位移加载条件下微小尺寸单晶金属的应变突变模型及其间歇性塑性变形行为研究

微压缩实验发现,微小尺度单晶金属柱体在塑性变形过程中会发生显著的应变突变,呈现出特殊的间歇性塑性流动特征。本文以数百纳米直径的单晶Au柱体为研究对象,探讨其在位移加载条件下的间歇性流动行为。首先根据位移加载条件下的塑性变形特征,提出了分析其应变突变的三阶段模型。进一步结合经典晶体塑性理论框架的有限元方法,建立了以二阶功参量为基础的连续塑性力学模型。通过与实验结果相对比发现,新模型能够较好地描述位移加载条件下微小尺度面心立方单晶金属材料的应变突变现象,能够合理预测单晶柱体的特殊变形行为。此外,二阶功准则作为位移加载条件下应变突变现象的判据是有效的。进而使用该理论模型,探讨了微小金属柱体应变突变随机性、尺寸相关性以及率敏感性等问题。     

Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression

The size dependent deformation of Cu single crystal micropillars with thickness ranging from 0.2 to 2.5 μm subjected to uniaxial compression is investigated using a Multi-scale Dislocation Dynamics Plasticity (MDDP) approach. MDDP is a hybrid elasto-viscoplastic simulation model which couples discrete dislocation dynamics at the micro-scale (software micro3d) with the macroscopic plastic deformation. Our results show that the deformation field in these micropillars is heterogeneous from the onset of plastic flow and is confined to few deformation bands, leading to the formation of ledges and stress concentrations at the surface of the specimen. Furthermore, the simulation yields a serrated stress–strain behavior consisting of discrete strain bursts that correlates well with experimental observations. The intermittent operation and stagnation of discrete dislocation arms is identified as the prominent mechanism that causes heterogeneous deformation and results in the observed macroscopic strain bursts. We show that the critical stress to bow an average maximum dislocation arm, whose length changes during deformation due to pinning events, is responsible for the observed size dependent response of the single crystals. We also reveal that hardening rates, similar to that shown experimentally, occur under relatively constant dislocation densities and are linked to dislocation stagnation due to the formation of entangled dislocation configuration and pinning sites.     

A stochastic model for the temporal aspects of flow intermittency in micropillar compression

Systematic experimental investigations have demonstrated that the plastic deformation of micropillar proceeds through a sequence of intermittent bursts, the sizes of which follow power-law statistics. In this study, a stochastic model based on the power-law distribution of burst size is formulated in the framework of crystal plasticity in order to investigate the temporal aspects of flow intermittency in micropillar compression. A Monte Carlo simulation scheme is developed to determine the burst size when a burst activity is captured. This burst size is considered as the displacement boundary condition of burst deformation. Three-dimensional finite element analysis of the model is performed and its predictions are validated by comparison with results from both micro-compression experiments and simulation tests of bulk crystals using the classic crystal plasticity finite element method (CPFEM). The model provides a reasonable prediction of stress–strain responses both at the macroscopic and microscopic scales. Finally, the capability of this model is shown with applications to the intermittent plastic deformation in micropillar compressions, in particular for their burst time durations and burst velocities. The results from such stochastic finite element analysis are shown to be consistent with earlier experimental findings and results of mean-field theory.     

The role of the weakest-link mechanism in controlling the plasticity of micropillars

We present a computational study on the effects of sample size on the strength and plastic flow characteristics of micropillars under compression loading. We conduct three-dimensional simulations using the parametric dislocation dynamics coupled with the boundary element method. Two different loading techniques are performed. The plastic flow characteristics as well as the stress-strain behavior of simulated micropillars are shown to be in general agreement with experimental observations. The flow strength versus the diameter of the micropillar follows a power law with an exponent equal to -0.69. A stronger correlation is observed between the flow strength and the average length of activated dislocation sources. This relationship is again a power law, with an exponent -0.85. Simulation results with and without the activation of cross-slip are compared. Discontinuous hardening is observed when cross-slip is included. Experimentally observed size effects on plastic flow and work-hardening are consistent with a “weakest-link activation mechanism”.     

