Sub-Grain Scale Digital Image Correlation by Electron Microscopy for Polycrystalline Materials during Elastic and Plastic Deformation

Damage during loading of polycrystalline metallic alloys is localized at or below the scale of individual grains. Quantitative assessment of the heterogeneous strain fields at the grain scale is necessary to understand the relationship between microstructure and elastic and plastic deformation. In the present study, digital image correlation (DIC) is used to measure the strains at the sub-grain level in a polycrystalline nickel-base superalloy where plasticity is localized into physical slip bands. Parameters to minimize noise given a set speckle pattern (introduced by chemical etching) when performing DIC in a scanning electron microscope (SEM) were adapted for measurements in both plastic and elastic regimes. A methodology for the optimization of the SEM and DIC parameters necessary for the minimization of the variability in strain measurements at high spatial resolutions is presented. The implications for detecting the early stages of damage development are discussed.     

On the strain hardening and texture evolution in high manganese steels: Experiments and numerical investigation

We present a systematic investigation on the strain hardening and texture evolution in high manganese steels where twinning induced plasticity (TWIP) plays a significant role for the materials' plastic deformation. Motivated by the stress–strain behavior of typical TWIP steels with compositions of Fe, Mn, and C, we develop a mechanistic model to explain the strain-hardening in crystals where deformation twinning dominates the plastic deformation. The classical single crystal plasticity model accounting for both dislocation slip and deformation twinning are then employed to simulate the plastic deformation in polycrystalline TWIP steels. While only deformation twinning is activated for plasticity, the simulations with samples composed of voronoi grains cannot fully capture the texture evolution of the TWIP steel. By including both twinning deformation and dislocation slip, the model is able to capture both the stress–strain behaviors and the texture evolution in Fe–Mn–C TWIP steel in different boundary-value problems. Further analysis on the strain contributions by both mechanisms suggests that deformation twinning plays the dominant role at the initial stage of plasticity in TWIP steels, and dislocation slip becomes increasingly important at large strains.     

Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal

This is a study of plastic strain localization, surface roughening and of the origin of these phenomena in polycrystals. An oligocrystal aluminum sample with a single quasi-2D layer of coarse grains is plastically deformed under uniaxial tensile loading. During deformation, the history of strain localization, surface roughening, microstructure and in-grain fragmentation is carefully recorded. Using a crystal plasticity finite element model, corresponding high-resolution simulations are conducted. A series of comparisons identifying aspects of good and of less good match between model predictions and experiments is presented. The study suggests that the grain topology and microtexture have a significant influence on the origin of strain heterogeneity. Moreover, it suggests that the final surface roughening profiles are related both to the macro strain localization and to the intra-grain interaction. Finally slip lines observed on the surface of the samples are used to probe the activation of slip systems in detail. The study concludes with an assessment of the limitations of the crystal plasticity model.     

An experimental study on grain deformation and interactions in an Al-0.5%Mg multicrystal

Heterogeneous plastic deformation behavior of a coarse-grained Al-0.5%Mg multicrystal was investigated experimentally at the individual grain level. A flat uniaxial tensile specimen consisting of a single layer of millimeter-sized grains was deformed quasi-statically up to an axial strain of 15% at room temperature. The initial local crystallographic orientations of the grains and their evolutions after 5, 12, and 15% plastic strains were measured by electron backscattered diffraction pattern analysis in a scanning electron microscope. The local in-plane plastic strains and rigid body rotations of the grains were measured by correlation of digital optical video images of the specimen surface acquired during the tensile test. It is found that both intergranular and intragranular plastic deformation fields in the aluminum multicrystal specimen under uniaxial tension are highly heterogeneous. Single or double sets of slip-plane traces were predominantly observed on the electro-polished surfaces of the millimeter-sized grains after deformation. The active slip systems associated with these observed slip-plane traces were identified based on the grain orientation after deformation, the Schmid factor, and grain interactions in terms of the slip-plane trace morphology at grain boundaries. It is found that the aluminum multicrystal obeys neither the Sachs nor the Taylor polycrystal deformation models but deforms heterogeneously to favor easy slip transmission and accommodation among the grains.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.     

