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.     

金属材料平面应变拉伸变形局部化有限元分析

本文对于涉及韧性金属大变形中颈缩与剪切带断裂一类高度非线性变形局部化问题进行了弹塑性有限元数值模拟。采用改进的Ｊ２形变理论微分形式公式与交叉三角形四边形单元有限元网格，详细研究了应变硬化指数及初始表面不均匀特性的平面应变拉伸颈缩和剪切带形成的综合影响，给出此类问题的断裂机制图。     

A finite thickness band method for ductile fracture analysis

We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffness of the material degrades. An embedded weak discontinuity is introduced when the condition for loss of ellipticity is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. Also since the constitutive relation for a progressively cavitation solid is used inside the band in the post-localization regime, the traction-opening relation across the band depends on the stress triaxiality. The methodology is illustrated through several example problems including mode I crack growth and localization and failure in notched bars. Various finite element meshes and values of the thickness of the localization band are used in the calculations to illustrate the convergence with mesh refinement and the dependence on the value chosen for the localization band thickness.     

Macroscopic yield criteria for plastic anisotropic materials containing spheroidal voids

The combined effects of void shape and matrix anisotropy on the macroscopic response of ductile porous solids is investigated. The Gologanu–Leblond–Devaux’s (GLD) analysis of an rigid-ideal plastic (von Mises) spheroidal volume containing a confocal spheroidal cavity loaded axisymmetrically is extended to the case when the matrix is anisotropic (obeying Hill’s [Hill, R., 1948. A theory of yielding and plastic flow of anisotropic solids. Proc. Roy. Soc. London A 193, 281–297] anisotropic yield criterion) and the representative volume element is subjected to arbitrary deformation. To derive the overall anisotropic yield criterion, a limit analysis approach is used. Conditions of homogeneous boundary strain rate are imposed on every ellipsoidal confocal with the cavity. A two-field trial velocity satisfying these boundary conditions are considered. It is shown that for cylindrical and spherical void geometries, the proposed criterion reduces to existing anisotropic Gurson-like yield criteria. Furthermore, it is shown that for the case when the matrix is considered isotropic, the new results provide a rigorous generalization to the GLD model. Finally, the accuracy of the proposed approximate yield criterion for plastic anisotropic media containing non-spherical voids is assessed through comparison with numerical results.     

Experimental investigation into plastic damage of microvoids with interaction

A mechanism of plastic flow localization in ductile matter near microvoids is studied. The voids with the size-scale of micromillimeter exist in sheet specimens under tensile loading, and the plastic strain field around voids is obtained by digital image processing of deformed grids. The size growth of the microvoids, the spacing change of the neighboring voids, and the development of shear bands in the ligament between the voids, are presented by experimental results accompanied with the plastic strain distribution, that gives good interpretation to the process of void growth and coalescence with the flow localization in the ligaments. The project supported by the National Natural Science Foundation of China     

Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states.The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix.The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality.The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.     

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.     

Potential flow model of cavitation-induced interfacial fracture in a confined ductile layer

Fracture of a thin ductile layer sandwiched between stiff substrates often results from growth and coalescence of microscopic cavities ahead of an extending crack. Cavitation induced by plastic flow in a confined, ductile layer is analyzed here to evaluate the interfacial fracture toughness of such sandwich structures. For rigid-plastic materials, a new method is proposed in which the potential flow field of a fluid is used to approximate the plastic deformation. The principle of virtual work rate is applied to determine the equivalent traction-separation law. The method is demonstrated and validated for spherically symmetric cavity growth, for which an exact solution exists. We then study in detail the growth of an initially spherical cavity in a cylindrical bar of finite length subject to uniform traction at its ends. The results show that the stress-separation curves depend strongly on initial cavity size and the strain-hardening exponent, and weakly on the nominal strain. The method has clear advantages over numerical methods, such as finite-element analysis, for parametric study of cavity growth with large plastic deformation.     

Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids

The diffuse mode bifurcation of elastoplastic solids at finite strain is investigated. The multiplicative decomposition of deformation gradient and the hyperelasto-plastic constitutive relationship are adapted to the numerical bifurcation analysis of the elastoplastic solids. First, bifurcation analyses of rectangular plane strain specimens subjected to uniaxial compression are conducted. The onset of the diffuse mode bifurcations from a homogeneous state is detected; moreover, the post-bifurcation states for these modes are traced to arrive at localization to narrow band zones, which look like shear bands. The occurrence of diffuse mode bifurcation, followed by localization, is advanced as a possible mechanism to create complex deformation and localization patterns, such as shear bands. These computational diffuse modes and localization zones are shown to be in good agreement with the associated experimental ones observed for sand specimens to ensure the validity of this mechanism. Next, the degradation of horizontal sway stiffness of a rectangular specimen due to plane strain uniaxial compression is pointed out as a cause of the bifurcation of the first antisymmetric diffuse mode, which triggers the tilting of the specimen. Last, circular and punching failures of a footing on a foundation are simulated.     

The void-size effect on plastic flow localization in the Gurson model

Recent studies have shown that the size of microvoids has a significant effect on the void growth rate. The purpose of this paper is to explore whether the void size effect can influence the plastic flow localization in ductile materials. We have used the extended Gurson‘s dilatational plasticity theory, which accounts for the void size effect, to study the plastic flow localization in porous solids with long cylindrical voids. The localization model of Rice is adopted, in which the material inside the band may display a different response from that outside the band at the incipient plastic flow localization. The present study shows that it has little effect on the shear band angle.     

A physical model for nucleation and early growth of voids in ductile materials under dynamic loading

Spall fracture and other rapid tensile failures in ductile materials are often dominated by the rapid growth of voids. Recent research on the mechanics of void growth clearly shows that void nucleation may be represented as a bifurcation phenomenon, wherein a void forms spontaneously followed by highly localized plastic flow around the new void. Although thermal, viscoplastic, and work hardening effects all play an essential role in the earliest stages of nucleation and growth, the flow becomes dominated by spherical radial inertia, which soon causes all voids to grow asymptotically at the same rate, regardless of differences in initial conditions or constitutive details, provided only that there is the same density of matrix material and the same excess loading history beyond the cavitation stress.These two facts, initiation by bifurcation at a cavitation stress, at which a void first appears, and rapid domination by inertia, are used to postulate a simple, but physically realistic, model for nucleation and early growth of voids in a ductile material under rapid tensile loading. A reasonable statistical distribution for the cavitation stress at various nucleation sites and a simple similarity solution for inertially dominated void growth permit a simple calculation of the initiation and early growth of porosity in the material.Parametric analyses are presented to show the effect that loading rate, peak loading stress, density of nucleation sites, physical properties of the material, etc. have on the applied pressure and distribution of void sizes when a critical porosity is reached.     

Modeling of crack growth in ductile solids: a three-dimensional analysis

A population of several spherical voids is included in a three-dimensional, small scale yielding model. Two distinct void growth mechanisms, put forth by [Int. J. Solids Struct. 39 (2002) 3581] for the case of a two-dimensional model containing cylindrical voids, are well contained in the model developed in this study for spherical voids. A material failure criterion, based on the occurrence of void coalescence in the unit cell model, is established. The critical ligament reduction ratio, which varies with stress triaxiality and initial porosity, is used to determine ligament failure between the crack tip and the nearest void. A comparison of crack initiation toughness of the model containing cylindrical voids with the model containing spherical voids reveals that the material having a sizeable fraction of spherical voids is tougher than the material having cylindrical voids. The proposed material failure determination method is then used to establish the fracture resistance curve (J–R curve) of the material. For a ductile material containing a small volume fraction of microscopic voids initially, the void by void growth mechanism prevails, which results in a J–R curve having steep slope. On the other hand, for a ductile material containing a large volume fraction of initial voids, the multiple voids interaction mechanism prevails, which results in a flat J–R curve. Next, the effect of T-stress on fracture resistance is examined. Finally, nucleation and growth of secondary microvoids and their effects on void coalescence are briefly discussed.     

Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking

Cleavage fracture in ferritic steels is often initiated in brittle carbides randomly distributed in the material. The carbides break as a result of a fibre loading mechanism in which the stress levels in the carbides are raised, as the surrounding ferrite undergoes plastic deformation. The conditions in the vicinity of the nucleated micro-crack will then determine whether the crack will penetrate or be arrested by the ferrite. The ferrite is able to arrest nucleated cracks through the presence of mobile dislocations, which blunt and shield the microcrack and thus lowers the stresses at the crack tip. Hence, the macroscopic toughness of the material directly depends on the ability of the ferrite to arrest nucleated micro-cracks and in turn on the plastic rate sensitivity of the ferrite. The initiation of cleavage fracture is here modelled explicitly in the form of a micro-crack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder or in a few cases an elastic sphere and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, where the tractions are governed by a modified exponential cohesive law. It is shown that the critical stress, required to propagate a microcrack from a broken carbide, increases with decreasing plastic rate sensitivity of the ferrite. The results also show that a low stress triaxiality and a high aspect ratio of the carbide promote the initiation of cleavage fracture from a broken carbide.     

Hydrogen induced shear localization of the plastic flow in metals and alloys

Hydrogen enhanced localized plasticity (HELP) is a viable mechanism for hydrogen embrittlement supported by experimental observations. According to the HELP mechanism, hydrogen induced premature failures result from hydrogen induced plastic instability which leads to hydrogen assisted localized ductile processes. The objective of this work is to reveal the role of hydrogen in possibly localizing the macroscopic deformation into bands of intense shear using solid mechanics methodology. The hydrogen effect on material deformation is modeled through the hydrogen induced volume dilatation and the reduction in the local flow stress upon hydrogen dissolution into the lattice. Hydrogen in assumed to reside in both normal interstitial lattice sites (NILS) and reversible traps associated with the plastic deformation. The analysis of the plastic deformation and the conditions for plastic flow localization are carried out in plane strain uniaxial tension. For a given initial hydrogen concentration in the unstressed specimen, a critical macroscopic strain is identified at which shear localization commences.     

Structural bifurcation for ductile necking localization

Necking localization is common unstable behavior in ductile solids. This paper describes the unified necking localization mechanism. After describing one-dimensional instability problem, general material and structural instability criteria are formulated and the formulation is validated by non-linear finite element analysis. The trigger of necking localization is structural bifurcation and the behavior from a uniformly deformed state to ultimate localization just before fracture is continuous structural instability.     

Vapor pressure and void size effects on failure of a constrained ductile film

To achieve certain properties, semiconductor adhesives and molding compounds are made by blending filler particles with polymer matrix. Moisture collects at filler particle/polymer matrix interfaces and within voids of the composite. At reflow temperatures, the moisture vaporizes. The rapidly expanding vapor creates high internal pressure on pre-existing voids and particle/matrix interfaces. The simultaneous action of thermal stresses and internal vapor pressure drives both pre-existing and newly nucleated voids to grow and coalesce causing material failure. Particularly susceptible are polymeric films and adhesives joining elastic substrates, e.g. Ag filled epoxy. Several competing failure mechanisms are studied including: near-tip void growth and coalescence with the crack; extensive void growth and formation of an extended damaged zone emanating from the crack; and rapid void growth at highly stressed sites at large distances ahead of the crack, leading to multiple damaged zones. This competition is driven by the interplay between stress elevation induced by constrained plastic flow and stress relaxation due to vapor pressure assisted void growth.A model problem of a ductile film bonded between two elastic substrates, with a centerline crack, is studied. The computational study employs a Gurson porous material model incorporating vapor pressure effects. The formation of multiple damaged zones is favored when the film contains small voids or dilute second-phase particle distribution. The presence of large voids or high vapor pressure favor the growth of a self-similar damage zone emanating from the crack. High vapor pressure accelerates film cracking that can cause device failures.     

