were observed. Thus, the samples remained fairly dense, suggesting that any eventual change occurred on a much smaller scale.The influence of the thermal treatment on the mechanical properties of the POO series was evaluated by measuring the hardness ( Right) via nanoindentation measurements. Both hardness and Young’s modulus displayed similar behavior, the deeper the penetration, the lower the values obtained suggesting a stiffer surface and softer interior. Such behavior was in agreement with the XRD data that revealed ordered, thus stiffer, molecular arrangements on the surface from the development of lamellae structure and carbon-rich products such as graphene precursors. At 4500 nm penetration, the difference in hardness between POO and PI-60 was about 70 MPa, which corresponds to 50% enhancement comparable to polymer-graphene nanocomposites Electrical measurements as a function of frequency and temperature also revealed significant increase of permittivity of the materials with the time of thermal treatment, ; which make the POO-series as potential materials for the production of dielectric components. The enhancement was attributed to the formation of free radicals and polar groups trapped in the samples after the treatment. Moreover, the possible formation of BSU works as significant unsaturated regions enabling overlapping of π-orbitals increasing locally the electronic density, but not to the point of cause electronic conduction POO was successfully synthesized by polycondensation reactions and thermal imidization, as confirmed by FTIR. TGA under Ar atmosphere revealed higher thermal stability with residual mass yield about 50 wt% at 1253 K. Complementary, Py/MS-GC showed CO2 among the major product of thermal decomposition. The data helped to set a model to describe the thermal decomposition process of POO, which included the possible formation of BSU. The evaluation of the physical properties showed that even at the onset temperature of thermal decomposition (773 K) was enough to increase not only the hardness of the material up to 50%, but also the dielectric permittivity (60%). Such enhancements were correlated with structural changes that took place in the material. This study presents the viability to produce PI-carbon rich materials with improved compatibility between the organic (PI) and inorganic (carbon) parts, mixed at molecular level, with properties that can be tuned by the time of thermal treatment. Moreover, the PI treated at 773 K afford suitable materials, for instance, to the development of flexible and mechanically strength membranes for purification of gases (e.g. hydrogen), as well as dielectric films and coatings for electronic devices.The following is the supplementary data related to this article:Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.polymdegradstab.2016.05.001Elastic properties and antistructural modeling for Nickel-Zinc ferrite-aluminatesIn this study, elastic properties of nanocrystalline Ni-Zn-Al ferrite synthesized by citrate-gel autocombustion method has been presented. X-ray diffraction and Infrared spectroscopy confirms the formation of spinel phase. Elastic properties are estimated from force constants and lattice constant determined from FTIR and XRD respectively. The observed variation of elastic constants has been interpreted in terms of strength of interatomic bonding and electronic configuration of the cations involved in the system. The average grain size has been observed to decrease with Al3+ substitution. A new antistructural modeling for describing of active surface centers is discussed. With this new antistructural modeling the changes in concentration of donor's active centers Ni′B and acceptor's active centers FeA• and AlA• was explained.Nickel-Zinc ferrite is promising magnetic material for high frequency applications due to its high electrical resistivity, low magnetic coercivity and low eddy current losses. It is crystallized in to mixed spinel structure (general chemical formula AB2O4) in which Zn2+ and Ni2+ ions preferentially occupy A and B sites respectively, whereas Fe3+ ions are distributed in to both A- and B-sites. The magnetic and electrical properties are governed by the orientation, type and valence state of cations present at A and B sites. In general, the magnetic moment of A and B sites are aligned in a direction opposite to each other. Therefore, redistribution of cations or substitution of other ions abruptly enhance or reduce the physical properties.Over the five decades extensive work has been carried out by various researchers on this ferrite employing a variety of synthesizing procedures or by incorporating a number of substituent ions and additives, in a direction to improve the existing properties []. However, more efforts are still have been carried out to develop Ni-Zn ferrite with superior electro-magnetic properties at higher frequencies. When a ceramic material like ferrite is subjected to high magnetic field, electric field, pressure or temperature, large stresses are developed in the material. This stress the inter-atomic and inter-ionic forces in spinel lattice, which further affects the physical properties of the material. Therefore, the study of elastic properties is important to understand and to avoid losses due to stress during fabrication and service. The elastic moduli values represents mechanical strength, fracture toughness and thermal shock resistance. These, mechanical properties have critical importance in the incorporation of the material in to a functional device and its suitability for a specific application.Gtierrez-Lopez observed a correlation between density and elastic modulus []. S Ramana Murthy reported that increasing Ni content in Ni-Zn ferrite has resulted an increase in the binding forces between atoms due to the increase in magnetic anisotropy []. On the other hand, elastic moduli and Debye temperature decreases with increasing Zn2+ composition due to its lower contribution for the bond formation []. These observations confirms that selecting a proper Ni to Zn ratio, it is possible to obtain a ferrite with desired electromagnetic properties for a specific application. The authors previously reported the influence of Al3+ substitution on Ni–Zn ferrite describing the structural and electromagnetic properties []. It was observed that Al3+ions statistically distributed among the available A- and B-sites and enhance magnetic and electrical properties. On the other hand, study of elastic properties helps to understand the binding forces and thermal properties like specific heat and Debye temperature and the suitability of the material for a specific application. Also, perusal of literature indicate that there very few reports are available on elastic properties of Al3+ substituted mixed ferrites [], but no efforts have been made to investigate the elastic behaviour of Al3+substituted Zn0.5Ni0.5AlxFe2-xO4 composition in particular. Therefore, the present work focused to investigate the effect of Al3+ substitution on elastic properties of Ni-Zn nanoferrites. An addition to the above, antistructure modeling have not been investigated in detail for this system. In the light of above facts, this comprehensive study helps to correlate elastic behaviour with other physical properties of nano ferrite materials.According to the chemical formula Zn0.5Ni0.5AlxFe2-xO4 (0.0 ≤ x ≤ 0.25) samples were prepared thorough nitrate citrate auto-combustion synthesis, using AR grade chemicals: nickel nitrate Ni(NO3)2·6H2O, zinc nitrate Zn(NO3)2·6H2O, iron nitrate Fe(NO3)3·9H2O, and aluminum nitrate Al(NO3)3·9H2O as starting materials. The chemical reaction during the process can be described as follow:0.5Ni(NO3)2·6H2O + 0.5Zn(NO3)2·6H2O + хAl(NO3)3·9H2O + (2-х)Fe(NO3)3·9H2O + + С6Н8О7·Н2О→Zn0.5Ni0.5AlxFe2-xO4 + 6СО2 + 5.5NO2 + 1.25N2 + 29H2OThe detailed procedure of synthesis is discussed elsewhere []. The as-prepared powders of all the samples were sintered at 1000 °C for 4 h.The X-ray diffraction measurements were carried out by X-ray diffractometer (PAN Analytical X'pert Pro) with Cu-Kα (λ = 1.5406 Å) radiation to ensure single-phase, nature of the prepared samples. The Infrared spectra for all the samples were recorded with FT-IR spectrophotometer (Shimadzu FT-IR Prestiage 21) using KBr pellets in the range 4000–400 cm−1. SEM micrographs were recorded on the LEO 435 VP microscope at 30 kV accelerating voltage.X-ray powder diffraction (XRD) patterns of Zn0.5Ni0.5AlxFe2-xO4 (0.0 ≤ x ≤ 0.25) is shown in . All the reflection planes are indexed and corresponds to spinel structure with space group Fd3m. No additional phases related to un-reacted ingredients or impurity were observed. This confirms the successful substitution of Al3+ for Fe3+ in the spinel system and formation of single spinel phase. The lattice constant values for the compositions were determined using the Bragg's relation [. It is observed that the lattice parameter decreases with increasing Al3+ concentration (x). This variation can be explained on the basis of difference in the ionic radii of Al3+ and Fe3+ ions. In the present system, the larger cations, Fe3+ (0.645 Å) are replaced with smaller Al3+ ions (0.535 Å). The observation variation in the positions of peaks corresponding to (220) and (311) are shown in . Intensity and position these planes are sensitive to the distribution of cations in A and B site. It is clear that, a shift in the position of the peaks is observed with increasing Al3+ substitution. shows the SEM micrographs of Zn0.5Ni0.5AlxFe2-xO4 (x = 0.0, 0.1) samples. It is observed that samples exhibit uniform, spherical, with soft agglomeration and narrow grain size distribution. The grain size has been estimated using Image J V4.1 software and shown as a function of Al3+concentration in c. Complete analysis of microstructure for the present series is reported in our previous work []. The grain size has been found to decrease with increasing Al3+ concentration.The Infrared spectroscopy is a non-destructive tool useful to elucidate the structural properties of the ferrite materials. One can obtain information about the position and occupation of the ions in the spinel lattice from IR spectra. According to Waldron classification [], two main broad metal oxygen absorption bands are present in the IR spectrum. The frequency bands ν1 and ν2 are around 600 cm−1 and 400 cm−1 represent the tetrahedral metal-oxygen and octahedral metal-oxygen vibration complexes respectively. The high frequency absorption band ν1 is due to the stretching vibrations of tetrahedral metal ion and oxygen bonding, while that of the low frequency band ν2 is caused by the metal-oxygen vibrations in octahedral sites. Any kind of modification in mass of the cations due to their replacement, cation-oxygen distance and bonding force affect the vibrational frequency, which reflect in absorption band position.shows the infrared spectra of Zn0.5Ni0.5AlxFe2-xO4 samples. All the samples exhibit two prominent absorption bands (ν1,ν2) and are listed in . It is clear that, the absorption bands are slightly shifted towards higher frequency side. i.e, from 576 cm−1 – 582 cm−1(ν1) and from 401 cm−1 – 406 cm−1(ν2) with respect to Al3+ concentration (x). It is well known that, the change in bond length has an inverse relation with the band frequency []. X-ray diffraction study shows that the lattice parameter (ao), tetrahedral bond length d(MA-O) and octahedral bond length d(MB-O) decrease () with increasing Al3+ concentration (x). Therefore, such increase in the frequency of absorption is due to the decrease in tetrahedral and octahedral bond lengths. The splitting of ν1 and ν2 into shoulders has not been observed in the present system suggest the absence of Fe2+ ions at octahedral site. The force constants of tetrahedral and octahedral sites Kt and Ko, respectively are calculated using the following relations and listed in where M1 and M2 are molecular weights of respective cations on A and B sites. It is observed from that both the force constants follow the same non-linear trend. This variation is due to the difference in the ionic radii of Fe3+ and Al3+ ions and their fractional occupancy ratio into A- and B-sites. It is well known that force constant and bond length in spinel ferrite are inversely related to each other []. The decrease in mean ionic radii of the site (rA and rB) result () in lowers the force constant and reduces the repulsive force between ions.In engineering practice Young modulus, Bulk modulus, Rigidity modulus and Poisson's ratio are considered as important for isotropic and homogeneous materials like spinel ferrites. The stiffness constants C11 and C12 are calculated using the following relations and depicted in StiffnessconstantsC11=Kava,C12=C11σ(1−σ)where Kav is average force constant Kav=(KO+KT)/2; a – is lattice parameter, σ is Poisson's ratio: σ=0.324∗(1−1.043∗P), P is porosity (that C11 increases with increasing Al content, whereas C12 follows an inverse trend. In general, these parameters depends on the force constant (K) and tightness of bonding between atoms in the lattice. The non-linear variation in stiffness constants is attributed to the distribution of cations in A and B sites. The substitution of Al3+ ions at the expense of Fe3+ ions affects the force constant, which in turn responsible for the observed changes in stiffness constants. It has been established that geometry and distribution of pores strongly influence the elastic properties. In the present work, decrease in C12 constant is majorly attributed to variation in porosity. depicts the variation of Poisson's ratio with Al3+ composition x. The Poisson's ratio (σ) shows a nonlinear behaviour with increasing Al concentration. The value of σ is ranging from 0.273 to 0.290. In general, ‘σ’ values are lying in the range from −1 to 0.5, which is in conformity with the theory of isotropic elasticity. The elastic moduli of the ferrite specimens are calculated using stiffness constants and Poison ratio as follows:Young'smodulus(E)=(C11−C12)(C11+2C12)(C11+C12) that, E and G are found to increase continuously with increasing Al3+ constant, whereas B follows opposite trend. The observed increase in E and G suggest that the deformation of the solid is difficult and the solid has a strong tendency to retain its original equilibrium position []. Wooster reported that, changes in the elastic moduli is due to the variations in interatomic binding forces in the spinel lattice. The strength of interatomic bonding depends upon the distance of interatomic bonding and type of cations involved in bond formation []. The replacement of large Fe3+cation (0.64 Å) by a quite smaller Al3+ion (0.535 Å) in the system reduces the interatomic bond length, and as a result one can expect an increase in the strength of interatomic bonding, which inturn increases the elastic moduli values. In such case, lattice energy is expected to increase with an increase in Al3+concentration (x) in system []. Similar increase in elastic moduli is observed with increasing Al3+ content in other mixed ferrites [ that Bulk modulus follows opposite trend with Al3+ concentration. This difference in B may be due to the decrease in poison's ratio (where it depends on porosity), cationic re-distribution and variation in a and KT values. It can be seen from that the rate of decrease of a is higher than rate of decrease of KT, which results in decrease in B with Al3+content. The elastic moduli values are found to be higher than the reported values in the literature []. This variation is due to the contraction of unit cell volume, large elastic energy and grain size reduction effect. Since smaller grains have large number of grain boundaries, which impede dislocation motion and enhance not only the strength of the material but also its toughness.The longitudinal elastic wave velocity (Vl), transverse (Shear) wave velocity (Vs) and mean velocity (Vm) are calculated using following equations:Go is the rigidity modulus with zero porosity using the following equation [where h is Planck constant (h = 6.626 × 10−34 J s), k is Boltzmann constant (k = 1.38 × 10−23 J K−1), NA is Avogadro's number (NA = 6.022 × 1023 mol−1), M is molecular weight of the sample, q is number of atoms in the unit formula (for present ferrites q = 7), ρ is the density of the sample. shows the variation of elastic wave velocity (Vl,VS and Vm) as a function of Al3+ concentration. It is observed that both the velocity (VL and VS) increases with increasing Al3+ content. The decrease in velocity with Al3+ content is ascribed to the difference in the molecular weights of Fe (55.845 g/mol) and Al (26.9815 g/mol).The Debye temperature is an important parameter, which helps to understand the variations in thermodynamic properties such as mean square atomic displacement i.e. the maximum displacement takes place, specific heat, melting temperature, or vibrational entropy []. The variation of Debye temperature (D) is shown in . It is clear that The Debye temperature increases with Al3+content, this variation is related to the increase in wave number of the IR bands, strength of interatomic bonds and hindering of lattice vibrations by the substitution of Al3+.Antistructural modeling gives a more better understanding on the nature and role of lattice defects in different processes []. Antistructural mechanism provides superposition of the crystal structure with spinel antistructure V''AV'''2BV4••O. Detailed explaining of interaction between metal cations and spinel vacancies respectively can be writing as follow:where ● – an excess positive charge, ''– a double excess negative charge, ''' - a triple excess negative charge, ×– an effective zero charge, V – the cationic and anionic vacancies, A – tetrahedral position, B – octahedral position, O – oxygen position. With the Kröger-Vink notation, in the spinel antistructure one negatively charged cation vacancy V″A and two negatively charged cation vacancies V‴B are treated as the charge balancing vacancies to the four positively charged oxygen vacancies VO••. Antistructural modeling for some of the Ni-Zn ferrites-aluminates can be written as follow:(Zn0.502+Fe0.50−x+y3+Alx−y3+)A[Ni0.502+Fe1.50−y3+Aly3+]B(O42−)O+V″A[V‴2]B(V4••)O→→(Zn0.50×Fe0.50−x+y•Alx−y•)A[Ni′0.50Fe1.50−y×Aly×]B(O4×)Owhere 0.00 ≤ x ≤ 0.25; 0.00 ≤ y ≤ 0.20 (the range of values x and y were calculated on the basis of Rietveld refinement). Thus, superposition of antistructure and crystal chemical formulas of Al-doped Ni-Zn ferrite give us new information about nature of active centers on the surface ( we can see that concentration of negatively charged donor active centers Ni′B are still constant with Al3+content increase. shows the concentration of active centers in tetrahedral (A) sites (Al and Fe) as a function of Al3+content. It is clear that concentration of positively charged acceptor active centers AlА• and FeА• follows opposite trend. Crystallo-quasichemical formulas gives us new and clear information about active centers: ZnA2+, AlB3+ and FeB3+ does not will be active centers in any chemical reactions because they have an effective zero charge, while FeA3+, AlA3+, and NiB2+ will be an active centers in the catalysis, adsorption or other processes in gaseous or liquid environment.In this report, influence of Al3+ substitution on elastic properties of Ni-Zn ferrite has been estimated from Infrared spectroscopy. The observed variations elastic constants reveled that Al3+ substitution strengthens the interatomic bonding. The average grain reduced with increasing Al3+ content. The elastic wave velocity and Debye temperature are increased with increasing Al3+ concentration. A new antistructural modeling for describing of active surface centers is discussed. The change in concentration of donor's active centers Ni′B and acceptor's active centers FeA• and AlA• was explained. The concentration of positively charged acceptor active centers AlА• increases with Al content while the concentration of positively charged acceptor active centers FeА• decreases.Evaluation of elastoplastic properties of DLC coating on SKD61 steel by optical indentation microscopyDiamond-like carbon (DLC) is well known as the unique properties of very hard, very low friction and low wear. That is why, the DLC coating has succeeded in commercializing on various field, including tools and/or dies' surface treatment. The life times of tools and dies are extended significantly. However, the mechanical properties of the DLC coating have not been understood well, yet. One of the authors (TM) has developed a novel method to measure the mechanical properties, such as Young's modulus, through the in situ determination of a true contact area during an optically transparent tip indentation by observing the contact image with CCD camera. The system, we called “Optical Indentation Microscopy” (OIM), enables one to determine true indentation stress-strain property. With this OIM, we have measured the mechanical properties of DLC coated and uncoated SKD61 (JIS or X40CrMoV5-1, ISO) steel samples. DLC coating made by our bipolar pulse PBII system. The thickness of DLC coatings were about 7 µm. Berkovich shape tip for usual indentation test and spherical-corn shape diamond indenter tip (0.4 mm in radius) for OIM were used. The maximum load and depth were about 2.5 N and 1 µm, respectively. Usual indentation test with Berkovich tip revealed that the DLC coated sample is harder than uncoated one, and the load-total penetration depth plots in logarithm shows the data of the DLC coated sample can be analyzed as if the tip shape is spherical. From the result of OIM, Young's modulus, yield stress and elastic limit of the DLC coated and uncoated SKD61 samples are 156 GPa and 201 GPa, 2.4 GPa and 2.6 GPa, and 2.2 GPa and 1.1 GPa, respectively. The DLC coating can improve the elastic limit of SKD61 by 100%. This effect of DLC coating is very useful to improve the lifetime of tools and dies.Diamond-like carbon (DLC) is well known as the unique properties of very hard, very low friction and low wear. That is why, the DLC coating has succeeded in commercializing on various field, including tools and/or dies' surface treatment. The life times of tools and dies are extended significantly. However, the mechanical properties of the DLC coating have not been understood well, yet.Usually, indentation test with Vickers or Knoop tip is suitable to investigate mechanical properties of bulk materials. However, the test is not suitable for thin films because the effect of substrate is not negligible. So, instrumented indentation test, so-called nano-indentation test, which measures indentation load (P) and total penetration depth (ht) simultaneously, is commonly used in order to evaluate mechanical properties of thin films.Unfortunately, the height of real contact end between sample surface and indentation tip, which is directly related contact area (Ac), can not be measured with this method. In evaluation of hardness and Young's modulus from the instrumented indentation test, Oliver and Pharr approximation The OIM can measure mechanical properties, such as Young's modulus, through the in situ determination of true contact area during an optically transparent tip indentation by observing the contact image with CCD video camera In this paper we measured the mechanical properties of DLC coated and uncoated steel samples with the OIM, and made some comparison between the results obtained by a usual instrumented indentation test and our OIM system.DLC coating was carried out by our PBII system. The outline of our PBII system using bipolar pulses has been described in our previous paper A mirror polished SKD61 (JIS or X40CrMoV5-1, ISO) steel disk (25 mm ϕ x 5 mm) was used as a substrate. DLC coating process consists of: (1) Ar plasma sputter cleaning at − 2 kV, (2) carbon ion implantation at − 20 kV using CH4 plasma, then (3) DLC deposition with +2 kV and − 5 kV pulses with 4 kHz repetition under toluene plasma. Process times of (1), (2), and (3) were 30 min, 30 min and 4 h, respectively.Raman spectroscopy was measured to determine the properties of coated DLC with Horiba, HR-800MX. Film thickness was evaluated by a laser microscope (Olympus, OLS3000) and it was about 7.1 μm.Schematic of our OIM system is shown in . Spherical-conical shape (0.40 mm in radius at the end and 90o in angle) diamond tip was used as objective lens and indenter tip. Briefly, main body is optical microscope (Olympus, BX-51 M) and added with a computer controlled piezo-actuator in Z-axis, which applies displacement (or load) to the sample, and a load cell and a CCD camera, they were connected to the computer which evaluates indentation load and contact area. The details of OIM system were described in Miyajima and Sakai shows the result of Raman spectroscopy and two broad peaks around 1332 cm− 1 (D-band) and 1580 cm−1 (G-band) represents the feature of DLC films. The film we made was confirmed typical DLC structure. shows the Vickers hardness of DLC coated and uncoated SKD61 samples. It is not so clear the increase of hardness by DLC coating, especially for 49 and 98 N loads the increase is only 0.2 GPa. For 9.8 N load, the increase is more than 1.0 GPa and the increase is apparent. In macroscopic scale, the effect of DLC coating on hardness is very limiting. That's why; we need more precise measurement technique, like a nano-indentation or usual instrumented indentation test. shows the results of usual instrumented indentation test with Berkovich tip. In P1/2–ht plots (a) shows a very clear difference between DLC coated and uncoated SKD61 steel samples. For the uncoated sample, both of loading process and unloading process show linear relationship clearly. It represents the uniformity of the sample. On the other hand, for DLC coated SKD61 sample shows smaller penetration than uncoated one, which means the DLC coated one is harder than uncoated one, especially in small penetration region, as expected.The data for loading process of DLC coated sample shows a curve, which means the mechanical properties of the composite material changes gradually. The P–ht plots in logarithm (b), shows the difference between DLC coated and uncoated samples. Uncoated sample shows that P proportional to ht2 and DLC coated sample shows P proportional to ht1.5. From Snedon's old work According this, n |
= 2 for uncoated sample means the tip is cone shape (or Berkovich). On the other hand, n |
= 1.5 for DLC coated sample means the tip is sphere shape nevertheless the real tip shape is Berkovich shape. The thickness of DLC coating is about 7 μm and the penetration of indentation tip is less than 1 μm. The result of DLC coated sample can be considered that the DLC coating itself becomes a secondary tip, which indents SKD61 substrate like spherical indenter. This result is very interesting and we must study more near future.Theoretical back ground of sphere and plane contact based on the Hertz theory can be summarized as follows where R is a tip radius of spherical indenter, and E⁎ is an effective Young's modulus of indenter tip and sample material, that is 1/E⁎ = (1 − νi2)/Ei |
