非均匀材料的应变软化及叠层复合材料破坏过程的数值模拟

用有限元方法模拟了非均匀叠层材料的固体力学行为和破坏过程,各层材料性质的初始非均匀性采用某一给定的统计规则描述.用三维网格对试件进行有限元剖分,每个单元具有各自的均匀各向同性常量以反映总体的非均匀性.加载过程中不同单元破坏次序不同,因而整体等效应力应变关系表现出复杂的非线性性.通过数值计算,在选定的具体条件下,模拟了在逐步加载过程中,叠层材料应力应变场的变化和不同单元依次破坏直至试件整体破坏的过程.算例中叠层材料由14~15层构成,使用的网格数约为几千个.用该方法得到的非线性等效应力应变曲线与文[11,12]中叙述的拉伸作用下应变超过某一值后,材料发生应变软化现象的试验数据符合较好,趋势相当一致,因此可以设想是对应变软化原因的一种解释.     

Deformation textures produced in diamond anvil experiments, analysed in radial diffraction geometry

Diamond anvil cells may not only impose pressure upon a sample but also a compressive stress that produces elastic and plastic deformation of polycrystalline samples. The plastic deformation may result in texture development if the material deforms by slip or mechanical twinning, or if grains have a non-equiaxed shape. In radial diffraction geometry, texture is revealed by variation of intensity along Debye rings relative to the compression direction. Diffraction images (obtained by CCD or image plate) can be used to extract quantitative texture information. Currently the most elegant and powerful method is a modified Rietveld technique as implemented in the software package MAUD. From texture data one can evaluate the homogeneity of strain in a diamond anvil cell, the strain magnitude and deformation mechanisms, the latter by comparing observed texture patterns with results from polycrystal plasticity simulations. Some examples such as olivine, magnesiowuestite, MgSiO(3) perovskite and ε-iron are discussed.     

A study on the determination of mechanical properties of a power law material by its indentation force–depth curve

In this study a novel optimization approach is proposed to extract mechanical properties of a power law material whose stress–strain relationship may be expressed as a power law from its given experimental indentation P–h curve. A set of equations have been established to relate the P–h curve to mechanical properties E, σ _y and n of the material. For the loading part of a P–h curve this approach is based on the assumption that the indentation response of an elastic–plastic material is a linear combination of the corresponding elastic and elastic–perfect plastic materials. For the unloading part of the P–h curve it is based on the assumption that the unloading response of the elastic–plastic material is a linear combination of the full contact straight line and the purely elastic curve. Using the proposed optimization approach it was found that the mechanical properties of an elastic–plastic material usually cannot be decided uniquely by using only a single indentation P–h curve of the material. This is because in general a few matched sets of mechanical properties were found to produce a given P–h curve. It is however possible to identify the best matched set of mechanical properties by knowing some background information of the material. If the best matched material is identified, the predictions of mechanical properties are quite accurate.     

Revealing the Pressure-Induced Softening/Weakening Mechanism in Representative Covalent Materials

Diamond, cubic boron nitride(c-BN), silicon(Si), and germanium(Ge), as examples of typical strong covalent materials, have been extensively investigated in recent decades, owing to their fundamental importance in material science and industry. However, an in-depth analysis of the character of these materials' mechanical behaviors under harsh service environments, such as high pressure, has yet to be conducted. Based on several mechanical criteria, the effect of pressure on the mechanical properties of these materials is comprehensively investigated.It is demonstrated that, with respect to their intrinsic brittleness/ductile nature, all these materials exhibit ubiquitous pressure-enhanced ductility. By analyzing the strength variation under uniform deformation, together with the corresponding electronic structures, we reveal for the first time that the pressure-induced mechanical softening/weakening exhibits distinct characteristics between diamond and c-BN, owing to the differences in their abnormal charge-depletion evolution under applied strain, whereas a monotonous weakening phenomenon is observed in Si and Ge. Further investigation into dislocation-mediated plastic resistance indicates that the pressure-induced shuffle-set plane softening in diamond(c-BN), and weakening in Si(Ge), can be attributed to the reduction of antibonding states below the Fermi level, and an enhanced metallization, corresponding to the weakening of the bonds around the slipped plane with increasing pressure, respectively. These findings not only reveal the physical mechanism of pressure-induced softening/weakening in covalent materials, but also highlights the necessity of exploring strain-tunable electronic structures to emphasize the mechanical response in such covalent materials.     

Initial damage induced by thermal residual stress and microscopic failure analysis of carbon-fiber reinforced composite under shear loading

In order to study the mechanical properties and the progressive failure process of composite under shear loading, a representative volume element (RVE) of fiber random distribution was established, with two dominant damage mechanisms – matrix plastic deformation and interfacial debonding – included in the simulation by the extended Drucker–Prager model and cohesive zone model, respectively. Also, a temperature-dependent RVE has been set up to analyze the influence of thermal residual stress. The simulation results clearly reveal the damage process of the composites and the interactions of different damage mechanisms. It can be concluded that the in-plane shear fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation. The progressive damage process and final failure mode of in-plane shear model which are based on constitute are very consistent with the observed result under scanning electron microscopy of V-notched rail shear test. Also, a transverse shear model was established as contrast in order to comprehensively understand the mechanical properties of composite materials under shear loading, and the progressive damage process and final failure mode of composite under transverse shear loading were researched. Thermal residual stress changes the damage initiation locations and damage evolution path and causes significant decreases in the strength and fracture strain.     

