单轴循环载荷下镁合金宏观塑性本构关系研究

基于微观织构演化,本文对镁合金的宏观塑性本构模型进行了改进,得到了室温下镁合金AZ31B和AZ61A单轴循环拉压载荷作用下的应力应变曲线。模型中区分了滑移、孪晶与去孪三种不同微观塑性变形机制,并且研究了它们对材料宏观循环塑性行为的影响。通过引入初始非零背应力来模拟循环应力应变曲线中拉压不对称性,给出了材料在单轴循环拉压载荷下背应力及屈服面的演化规律,并运用线性预测塑性回拉技术与隐式积分法求解相应的非线性方程组,编写了与.ABAQUS接口的UMAT用户子程序。预测与实验结果的比较显示该模型能较好地模拟镁合金材料在单轴循环拉压载荷作用下的力学行为,具有较高的准确性与良好的实用性。     

DP钢板应变路径多步演变下的弹塑性力学行为

针对DP高强双相钢板在复杂载荷作用下的弹塑性力学特征,提出利用三步拉伸力学实验,对比分析单轴循环加载和非等轴加载下材料的各向异性硬化、永久软化和弹性模量衰减特性等力学行为,揭示应变路径多步演变下的弹塑性力学特性。研究结果表明：材料再加载初期的瞬态行为与应变路径有关,在初期瞬态阶段显示出明显的各向异性,且再加载角度、预应变量以及马氏体含量的增加都会加剧两种DP钢过渡期后的应力软化行为。同时对不同加载下DP钢弹性模量的演化进行了对比,发现弹性模量的衰减程度也随着再加载角度,预应变量和马氏体含量的增加而增加,弹性模量衰减程度在多步非等轴加载比单轴循环载荷作用下表现更明显。     

高应变率载荷下纯钛的非连续冲击疲劳失效模型及其微观机理

基于传统的分离式霍普金森拉杆系统,设计了应变控制的冲击疲劳寿命测试实验,研究了冲击疲劳加载下纯钛的微观演化机制及冲击疲劳对材料宏观力学行为的影响。通过对不同冲击疲劳试验阶段的试样开展准静态力学性能测试,借助扫描电子显微镜(scanning electron microscope, SEM)和电子背散射衍射(electron backscatter diffraction,EBSD)技术表征试样在不同阶段的微观组织以及冲击疲劳失效后的断口形貌,研究纯钛在冲击疲劳失效过程中的循环硬化/软化规律及其微观演化机制。结果表明：通过改变子弹长度可以实现应变控制的冲击疲劳寿命测试;Manson-Coffin疲劳寿命模型可以较好地反映纯钛的冲击疲劳寿命与应变幅值之间的关系;纯钛在冲击疲劳失效过程中表现出循环硬化的现象,这主要是疲劳过程中孪生变形引起的细晶强化和塑性变形引起的应变硬化共同作用的结果,纯钛的冲击疲劳损伤主要表现为变形能力的损失。     

高弹态未硫化橡胶在不同变形模式下的循环加卸载力学行为

对高弹态未硫化橡胶实施了不同变形模式(单轴拉伸和压缩)的循环力学实验，以考察其黏超弹性响应以及应变率对力学行为的影响。结果表明，材料的拉伸、压缩性能与加载速率和变形历史均有着显著的相关性。对于循环拉伸变形，应力-应变曲线的非线性特征较为明显，材料表现出类似于屈服的性质，且随着循环次数和变形量增加，迟滞损耗的积累趋势逐渐减弱；而对于循环压缩变形，应力-应变关系接近线弹性，且随着循环次数和变形量增加，材料刚度和迟滞损耗积累的趋势都逐渐增强。针对上述实验结果，在经典的Bergstrom-Boyce模型中引入损伤变量，对未硫化橡胶的应变率相关性和Mullins效应进行表征。理论计算结果表明，这种非线性黏超弹模型能够较好地描述未硫化橡胶在不同载荷条件下的变形响应与应力软化特征。     

循环软化45碳钢和循环硬化304不锈钢的棘轮行为实验研究

对循环软化45碳钢的单轴应力循环下的平均应力、应力幅值以及先前应变循环对棘轮效应的影响进行了实验研究;并对循环硬化的304不锈钢进行了多种非比例循环加载路径下路径形状、路径等效应力幅值、平均应变与平均应力对材料棘轮变形行为的影响实验．发现平均应力和应力幅值及其历史对于材料的棘轮行为都有很大的影响．     