Randomness and slip avalanches in gradient plasticity

While localization of deformation at macroscopic scales has been documented and carefully characterized long ago, it is only recently that systematic experimental investigations have demonstrated that plastic flow of crystalline solids on mesoscopic scales proceeds in a strongly heterogenous and intermittent manner. In fact, deformation is characterized by intermittent bursts (‘slip avalanches’) the sizes of which obey power-law statistics. In the spatial domain, these avalanches produce characteristic deformation patterns in the form of slip lines and slip bands. Unlike to the case of macroscopic localization where gradient plasticity can capture the width and spacing of shear bands in the softening regime of the stress–strain graph, this type of mesoscopically jerky like localized plastic flow is observed in spite of a globally convex stress–strain relationship and may not be captured by standard deterministic continuum modelling. We thus propose a generalized constitutive model which includes both second-order strain gradients and randomness in the local stress–strain relationship. These features are related to the internal stresses which govern dislocation motion on microscopic scales. It is shown that the model can successfully describe experimental observations on slip avalanches as well as the associated surface morphology characteristics.     

超高强度钢AF1410塑性流动特性及其本构关系

在本文中,为揭示超高强度钢AF1410的塑性流动性,并研究其塑性流动本构关系,利用CSS4410电子万能试验机和改进的Hopkinson拉压杆技术,对AF1410钢在温度从100K到600K,应变率从0.001/s到2000/s,塑性应变超过20%的塑性流动特性进行了试验研究。结果表明,拉伸加载下AF1410钢屈服强度低于压缩屈服强度,且随应变率增加,拉压屈服强度差值越来越大;该材料塑性流动应力对应变率敏感性低,而对温度较为敏感;随应变率的提高,该材料拉伸失效应变减小,但温度对失效应变无明显影响。最后基于位错的运动学关系,借助试验数据,获得了AF1410钢的塑性流动物理概念本构模型,并通过与经典J-C模型的结果对比对该物理概念本构模型进行了评估分析,表明该物理概念本构模型在较宽温度和应变率范围能较好的预测AF1410钢的塑性流动应力。     

Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations

This work is a review of experimental methods for observing and modeling the anisotropic plastic behavior of metal sheets and tubes under a variety of loading paths, such as biaxial compression tests; biaxial tension tests on metal sheets and tubes using closed-loop electrohydraulic testing machines; the abrupt strain path change method for detecting a yield vertex and subsequent yield loci without unloading; in-plane stress reversal tests on metal sheets; and multistage tension tests. Observed material responses are compared with the predictions of phenomenological plasticity models. Special attention is paid to the plastic deformation behavior of materials commonly used in industry, and to verifying the validity of conventional anisotropic yield criteria for those materials and associated flow rules at large plastic strains. The effects of using appropriate anisotropic yield criteria on the accuracy of simulations of forming defects, such as large springback and fracture, are also presented to highlight the importance of accurate material testing and modeling.     

新型铝锡硅合金高温塑性变形流变应力的研究

采用高温等温压缩变形方法,在温度为373-673K范围和应变速率为0.001-1.0s^-1范围内,测定了新型Al-10Sn-4Si合金的流变应力曲线,结果表明,该合金为正应变速率敏感材料并且具有稳态流变特征;稳态流变应力随变形速率的增加而增大,随变形温度的升高而降低,通过回归分析,建立了该合金高温塑性变形时稳态流变应力的半经验方程,这种稳态流变特征与动态回复、动态再结晶及局部晶界粘滞性流动行为有关,受热激活过程控制。     

Constitutive modeling of ice in the high strain rate regime

The objective of the present work is to propose a constitutive model for ice by considering the influence of important parameters such as strain rate dependence and pressure sensitivity on the response of the material. In this regard, the constitutive model proposed by Carney et al. (2006) is considered as a starting basis and subsequently modified to incorporate the effect of brittle cracking within a continuum damage mechanics framework. The damage is taken to occur in the form of distributed cracking within the material during impact which is consistent with experimental observations. At the point of failure, the material is assumed to be fluid-like with deviatoric stress almost dropping down to zero. The constitutive model is implemented in a general purpose finite element code using an explicit formulation. Several single element tests under uniaxial tension and compression, as well as biaxial loading are conducted in order to understand the performance of the model. Few large size simulations are also performed to understand the capability of the model to predict brittle damage evolution in un-notched and notched three point bend specimens. The proposed model predicts lower strength under tensile loading as compared to compressive loading which is in tune with experimental observations. Further the model also asserts the strain rate dependency of the strength behavior under both compressive as well as tensile loading, which also corroborates well with experimental results.     

