A thermodynamically consistent model of static and dynamic recrystallization

We propose a thermodynamically consistent model of static and dynamic recrystallization for metals during and after severe plastic deformations that is capable of predicting the evolution of dislocation density as well as mean grain size.     

A perturbation analysis of the unstable plastic flow pattern evolution in an aluminum alloy

In the tensile loading of sheet metals made from some polycrystalline aluminum alloys, a single deformation band appears inclined to the elongation axis in the early stage of deformation, and symmetric double bands are observed in the later stage. This evolution of spatial characteristics of such an unstable plastic flow pattern in a polycrystalline aluminum alloy has been analyzed by a perturbation method. A small number of slip modes are taken to describe the tensile strain. A rate-dependent constitutive equation is used for each slip mode to account for the interaction between dislocations and solute atoms in dynamic strain aging. Unconstrained and constrained models are used to impose appropriate loading conditions at the early and later deformation stages, respectively. Both plane-strain and plane-stress cases are considered. It is found out that the change of boundary conditions and material inhomogeneity during the course of plastic deformation are closely related to the evolution of spatial characteristics of shear band (the Portevin–Le Chatelier band) patterns observed in experiments.     

What is behind the plastic strain rate?

The plastic strain rate plays a central role in macroscopic models on elasto-viscoplasticity. In order to discuss the concept behind this quantity, we propose, first, a kinetic toy model to describe the dynamics of sliding layers representative of plastic deformation of single crystalline metals. The dynamic variable is given by the distribution function of relative strains between adjacent layers, and the plastic strain rate emerges as the average hopping rate between energy wells. We demonstrate the behavior of this model under different deformations and how it captures the elastic-to-plastic transition. Second, the kinetic toy model is reduced to a closed evolution equation for the average of the relative strain, allowing us to make a direct link to macroscopic theories. It is shown that the constitutive relation for the plastic strain rate does not only depend on the stress, but also on the macroscopic applied deformation rate, contrary to common practice.     

基于扰动状态概念的软岩蠕变本构模型与试验验证

软岩材料的蠕变过程从初始加载阶段开始即容易产生塑性变形,这与硬岩存在较大差异,而传统的元件模型仅在应力超过某一阈值后才开始描述其粘塑性行为。通过分析岩石加卸载时效变形过程中弹塑性状态的演变规律,以扰动状态理论为基础,确定了以塑性变形为变量的扰动因子函数,并通过塑性变形随时间的变化特征进一步建立了以时间为自变量的蠕变扰动因子演化方程。在此基础上,针对泥质页岩的蠕变变形过程,选取Burgers和Bingham模型分别描述扰动状态理论中的相对完整状态和完全调整状态,并选取蠕变扰动因子为权重函数建立了基于扰动状态理论的蠕变本构模型。通过泥质页岩的室内蠕变特性试验对模型进行有效性检验表明,理论曲线与实测曲线的逼近程度较高,蠕变扰动函数能随时间的发展持续调整相对完整状态向完全调整状态转换的过程,较高应力状态下软岩进入完全调整状态的速率较快,相对传统模型该模型具有更好的非线性及阶段协调性,可较好地描述软岩的初始、稳定和加速蠕变阶段。     

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.     

A continuum model for initiation and evolution of deformation twinning

Within continuum dislocation theory the plastic deformation of a single crystal with one active slip system under plane-strain constrained shear is investigated. By introducing a twinning shear into the energy of the crystal, we show that in a certain range of straining the formation of deformation twins becomes energetically preferable. An energetic threshold for the onset of twinning is determined. A rough analysis qualitatively describes not only the evolving volume fractions of twins but also their number during straining. Finally, we analyze the evolution of deformation twins and of the dislocation network at non-zero dissipation. We present the corresponding stress-strain hysteresis, the evolution of the plastic distortion, the twin volume fractions and the dislocation densities.     

Self-consistent modeling of large plastic deformation, texture and morphology evolution in semi-crystalline polymers

A self-consistent model for semi-crystalline polymers is proposed to study their constitutive behavior, texture and morphology evolution during large plastic deformation. The material is considered as an aggregate of composite inclusions, each representing a stack of crystalline lamellae with their adjacent amorphous layers. The deformation within the inclusions is volume-averaged over the phases. The interlamellar shear is modeled as an additional slip system with a slip direction depending on the inclusion's stress. Hardening of the amorphous phase due to molecular orientation and, eventually, coarse slip, is introduced via Arruda-Boyce hardening law for the corresponding plastic resistance. The morphology evolution is accounted for through the change of shape of the inclusions under the applied deformation gradient. The overall behavior is obtained via a viscoplastic tangent self-consistent scheme. The model is applied to high density polyethylene (HDPE). The stress-strain response, texture and morphology changes are simulated under different modes of straining and compared to experimental data as well as to the predictions of other models.     