金属基复合材料单向和循环变形行为的数值模拟研究

利用晶体细观力学模型，依据组元材料的单晶体变形性质，以Ａｌ－Ａｌ２Ｃｕ自生复合材料为模型材料，用数值法模拟其拉伸和循环拉伸变形过程，得到了与有关实验结果相符的应力－应变曲线，研究了增强相间距和循环加载过程对复合材料变形行为的影响，通过考虑变形过程中组元相及其界面的应力分布规律，分析研究了循环变形过程中基体Ｂａｕｓｃｈｉｎｇｅｒ效应对于复合材料微观变形与损伤机制的作用，结果表明，晶体细观力学模拟计算     

双相不锈钢循环微变形行为的原位试验研究

对双相不锈钢开展拉伸和应力循环控制下的原位试验研究,选择特征区域对其局部微变形行为的产生、分布和演化进行了研究和讨论．结果表明：双相不锈钢在较低的载荷作用下内部出现明显的应变梯度,随着拉伸载荷或循环周次的增长,其局部微应变不断增加,最大应变在奥氏体相、小晶粒、狭窄晶粒和不平整的晶界区不断汇集,同一时刻的局部最大微应变远大于宏观应变;循环载荷作用下双相不锈钢在微观尺度产生了局部微棘轮变形效应,微棘轮应变随着循环周次的增加不断累积,其增长速度逐渐降低并趋于饱和;随着循环周次的增加,最大微棘轮变形区逐渐扩展、联通形成大塑性变形带,晶粒走向呈45°方向时,变形带贯穿两相向垂直加载方向发展,而晶粒呈树根状走向时,由于受到两相交互和铁素体的阻碍作用,微棘轮变形带主要集中在奥氏体中沿着奥氏体晶粒走向发展．     

不同加载状态下TA2钛合金绝热剪切破坏响应特性

一般认为绝热剪切现象在宏观上表现为材料动态本构失稳,即热软化大于应变硬化.本文采用帽型受迫剪切试样研究TA2钛合金的动态力学特性和本构失稳过程.首先对剪切区加载应力状态进行理论和数值分析,通过合理设计帽型试样,剪切区变形可近似按剪切状态处理;结合二维数字图像相关法(two-dimensional digital image correlation,DIC-2D)直接测试试样剪切区应变演化,给出帽型受迫剪切实验的等效应力-应变响应曲线.进一步,利用Hopkinson压杆对TA2钛合金开展动态压缩及帽型剪切对比试验研究,比较压缩、剪切试验得到的等效应力-应变曲线,采用"冻结"试样方法分析试样中绝热剪切局域化演化过程,探讨不同加载状态下TA2钛合金的绝热剪切破坏现象及其动态力学响应特性.实验结果表明,在塑性变形初始阶段,动态压缩及剪切加载下的等效应力-应变曲线符合较好,但随塑性损伤发展及绝热剪切带形成,两者出现分离,表明损伤及绝热剪切演化过程与应力状态相关.剪切试样实验得到的本构"软化"特性能够反映绝热剪切带起始、破坏演化过程的力学响应特性,而在动态压缩实验中,即使试样中已出现双锥形的绝热剪切带及局部裂纹分布,其表观等效应力-应变曲线并不出现软化特征,动态压缩实验无法得到关于绝热剪切起始、发展以及破坏的本构软化响应特性.     

沿指定应力路径加载的有限元RVE模型研究

在细观尺度上建立能反映材料微观组织结构又能反映统计意义上宏观力学性能的代表性体积单元（Representative Volume Element, RVE）,对其进行复杂加载下的数值研究,是目前预测材料宏观力学性能较有效的方法。本文从理论上分析并提供了对正六面体RVE在任意应力状态及任意应力路径下加载及宏观应力、应变计算的方法,用有限元软件ABAQUS实现了数值计算过程,并用此方法对循环加载下缺口圆棒颈部中心和边缘位置进行了RVE分析。结果表明：（1）此方法能准确的控制并实现正六面体RVE在任意应力状态及应力状态路径下加载;（2）通过RVE分析,可用于复杂加载下试样局部细观结构变化的研究。     

应力波与缺陷相互作用的宏观微观数值模拟

分别利用LS-DYNA3D有限元程序以及分子动力学方法,从宏观与微观两个层次模拟在动态拉伸载荷作用下含有预置缺陷的薄板中的塑性区形成与演化过程,以及随之而来的动态失效行为。计算结果表明,动态加载下塑性区的形成是应力波与缺陷相互作用以及应力波与应力波相互作用的结果。宏观尺度的LS-DYNA模拟与微观尺度的分子动力学模拟展现出相似的物理特征,即动态载荷下裂纹将萌生在缺陷边缘的前端,然后与缺陷边界连接,最终导致整体破坏。     