The evolution of crystalline stresses of a polycrystalline metal during cyclic loading

The presence of a positive average applied stress during cyclic uniaxial loading leads to a reduction in fatigue life of metallic parts. The metals are typically polycrystalline, with stresses varying from crystal to crystal due to differences in lattice orientation and slip system strength. Simulations enable us to better understand how polycrystals behave under cyclic loading and how the changing stress over many cycles influences fatigue life. Specifically, uniaxial cyclic simulations of pre-strained HY100 steel were conducted using an elastic viscoplastic continuum slip model employing a Taylor hypothesis. Stress-controlled loading conditions were employed to mimic fatigue tests on cold-bent bar specimens for three different load levels. The macroscopic axial strains and the crystal axial stresses were monitored during the cycles. The stress–strain response for the first cycle was used to determine the load input for the material point simulations. The peak values of crystal axial stress were found to evolve continuously with the number of loading cycles. It was found that the stress change in a crystal is influenced not only by its own orientation but also by the orientations of the other crystals in the aggregate. Furthermore, the distribution of crystal stresses after thousands of cycles at a lower stress amplitude closely resembled the distribution after tens of cycles at a larger stress amplitude.     

A two-dimensional dislocation dynamics model of the plastic deformation of polycrystalline metals

Two-dimensional dislocation dynamics (2D-DD) simulations under fully periodic boundary conditions are employed to study the relation between microstructure and strength of a material. The material is modeled as an elastic continuum that contains a defect microstructure consisting of a preexisting dislocation population, dislocation sources, and grain boundaries. The mechanical response of such a material is tested by uniaxially loading it up to a certain stress and allowing it to relax until the strain rate falls below a threshold. The total plastic strain obtained for a certain stress level yields the quasi-static stress-strain curve of the material. Besides assuming Frank-Read-like dislocation sources, we also investigate the influence of a pre-existing dislocation density on the flow stress of the model material. Our results show that - despite its inherent simplifications - the 2D-DD model yields material behavior that is consistent with the classical theories of Taylor and Hall-Petch. Consequently, if set up in a proper way, these models are suited to study plastic deformation of polycrystalline materials.     

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。     

Spatiotemporally inhomogeneous plastic flow of a bulk-metallic glass

With geometrically-constrained specimens, the spatiotemporally inhomogeneous deformation of a Zr-based bulk-metallic glass in uniaxial, quasistatic, compression was investigated. Decreasing the height/width ratio of specimens from 2 to 0.5 significantly increases the plastic strain from 2% to about 80%. Using an infrared camera, we first observe in situ dynamic shear-banding operations during compression at various strain rates. The shear banding is highly dependent on strain rates, either intermittent at the lower strain rate or successive at the higher strain rate. Scanning electron microscopy observations show the spatiality of the rate-dependent shear banding. The serrated plastic flow is a result of the shear-banding operations. At the lower strain rate, more simultaneous shear-banding operations result in more obvious serrations, while at the higher strain rate, fewer simultaneous shear-banding operations cause less obvious serrations.     

Effects of stress invariants and reverse loading on ductile fracture initiation

Recent research studies on ductile fracture of metals have shown that the ductile fracture initiation is significantly affected by the stress state. In this study, the effects of the stress invariants as well as the effect of the reverse loading on ductile fracture are considered. To estimate the reduction of load carrying capacity and ductile fracture initiation, a scalar damage expression is proposed. This scalar damage is a function of the accumulated plastic strain, the first stress invariant and the Lode angle. To incorporate the effect of the reverse loading, the accumulated plastic strain is divided into the tension and compression components and each component has a different weight coefficient. For evaluating the plastic deformation until fracture initiation, the proposed damage function is coupled with the cyclic plasticity model which is affected by all of the stress invariants and pervious plastic deformation history.For verification and evaluation of this damage-plasticity constitutive equation a series of experimental tests are conducted on high-strength steel, DIN 1.6959. In addition finite element simulations are carried out including the integration of the constitutive equations using the modified return mapping algorithm. The modeling results show good agreement with experimental results.     

