A numerical modelling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity

A FE modelling of the elastoplastic interactions occurring within a 3D polycrystal subjected to diffusive phase transformation is proposed. The parent polycrystal is represented by a Voronoi tessellation, where grains differ in shape, size and crystallographic orientation. Grains of the new phase nucleate at favourable sites of the parent polycrystal then grow isotropically, following specific kinetics. This process can result in various product polycrystal morphologies where grains are distinguished by their morphologies and their crystallographic orientations, and have crystalline properties different from those of the parent grains. Application is performed on the austenite-to-ferrite transformation of a low carbon steel, by analysing different basic cases of transformation history with different constitutive modellings. Microplasticity and its related internal stresses are shown to develop during the phase transformations and to affect significantly the elastoplasticity of the product medium.     

高载下单晶铜和单晶硅的径向纳动与损伤行为研究

采用纳米压痕仪研究了单晶铜和单晶硅径向纳动的运行特点和损伤过程.结果表明:径向纳动的残余压痕深度随循环次数增加急剧减小,而纳动循环中载荷-位移曲线在闭合前表现为1个迟滞环;试样在首次径向纳动循环中耗散的能量最大,其后逐渐减小并趋于稳定;材料的接触刚度和弹性模量在最初几次纳动循环中增加较快,随后变化趋于平缓;尽管2种材料的压痕投影面积均随纳动循环次数增加而增大,但由于损伤机制不同,使其径向纳动损伤显示出各自不同特点,其中单晶铜主要表现为压痕边缘的皱褶堆积,而单晶硅表现为塑性区边界裂纹的萌生与扩展.     

A computational model for the indentation and phase transformation of a martensitic thin film

We propose a computational model for a stress-induced martensitic phase transformation of a single-crystal thin film by indentation and its reverse transformation to austenite by heating. Our model utilizes a surface energy that allows sharp interfaces with finite energy and a penalty that forces the film to lie above the indenter and undergo a stress-induced austenite-to-martensite phase transformation. We introduce a method to nucleate the martensite-to-austenite phase transformation since in our model the film would otherwise remain in the martensitic phase in a local minimum of the energy.     

伪弹性TiNi合金圆薄板的准静态力学行为实验研究

采用阴影云纹和应变片方法对伪弹性TiNi合金圆板在固支条件下的准静态力学行为进行了实验研究,得到了载荷位移曲线、全场离面位移和局部应变等数据.载荷位移曲线呈现非线性、滞回耗能和无残余变形的特性,表明试样已经发生马氏体相变.应变测量显示,相变局限于加载中心较小区域,相变区内,环向应变大于径向应变,且拉伸侧应变大于压缩侧的应变.有限元模拟揭示出相变区内两侧表层的相变范围、相变铰区和马氏体相含量的不对称分布规律.     

Phase-field slip-line theory of plasticity

A variational approach to determine the deformation of an ideally plastic substance is proposed by solving a sequence of energy minimization problems under proper conditions to account for the irreversible character of plasticity. The flow is driven by the local transformation of elastic strain energy into plastic work on slip surfaces, once that a certain energetic barrier for slip activation has been overcome. The distinction of the elastic strain energy into spherical and deviatoric parts is used to incorporate in the model the idea of von Mises plasticity and isochoric plastic strain. This is a “phase field model” because the matching condition at the slip interfaces is substituted by the evolution of an auxiliary phase field that, similar to a damage field, is unitary on the elastic phase and null on the yielded phase. The slip lines diffuse in bands, whose width depends upon a material length-scale parameter.Numerical experiments on representative problems in plane strain give solutions with noteworthy similarities with the results from classical slip-line field theory, but the proposed model is much richer because, accounting for elastic deformations, it can describe the formation of slip bands at the local level, which can nucleate, propagate, widen and diffuse by varying the boundary conditions. In particular, the solution for a long pipe under internal pressure is very different from the one obtainable from the classical macroscopic theory of plasticity. For this case, the location of the plastic bands may be an insight to explain the premature failures that are sometimes encountered during the manufacturing process. This practical example enhances the importance of this new theory based on the mathematical sciences.     

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress-strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading-reloading cycles are presented.     

TiNi合金冲击相变过程中温度变化规律的实验研究

针对初始SME(shape memory effect)和PE(pseudo-elastic)状态TiNi合金试样,采用带有红外测温系统的SHPB冲击压缩装置,实时测量了冲击相变过程中两种材料试样表面瞬态温度,并根据实验结果计算了相应的温度变化。实验结果表明,冲击加载相变过程中,温度随相变应变的增大而升高,当应变最大时,温度最高;卸载过程中,对初始PE状态试样,温度降低,对初始SME状态试样,温度保持最高温度不变或降低,这同加载最高温度有关;卸载完成后,两种试样温度均高于其初始温度。计算温度结果表明,相变耗散功对加、卸载相变过程中温度变化的作用不可忽略。     

