The yield behaviour of an array of metal-coated fibres

The biaxial compaction of a square array of metal-coated fibres (MCFs) is examined using the finite element method. The array is first compacted to a certain density using biaxial loading paths consistent with those for hydrostatic and closed-die compaction. The yield surfaces are then constructed at various stages of the densification. The size and shape of the yield surface depend on the loading history, relative density and on the fibre volume fraction. The yield surface after hydrostatic compaction has a corner at the initial loading point. However, the location of the corner on the yield surface after closed-die compaction depends on the relative density and the fibre volume fraction. The numerical results of the hydrostatic yield surface over a range of loading path are in good agreement with Fleck (1995) micro-mechanical model originally developed for the compaction of a random array of homogeneous particles.     

Elasticity, fracture and yielding of cold compacted metal powders

The behaviour of powder compacts is modelled by explicitly introducing the possibility of plastic loading, elastic unloading and decohesion at contacts. The study is limited to cold compaction and to perfectly plastic materials for which the analysis of Mesarovic and Johnson (J. Mech. Phys. 48 (2000) 2009) is used. We model the compact behaviour both with an analytical approach based upon a mean field assumption and with the discrete element method (DEM) that allows force equilibrium to be treated in a realistic manner. Using these two approaches, we are able to predict the effective elastic properties of a powder compact at the onset of unloading. The knowledge of the conditions that lead to decohesion at the contact scale is used to model the fracture of the powder compact (green strength). It is shown that, in first approximation, green strength is inversely proportional to the size of the powder particles. The two methods are used to generate failure and yield surfaces for axisymmetric conditions. Both isostatic and close die conditions are studied.     

基于颗粒物质力学的铁粉末压制中摩擦特性对力链演化影响

结合颗粒物质力学理论,通过离散元法实现铁粉末压制过程模拟并通过压制方程进行验证,针对粉末体系中的力链演化问题,提出力链特征定量分析方式,进一步通过分析不同颗粒间摩擦系数、侧壁摩擦系数与颗粒运动状态转变的方式,探讨摩擦特性对力链量化特征的影响,从而建立摩擦行为与力链演化间的联系. 研究结果表明:随颗粒间摩擦系数增大,整体力链数目变少,力链方向系数、承载不均匀度及单位屈曲度均变大,而随侧壁摩擦系数增大,力链特征差异较小,则颗粒间摩擦系数较侧壁摩擦系数对力链特征演化具有更显著影响. 同时发现,颗粒接触状态的改变与力链特征演化间具有对应性. 研究成果将进一步拓展粉末压制中考虑摩擦行为及力链演化过程在内的粉体致密化行为理论.      

A finite strain constitutive model for metal powder compaction using a unique and convex single surface yield function

Constitutive modelling of metal powder compaction processes is a challenge in view of realistic simulations. To this end, the article under consideration has two objectives: the first goal is to present a new unique and convex single surface yield function for pressure dependent materials, which is also applicable to other areas of granular materials such as soils or concrete. The flexibility is shown at various materials. The yield function is based on a log-interpolation of two known simple yield functions. A convexity proof of the new yield function is provided. The second objective is to propose a new rate-independent finite strain plasticity model for metal powder compaction, which is based on the multiplicative decomposition of the deformation gradient into an elastic and a plastic part with evolution equations for internal variables representing the basic behaviour of powder materials under compaction conditions. These variables are used for the evolution of the yield function in order to represent the compressible hardening behaviour of powder materials. On the basis of the constitutive model, the material parameters are identified at experimental data of copper powder.     

Correlation mechanism of friction behavior and topological properties of the contact network during powder compaction

The effect of friction behavior on the compacted density is significant, but the relationship between the topological properties of the contact network and friction behavior during powder compaction remains unclear. Based on the discrete element method (DEM), a DEM model for die compaction was established, and the Hertz contact model was modified into an elastoplastic contact model that was more suitable for metal-powder compaction. The evolution of the topological properties of the contact network and its mechanism during powder compaction was explored using the elastoplastic contact model. The results demonstrate that the friction behavior between the particles is closely related to the topological properties of the contact network. Side wall friction results in smaller clustering coefficient (CC) and excess contact (EC) in the lower region near the side wall. Corresponding to this phenomenon, the upper region near the side wall has more high-stress particles when the major principal stress threshold was considered, and the CC and EC are significantly higher than those in the other regions. This study provides a theoretical basis for improving powder compaction behavior.     

