孪生诱发塑性对V-5Cr-5Ti合金应变硬化行为的影响

钒合金(V-Cr-Ti)作为潜在重要的聚变反应堆用结构材料, 近年来受到广泛的关注. 为了研究 V-5Cr-5Ti 合金不同应变率压缩下的应变硬化行为, 特别是孪生对塑性变形的影响, 以位错密度和孪晶演化为基础, 建立了该合金的应变硬化模型. 模型中考虑了孪晶中的位错滑移对材料塑性应变的贡献. 模拟结果表明, 由于孪生诱发塑性, 从而使动态压缩时的位错密度小于准静态加载时的, 这使得 V-5Cr-5Ti 合金在动态压缩时的应变硬化率比准静态加载时的小. 当孪晶形成后, 位错滑移引起的塑性应变率随应变增大而增大, 并逐渐接近加载应变率, 而孪生引起的塑性应变率则随应变增大而减小.      

微纳米晶金属的应变率敏感性及应变硬化行为分析

基于亚微米、纳米晶粒组织塑性变形过程中多种变形机制(位错机制、扩散机制及晶界滑动机制)共存,建立了理论模型,用于定量研究亚微米、纳米晶粒组织的塑性变形行为.以铜为模型材料,计算分析了晶粒尺度、应变率以及温度对亚微米、纳米晶粒组织塑性变形行为的影响.结果表明:相比粗晶铜,亚微米晶铜表现出明显的应变率敏感性,并且应变率敏感系数随晶粒尺度及变形速率的减小而增大;同时,增大变形速率或降低变形温度都能提高材料的应变硬化能力,延缓颈缩发生,进而提高材料的延性.计算分析结果与实验报道吻合.     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为,本文建立了基于微结构演化的塑性本构模型。首先,采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验,并对其在不同应变程度下的微结构演化特征进行了分析。研究发现,影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程,并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响,进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后,根据隐式应力更新算法对新模型进行了有限元实现,并与实验结果进行比较,验证了新模型的合理性和预测精度。     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为,本文建立了基于微结构演化的塑性本构模型。首先,采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验,并对其在不同应变程度下的微结构演化特征进行了分析。研究发现,影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程,并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响,进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后,根据隐式应力更新算法对新模型进行了有限元实现,并与实验结果进行比较,验证了新模型的合理性和预测精度。     

Modeling the effects of material non-linearity using moving window micromechanics

In the analysis of materials with random heterogeneous microstructure the assumption is often made that material behavior can be represented by homogenized or effective properties. While this assumption yields accurate results for the bulk behavior of composite materials, it ignores the effects of the random microstructure. The spatial variations in these microstructures can focus, initiate and propagate localized non-linear behavior, subsequent damage and failure. In previous work a computational method, moving window micromechanics (MW), was used to capture microstructural detail and characterize the variability of the local and global elastic response. Digital images of material microstructure described the microstructure and a local micromechanical analysis was used to generate spatially varying material property fields. The strengths of this approach are that the material property fields can be consistently developed from digital images of real microstructures, they are easy to import into finite element models (FE) using regular grids, and their statistical characterizations can provide the basis for simulations further characterizing stochastic response. In this work, the moving window micromechanics technique was used to generate material property fields characterizing the non-linear behavior of random materials under plastic yielding; specifically yield stress and hardening slope, post yield. The complete set of material property fields were input into FE models of uniaxial loading. Global stress strain curves from the FE–MW model were compared to a more traditional micromechanics model, the generalized method of cells. Local plastic strain and local stress fields were produced which correlate well to the microstructure. The FE–MW method qualitatively captures the inelastic behavior, based on a non-linear flow rule, of the sample continuous fiber composites in transverse uniaxial loading.     