+ (1 − νs2)/Es, where a suffix “i” indicates the indenter of diamond tip and a suffix “s” indicates the measured sample. The Eq. of can change using a diameter of contact area (d), which can be obtained directly using the images of CCD camera in indentation measurement,Therefore, the relationship between mean contact pressure (pm) and indentation strain (d/R) is obtained as follows The results of OIM with a spherical-conical shape (0.40 mm in radius at the end and 90o in angle) diamond tip for DLC coated and uncoated SKD61 samples as pm–d/R plots are shown in . It is very clear that the relationship between pm and (d/R) shows linear for both samples, except the maximum region of indentation strain where it starts yielding. From the slope of each line, Young's modulus of each sample can be obtained and they are 201 GPa and 156 GPa for uncoated SKD61 and DLC coated SKD61, respectively. Using OIM, we can directly obtain the values of Young's modulus and it is revealed that the Young's modulus of the DLC coated sample is smaller than that of uncoated one.The result of the Young's modulus of the DLC coated SKD61 sample is smaller than that of uncoated SKD61 sample seems curious. To remember the results of b, the DLC coating acts as a secondary tip which indents SKD61 substrate and an effective tip radius becomes larger than that of the actual diamond tip, that is, the value of “R” in the Eq. must be larger than 0.4 mm. However, we have used the value of 0.4 mm for “R” in the evaluation of the Young's modulus of the DLC coated SKD61 sample as a whole.Yield stress (Y) is also obtained from the data shown in a, that is the value of pm (the ratio of P and Ac) at the beginning of yield or critical point, and the values of pm at critical points for uncoated and DLC coated samples are 2.6 GPa and 2.4 GPa, respectively. So, the values of yield stress for uncoated and DLC coated samples are almost same, instead of the large difference of Young's modulus.To see the yield point precisely, P–Ac plots is shown in b. The critical points (shown as C.P. in the figure) of both samples, where they start to fail the fitting curves shown in the figure, are very different points in this P–Ac plots. Apparently, the value of critical indentation load (Pc), or elastic limit, for the DLC coated sample (2.2 GPa) is 2 times larger than that of the uncoated sample (1.1 GPa). It means that the DLC coating can improve the elastic limit of SKD61 by 100%. This effect of DLC coating is very useful to improve the lifetime of tools and dies., the data of loading process is re-plotted in P2/3–Ac plane in c. In this plots, the fitting curves in b become linear lines; therefore, it becomes easier to find out the critical points. To see the inserted figures in c, data points deviate from the fully elastic linear relationship shown as solid lines in the figures, at the critical points for both samples. Anyway, using the OIM we can easily evaluate the elastic limit of materials even if the material is composite of hard and soft materials.From the both results of an usual instrumented indentation test with Berkovich tip and OIM with a spherical-conical shape tip, it can be said that the relatively thick DLC coating (7.1 μm) acts as a stress shield against the substrate materials. We will examine different DLC coatings in thickness and in composition near future.We have applied a new method to measure the mechanical properties of DLC/metal system, such as Young's modulus, through the in situ determination of true contact area during an optically transparent tip indentation by observing the contact image with a CCD camera. The system, we called “Optical Indentation Microscopy” (OIM), enables one to determine true indentation stress-strain property. With this OIM, we have measured the mechanical properties of DLC coated (by our bipolar pulse PBII system) and uncoated SKD61 (JIS or X40CrMoV5-1, ISO) steel samples, and we get the following results.Usual indentation tests with Berkovich tip revealed that the DLC coated sample is harder than uncoated one, and the load-total penetration depth plots in logarithm shows the data of the DLC coated sample can be analyzed as if the tip shape is spherical. From the result of OIM, Young's modulus, yield stress and elastic limit of the DLC coated and uncoated SKD61 samples are 156 GPa and 201 GPa, 2.4 GPa and 2.6 GPa, and 2.2 GPa and 1.1 GPa, respectively. The DLC coating can improve the elastic limit of SKD61 by 100%. This effect of DLC coating is very useful to improve the lifetime of tools and dies. Using the OIM we can easily evaluate the elastic limit of materials even if the material is composite of hard and soft materials.Bearing capacity of a square model footing on sand reinforced with shredded tire – An experimental investigation► Using waste tires in civil applications may be feasible to consume the scrap tires. ► Shredded rubber mixed with soil acts as reinforcing materials beneath the footing. ► The performance of rubber-reinforced soil increases in presence of soil cap. ► Bearing capacity of rubber-reinforced bed obtained 2.68 times of unreinforced bed. ► Findings lead to overall saving in soil material costs and recycling of tires waste.Recycling rubber from waste tires has become one of the major challenges worldwide. The use of waste tires in geotechnical applications may be feasible as an alternative way to consume the huge stockpile of scrap tire, with a better understanding of the behavior of rubber–soil mixture. The objective of this study was to investigate the feasibility of using rubber shreds, randomly distributed into the soil, as soil reinforcement beneath the footing. A series of laboratory tests were conducted to obtain the bearing capacity of a square footing rested on shredded rubber-reinforced soil. The results show that the efficiency of rubber reinforcement was increased by addition of rubber content, the thickness of rubber-reinforced soil layer and the soil cap thickness up to the optimum values of these parameters, after that, with a further increase in each of these parameters, the bearing capacity decreases. For the optimum value of rubber content of 5% at footing settlement level of 5%, the maximum improvement in bearing capacity of rubber-reinforced bed was obtained as 2.68 times of the unreinforced bed. This value of improvement was achieved using the optimum thickness of reinforced layer of 0.5 times of footing width and the optimum thickness of soil cap of 0.25 times of footing width. The findings strongly suggest the use of rubber shreds obtained from non-reusable tires as a viable alternative way for improving the soil behavior, particularly when environmental interest is considered.In the recent decades, hundreds of millions of scrap tires are generated and accumulated in the worldwide, due to the developing industry and growing population As a practical point of view, the use of waste rubbers may be offered in geotechnical applications due to four advantages; (1) the re-use of waste materials such as tires and tubes, reduction in environmental health hazard and saving huge spaces and costs to maintenance of wastes, (2) the reduction in consumption of competent natural soil and its cost saving benefit, (3) soil reinforcement, which can demonstrate a substantial increase in shear strength of mixture compared to soil alone, and (4) the exhibition of a higher capacity to absorb and to dissipate energy than soil alone and tend to decrease the stress and shocks transferred into the ground when subjected by dynamic loads.Reinforced earth technique has been gaining popularity in the field of geotechnical engineering due to its highly versatile and flexible nature. The application of waste tires in various forms, has been recently developed in reinforcing soil for a variety of geotechnical applications ranging from retaining structures and earth embankments, asphalt pavement and paving system, foundation beds and other applications The waste tires in the form of shredded rubbers when mixed with soil behave as reinforced soil, similar to fiber-reinforced soil. Experimental results reported by various researchers The above literature review clearly indicates that several studies have been reported on the behavior and properties of rubber/fiber reinforced soil mixture. Among them, the available studies on footing supported by shredded rubber–soil mixture are limited. The soil mixed with randomly-distributed tire shreds is expected to behave as reinforced soil layer beneath the footing. To promote the recycling of tire wastes on a large-scale in geotechnical applications where bulk utilization of waste materials is possible, in the present study, experimental results to investigate the response of square footings built on shredded rubber-reinforced soil are presented. The bearing pressure at different settlement ratios of footing are evaluated. The various parameters studied in this testing program include the rubber content, the thickness of reinforced layer, and the thickness of soil cap layer over the reinforced layer which it may presumably increase the benefit of rubber–soil mixture A physical model test was conducted in a test bed-loading frame consisting of the testing tank, the loading system and the data acquisition system. The general arrangement of the testing apparatus is schematically shown in The testing tank is designed as a rigid box with plan dimensions of 700 mm × 700 mm, and 600 mm in height, encompassing the unreinforced natural soil, the replaced rubber–soil mixture (reinforced layer), the soil cap layer, and footing model. The back and side faces of the tank consist of smooth MDF sheets of 20 mm thickness, which are permanently fixed to channel sections. To allow the visual observations of the sand reinforcement system, as well as photo scanning, the front face of the tank is made of 20 mm thick Plexiglas. To prevent undesirable movement of the four sides of the tank the rigidity of the tank has been guaranteed by using a stiff steel section of U-100 on four sides of the tank. According to some preliminary test results (not further reported here), under a maximum applied loading stress of 1000 kPa on the model foundation, the measured deflection of sides of the tank were very small demonstrating that they would be negligible at the stress levels applied in the main tests program. Also during the tests, no differential settlement between the two ends of the footing (loading plate) was observed.Loading system includes the loading frame, the pneumatic cylinder, and the controlling unit. The loading frame consists of two stiff and heavy steel columns and a horizontal beam that supports the pneumatic actuators. The two pneumatic actuators which have the internal diameters of 80 and 160 mm may produce monotonic or repeated loads with maximum capacity of 12 kN depending on the intensity of the input compressed air.The data acquisition system was developed to automatically read and record both the load and the settlement. An S-shaped load cell with an accuracy of ±0.01% and a full-scale capacity of 15 kN was placed between the loading shaft and the footing to precisely measure the pattern of the applied load. Two linear variable differential transducers (LVDTs) with accuracies of 0.01% over their full range (100 mm) were placed on the two sides of the footing model to measure the average settlement of the footing during loading. To ensure accurate readings, all of the devices were calibrated prior to each series of tests.The natural granular soil passing through 25.4 mm sieve was used as natural ground, soil cap, and in mixture of rubber–soil as reinforced layer (). It was dry with grain sizes between 0.07 and 25.4 mm, D50 |
= 1.65 mm and Gs |
= 2.64. The maximum and minimum porosities of this soil were obtained 0.91 and 0.65, respectively. The grain size distribution of this soil is shown in . The soil is classified as poorly graded sand (SP) according to the Unified Soil Classification System Shredded tire rubbers used in this study, as an alternative reinforcement material was clean and free of any steel and cord. They are provided cutting from waste soft tube tires of motorcycle with a special cutter into rectangular shape. The nominal size of the tire shreds of 10 mm in width and about 30–50 mm in length was selected (aspect ratio between 3 and 5). This range of aspect ratio (ratio of length/width) was selected to achieve the maximum performance in increasing the bearing capacity of foundation bed and in decreasing the soil surface settlement and a view of the shredded rubber used, is shown in The schematic layout of the trench, which contains the unreinforced soil as natural ground, the rubber-reinforced soil (rubber–soil mixture), the soil cap (the unreinforced soil over the reinforced layer), and the footing, is shown in . To simulate the natural ground and to prepare the rubber-reinforced layer and the soil cap layer in the testing tank, the compaction method is used. The compaction energy produced by means of pneumatic cylinder (the used pneumatic cylinder to apply the static load during each test, see Section ) which applies constant pressure on a wooden stiff plate (690 mm × 690 mm in plan dimensions). The dimensions of the wooden plate was 10 mm less than the dimensions of the tank, so a 5 mm wide gap was provided on each side of the tank to prevent contact between the wooden plate and the sides of the tank. The wooden plate is approximately fitted on the soil surface so all the energy will transfer uniformly to bed. Before compaction of the soil layers in the tank, compaction system was calibrated at different compaction energy (i.e. using the uniform pressure applied on the wooden plate) and number of compaction repetitions for the soil layers of 25 mm in thickness. The necessary compaction energy and number of compaction effort can be selected to achieve the desired density for each test.The relative density of unreinforced soil to simulate the natural ground and the relative density of topmost unreinforced soil layer as a soil cap layer (see ) were selected at 66%. This relative density was produced using constant pressure of 25 kPa which applied two times on wooden plate. To ensure that the calibration system produces the proper relative density, the soil density was measured for several tests, and the maximum difference in the soil density was around 1–2%. The same compaction effort used to prepare the rubber–soil mixture and the soil cap beneath the footing in all tests. It should be noted that, although in practice, the relative density of natural ground (as the former) might be denser or might be usually compacted, in this study the relative density of soil cap and natural ground are kept the same.Tire shreds content, Rc was selected at 2.5%, 5% and 7.5% volume of shreds compared to total volume of soil–rubber mixture layer (see ). For obtaining a desirable mixture, the soil and the tire shreds were carefully mixed using a mixer. Special care was taken to mix thoroughly the tire shreds and the soil, in order to produce a reasonably uniform rubber–soil mixture.The foundation bed with thickness of 600 mm includes natural ground, rubber–soil mixture and soil cap was compacted in layers of 25 mm in thickness until the soil cap reached the footing level. The square footing model was placed in the center of the soil bed. The footing model was made of a steel rigid plate and measured 100 mm × 100 mm in plan dimensions and 20 mm in thickness. The base of footing model was roughened by covering it with epoxy glue and rolling it in sand. To provide vertical loading alignment, a small semispherical indentation was made at the center of the footing model. A load cell was placed on the loading shaft to record the applied loads, and two LVDTs were placed on the footing model to measure the settlement of the footing during loading. The static load was increased at a rate of 1.0 kPa per second.The details of the shredded rubber content, the thickness of rubber-reinforced soil layer, and the soil cap thickness in each model test are given in Some 51 tests in different series were planned and performed in this study to investigate the effects of the rubber content, the thickness of rubber-reinforced soil layer (hrs/B), and the thickness of soil cap (hs/B) on the response of footing. The details of both the unreinforced and shredded rubber-reinforced tests are listed in . A test on fully unreinforced soil (without a soil–rubber mixture) was performed to provide a reference load capacity that allows quantification of the improvements due to a layer of rubber soil reinforcement. Of these 51 tests, 14 tests were repeated carefully at least twice to examine the performance of the apparatus, the accuracy of the measurements, the repeatability of the system, the reliability of the results, and the consistency of the data. The results of multiple trial tests exhibited maximum differences of around 6–8%. This difference was considered to be small and is subsequently neglected. This process demonstrated that the adopted procedures produced repeatable tests within the bounds that can be expected from geotechnical testing apparatuses.In this section, the results of the laboratory model tests are presented with a discussion highlighting the effects of the different parameters. The value of bearing pressure of the footing rested on the unreinforced bed and on the reinforced bed, under monotonic load, at different level of footing settlement is investigated. The presentation of all the result figures would have made the paper lengthy, so only a selection is presented. gives examples of bearing pressure-settlement response of the unreinforced and reinforced foundation beds obtained varying the thickness of soil cap, hs/B and the thickness of rubber-reinforced soil, hrs/B at the content of tire shreds of 5%. As can be seen, in the case of both the unreinforced and rubber-reinforced soil bed, it is apparent that no clear failure point is evident in pressure-settlement behavior. Beyond a settlement of 8–15% there is a reduction in the slope of the pressure-settlement curve. This leads to a reduction in the load carrying capacity of the footing indicated by the softening in the slope of the pressure-settlement responses. Beyond this stage, the slope of the curve remains almost constant with the footing bearing pressure continuously increasing.a, it may be clearly observed that, for the foundation bed without soil cap (hs/B |
= 0), with increasing the thickness of reinforcement layer, hrs/B both stiffness and bearing pressure at a specified settlement considerably increase compared to those obtained of unreinforced bed. The similar trend is observed in the presence of soil cap (hs/B≠ |
0) over the reinforced layer in b and c. But for the rubber-reinforced soil layer of hrs/B |
= 1.5, the pressure-settlement curve is located lower than the pressure-settlement curve of unreinforced bed at any footing settlement level. It may be attributed to more compressibility and settlement of foundation bed and consequently the reduction in reinforcing effect of rubber–soil mixture. Likewise, from a it may be also expected with increase in the thickness of rubber–soil mixture (hrs/B |
> 1.5), the bearing pressure of footing goes less than the unreinforced bed (similar to b and c). A comparative investigation of pressure-settlement curves in shows clearly that for the given rubber content, regardless of soil cap thickness, hs/B, there is an optimum thickness of rubber-reinforced soil layer, hrs/B which delivers the maximum bearing pressure.It is interesting to note that the pressure-settlement response of the other tests (not reported here due to manuscript length restrictions) introduce optimum values of rubber content, Rc and soil cap thickness, hs/B. These optimum values warranted the maximum footing bearing capacity at any footing settlement level, the details of which are presented in later sections.It should be noted that, in most of the researches dealing with bearing capacity of footings, the performance of footing due to the provision of different reinforcements is only investigated by considering the bearing capacity at failure point without considering the settlement limit criterion (e.g., The optimum value of the rubber content is obtained from testing program described in . The tests are done for different rubber contents, Rc different thicknesses of soil cap, hs/B and different thicknesses of rubber-reinforced soil, hrs/B. The corresponding bearing pressure with rubber content for different values of hrs/B |
= 0.25, 0.5, 1, and 1.5, while hs/B value is kept constant (hs/B |
= 0.25) at different values of settlement is depicted in This figure may be classified into two groups; one for hrs/B |
⩽ 1 (first group), and the other for hrs/B |
= 1.5 (second group). For the first group (a–c) the improvement in bearing capacity initially is increasing when rubber content increases from 0% to around 5%, but, thereafter, the bearing capacity decreases with rubber content, regardless of the footing settlement ratio, s/B and the thickness of rubber-reinforced layer, hrs/B. For example, in the case of hrs/B |
= 0.5 and hs/B |
= 0.25 (b), the bearing pressure obtained at settlement ratio of s/B |
= 2.5%, is about 50 kPa, 118 kPa, 154 kPa, and 87 kPa for 0%, 2.5%, 5%, and 7.5% of rubber content, respectively. These values show that the bearing pressure increases about 136%, 208% and 74%, respectively for 2.5%, 5% and 7.5% of rubber content compared to that of the unreinforced bed.The results depict an optimum shred rubber content around 5% which delivers the maximum increase in the bearing capacity. The increase in performance improvement with rubber content of 5% could be due to the available competent reinforced layer beneath the footing. The decrease in bearing capacity after optimum content of rubber may be attributed to swapping the soil grains with soft material, like rubber, and also possible increasing the void ratio of mixture tends to the compressibility of mixture – consequently leading to increase in the footing settlement. It may be expected when the rubber content increases to more than 7.5%, the bearing pressure of footing leads to less than the bearing pressure of unreinforced bed. The excess of soft rubber particles separates soil particles and forms a soft rubber fabric and consequently decreases the bearing capacity of footing due to significant compressible foundation bed.d) where a thicker layer of rubber–soil mixture (hrs/B |
= 1.5) is employed in foundation bed, the general trend in variations of bearing pressure of footing with rubber content, is similar to those obtained for the first group (hrs/B |
⩽ 1). In this case, at the settlement ratio of s/B |
= 2.5%, the optimum shred rubber content is obtained around 2.5% which has only delivered a 56% enhancement in bearing pressure of footing while in the first group using hrs/B |
= 0.5 and 5% of rubber, 208% enhancement in bearing pressure of footing has been delivered at the same settlement ratio. It is, therefore, inferred that use of the thicker mixture (hrs/B |
= 1.5) could not be compared to that of the thinner mixture even where the optimum rubber content used in the rubber–soil mixture layer. Consequently, the second group is not as efficient as the first one to be considered in practical design. The effect of hrs/B is discussed in the next section. depicts the variation in bearing pressure with the thickness of rubber-reinforced soil (hrs/B) for the experiments with the three different rubber contents of 2.5%, 5% and 7.5% and unreinforced soil bed at different footing settlement ratio, s/B. The rubber-reinforced layer was placed at a depth of 0.25 time of the footing width (hs/B |
= 0.25) from the base of the footing.From this figure, it has been found that with an increase in hrs/B ratio, the value of bearing pressure increases up to the value of hrs/B |
= 0.5, approximately, after which, with further increase in hrs/B ratio, the value of bearing pressure decreases at all settlements, irrespective of rubber content used in the mixture. As can be seen from b, at settlement ratio of 2.5% (s/B |
= 2.5%), the bearing pressure increases about 100%, 206%, and 62%, respectively for 0.25, 0.5, and 1 of rubber-reinforced layer thickness ratio (hrs/B) compared to that of the unreinforced bed. Overall, these results reveal that at all footing settlement level, regardless of rubber content value, the maximum improvement in the bearing pressure of footing have been obtained at optimum thickness of rubber-reinforced soil layer (hrs/B |
= 0.5).In the case of hrs/B |
= 1.5, the rubber content of 5% and the settlement ratio of s/B |
= 2.5%, the value of bearing pressure of footing reaches around 0.9 (=45/50) times of the unreinforced bed. Overall, in the presence of soil cap, irrespective of footing settlement level, when the thickness of rubber-reinforced soil layer reaches around 1.5 times of the footing width, the reinforcing efficacy of mixture becomes negligible. Therefore, it would be expected that the increase in the thickness of rubber–soil mixture more than 1.5 times of the footing width (hrs/B |
> 1.5) leads to more significant reduction in bearing pressure value and more significant enhancement in footing settlement value.The observed reduction in bearing pressure due to the increase in the thickness of reinforced layer beyond its optimum value (hrs/B |
= 0.5) may be attributed to the increase in compressibility and settlement of layer which attenuate the reinforcing effect of rubber in mixture. In this case, although the void ratio of mixture layer is kept constant during the compaction of mixture, the total void space between the soil particles of mixture and compressibility of mixture is increased. This phenomenon increases the footing settlement and decreases the footing bearing capacity value. Likewise, with increase in the thickness of rubber-reinforced layer more than 1.5 times of the width of the footing, the behavior of mixture changes from a relevant reinforcing material to highly compressible material, which may provide an undesirable effect on the footing response.In order to investigate clearly the beneficial effect of the soil cap over the rubber–soil mixture layer, the variation of bearing capacity with the soil cap thickness at different levels of footing settlement, are shown in . This figure shows the results of tests including 2.5%, 5%, and 7.5% of rubber in the rubber-reinforced layer of 50 mm in thickness (hrs/B |
= 0.5). The rubber-reinforced layer was placed at depths of 0, 0.25 and 0.5 times of the footing width (hs/B |
= 0, 0.25 and 0.5) from the base of the footing.This figure depicts that the bearing pressure increases as the hs/B ratio increases, up to approximately 0.25, but decreases as the hs/B ratio increases further, irrespective of the footing settlement level. For example, for the reinforcement layer containing 5% of rubber and thickness ratio of 0.5 (hrs/B |
= |
0.5) at settlement ratio of s/B |
= 2.5%, the bearing pressure obtained as 66 kPa, 135 kPa, and 106 kPa for the thickness of the soil cap (hs/B ratio) equals 0, 0.25 and 0.5, respectively. These values indicate that the maximum improvement in bearing pressure obtained for the soil cap thickness of around 0.25 (it seems a value between 0.25 and 0.35; 0.25 < |
hs/B |
< 0.35), known as an optimum value of soil cap thickness. It delivers 104% and 27% increase in bearing capacity compared to those of hs/B |
= 0 and 0.5, respectively. It should be noted that the bearing pressure values of rubber reinforced bed at footing settlement of 2.5% (s/B |
= 2.5%) have been increased as compared to that of the unreinforced bed (the bearing pressure of unreinforced bed is about 50 kPa), irrespective of the thickness of soil cap and rubber content.There are two probable explanations for this optimum hs/B value (hs/B |
= 0.25). One is that for hs/B |
< 0.25 the overburden is not sufficient to develop enough frictional resistance at the interface between the soil cap and reinforcement layer. Secondly, reference to Boussinesq’s stress distribution Increasing hs/B beyond 0.25–0.35 means that the layer of rubber-reinforced soil is located out of the most effective zone, so a decrease in value of bearing pressure was observed at all settlements. It may be expected when the depth of placement of reinforced layer, hs increases about 1–2 times the footing width (hs/B |
