高压、高应变率与低压、高应变率实验的本构关联性

 指出Johnson-Cook（J-C）、Zerilli-Armstrong（Z-A）、Bodner-Parton（B-P）本构方程在一定条件下的适用性,表明对于低压、高应变率实验,单一曲线假定似乎可以采用。通过等效应力、等效应变,可以将不同应力状态下的流动应力函数采用统一的方程描述。然而,这些本构方程的确立,并不包括平面冲击波实验。对适合于平面冲击波实验的Steinberg-Cochran-Guinan（SCG）本构方程,讨论了其方程中所包含的高压与高应变率耦合效应。指出,以剪切模量度量的流动应力具有应变率相关性。基于温度效应的新发现以及直接测量平面冲击波流动应力的新进展,分别用J-C本构及SCG本构方程估算了钨材料在高压、高应变率加载下的流动应力。结果表明,采用J-C本构估算的流动应力仅在压力为10 GPa以下才能与实验数据相近,当压力高于10 GPa时,流动应力只能采用SCG本构估算。也指出了高压、高应变率本构方程与低压、高应变率本构方程所对应的不同物理背景。     

Plastic deformation properties of Zr–Nb–Ti–Ta–Hf high-entropy alloys

We have investigated the plastic deformation properties of single-phase Zr–Nb–Ti–Ta–Hf high-entropy alloys from room temperature (RT) up to 300 °C. Uniaxial deformation tests at a constant strain rate of 10^?4?s^?1 were performed, including incremental tests such as stress relaxations, strain-rate changes, and temperature changes in order to determine the thermodynamic activation parameters of the deformation process. The microstructure of deformed samples was characterized by transmission electron microscopy. The strength of the investigated Zr–Nb–Ti–Ta–Hf phase is not as high as the values frequently reported for high-entropy alloys in other systems. At RT we measure a flow stress of about 850 °C. We find an activation enthalpy of about 1 eV and a stress dependent activation volume between 0.5 and 2 nm³. The measurement of the activation parameters at higher temperatures is affected by structural changes evolving in the material during plastic deformation.     

Elasto-plastic behaviour of thin metal films

By extracting the variation of the plastic strain rate from measurements of the stress–strain curves of thin films of varying thickness, the large extent of the microdeformation stage was determined for tensile deformation of free-standing thin films, as well as for films on substrates deformed by cyclic heating. The stress varies dramatically with strain during this stage. It is demonstrated that this behaviour is common to most fine-grained polycrystals, and that the extent of the microdeformation stage is much larger than the conventional 0.2% proof strain, and depends both on the material as well as on the measurement technique. Therefore a careful analysis of this stage is essential in measuring the mechanical behaviour of these materials.     

Influence of dispersoids on microstructure evolution and work hardening of aluminium alloys during tension and cold rolling

The influence of dispersoids on work hardening of aluminium during tension and cold rolling has been studied by comparing Al–Mn alloys containing similar amounts of solutes but various dispersoid densities. The microstructure evolution with deformation strain was examined in transmission and scanning electron microscopy. It is found that a high density of fine dispersoids strengthens the materials significantly, but their strengthening effect diminishes as the strain increases. From a series of Bauschinger tests, it is found that the internal stress, due to particles, increases rapidly at the initial stage of deformation, but saturates at strains larger than 5%. It is concluded that the internal stress makes a small contribution to the work hardening and contributes to less than 10% of the total flow stress during monotonic loading at strains larger than 5%. The work-hardening behaviour has been correlated to the corresponding microstructure, and the strengthening mechanisms are discussed.     

Elastic–plastic transition in three-dimensional random materials: massively parallel simulations,fractal morphogenesis and scaling functions

Elastic–plastic transitions were investigated in three-dimensional (3D) macroscopically homogeneous materials, with microscale randomness in constitutive properties, subjected to monotonically increasing, macroscopically uniform loadings. The materials are cubic-shaped domains (of up to 100?×?100?×?100 grains), each grain being cubic-shaped, homogeneous, isotropic and exhibiting elastic–plastic hardening with a J ₂ flow rule. The spatial assignment of the grains’ elastic moduli and/or plastic properties is a strict-white-noise random field. Using massively parallel simulations, we find the set of plastic grains to grow in a partially space-filling fractal pattern with the fractal dimension reaching 3, whereby the sharp kink in the stress–strain curve of individual grains is replaced by a smooth transition in the macroscopically effective stress–strain curve. The randomness in material yield limits is found to have a stronger effect than that in elastic moduli. The elastic–plastic transitions in 3D simulations are observed to progress faster than those in 2D models. By analogy to the scaling analysis of phase transitions in condensed matter physics, we recognize the fully plastic state as a critical point and, upon defining three order parameters (the ‘reduced von-Mises stress’, ‘reduced plastic volume fraction’ and ‘reduced fractal dimension’), three scaling functions are introduced to unify the responses of different materials. The critical exponents are universal regardless of the randomness in various constitutive properties and their random noise levels.     