基于塑性体积应变的岩石损伤变形特性实验研究

为分析岩石塑性变形与损伤的关系,在定义岩石的初始损伤和临界损伤,提出塑性体积应变分析方法,从而以塑性体积应变为损伤变量,采用归一化方法建立岩石的损伤本构模型。采用递增循环加载实验确定岩石损伤本构模型中的弹性卸载模量和弹性应变比例系数两个参数。通过实验和理论分析得出:当荷载较小时,普通单轴压缩状态下岩石损伤随荷载的增加具有减小趋势,荷载超过一定数值后,岩石损伤才开始增加;单轴递增循环压缩状态下当循环荷载大于约35%峰值强度后,卸载后岩石的损伤具有增加的趋势,小于该荷载之前具有减小的趋势。整个加载过程的理论应力-应变曲线能很好地与实验结果相吻合,在循环加载区间理论结果还能体现出岩石实验结果中的回滞环。     

Texture development and plastic anisotropy of B.C.C. strain hardening sheet metals

A Taylor-like polycrystal model is adopted here to investigate the plastic behavior of body centered cubic (b.c.c.) sheet metals under plane-strain compression and the subsequent in-plane biaxial stretching conditions. The <111> pencil glide system is chosen for the slip mechanism for b.c.c. sheet metals. The {110} <111> and {112} <111> slip systems are also considered. Plane-strain compression is used to simulate the cold rolling processes of a low-carbon steel sheet. Based on the polycrystal model, pole figures for the sheet metal after plane-strain compression are obtained and compared with the corresponding experimental results. Also, the simulated plane-strain stress—strain relations are compared with the corresponding experimental results. For the sheet metal subjected to the subsequent in-plane biaxial stretching and shear, plastic potential surfaces are determined at a given small amount of plastic work. With the assumption of the equivalence of the plastic potential and the yield function with normality flow, the yield surfaces based on the simulations for the sheet metal are compared with those based on several phenomenological planar anisotropic yield criteria. The effects of the slip system and the magnitude of plastic work on the shape and size of the yield surfaces are shown. The plastic anisotropy of the sheet metal is investigated in terms of the uniaxial yield stresses in different planar orientations and the corresponding values of the anisotropy parameter R, defined as the ratio of the width plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial tensile loading. The uniaxial yield stresses and the values of R at different planar orientations from the polycrystal model can be fitted well by a yield function recently proposed by Barlat et al. (1997b).     

On the interplay between strain rate and strain rate sensitivity on flow localization in the dynamic expansion of ductile rings

In this work a stability analysis on flow localization in the dynamic expansion of ductile rings is conducted. Within a 1-D theoretical framework, the boundary value problem of a radially expanding thin ring is posed. Based on a previous work, the equations governing the stretching process of the expanding ring are derived and solved using a linear perturbation method. Then, three different perfectly plastic material constitutive behaviours are analysed: the rate independent material, the rate dependent material showing constant logarithmic rate sensitivity and the rate dependent material showing non-constant and non-monotonic logarithmic rate sensitivity. The latter allows to investigate the interaction between inertia and strain rate sensitivity on necking formation. The main feature of this work is rationally demonstrate that under certain loading conditions and material behaviours: (1) decreasing rate sensitivity may not lead to more unstable material, (2) increasing loading rate may not lead to more stable material. This finding reveals that the relation between rate sensitivity and loading rate controls the unstable flow growth. Additionally a finite element model of the ring expansion problem is built in ABAQUS/Explicit. The stability analysis properly reflects the results obtained from the numerical simulations. Both procedures, perturbation analysis and numerical simulations, allow for emphasizing the interplay between rate sensitivity and inertia on strain localization.     

Theoretical and numerical investigations on confined plasticity in micropillars

Multiscale dislocation dynamic simulations are systematically carried out to reveal the dislocation mechanism controlling the confined plasticity in coated micropillar. It is found that the operation of single arm source (SAS) controls the plasticity in coated micropillar and a modified operation stress equation of SAS is built based on the simulation results. The back stress induced by the coating contributes most to the operation stress and is found to linearly depend on the ‘trapped dislocation’ density. This linear relation is verified by comparing with the solution of the current higher-order crystal plasticity theory and is used to determine the material parameters in the continuum back stress model. Furthermore, based on the linear back stress model and considering the stochastic distribution of SAS, a theoretical model is established to predict the upper and lower bound of stress–strain curve in the coated micropillars, which agrees well with that obtained in the dislocation dynamic simulation.