An analysis of ductile rupture in notched bars

Ductile fracture in axisymmetric and plane strain notched tensile specimens is analyzed numerically, based on a set of elastic-plastic constitutive relations that account for the nucleation and growth of microvoids. Final material failure by void coalescence is incorporated into the constitutive model via the dependence of the yield function on the void volume fraction. In the analyses the material has no voids initially; but as the voids nucleate and grow, the resultant dilatancy and pressure sensitivity of the macroscopic plastic flow influence the solution significantly. Considering both a blunt notch geometry and a sharp notch geometry in the computations permits a study of the relative roles of high strain and high triaxiality on failure. Comparison is made with published experimental results for notched tensile specimens of high-strength steels. All axisymmetric specimens analyzed fail at the center of the notched section, whereas failure initiation at the surface is found in plane strain specimens with sharp notches, in agreement with the experiments. The results for different specimens are used to investigate the circumstances under which fracture initiation can be represented by a single failure locus in a plot of stress triaxiality vs effective plastic strain.     

Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements

This paper is concerned with the multiscale simulation of plastic deformation of metallic specimens using physically-based models that take into account their polycrystalline microstructure and the directionality of deformation mechanisms acting at single-crystal level. A polycrystal model based on self-consistent homogenization of single-crystal viscoplastic behavior is used to provide a texture-sensitive constitutive response of each material point, within a boundary problem solved with finite elements (FE) at the macroscale. The resulting constitutive behavior is that of an elasto-viscoplastic material, implemented in the implicit FE code ABAQUS. The widely-used viscoplastic selfconsistent (VPSC) formulation for polycrystal deformation has been implemented inside a user-defined material (UMAT) subroutine, providing the relationship between stress and plastic strain-rate response. Each integration point of the FE model is considered as a polycrystal with a given initial texture that evolves with deformation. The viscoplastic compliance tensor computed internally in the polycrystal model is in turn used for the minimization of a suitable-designed residual, as well as in the construction of the elasto-viscoplastic tangent stiffness matrix required by the implicit FE scheme.Uniaxial tension and simple shear of an FCC polycrystal have been used to benchmark the accuracy of the proposed implicit scheme and the correct treatment of rotations for prediction of texture evolution. In addition, two applications are presented to illustrate the potential of the multiscale strategy: a simulation of rolling of an FCC plate, in which the model predicts the development of different textures through the thickness of the plate; and the deformation under 4-point bending of textured HCP bars, in which the model captures the dimensional changes associated with different orientations of the dominant texture component with respect to the bending plane.     

材料的微结构损伤与韧性断裂

Ⅰ.前言50年代起至60年代,国际上开展了材料宏观力学性能的大量研究,提出了应力强度因子K和J积分,确定了断裂韧性参数的测定方法,创立了断裂力学学科并制定了规范,对材料的断裂、疲劳性能的预测和安全设计做出了很大贡献。进入70年代后开始注意到现有技术远远不能认识和控制各类裂纹的起因和发展。例如,K和J不能解决裂纹的稳态扩展、复      

Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals

In order to model the effects of grain boundaries in polycrystalline materials we have coupled a crystal-plasticity model for the grain interiors with a new elastic-plastic grain-boundary interface model which accounts for both reversible elastic, as well irreversible inelastic sliding-separation deformations at the grain boundaries prior to failure. We have used this new computational capability to study the deformation and fracture response of nanocrystalline nickel. The results from the simulations reflect the macroscopic experimentally observed tensile stress-strain curves, and the dominant microstructural fracture mechanisms in this material. The macroscopically observed nonlinearity in the stress-strain response is mainly due to the inelastic response of the grain boundaries. Plastic deformation in the interior of the grains prior to the formation of grain-boundary cracks was rarely observed. The stress concentrations at the tips of the distributed grain-boundary cracks, and at grain-boundary triple junctions, cause a limited amount of plastic deformation in the high-strength grain interiors. The competition of grain-boundary deformation with that in the grain interiors determines the observed macroscopic stress-strain response, and the overall ductility. In nanocrystalline nickel, the high-yield strength of the grain interiors and relatively weaker grain-boundary interfaces account for the low ductility of this material in tension.