内部爆炸作用下20钢柱壳的变形及相变

研究冲击波作用下金属微观组织变化对于理解柱壳结构在高应变率下的变形及破坏极为重要。实验通过对20钢金属柱壳在内部爆炸载荷作用下的爆炸回收碎片截面进行微观分析,探讨冲击波作用下材料的组织演化、相变特征,同时使用有限元方法对柱壳膨胀断裂过程中的热力学特征进行分析。研究发现:20钢柱壳近内表面满足α→ε相变热力学条件的有限深度区域内,α晶粒内可见明显的平行滑移线分布特征;电子背散射衍射揭示了平行滑移线区域内组织碎化,且存在{112}<111>和{332}<113>两种孪晶,同时平行滑移线的碎化组织区域中存在密排六方晶格(HCP)的ε相结构,而试样原始组织及爆炸后除试样壁厚内部(0～3.0 mm)区域外均未见ε相结构残留。分析认为:冲击过程中发生了α→ε相变;相变引发的材料性能改变将可能影响断裂破坏过程;考虑冲击波作用下金属材料动态相变对结构变形与破坏的影响,对这类柱壳变形及破坏的精密物理模拟具有重要意义,有必要开展进一步研究。     

单晶硅的纳米力学响应及其相变机制

硅在大规模集成电路、MEMS/NEMS、半导体工业中具有不可替代作用,但是目前对硅的塑性变形及其相变机制的理解远未成熟.采用大规模分子动力学模拟研究(100)面的单晶硅在球形金刚石压头纳米压入过程中的纳米力学响应、相变过程和相分布规律.结果表明:在弹性变形阶段载荷-压深曲线与Hertz接触理论预测结果相吻合.两者的分离点准确地预示了塑性变形的发生.金刚石结构的Si-I相向体心结构的BCT5相转变导致了单晶硅初始的塑性变形.初始形成的BCT5相在次表面形成了一个倒置的金字塔形结构.Si-II相的形成则稍微滞后一些.在较大的载荷下BCT5在压入面上形成一个四重对称的图案分布.相对于小压头条件下大的BCT5相区,大压头更有利于SiII相的发展.卸载后生成的高压Si-II相和BCT5相全部转变为非晶硅.研究结果确认了单晶硅纳米压入中BCT5相的存在;揭示了单晶硅塑性变形的相变机理,即Si-I转变为BCT5和Si-II相;并强调了Si-I相向BCT5相转变对于单晶硅塑性变形的重要作用.     

CuAlNi单晶应力诱发马氏体相变与微结构演化的实验观察与分析

基于CuAlNi形状记忆合金单晶的一维准静态拉伸实验,着重研究相变过程中条带状马氏体的微观结构.通过金相显微镜对整个试样表面进行拍照,并利用图像处理技术和均匀化的方法,提取到了不同载荷下马氏体的含量(相分量)和条带的数量(界面数)在试样各处的分布与变化情况,找到了加载和卸载过程中相变微结构的演化规律,从而实现了对条带状马氏体相变微结构的量化处理.     

双相高强钢FeNiAlC的动态剪切行为及微结构机理

绝热剪切带是金属材料在高应变率载荷下常见的一种失效模式。利用霍普金森压杆装置,对双相钢Fe-24.86Ni-5.8Al-0.38C不同微结构的帽形样品施加冲击载荷,研究它的动态剪切变形行为及微结构机理。先通过对固熔处理得到的粗晶态样品进行大应变冷轧获得冷轧态样品,再使用透射电子显微镜和扫描电子显微镜表征两种样品冲击前后微结构的变化差异。结果表明,双相钢FeNiAlC拥有较优异的动态剪切性能,剪切强度达1.3 GPa,均匀剪切应变达1.5。变形前,材料由奥氏体相和马氏体相构成,马氏体体积分数约为20%。变形过程由位错滑移和孪生变形主导,但因应变速率较高致使马氏体相变被抑制。不同微结构样品内均形成绝热剪切带,带内发生动态再结晶,形成超细晶粒,平均晶粒尺寸约300 nm,且剪切带内不发生相变;冷轧态剪切带宽度的实验值（14.6 μm）与理论计算值(12.3 μm)较好吻合,而粗晶态剪切带宽度的实验值（14.6 μm）与理论计算值（30 μm）相差甚远,初步分析可能是因为粗晶态样品应变较大基本不满足完全绝热的理论条件。在变形过程中,粗晶态因塑性变形做功产生的绝热温升高达720 K,而冷轧态的只有190 K。通过实验结果与热塑模型分析,得出绝热温升不是形成绝热剪切带的唯一因素,而应考虑材料的微观结构和局部化变形等的共同影响。     

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.     

Large Deformation of Nitinol Under Shear Dominant Loading

Full-field quantitative strain maps of phase transformation and plasticity in Nitinol under large shear-dominated deformation are presented. To achieve a shear-dominated deformation mode with relatively uniform stresses and strains, a shear compression specimen (SCS) geometry was utilized. Shear deformation appears to impede the development of the strain localization during phase transformation that is seen in uniaxial testing. The shear-dominant deformation of Nitinol in the plastic regime exhibits low hardening and results in the development of significant strain inhomogeneity.     