Hardening and softening during fatigue fracture

Summary The comparison of the change of hardness and plastic deformation amplitude at a constant stress loading or stress amplitude at a constant deformation loading during the fatigue process shows some singularity of the hardening and softening effects. These effects were investigated on mean carbon and low-alloyed steel and on globular cast iron.The fatigue fractures at cycle numbers 10⁴÷10⁶ under stresses below the yield strength predominate in the softening process, which arises after an inconsiderable hardness increase extends in the region to 0·2 from the fracturing cycle number. Under the stresses above the yield strength, which in some cases for annealed and coarse-grained states are below the fatigue limit, the hardening process predominates, followed by a hardness increase in the field up to 0·25 and above the fracturing cycle number.At low cycle fatigue fractures with cycle numbers < 10⁴ depending on the cyclic plastic properties of steels the fatigue process can be followed by a continuous hardening or softening till fracture. This process is characterized by the change of the deformation amplitude and a one-sided accumulation of plastic deformations at a constant amplitude of active stresses. The one-sided accumulation of deformations commonly ends in a quasistatic failure. Under loading with a constant deformation amplitude during softening a fatigue fracture takes place as a result of damage accumulation under the alternating stresses with amplitudes decreasing with cycle number.     

Effect of temperature on the anisotropy of AZ31 magnesium alloy rolling sheet under high strain rate deformation

In order to investigate the effect of temperature on the anisotropic behaviour of AZ31 magnesium alloy rolling sheet under high strain rate deformation, the Split Hopkinson Pressure Bar was used to analyse the dynamic mechanical properties of AZ31 magnesium alloy rolling sheet in three directions, rolling direction(RD), transverse direction (TD) and normal direction (ND). The texture of the rolling sheet was characterised by X-ray analysis and the microstructure prior and after high strain rate deformation was observed by optical microscope (OM). The results demonstrated that AZ31magnesium alloy rolling sheet has strong initial {0?0?0?2} texture, which resulted at the obvious anisotropy in high strain rate deformation at 20 °C. The anisotropy reflected in stress–strain curve, yield stress, peak stress and microstructure. The anisotropy became much weaker when the deformation temperature increased up to 250 °C. Continuing to increase the deformation temperature to 350 °C the anisotropy of AZ31 rolling sheet essentially disappeared. The decreasing tendency of anisotropy with increasing temperature was due to the fact that when the deformation temperature increased, the critical resolved shear stress (CRSS) for pyramidal 〈c + a〉 slip, which was the predominant slip mechanism for ND, decreased close to that of twinning, which was the predominant deformation mechanism for RD and TD. The deformation mechanism at different directions and temperatures and the Schmid factor (SF) at different directions were discussed in the present paper.     

含微孔洞脆性材料的冲击响应特性与介观演化机制

微孔洞显著地影响着脆性材料的冲击响应,理解其介观演化机制和宏观响应规律将使微孔洞有利于而无害于脆性材料的工程应用.通过建立能够准确表现材料弹性性质和断裂演化的格点-弹簧模型,本文揭示了孔洞的演化对于脆性材料的影响.冲击下孔洞导致的塌缩变形和从孔洞发射的剪切裂纹所导致的滑移变形产生了显著的应力松弛,并调制了冲击波的传播.在多孔脆性材料中,冲击波逐渐展宽为弹性波和变形波.变形波在宏观上类似于延性金属材料的塑性波,在介观上对应于塌缩变形和滑移变形过程.样品中的气孔率决定了脆性材料的弹性极限,气孔率和冲击应力共同影响着变形波的传播速度和冲击终态的应力幅值.含微孔洞脆性材料在冲击波复杂加载实验、功能材料失效的预防、建筑物防护等方面具有潜在的应用价值.所获得的冲击响应规律有助于针对特定应用优化设计脆性材料的冲击响应和动态力学性能.     

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.     