基于晶体塑性理论研究铝材料高压高应变率下的强度特性

为了了解金属材料在极端加载下复杂动态响应过程中的多种机制和效应，重点针对Al材料在高压、高应变率加载下的塑性变形机制，在经典晶体塑性模型的基础上，对其中的非线性弹性、位错动力学和硬化形式进行改进，建立适用于高压、高应变率加载下的热弹-黏塑性晶体塑性模型。该模型可以较好地描述单晶铝和多晶铝材料屈服强度随压力的变化过程，相比宏观模型，用该模型还获得了多晶Al材料在冲击加载下的织构演化规律，揭示了织构择优取向行为和压力的关系。     

A cyclic plasticity model for single crystals

The Armstrong–Frederick type kinematic hardening rule was invoked to capture the Bauschinger effect of the cyclic plastic deformation of a single crystal. The yield criterion and flow rule were built on individual slip systems. Material memory was introduced to describe strain range dependent cyclic hardening. The experimental results of copper single crystals were used to evaluate the cyclic plasticity model. It was found that the model was able to accurately describe the cyclic plastic deformation and properly reflect the dislocation substructure evolution. The well-known three distinctive regimes in the cyclic stress–strain curve of the copper single crystals oriented for single slip can be reproduced by using the model. The model can predict the enhanced hardening for crystals oriented for multislip, showing the model's ability to describe anisotropic cyclic plasticity. For a given loading history, the model was able to capture not only the saturated stress–strain response but also the detailed transient stress–strain evolution. The model was used to predict the cyclic plasticity under a high–low loading sequence. Both the stress–strain responses and the microstructural evolution can be appropriately described through the slip system activation.     

Micromechanical quantification of elastic,twinning, and slip strain partitioning exhibited by polycrystalline,monoclinic nickel–titanium during large uniaxial deformations measured via in-situ neutron diffraction

We draw upon existing knowledge of twinning and slip mechanics to develop a diffraction analysis model that allows for empirical quantification of individual deformation mechanisms to the macroscopic behaviors of low symmetry and phase transforming crystalline solids. These methods are applied in studying elasticity, accommodation twinning, deformation twinning, and slip through neutron diffraction data of tensile and compressive deformations of monoclinic NiTi to ~18% true strain. A deeper understanding of tension–compression asymmetry in NiTi is gained by connecting crystallographic calculations of polycrystalline twinning strains with in situ diffraction measurements. Our analyses culminate in empirical, micromechanical quantification of individual elastic, accommodation twinning, deformation twinning, and slip contributions to the total macroscopic stress–strain response of a monoclinic material subjected to large deformations. From these results, we find that 20–40% of the total plastic response at high strains is due to deformation twinning and 60–80% due to slip.     

The role of texture in tension–compression asymmetry in polycrystalline NiTi

The purpose of the present study is to thoroughly understand the stress–strain behavior of polycrystalline NiTi deformed under tension versus compression. To do this, a micro-mechanical model is used which incorporates single crystal constitutive relationships and experimentally measured polycrystalline texture into the self-consistent formulation. For the first time it is quantitatively demonstrated that texture measurements coupled with a micro-mechanical model can accurately predict tension/compression asymmetry in NiTi shape memory alloys. The predicted critical transformation stress levels and transformation stress–strain slopes under both tensile and compressive loading are consistent with experimental results. For textured polycrystalline NiTi deformed under tension it is demonstrated that the martensite evolution is very abrupt, consistent with the Luders type deformation experimentally observed. The abrupt transformation under tension is attributed to the fact that the majority of the grains are oriented along the [111] crystallographic direction, which is soft under tensile loading. Since single crystals of the [111] orientation are hard under compression it is also demonstrated that under compression the martensite in textured polycrystalline NiTi evolves relatively slower.     

Micro-experimental study of large plastic deformation for high-purity polycrystalline aluminum

This paper aims at revealing various micro- deformation characteristics, such as crystalline slip and grain boundary slide, which are recorded under scanning electronic microscope for high-purity aluminum tensile specimen at room temperature. These experimental data provide us direct evidence for shear localization near the grain boundary network via multi- directional grain boundary slide. The nonuniform deformation induced in the grain interiors would have decisive effect on the plastic flow and failure of polycrystalline materials. Sponsored by the National Natural Science Foundation of China and the Fok Ying- Tung Education Foundation.     

Orientation evolution in Hadfield steel single crystals under combined slip and twinning

The tensile deformation response and texture evolution of aluminum alloyed Hadfield steel single crystals oriented in the 〈1 6 9〉 direction is investigated. In this material, the strain hardening response is governed by the high-density dislocation walls (HDDWs) that interact with glide dislocations. A microstructure-based visco-plastic self-consistent model was modified to account for mechanical twinning in addition to the prevailing contribution of the HDDWs. Simulations revealed the contribution of twinning to the overall work hardening at the later stages of deformation. Moreover, both the deformation response and the rotation of the loading axis associated with plastic flow are successfully predicted even at the high-strain levels attained (0.53). Predicting the texture evolution serves as a separate check for validating the model, motivating its utilization in single and polycrystals of other alloys that exhibit combined HDDWs and twinning.     