A mesoscale investigation of strain rate effect on dynamic deformation of single-crystal copper

A combined finite element (FE) simulation and discrete dislocation dynamics (DD) approach has been developed in this paper to investigate the dynamic deformation of single-crystal copper at mesoscale. The DD code yields the plastic strain based on the slip of dislocations and serves as a substitute for the 3D constitutive form used in the usual FE computation, which is implemented into ABAQUS/Standard with a user-defined material subroutine. On the other hand, the FE code computes the displacement and stress field during the dynamic deformation. The loading rate effects on the yield stress and the deformation patterning of single-crystal copper are investigated. With the increasing of strain rate, the yield stress of single-crystal copper increases rapidly. A critical strain rate exists in each single-crystal copper block for the given size and dislocation sources, below which the yield stress is relatively insensitive to the strain rate. The dislocation patterning changes from non-uniform to uniform under high-strain-rate. The shear stresses in the bands are higher than that in the neighboring regions, which are formed shear bands in the crystal. The band width increases with the strain rate, which often take places where the damage occurs.     

Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I

A Phenomenological Mesoscopic Field Dislocation Mechanics (PMFDM) model is developed, extending continuum plasticity theory for studying initial-boundary value problems of small-scale plasticity. PMFDM results from an elementary space-time averaging of the equations of Field Dislocation Mechanics (FDM), followed by a closure assumption from any strain-gradient plasticity model that attempts to account for effects of geometrically necessary dislocations (GNDs) only in work hardening. The specific lower-order gradient plasticity model chosen to substantiate this work requires one additional material parameter compared to its conventional continuum plasticity counterpart. The further addition of dislocation mechanics requires no additional material parameters. The model (a) retains the constitutive dependence of the free-energy only on elastic strain as in conventional continuum plasticity with no explicit dependence on dislocation density, (b) does not require higher-order stresses, and (c) does not require a constitutive specification of a ‘back-stress’ in the expression for average dislocation velocity/plastic strain rate. However, long-range stress effects of average dislocation distributions are predicted by the model in a mechanistically rigorous sense. Plausible boundary conditions (with obvious implication for corresponding interface conditions) are discussed in some detail from a physical point of view. Energetic and dissipative aspects of the model are also discussed. The developed framework is a continuous-time model of averaged dislocation plasticity, without having to rely on the notion of incremental work functions, their convexity properties, or their minimization. The tangent modulus relating stress rate and total strain rate in the model is the positive-definite tensor of linear elasticity, and this is not an impediment to the development of idealized microstructure in the theory and computations, even when such a convexity property is preserved in a computational scheme. A model of finite deformation, mesoscopic single crystal plasticity is also presented, motivated by the above considerations.Lower-order gradient plasticity appears as a constitutive limit of PMFDM, and the development suggests a plausible boundary condition on the plastic strain rate for this limit that is appropriate for the modeling of constrained plastic flow in three-dimensional situations.     

Modelling of the internal stress in dislocation cell structures

The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behavior of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations.     

Plastic Flow Localization in Commercial Zirconium Alloys

The behavior of plastic flow curves and patterns of plastic strain localization were studied for tension of samples of Zr — 1% Nb (É110 alloy) and Zr — 1% Nb — 1.3% Sn — 0.4% Fe (É635 alloy) were studied. The relationship of the localization kinetics with the strain hardening law in plastic flow and transition to fracture is established. The dislocation microstructure of the alloys in strain localization and prefracture zones is examined.     

A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales

Plastic flow in crystal at submicron-to-nanometer scales involves many new interesting problems. In this paper, a unified computational model which directly combines 3D discrete dislocation dynamics (DDD) and continuum mechanics is developed to investigate the plastic behaviors at these scales. In this model, the discrete dislocation plasticity in a finite crystal is solved under a completed continuum mechanics framework: (1) an initial internal stress field is introduced to represent the preexisting stationary dislocations in the crystal; (2) the external boundary condition is handled by finite element method spontaneously; and (3) the constitutive relationship is based on the finite deformation theory of crystal plasticity, but the discrete plastic strains induced by the slip of the newly nucleated or propagating dislocations are calculated by dislocation dynamics methodology instead of phenomenological evolution equations used in conventional crystal plasticity. These discrete plastic strains are then localized to the continuum material points by a Burgers vector density function proposed by us. Various processes, such as loop dislocation evolution, dislocation junction formation etc., are simulated to verify the reliability of this computational model. Specifically, a uniaxial compression test for micro-pillars of Cu is simulated by this model to investigate the ‘dislocation starvation hardening’ observed in the recent experiment.     