Thermomechanical response of an Ni–Ti–Cr shape-memory alloy at low and high strain rates

The thermomechanical response of an Ni–Ti–Cr shape-memory alloy is investigated at various initial temperatures, over a wide range of strain rates, using an Instron hydraulic testing machine and one of the modified split-Hopkinson-bar systems at the Center of Excellence for Advanced Materials, University of California, San Diego. The transition stress for the stress-induced martensite formation is observed to be quite sensitive to the initial deformation temperature, but the yield stress of the resulting martensite is not. The linear transition stress–temperature relation with a slope of 8.5?MPa?K^?1, obtained in a quasistatic loading regime, seems to remain valid for strain rates up to 500–700?s^?1. The transition stress and the yield stress of the stress-induced martensite show strain-rate sensitivity, increasing monotonically with increasing strain rate. There exists a certain critical strain rate at which the transition stress equals the yield stress of the material. This critical strain rate determines the material's deformation behaviour; the material deforms by the formation of stress-induced martensites and their subsequent yielding, when the strain rate is less than this critical value, and through dislocation-induced plastic slip of the parent austenite, when the strain rate exceeds the critical value. It appears that the critical strain rate increases slightly with decreasing initial temperature.     

Discrete element simulation of localized deformation in stochastic distributed granular materials

The deformation in granular material under loading conditions is a problem of great interest currently. In this paper, the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modified distinct element method under the plane strain conditions, and the influences of the confining pressure, the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded, based on the numerical simulation testing, that two crossed shear sliding planes may occur inside the granular assembly, and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes, it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last, the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

高应变率下材料行为的分子动力学研究

 本文用分子动力学方法研究了高应变率下晶体材料的力学行为。在冲击加载下，晶体材料中产生了位错和塑性变形。在强冲击时还可出现相变变化。在讨论应变率变化时，获得了屈服强度随应变率增大而增高的结果。     

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.     

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.     

Finely striped structure at the edges of localized deformation bands

Under conditions of high-rate loading, plastic strain localization is a result of tension in the zone of interference of unloading waves rather than of thermal softening. At stresses close to the dynamic strength of the material, the microstructure of localized strain bands consists of strongly deformed material, with a large number of incipient microdiscontinuities. At stresses below the Hugoniot elastic limit, the microstructure looks as a set of barely visible stripes. The finely striped structure at the edges of the bands of a spall damage arises as a result of the stretching of initially rounded damage centers attached to the matrix material during dynamic deformation.     

Effects of Filler Content on Mechanical Properties of Macroporous Composites

The mechanical properties of hydroxyapatite related macroporous biocomposites (MPBs) are influenced by a number of factors, such as the pore size, the filler content and the properties of the matrix and the inclusion. Failure often occurs when the strength of the implant cannot bear the applied mechanical load. In this study, the effects of filler content on the mechanical properties of MPBs have been investigated. A finite element (FE) unit cell model of a macroporous hydroxyapatite–polyetheretherketone (HA–PEEK) biocomposite structure with uniform and interconnected pores has been constructed. In the FE model, the HA particles were assumed to have random distribution, and particle volume fraction would be varied in the PEEK matrix. The material behaviours of both HA and PEEK have been implemented in the ABAQUS finite element code. HA was modelled to exhibit elastic behaviour and undergo plastic softening to a residual strength when a critical stress was reached, while the PEEK matrix would follow elastic–plastic behaviour. The macroscopic compressive stress–strain relations of the macroporous biocomposite structures have been predicted. Increasing particle volume fraction could lead to an increase in the compressive elastic modulus of the structures but a reduction in the compressive strength. The von Mises stress distribution and the effect of stress concentration in the structures with different filler content are also discussed. The proposed model could provide macro-structural and microscopic information of the macroporous biocomposite structure to the designers in order to facilitate the fabrication of this kind of structure with optimum mechanical properties.     

A numerical study of the mechanical behavior at contact between particles of dissimilar elastic–ideally plastic materials

In the present study contact between elastic–ideally plastic dissimilar spheres are investigated in detail. The investigation is based on numerical methods and in particular the finite element method. The numerical results presented are discussed with respect to correlation of global contact properties as well as the behavior of local field variables such as contact pressure distribution and the evolution of the effective plastic strain. Large deformation effects are accounted for and discussed in detail. The constitutive behavior is described by classical Mises plasticity. It is shown that correlation of the dissimilar contact problem can be accurately achieved based on the Johnson contact parameter with the representative stress chosen as the yield stress of the softer material.     

原子模拟钛中微孔洞的结构及其失效行为

六角金属由于其各向异性等特点,在塑性变形等过程中容易产生形状和构型都相对复杂的点缺陷团簇.这些团簇之间及其与运动位错等缺陷的相互作用直接影响材料的物理和力学性能.然而对相关问题的原子尺度、尤其是空位团簇的演化和微孔洞的形成乃至裂纹形核扩展等的理解还不全面.本文采用激发弛豫算法结合第一原理及原子间作用势,系统考察了钛中的空位团簇构型及不同构型间的相互转变,给出了不同尺寸空位团簇的稳定和亚稳构型、空位团簇合并分解和迁移的激发能垒等关键参数,发现较小的空位团簇形成稳定构型,较大的空位团簇呈现出空间对称分布趋势进而形成微孔洞;采用高通量分子动力学模拟系统研究了不同尺寸的空位团簇在拉应力作用下对变形过程的影响,发现这些空位团簇可以形成层错,并对微裂纹的形核产生影响.