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.     

Modeling of intra-crystalline hardening of materials with particles

A two-level homogenization approach is developed for the micromechanical modeling of the elastoplastic behavior of polycrystals containing intracrystalline non-shearable particles. First, a micro-meso transition is employed to establish a constitutive relation for a single crystal containing particles. The behavior of an equivalent single crystal with particles is derived from the classical formulation of plasticity of the single crystal based on the Schmid's law and crystallographic gliding. Then, the transition to the macroscopic scale is performed with a self-consistent scheme to determine the elastoplastic behavior of the macro homogeneous material. The obtained global behavior is characterized by a mixed anisotropic and kinematic hardening related to an evolution of inter- and intra-granular material microstructure. Results have been analyzed in light of second and third order internal stresses developed during the plastic flow. Especially, yield surfaces have been determined for various preloadings and particle volume fractions.     

A theoretical investigation of the influence of dislocation sheets on evolution of yield surfaces in single-phase B.C.C. polycrystals

Accurate and reliable predictions of yield surfaces and their evolution with deformation require a better physical representation of the important sources of anisotropy in the material. Until recently, the most physical approach employed in the current literature has been the use of polycrystalline deformation models, where it is assumed that crystallographic texture is the main contributor to the overall anisotropy. However, recent studies have revealed that the grain-scale mesostructural features (e.g. cell-block boundaries) may have a large impact on the anisotropic stress-strain behaviour, as evidenced during strain-path change tests (e.g. cross effect, Bauschinger effect).In previous papers, the authors formulated an extension of the Taylor-type crystal plasticity model by incorporating some details of the grain-scale mesostructural features. The main purpose of this paper is to study the evolution of yield surfaces in single-phase b.c.c. polycrystals during deformation and strain-path changes using this extended crystal plasticity model. It is demonstrated that the contribution of the grain-scale substructure in these metals on yield loci is comparable in magnitude to the effects caused by the differences in texture. Furthermore, it is shown that the shape of yield loci cannot be predicted accurately by the traditional polycrystalline deformation model with equal slip hardening. The trends predicted by the extended crystal plasticity model are in much better agreement with the experimental evidence reported in the literature than those represented in classical treatments by isotropic and kinematic hardening.     

Size-effects on yield surfaces for micro reinforced composites

Size effects in heterogeneous materials are studied using a rate independent higher order strain gradient plasticity theory, where strain gradient effects are incorporated in the free energy of the material. Numerical studies are carried out using a finite element method, where the components of the plastic strain tensor appear as free variables in addition to the displacement variables. Non-conventional boundary conditions are applied at material interfaces to model a constraint on plastic flow due to dislocation blocking. Unit cell calculations are carried out under generalized plane strain conditions. The homogenized response of a material with cylindrical reinforcing fibers is analyzed for different values of the internal material length scale and homogenized yield surfaces are presented. While the main focus is on initial yield surfaces, subsequent yield surfaces are also presented. The center of the yield surface is tracked under uniaxial loading both in the transverse and longitudinal directions and an anisotropic Bauschinger effect is shown to depend on the size of the fibers. Results are compared to conventional predictions, and size-effects on the kinematic hardening are accentuated.     

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。     

Microstructure evolution of compressible granular systems under large deformations

We report three-dimensional particle mechanics static calculations that predict the microstructure evolution during die-compaction of elastic spherical particles up to relative densities close to one. We employ a nonlocal contact formulation that remains predictive at high levels of confinement by removing the classical assumption that contacts between particles are formulated locally as independent pair-interactions. The approach demonstrates that the coordination number depends on the level of compressibility, i.e., on Poisson's ratio, of the particles. Results also reveal that distributions of contact forces between particles and between particles and walls, although similar at jamming onset, are very different at full compaction. Particle–wall forces are in remarkable agreement with experimental measurements reported in the literature, providing a unifying framework for bridging experimental boundary observations with bulk behavior.     