白光散斑相关法多尺度分析Portevin-Le Chatelier剪切带变形

在适当的温度、应变率或预变形下,合金材料的拉伸试验中,将会出现伴随雪崩式剪切变形带的锯齿形塑性失稳、即PLC(Portevin-Le Chatelier)效应。本文利用图像相关求位移场的方法,对恒定加载应变率下(10-4/s),拉伸铝合金(A2017)试件时出现的PLC效应从宏观剪切带变形到微观晶粒变形等多尺度进行了观察和定量化的分析。通过对PLC效应发生时采集的试件表面的白光散斑图进行相关运算,得到试件表面剪切变形区域各点的精细位移,并在此基础上计算出剪切带区域的应变分布及剪切带的宽度。实验结果显示,当PLC效应发生时,剪切带区域的应变曲线呈台阶型,带的前后边缘应变梯度较大,中间近似呈平台状,带外区域应变值接近零,塑性拉伸变形主要集中在带内。     

镁合金晶体塑性本构模型与非均匀孪生变形分析

微结构演化对镁合金材料力学性能有着显著的影响，为了揭示镁合金宏观塑性各向异性特性与非均匀孪生变形的关系，开展了不同路径下的单轴加载试验以及采用含滑移、孪生机制的晶体塑性本构模型对试验条件下的镁合金变形行为进行数值模拟研究。文中本构模型描述了滑移与孪生变形机制以及晶格转动的机制，同时研究采用三维微结构代表性有限元模型，其包含晶粒尺寸、晶向和晶界倾角等微结构参数。研究结果表明，轧制镁合金具有强烈的宏观塑性各向异性行为，并对这种镁合金塑性各向异性行为的模拟结果以及多晶织构的模拟演化结果与试验测量进行对比，结果都基本吻合。对孪生非均匀变形模拟分析表明，镁合金宏观塑性各向异性行为与滑移、孪生变形机制的不同启动组合紧密相关，同时多晶体内应力的非均匀分布受到孪生变形的严重影响。而不同晶粒尺寸的晶粒所发生的孪生变形有比较大的差异，造成孪晶变体在晶粒内的分布极不均匀。本研究可为通过微结构的合理配置来设计和控制材料的力学性能提供理论依据.     

含冷却孔镍基合金次级取向效应的应变梯度晶体塑性有限元研究

单晶镍基合金具有优异的耐高温、高强、高韧等性能, 这些力学性能受制造过程引入的次级取向和冷却孔的影响. 已有研究大多关注单孔薄板的变形机理和力学性能, 而工程中应用的往往是多孔薄板, 当前亟需阐明多孔的塑性滑移带变形机理、次级取向效应以及冷却孔引起的应变梯度效应. 文章采用基于位错机制的非局部晶体塑性本构模型对含冷却孔镍基单晶薄板的单拉变形进行了数值模拟. 此模型基于塑性滑移梯度与几何必需位错的关系引入了位错流动项, 因此可有效刻画非均匀变形过程中的应变梯度效应. 为了全面揭示含孔镍基薄板的次级取向效应, 系统研究了[100]和[110]取向(两种次级取向)下镍基薄板的单拉变形行为, 并重点探究了在两种次级取向下冷却孔数量对薄板塑性行为的影响. 此外, 还分析了镍基合金板变形过程中各个滑移系上分切应力变化、主导滑移系开动以及几何必需位错密度的演化过程, 并讨论了塑性滑移量及其分布特征对不同次级取向镍基合金板强度的影响. 研究表明, 单孔和多孔的[110]薄板抗拉强度均低于[100]薄板, 多孔薄板的塑性变形过程比单孔薄板更为复杂且受次级取向影响更大, 并且发生滑移梯度位置主要位于冷却孔附近以及塑性滑移带区域. 研究结果可为工程中镍基合金的设计和服役提供理论指导.      