A study of the hot and cold deformation of twin-roll cast magnesium alloy AZ31

Recent advances in twin-roll casting (TRC) technology of magnesium have demonstrated the feasibility of producing magnesium sheets in the range of widths needed for automotive applications. However, challenges in the areas of manufacturing, material processing and modelling need to be resolved in order to fully utilize magnesium alloys. Despite the limited formability of magnesium alloys at room temperature due to their hexagonal close-packed crystalline structure, studies have shown that the formability of magnesium alloys can be significantly improved by processing the material at elevated temperatures and by modifying their microstructure to increase ductility. Such improvements can potentially be achieved by processes such as superplastic forming along with manufacturing techniques such as TRC. In this work, we investigate the superplastic behaviour of twin-roll cast AZ31 through mechanical testing, microstructure characterization and computational modelling. Validated by the experimental results, a novel continuum dislocation dynamics-based constitutive model is developed and coupled with viscoplastic self-consistent model to simulate the deformation behaviour. The model integrates the main microstructural features such as dislocation densities, grain shape and grain orientations within a self-consistent viscoplasticity theory with internal variables. Simulations of the deformation process at room temperature show large activity of the basal and prismatic systems at the early stages of deformation and increasing activity of pyramidal systems due to twinning at the later stages. The predicted texture at room temperature is consistent with the experimental results. Using appropriate model parameters at high temperatures, the stress–strain relationship can be described accurately over the range of low strain rates.     

Effect of pretreatment on microdeformation development in hcf polycrystals of substitutional solid solutions

The effect of small plastic deformation and subsequent free-state aging even under a load on microplastic deformation development in hcp polycrystals of substitutional solid solutions is investigated on Cu-Al and Cu-Ni alloys. It is established that in the temperature interval 77–300°K the effect of deformation pretreatment on subsequent microdeformation development is independent of the temperature at which it occurs, but is determined only by the temperature of secondary deformation. At the same time a clear correlation is observed between the change in the macroscopic elasticity limit and the shape of the microdeformation curve. If the macroscopic elasticity limit (σ″)after deformation pretreatment is larger than the friction strain (σ _F), the stress-strain diagram is a second-order parabola, as in the case of annealed alloys. If the macroscopic elasticity limit after deformation pretreatment equals the friction strain, the shape of the curveσ=f (?) changes considerably. A stage of plastic deformation, on which the linear dependence ofσ on ?_P is conserved, is observed on the stress-strain curves after the range of elastic deformation. The mechanism of microplastic deformation development in predeformed alloys is treated by the statistical theory of microdeformation of polycrystals.     

Alternate stresses and temperature variation as factors of influence of ultrasonic vibration on mechanical and functional properties of shape memory alloys

It is known that the main factors in a variation in the shape memory alloy properties under insonation are heating of the material and alternate stresses action. In the present work the experimental study of the mechanical behaviour and functional properties of shape memory alloy under the action of alternate stresses and varying temperature was carried out. The data obtained had demonstrated that an increase in temperature of the sample resulted in a decrease or increase in deformation stress depending on the structural state of the TiNi sample. It was shown that in the case of the alloy in the martensitic state, a decrease in stress was observed, and on the other hand, in the austenitic state an increase in stress took place. It was found that action of alternate stresses led to appearance of strain jumps on the strain–temperature curves during cooling and heating the sample through the temperature range of martensitic transformation under the constant stress. The value of the strain jumps depended on the amplitude of alternate stresses and the completeness of martensitic transformation. It was shown that the heat action of ultrasonic vibration to the mechanical behaviour of shape memory alloys was due to the non-monotonic dependence of yield stress on the temperature. The force action of ultrasonic vibration to the functional properties was caused by formation of additional oriented martensite.     

Scaling relationships in sharp conical indentation of shape memory alloys

Based on dimensional analysis and finite element calculations, several scaling relationships in the indentation of shape memory alloys with a sharp conical indenter were obtained. These scaling relationships illustrate the dependence of the indentation response on the material properties of shape memory alloys, such as phase transition and plastic deformation. It is shown that the yield stress and strain-hardening exponent of transformed martensite play important roles in the indentation response, in addition to the phase transition properties. Additionally, the general relationships between indentation hardness and phase transition stress, maximum transition strain, martensite yield stress and the strain-hardening exponent of shape memory alloys were obtained. The results show that the indentation hardness of shape memory alloys is not proportional to the phase transition stress or to the martensite yield stress, and cannot be used directly to measure the phase transition stress or the yield stress of shape memory alloys.     