= 1–2), the influence of rubber reinforcement becomes practically negligible and the rubber-reinforced bed behaves like an unreinforced case. At this value of hs/B, stress applied by the footing is concentrated on the unreinforced soil mass (soil cap) above the rubber reinforcement so that the failure mechanism tends to the unreinforced one. Such a finding is not unexpected as a simple stress analysis (e.g. according to Boussinesq The beneficial effect of soil cap over rubber–soil mixture on the enhancement of bearing capacity of footing confirms the result of Bosscher et al. The results presented herein provide significant encouragement for the application of randomly distributed shredded rubber as soil reinforcement, similar to conventional geosynthetic reinforcement to improve the strength and settlement behavior of foundation bed. But it should be noted that the present experimental results are based on the tests conducted on a small model of square footing and they are obtained for only one type of shredded rubber, one size of footing width, and one type of soil. Thus, full application should only be made after considering the above limitations. However, further study is needed to assess other important factors such as the importance of shred length, the economic aspects of using shredded waste tires as soil reinforcement compared to other reinforcement materials, the effectiveness of shredded waste tires as soil reinforcement in cohesive soils, and to see if results obtained in the laboratory are representative of field applications.Although, the results of this study may be somewhat different to full-scale foundation behavior in the field, the general trend may be similar. Overall, qualitatively, this study provides insight into the basic mechanism that establishes the bearing pressure versus settlement response of the shredded rubber-reinforced soil bed and would be very useful and a fruitful avenue for future studies. On the whole, these results could be helpful in designing large-scale model tests and their simulation through numerical models.In this study, a series of laboratory tests under monotonic load has been carried out on square footings supported on the rubber reinforced and unreinforced soil beds. The test results have been used to assess and understand the potential benefits of reinforcing soil with rubber shreds and soil cap in terms of the increased bearing pressure of footing compared with footing on unreinforced beds. Based on the results obtained, the following conclusions are derived:The results prove the usefulness in recycling of tires waste in geotechnical aspects of waste management. These lead to overall saving in competent soil material costs and re-use of tires waste.The results strongly suggest the re-use of tire waste in the form of shredded rubber mixed with soil as reinforcing elements beneath the footing. From the results of tests, the bearing capacity of footing increases with increase in the rubber content, the thickness of rubber-reinforced soil layer and the soil cap thickness up to their optimum values, after which the bearing pressure decreases.The optimum percentages of shredded waste tire rubber are measured around 5% of the total volume of soil-rubber mixture. This leads to the maximum improvement in bearing capacity of footing regardless of soil cap thickness and the thickness of reinforcement layer.Tire shreds-soil mixture used as a reinforcement layer under footing base performs more effective when covered by a soil cap layer compared to tire shreds-soil mixtures without a soil cap layer. The optimum depth of soil layer beneath the footing (i.e. the thickness of soil cap layer over the mixture) is obtained approximately 0.25 times the footing width (hs/B |
= 0.25) which results the best performance in increasing the bearing capacity.The optimal thickness of the rubber-reinforced soil layer to achieve the maximum improvement in bearing capacity of footing is measured to be approximately 0.5 times of the width of the footing. More increase in the thickness of rubber–soil mixture than its optimum value increased the compressibility and the settlement of foundation bed, and consequently the reduction in reinforcing effect of rubber–soil mixture. It may reduce the performance of foundation bed compared to fully unreinforced bed.At all the footing settlement levels, bearing pressure of footing has substantially increases for shredded rubber-reinforced bed, when considering the optimum values of soil cap thickness, the thickness of rubber-reinforced soil layer and the rubber content compared to unreinforced bed. At the settlement level of 5%, maximum improvement in bearing capacity was observed as the value of bearing capacity of footing reaches around 2.68 times of the unreinforced bed.Based on the above findings, it can be concluded that the use of shredded tire-soil mixtures as reinforcement layer in foundation bed beneath the footing is very promising and should be promoted. Performance of the rubber shreds by considering the optimum values of effective parameters was quite satisfactory and emphasize that shredded waste tires could be useful as reinforcement material in geotechnical applications. Conceivably, the results of this study could be extended in pavement project subjected by repeated load similar to traffic load in future study. Additionally, this use is beneficial to the environment in that a waste material is recycled.Ab initio calculations of elastic constants and thermodynamic properties of NiAl under high pressuresWe have investigated the structural and elastic properties of NiAl under high pressures using norm-conserving pseudopotentials within the generalized gradient approximation correction (GGA) in the frame of density functional theory. The calculated pressure dependence of the normalized volume is in excellent agreement with the experimental results. The elastic constants and anisotropy as a function of applied pressure, the ratio of the normalized volume V/V0 with the applied pressure are presented. The variations of bulk modulus, anisotropy and the brittleness with the pressure are investigated. Through the quasi-harmonic Debye model, we also study the thermodynamic properties of NiAl. The thermal expansion versus temperature and pressure, the thermodynamic parameters (Debye temperature and specific heat) with pressure P, and the heat capacity of NiAl at various pressures and temperatures are estimated.NiAl possesses the stable B2(cP2) crystal structure, which consists of two interpenetrating primitive cubic cells, where Al atoms occupy the cube corners of one sublattice and Ni atoms occupy the cube corners of the second sublattice. NiAl has been studied extensively as a potential structure material in the aerospace industry for over three decades because of its high melting temperature, low density, good environmental resistance, high thermal conductivity, attractive modulus, etc. In our case, we focus on investigating the EOS (equations of state) and the elastic properties of the NiAl from −20GPa to 60GPa by the plane-wave pseudopotential density functional theory method through the Cambridge serial total energy package (CASTEP) program In the electronic investigation, all calculations are performed based on the plane-wave pseudopotential density function theory (DFT) The energy–volume (E–V) curve can be obtained by fitting the calculated E–V results to the Birch–Murnaghan EOS ΔE(V)=E-E0=B0V0VnB0′+11-B0′+Vn1-B0′B0′(B0′-1)where E0 is the equilibrium energy at zero pressure. The pressure P versus the normalized volume Vn is obtained through the following thermodynamic relationship:Where B0′=dB0dp and B0 are the pressure derivative of the bulk modulus and zero pressure bulk modulus, respectively.To calculate the total energy E and the corresponding volume V for NiAl, we take a series of different lattice parameters a and carry out total energy electronic structure calculations over a wide range of primitive cell volumes V, i.e., from 0.7V0 to 1.2V0, where V0 is the zero pressure equilibrium primitive cell volume. Through these calculations, we can obtain the equilibrium lattice parameters a (). It is found that the equilibrium lattice parameter and bulk modulus B are consistent with experimental data The ratio V/V0 as a function of the applied pressure together with the experimental and other theoretical results are plotted in , where V0 are their values at T |
= 0 and P |
= 0, respectively. Our obtained data are consistent well with the experiments The elastic constants are defined by means of a Taylor expansion of the total energy E(V,δ) for the system with respect to a small strain δ of the lattice primitive cell volume V. The energy of a strained system is expressed as follows E(V,δ)=E(V0,δ)+V0∑iτiξiδi+12∑ijCijδiξiδjξj,where E(V0,0) is the energy of the unstrained system with equilibrium volume V0, τi is an element in the stress tensor and ξi,ξj are factors of Voigt index. The pressure P versus the normalized volume Vn is obtained through the following thermodynamic relationship:There are three independent components of the elastic tensor for NiAl, i.e., C11, C12 and C44. To obtain all elastic constants, we at least need three independent strains listed in . For each strain, a number of small values of δ are taken to calculate the total energies for the strained crystal structure. The calculated E–δ points are then fitted to a second-order polynomial E(V,0), and the third-order derivatives of E(V,0) with respect to δ are easily obtained.If one is to calculate the average isotropic elastic moduli from the anisotropic single crystal elastic constants, the Voigt and Ress assumptions resulting in the theoretical maximum and the minimum values are useful. For the specific case of the cubic lattices, the shear modulus G, the Young’s modulus E, Poisson’s ratio σ and anisotropy factor (A) respectively. Where Gv |
= (2C′+3C44)/5, GR |
= 15(6/C′+9/C44)−1, C′ = (C11–C12)/2. GV and GR are the Voigt shear modulus and the Reuss shear modulus, respectively.The obtained elastic constants Cij, Bulk modulus B, Young’s modulus E, Shear modulus G and Poisson’s ratio σ at T |
= 0 are presented in , together with the experimental data and other theoretical results. The Ab initio computations of elastic constants Cij, the Bulk modulus B, Young’s modulus E and Shear modulus G of NiAl are close to the experimental data As known, the elastic constants determine the response of the crystal to external forces. They play an important part in determining the strength of the material. The single crystal shear moduli for the {1 0 0} plane along the [0 1 0] direction and for the {1 1 0} plane along the [11¯0] direction are simply given by G{100} |
= |
C44 and G{110}, respectively. Also listed in , are bulk modulus (B), shear modulus G{100} |
= |
C44 and G{110} |
= (C11−C12)/2, Young’s modulus(E) and E<100> |
= (C11−C12)[1 + |
C12/(C11 |
+ |
C12)], Poisson’s ratio (σ) and shear anisotropy factor (A), across the high pressures. It is surprising that the shear moduli G{100} are always higher than G{110} from 0 GPa to 60 GPa, indicating that it is easier to shear on the {1 1 0} plane along the [11¯0] direction rather than on the {1 0 0} plane along the [0 1 0] direction. Pettifor The Young’s modulus E and Poisson’s ratio σ are important for technological and engineering applications. The first one is defined as the ratio between stress and strain, and is used to provide a measure of the stiffness of the solid, i.e., the larger the value of E, the stiffer is the material. The second, the Poisson’s ratio provides more information about the characteristics of the bonding forces than any of the other elastic constants. The σ |
= 0.25 and 0.5 are the lower limit and upper limit for central force solids, respectively. In our case, the Poisson’s ratio increases with applied pressure (). The obtained σ values are very close to the value of 0.4 which indicate that the interatomic forces in the NiAl are predominantly central forces.The elastic anisotropy of crystals has an important implication in engineering science since it is highly correlated with the possibility to induce microcracks in the materials ) A are all bigger than 1. This shows the elastic anisotropy in NiAl. It has been recently proposed The dependence of bulk modulus B on temperature T (a) is investigated through the quasi-harmonic Debye model b. These results indicate that B increases with P at a given temperature and decreases with T at a given pressure. It shows the fact that the effect of increasing pressure on NiAl is the same as decreasing its temperature.At temperatures well above Debye temperature, the Debye temperature quantum effects can be neglected, we here make a calculation for the thermal expansion coefficient with temperature and pressure. The thermal expansion coefficient can be obtained from the temperature derivative of the lattice constants. The obtained variations of the thermal expansion α with temperatures and pressures are shown in a and b. Our results are nearly identical to that of Y. Wang et al. a). It is noted that at zero pressure α increases exponentially with T at low temperatures and gradually approaches a linear increase at high temperatures (a). At different temperatures (300, 600, 1600 K), the thermal expansion coefficients decrease nonlinearly at the lower pressure and decrease almost linearly at the higher pressure (b). When the pressure is above 120 GPa, the thermal expansion α of 1600 K is just a little larger than that of 600 K, as means that the temperature dependence of α is very small at high temperature and higher pressure., we show the heat capacity CV and the Debye temperature θ as a function of pressure P at the temperatures of 300 and 1800 K for NiAl. It is shown that at given temperatures (300 and 1800 K), the Debye temperatures increase almost linearly with applied pressures. However, the heat capacities decrease with the applied pressures, as is due to that the effect of increasing pressure on NiAl is the same as decreasing temperature of NiAl., the heat capacities of NiAl are plotted for several pressures. It is shown that the heat capacity CV fits T3 term in their low-temperatures at the given 0, 50, 90, 130 GPa. This is due to the harmonic approximations of the Debye model. When T |
> 1800 K, the CV is close to the Dulong–Petit limit.The elastic constants of NiAl at high pressure are computed by the norm-conserving pseudopotentials within the generalized gradient approximation in the frame of density functional theory. We carry out total energy calculations over a wide range of volumes from 0.7 V0 to 1.2 V0, and obtain the equilibrium ratio of the normalized volume V/V0 for a given volume. The obtained pressure dependence of the normalized volume is in excellent agreement with the experimental and other theoretical results.The elastic constants and the shear anisotropic factors A of NiAl at high pressure from −20 GPa to 60 GPa are also calculated. An analysis of the calculated parameters reveals the anisotropy in NiAl. That is, in the range of applied pressure, the anisotropy is remarkable. Finally, we investigate the thermodynamic properties, the relationships among the thermal expansion, temperature and pressure, as well as the variations of Debye temperature and specific heat with pressure.Strain effect on the mechanical and electronic properties of graphene-like B4P4C4 and B2P2C8: First-principles calculationIn this work, we predict two novel ternary graphene-like structures, B4P4C4 and B2P2C8 monolayer. Their structural, mechanical and electronic properties are systematically investigated based on first-principles methods. The results show that the intrinsic and the strained materials possess excellent dynamic, thermal and mechanical stability, which provide the possibility for experimental preparation. Calculation results show that the intrinsic B4P4C4 monolayer has the Dirac feature. Particularly, the intrinsic B2P2C8 monolayer exhibits unique double Dirac points and non-trivial topological property. It is found that the Dirac states in B4P4C4 monolayer can be effectively regulated by applying horizontal strain, exhibiting the characteristics of a semiconductor with a direct or indirect band gap even an intriguing semiconductor-metal transition. In contrast, the intrinsic B2P2C8 monolayer is not sensitive to biaxial strain and its stability and semi-metal state preserve well like graphene, which benefits by its non-trivial topological property. Additionally, the calculated Young's modulus and Poisson's ratio show the mechanical anisotropy and excellent resistance of deformation of both the structures. Our work expands the 2D material family and these outstanding properties make B4P4C4 and B2P2C8 monolayer promising candidates for potential applications in battery, super capacitor, sensor and other fields.Since the discovery of two-dimensional (2D) graphene [], low dimensional materials, such as transition metal dichalcogenides (TMDs) [], transition metal carbides or nitrides (MXenes) [] et al. have received tremendous attention. And these kinds of graphene-like materials have sprung up []. The distinctive electronic properties like massless Dirac fermions [], half-integer/fractional/fractal quantum Hall effect [] make graphene one of the most promising materials for applications in nanoelectronics and these properties exist in the form of the Dirac point which originates from the unique linear band dispersion near the Fermi level. Surface/edge state [] can be used to analyze the Dirac point and topological property of materials. The surface states of different crystal surface are observed by experimental methods such as angle-resolved photoemission spectroscopy technique (ARPES) []. Inspired by the intriguing Dirac point in honeycomb graphene, people stimulate widespread attention to 2D materials to reveal their unknown physical properties and explore their potential applications in nanoscale devices. Among hundreds of 2D materials that have been discovered, a crowd of 2D carbon allotropes (graphene, graphyne and phagraphene) [], silicene and germanene (graphene-like silicon and germanium, respectively) [], organometallic crystals as well as some other systems have been predicted to be Dirac materials []. With the further advancement of theoretical researches, more and more such materials will be discovered and provide reliable support for experimental synthesis to satisfy numerous practical applications.The existence of Dirac point requires symmetry and band overlap at the Fermi level and it is summarized that the hexagonal structure is the most favorable for the existence of Dirac point amongst all the predicted and synthesized 2D materials []. As a close neighbour of the carbon element, the 2D structure of boron (B) has also attracted wide attention []. However, the monolayer of boron with a hexagonal structure in an electron-deficient state is difficult to exist stably, giving rise to its impossibility to prepare a single-layer boron Dirac material []. Phosphorene (P) has high carrier mobility in nanosheets and nanoribbons, but the poor chemical stability in this element limits the potential applications in devices []. Ulteriorly, theoretical prediction and experimental successful synthesis by chemical vapor deposition (CVD) of hexagonal boron phosphide solve these problems []. Hexagonal boron phosphide is a direct band gap (0.81–1.81 eV) semiconductor of atomic thickness, indicating that h-BP is a promising candidate material for electronic and optoelectronic devices, and its mechanical stability and high thermal stability are successively proven []. In order to improve the conductivity of such semiconductor material and explore its possibility of becoming a Dirac material, C atom is doped in the system for its good performance in improving the conductivity of systems. The narrowing or disappearance of the band gap of h-BP leads to the possibility of forming Dirac point. Recently, the exploration of new 2D ternary material using h-BP monolayer as starting material has been initiated and a new graphene-like ternary 2D material is predicted: BPC2 monolayer, which is semi-metal with a Dirac cone and has cohesive energy value between those of graphene and h-BP [Based on abundant previous researches and inspired by many excellent works, we adjust the ratio of each element (B, P, C) and predict two novel forms of ternary graphene-like Dirac materials: B4P4C4 and B2P2C8 monolayer utilizing the particle-swarm optimization (PSO) algorithm []. Both B4P4C4 and B2P2C8 possess the honeycomb lattice with outstanding thermal, dynamical and mechanical stability. Band structure calculations indicate that the intrinsic B4P4C4 monolayer has the Dirac feature but is topologically trivial. Particularly, the intrinsic B2P2C8 monolayer exhibits unique of double Dirac points and non-trivial topological property. The horizontal biaxial and uniaxial strain are applied on the materials to explore the sensitivity of the electronic characteristics to strain and reveal the tuning mechanism. We believe that our work will contribute to the future application of boron phosphide monolayer in different fields.The PSO method as implemented in the CALYPSO [] code interfaced with Vienna ab initio simulation package (VASP) [] is employed to locate the low-energy structures of 2D BPCx (x = 1, 2, and 4) []. To ensure convergence, the numbers of generation and population size are set to be 30. And for better querying of the configurations, 1 to 4 formula units in each unit cell are used. Finally, three ground state structures were found with stoichiometry of B4P4C4, BPC2, and B2P2C8. Interestingly, BPC2 is exactly the structure reported previously [The structure relaxations are performed by Density Functional Theory (DFT) [] as implemented in the VASP within the generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional []. The projected augmented wave (PAW) method is used to represent the interaction between ion core and valence electron []. The plane wave kinetic energy cutoff is set to be 600 eV. The criteria of convergence for energy and atomic force are 10−5 eV and 0.02 eV/Å, respectively. The Brillouin zone is sampled with Monkhorst–Pack k-point grid of 7 × 7 × 1 for structure optimization and a denser k-point mesh of 11 × 11 × 1 for the static self-consistent calculations. The vacuum space of 25 Å along z direction is set to avoid the periodic image interactions. The topological property is analyzed by using WannierTools [] and the input file of WannierTools is constructed by Quantum Espresso (QE) []. The dynamic stability of all structures is confirmed by phonon calculations using a 3 × 3 × 1 supercell via the force-constant method []. First-principles molecular dynamics (MD) with NVT thermostat using the Nosé algorithm [] is performed at 300 K for 5 ps, with a time step of 1 fs to verify the thermal stability of all structures.The fully optimized structures of B4P4C4 and B2P2C8 are presented in Graphene is considered to be one of the most promising materials for energy storage, optoelectronic device field and manufacturing membrane materials due to its superior thermal, chemical, mechanical stability and other unique properties []. So relevant calculations are made to study the stability of the both novel graphene-like materials. The phonon dispersion along the high-symmetry lines in the first Brillouin zone are shown in (a and b). There is no soft mode in the Brillouin zone, suggesting that B4P4C4 and B2P2C8 are stable.In practical applications, structural stability at room temperature are important. Hence, the thermal stability of B4P4C4 and B2P2C8 are studied with first-principles molecular dynamics at 300 K. The free energy evolution is illustrated with black lines in (c), and the total energy is nearly fluctuating around a constant value throughout the simulation and after 5000 steps there are no substantial deformations in both B4P4C4 and B2P2C8. These results indicate that B4P4C4 and B2P2C8 are thermodynamically stable at room temperature.As graphene-like materials, the mechanical stability of B4P4C4 and B2P2C8 is also estimated by evaluating the independent elastic constants using density functional theory-based methods []. Normally, the elastic constants of a mechanically stable 2D material obey the Born criteria: C11C22-C212>0 and C66 > 0 []. The related elastic constants of B4P4C4 (B2P2C8) are listed in , which satisfies all of the above-mentioned conditions. The stability analysis above makes it possible to synthesize the predicted structures in experiment.The mechanical property of graphene has been studied experimentally or predicted theoretically []. Excellent mechanical property allows materials to be widely applied in integrated electronics, thermal materials, and electromechanical devices. Based on the elastic constants, the Young's modulus and Poisson's ratio of two predicted materials can be calculated. The values of Young's modulus and Poisson's ration depend on the in-plane angle θ, where θ is the angle with respect to the positive x direction of the structure []. The calculated Young's modulus and Poisson's ratio, as shown in , indicating the mechanical anisotropy of B4P4C4 and B2P2C8. Mechanical anisotropy is a relatively common property of 2D materials and the magnitude is directly proportional to the difficulty of peeling 2D materials from bulks into atomic thickness monolayer. To effectively direct the mechanical exfoliation, Ji et al. quantify the difficulty level of exfoliation of atomic thickness materials [(a), the maximal value of Young's modulus is at the angular bisectors of the axial directions and the maximum of B4P4C4 and B2P2C8 is 180.44 N/m and 247.14 N/m, respectively. The minimal value of Young's modulus of both materials is along the axial direction except for the difference that B4P4C4 is along the x direction (168.87 N/m) while the minimal value of Young's modulus of B2P2C8 is along the y direction (215.96 N/m). This indicates that stretching these 2D materials along the diagonals of the unit cell is harder than along the axial directions. These values are comparable to the pristine monolayer graphyne with the value of 162 N/m, but smaller than those of graphene (~340 N/m). Such significantly Young's modulus of high value shows the structures own excellent rigidity and exhibit the ability of resisting deformation and B2P2C8 is more resistant to deformation compared to B4P4C4. As demonstrated in (b), the tendency of Poisson's ratio is similar to the behavior of Young's modulus. The calculated Poisson's ratios of B4P4C4(B2P2C8) are between 0.29 and 0.37(0.29–0.34). These values are comparable to that of cp-graphyne (0.30) [] and almost twice that of graphene (0.186).Previous studies have shown that graphene exhibits unique electronic properties under biaxial and uniaxial strain []. To evaluate the electronic performance of the pristine B4P4C4 and B2P2C8 monolayer, we investigate their band structures, projected band structures and the corresponding partial density of states (PDOS). As shown in (c), the bands are plotted along the first Brillouin zone with the high-symmetry points [Γ(0, 0, 0)→K(12,0,0)→M(12,12,0)→ Γ(0,0,0)→R(0,12,0)→M(12,12,0)]. It can be seen from (a) that the monolayer B4P4C4 is a zero-band-gap semi-metal with the conduction band minimum (CBM) and the valence band maximum (VBM) touching each other at the Γ point. As shown by projected band structure, the CBM and VBM are mainly contributed by the C and P atoms, respectively. The PDOS also shows that the state is chiefly composed of hybridized p orbitals from the P and C atoms. Seen from (b), the projected band structure and the PDOS of the B2P2C8 monolayer show that the CBM and VBM are principally contributed by the C atoms (p orbitals). However, there is a band inversion around the Γ point, giving rise to CBM and VBM contact at the point D1 (0, 0.02, 0), on the right side of the Γ point on the Fermi level, demonstrating that B2P2C8 is also a graphene-like semi-metal material. Furthermore, we have also calculated the 3D band structure of B4P4C4 and B2P2C8, as shown in (d and e), to confirm the existence of the Dirac point and reflect the band characteristics of the complete Brillouin zone. Interestingly, as illustrated in (e), we find another Dirac point D2 (0, −0.02, 0) at the symmetrical position of point D1, indicating that B2P2C8 is a double Dirac point semi-metal 2D material.The topological property is determined by Z2 number [ shows the Wannier charge center evolution for the time-reversal invariant planes of B4P4C4 and B2P2C8. The Z2 number of B4P4C4 equals to 0, indicating its topologically trivial property. While the Z2 number of B2P2C8 equals to 1, which indicates its non-trivial topological property and the material is robust. As shown in ] spectrum (SSS) for 001 