Mechanical effects of the self-organization of dislocations and related critical characteristics

The effects of the dislocation pattern formed due to the self-organization of the dislocations in crystals on the macroscopic hardening and dynamic internal friction (DIF) during deformation are studied. The classic dislocation models for the hardening and DIF corresponding to the homogeneous dislocation configuration are extended to the case for the non-homogeneous one. In addition, using the result of dislocation patterning deduced from the non-linear dislocation dynamics model for single slip, the correlation between the dislocation pattern and hardening as well as DIF is obtained. It is shown that in the case of the tension with a constant strain rate, the bifurcation point of dislocation patterning corresponds to the turning point in the stress versus strain and DIF versus strain curves. This result along with the critical characteristics of the macroscopic behavior near the bifurcation point is microscopically and macroscopically in agreement with the experimental findings on mono-crystalline pure aluminum at temperatures around 0.5T _m . The present study suggests that measuring the DIF would be a sensitive and useful mechanical means in order to study the critical phenomenon of materials during deformation. The project supported by the National Natural Science Foundation of China under the Grand 19702019 & 19891180-4 and by the Chinese Academy of Sciences under the Grand KJ951-1-201.     

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.     

Determination of material intrinsic length and strain gradient hardening in microbending process

Microbending experiments of pure aluminum show that the springback angles increase with the decrease of foil thickness, which indicates obvious size effects and attributes to plastic strain gradient hardening. Then a constitutive model, taking into accounts both plastic strain and plastic strain gradient hardening, is proposed to analyze the microbending process of thin foil. The model is based on the relationship between shear yield stress and dislocation density, in which the material intrinsic length is related to material properties and average grain numbers along the characteristic scale direction of part. It is adopted in analytical model to calculate the non-dimensional bending moment and predict the springback angle after microbending. It is confirmed that the predictions by the proposed hardening model agree well with the experimental data, while those predicted by the classical plasticity model cannot capture such size effects. The contribution of plastic strain gradient increases with the decrease of foil thickness and is independent on the bending angle.     

Finite element modeling of porous titanium

The porous microstructures of metallic foams cause microscopic stress and strain localization under deformation which reduces the damage tolerance and therefore limits application of the materials. In this paper, the deformation of a relatively low porosity porous titanium is examined using two-dimensional (2D) plane strain and three-dimensional (3D) finite element models to identify the accuracy and limitations of such simulations. To generate the finite element models, a simulated microstructure was created based on micrographs of an experimental material. Compared to the 2D models, the 3D models require smaller model size to obtain convergent results. The macroscopic responses predicted by the 3D models are in reasonable agreement with experimental results while the 2D models underestimated the response. In addition, 3D models predicted more uniform microscopic field variable distributions. 2D models predicted higher probability of Von Mises stress and equivalent plastic strain exceeding a certain value and therefore overestimate the failure probability of the material.     

Dislocation-mediated strain hardening in tungsten: Thermo-mechanical plasticity theory and experimental validation

A self-consistent thermo-mechanical model to study the strain-hardening behavior of polycrystalline tungsten was developed and validated by a dedicated experimental route. Dislocation–dislocation multiplication and storage, as well dislocation-grain boundary (GB) pinning were the major mechanisms underlying the evolution of plastic deformation, thus providing a link between the strain hardening behavior and material's microstructure. The microstructure of the polycrystalline tungsten samples has been thoroughly investigated by scanning and electron microscopy. The model was applied to compute stress–strain loading curves of commercial tungsten grades, in the as-received and as-annealed states, in the temperature range of 500–1000 °C. Fitting the model to the independent experimental results obtained using a single crystal and as-received polycrystalline tungsten, the model demonstrated its capability to predict the deformation behavior of as-annealed samples in a wide temperature range and applied strain. The relevance of the dislocation-mediated plasticity mechanisms used in the model have been validated using transmission electron microscopy examination of the samples deformed up to different amounts of strain. On the basis of the experimental validation, the limitations of the model are determined and discussed.     