Volume-weighted mixture theory for granular materials

In the present work we treat granular materials as mixtures composed of a solid and a surrounding void continuum, proposing then a continuum thermodynamic theory for it. In contrast to the common mass-weighted balance equations of mass, momentum, energy and entropy for mixtures, the volume-weighted balance equations and the associated jump conditions of the corresponding physical quantities are derived in terms of volume-weighted field quantities here. The evolution equations of volume fractions, volume-weighted velocity, energy, and entropy are presented and explained in detail. By virtue of the second law of thermodynamics, three dissipative mechanisms are considered which are specialized for a simple set of linear constitutive equations. The derived theory is applied to the analysis of reversible and irreversible compaction of cohesionless granular particles when a vertical oscillation is exerted on the system. In this analysis, a hypothesis for the existence of a characteristic depth within the granular material in its closely compacted state is proposed to model the reversible compaction.     

Numerical determination of initial and subsequent yield surfaces of open-celled model foams

In the present work, the overall yield behaviour of a three-dimensional model foam is investigated by microstructural modeling and numerical homogenisation. The analyses are performed on an elasto-plastic lattice of tetrakaidecahedral cells which provides a surrogate model for metallic foams with open cells. For the determination of the macroscopic yield surfaces in strain space as well as in stress space, a strain-energy based homogenisation scheme is applied to a representative volume element. This scheme is derived directly from the Hill principle and thus assures the physical consistency with mechanically defined effective properties in a natural manner. By tracing the evolution of the overall yield surface, the different hardening mechanisms are addressed. It is found that for complex load histories the yield surfaces are not only shifted but may also change their shape and size considerably.     

离散元法铁粉末压制中粒径分布对力链演化机制的影响

为阐明粒径分布对铁粉压制中体系内部细观力学行为的影响, 基于离散元理论, 通过改变铁粉颗粒粒径分布建立压制模型, 结合力链提取方法, 通过对力链空间分布、力链数目、力链长度和力链方向性的分析, 探究粒径分布对力链演化的影响机理. 研究结果表明: 不同粒径分布的粉体压制时形成的力链空间分布具有差异, 粒径分布范围越小, 形成的力链分布越集中, 反之, 粒径分布范围越大, 形成的力链分布越松散且均匀; 在粉末压制时, 粒径分布对力链数目也有影响, 具体表现为随着粉体的粒径分布范围变大, 力链总数逐渐减少; 粉体的粒径分布对颗粒形成短力链的数目起着显著影响, 而对力链长度的影响较为有限; 随着粒径分布范围的增大, 力链的方向由均匀分布逐渐集中在特定角度方向, 表现出一定各向异性, 形成的交叉力链网络结构有利于提高粉体致密化程度. 本文为从粉体粒径分布影响层面拓展粉末压制细观力学理论提供基础, 亦为进一步结合粉体粒径分布及体系内力链演变过程改善粉末致密化行为提供指导.      

Third body modeling in fretting using the combined finite-discrete element method

A new approach was developed for modeling the effect of the third body on fretting. This was accomplished using the combined finite-discrete element method (FDEM) in which the third body is analyzed as discrete elements while the first bodies are modeled using finite elements. This approach provides a link between large scale models which treat the mass of wear debris as a single or small number of bodies and small scale models which only study a control volume. The FDEM was used to analyze the behavior of third body particles between flat sliding surfaces. When the third body mass is composed of unconnected particles, it behaves as a Newtonian fluid, but this behavior ceases when the particles are connected into platelets. The FDEM was also used to study the behavior of third body particles inside a Hertzian line contact. As the number of particles and platelet size increase the load carried by the worn slip zone grows larger in relationship to the unworn stick zone.     