surface of B2P2C8 in the presence of spin–orbit coupling is calculated by WannierTools. It is obvious that the calculated SSS exhibits that the linear band dispersion close to the Fermi level is topologically non-trivial. (b) shows an iso-energy (Fermi energy) plot of the surface state spectrum in the first Brillouin zone. This plot shows that its Fermi surface consists of two points around Γ points. These two points are Dirac points and this result is consistent with 3D band structure of B2P2C8 in Graphene is always a zero band-gap semiconductor with symmetrical strain distribution while applying asymmetrical strain distributions can lead to the opening of band gaps of graphene at the Fermi level []. Inspired by this, it is reasonable to investigate whether horizontal strain can effectively modulate the electronic property of B4P4C4 and B2P2C8. The strain parameter μ is defined as μ = (a – a0)/a0, where a and a0 are the lattice constants with and without strain, individually. Positive and negative values represent tensile and compressive strain. Sun et al. reported their experimental work about buckled CdS nanowires and the tensile strain can be increased up to 11% []. Hence in this work, the range of strain parameter μ are set from −10% to 10%. It is deserved to be mentioned that the phonon spectrum and the molecular dynamics results (represented with red lines in ) indicate that both B4P4C4 and B2P2C8 monolayer maintain dynamic and thermal stability under the uniform strain of 10%. shows the band structures of B4P4C4 monolayer under biaxial and uniaxial strain. It is obvious that some states near the Fermi level are sensitive to strain and we mark the CBM under different strains and connect them with red lines. As shown in (a), with the increasing of the uniform tensile strain from 0% to 10%, the CBM gradually rises at the Γ point and the band gap increases from 0 eV to 0.28eV, maintaining the characteristic of direct-band-gap. In (b), the CBM have the increasing tendency under the uniaxial tensile strain along x-axis and the VBM located at the Γ point moves to the point located at the Γ → K path as the tensile strain increases to 6%, indicating that the band gap can't maintain a direct band gap. The new VBM continues to increase until it crosses the Fermi level at 10% strain, demonstrating a semiconductor–metal transition. Before the occurrence of phase transition, the band gap varies from 0 eV to 0.44eV. (c) shows the VBM and the CBM transfers from Γ point to the position between the Γ and K points under the compressive strain along y-axis of −6% and −8%, respectively. The largest indirect band gap of 0.34 eV can be observed when μ equals −10%., the total energy, band gap and effective mass of the structures, which are the functions of strain, are calculated. In (a), the total energy of B4P4C4 monolayer under the equilibrium state is always the lowest and with the change of the lattice constant, the energy increases. The band gap in (b) shows no significant change when applying the biaxial compressive strain, tensile strain along the y-axis and compressive strain along the x-axis. The band gap is more sensitive to the uniaxial compressive strain along x-axis compared to biaxial compressive strain and the semiconductor-metal phase transition happens when the uniaxial compressive strain applied on B4P4C4 monolayer goes up to 8%. This result is consistent with the slightly inferior ability of resisting deformation in the x direction. The evolution of band structures under strain consequently alters the effective mass of the carries which depends on the curvature of the band edges near the Fermi level. (c) demonstrates the tendency of the calculated effective masses of the electrons (me) and the holes (mh) under different strains. With the changes of strain, the slopes of the band edges show different degrees of diminution, resulting in an overall increasing trending of the effective masses of the electrons and the holes. Moreover, the effective masses of the carriers under the uniaxial compressive strain along x direction have steeper tendency of increase comparing to those along y direction and biaxial strain. shows the band structures of B2P2C8 monolayer under biaxial and uniaxial strain. As depicted in (a), biaxial strain from −6% and 6% can hardly modify the band structure of B2P2C8 monolayer around the Fermi level and this result is a good confirmation of the topological property of B2P2C8. It also demonstrates that the material is not sensitive to biaxial strain, similar to graphene. However, as illustrated in (b and c), uniaxial strain can open the band gaps of B2P2C8 monolayer. The compressive strain of −6% along the y-axis induces the indirect band gap increase from 0 to 0.14 eV. It can be seen that the VBM transfers to the position between the Γ and K point and stays around the Fermi level, while the CBM moves from Γ point to the point along Γ → K path and keeps rising before the tensile strain up to 8% and then falls. The indirect band gap increases from 0 to 0.19 eV as the tensile strain along the x-axis varying from 0 to 6%, and decreases to 0.11 eV when the strain is up to 8%. When the tensile strain goes beyond 8.5%, the VBM crosses the Fermi level, inducing the semiconductor-metal transition. shows the top and side views of the partial charge density of the CBM at Γ point of B4P4C4 and B2P2C8 under the applied biaxial strain of −4%, 0, 10% and the uniaxial strain along the x-axis of −4%, 0, 6%, respectively. As mentioned in (a and b), the CBMs of B4P4C4 and B2P2C8 monolayers originate from C atoms. However, with the strain changing from compression to tension, the charge gradually transfers from P atom to C atom according to the bader charge analysis []. The consistent increasing of the conduction band at the Γ point coincides with the transfer of charge.In this work, we have predicted two graphene-like 2D materials, B4P4C4 and B2P2C8, from a global structure search and systematically studied the structural, mechanical, and electronic properties using first-principle calculations. Band structure, bader charge, PDOS, partial charge density, and projected band structures are calculated. The results indicate that these two honeycomb ternary materials possess excellent dynamic, thermal and mechanical stability. The intrinsic B4P4C4 monolayer has the Dirac feature and shows topologically trivial. Interestingly, the intrinsic B2P2C8 monolayer exhibits unique electronic property of double Dirac point and topologically non-trivial property. We also demonstrate that the Dirac states in these materials can be effectively modulated by applying horizontal strain. For B4P4C4 monolayer, when applying the biaxial tensile strain, the compressive strain along y-axis and the tensile strain along x-axis, the structure exhibits the characteristics of a semiconductor with a direct or indirect band gaps within 0.44 eV. With the increase of the tensile strain along x-axis to 10%, the band gap decreases from 0.44 eV to 0 eV, demonstrating a semiconductor-metal transition. However, the intrinsic B2P2C8 monolayer is sensitive to the uniaxial strain instead of the biaxial strain, which is similar to graphene. Additionally, the calculated Young's modulus of B4P4C4(B2P2C8) monolayer ranging from 168.87(215.96) N/m to 180.44(247.14) N/m and Poisson's ratio of 0.29–0.37(0.29–0.34) show the mechanical anisotropy and excellent resistance of deformation of the structures. Our work enriches the 2D material family and these outstanding properties make them promising candidates for potential applications in battery, super capacitor, sensor and other fields.All data used during the study is available from the corresponding author by request.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in the manuscript “Strain effect on the mechanical and electronic properties of graphene-like B4P4C4 and B2P2C8: first-principles calculation”.Fabrication and characterization of WC particles reinforced NiFe composite coating by jet electrodepositionFe composite coating is widely used in the industrial field because of its excellent mechanical properties. If its mechanical properties are improved, its application will be further promoted. In this paper, Ni-Fe-WC composite coatings were prepared by jet electrodeposition (JED). The effects of deposition temperature and deposition current density on the composition and structure of the coatings were investigated. The results show that with the increase of the deposition current density or deposition temperature, the content of WC particles in the coating is increased. When the deposition current density is 100 A/dm2 and the deposition temperature is 50 °C, the content of WC particles reaches the maximum value of 1.45 wt%. The wear resistance and corrosion resistance of the coating are all enhanced with the increase of WC particles. The optimum wear resistance and corrosion resistance are increased by 45.3% and 75.4% respectively. With the increase of the deposition current density or deposition temperature, the grain orientation of the coating gradually changes from (111) to (200) and (220). When the deposition current density is 50 A/dm2 and the deposition temperature is 30 °C, the coating has a (111) fully oriented structure. The adhesion force of coating and substrate is positively correlated with TC(111). When TC(111) is 100%, the maximum adhesion force is more than 60 N. The lower deposition current density or higher deposition temperature can promote the nucleation of metal atoms and inhibit the growth of nucleation, the average grain size of the coating decreases and the strength of the coating increases accordingly. This study can provide theoretical support for the preparation of particle enhanced NiFe composite coatings with required properties.The Ni-Fe-WC composite coating were prepared by jet electrodeposition (JED). The increase of WC particles improved the wear resistance and corrosion resistance of coating. The small average grain coating has high strength and large average grain coating has good ductility. The adhesion force of coating increases with the increment of TC(111) and NiNickel-based alloys are widely used in military, aviation, automotive, instrumentation, medical treatment and other industries due to the excellent mechanical properties and the relatively cheap price [Fe alloy is one of the common nickel-based alloys, which are broadly utilized in specific industrial applications including computer storage, optical disc, magnetic tape recorder heads, solenoid valves, MEMS, magnetic shielding equipment surface and so on [Fe coating mainly includes cold spraying [], etc. Electrodeposition is the most common method for preparing NiFe alloy coatings because of its simple equipment, low cost and the ability to prepare nanostructure coatings with controllable thickness.However, with the increasingly strict industrial requirements, the NiFe alloy coating needs to serve in a more demanding environment, so the NiFe alloy coating is put forward better mechanical properties and corrosion performance requirements. Researchers have proposed a variety of methods to enhance the performances of NiFe coatings, of which adding a second reinforcing phase is a commonly used and effective means []. The reinforcing phase includes high hardness particles, metal powders, or rare earth oxides. When the metal coating is mixed with micro/nanoparticles, the particles play a dispersive hardening effect in the coating, and the coating hardness, wear resistance, corrosion resistance and mechanical properties can be significantly improved. Different types of particles can be added according to the required coating properties []. In recent years, many researchers have prepared particle-enhanced NiFe composite coatings by conventional immersion electrodeposition. The results show that the overall performance of NiFe coatings with reinforcing phase particles are significantly improved. Aliofkhazraei et al. [] reviewed the effects of ceramic particles, oxide particles and non-oxide particles on the hardness, thickness, surface roughness and wear resistance of nickel-based coatings. It is considered that the hard particles embedded in the metal coating can refine the grain of the coating, and the addition of non-viscous lubricant particles can significantly improve the wear resistance. The multilayer Ni-Fe-Al2O3 composite coating was prepared by different duty cycle pulse current. It was found that the hardness and wear rate of ML coating were significantly better than that of single coating. The mechanical properties of the whole coating could be improved by decreasing duty cycle and increasing frequency [] found that Al2O3 particles with 0.5 μm particle size have high hardness and excellent corrosion resistance, so adding Al2O3 to NiFe coating can optimize its properties, and it is found that reducing Fe content and increasing particle content are beneficial to improve the wear resistance and corrosion resistance of coating. Li et al. [] selected ZrO2 particles with high hardness and corrosion resistance as reinforcement phase, and prepared Ni-Fe-ZrO2 composite coating by pulse electrodeposition. It was found that the corrosion resistance of the coating was related to the content of Fe and the concentration of ZrO2. The coating of 74.7% Ni, 16.8% Fe and 8.5% ZrO2 had the best anti-corrosion. Yousefi et al. [] believed that TiO2 particles had high hardness, excellent wear resistance and corrosion resistance, and were an excellent choice as reinforcing phase. The Ni-Fe-TiO2 composite coating was prepared by pulse electrodeposition. It was found that the friction coefficient and wear rate of the coating could be decreased by decreasing Fe content and increasing TiO2 particles. The maximum wear rate decreased by about 40%. Rasooli et al. [] showed that Cr2O3 particles with excellent corrosion resistance could be used as reinforcement phase, and investigated the relationship between the concentration of Cr2O3 nanoparticles and the anti-wear and anti-corrosion of Ni-Fe-Cr2O3 coating. The results show that as the Cr2O3 nanoparticles concentration of plating solution reaches 6 g/L, the nanoparticles content of Ni-Fe-Cr2O3 coating is the maximum. Meantime, the properties of anti-wear and anti-corrosion are the most outstanding. Safavi et al. [] considered that Y2O3 nanoparticles have excellent corrosion resistance and good mechanical properties. The anti-corrosion property of NiFe coating was effectively improved by adding Y2O3 nanoparticles and glycerin.WC nanoparticles have advantages of high hardness, excellent stability and relatively low non-expensive price, so attracted extensive attention in the area of preparing particle-reinforced coating. Liu et al. [] used laser to continuously prepare Ni-WC coating on copper substrate, and found that the hardness and anti-wear property of coating got a significant improvement due to the adding of WC. Luo et al. [] used electrochemical deposition method to prepare NiP composite coatings, and modified the NiP coating by adding WC particles. The results showed that the micro-hardness and anti-corrosion property of the coating were increased by about 50% and 3 times after the addition of WC nanoparticles. Elkhoshkhany et al. [] used plating method to prepare Ni-WC composite coating on nickel substrate. When the WC particles content in solution was increased to 8 g/L, the grain size of prepared coating was the smallest, the hardness and anti-corrosion property were obviously enhanced.The adding of reinforcing phase particles can effectively enhance the performances of NiFe coating. However, the size of reinforcing phase particles is micro or nano, and the hard particles of this size have higher surface energy, so that the vast majority of particles exist with the form of agglomeration []. In the process of preparing coatings by conventional immersion electrodeposition, the agglomeration state is difficult to be broken only by stirring, so it is easy to get composite coatings with uneven particle distribution, which seriously affects the stability and consistency of coating properties. JED is a kind of local high-speed unconventional electrodeposition method. The plating solution is jetted to the surface of cathode, and electrodeposition is carried out only where the liquid column contacts. The high-speed flowing plating solution can quickly supplement the metal ions consumed near the cathode and effectively avoid the occurrence of concentration polarization. In the process of preparing the particle reinforced composite coating, particles with high momentum collide with the surface of substrate, which can effectively break the agglomeration state, and finally obtain more uniform and stable coatings []. Therefore, JED used to prepare nanoparticle-enhanced composite coating has the superiorities of efficient preparation efficiency and excellent coating quality [], so it has attracted the focus of researchers. Wang et al. [] used JED to prepare Ni-CeO2 coatings, and found that the anti-corrosion property of coating improved with the increment of CeO2 nanoparticles. Ma et al. [] used ultrasonic-assisted pulsed JED to prepare Ni-AlN coatings. Compared with the single JED, the introduction of ultrasonic makes the structure of the coating more denser, and can increase AlN particles content within coating, and finally enhance the hardness and anti-wear property of coating. Ji et al. [] used JED to prepare Ni-graphene films, and found that the hardness of prepared coating was improved with the increment of graphene concentration. When the concentration of graphene was 0.5 g/L, the prepared coating had the best anti-corrosion property. Xia et al. [] used JED to prepare Ni-TiN thin films and analyzed the impact of TiN particles concentration within plating solution on the properties of coating. They found that the coatings prepared when the TiN concentration was 5 g/L had the highest hardness and the best corrosion resistance. Jiang et al. [] used magnetic field-assisted JED to prepare Ni-SiC coatings. Compared with single JED, magnetic field-assisted JED can effectively increase the SiC particles content within coating, and further enhance the anti-wear property of coating.According to literature, although researchers have made great efforts to enhance the mechanical performances of NiFe coatings, but most of them focus on the use of conventional immersion electrodeposition technology. The use of JED to prepare NiFe coatings has not been reported. It is of great significance for researchers to broaden their understanding of NiFe coatings with better properties by JED. Therefore, this research use JED to prepare the Ni-Fe-WC composite coatings for the first time. The adhesion, strength, hardness, anti-corrosion property and anti-wear property of Ni-Fe-WC coating were systematically analyzed in terms of its composition and structure. The adsorption mechanism of WC particles in the process of JED was also studied. The research has made some theoretical and technical achievements, which can provide support for the preparation of particle-enhanced NiFe composite coatings with required properties.The reagents used in the experiment are all analytical grade. The average size of WC particles is 300 nm. The composition of plating solution and experimental parameters are demonstrated in . The solution is prepared with deionized water. The solution was prepared by ultrasonic treatment for 30 min, and then magnetic stirring for 2 h to ensure that the WC particles were evenly dispersed into the plating solution. The substrate material is medium carbon steel, which is pretreated before the experiment. The process of pretreatment is fine grinding and cleaning. depicts the experimental device. The device is composed of four main parts: movement control unit, plating solution circulation unit, heating and stirring unit and DC power supply. The system can accomplish the change of deposition track, scanning rate, nozzle and substrate distance, as well as the control of deposition current density, plating solution velocity, deposition temperature and coating thickness. When the power is switched on, current is transmitted through the titanium rod to the nickel and iron spheres in close contact, which act as anode. The substrate acts as cathode. Nickel and iron balls are electrolyzed to supplement consumed Fe2+ and Ni2+ of plating solution. Heating magnetic stirrer is used to heat and stir the plating solution of plating bath in order to keep a constant temperature and prevents WC particles from agglomerating. The pump is used for circulating plating solution, and through adjusting the external voltage of the pump to control the injection velocity. The PC controller sets the moving path of the nozzle and then the coating of the desired shape is prepared.The structure of Ni-Fe-WC composite coating was represented by a X-ray diffractometer (XRD). The morphology and composition of Ni-Fe-WC composite coating were observed through a scanning electron microscopy (SEM) equipped with energy dispersive spectrometer (EDS). The surface roughness of Ni-Fe-WC composite coating was tested by a contact roughness measuring instrument, and the sampling length was 4 mm. The hardness of Ni-Fe-WC composite coating was measured by an automatic micro-hardness tester equipped with diamond indentation, and the measurement parameters were 100 g load force and 15 s holding time. According to the ASTM standard, the results of micro-hardness test are the average of the 5 tests. The adhesion strength of Ni-Fe-WC composite coating was quantitatively expressed by a scratch tester with diamond tool (WS-2004). The test form was linear loading under dynamic load, the length was 4 mm, and the loading rate was 15 N/mm. The corrosion resistance of Ni-Fe-WC composite coating was characterized by a electrochemical workstation (CHI-760e) in 3.5 wt% NaCl solution at room temperature. The polarization curves were documented at range of −300 mV to +300 mV (relative to Eocp), and the scan speed was 0.002 V/s. The electrochemical impedance spectroscopy (EIS) investigations were documented at a frequency range of 105 to 10−2 Hz, and the amplitude of signal sinusoidal was 10 mV. The wear resistance of Ni-Fe-WC composite coating was characterized by a friction and wear testing machine (CFT-1, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences). Because the NiFe coating is used in the surface modification of key industrial equipment or precision instruments [], its service environment has the characteristics of dry and room temperature, small load and long time. Therefore, the parameters set in this friction experiment are as follows: The test type was linear reciprocated friction. The test environment was dry condition at room temperature. The counterpart was ceramic ball with a diameter of 6 mm, the load was 500 g, the linear velocity was 50 mm/s, the grinding track length was 5 mm, and the test time was 2 h. The 3D contours of wear marks were measured by a KEYENCE vhx-5000 super depth of field 3D microscope. The strength and elongation of Ni-Fe-WC composite coating were measured by an electronic universal testing machine (WDW-100D), and the tensile rate was 0.5 mm/min.Effect of deposition current density and deposition temperature on the composition of Ni-Fe-WC coatingIn the process of JED, the deposition current density and deposition temperature are important factors that affect the properties of particle reinforced composite coatings. This section studied their influence on the composition of Ni-Fe-WC coating. The deposition current densities are 50 A/dm2 and 100 A/dm2. The deposition temperatures are 30 °C, 40 °C, and 50 °C. The EDS spectrum images of Ni-Fe-WC composite coatings are presented in . Since only WC particles in the coating contain W element, the content of WC particles can be converted from the W element content by where WWC and WW are the mass fraction (%) of WC and W in the coating, MWC and MW are the molar mass (g/mol) of WC and W., the ratio of Ni: Fe and WC particles content of the coating increase with the rise of deposition current density or deposition temperature. The deposition mechanism of NiFe alloys has been systematically and extensively studied []. In the early studies of Vagramyan and Fatueva, it was proved that the presence of Fe ions inhibited the deposition of Ni, leading to the preferential deposition of Fe over Ni under many conditions. Such preferential metal deposition with negative potential belongs to abnormal co-deposition behavior [] found that Fe deposition is controlled by diffusion and Ni deposition is controlled by activation during the preparation of NiFe alloys. The speed of metal ion consumption is an important factor that determines the effect of hand diffusion on electrodeposition. Pavithra and Hegde [] found that the content of precious metals in the coating increased with the increase of current density or electrolyte temperature. As shown in , the content of Fe in the coating is much higher than the content of Fe2+ in the electrolyte, indicating that the process of preparing Ni-Fe-WC composite coating by JED also belongs to abnormal co-deposition. In the process of JED, the increase of deposition current density leads to the rapid consumption of metal ions, the increase of deposition temperature can improve the activity of ions, and the high-speed jetting greatly reduces the influence of diffusion on the electrodeposition behavior, thus impeding the abnormal co-deposition behavior. Therefore, increasing the deposition current density or deposition temperature is beneficial to the reduction of Ni2+, while inhibiting the reduction of Fe2+, and eventually increasing the content of Ni in the deposition layer.The adsorption mechanism of WC particles in the JED is shown in (b). In the process of JED, WC particles surrounded by hydrated ion groups impact on the surface of substrate, and the model can be simplified as a single WC particle surrounded by a large number of Ni2+ and Fe2+. Guglielmi [] expounded the mechanism of particle adsorption in the process of composite electrodeposition. They think that in the process of preparing particle reinforced composite coating, some particles near the substrate have a certain probability to stay on the substrate surface. The adsorbed particles can be divided into strongly adsorbed particles and weakly adsorbed particles, and the residence time of strongly adsorbed particles is longer than that of weakly adsorbed particles. In the process of electrodeposition, the deposition temperature affects the activity of metal ions. At high temperature, ions are more active and easier to be reduced []. The deposition current density affects the rate of ion reduction, and the rate of ion reduction is faster at high deposition current density. Under the conditions of low deposition temperature and low deposition current density, the number of reduced metal atoms per unit time is small, so those weakly adsorbed particles cannot be captured and fixed. Even some large-size strongly adsorbed particles are likely to be washed away because they are fixed loosely. Only small-size strongly adsorbed particles will be fixed. With the increase of deposition temperature and deposition current density, the number of reduced metal atoms per unit time increases significantly due to the significant increase in the activity and reduction rate of metal ions. The metal atoms have enough time to capture the strongly adsorbed particles and even have a certain chance to capture some small-size weakly adsorbed particles. In general, the WC particles content within Ni-Fe-WC composite coating increases with the increase of deposition temperature or deposition current density.Since most particle-enhanced composite coatings are used for surface modification on key parts of industrial equipment, these parts need to face long-term wear or corrosion, so they are required to have high hardness, excellent anti-wear and excellent anti-corrosion. This section focuses on the effect of WC particles on these properties of Ni-Fe-WC coating.The morphologies and surface roughnesses of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters are demonstrated in . It is obvious that when the deposition temperature reaches 30 °C, there are more holes, pits and other defects on the surface of coating. With the increment of deposition temperature, the number of defects diminishes gradually. As the deposition temperature reaches 50 °C, there are no obvious defects on coating surface. At low deposition current density (50 A/dm2), the coating surface roughness Ra is 0.197 μm, 0.217 μm and 0.288 μm with the deposition temperature increasing from 30 °C to 50 °C, respectively. At high deposition current density (100 A/dm2), the coating surface roughness Ra is 0.359 μm, 0.436 μm and 0.518 μm with the deposition temperature increasing from 30 °C to 50 °C, respectively. It is obvious that with the increase of deposition temperature or deposition current density, the coating surface roughness increases but the defect decreases. The reason for this phenomenon is that the Ni-Fe-WC composite coating prepared by JED at high deposition temperature or high current density contains more WC particles, and the increase of WC particles makes the surface roughness of the coating higher. Meanwhile, in the process of JED, WC particles are more easily to fill in the defects such as pinholes, which can effectively improve the surface quality [The thickness of the coating samples used to measure the hardness is about 70 μm, and the surface micro-hardness and cross-section micro-hardness of each coating are measured. shows the cross-section micro-hardness of Ni-Fe-WC composite coating at different distances from the substrate/coating interface. The micro-hardness of substrate is about 260 HV. The micro-hardness of same coating at different depths has no obvious fluctuation, indicating that the coating is relatively uniform. (b) shows the surface micro-hardness of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters.(a) and (b), it is obvious that the surface micro-hardness and cross section micro-hardness of single coating were almost identical. (c) shows the cross section SEM of Ni-Fe-WC composite coating prepared at 100 A/dm2 and 50 °C after hardness test. The cross-section element distribution of the coating is also analyzed ((d)). In the process of JED, the high speed flushing makes the WC particles uniformly distributed in the coating, so that the performances of coating keep consistent. Meanwhile, the coating average micro-hardness also increases with the increment of WC particles content. This is because WC particles can help to strengthen the coating structure [shows the friction coefficients of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters. The friction coefficient initially increases rapidly and then stabilizes within a few minutes from (b). The reason for this trend is that the surface oxide film is rubbed at the initial stage of friction. Generally speaking, the wear resistance of oxide film is stronger than that of coating, so the friction coefficient is lower. With the increase of friction time, the oxide film of the coating is gradually worn off, and the friction coefficient is gradually stable. (c) shows the average friction coefficient of Ni-Fe-WC composite coating decreases with the increment of WC particles content. The small friction coefficient of coating indicates its strong wear resistance. shows the wear morphologies of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters. The worn morphology of coatings with different WC particles content is obviously different.(a), when the content of WC particles in the coating is the least, the worn surface has two obvious areas. Lightly worn areas show ploughing grooves parallel to the direction of friction. The ploughing grooves are caused by the interaction between microcutting and plastic deformation, which is a typical abrasive wear characteristic []. In ploughing, the material is displaced on either side of abrasion groove without being removed []. In the severe wear area, there is a large area of friction product adhesion, which is caused by severe plastic deformation and delamination, which is a typical adhesive wear, and the material removal is more []. With the increase of deposition temperature, the content of WC particles in the coating increases, and the area of severe wear gradually decreases, indicating that the adhesive wear is reduced ((d–f), the worn surface morphologies of the coating prepared at high deposition current density also mainly presents ploughing grooves after wear, with no obvious wear products attached, but there are a certain number of large pits. The occurrence of large pits is due to the large amount of material removal during wear. With the increase of WC particles content, the number of large pits decreases gradually, indicating that the material removal volume decreases gradually. As shown in (f), when the WC particles content of the coating is the highest, the surface of the worn coating has only ploughing grooves, indicating that the wear mechanism of the coating is only abrasive wear.The wear rate of the Ni-Fe-WC composite coating can be calculated by where V represents wear volume, S represents sectional area of wear trace, D represents length of wear trace, P represents load, S represents total wear distance, T represents friction time. shows the three-dimensional morphologies of wear traces. (b) shows the cross-section size of wear traces, and sectional area S can be obtained by integrating from it. (c) shows the calculation results of wear rates. The results of wear rates are the average of the 5 tests. It is obvious that with the increment of WC particles content, the wear rate of Ni-Fe-WC composite coating gradually decreases, which represents the improvement of its wear resistance. shows the polarization curves of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters, and the corrosion current density (Icorr) and corrosion potential (Ecorr) can be obtained by Tafel extrapolation method. As Fe content decreased from 43.84 wt% to 29.08 wt% and WC particles content increased from 0.79 wt% to 1.45 wt%, the Ecorr increases from −0.562 V to −0.435 V, and the Icorr decreases from 12.12 μA/cm2 to 2.98 μA/cm2. High corrosion potential and low corrosion current density indicate excellent anti-corrosion property of coating []. The composition and structure of particle-reinforced NiFe coating are the main factors affecting its corrosion resistance. In the electrochemical corrosion process of NiFe coating, Fe is more likely to lose electrons than Ni, which is due to the higher activity of Fe and lower potential. Safavi et al. [] found that with the increase of Fe: Ni ratio, the structure of NiFe coating gradually changes from Ni-Fe(FCC) to Ni-Fe(BCC), and the corrosion resistance of the coating decreases. Therefore, the NiFe alloy coating with high Fe content has poor corrosion resistance. Feng et al. [] found that the reinforcing phase particles are electrochemically neutral and can fill the defects in the electrodeposition process. When corrosion occurs, evenly distributed particles can act as a barrier to reduce the effective contact area with the electrolyte, thereby limiting the occurrence and diffusion of inert corrosion. However, according to the study of Wang et al. [], agglomeration of reinforcing phase particles in the coating is not conducive to improving the corrosion resistance of the coating, and even leads to the weakening of the corrosion resistance. In this paper, during the preparation of Ni-Fe-WC composite coating in the process of JED, Fe content decreases and WC particle content increases with the increase of deposition current density or deposition temperature ((a)), and the coating structure transforms from Ni-Fe(BCC) to Ni-Fe(FCC) ((a–b)). Moreover, the WC particles are uniformly distributed in the coating without agglomeration ((c–d)). Therefore, with the decrease of Fe content and the increase of WC particles content, the Ecorr shifted to a positive number, and the Icorr decreased.EIS is a strong and lossless electrochemical procedure that can be used to confirm electrochemical reactions of the electrode/electrolyte interface. EIS spectrum is usually shown in the form of Bode or Nyquist plot. shows the typical Nyquist plots of EIS spectra. It is clear that the Nyquist plots consist of incomplete semicircular arcs whose diameters reflect the corrosion resistance of machined surfaces. Generally speaking, the larger the capacitance arc diameter, the stronger the coating corrosion resistance []. The value of the capacitance arc in the Nyquist curve can be quantitatively characterized by a value graph of frequency in the Bode graph. (b) shows the log(f) vs. log(|Z|) Bode plots of EIS spectra. In high-frequency region (104–105 Hz), the log|Z| is similar, indicating that the impedance of 3.5 wt% NaCl solution is about 25 Ω·cm2. In low-frequency region (10−2–10−1 Hz), the log|Z| is significantly different, demonstrates that the impedance of Ni-Fe-WC composite coating is different. The anti-corrosion property of coating improves with the increment of impedance. (c) shows the log(f) vs. Angle Bode plots of EIS spectra. It is obvious that the value of the maximum phase angle ranged from 60°–80°. A larger phase angle range show that the coating has stronger capacitance characteristics and has better dielectric property to avoid the ionic flow of electrolyte, indicating that the coating surface has strong corrosion resistance. The EIS data is fitted by calculated by electrical equivalent circuit (EEC). As observed in (d), the EEC of Ni-Fe-WC composite coating can be represented by R(Q(R(CR))). Rs stand solution resistance, CPEc stand constant phase element, Rc stand coating resistance, Cdl stand double-layer pseudo-capacitance, Rct stand charge transfer resistance. The impedance of CPEc is defined as QCPE = [Y1(jw)n]−1, where w is the angular frequency (rad s−1), Y1 is the CPE admittance, j is the imaginary number (−1), and n with a value of 0–1 represents the relaxation dispersion. When the value of n is 1, the CPE is a pure capacitor with a capacitance of Y1. It is believed that the smaller the n value is and the more defects will be on the surface as well as the pitting corrosion is more likely to occur. shows the fitting results of EEC. With the WC particles content increase from 0.79 wt% to 1.45 wt%, the n value of CPEc increases from 0.6221 to 0.9077, the Rc increases from 1.025 × 103 Ω·cm2 to 1.547 × 103 Ω·cm2, and the Rct increases from 1.212 × 104 Ω·cm2 to 5.457 × 104 Ω·cm2. This indicates that WC particles not only help to improve the impedance of coating, but also make coating have better capacitance characteristics. The anti-corrosion property of Ni-Fe-WC composite coating is enhanced with the increase of WC particles content. shows the XRD spectra of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters. All spectra of Ni-Fe-WC composite coatings present obvious (Ni, Fe) alloy structure phase, showing obvious (111), (200), (220) grain orientation peaks. Due to the relatively small content of WC particles, there is no obvious WC phase peak in XRD patterns [At the same time, the grain orientation coefficient (texture coefficients) and grain size of Ni-Fe-WC composite coating are calculated. The grain orientation coefficients of different crystal planes can be obtained from ], where TC(hkl) presents texture coefficient of (hkl) orientation, I(hkl) presents tested intensity of (hkl) reflection, I0(hkl) presents powder diffraction intensity of Iron Nickel. The grain orientation coefficients of (111), (200) and (220) planes are calculated (n = 3).The average grain size of coating can be obtained from ], where D(hkl) represents grain size of (hkl) orientation, B represents half-height width of diffraction peak, γ represents the wavelength of Cu-Kα, θ represents Bragg angle and K represents the constant. shows the grain orientation coefficients and average grain sizes of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters. Under the condition of low deposition current density (50 A/dm2), the average grain size of Ni-Fe-WC coating is 15.4 nm, 13.5 nm and 12.1 nm with increasing deposition temperature from 30 °C to 50 °C, respectively. Under the condition of high deposition current density (100 A/dm2), the average grain size of Ni-Fe-WC coating is 17.5 nm, 15.3 nm and 12.8 nm with increasing deposition temperature from 30 °C to 50 °C, respectively. The results show that decreasing deposition current density or increasing deposition temperature all can contribute to grain refinement during the preparation of Ni-Fe-WC composite coating by JED.(b) shows the schematic diagram of nucleation and grain growth during JED. On the substrate, the reduced metal atoms aggregate to form crystal nucleus, which continue to absorb metal atoms and eventually grow into grains. Since nucleation and grain growth occur simultaneously, the two processes are in a competitive relationship. For a single atom, it can only be used for nucleation or grain growth. With the increase of deposition temperature, more atoms tend to be used for nucleation, so the nucleation number is more in per unit time and area. Due to fast nucleation speed and slow grain growth rate, the average grain size of coating is small. With the increase of deposition current density, more atoms tend to be used for grain growth, the nucleation number is less in per unit time and area. Due to slow nucleation speed and fast grain growth rate, the average grain size of coating is large.Except the excellent properties of anti-wear and anti-corrosion, the performances of high adhesion and high strength are also important for particle enhanced composite coating. High adhesion coating is less likely to fall off in the substrate and has a long service life. High strength coating with can better adapt to the impact of applied load and protect the substrate from damage.The binding strength between coating and substrate can be accurately expressed by adhesion force. As shown in , the force applied to the position of first crack on scratch is the adhesion force. Under the condition of low deposition current density (50 A/dm2), the adhesion force is about >60 N, 42.9 N and 38.4 N with increasing deposition temperature from 30 °C to 50 °C, respectively. Under the condition of high deposition current density (100 A/dm2), the adhesion force is 37.1 N, 36.2 N and 35.4 N with increasing deposition temperature from 30 °C to 50 °C, respectively.Due to the structures of all Ni-Fe-WC composite coatings are (111) preferred orientation, so the influence of (111) orientation structure on adhesion force is mainly analyzed. As shown in , under the condition of low deposition current density (50 A/dm2), all (111) orientation peaks of Ni-Fe-WC composite coatings contain two peaks, which correspond to the phase of Ni-Fe(BCC) and Ni-Fe(FCC) respectively. As shown in (b), under the condition of high deposition current density (100 A/dm2), all (111) orientation peaks of Ni-Fe-WC composite coatings contain only one peak, which is the Ni-Fe(FCC) phase. As shown in (c), the substrate is medium carbon steel with (111) grain orientation, and its cell structure is Fe(BCC). Because the structure of Fe(BCC) and Ni-Fe(BCC) is very similar, the binding strength of Fe(BCC) and Ni-Fe(BCC) is higher than that between Fe(BCC) and Ni-Fe(FCC). The more proportions of TC(111) and Ni-Fe(BCC), the higher the adhesion force. According to (a), under the condition of low deposition current density (50 A/dm2), with the increase of deposition temperature, not only TC(111) decreases gradually, but also the proportion of Ni-Fe(BCC) structure in the coating, so the adhesion force decreases gradually. According to (b), under the condition of high deposition current density (100 A/dm2), the adhesion forces of all coatings is lower than that of coatings fabricated at 50 A/dm2 deposition current density, because there is only Ni-Fe(FCC) structure. The adhesion force decreases with the decrease of TC(111).The strength and ductility of Ni-Fe-WC composite coatings are measured by tensile method. The sample is 100 μm thick Ni-Fe-WC composite coatings with 1 mm thick substrate. shows the samples after tensile fracture. (b) shows the elongation-strength curves. The ultimate strength of the substrate is 450.4 MPa, and the elongation is about 31.4%. Compared with the only substrate, the strengths of Ni-Fe-WC composite coatings with substrate are all improved, but the elongations are all decreased. The strength can be calculated by where σy is the yield strength, σ0 is the friction stress, k is the stress concentration factor, and D is the average grain size. It is clear from that the coating strength increases with the decrease of grain size. (c) shows ultimate strength and elongation of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters. Under the condition of low deposition current density (50 A/dm2), with the deposition temperature increasing from 30 °C to 50 °C, the average grain size decreases from 15.4 nm to 12.1 nm, the ultimate strength increases from 543.3 MPa to 649.5 MPa, and the elongation decreases from 22.2% to 13.5%. Under the condition of high deposition current density (100 A/dm2), with the deposition temperature increasing from 30 °C to 50 °C, the average grain size of the coating decreases from 17.5 nm to 12.8 nm, the ultimate strength increases from 469.2 MPa to 613.2 MPa, and the elongation decreases from 26.1% to 14.2%.The radar diagrams of the performance distribution of Ni-Fe-WC composite coatings fabricated by JED under diverse experimental parameters are shown in . Under the condition of low deposition current density and low deposition temperature, the WC particles content within the prepared coating is minimum, so the surface roughness is lowest. Moreover, the coating has most NiFe (BCC) structure, so the adhesion force is largest. Under the condition of low deposition current density and high deposition temperature, the nucleation process is promoted while the grain growth is inhibited, so the average grain size of coating is smallest and the coating strength is largest. Under the condition of high deposition current density and low deposition temperature, the nucleation process is inhibited and the grain growth is promoted, so the average grain size of coating is largest and the ductility of the coating is largest. Under the condition of high deposition current density and high deposition temperature, the WC particles contents within the prepared coating are highest and the surface defects are least. Moreover, the hardness, wear resistance and corrosion resistance of coating all are best.Ni-Fe-WC composite coatings were fabricated by JED under diverse experimental parameters. The effects of deposition temperature and deposition current density on the composition, structure and various mechanical properties of coating were also explored. The main research are as follows:The composition of the coating mainly affects its wear resistance and corrosion resistance. With the increase of the deposition current density or deposition temperature, the WC particles content within the coating increases. The increase of WC particles improved the wear resistance and corrosion resistance of coating.The decrease of deposition current density or the increase of deposition temperature can promote the nucleation of metal atoms. The increase of the deposition current density or decrease the deposition temperature can promote the growth of crystal nucleus. The small average grain coating has high strength and large average grain coating has good ductility.The binding strength between coating and substrate is mainly affected by coating structure. The adhesion force of coating increases with the increment of TC(111) and NiThe manuscript was written by Hui Jin and Renjie Ji. Experiments were designed by Yonghong Liu, Fan Zhang, Chi Ma and Shenggui Liu. Tiancong Dong and Shuo Liu performed the experiments. All authors have given approval to the final version of the manuscript.), the Science and Technology Support Plan for ), and the Graduate Innovation Protect of 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.α-Tocopherol-doped irradiated UHMWPE for high fatigue resistance and low wearLongevity of total joints has been compromised by wear and fatigue of ultrahigh molecular weight polyethylene (UHMWPE) components. Crosslinking reduces UHMWPE wear, but combined with postirradiation melting, also reduces its fatigue strength, therefore limiting its use in high-stress applications. We hypothesized that a lipophilic antioxidant (α-tocopherol, α-T) can protect UHMWPE against oxidation eliminating the need for postirradiation melting of crosslinked UHMWPE and improve its fatigue strength. To test these hypotheses, 65- and 100-kGy irradiated, α-T-doped and subsequently γ-sterilized UHMWPE were used. (I) α-T-doped irradiated UHMWPEs showed significantly lower oxidation levels (0.48±0.25 and 0.44±0.06) compared to 100-kGy irradiated UHMWPE (3.74±0.16) after 5 weeks of accelerated aging at 80°C in air. (II) Wear rate of α-T-doped irradiated UHMWPE (1.9±0.5, and 0.9±0.1 mg/million cycles (MC) for 65- and 100-kGy irradiated UHMWPE, respectively) were comparable to that of 100-kGy irradiated/melted UHMWPE (1.1±0.7 mg/million cycles). (III) The stress intensity factor at crack inception (ΔKi) of 100-kGy irradiated UHMWPE increased significantly upon doping with α-T from 0.74 to 0.87 MPa m1/2 (p<0.01). The ΔKi for the 100-kGy irradiated and melted UHMWPE, currently in clinical use, was 0.55 MPa m1/2. Doping with α-T eliminated the need for postirradiation melting to protect irradiated UHMWPE against long-term oxidation. The fatigue strength was improved by 58% for α-T-doped 100-kGy irradiated UHMWPE compared to irradiated and melted UHMWPE. The increase in oxidative stability of α-T-doped UHMWPE is attributed to the ability of α-T to react with peroxy free radicals on lipid chains and arrest the oxidation reactions. The improved fatigue strength is attributed to the increase in plasticity of UHMWPE due to the lipophilic nature of α-T.Ultrahigh molecular weight polyethylene (UHMWPE) has been the material of choice for the load-bearing, articulating surface for the metal/articular pair used in total joint arthroplasty Adhesive/abrasive wear is the primary cause of failure in total hips as it is a source of particulate debris leading to peri-prosthetic osteolysis Radiation crosslinking and melting increases the wear and oxidation resistance of UHMWPE High toughness and high fatigue strength of polymers are attributed to energy absorbing mechanisms such as cavitation and plastic deformation The major energy absorbing mechanism in UHMWPE is the plastic deformation of the crystalline domains (crystal plasticity), which depends on ductility and crystallinity. We postulate that crosslinking and melting decrease fatigue strength of UHMWPE by a combination of two separate factors. First, the crosslinks formed during irradiation reduce the chain mobility of UHMWPE, decreasing its ductility We hypothesized that the incorporation of an antioxidant would prevent oxidation and could be used instead of postirradiation melting to protect UHMWPE against oxidation. We further hypothesized that a lipophilic antioxidant would locally plasticize the irradiated UHMWPE, improving its fatigue strength.We used α-tocopherol (also called α-T, vitamin E) as the lipophilic antioxidant compound (). α-T is biocompatible and is lipophilic owing to its phytyl tail, providing favorable interactions with UHMWPE. Furthermore, it is an antioxidant which can serve the purpose of eliminating long-term adverse effects of postirradiation oxidation. Kamal-Eldin and Appelqvist ). The chroman ring becomes resonance stabilized and subsequently reacts further with free radicals. In the presence of oxygen and oxidized species, the average reduced molecule per molecule of α-T is theoretically 2.0 Irradiated UHMWPE without postirradiation stabilization oxidizes to a large extent because the residual free radicals react with diffusing oxygen molecules, forming one peroxy free radical and one primary carbon free radical, which induces more oxidation. Typically, oxidative stability of irradiated UHMWPE is measured by accelerated aging methods Our objectives for this study were to investigate the effect of α-T on: (1) the oxidative stability of irradiated (highly crosslinked) UHMWPE as a means to eliminate postirradiation melting, (2) fatigue strength of irradiated UHMWPE, and (3) the wear behavior of irradiated UHMWPE to prove that low wear exhibited by crosslinked UHMWPE was not compromised in the presence of α-T.In the following studies, artificial aging and infrared spectroscopy were used to determine the effect of α-T on the oxidative stability of UHMWPE. Fatigue crack propagation testing was used to measure the fatigue resistance and bidirectional POD testing was used to determine the wear resistance of α-T-doped irradiated UHMWPE.Consolidated GUR 1050 UHMWPE bar stock (Perplas Ltd., Lancashire, UK) was γ-irradiated to 65- and 100-kGy (Steris Isomedix, Northborough, MA). Cubes (2 cm) for diffusion and oxidative stability experiments, cylindrical pins (9 mm diameter, 13 mm length) for POD wear testing and compact tension (CT) specimens (ASTM E-647 A1) for fatigue crack propagation testing were machined from these irradiated UHMWPEs. Samples were then doped with α-T for 16 h at room temperature or 100°C in air. Following doping, the samples were further γ-sterilized at a dose of 27 kGy. These two test groups will be referred to as α-T-92 and α-T-127 with a total radiation dose of 92 and 127 kGy, respectively.The preparation of relevant control materials for each testing condition is detailed in each of the following sections. A summary of test and control samples used in this study are given in -Tocopherol was purchased from Fischer Scientific (Houston, TX) and used without further processing.To measure the extent of α-T diffusion into UHMWPE, 2 cm cubes of 100-kGy γ-irradiated UHMWPE (Steris Isomedix, Northborough, MA) (CI 100) were immersed in α-T at 100°C for 16 h under 0.5–0.6 atm of nitrogen pressure. Pressure was applied by first purging the oven with nitrogen, then applying vacuum and then adjusting the amount of nitrogen.To measure the diffusion profile, a cross-section was cut out of the immersed cube (100–150 μm) using an LKB Sledge Microtome (Sweden). The thin cross-section was then analyzed using a BioRad UMA 500 infrared microscope (Natick, MA). Infrared spectra were collected with an aperture size of 50×50 μm2 as a function of depth away from one of the edges that coincided with the free surface of the cube. The infrared spectra of UHMWPE and α-T are shown in along with the spectrum of a thin UHMWPE section with a thin layer of α-T spread over it. The absorbance between 1226 and 1295 cm−1 is characteristic of α-T and UHMWPE does not absorb near these frequencies. With a selection of internal reference that is proportional to the beam path length, one can accurately calculate the relative composition of the material. For UHMWPE, the 1895 cm−1 wave number for the CH2 rocking mode is a typical choice as an internal reference We studied the protective effects of α-T on the oxidation of irradiated UHMWPE during artificial aging using α-T-92 and α-T-127 samples that had been doped at room temperature. The objective of this study was to show that the oxidation levels of a high-dose irradiated, aggressively aged UHMWPE would be much higher than that of a high-dose irradiated/α-T stabilized and aggressively aged UHMWPE. Therefore, the control used in this study was 100-kGy γ-irradiated UHMWPE (CI 100) without postirradiation stabilization.Accelerated aging was performed by placing cubes (n=3) in an oven at 80°C in air for 5 weeks. These aggressive conditions for aging were chosen in order to simulate extreme oxidation levels in UHMWPE and to show the protective effects of α-T even under these aggressive conditions. After aging, the cubes were microtomed to thin sections (100–200 μm) using an LKB Sledge Microtome (Sweden). A BioRad UMA 500 infrared microscope (Natick, MA) was used to measure the extent and depth of oxidation. Infrared spectra were collected with an aperture size of 50×50 μm2 as a function of depth away from one of the edges that coincided with the free surface of the cube. The infrared spectra were analyzed to calculate an oxidation index, as the ratio of the areas under the 1740 cm−1 carbonyl and 1370 cm−1 methylene stretching absorbances.Fatigue crack propagation testing was performed on a MiniBionix 858 (MTS, Eden Prairie, MN) following ASTM E-647, the standard method for the measurement of fatigue crack growth rates. We used compact tension (CT) specimens of Type A1, precracked the notch and conducted the tests with a stress ratio of 0.1 in a 40°C water bath to simulate the in vivo temperature of an articulating joint.Unirradiated, 25-kGy γ-irradiated (conventional), accelerated aged conventional, 100-kGy γ-irradiated (CI 100) and 100-kGy γ-irradiated/melted UHMWPE (CISM) were used as controls. These controls were chosen to investigate the separate effects of irradiation, aging and melting on UHMWPE. The α-T-doped samples (α-T-92 and α-T-127) were tested in two distinct concentration regimes that were observed. First, the stress intensity factor at crack inception was measured within the α-T-rich surface region. Second, the same measurement was repeated after driving the crack tip well into the bulk of the test sample, at least 3 mm from the original notch tip, to measure the fatigue strength of the α-T-poor bulk region.POD wear testing was done to determine the wear resistance of high-dose irradiated UHMWPEs subsequently doped with α-T. The wear rates of unaged and accelerated aged α-T-92 and α-T-127 samples that had been doped at room temperature were compared to literature values of unaged and aged conventional 25-kGy γ-irradiated (in N2), 100-kGy electron beam irradiated and melted and 105-kGy γ-irradiated and -annealed UHMWPEs that we previously reported Unaged and accelerated aged cylindrical α-T-92 and α-T-127 samples were tested on a custom-built bidirectional POD wear tester at a frequency of 2 Hz before or after accelerated aging as described above ethylenedimainetetraaceticacid as metal chelating agent. Wear was quantified gravimetrically at 0.5 million cycle intervals. Initially, we subjected the pins to 200,000 cycles of POD testing to remove any loosely bound α-T. Thereafter, pins of each group (n=3) were tested for a total of 2 million cycles. The wear rate was calculated by a linear regression of weight change versus number of cycles from 0.5 to 2 million cycles.We qualitatively analyzed the fatigue fracture surface of a CT specimen of α-T-92. The fracture surface of the sample was gold coated using an Edward Sputter Coater S150B and observed under an optical microscope (Olympus SZX12, Melville, NY).In the following studies, statistical analysis was performed using a Student's t-test for two-tailed distributions with equal variance.In order to measure the extent and depth of α-T diffusion, we obtained infrared spectra of 100-kGy irradiated UHMWPE that had been doped with α-T. The change in the α-T absorbance as a function of depth away from the free surface is shown in . Diffusion profiles of α-T in 100-kGy irradiated UHMWPE at 100°C are shown in . This figure demonstrates the α-T-rich and -poor regions. From the surface to as deep as 500 μm, there was a large concentration of α-T whereas beyond this depth, the bulk of the polymer contained no detectable α-T. α-T-rich and -poor regions are also qualitatively observed in the optical micrograph of the fracture surface of a α-T-92 CT specimen (The effects of aging on the oxidation of undoped and α-T-doped samples (at room temperature) are shown in . The curves represent averages of three samples. The 100-kGy γ-irradiated control samples (CI 100) showed significantly higher oxidation levels when compared to α-T-92 and α-T-127; maximum oxidation indices were 3.74±0.16, 0.48±0.25 (p<0.001) and 0.44±0.06 (p<0.001), respectively. The presence of α-T protected irradiated UHMWPE against oxidation during 5-week accelerated aging at 80°C in air.The stress intensity factor range at crack inception (ΔKi) for undoped samples is shown in . The decrease in fatigue strength of the GUR 1050 upon γ-sterilization at a low dose of 25 kGy was not significant in the unaged specimens (p>0.1); however, aged conventional UHMWPE showed significantly lower fatigue strength (p<0.01) compared to unaged UHMWPE. Irradiation to 100 kGy (CI-100) significantly reduced the fatigue resistance of UHMWPE (p<0.01). CISM samples that were 100-kGy irradiated and melted had lower fatigue strength than CI-100 that were only irradiated to 100 kGy (p<0.001).For the α-T-doped samples, there were two different regimes of fatigue crack propagation () corresponding to different concentration of α-T within the sample. The values obtained from the surface region were higher than the bulk values for both α-T-92 and α-T-127 samples (). Although the bulk values for α-T-92 and α-T-127 samples prior to α-T doping were similar, the samples with less irradiation (α-T-92) prior to α-T doping had higher fatigue resistance.The wear rate of the α-T-92 and α-T-127 samples did not change upon aging (p>0.05, ). The wear rate of α-T-92 was 111% higher than that of α-T-127.Ionizing radiation and subsequent melting increases the wear resistance of UHMWPE, but decreases its mechanical properties, especially fatigue resistance. Crosslinking that results from irradiation reduces the wear of UHMWPE. Postirradiation melting is necessary to remove the residual free radicals that would otherwise cause oxidative embrittlement in the long term. Our aim was to create a wear-, oxidation- and fatigue-resistant material by the incorporation of α-T (a lipophilic antioxidant) into irradiated UHMWPE, eliminating the need for postirradiation melting. α-T is an antioxidant which can serve the purpose of eliminating long-term adverse effects of postirradiation oxidation. As described above, it acts on alkyl, oxy and peroxy free radicals on lipids to spare them from further reaction with oxygen.The presently used doping conditions (16 h and 100°C) resulted in a surface region (<500 μm) that was rich in α-T (). The 16-h duration for α-T doping was chosen to comply with practical considerations for the potential use of this technique in manufacturing. We chose to increase diffusion by using elevated temperatures but elected not to go above 100°C to avoid any decrease in the crystallinity of UHMWPE upon cooling down.The 100-kGy irradiated UHMWPE (CI-100) oxidized more than the irradiated and α-T-doped UHMWPE (α-T-92 and α-T-127) after accelerated aging. This was presumably a manifestation of the strong antioxidant and scavenging ability of α-T, supporting our hypothesis that α-T can provide oxidative stability to irradiated UHMWPE eliminating the need for postirradiation melting.We examined the effects of sterilization, sterilization and aging, high-dose irradiation and melting subsequent to irradiation on the fatigue strength of UHMWPE to determine how each of these UHMWPEs compared to α-T-doped test samples. shows the fatigue behavior of conventional and highly crosslinked contemporary UHMWPEs.Although conventional UHMWPE had high fatigue resistance, γ-sterilization in air made it prone to oxidation following accelerated aging, hence significantly lowering its fatigue resistance to values below that for unaged crosslinked material. Compared to conventional material, crosslinked UHMWPE displayed much lower fatigue resistance presumably due to decreases in chain mobility with increased crosslinking as mentioned above. Also, there was a significant decrease in fatigue resistance associated with melting subsequent to irradiation likely due to a decrease in chain mobility and hence amorphous content available for recrystallization after crosslinking.Our second hypothesis was that α-T would form a blend with UHMWPE to increase its fatigue strength.The fatigue resistance of crosslinked UHMWPE increased with the addition of α-T as was measured at the border region of the irradiated and α-T-doped UHMWPE. The fatigue strength was lower in the bulk of the α-T-doped samples because the concentration of α-T decreased to undetectable levels. The fracture surface of one of the doped samples supports this observation with a more ductile fracture appearance near the α-T rich surface region (). This ductile surface region also coincided with the measured diffusion profile for α-T (). These observations are in support of our hypothesis that a lipophilic compound compatible with UHMWPE would increase the fatigue resistance of irradiated UHMWPE.One limitation of the use of diffusion to blend α-T with UHMWPE is the limited depth of α-T distribution. We recognize this limitation and our current studies focus on obtaining deeper penetration of α-T throughout UHMWPE. Preliminary studies are already encouraging in obtaining a uniform distribution through CT specimens.The incorporation of α-T did not adversely affect the wear resistance of irradiated UHWMPE. The wear rate of the α-T-92 and α-T-127 doped at room temperature were comparable to the wear rates of contemporary highly crosslinked UHMWPEs previously reported by our group Our results supported our hypotheses that an antioxidant molecule, one that is compatible with UHMWPE, would be able to protect it from postirradiation oxidation and form a blend with improved fatigue resistance. Despite the gradient in concentration of α-T across our samples and a relatively low concentration of α-T, oxidative stability of irradiated UHMWPE was improved. The antioxidant capabilities of α-T on UHMWPE have been investigated here; however, the mechanism by which it provides higher fatigue resistance to UHMWPE is not yet known. We have presumed that the local plasticization effect of such a lipophilic molecule would participate in energy absorbing mechanisms around the fatigue crack. Consequently, the effect of α-T on the morphology and hence the crystal plasticity of UHMWPE warrants further investigation. Our current and future work focus on investigating the morphology around a crack tip of irradiated UHMWPE in the absence and presence of α-T by optical and diffraction methods to quantify plasticization on a local scale.Future work will also include testing of irradiated and α-T doped UHMWPE test samples on hip and knee simulators. Such experiments are delayed until the optimum radiation dose level, α-T concentration and doping methodology is developed.We have created a highly crosslinked UHMWPE blended with the lipophilic antioxidant α-tocopherol that showed oxidation and wear resistance comparable to contemporary highly crosslinked/melted UHMWPEs and fatigue resistance higher than these contemporary crosslinked UHMWPEs. These are encouraging results on the way to creating a novel material that will allow the use of low-wear crosslinked UHMWPE in high-stress orthopedic applications and increase the longevity of joint implants in general.Wear and mechanical property studies on ascast and 3H forged homogenized Al25Mg2Si2Cu4Ni alloy at constant speedIn present study, Al25Mg2Si2Cu4Ni alloy is experimental used for investigating wear (friction coefficient) and mechanical properties in ascast and 3h homogenized forged conditions at constant speed. The sliding wear behavioral tests were carried out on a pin on disc apparatus for mechanical property studies universal testing machine was used. The hardness tests were carried out on Brinell hardness tester. To analyze worn out surfaces of as cast as well as forged samples, Scanning Electron Microscope was used. Wear and mechanical properties study of 3r homogenized forged Al25Mg2Si2Cu4Ni alloy samples reveal better tensile strength, yield stress, compression strength and coefficient of friction as compared to the as cast ones, due to formation of secondary precipitate in the matrixEffects of addition of yttrium on properties and microstructure for China Low Activation Martensitic (CLAM) steelThe effects of yttrium on properties and microstructure for China Low Activation Martensitic (CLAM) steel have been investigated. The tensile test shows that the addition of 0.2% yttrium decreases the strength of CLAM steel before irradiation. The results obtained by positron annihilation lifetime measurements of the CLAM, F82H and T91 steels irradiated by 80 MeV 19F ions to 10 dpa demonstrate that the irradiation resistant property of CLAM steel with yttrium is much better than that of other two steels. The SEM and TEM observations suggest the addition of yttrium both refines the martensitic lath structure and leads to the precipitation of big Y2Fe17C0.75 compound.Reduced activated ferritic/martensitic (RAFM) steels are, so far, the most promising materials for structural components of D–T fusion demonstrative devices due to their maturity as industrial materials as well as their superior irradiation resistance in physical and mechanical properties To ensure the feasibility and safety of fusion energy systems employing RAFM steel, there are still several issues to be solved, which include the synergistic effects of fusion-relevant helium generation and atomic displacement damage on microstructural stability and mechanical properties A series of R&D activities on structural material China Low Activation Martensitic (CLAM) steel, which is underdeveloped in ASIPP (Institute of Plasma Physics, Chinese Academy of Sciences) and with the nominal compositions of 9Cr1.5WVTa, are being carried out The objective of this paper is to examine the effect of 0.2% yttrium on the tensile property and microstructure before irradiation and on the irradiation property after heavy ions irradiation.The materials used are CLAM (HEAT 0408B), CLAM (HEAT 0408C), F82H and T91 steels. The experiment alloy of CLAM (HEAT 0408C) was melted in a 25 kg vacuum induction furnace. At the first step the appropriate amounts of pure iron, carbon, tungsten, vanadium, manganese and tantalum were melted together, and then the yttrium granules with at least 99.9% purity were added. Its chemical composition is listed in . The ingot was hot forged at 1423 K into bar and then was rolled into 4 mm-plate. The heat treatments were normalized at 1253 K × 30 min/air cooled (AC), followed by tempering at 1033 K × 90 min/AC.CLAM (HEAT 0408B) steel is the base alloy without yttrium, and the details of metallurgical process and composition for which can be found in Refs. Tensile test was conducted at room temperature (RT), 773 and 873 K with a gauge section of 24 mm × 10 mm × 3 mm in the air. The sample was taken along the rolling direction. The 0.2% proof strength was measured as yield strength.Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) observations were made with a Sirion 200 operated at 30 kV and a JEOL-2010 electron microscope operated at 200 kV.The heavy-ion irradiation experiment was carried out at the HI-13 tandem accelerator in the China Institute of Atomic Energy. All the samples of CLAM (HEAT 0408C), F82H and T91 used in the irradiation experiments were grinded and then polished mechanically to a mirror-like surface to remove the layer of oxides sufficiently. The samples were irradiated at RT by 80 MeV 19F ions. In order to ensure that the irradiation was carried out at RT, the irradiating beam current was limited to ∼0.3 μA and the samples were tightly contacted with the irradiation metallic chamber wall of that was cooled with water. The irradiation doses were 10.0 dpa and the damage rate was 2.8 × 10−4 |
dpa/s. The total dpa created by the heavy ion irradiation in the samples was calculated using TRIM program The radiation damage generated in the samples was examined by a positron annihilation lifetime technique. The positron annihilation lifetime measurements were performed at RT by means of a conventional fast–fast coincidence positron lifetime spectrometer consisting of a pair of BaF2 scintillation detectors, the time resolution of which is 205 ps for 60Co γ-rays. Besides the source components, all measured positron lifetime spectra were well fitted by two lifetime components with a fitting variance of less than 1.3.The short lifetime τ1 is defined to be a weighted average value of annihilation lifetimes of the free positrons and the positrons trapped at the mono-, di-vacancies and dislocations, and the long lifetime τ2 is attributed to the vacancy clusters or voids. The longer lifetime τ2 means the larger size of the vacancy cluster. I1 and I2 are the relative intensities of τ1 and τ2, respectively.The tensile tests were carried out at RT, 773 and 873 K for CLAM steel. The results are shown in It is clear that the ultimate tensile strength (UTS) and yield strength (YS) decrease with the increasing temperature. However, the strength of CLAM (HEAT 0408C) with the addition of yttrium is lower than that of CLAM (HEAT 0408B) at all test temperature. For CLAM (HEAT 0408B), the UTS and YS are 669 and 509 MPa at RT, while 322 and 208 MPa at 873 K, respectively. The differences in UTS and YS for the heats of CLAM are 39 and 27 MPa at RT, and 9 and 17 MPa at 873 K. The differences between them are decreased as the temperature increasing.The percentage of elongation is almost the same for these two kinds of steels.The irradiation experiments to 10 dpa for CLAM (HEAT 0408C), F82H and T91 steels were carried out and the results of positron lifetime measurements are shown in For the samples before irradiation, τ1 and τ2 are 139 and 284 ps for CLAM, 135.3 and 245 ps for F82H and 140.9 and 291.2 ps for T91. It is clear that the amounts of mono- and di-vacancies and dislocations are similar for these three kinds of samples, while F82H has the least vacancy clusters or voids before irradiation.However, the result before irradiation is much different with that of reported by Sato et al. For the samples after irradiation, τ1 is 138 ps for CLAM, which is almost same as that of the un-irradiated one, and τ2 is 292 ps; while τ1 and τ2 are 139.9 and 314.4 ps for F82H, and 145.5 and 327 ps for T91. It shows that the difference of τ1 is very small for all three steels, while the variation of τ2 is much larger for F82H and T91 than that for CLAM before and after irradiation.It shows that the irradiation generates larger vacancy clusters or voids in F82H and T91 steels than in CLAM steel. It reveals that the CLAM steel has better irradiation resistant property compared with F82H and T91 steels.The microstructure image of tensile specimen at RT with SEM observation on the fractured surface is shown in It indicates the ductile transgranular failure with void coalescence. And it can be seen that the cracks are formed along the big particles in the grain. The result of energy dispersive spectrometer (EDS) analysis shows it is a cluster enriched with yttrium, as shown in The results of TEM observation for the tensile specimen at 873 K are shown in . It exhibits that the microstructures for both CLAM (HEAT 0408B) and CLAM (HEAT 0408C) steels are mixture of lath-martensite phase and well-tempered martensite phase containing M23C6 carbides as main precipitation (∼30–200 nm size) and MC type particles (∼5–50 nm size). In addition, it seems that the width of lath is smaller for the CLAM (HEAT 0408C) than that of CLAM (HEAT 0408B).While there were also some big elliptical particles found, as shown in and the corresponding electron diffraction pattern in (b). These precipitates are Y2Fe17C0.75 with the structure of hexagonal lattice and the cell parameters of a |
= 0.8571 nm and c |
= 1.247 nm The mechanism of element yttrium in steel is complex and mainly depends on the structure, size, amount and distribution of precipitates. The effect of yttrium in the CLAM steel could be illustrated from two opposite aspects.On one hand, yttrium is an active element and segregates easily in the grain boundary, which can inhibit the grain growth and pin the lath boundaries. This was shown in . The finer martensite structure is favorable for the improving mechanical properties. In addition, it is stable and good to resist the irradiation damage, which is responsible for better irradiation resistance for the samples of CLAM compared with those of F82H and T91. The irradiation resistance induced by the addition of yttrium is also observed in the ODS steel On the other hand, there were some big particles found and identified as the compound of Y2Fe17C0.75. It is detected that this is a relative softer phase than the matrix, which leads to stress concentration that would promote cracking in the matrix around it and premature failure of the material, as shown in . It indicates that just these precipitates deteriorate the mechanical property and result in the decreasing of tensile strength.It suggests the big compounds of Y2Fe17C0.75 probably are produced in the process of melting. However, the phase of yttrium oxide is not observed although it is thermodynamically the most favorable compound of yttrium in these steels. The reason needs further studies. The metallurgy technology needs to be improved to reduce this kind of precipitates.The tensile tests at RT, 773 and 873 K were carried out for the CLAM steel. The results show that the addition of yttrium decreases the tensile strength.The irradiation experiments to 10 dpa by 19F ions were conducted. From the positron lifetime data, the samples of CLAM have much smaller size variation of defects compared with those of F82H and T91 after irradiation. Therefore, CLAM has the best irradiation resistant property among the three steels samples investigated in the present experiment. Further investigation of irradiation effects for CLAM steel is still on going.The microstructure observations illustrate that yttrium refines the grain and martensitic lath structure, which improves the properties. But the big precipitates of Y2Fe17C0.75 deteriorate the properties. The reason needs to be studied further and the metallurgy technology needs to be improved to achieve much better property for CLAM steel.Process and metallurgical evaluation of outlet pigtails damage in the primary steam reformer of an industrial ammonia plantIn spite of improvements in reformer tube metallurgy and manufacture, outlet pigtail tubes are now seen as a critical and weak link component of primary steam reformer in ammonia plants and often require replacement before the reformer tubes. The present work has been focused to find out causes of damaging 12 outlet pigtails of primary steam reformer in the ammonia plant of Shiraz Petrochemical Complex (SPC) after 7–8.5 years of operation from metallurgical and process point of view. A process evaluation based on operating variables and a detailed metallurgical investigation based on microstructural assessment, chemical and reduced thickness analysis, micro hardness measurements, metallography and tensile properties of pigtail samples has been performed. The obtained findings demonstrated that the failure of outlet pigtails was attributed to over-design operating temperatures. Under operation at high temperature, the pigtails undergo the advance stage of irreversible creep and failed before their designing life span.The steam-methane reformer (SMR) furnaces are widely used in the petrochemical industry for production of synthesis gas in ammonia and methanol plants During service, depending upon the operating conditions, several mechanisms such as creep, fatigue, corrosion and oxidation become operative. Accumulation of microstructural damages in the components due to prolong operation decreases their load bearing capacity thereby limiting the lives of the components Inevitably, the service life of components such as the reformer tubes and process gas manifold is limited. Hence, pigtail damage is an industry-wide problem and their failure is a common cause of production loss, plant down-time and potential risk to plant personnel The ammonia plant in Shiraz Petrochemical Complex has been designed to produce 1200 MTD of liquid ammonia from natural gas via the relatively standard processes of steam reforming and synthesis gas generation by CO conversion, CO2 removal and methanation. The primary reformer of the plant is a standard top-fired Humphreys and Glasgow (H&G) designed radiant box is a schematic front view of the primary steam reformer. The primary reformer in the plant is a furnace containing 352 catalyst tubes arranged in eight radiant chambers of 44 tubes each. The catalyst tubes are vertically installed and supported by concrete counterweights. The feed gas, consisting of natural gas and steam, enters from the top end at a temperature of 365 °C and pressure of 35 kg/cm2 and flows down through the catalyst in individual tubes before coming out at a temperature of 780 °C and a pressure of 30.5 kg/cm2. Heat is provided by firing of 117 burners which arranged in nine rows and firing downwards. The heat is transferred to the tubes through radiation and the metal temperature is maintained between 870 °C–890 °C. The composition of feed gas with the operating conditions and specifications of primary reformer are given in The pigtail material was INCOLOY 800 HT, which is the industry standard for pigtail construction. It is a Fe–Ni–Cr alloy with additions of aluminum and titanium. The pigtails had a design temperature of 833 °C ID 26.5 mm and 5.8 mm sound wall thickness. They set to operate at a mean temperature of 818 °C under an internal pressure of 33.5 kg/cm2. Measuring of outlet process gas temperature of catalyst-filled tubes is performed by 32 installed thermocouples at the end of some tubes which are shown in by red circles. The pigtail tubes with individual insulation on each are covered by insulation wool and cotton foil of thickness 62 mm and 6 mm, respectively. shows the failure of outlet pigtail 179.Tube failures not only result in total plant shutdowns but can also cause damage to other associated equipment such as catalyst tubes and refractory. After replacement of the damaged pigtail, a subsequent pigtail failure occurred for tube 135. After that, the plant experienced the failure of other ten outlet pigtails. All pigtails ruptured in the bottom portion adjacent to the center of radiant chamber, except for pigtails 48 and 311. The ruptures were found to be in the longitudinal direction. We observed the pigtails have negligible deflections after 7–8.5 years of operation under nominal capacity. Both inner and outer surfaces of the service exposed reformer tubes were examined. The tube showed the presence of rather black adherent oxide scale at the outer surface, which is an indicative of prevalence of high temperature. Sign of any localized damage in the form of pits were not observed and the expansion in the outer diameter of the tube was not significant. It is generally economical to run the primary reformer at as high a temperature typically 700–900 °C as well as by low pressure. Because of the creep limit of the reformer tubes, there is a limit to the operating temperature for a given pressure. The failure of an outlet header can result not only in a plant shutdown, but will also take a longer time to put back into service. It also has the potential to damage the adjacent pigtails. So, a detailed investigation was carried out on the failed pigtails though they had served under the design creep life of 100,000 h. This is particularly important, bearing in mind that re-tubing of the ammonia plant primary reformer was performed in 2001. This following further failure the decision to undertake a formal root cause analysis was made.The evaluation procedure includes both process variables and metallurgy analysis and experimental techniques. The material for the pigtail tubes shall be in accordance with ASTM B407 Alloy UNS N08811.In the current study, the aim of the metallurgical analysis and experiments was mainly to identify geometry analysis, chemical analysis, reduced thickness analysis, counterweights, micro hardness measurements, metallography, Scanning Electron Microscopy, metallurgical assessment of creep damage and finally tensile mechanical properties of the pigtail material.For the purpose of determining mechanical properties