Temperature dependence of mechanical properties and pressure sensitivity in metallic glasses below glass transition

An experimental investigation into the variation of the mechanical properties (yield stress, yield strain, elastic moduli, hardness) from sub-ambient temperature (77 K) to that just below the glass transition temperature, of different bulk metallic glasses was conducted. Particular emphasis was on the constraint factor, the ratio of hardness to compressive yield stress, which is taken to be the proxy for the temperature dependence of pressure sensitive plastic flow. All the mechanical properties, except the constraint factor, decrease linearly, throughout the temperature range examined, with temperature and when normalized exhibit certain universal tendencies. The constraint factor was found to increase, monotonically but not necessarily linearly, with temperature. Finite element analyses, with pressure dependent constitutive behaviour, were performed in order to extract pressure sensitivity from the indentation load-displacement curves reported by Schuh et al. in 2004. This, in turn, was used to predict the variation of constraint factor with temperature. A good correlation suggests that the increase in constraint factor with temperature is indeed associated with enhanced pressure sensitivity.     

Dislocation density-based constitutive model for the mechanical behaviour of irradiated Cu

Performance degradation of structural steels in nuclear environments results from the formation of a high number density of nanometre-scale defects. The defects observed in copper-based alloys are composed of vacancy clusters in the form of stacking fault tetrahedra and/or prismatic dislocation loops that impede the motion of dislocations. The mechanical behaviour of irradiated copper alloys exhibits increased yield strength, decreased total strain to failure and decreased work hardening as compared to their unirradiated behaviour. Above certain critical defect concentrations (neutron doses), the mechanical behaviour exhibits distinct upper yield points. In this paper, we describe the formulation of an internal state variable model for the mechanical behaviour of such materials subject to these (irradiation) environments. This model has been developed within a multiscale materials-modelling framework, in which molecular dynamics simulations of dislocation–radiation defect interactions inform the final coarse-grained continuum model. The plasticity model includes mechanisms for dislocation density growth and multiplication and for irradiation defect density evolution with dislocation interaction. The general behaviour of the constitutive (homogeneous material point) model shows that as the defect density increases, the initial yield point increases and the initial strain hardening decreases. The final coarse-grained model is implemented into a finite element framework and used to simulate the behaviour of tensile specimens with varying levels of irradiation-induced material damage. The simulation results compare favourably with the experimentally observed mechanical behaviour of irradiated materials.     

Prediction of flow stress and textures of AZ31 magnesium alloy at elevated temperature

The viscoplastic behaviour of magnesium alloys at high temperatures leads to highly temperature-dependent mechanical properties. While at high strain rates a notable strain hardening response is observed, at low strain rates the material shows a smooth plastic response with negligible amount of hardening. This complicated behaviour is due to different deformation mechanisms that are active at different strain rate regimes, resulting in different strain rate sensitivity parameters. In this study we show, by utilizing both numerical simulations and experiments, that this behaviour can be predicted by a model that combines two deformation mechanisms, grain boundary sliding mechanism and dislocation glide mechanism. We discuss the importance of each deformation mechanism at different strain rate regimes based on the findings of modelling and experimental results for AZ3 magnesium alloy. By developing a model that includes the above-mentioned two deformation mechanism, the prediction of flow properties is expanded to a wide range of strain rate regimes compared to previous study. The obtained numerical findings for the stress–strain behaviour as well as texture evolution show good agreement with the experimental results.     

Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT

The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.     

Cyclic deformation and fatigue cracking behaviour of polycrystalline Cu,Cu–10 wt% Zn and Cu–32 wt% Zn

The cyclic deformation behaviour of polycrystalline Cu, Cu–10 wt% Zn and Cu–32 wt% Zn was systematically investigated in the plastic strain amplitude range of 1 × 10^?4–4 × 10^?3. The differences in the cyclic stress–strain (CSS) responses and fatigue cracking behaviour between Cu, Cu–10 wt% Zn and Cu–32 wt% Zn were compared. It was found that the occurrence of a cyclic saturation for Cu–10 wt% Zn and Cu–32 wt% Zn strongly depends on the applied strain amplitude, whereas polycrystalline Cu always displays cyclic saturation. Surface deformation morphologies were analyzed by scanning electron microscopy (SEM). One of the major features observed is that the slip bands become increasingly homogenous with Zn addition. The fatigue cracks were found to frequently nucleate along the annealing twin boundaries (TBs) in Cu–10 wt% Zn and Cu–32 wt% Zn, but not in polycrystalline Cu. Based on these experimental results, the cyclic deformation response and fatigue cracking behaviour are discussed, and a developed TB cracking mechanism is proposed to explain the difference in fatigue cracking mechanisms in Cu, Cu–10 wt% Zn and Cu–32 wt% Zn.     