应变硬化薄板夹持型滚弯成形过程分析

现存文献对薄板的连续滚弯成形过程的数学模拟多限于讨论三辊轮解锥型弯板过程,且基于较多的假定和板的小变形情况。而开发有更多的功能和更高的生产效率的四辊轮连续弯板机需研究夹持型滚弯成形过程。本文将「１」的工作,理想塑性材料平面应变薄板的夹持型连续滚弯成形过程的弹塑性大变形弯曲的力学分析,推广至一般应变硬化材料的情形。得出了控制微分方程的解析解。采用固支边界条件模拟刚度很大的平持系统对板的夹持。通过对线     

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.     

1Cr18Ni9Ti不锈钢的非比例循环强化性能

对1Cr18Ni9Ti不锈钢进行了各种比例和非比例循环本构实验,其中包括圆路径、正方形、正菱形、蝶形、三角形和两种十字形应变路径。表明其具有明显的非比例循环附加强化。在相同的等效应变幅值上,材料的附加强化与路径密切相关。对于圆路径,其附加强化度最大可达60％。通过对不同应变历史的实验研究表明,先前小的非比例度的加载历史对后继大的非比例度路径的强化没有影响;而先前大非比例度的加载路径对后继小非比例度路径的循环强化有较大影响。     

A conventional theory of mechanism-based strain gradient plasticity

There exist two frameworks of strain gradient plasticity theories to model size effects observed at the micron and sub-micron scales in experiments. The first framework involves the higher-order stress and therefore requires extra boundary conditions, such as the theory of mechanism-based strain gradient (MSG) plasticity [J Mech Phys Solids 47 (1999) 1239; J Mech Phys Solids 48 (2000) 99; J Mater Res 15 (2000) 1786] established from the Taylor dislocation model. The other framework does not involve the higher-order stress, and the strain gradient effect come into play via the incremental plastic moduli. A conventional theory of mechanism-based strain gradient plasticity is established in this paper. It is also based on the Taylor dislocation model, but it does not involve the higher-order stress and therefore falls into the second strain gradient plasticity framework that preserves the structure of conventional plasticity theories. The plastic strain gradient appears only in the constitutive model, and the equilibrium equations and boundary conditions are the same as the conventional continuum theories. It is shown that the difference between this theory and the higher-order MSG plasticity theory based on the same dislocation model is only significant within a thin boundary layer of the solid.     

Mechanism-based strain gradient plasticity in C0 axisymmetric element

Non-uniform plastic deformation of materials exhibits a strong size dependence when the material and deformation length scales are of the same order at micro- and nano-metre levels. Recent progresses in testing equipment and computational facilities enhancing further the study on material characterization at these levels confirmed the size effect phenomenon. It has been shown that at this length scale, the material constitutive condition involves not only the state of strain but also the strain gradient plasticity. In this study, C⁰ axisymmetric element incorporating the mechanism-based strain gradient plasticity is developed. Classical continuum plasticity approach taking into consideration Taylor dislocation model is adopted. As the length scale and strain gradient affect only the constitutive relation, it is unnecessary to introduce either additional model variables or higher order stress components. This results in the ease and convenience in the implementation. Additional computational efforts and resources required of the proposed approach as compared with conventional finite element analyses are minimal. Numerical results on indentation tests at micron and submicron levels confirm the necessity of including the mechanism-based strain gradient plasticity with appropriate inherent material length scale. It is also interesting to note that the material is hardened under Berkovich compared to conical indenters when plastic strain gradient is considered but softened otherwise.