Investigation of mechanically attrited structures induced by repeated impacts on an AISI1045 steel

Under repeated impact loadings – shot peening process, surface mechanical attrition treatment, erosive wear – metallic surfaces undergo severe plastic deformation which leads sometimes to a local change of their microstructure. These mechanically attrited structures (MAS) exhibit very interesting physical properties: high hardness, better tribological properties, etc. Consequently it is of primary importance to understand the mechanism explaining how these MAS are created and grow under such loadings. In this article, this mechanism is investigated with the help of a coupled experimental and finite element approach. First, the MAS are generated on an AISI1045 steel with a micro-impact tester which allows to know the impact energy and the location of impacts with a very good accuracy. The evolution of the MAS shape as a function of the impact number is presented. Then, the finite element investigation is presented. It is shown that a macroscopic stabilized elastic regime is reached after one hundred impacts. It also appears that a close cycle of plastic strain is observed locally in the zone where material transformation should happen during this regime. The severe plastic deformation achieved after a given number of cycles may thus explain the material transformation. Based on these results, we propose a mechanism based on a plastic strain threshold to explain the growth of the MAS. The resulting MAS size and shape appear to be in very good agreement with the experimental results. Finally, we conclude on the influence of the mechanical parameters that are involved in the proposed mechanism.     

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.     

Numerical analysis and elastic–plastic deformation behavior of anisotropically damaged solids

The present paper is concerned with the numerical modelling of the large elastic–plastic deformation behavior and localization prediction of ductile metals which are sensitive to hydrostatic stress and anisotropically damaged. The model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics. The formulation relies on a multiplicative decomposition of the metric transformation tensor into elastic and damaged-plastic parts. Furthermore, undamaged configurations are introduced which are related to the damaged configurations via associated metric transformations which allow for the interpretation as damage tensors. Strain rates are shown to be additively decomposed into elastic, plastic and damage strain rate tensors. Moreover, based on the standard dissipative material approach the constitutive framework is completed by different stress tensors, a yield criterion and a separate damage condition as well as corresponding potential functions. The evolution laws for plastic and damage strain rates are discussed in some detail. Estimates of the stress and strain histories are obtained via an explicit integration procedure which employs an inelastic (damage-plastic) predictor followed by an elastic corrector step. Numerical simulations of the elastic–plastic deformation behavior of damaged solids demonstrate the efficiency of the formulation. A variety of large strain elastic–plastic-damage problems including severe localization is presented, and the influence of different model parameters on the deformation and localization prediction of ductile metals is discussed.     

Non-equilibrium grain boundary structure and inelastic deformation using atomistic simulations

Grain boundary influence on material properties becomes increasingly significant as grain size is reduced to the nanoscale. Nanostructured materials produced by severe plastic deformation techniques often contain a higher percentage of high-angle grain boundaries in a non-equilibrium or energetically metastable state. Differences in the mechanical behavior and observed deformation mechanisms are common due to deviations in grain boundary structure. Fundamental interfacial attributes such as atomic mobility and energy are affected due to a higher non-equilibrium state, which in turn affects deformation response. In this research, atomistic simulations employing a biased Monte Carlo method are used to approximate representative non-equilibrium bicrystalline grain boundaries based on an embedded atom method potential, leveraging the concept of excess free volume. An advantage of this approach is that non-equilibrium boundaries can be instantiated without the need of simulating numerous defect/grain boundary interactions. Differences in grain boundary structure and deformation response are investigated as a function of non-equilibrium state using Molecular Dynamics. A detailed comparison between copper and aluminum bicrystals is provided with regard to boundary strength, observed deformation mechanisms, and stress-assisted free volume evolution during both tensile and shear simulations.     

膨胀环受力历史对应力应变关系的影响

利用两类实验装置开展了无氧铜TU1膨胀环实验研究,发现:电磁膨胀环在加载阶段,样品受体力作用,满足均匀变形的假定;而爆炸膨胀环在加载阶段,样品内壁受面力冲击作用,不满足均匀变形的假定。针对这个差异,发展了一种考虑冲击阶段变形不均匀性的新方法,利用回收样品几何变形,将冲击阶段试样环内轴向塑性应变、径向塑性应变纳入等效塑性应变的计算中,通过修正后的方法更准确地获得了材料的应力应变关系。     

Plastic behavior of a nickel-based alloy under monotonic-tension and low-cycle-fatigue loading

The plastic behavior of an annealed HASTELLOY^® C-22HS™ alloy, a face-centered cubic (FCC), nickel-based superalloy, was examined by in-situ neutron-diffraction measurements at room temperature. Both monotonic-tension and low-cycle-fatigue experiments were conducted. Monotonic-tension straining and cyclic-loading deformation were studied as a function of stress. The plastic behavior during deformation is discussed in light of the relationship between the stress and dislocation-density evolution. The calculated dislocation-density evolution within the alloy reflects the strain hardening and cyclic hardening/softening. Experimentally determined lattice strains are compared to verify the hardening mechanism at selected stress levels for tension and cyclic loadings. Combined with calculations of the dislocation densities, the neutron-diffraction experiments provide direct information about the strain and cyclic hardening of the alloy.     

Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling

The paper presents a numerical analysis of the inelastic deformation process in porous rocks during different stages of its development and under non-equiaxial loading. Although numerous experimental studies have already investigated many aspects of plasticity in porous rocks, numerical modeling gives valuable insight into the dynamics of the process, since experimental methods cannot extract detailed information about the specimen structure during the test and have strong limitations on the number of tests. The numerical simulations have reproduced all different modes of deformation observed in experimental studies: dilatant and compactive shear, compaction without shear, uniform deformation, and deformation with localization. However, the main emphasis is on analysis of the compaction mode of plastic deformation and compaction localization, which is characteristic for many porous rocks and can be observed in other porous materials as well. The study is largely inspired by applications in petroleum industry, i.e. surface subsidence and reservoir compaction caused by extraction of hydrocarbons and decrease of reservoir pressure. Special attention is given to the conditions, evolution, and characteristic patterns of compaction localization, which is often manifested in the form of compaction bands. Results of the study include stress-strain curves, spatial configurations and characteristics of localized zones, analysis of bifurcation of stress paths inside and outside localized zones and analysis of the influence of porous rocks properties on compaction behavior. Among other results are examples of the interplay between compaction and shear modes of deformation.To model the evolution of plastic deformation in porous rocks, a new constitutive model is formulated and implemented, with the emphasis on selection of adequate functions defining evolution of yield surface with deformation. The set of control parameters of the model is kept as short as possible; the parameters are carefully selected to have simple and intuitive physical interpretation whenever possible. Results demonstrate that evolution of the yield surface with deformation has major influence on the resulting characteristics of deformation patterns, which is not sufficiently acknowledged in the literature.     

金属材料的率-温耦合响应与动态本构关系综述

金属材料在冲击、爆炸等高应变率加载下的塑性流动行为具有不同于静载下的率-温耦合性和微观机制。航空航天、航海、能源开采、核工业、公共安全、灾害防治等方面的金属结构设计与性能评估需要进行大量的动载实验和数值模拟,建立准确的材料动态本构模型是结构数值模拟可靠性的基础和关键。本文中,总结了金属材料的率-温耦合变形行为及内在机理,回顾了金属动态本构关系研究的起源与发展脉络,分别针对唯象模型、具有物理基础的模型和人工神经网络模型进行了详细介绍和横向比较。唯象模型和人工神经网络模型分别因易应用和高预测精度而受到青睐,基于物理概念的宏观连续介质模型可以描述体现内部演化的真实物理量,从而涵盖更大的应变范围,更好地反映应变率、温度和应变的影响机制。     

On kinematic,thermodynamic, and kinetic coupling of a damage theory for polycrystalline material

The paper proposes a new consistent formulation of polycrystalline finite-strain elasto-plasticity coupling kinematics and thermodynamics with damage using an extended multiplicative decomposition of the deformation gradient that accounts for temperature effects. The macroscopic deformation gradient comprises four terms: thermal deformation associated with the thermal expansion, the deviatoric plastic deformation attributed to the history of dislocation glide/movement, the volumetric deformation gradient associated with dissipative volume change of the material, and the elastic or recoverable deformation associated with the lattice rotation/stretch. Such a macroscopic decomposition of the deformation gradient is physically motivated by the mechanisms underlying lattice deformation, plastic flow, and evolution of damage in polycrystalline materials. It is shown that prescribing plasticity and damage evolution equations in their physical intermediate configurations leads to physically justified evolution equations in the current configuration. In the past, these equations have been modified in order to represent experimentally observed behavior with regard to damage evolution, whereas in this paper, these modifications appear naturally through mappings by the multiplicative decomposition of the deformation gradient. The prescribed kinematics captures precisely the damage deformation (of any rank) and does not require introducing a fictitious undamaged configuration or mechanically equivalent of the real damaged configuration as used in the past.     

Dynamic plastic deformation of hexagonal frames

The dynamic plastic response of a hexagonal frame to an internal pressure pulse of arbitrary shape is analyzed, including large-deformation geometric effects that result in redistribution of the bending and membrane reactions. Peak pressures of several multiples of the static yield load are considered, and the frame material is assumed to be rigid perfectly plastic. The effect of pulse shape on final plastic deformation is determined by numerically solving the governing sets of differential equations for a variety of parameter combinations. In the small deformation range, the permanent plastic deformation is shown to be dependent on an effective pressure, defined in terms of the first moment of the pressure pulse; the response duration is proportional to the pulse duration. In the large deformation range, the permanent plastic deformation is a function of the average pressure applied during the response, and the response duration depends on a characteristic time constant which is a function of material properties and hexagon size.     

Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in Zircaloy-2

A crystal plasticity finite element code is developed to model lattice strains and texture evolution of HCP crystals. The code is implemented to model elastic and plastic deformation considering slip and twinning based plastic deformation. The model accounts for twinning reorientation and growth. Twinning, as well as slip, is considered to follow a rate dependent formulation. The results of the simulations are compared to previously published in situ neutron diffraction data. Experimental results of the evolution of the texture and lattice strains under uniaxial tension/compression loading along the rolling, transverse, and normal direction of a piece of rolled Zircaloy-2 are compared with model predictions. The rate dependent formulation introduced is capable of correctly capturing the influence of slip and twinning deformation on lattice strains as well as texture evolution.