A physical interpretation of softening of pressure-sensitive and anisotropic materials

Several new dynamic models are proposed to explain the mechanical behaviour of softening of pressure-sensitive and anisotropic materials at a macroscopic level. If a pressure-sensitive material is loaded by a force and a variable pressure or an anisotropic material is subjected to a load with a changeable loading direction relative to the material frame, their stress–strain relationships become more complicated. Mechanical behaviours of these stress–strain relationships have to cover the feature concerning the change of pressure or loading direction, i.e. mechanical properties of pressure-sensitive material corresponding to different pressure state or anisotropic material relating to different loading direction will play an important role in deciding their stress–strain relationships. Such shift of material properties due to the variable pressure or loading history may significantly expand the traditional concept of the stability of material deformation, and the second order of plastic work being negative may be a response of stable plastic deformation, which is commonly called softening.     

Difference approach to the analysis of resistivity recovery data for irradiated short-range ordered alloys

Electrical resistivity recovery (RR) data for irradiated concentrated alloys typically consist of two inseparable parts, one resulting from defect annihilation and the other from short-range order (SRO) effects. These parts exhibit different behaviour and often follow opposite trends. Therefore, in this case, analysis of RR data within the conventional method is too complicated. A new approach to data analysis of such a two-component RR is proposed. The approach involves a new quantity, the difference RR (DRR), which is composed of RR dependences of two similar samples irradiated to different defect concentrations. It is shown that the SRO formation proper and the stages corresponding to the onset of long-range migration of Frenkel pair defects, formed in each part of RR, can be clearly related to certain features of the DRR plots. This interrelationship allows detecting and identifying these stages in each part of RR separately. The validity of the approach is illustrated by analysis of the available pairwise RR data for Fe–16Cr–20Ni and Fe–4Cr alloys. It makes it possible to detect the small contribution from the SRO formation to RR in Fe–4Cr, which we failed to observe previously. It is shown that stage III of Fe–4Cr, which has a negligible contribution to the part of RR induced by defect annihilation, is clearly observed in the part induced by SRO formation.     

Modelling of martensite slip and twinning in NiTiHf shape memory alloys

High-temperature shape memory alloy NiTiHf holds considerable promise for structural applications. An important consideration for these advanced alloys is the determination of the magnitude of the twinning stress. Theoretical stresses for twinning and dislocation slip in NiTiHf martensites are determined. The slip and twinning planes are (0?0?1) and (0?1?1) for monoclinic and orthorhombic crystals, respectively. The determination of the slip and twinning stress is achieved with a proposed Peierls–Nabarro-based formulation informed with atomistic simulations. In the case of the twin, multiple dislocations comprising the twin nucleus are considered. The overall energy expression is minimized to obtain the twinning and slip stresses. The magnitude of the predicted twinning stresses is lower than slip stresses which explains why the NiTiHf alloys can undergo reversibility without plastic deformation. In fact, the predicted critical resolved shear stress levels of 433?MPa for slip and 236?MPa for twinning in the case of 12.5% Hf agree very well with the experimental measurements. The high slip resistance confirms that these materials can be very attractive in load-bearing applications.     

Strain glass behaviour of Ni–Co–Mn–Sn ferromagnetic shape memory alloys

We report the direct experimental observations of the glassy behaviour in Ni–Co–Mn–Sn ferromagnetic shape memory alloys by doping sufficient substitutional point defect Co into the Ni sites (9 at%). The results showed that high level of Co doping had caused the complete suppression of the martensitic transformation and introduction of a strain glass transition in Ni–Co–Mn–Sn alloys. The strain glass transition was definitively characterized by the dynamic mechanical anomalies following the Vogel–Fulcher relationship and the signature nonergodicity of the frozen glass using a zero‐field‐cooled/field‐cooled heating measurement of static strain. The findings clarified the cause of vanishing of the martensitic transformation in Ni–Co–Mn–Sn alloy with high Co doping levels and the generality of glassy state in Ni–Mn based ferromagnetic shape memory alloys with high level of foreign elements doping. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

A microstructure-based yield stress and work-hardening model for textured 6xxx aluminium alloys

The plastic properties of an aluminium alloy are defined by its microstructure. The most important factors are the presence of alloying elements in the form of solid solution and precipitates of various sizes, and the crystallographic texture. A nanoscale model that predicts the work-hardening curves of 6xxx aluminium alloys was proposed by Myhr et al. The model predicts the solid solution concentration and the particle size distributions of different types of metastable precipitates from the chemical composition and thermal history of the alloy. The yield stress and the work hardening of the alloy are then determined from dislocation mechanics. The model was largely used for non-textured materials in previous studies. In this work, a crystal plasticity-based approach is proposed for the work hardening part of the nanoscale model, which allows including the influence of the crystallographic texture. The model is evaluated by comparison with experimental data from uniaxial tensile tests on two textured 6xxx alloys in five temper conditions.