On the evolution of lattice deformation in austenitic stainless steels—The role of work hardening at finite strains

In this work, a three dimensional crystal plasticity-based finite element model is presented to examine the micromechanical behaviour of austenitic stainless steels. The model accounts for realistic polycrystal micromorphology, the kinematics of crystallographic slip, lattice rotation, slip interaction (latent hardening) and geometric distortion at finite deformation. We utilise the model to predict the microscopic lattice strain evolution of austenitic stainless steels during uniaxial tension at ambient temperature with validation through in situ neutron diffraction measurements. Overall, the predicted lattice strains are in very good agreement with those measured in both longitudinal and transverse directions (parallel and perpendicular to the tensile loading axis, respectively). The information provided by the model suggests that the observed nonlinear response in the transverse {200} grain family is associated with a competitive bimodal evolution of strain during inelastic deformation. The results associated with latent hardening effects at the microscale also indicate that in situ neutron diffraction measurements in conjunction with macroscopic uniaxial tensile data may be used to calibrate crystal plasticity models for the prediction of the inelastic material deformation response.     

Modeling lattice strain evolution at finite strains and experimental verification for copper and stainless steel using in situ neutron diffraction

An elasto-plastic self-consistent (EPSC) polycrystal model is extended to account, in an approximate fashion, for the kinematics of large strains, rigid body rotations, texture evolution and grain shape evolution. In situ neutron diffraction measurements of the flow stress, internal strain, texture and diffraction peak intensity evolutions were performed on polycrystalline copper and stainless steel, up to true tensile strains of ε = 0.3. Suitably adjusted slip system hardening model parameters enable the model to quantitatively describe the flow stress of the polycrystalline aggregate. Quantitative predictions of the texture evolution and the internal strain evolution along the stress axis are good, while predictions of transverse internal strains (perpendicular to the tensile loading direction) are less satisfactory. The latter exhibit a large dispersion from grain to grain around a macroscopic average, and the implications of this finding for the interpretation of in situ neutron diffraction method are explored. Finally, as a demonstration of the applicability of the model to problems involving finite rotation, as well as deformation, simulations of simple shear were conducted which predict a texture evolution in agreement with published experimental data, and other modeling approaches as well.     

Micro-crack tip fracture of commercial grade aluminum under mixed mode loading

In situ tensile tests were made in a scanning electron microscope (SEM) to investigate the deformation and micro-fracture in the immediate vicinity of a micro-crack tip in commercial pure aluminum with large-size crystal. Examined are the slip line field, stress intensity factor, strain energy density factor and crack tip opening displacement (CTOD) for mixed mode loading. Blunting and sharpening effects are observed. The latter is controlled by localized slip while the former by uniformed slip of the operating slip system with the highest crack tip Schmid factor. The operating slip system depends on the crystallographic orientation of crystal containing micro-cracks.The damage and fracture take place in the blunted region and depend on the coarsening and spacing of uniformed slip lines. The mixed mode micro-crack propagates along the direction where the voids grow and coalesce into the micro-crack. The direction also depends on the orientation of the applied loading. This suggests that the formation of macro-fracture mechanics could be applied. In particular, the minimum strain energy density criterion is suitable for determining the direction of micro-crack instability in the mixed mode. The in situ data were used to yield a nearly constant critical, minimum strain energy density factor for onset of micro-cracking.     

CrMnFeCoNi纳米晶温度相关的拉伸行为研究

摘要：高熵合金是一种由多种主元元素组成的新型合金。实验研究表明等原子比CrMnFeCoNi高熵合金在低温下具有比室温更高的拉伸强度和断裂韧性。本文针对这一现象，利用分子动力学模拟对平均晶粒尺寸为6 nm的CrMnFeCoNi纳米晶在300、200和77 K下分别进行拉伸模拟。模拟研究揭示了纳米尺度CrMnFeCoNi高熵合金力学行为的温度效应和强韧机理。微结构演化分析表明：低温下，塑性变形阶段，滑移系开动的较少，位错滑移所受的阻力越大，屈服强度和抗拉强度越大；模型破坏时，孔洞缺陷形核较慢，更多孔洞缺陷演化成断口，更多的断口分摊拉伸应变，使得高熵合金纳米晶的低温韧性更好。     

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.     

非稳态载荷下轮轨滚动接触及其钢轨波磨研究

利用有限元法,考虑材料反复滚压条件下棘轮效应和局部滑动的影响,研究了非稳态机车和车辆车轮载荷作用下轮轨滚动接触的弹塑性应力、应变和变形,进而分析了塑性流动型钢轨波浪形磨损的形成和发展过程以及波谷和波峰处材料的力学行为.结果表明:在非稳态载荷作用下,钢轨接触表面产生不均匀塑性变形引起的波磨,波磨发展速率呈衰减趋势,最终趋于稳定状态;在相同载荷下,与车辆车轮相比,机车车轮对钢轨波磨影响较大;波谷处的残余应力、应变和变形大于波峰处.