and creep analysis of service exposed pigtails, ten damaged pigtails were selected based on the results of visual examination and microstructural study. The investigation was carried out on all damaged pigtails except of pigtails # 138 and #311. In order to study the influence of service exposure on mechanical properties and creep analysis of the damaged pigtails, unfailed samples from the same reformer pigtail were additionally selected for the purpose of comparison., ten samples that designate #1 to #10 from the damaged pigtails were prepared and selected for the examination.The current industry standard material for steam reformer pigtails is alloy 800 HT which includes iron–nickel–chromium with additions of aluminum and titanium To examine of reduced thickness, the geometry dimension both curved and straight parts from each pigtails was measured for 10 of the pigtails.With referring to L.A. Spyrou and et al. shows a representation of the applied loads on the pigtails.Counterweights A2 and A2 are applied at both ends of a beam supporting 11 pigtails, whereas counterweight A1 is applied at the center of a beam supporting 22 pigtails.Micro hardness measurements were performed on selected metallographic specimens. Vickers hardness test of the specimens was carried out from OD to ID of samples at room temperature. An automat Vickers hardness testing system model AAV-504 was used with an applied load of 10 kg.Samples were cut from failed sections and away from failure for metallographic examination. Circumferential and longitudinal cross sections of the samples were examined at the location of failure. The samples were examined before and after etching using optical microscopy and scanning electron microscopy (SEM). Etching was made using modified glyceregia (40 ml HNO3 + 40 ml HCl + 20 ml glycerol). Major elemental analysis was performed by X-ray fluorescence (XRF) and minor and trace elements by Inductive Coupling Plasma (ICP) spectroscopy.The scanning electron microscopy was carried out on sample #3 and others samples. The microstructure was observed using a SEM model Philips FEI XL.In order to perform the metallographic analysis and determining the creep behavior of damaged pigtail tubes, specimens were prepared on transverse cross section.It is essential to identify process variable may be caused to the exit pigtail failure. Abnormal operating conditions either on the furnace side or process side are the prime suspects. Due to load fluctuations, it is also unlikely that a constant metal temperature is maintained during service.The most common furnace problems are related to poor burner trimming and misdistribution of flue gas. Poor burner trimming, leads to local over-firing and poor combustion air control. This will result in local low excess air levels and consequently hotter flue gas. This type of problem is likely to appear as a region in which several adjacent tubes are running hot. Therefore, it is very important that the furnace problems are eliminated as a possible cause of hot tubes before any process side problems are diagnosed.With aged steam reforming catalyst, a design gas outlet composition achieved at high tube outlet temperature with approximately the same heat flux across the tube wall. With more active steam reforming catalyst, the design outlet composition may be achieved at a lower tube outlet temperature at constant heat flux. Hence, a lower catalyst activity causes insufficient heat to be removed by the reforming reaction, leading to an increase in tube wall temperature.Mal-distribution flow of process gas in catalyst-filled tubes, resulting from high pressure drop in one or more tubes will give rise to a lower than average flow through the affected tubes. This can result in an increase in tube wall temperature for those tubes with low flow Metallurgical study of creep behavior was performed on all samples of damaged pigtail tubes (both curved and straight parts). The metallographic results of creep damage are presented in . All the specimens, except two, at the curved and straight parts exhibited the advance stage of creep behavior.The straight part (L) of Specimen #1 and #5 exhibited only the initial stage of creep damage in the form of isolated cavities. The curved part and the straight part of sample #2 and the curve part of the sample #4 exhibited the stage of oriented cavities. While the curved part and the straight part of specimen #3 and #6 and the curve part of the sample #1 and #5 exhibited the advanced stage of microcracks. The grain size for all specimens lies in the range of ASTM No. 3–4. In the curved parts, the grain size was not homogeneous and smaller than the straight parts reaching size ASTM No. 4–5. The material shall have a grain size corresponding to ASTM No. 5 (0.0025 inch average diameter).SEM microphotographs for sample #3 (178) from the transverse section of the OD are shown in . The microphotographs further confirm that the cracks have been formed by linkage of voids as shown in In the present case of the failed pigtails, the optical and electron microscopic studies revealed the presence of voids and micro cracks in the sample near the location of rupture. The cracks were indication of cumulative long term exposure of relatively higher temperatures than the normal operating temperature of bulk outlet gas. Cracks have been formed by the linkage of voids. The observed voids and micro cracks are typical of creep damage. The presence of creep voids and fissures as well as the observation of tube expansion indicate that the failure of the pigtail was due to accumulated creep damage caused by higher temperature in the localized area.A little precipitate observed within the sample of failed pigtail 178 and other samples. The results of the laboratory indicated the precipitates were carbide precipitates. Location of the precipitates showed with regions A and B in (d). Carbon is absorbed into a material at elevated temperature while in contact with a carbonaceous material or carburizing environment indicate that the values of Vickers hardness are lower than the minimum hardness value of 142 at room temperature for alloy 800 HT. The lower hardness values obtained may be associated with the combined effects of grain boundary cavitation and the carbide coarsening.The information describing the chemical composition and grain size of various grades of INCOLOY 800 are presented in indicate that the composition of components is within the limits set by ASTM B407.The mechanical tensile properties were measured in the straight part position of damaged pigtails. The results are compared with the specified values for an unfailed pigtail which are given in . Comparing the obtained results with ASTM specifications indicates that the values are within the limits and there is a slight decrease of the elongation which is normal due to 7–8.5 years of operation. indicate a thickness reduction of 29.1–33.2% for curved and 15.2–20.5% for straight parts in all pigtails. and based on a process gas pressure of 30.5 kg/cm2, mass density of pigtails (7950 kg/m3), mass density of insulation layer (138 kg/m3), mass density of aluminum foil (380 kg/m3), the counterweights A1, A2, A3 of m1 |
= 95 kg, m2 |
= 51 kg, and m2 |
= 48 kg, the magnitude of counterweights on a single pigtail will be equal to:F1=m1.gn=42.36NF2=m2.gn=45.48NF3=m3.gn=42.36NWhere, n is the number of pigtails under the beam support.The total vertical force on a pigtail due to the counterweights is:The distributed load per unit length of the beam elements is q=ρpigtailR0,p2−Ri,p2+ρinsuR02−Ri2insu+ρCottonfoilR02−Ri2cottonfoil.gWhere, Ri , pigtail |
= 13.25mm , Ro , pigtail |
= 19.05mm, Ri , insu |
= 19.05m, Ro , insu |
= 101.5mm, Ri , foil |
= 101.5mm and Ro , foil |
= 104.5mm , g = 9.81 N/kg is the acceleration of gravity and the total length of the pigtail is 4.285 m.Hence, substituting the above parameters in Eq. , the total vertical load on a pigtail due to self-weight is:The above calculations show that the counterweight is equal to the self-weight of the pigtails:Based on the calibrated flow records on natural gas fuel and combustion air streams, the excess air for the primary reformer burners was in the range of 12.5–13.5% where this value was within the design range specification (12–15%). Average flue gas temperature based on measurements in the channels of exit flue gas from furnace was varied in the range of 940 to 1185 °C as given in The flue gas temperature in channel #4 has a large deviation from design. This deviation is resulted from low flow area of the channel. Low flow area leads to flow misdistribution of the flue gas and consequently process side problems.The operation life of a primary reformer catalyst charge is typically 4 years for a top-fired reformer Mal-distribution flow of process gas in catalyst-filled tubes, resulting from high pressure drop in one or more tubes will give rise to a lower than average flow through the affected tubes. This can result in an increase in tube wall temperature for those tubes with low flow The process temperatures of reformer tube outlet ends were tackled using the installed thermocouples which are evenly distributed over 32 catalyst tube outlet ends (). Process steam feed minor fluctuations were observed but no appreciable change in the bulk gas inlet and outlet temperatures. However, as shown in , the thermocouple installed in rows 3–5 indicated a 20–100 °C higher temperature compared to other thermocouples.The pigtails are designed for a specified life span, even if the operating conditions are always maintained within the design limits. However, they can fail much earlier as the result of metallurgical and process factors. These factors are able to promote the evolution and progression of grain boundary cavity nucleation, coalescence, microcrack formation and eventual cracks. The investigation in the present study demonstrated that the failure of the outlet pigtails made of INCOLOY 800 HT was due to accumulated creep damage caused by the operating temperature of the out pigtails that measured by installed thermocouples on the bottom of the catalyst-filled tubes. During normal operation of the furnace, they were subjected to temperatures over the design temperature. The evidences of carbides coarsening inside the grain support the overheating of outlet tube pigtail.Chemical composition analysis of the damaged pigtail confirmed conformance within the limit range requirements of the material specifications. The damaged pigtails mainly occurred in high temperature region of radiant zone and randomly failures of them were independent of quality defect in tube manufacturing operations include welding, bending and annealing.The metallographical analysis suggested that the dominant failure mechanism is creep. Applied load analysis of the outlet pigtails system design indicated that the system loading is not the stress that caused the cracking of the pigtails. Their outer diametrical growth was 15.8% at the straight part and 21.5% at the curve part. Based on the above observations and facts, the authors suggest the following recommendations:Prevention of overheating during service.Uniform distribution of the flue gas flow.Controlling the rates of heating during start up and shut downs.Preparation and characterization of a thermostable and biodegradable biopolymers using natural cross-linkerThe present study describes preparation and characterization of a thermally stable and biodegradable biopolymer using collagen and a natural polymer, alginic acid (AA). Required concentration of alginic acid and collagen was optimized and the resulting biopolymer was characterized for, degree of cross-linking, mechanical strength, thermal stability, biocompatibility (toxicity) and biodegradability. Results reveal, the degree of cross-linking of alginic acid (at 1.5% concentration) with collagen was calculated as 75%, whereas it was 83% with standard cross-linking agent, glutaraldehyde (at 1.5% concentration). The AA cross-linked biopolymer was stable up to 245 °C and Exhibits 5–6-fold increase in mechanical (tensile) strength compared to plain collagen (native) materials. However, glutaraldehyde cross-linked material exhibits comparatively less thermal stability and brittle in nature (low tensile strength). With regard to cell toxicity, no cytotoxicity was observed for AA cross-linked material when tested with mesenchymal cells and found degradable when treated with collagenase enzyme. The nature of bonding pattern and the reason for thermal stability of AA cross-linked collagen biopolymer was discussed in detail with the help of bioinformatics. A supplementary file on efficacy of AACC as a wound dressing material is demonstrated in detail with animal model studies.With regard to use of biopolymers as biomaterials, according to Park However, the low denaturation temperature of collagen restricts its application as suitable biopolymers for clinical applications Alginic acid, a linear anionic copolymer of 1,4 linked β--mannuronic acid (M) 1,4 linked α-guluronic acid (G) arranged as homopolymeric or heteropolymeric block (GG, MM and GM), constitutes major structural polysaccharide of brown seaweeds (phaeopyta), found non-toxic, non-carcinogenic, biocompatible, sterilizable and offers cheap processing technique. Alginic acid and its sodium/calcium salts have long been used in food, cosmetics, drugs, drug delivery, and tissue engineering etc. Alginate wound dressing has recently been introduced for heavy exudation wounds as occlusive dressing by Pharmacy industries. It is reported that exchange of ions by calcium salts of alginic acid and wound exudates accelerates the healing process The present study focuses, role of alginic acid as a sole cross-linking agent for the preparation of collagen based thermostable biopolymer using bovine skin Type I collagen. Further, the study demonstrates physical, chemical, mechanical, biocompatible (toxicity), biodegradable properties of the reconstituted collagen–alginic acid cross-linked biopolymer. The various possible interactions between alginic acid and collagen and the binding energy calculations for the interactions and the reasons behind the stability and degradability of the biopolymer material prepared are discussed in detail.Alginic acid (AA), picrylsulfonic acid [2,4,6-trinitrobenzene sulfonic acid (TNBS)], glutaraldehyde and collagenase enzyme (Clostridium histolyticum) were obtained from Sigma–Aldrich (USA). Bovine skin obtained from slaughterhouse was used as a source material for Type I collagen. All the other reagents were of Analytical Reagent grade and used without further purification.Collagen from bovine skin was extracted as per the steps followed in the flow chart summarized below. Since collagen was extracted using acetic acid, the resultant collagen was designated as acid soluble collagen (ASC) and all the cross-linking studies were carried out only with reconstituted ASC (RASC).[*Flayed skins immediately transferred to the laboratory using ice cold containers and washed thrice with phosphate buffered saline (pH 7.2) for the period of 4 h with intermittent change in the buffer at 1 h interval to remove blood, dung, sand and other particles. The washed skin was further treated with lime at pH (11.0–12.0) and sodium sulphide (1.0–2.0%) for the period of 2–4 h and again washed thrice with phosphate buffered saline. This process eventually removes the flesh and the hair. The resultant material was used for extraction of collagen.]RASC obtained from the above procedure was subjected to SDS-PAGE analysis to assess the purity and molecular profile. In brief, electrophoresis was carried out using 8% polyacrylamide gel. Followed by electrophoresis, gel was stained with coomassie blue and destained with the mixture of methanol and acetic acid. Molecular weight marker from Sigma (USA) was used to measure the molecular weight of the bands appeared.Different concentrations (0.5, 1.0, 1.5, 2.0, 3.0, 4.0, and 5.0%) of homogenized solution of AA were prepared by dissolving the required quantities in 70 (mM) sodium phosphate buffer (pH 6.5) under stirring for overnight at room temperature. About 0.5% RASC [dissolved in 0.005 M acetic acid] was mixed with different concentration of AA at 3:1 ratio respectively and the homogenized solution obtained upon stirring for 30 min at room temperature, incubated for overnight at 4 °C. Followed by incubation the reaction mixture was then transferred to polypropylene plate (Tarson, India) and air-dried at 37 °C for 12 h. The biopolymer material obtained in the form of sheets from the above process was designated as AA cross-linked collagen (AACC). Cross-linking of collagen with glutaraldehyde was also carried out for comparisons. Glutaraldehyde (at 1.5% concentration) was mixed with 0.5% of collagen and sheet was prepared according to the procedure summarized above. In addition, a separate collagen sheet material without cross-linker was also made accordingly and used for comparative analyses. The dried polymer sheets were further subjected to the following analyses.Samples of native, AA cross-linked collagen (AACC) and glutaraldehyde cross-linked biopolymer materials (GCC) were tested for their physical appearance, smoothness, transparency by physical and feel observations and thickness using screw gauge.Functional group analysis (FT-IR) for native, AACC and GCC biopolymer material was made by spectrum one (PerkinElmer Co., USA model) FT-IR instrument.Tensile strength (MPa) of plain material and the cross-linked material (GCC and AACC) was measured using Universal Testing machine (INSTRON model 1405) at a cross head speed of 5 mm/min.Thermal decomposition analysis of the biopolymer material (Native, GCC and AACC) was carried out under nitrogen (40 and 60 ml/min) using TGA Q 50(V20.6 build 31) instrument.Thermal properties of plain and cross-linked biopolymer material (GCC and AACC) was analyzed using differential scanning calorimeter, model-DSC Q 200(V 23.10 Build 79) with standard mode at nitrogen (50 ml/min) atmosphere.SEM micrograph analysis of plain and cross-linked biopolymer material AACC was made by using JEOL JSN 6360 (Japan) instrument after sputter coated with gold.Degree of cross-linking was quantified using TNBS assay according to the procedure summarized by Bubnis and Ofner A mesenchymal stem cell from bone marrow was used for cell toxicity assay. Culturing and characterization of the cells were carried out as per the method of Mangalagowri For cell adhesion assessment, biopolymer of AA cross-linked collagen was developed on cover slip separately under sterile condition and was carefully transferred to 24-well plates and again UV was sterilized to avoid further contamination. Followed by UV sterilization, cells obtained from the above step was seeded (1.5 × 106) and incubated along with growth medium for the period of 9 days. The medium was changed at regular intervals (every 24 h). Samples were with drawn from 24-well plates at 3, 6 and 9 days and viewed for cell adhesion and the images were photographed accordingly.In the present study, we follow two different procedures to assess the biodegradability of biopolymer material obtained by cross-linking of AA with RASC. The first procedure demonstrates the measurement of release of hydroxy proline by the enzymatic treatment of AACC and native polymer -leucine (Hi-Media, India) and the buffer alone serves as reference. In the case of hydroxy proline assay, 100–200 μl of supernatant was mixed with 1.0 ml of chloramine T and incubated at room temperature for 20 min and 1 ml of perchloric acid (70%) was added and the incubation continued at room temperature for 5 min and then 1 ml of 20% PDAB (para-dimethyl amino benzaldehyde) was added and incubated at 60 °C in water bath for 20 min and the absorbance of the resulting solution was measured at 557 nm.For binding energy and bonding pattern assessment, docking study was followed. For the docking study, chemical structures are generated using ACD/ChemSketch Extraction procedures followed in the present study provides a pure RASC of Type I. Molecular profile study demonstrates () presence of two alpha chains (100 kDa) and one beta chain (200 kDa). With reference to physical observations made for the cross-linked biopolymer material prepared in the form of sheets, we obtained a clear transparent, smooth surfaced biopolymer material with thickness of 0.06–0.08 mm for AA cross-linked collagen sheets obtained after glutaraldehyde cross-linking showed a transparent film, with brittle nature. b illustrates FT-IR spectral details of (i) AA, (ii) native and (iii) AACC (1.5% of AA) respectively.With regard to mechanical property, alginic acids cross-linked collagen biopolymer material showed tensile strength of 11.56 MPa compared to the plain material collagen (2.11 MPa). About 5–6-fold increase in tensile strength was observed after cross-linked with AA. The tensile strength measurements of native, AACC and GCC were taken and the ultimate tensile strength (MPa) and maximum load (N) were represented in Thermo gravimetric analysis and the corresponding derivative peaks for all the experimental samples obtained for different percentage of AA was illustrated in . Thermal stability of AA was observed at 225 °C, whereas for the native collagen it was only 109 °C. When AA was cross-linked with native collagen at different concentrations, thermal stability increases as the percentage of AA increases up to 2.0%. Further increase in AA reduces the thermal stability of the resulting material. b displayed the thermal analysis of native and optimized concentration of cross-linked biopolymers (AACC and GCC). Initial 25% weight loss was observed at 230 and 219 °C for AACC and GCC respectively. Second maximum weight loss was observed at 379 and 354 °C for cross-linked biopolymers (AACC and GCC).Differential scanning calorimetric measurements of native, AACC and GCC was illustrated in . The melting temperature of AA was observed at 88 °C with the crystallization temperature as 247 °C. Melting temperature of native collagen was 96.98 °C. When collagen was cross-linked with different concentration of AA, the melting temperature gradually increased to 150 °C (up to 1.5% of AA) and decreased when the concentration of AA increases above 1.5%. b illustrated the melting temperature of GCC (151 °C) and AACC (149 °C).SEM analysis of AA cross-linked biopolymer material and a native collagen was displayed as . Followed by cross-linking, the biopolymer material exhibits more compact, homogenous, and highly dense with porous fibrillar structures with continuous layering. demonstrated degree of cross-linking measurements of AA cross-linked biopolymer material with increasing concentration of AA. Maximum degree of cross-linking of 75% was observed with 1.5% concentration of AA and 0.5% of acid soluble collagen (RASC). No further increase in degree of cross-linking with increasing concentration of AA was observed. However, the cross-linking degree of GCC was observed as 83%.Cell toxicity studies (MTT assay) revealed, fibroblast cells obtained from mesenchymal stem cells showed live cells with an increased optical density measured at 570 nm for the increased concentration of AA cross-linked biopolymer ((ii, a–c) illustrated the morphology of the cells in the medium supplemented with the cross-linked material (AACC) incubated for 3, 6 and 9 days. Cells were proliferated well and the confluence in growth and adhesion was evidenced from day 9 images. The morphology of live fibroblast cells in the form of spindle shape was clearly seen.With regard to the biodegradability assay, biopolymer material obtained upon cross-linking of AA with RASC found degradable in the presence of collagenase enzyme within the period of 4–20 h of incubation as assessed in terms of release of hydroxy proline and other amino acids as leucine (a and b). When compared to plain material, the release of both hydroxy proline and leucine was significantly less (P |