应力作用下NiTi形状记忆合金微结构演化的相场模拟及其本征应变率敏感性

基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型,实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度,从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为,并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.0005～15 s?1）力学行为的本征应变率敏感性。研究结果表明,单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生,未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象,在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中,NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积,拥有更优的超弹性变形能力。计算结果显示,在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性,应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。     

Fatigue-induced reversible/irreversible structural-transformations in a Ni-based superalloy

Cyclic loading and the subsequent fatigue-induced structural transformations have been investigated with in-situ neutron diffraction and thermal characterization for a single-phase, polycrystal nickel-based alloy. The lattice-strain evolution is compared with bulk parameters, such as the applied stress and thermal response as a function of the fatigue cycles. In-situ neutron-diffraction and temperature-evolution measurements identify the development of different stages in the fatigue-induced structural transformations, such as bulk hardening, softening, and eventual saturation. An increase in the dislocation density and the formation of planar-patterned dislocation structures are responsible for hardening during the early cycles. With further cyclic loading, the rearrangement of the dislocations results in cyclic softening. A transition is observed during the saturation cycles, which is characterized by the emergence of lattice-strain asymmetry in the loading and transverse directions. The dislocation density and dislocations-wall spacing are determined with diffraction-profile analyses and complemented by transmission-electron microscopy. The thermal behavior of the sample during deformation correlates with corresponding in-situ observation of the time-dependent dislocation structure. An anomaly during saturation cycles is believed to arise from dislocation self-organization – possibly during the formation of microcracks.     

Modeling of anisotropic softening phenomena: Application to soft biological tissues

A thermodynamically consistent dissipative model is proposed to describe softening phenomena in anisotropic materials. The model is based on a generalized polyconvex anisotropic strain energy function represented by a series. Anisotropic softening is considered by evolution of internal variables governing the anisotropic properties of the material. Accordingly, evolution equations are formulated and anisotropic conditions for the onset of softening are defined. In numerical examples, the model is applied to simulate the preconditioning behavior of soft biological tissues subjected to cyclic loading experiments. The results suggest that the general characteristics of preconditioning with different upper load limits are well captured including hysteresis and residual deformations. A model for the Mullins effect is obtained as a special case and shows very good agreement with experimental data on mouse skin.     

Cyclic plastic deformation and cyclic hardening/softening behavior in 304LN stainless steel

Low cycle fatigue experiments have been conducted on 304LN stainless steel in ambient air at room temperature. Uniaxial ratcheting behavior has also been studied on this material and in both engineering and true stress controlling modes. It is shown that material’s cyclic hardening/softening behavior in low cycle fatigue and in ratcheting is dependent not only on material but also on the loading condition. Improvement of ratcheting life and mean stress dependent hardening are observed in the presence of mean stress. A method based on the strain energy density (SED) is used to represent cyclic hardening/softening behavior of the material in this work. The decrease of SED with cycles is an indication that the life in low cycle fatigue and in ratcheting is improved. The SED represents the area of the hysteresis loops.     

Benchmark experiments and characteristic cyclic plasticity deformation

Key issues in cyclic plasticity modeling are discussed based upon representative experimental observations on several commonly used engineering materials. Cyclic plasticity is characterized by the Bauschinger effect, cyclic hardening/softening, strain range effect, nonproporitonal hardening, and strain ratcheting. Additional hardening is identified to associate with ratcheting rate decay. Proper modeling requires a clear distinction among different types of cyclic plasticity behavior. Cyclic hardening/softening sustains dependent on the loading amplitude and loading history. Strain range effect is common for most engineering metallic materials. Often, nonproportional hardening is accompanied by cyclic hardening, as being observed on stainless steels and pure copper. A clarification of the two types of material behavior can be made through benchmark experiments and modeling technique. Ratcheting rate decay is a common observation on a number of materials and it often follows a power law relationship with the number of loading cycles under the constant amplitude stress controlled condition. Benchmark experiments can be used to explore the different cyclic plasticity properties of the materials. Discussions about proper modeling are based on the typical cyclic plasticity phenomena obtained from testing several engineering materials under various uniaxial and multiaxial cyclic loading conditions. Sufficient experimental evidence points to the unambiguous conclusion that none of the hardening phenomena (cyclic hardening/softening, strain range effect, nonproportional hardening, and strain hardening associated with ratcheting rate decay) is isotropic in nature. None of the hardening behavior can be properly modeled with a change in the yield stress.     