Molecular dynamics simulation study of microstructure evolution during cyclic martensitic transformations

Shape memory alloys (SMA) exhibit a number of features which are not easily explained by equilibrium thermodynamics, including hysteresis in the phase transformation and “reverse” shape memory in the high symmetry phase. Processing can change these features: repeated cycling can “train” the reverse shape memory effect, while changing the amount of hysteresis and other functional properties. These effects are likely to be due to formations of localised defects and these can be studied by atomistic methods. Here we present a molecular dynamics simulation study of such behaviour employing a two-dimensional, binary Lennard-Jones model. Our atomistic model exhibits a symmetry breaking, displacive phase transition from a high temperature, entropically stabilised, austenite-like phase to a low temperature martensite-like phase. The simulations show transformations in this model material proceed by non-diffusive nucleation and growth processes and produce distinct microstructures. We observe the generation of persistent lattice defects during forward-and-reverse transformations which serve as nucleation centres in subsequent transformation processes. These defects interfere the temporal and spatial progression of transformations and thereby affect subsequent product morphologies. During cyclic transformations we observe accumulations of lattice defects so as to establish new microstructural elements which represent a memory of the previous morphologies. These new elements are self-organised and they provide a basis of the reversible shape memory effect in the model material.     

Defects in crystalline materials and their relation to mechanical properties

This paper is divided into two major sections. The first of these describes the types of defects which may arise in crystalline materials. These may be classified as point, line, sheet and volume defects, examples of the four groups being vacancies, dislocations, grain boundaries and precipitates. The basic defects of crystal structures are first described, particular attention being paid to dislocation lines and the way in which a perfect dislocation may dissociate into two partial dislocations and a ribbon of stacking fault. The motion of defects, including glide, climb and cross-slip is discussed. This section ends with a summary of the ways in which basic defects may interact and combine, and be used to describe such microstructural features as deformation twins and precipitate boundaries. These defects form the basis of the mechanisms, given in the second part of the paper, which have been used to explain the various phenomena of hardening and fracture. No attempt has been made to give detailed theories of these mechanical properties. The treatment is intended for the nonspecialist, interested in obtaining an understanding of how a knowledge of the microstructure of materials may be applied to specific problems.     

Computational analysis of liquid crystalline elastomer membranes: Changing Gaussian curvature without stretch energy

Liquid crystalline elastomers (LCEs) can undergo extremely large reversible shape changes when exposed to external stimuli, such as mechanical deformations, heating or illumination. The deformation of LCEs result from a combination of directional reorientation of the nematic director and entropic elasticity. In this paper, we study the energetics of initially flat, thin LCE membranes by stress driven reorientation of the nematic director. The energy functional used in the variational formulation includes contributions depending on the deformation gradient and the second gradient of the deformation. The deformation gradient models the in-plane stretching of the membrane. The second gradient regularises the non-convex membrane energy functional so that infinitely fine in-plane microstructures and infinitely fine out-of-plane membrane wrinkling are penalised. For a specific example, our computational results show that a non-developable surface can be generated from an initially flat sheet at cost of only energy terms resulting from the second gradients. That is, Gaussian curvature can be generated in LCE membranes without the cost of stretch energy in contrast to conventional materials.     

Modelling of laminated microstructures in stress-induced martensitic transformations

This paper is concerned with micromechanical modelling of stress-induced martensitic transformations in crystalline solids, with the focus on distinct elastic anisotropy of the phases and the associated redistribution of internal stresses. Micro-macro transition in stresses and strains is analysed for a laminated microstructure of austenite and martensite phases. Propagation of a phase transformation front is governed by a time-independent thermodynamic criterion. Plasticity-like macroscopic constitutive rate equations are derived in which the transformed volume fraction is incrementally related to the overall strain or stress. As an application, numerical simulations are performed for cubic β₁ (austenite) to orthorhombic γ₁′ (martensite) phase transformation in a single crystal of Cu-Al-Ni shape memory alloy. The pseudoelasticity effect in tension and compression is investigated along with the corresponding evolution of internal stresses and microstructure.     

A stress-gradient based criterion for dislocation nucleation in crystals

Dislocations are the main lattice defects responsible for the strength and ductility of crystalline solids. The generation of new dislocations is an essential aspect of crystal defect physics, but a fundamental understanding of the mechanical conditions which lead to dislocation nucleation has remained elusive. Here, we present a nucleation criterion motivated from continuum thermomechanical considerations of a crystalline solid undergoing deformation, and demonstrate the criterion's ability to correctly predict dislocation nucleation via direct atomistic simulations. We further demonstrate that the commonly held notion of a nucleation criterion based on the magnitude of local stress components is incorrect.