< 0.05) in the cross-linked biopolymer material. With regard to GCC, the materials are degradable (results not shown).Results on binding energy calculations based on bioinformatics tools for the cross-linking of AA and RASC using AutoDock software ( depicts the values for the binding energy, interaction sites, hydrogen bond sites and bond distance respectively. Binding energy of −7.28 was observed when Ala (11) residue of A chain of collagen interacting with AA through Nitrogen of alanine and forming three hydrogen bond with bond distance of about 3.08, 2.97 and 2.92. Glycine (7) of C chain of collagen interacted with AA through oxygen (of –OH group) and forming three hydrogen bonds with the bond distance of 3.98, 2.67, and 2.55. Similarly Serine (9) of C chain of collagen also forms one hydrogen bond through Nitrogen with bond distance of 3.15.Preparation of stable, biocompatible and biodegradable collagen based biopolymer materials, reduces most of the problems associated with the clinical applications of synthetic, metallic and polymeric biomaterials. The current scenario in the replacement therapy requires materials of biocompatible and biodegradable nature due to the disadvantages like, toxicity, carcinogenicity observed with the current polymeric and other synthetic materials, urges the scientific society to prepare materials of natural origin. Use of natural material alone could not serve the purposes and most of the natural materials need some blends. The choice of blend finally decides the application of the materials. In the present study, we aimed to produce a biocompatible and biodegradable, flexible and thermally stable biopolymer material using natural material AA and the reconstituted skin collagen. Type I collagen from bovine skin when cross-linked with AA provide a stable biopolymer material with all the requisite properties as evidenced through the characteristic analyses made in the present study.The extraction procedure followed provides, a pure Type I collagen as evidenced from the molecular profile study. The typical Type I collagen contains [(α1)(I)2(α2)(I) 1] and SDS-PAGE pattern exhibits an intense band near 100 Kda followed by a faint band, corresponds to α1 and α2 chains respectively. In addition, a band observed near 200 Kda corresponds to β-chain. Similar kind of observations was made by Lin and Liu The cross-linked polymer material when subjected to FT-IR analysis, the overlapping region of –CO and –N–H bands in the range of 1600–1650 cm−1 as shown by the circle marking in b was observed. In addition, the intensity of primary amine –N–H– bending (out-of-plane) broad peak (655 cm−1) changed to sharp peak, and the peak intensity of –C–N– stretch (1400 cm−1) in native collagen found weak, whereas in cross-linked biopolymer material, the intensity of the peak is strong due to the formation of –CONH (amide) bond. The peak intensity of secondary amine –N–H– bending (1553 cm−1) was very strong in native collagen, whereas in AACC, it was very weak due to the absence of –NH2 group in lysine residue of collagen. In native collagen, we observed a overtone in the range of 3081 cm−1 due to secondary –N–H– bending at 1553 cm−1. However in AACC, the overtone was vanished due to cross-linking of –NH2 group of lysine residue with AA From the above schematic representation, we found collagen and AA cross-linked through covalent linkage (chemical cross-linking). When the required concentration of collagen and AA (I) was mixed, the reaction starts from the ester formation in AA (II) due to loss of water With regard to the thermal analyses of cross-linked biopolymer material and the plain (native) material, we observed an increase in thermal stability upon cross-linking with AA. Salome Machado et al. b emphasizes, sharp peak at 252 °C corresponds to AA alone and a broad peak at 326° C corresponds to collagen alone. When collagen was mixed with AA at increasing concentrations, shifting of collagen broad peak towards right side with an increase in peak intensity of AA and a decrease in peak intensity of collagen. This implies the cross-linking between collagen and AA. Nevertheless, when the concentration of AA increased to more than 1.5%, there is no appreciable increase in stability due to the non-availability of free molecules of collagen to interact with higher concentration of AA. Wu et al. a and b. The inter molecular multiple hydrogen bonding observed between AA and collagen in the present study is similar to the observations made by Madhan et al. ) received from the bioinformatics tools also confirm the intermolecular multiple hydrogen bonding. Thus, reverse to the bonding pattern of chitosan with collagen, both covalent and hydrogen bonding interactions occurs between collagen and alginic acid, which in turn increases the stability and mechanical property (tensile strength) of the resulting biopolymer material appreciably.Differential scanning calorimetric (DSC) studies recorded melting temperature differences among AA, native and cross-linked biopolymer material. The melting temperature of cross-linked collagen shifts towards right when the concentration of AA increases up to 1.5%. Further increase in concentration of AA, shift the melting temperature towards left and the presence of unreacted AA shifts the melting temperature despite the presence of cross-linked collagen.To further understand the mechanism of stabilization of cross-linked collagen, we carried out experiments on measurements of percentage of cross-linking degree using TNBS. The procedure adopted in the present study reveals; TNBS interact only with the free amino groups as shown below:As we discussed earlier, due to covalent bonding (between –COOH group of AA and –NH2– group of amino acid residue of collagen), the amino groups get interacted with AA which is reflected in the percentage of cross-linking degree (75%) at 1.5% of AA. When the concentration of AA increases, there is no further increase in percentage degree of cross-linking. As shown schematically below, the –NH2 groups in lysine residue of collagen is out of site when the concentration of AA increases, which results with no further increase in percentage degree of cross-linking (Followed by the preparation and characterization of the cross-linked biopolymer material using collagen and AA, biocompatibility (toxicity) studies were also carried out. Biocompatibility of the stabilized biopolymer is the most important property whenever a new material was prepared. If the prepared material is biocompatible, then most of the problem associated during the application of biopolymer material will be reduced. In general, biocompatibility is assessed using different cell lines. Mesenchymal cells were used to assess the biocompatibility of cross-linked biopolymer material. Theoretically, if the cross-linked collagen biopolymer material does not have any toxic groups and when tested for cell viability, cells should proliferate well and the optical density (OD) of the live cells should show an increased value. In the present study, cells treated with the resultant cross-linked material (AACC) showed an increase optical density (OD) values compared to untreated cells.In order to study the application of cross-linked collagen biopolymer materials as implants, it is necessary to assess the biodegradability of the biopolymer developed. Since, numbers of enzymes were produced upon various biochemical reactions inside the body, degradation studies using enzymes found reliable. In the present study, enzymatic degradation of cross-linked biopolymer material and native collagen material were studied and the results showed both the material degraded when treated with collagenase enzyme. However, the rate of release of leucine or hydroxy proline showed significant difference. In native collagen, release of hydroxy proline starts from the minute of exposure to enzymes compared to cross-linked collagen. When we compare the release of leucine and hydroxy proline, we found, amount of other amino acids measured as leucine release was high in comparison with hydroxy proline. This could be due to intermolecular hydrogen bonding between free hydroxyl group of hydroxy proline and –OH group of AA (OH⋯OH) which ultimately protects the material from the action of collagenase enzyme and the random action of collagenase enzyme releases amino acids mostly leucine compared to hydroxy proline. Thus, the results of the study showed the cross-linked collagen biopolymer material is biodegradable.In the present study the choice for the preparation of thermally stable and biodegradable biopolymer material was Type I collagen of bovine skin and a natural polymer AA. The reason for the selection of Type I collagen was due to its interaction with number of cells and its involvement in most of the human and animal diseases. Though numbers of studies were available for the different use of AA, its cross-linking potential with collagen has not yet in reports. The present study describes, the cross-linking ability of AA with collagen assessed using FT-IR, TGA, DSC, SEM and degree of cross-linking measurements using standard procedures. The results obtained and the schematic representation of the reaction mechanism summarized proves, AA was cross-linked with collagen in two pathways one through multiple intermolecular hydrogen bonding (proved by bioinformatics study) and second is by covalent linkage (proved by TNBS/percentage of cross-linking degree assay). The biopolymer material (sheet) prepared upon cross-linking of AA was the green method of preparation. No toxic compounds were involved in this preparation and the resultant material found application as wound dressing sheet in clinical applications. Supplementary file emphasize the efficacy of AACC as wound dressing material in comparison with AA and control is attached in the last session of the manuscript.Supplementary data associated with this article can be found, in the online version, at 07.05.Tp: computer modeling and simulations62.20.M: structural failure of materialsEffect of hydrogen on degradation mechanism of zirconium: A molecular dynamics studyUsing large scale molecular dynamics simulation, we investigate the deleterious effect of hydrogen in Zr. We consider both dilute and concentrated limit of H. In the dilute and concentrated H limits, we study the effect of 1–5 atomic percentage of hydrogen, and that of ε-ZrH2 precipitate having 5–10 nm diameters, respectively. From the stress–strain curves and micro-structure analysis at different strain values, we characterize the deformation behavior and correlate our result with previously reported mechanisms. We show hydrogen atoms in dilute limit help in dislocation multiplication, following the hydrogen-enhanced localized plasticity mechanism. In the concentrated limit, on the other hand, dislocations and cracks nucleate from precipitate–matrix interface, indicating the decohesion mechanism as primary method for Zr degradation. These findings are corroborated with a nucleation and growth model as expressed in Kolmogorov–Johnson–Mehl–Avrami equation.07.05.Tp: computer modeling and simulations62.20.M: structural failure of materialsZirconium (Zr) and its alloys have attracted much attention in the structural research community in past few decades due to its usage as cladding material for light water reactors. Zr is suitable as cladding material due to its very low capture cross-section of thermal neutrons and good corrosion resistance at high temperatures . In the present study we focus on two regions of the phase diagram, shown as encircled in : 1) The dilute limit of H, where Zr–H solid solution forms and 2) The concentrated limit of H where a few varieties of hydride phases are formed. Among different concentrated phases of hydride we focus on the ε-ZrH2 phase, which has the maximum amount of H incorporated.In the dilute limit of H, several different microscopic mechanisms underlying the H induced degradation have been proposed in literature. For example, several studies have reported H-induced lowering of the critical cleavage stress that affects opening up or propagation of cracks In the concentrated limit of H, the hydrides are brittle and produce cracks on application of stress, that reduces the performance and life expectancy of nuclear reactor, thereby increasing the cost of nuclear power plants. Various studies focusing on the deformation All the molecular dynamics simulation in this study are performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), developed at the Sandia National Laboratory We first consider the case of pure Zr in bulk. The atomic positions are first generated in accordance with the crystal symmetry, followed by a structural optimization. The energy per atom as a function of atomic volume is then fitted in order to obtain the relaxed lattice parameters and cohesive energy of pure Zr. Our obtained lattice parameters (a = 3.23 Å, c/a = 1.59) and cohesive energy (6.36 eV/atom) agree well with other theoretical The large scale simulations are performed on rectangular simulation cells having x, y, and z axes oriented along the [101¯0], [12¯10], and [0001] directions, respectively with dimensions 20.67 × 20.70 × 41.22 nm3. The total number of atoms considered are ∼750,000 for both the dilute and concentrated cases. To study the dilute limit, simulations are carried out with different percentages of H, where hydrogens are placed randomly in interstitial sites. In general, there are two interstitial locations in HCP Zr; octahedral, and tetrahedral. In the α-Zr phase the H atoms are placed in the octahedral site, which is the most stable site for our system. However, as shown in Ref. where fαij is the force vector between atoms i and j in the direction α, rβ is the distance vector in direction β, N is the number of neighboring atoms for atom i, N∗ is the total number of atoms, and V is the simulation cell volume. The volume-averaged stress tensor as defined in Eqn. is the same as the global stress used in previous MD simulations As the system is heated up from room temperature to higher temperature (∼850 K or above), two major changes happen. As depicted in , firstly the HCP Zr undergoes a phase transformation from α-Zr to β-Zr and secondly the solubility for H in α-Zr decreases very sharply. Thus, in order to study the effect of H in HCP Zr (α-Zr phase) the temperature in all of our simulations is set at 500 K. Furthermore, since this phase has a maximum solubility limit of 5.93 atomic percentage of H The stress–strain curves with various atomic percentages of H are shown in a, along with the case of pure Zr. The linear onset of the curves up to a certain strain indicate the elastic response, whereas for higher strains the curves gradually bend, indicating the onset of plastic deformation. When strain exceeds a certain level, damage in the structure develop and grows until rupture occurs around a strain of about 10%. The precise strain value at which rupture occurs depend on the H concentration (10.8% for pure Zr). It is found that with increase in percentage of H, linear elastic region decreases gradually and the non-linear elastic–plastic region increases, signifying a ductile failure. The strain value at which the material breaks down, the Ultimate Tensile Stress (UTS), decreases as the H content in the simulation cell is increased. This is highlighted in the zoomed in plot in a. In order to examine the effect of H, snapshots at different strain level with different percentage of H is studied. Using common neighbor analysis as calculated by OVITO b. In the hydrogen containing systems, it is seen that the initial number of HCP atoms is not 100% as opposed to the case with pure Zr. This is due to the fact that as H atoms are introduced as interstitials into the pure HCP Zr crystal structure, the local symmetry breaks down and surrounding Zr atoms no longer have HCP coordination. Accordingly, the initial percentage of HCP atoms reduces with increase in percentage of hydrogen content. The reduction of percentage of HCP atoms before the fracture compared to the no-load situation increases as the percentage of H increases. This indicates the fact that the strength of material reduces as more and more H is incorporated into Zr. The inset graph of b shows the percentage decrease of UTS compared to that of pure Zr, with increasing H concentration. It is to be noticed that even 1% inclusion of H into Zr may result in ∼8% reduction in UTS.Investigation of microstructures at several strain values may provide information regarding the deformation mechanisms related to the solute softening effect To further pinpoint the role of H in dislocation mediated process, atomistic simulation with very few H atoms are performed separately. A snapshot of the atomistic simulation with only two H atoms is shown in . As seen, dislocation nucleates far from H at 10.91% strain and with increase of strain to 10.94%, the nucleated dislocations are attracted towards the H atoms, as shown by the arrows, forming secondary nucleation centers. We note that the distance from the H atom to the nearest dislocation tip is quite large (more than 7 nm). As the applied load is increased, the number of displaced Zr atoms present in the pathway between the dislocation tip and the H atom increases. In such a situation, the dislocation starts interacting with the H atoms through the intermediate non-HCP (defected) Zr atoms. As the applied load is increased, the dislocations nucleate and grow within the volume. During the growth process of such dislocations, we observed that the dislocations bifurcate towards the directions, where H atoms are present. We did not find any significant diffusion of H atoms within the system, and H atoms are more like trapped. After bifurcation of those dislocations, they move along the bifurcated direction crossing the H atom (cf supplementary material In order to accommodate the applied load, deformation twinning is a common mode of plastic deformation that occurs in HCP metals, due to their very limited number of slip systems. Twinning generally nucleates in a lenticular shape (Orowan type), and grows with increasing applied load. Here, we observe a very similar twin-like lattice reorientation without an actual twinning plane, similar to what has recently been observed in magnesium . It shows a snapshot of the system with 2% H near the fracture point. Observation reveals that the boundary between the parent lattice (prismatic plane) and the ‘twinned’ lattice (basal plane) is composed predominantly of semi-coherent basal/prismatic interfaces instead of the twinning plane. The migration of this boundary is dominated by the movement of these interfaces undergoing basal/prismatic transformation via local rearrangements of atoms when a sufficiently high tensile stress is applied. The details of the atomic rearrangement for lattice reorientation in our case is different than what has been reported earlier for Mg As understood, the degradation in Zr–H solid solution is governed by nucleation of defected atoms, followed by their growth process towards ultimate failure of the material. In order to achieve further understanding of such degradation mechanism in a quantitative manner, we use the Kolmogorov–Johnson–Mehl–Avrami (KJMA) equation where, f is the volume fraction of the transformed (defected) phase, t is the time, n is the nucleation rate and k denotes the growth of the transformed phase. With reference to the present study, the percentage of atoms that are dislocated or displaced is considered as the transformed phase and the increasing strain plays the role of “t”.For each H containing system, the number of dislocated atoms first nucleate (resembling the beginning of KJMA's ‘S-shaped’ curve), then monotonically increase with increasing strain (resembling the mid part of ‘S-curve’) and finally saturate at the fracture point (resembling the end part of ‘S-shaped’ curve). Using standard fitting tools, we fit the evolution of non-HCP atoms at different strain values to the KJMA equation to obtain the values of k and n, as shown in the inset of for a representative case of 2% H in Zr. plots the variation of parameter k, representing the growth of the dislocated atoms and n, the nucleation rate as a function of the percentage of H. We find, while the parameter k increases monotonically with increase in the percentage of H, the parameter n, remains almost constant. Thus, H does not play much role in dislocation nucleation but strongly influence the dislocation multiplication process. This is in conformity with the inference drawn from microstructure analysis.This section focuses on the effect of H in the concentrated limit which forms ε-ZrH2 phase inside the bulk Zr. As mentioned three different sizes of the precipitate are studied: 5 nm, 7 nm and 10 nm in diameters respectively, while the parent Zr dimension remains the same as studied for dilute limit (20.67 × 20.70 × 41.22 nm3).The effect of ε-ZrH2 precipitate inside bulk Zr on the stress–strain curve is shown in a. In the figure we also show the stress–strain curve for Zr with 5% H to compare the nature of the curves in the dilute and concentrated limit. For all the three sizes of the precipitate, the nature of the stress–strain curves does not alter much from the parent Zr case, except for the decrement in UTS occurring at much lower strain values, indicating a brittle-like fracture. Compared to the dilute limit of H, where the stress–strain curves denote a ductile behavior in terms of the deviation from the linear nature of stress–strain curve, in the concentrated limit the stress–strain curves indicate brittle-like fracture maintaining the linear behavior until large strain values. It is found that with increase in the diameter of the precipitate, the strain value at which the material breaks down decreases. The main cause of the brittle nature of the fracture in the concentrated limit is the influence of precipitate on the cohesion of precipitate–matrix interface. As size of the precipitate gets bigger, the interface area increases, which in turn increases the chance of interfacial crack nucleation and thus the UTS decreases. Our observation suggests that in the concentrated limit of H, the hydrogen enhanced decohesion mechanism is instrumental for Zr degradation. In order to examine the effect of the precipitate-size, snapshots at different strain levels with different sizes of the precipitate are studied. Similar to the previous case of dilute limit, using common neighbor analysis, we identify the non-HCP atoms. The change in the percentage of HCP atoms in bulk Zr with applied strain is shown in b. The relative reduction of the percentage of HCP atoms indicate the fact that the strength of material reduces by incorporating precipitate. The inset in b shows the percentage decrease of UTS with increasing diameter of precipitate. It may be noticed that even with 2 nm diameter precipitate, which amounts to a ratio of precipitate volume and matrix volume of 0.002, may result into more than 25% of reduction in UTS. This may be compared with similar deleterious effect with 5% H in solid solution that results in 25.8% reduction in UTS.A detailed micro-structure analysis similar to that in the dilute limit, is carried out in the concentrated limit to reveal the role of ZrH2 precipitate in deformation mechanism. In all the simulations of Zr with its hydride under tensile load, the nucleation of dislocations are found to initiate at the precipitate–matrix interface. Once dislocations are accumulated, cracks are generated at the interface that lead towards ultimate failure of the material. A snapshot of the atomistic simulation with a ZrH2 precipitate of 5 nm in diameter is shown in , as a representative case (cf supplementary material Supplementary video related to this article can be found at http://dx.doi.org/10.1016/j.jnucmat.2015.07.031The following are the supplementary data related to this article:The movie shows that in the concentrated limit of H, dislocations nucleate from the ZrH2 precipitate–matrix interface, and with applied strain the micro-cracks are generated at the interface.The movie shows that in the dilute limit of H, dislocation nucleation points are far from the H atoms (made artificially bigger), and with applied strain the nucleated dislocations are attracted towards the H atoms, and dislocation multiplication happens in the close vicinity of H atoms., reflects the fact that both the parameters k and n increase with increase in the precipitate diameter. This can be understood from the fact that as the diameter of the precipitate increases, the interfacial area of ZrH2 with Zr matrix increases, which essentially enhances the number of available sites to nucleate a dislocation or crack. Compared to the dilute limit where the role of H is confined only in the dislocation multiplication process, the KJMA plots in the concentrated limit indicate the role of the precipitate size in both dislocation nucleation and growth mechanisms.Here we summarize our major findings towards degradation mechanisms of Zr due to H inclusion in the dilute and concentrated limits.In the dilute limit of H, dislocations nucleate far from H atoms. However, the nucleated dislocations are attracted towards the H atoms, and H atoms in solid solution with Zr helps in dislocation multiplication. Our atomistic simulations to this end support the HELP mechanism for Zr degradation. On the other hand, in the concentrated limit of H, dislocations are observed to nucleate from the precipitate–matrix interface. Accordingly, as precipitate volume fraction increases, the inter-facial area and the probability to nucleate such dislocation increases. At higher concentrations, our simulation indicates the decohesion mechanism as primary mechanism for Zr degradation.Solid solution H atoms lead towards a ductile fracture, in contrast ZrH2 precipitate in bulk Zr makes the material fail like a brittle fracture.Prismatic dislocations are observed in both the limits. Dislocation loops were observed near the precipitate matrix interface in the concentrated limit.Twin-like lattice reorientation is observed in both the limits of H inclusion.KJMA equation, introduced for the first time to identify the nucleation and growth process of the dislocated atoms in a metallic system, provide quantitative support to the above conclusions.Strain energy release rate for interfacial cracks in hybrid beamsThe finite element modeling and fracture mechanics concept were used to study the interfacial fracture of a FRP-concrete hybrid structure. The strain energy release rate of the interfacial crack was calculated by the virtual crack extension method. It is shown that the crack growth has three phases, namely, cracking initiation, stable crack growth and unstable crack propagation. The effects of geometric and physical parameters of the hybrid beam on the energy release rate were considered. These parameters include Young’s moduli of the FRP, the concrete and the adhesive, thickness of the FRP plate and adhesive, and the distance of FRP plate end from the beam end. The numerical results show that the energy release rate of the interfacial crack is influenced considerably by these parameters. The present investigation can contribute to the mechanism understanding and engineering design of the hybrid structures.A fiber reinforced plastic (FRP) composite has a high stiffness and strength, low weight, corrosion resistance, and electromagnetic neutrality. Retrofitting process of the existing structures is quick and simple due to the excellent performances of the FRP composite and especially its lower weight. External strengthening of concrete beams by means of high-strength FRP composites can significantly enhance its strength and ductility as well as result in large energy absorption capacity (). The performance enhancement of such hybrid beams, however, depends on bonding quality and property of interface between the concrete and FRP.Previous researches on the interfacial stresses have been shown that there are stress concentrations at the ends of the FRP sheet because of material discontinuity (). Approximate models were developed and can be used to investigate the forms of the interfacial stresses. The stress concentration can cause the cracking of the interface near the ends of the FRP sheet. Therefore, the concepts of the interfacial fracture mechanics should be introduced.Cracking of an interface is controlled by the fracture mechanics, such as stress intensity factors or the energy release rate. These qualities can be measured by specially designed experiments. Test specimens and technologies have been developed for investigations of the interfacial fracture in FRP-concrete hybrid beams (). It is pointed out that the FRP plate would peel from the concrete near the end of the plate. Under the delaminated loading, longitudinal and diagonal cracks will be produced in the concrete near the adhesive layer. These cracks rapidly propagate to the position of the applied loads. As a result, FRP plate will peel from the concrete. Therefore, the initial cracking of interface between the concrete and FRP plate is a primary factor to impact the performance of the interface.The numerical modeling of the interfacial crack in hybrid beams can provide quantitative analysis for the mechanism of delamination of the interface in the hybrid beams. In present paper, the concepts of fracture mechanics are used to simulate numerically the interfacial cracking in the FRP-concrete hybrid beams. In the next section, the basic theories on the interfacial fracture mechanics are briefly introduced. Then finite element analyses of hybrid beam are described in Section . A series of the finite element calculations were carried out for different parameters in the models. The numerical results, which show the parameter effects on the interfacial cracking, are given in Section . Finally, the conclusions from this research are outlined.The toughness of a material with cracks can be characterized by a stress intensity factor or strain energy release rate. For a stable crack at the bimaterial interface, the stress intensity factor is defined as a complex form by stress fields near the crack tip (where ε is oscillation coefficient and can be represented asβ=12μ1(1-2ν2)-μ2(1-ν2)μ1(1-2ν2)+μ2(1-ν2),where μi and νi are shear modulus and Poisson ratio, respectively, of material i (i |
= 1, 2) between which the interface exists.It is noted that K1 and K2 in the complex stress intensity factor K do not correspond to KI of mode I and KII of mode II, respectively.The strain energy release rate relates to the stress intensity factor bywhere E¯i=Ei/(1-νi2) for plane strain problem, E¯i=Ei for plane stress problem, and Ei is Young’s modulus, andThe growth of the interfacial crack is described by a criterion expressed in term of the stress intensity factor or the strain energy release rate.The present paper focuses on calculations of the strain energy release rate of the interfacial cracks in the FRP-concrete beams using finite element analysis. The virtual crack extension method is used in the calculations (). In fact, for a crack with length L, one can calculate strain energy U1 of the system. A small virtual extension ΔL of the crack is assumed and the strain energy U2 is then calculated for the system with crack length L |
+ ΔL. The strain energy release rate in the virtual extension of the crack can be written aswhere b is wideness of the crack or beam.The finite element modeling for the strain energy release rate of the interfacial cracks in hybrid beam is described in this section. Consider a simply supported hybrid beam subjected a transverse force P. The concrete beam is externally strengthened by means of bonding of FRP plate at the bottom of concrete beam. shows the analytical model with initial interfacial cracks at the ends of FRP plate. The parameters used in FE analysis are as follows:The concrete beam section b |
× |
h |
= 200 mm × 300 mm; Length of beam L |
= 2300 mm;Distance of the FRP plate end from the hinge support L0 |
= 100 mm;Thickness of the FRP plate tp |
= 4 mm; Thickness of the adhesive ta |
= 2 mm;Young’s modulus of the concrete Ec |
= 30 GPa; Poisson ratio of the concrete νc |
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