A viscoplastic constitutive model incorporating dynamic strain aging effect during cyclic deformation conditions

In this paper, a viscoplastic constitutive model previously proposed by the authors was extended to apply to the cyclic deformation analysis of the modified 9Cr-1Mo steel. A series of cyclic deformation tests were conducted on modified 9Cr-1Mo steel at various temperatures, including those under anisothermal conditions. Furthermore, cyclic evolution of state variables used in the authors' constitutive model was experimentally measured. Based on the test results, cyclic softening behavior depending on the temperature and its history was introduced into the constitutive model. The extended model was applied to simulations of inelastic deformation behavior under monotonic tension, stress relaxation, creep, isothermal cyclic deformations including stress relaxation and anisothermal cyclic deformations. It was found that the present constitutive model has a capability of describing the inelastic deformation behavior of modified 9Cr-1Mo steel adequately at various loading conditions.     

Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model

In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic–plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described.     

Discrete dislocation dynamics modelling of mechanical deformation of nickel-based single crystal superalloys

Discrete dislocation dynamics (DDD) has been used to model the deformation of nickel-based single crystal superalloys with a high volume fraction of precipitates at high temperature. A representative volume cell (RVC), comprising of both the precipitate and the matrix phase, was employed in the simulation where a periodic boundary condition was applied. The dislocation Frank-Read sources were randomly assigned with an initial density on the 12 octahedral slip systems in the matrix channel. Precipitate shearing by superdislocations was modelled using a back force model, and the coherency stress was considered by applying an initial internal stress field. Strain-controlled loading was applied to the RVC in the [0 0 1] direction. In addition to dislocation structure and density evolution, global stress-strain responses were also modelled considering the influence of precipitate shearing, precipitate morphology, internal microstructure scale (channel width and precipitate size) and coherency stress. A three-stage stress-strain response observed in the experiments was modelled when precipitate shearing by superdislocations was considered. The polarised dislocation structure deposited on the precipitate/matrix interface was found to be the dominant strain hardening mechanism. Internal microstructure size, precipitate shape and arrangement can significantly affect the deformation of the single crystal superalloy by changing the constraint effect and dislocation mobility. The coherency stress field has a negligible influence on the stress-strain response, at least for cuboidal precipitates considered in the simulation. Preliminary work was also carried out to simulate the cyclic deformation in a single crystal Ni-based superalloy using the DDD model, although no cyclic hardening or softening was captured due to the lack of precipitate shearing and dislocation cross slip for the applied strain considered.     

Micromechanical model of the high temperature cyclic behavior of 9–12%Cr martensitic steels

9–12%Cr quenched and tempered martensitic steels are known to soften under cyclic loadings at high temperature. The present article proposes a model based on physical mechanisms described at the scale of slip systems. This model describes explicitly the microstructural recovery (corresponding to a decrease of the dislocation density and subgrain coarsening) observed experimentally. The scale transition is carried out in the framework of self-consistent homogenization schemes. The model assumptions and its physical basis are explicitly discussed. The parameters are identified on a very limited amount of experimental data. The model turns out to give very good predictions and extrapolations for the cyclic softening effect observed in uniaxial tension–compression loadings for strain ranges larger than 0.3%. Stress–relaxation and creep behavior can also be simulated for high stresses. In addition the cyclic softening effect is reproduced for multiaxial tension–torsion loadings.     

Modeling the low-cycle fatigue behavior of visco-hyperelastic elastomeric materials using a new network alteration theory: Application to styrene-butadiene rubber

Although several theories were more or less recently proposed to describe the Mullins effect, i.e. the stress-softening after the first load, the nonlinear equilibrium and non-equilibrium material response as well as the continuous stress-softening during fatigue loading need to be included in the analysis to propose a reliable design of rubber structures. This contribution presents for the first time a network alteration theory, based on physical interpretations of the stress-softening phenomenon, to capture the time-dependent mechanical response of elastomeric materials under fatigue loading, and this until failure. A successful physically based visco-hyperelastic model is revisited by introducing an evolution law for the physical material parameters affected by the network alteration. The general form of the model can be basically represented by two parallel networks: a nonlinear equilibrium response and a time-dependent deviation from equilibrium, in which the network parameters become functions of the damage rate (defined as the ratio of the applied cycle over the applied cycle to failure). The mechanical behavior of styrene-butadiene rubber was experimentally investigated, and the main features of the constitutive response under fatigue loading are highlighted. The experimental results demonstrate that the evolution of the normalized maximum stress only depends on the damage rate endured by the material during the fatigue loading history. The average chain length and the average chain density are then taken as functions of the damage rate in the proposed network alteration theory. The new model is found to adequately capture the important features of the observed stress-strain curves under loading-unloading for a large spectrum of strain and damage levels. The model capabilities to predict variable amplitude tests are critically discussed by comparisons with experiments.