竖直振动管中颗粒毛细效应的离散元模拟

将一根细管插入填充有颗粒的静止容器中并对管施加竖直振动,颗粒将在管内发生上升运动,并最终稳定在一定高度,这一现象与液体毛细效应类似,被称为颗粒毛细效应.为探究颗粒毛细效应过程中伴随的颗粒尺度动力学行为及机理,基于离散元方法建立颗粒运动模型,对颗粒毛细效应动力学过程和特性开展数值模拟研究.模拟再现了文献中实验得到的颗粒毛细效应全过程,给出了管内颗粒柱高度随时间的演变规律,结果表明,受到颗粒系统参数的影响,本模拟条件下颗粒毛细效应过程呈现单周期上升、倍周期上升和倍周期稳定三个阶段,在倍周期上升阶段颗粒柱上升速度逐渐减小,平缓过渡到稳定阶段.在此基础上,分析了管内颗粒速度场和填充率分布随时间的演变特性,揭示了颗粒毛细效应过程中由容器传输到管内的颗粒的占比分布.研究发现,管内不同高度位置颗粒的运动并不同步,随着管的振动,管内出现速度波,速度波的传播引起管内颗粒出现膨胀和压缩交替的情况,从而管内颗粒填充率随时间发生周期性波动;在上升阶段,越接近管壁由容器传输到管内的颗粒占比越大,在稳定阶段,管内上层颗粒的对流引起容器传输到管内的颗粒占比发生反转.      

Model of a plastically compressible material and its application to the analysis of the compaction of a porous body

This paper considers a model of a plastically compressible porous medium with a cylindricaltype yield condition and its associated constitutive relations, which ensure independent mechanisms of shear and compaction of the porous material. This allows one to use the wellknown theorems of plastic theory to analyze plastically compressible media and obtain analytical solutions for a number of boundaryvalue problems, including those taking into account conditions on strongdiscontinuity surfaces. Results from fullscale studies of the structural periodicity of noncompact materials using wavelet analysis were employed to choose a physical model for a porous body and determine the properties and dimensions of a representative volume. The problem of extrusion of a porous material through a conical matrix was solved.     

Microstructural effects on yield surface evolution in cubic metals using the viscoplastic ?-model

Polycrystalline yield surfaces of metals are a good way to characterize the anisotropy of plastic deformation. The evolution of these surfaces is impossible to accurately reproduce without taking into account the evolution of the material microstructure such as texture development. In this paper, a numerical computation of yield surfaces using the viscoplastic ?-model is proposed. Results concerning face-centered cubic metals subjected to a plane strain compression test are presented. The influence of several mechanical parameters (strain hardening, strain rate sensitivity coefficient and accumulated deformation) on subsequent yield surfaces evolution is studied. The analysis of the change in the shape and size of the yield surfaces shows that the results depend strongly on the parameter ? which controls the strength of the interactions in the polycrystal. In addition, the predictions are compared to the widely used viscoplastic self-consistent model as well as to experimental yield loci taken from the literature for various aluminum alloy sheets. A fairly good qualitative agreement between our ?-model results and the experimental ones is found. The probable links between the parameter ? and the microstructural features such as the stacking fault energy and the grain size of the polycrystal are also briefly discussed.     

金属材料辐照缺陷演化的分子动力学研究进展

辐照条件下,高能粒子在金属材料内部引入稠密的辐照缺陷,导致材料力学性能严重退化,缩短材料服役寿命,是辐照材料研究的关键问题。辐照缺陷多处在纳米尺度,故分子动力学方法是模拟辐照缺陷的有力工具,近年来被广泛用于研究辐照缺陷演化。本文总结了金属材料中辐照缺陷演化的分子动力学研究进展,介绍了级联碰撞、点缺陷、空洞、氦泡、Frank位错环、层错四面体等辐照缺陷,及其与位错、晶界等微结构的相互作用。分子动力学方法揭示的机制与模型,深化了学界对辐照效应的认识,有助于提高辐照材料力学性能和设计耐辐照材料。