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.     

半结晶聚合物损伤演化的实验表征与数值模拟

损伤本构模型对研究材料的断裂失效行为有重要意义, 但聚合物材料损伤演化的定量表征实验研究相对匮乏. 通过4种高密度聚乙烯(high density polythylene, HDPE)缺口圆棒试样的单轴拉伸实验获得了各类试样的载荷-位移曲线和真应力-应变曲线, 采用实验和有限元模拟相结合的方法确定了HDPE材料不同应力状态下的本构关系, 并建立了缺口半径与应力三轴度之间的关系;采用两阶段实验法定量描述了4种HDPE试样单轴拉伸过程中的弹性模量变化, 并建立了基于弹性模量衰减的损伤演化方程, 结合中断实验和扫描电子显微镜分析了应力状态对HDPE材料微观结构演化的影响. 结果表明缺口半径越小, 应力三轴度越大, 损伤起始越早、演化越快; 微观表现为: 高应力三轴度促进孔洞的萌生和发展, 但抑制纤维状结构的产生;基于实验和有限元模拟获得的断裂应变、应力三轴度、损伤演化方程等信息提出了一种适用于聚合物的损伤模型参数确定方法, 最后将本文获得的本构关系和损伤模型用于HDPE平板的冲压成形模拟, 模拟结果与实验结果吻合良好.      

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。     

金属材料脆性断裂机理的实验研究

材料的脆性断裂有许多准则和模型,但对脆断机理和变化规律缺乏合理的描述,给工程应用带来不便。本文对典型脆性材料球墨铸铁、灰铸铁分别进行了拉扭双轴断裂实验和常规拉伸、扭转破坏实验;对韧性金属材料合金钢进行了单轴拉伸颈缩破坏实验。通过上述实验分析了脆性材料和韧性材料发生脆性断裂的机理特征并选择应力三维度作为应力状态参数描述危险点的应力状态,同时考察了脆性材料和韧性材料发生脆性断裂的主导因素。结果表明:韧性材料45#钢和14CrNiMoV合金钢在颈缩断面心部应力三维度值较大时发生脆性拉断,而在颈缩断面边缘处应力三维度值较小时发生剪断;脆性材料球墨铸铁在应力三维度值为0.0～0.33之间变化时均发生脆性断裂;灰铸铁在应力三维度值大于0.0时发生脆性拉断,而在应力三维度值小于0.0时发生剪断。因此可以认为,材料的细观组织结构和危险点应力状态是影响断裂机理及变化规律的主要因素。对于同种材料,随着应力三维度代数值从小向大变化材料的断裂机制由塑性剪切断裂逐渐转变为脆性断裂。本文通过对几种材料的脆性断裂危险点和断裂方向的研究给出了脆断宏观破坏条件。     

Determining Stress–Strain in Rubber with In-Plane Biaxial Tensile Tester

The nominal stress–strain relationships of industrial rubber materials under multiaxial deformation are essential for precisely determining the constitutive laws of those materials. This paper proposes a new method for precisely estimating the nominal stress–stretch relationships of carbon-black-filled styrene butadiene rubbers (SBRs) under uniaxial tension, pure shear, and equibiaxial tension by using an in-plane biaxial tensile tester. The proposed method employs sheet-shaped rubber samples with notches for the pure-shear and equibiaxial tension tests to mitigate the influence of non-uniform deformation around the clamps. Finite element analysis and biaxial tensile tests were performed to verify the effectiveness of the proposed method. Performance evaluations based on both numerical calculations and experiments revealed that the proposed method enabled the precise calculation of the nominal stress–stretch relationship for uniform deformation from a tensile load and deformation of the reference area defined at the center of the samples.     

Anisotropic plasticity model coupled with Lode angle dependent strain-induced transformation kinetics law

A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations are embedded in the framework of finite strain isothermal rate-independent anisotropic plasticity. Experimental data for an anisotropic austenitic stainless steel 301LN is presented for uniaxial tension, uniaxial compression, transverse plane strain tension and pure shear. The model parameters are identified using a combined analytical–numerical approach. Numerical simulations are performed of all calibration experiments and excellent agreement is observed. Moreover, we make use of experimental data from ten combined tension and shear experiments to validate the proposed constitutive model. In addition, punch and notched tension tests are performed to evaluate the model performance in structural applications with heterogeneous stress and strain fields.     

基于J-C模型的镁合金MB2动静态拉伸破坏行为

为了研究不同应力状态和应变率条件下镁合金MB2的拉伸破坏行为,利用材料试验机和分离式Hopkinson拉杆(SHTB),对镁合金MB2的光滑及缺口圆柱试件进行了动静态拉伸加载;拟合得到了镁合金MB2的动静态拉伸本构关系,建立了其修正的Johnson-Cook失效破坏准则,并对不同试件的拉伸破坏行为进行了数值模拟;利用SEM对宏观破坏模式对应的微观损伤机理进行了分析。结果表明,随着应力三轴度的增加,镁合金MB2的等效破坏应变先增大后减小,宏观破坏模式由剪切转为正拉断,微观损伤机制由混合断裂转变为韧窝断裂;而随着应变率的增加,等效破坏应变不断减小,破坏模式不发生改变。Johnson-Cook本构关系和修正后的Johnson-Cook失效破坏准则能较好地拟合动态静态拉伸实验结果并预测不同试件的杯锥形破坏特征。     

Modification of the Gurson Model for shear failure

Recent experimental evidence points to limitations in characterizing the critical strain in ductile fracture solely on the basis of stress triaxiality. A second measure of stress state, such as the Lode parameter, is required to discriminate between axisymmetric and shear-dominated stress states. This is brought into the sharpest relief by the fact that many structural metals have a fracture strain in shear, at zero stress triaxiality, that can be well below fracture strains under axisymmetric stressing at significantly higher triaxiality. Moreover, recent theoretical studies of void growth reveal that triaxiality alone is insufficient to characterize important growth and coalescence features. As currently formulated, the Gurson Model of metal plasticity predicts no damage change with strain under zero mean stress, except when voids are nucleated. Consequently, the model excludes shear softening due to void distortion and inter-void linking. As it stands, the model effectively excludes the possibility of shear localization and fracture under conditions of low triaxiality if void nucleation is not invoked. In this paper, an extension of the Gurson model is proposed that incorporates damage growth under low triaxiality straining for shear-dominated states. The extension retains the isotropy of the original Gurson Model by making use of the third invariant of stress to distinguish shear dominated states. The importance of the extension is illustrated by a study of shear localization over the complete range of applied stress states, clarifying recently reported experimental trends. The extension opens the possibility for computational fracture approaches based on the Gurson Model to be extended to shear-dominated failures such as projectile penetration and shear-off phenomena under impulsive loadings.     

压缩-剪切复合应力下PMMA材料的静态力学特性研究

通过压缩具有一定倾斜角(0°,10°,15°,20°和25°)试件和双剪切模型试件,实现了单轴压缩、压缩-剪切复合应力以及纯剪切三种应力状态,得到PMMA(聚甲基丙烯酸甲酯)在相应应力状态下的应力-应变曲线,同时对不同应力状态下试件的破坏模式进行了分析。结果表明:在不同受力环境中材料的强度和破坏的机理不同;同单轴压缩状态下相比,材料在压缩-剪切复合应力状态下屈服极限、强度极限以及破坏应变均不同程度的增大,呈现明显的"剪切增强"现象。单轴压缩与压缩-剪切应力状态下试件的破坏模式均为在试件短对角面上出现明显的剪切屈服带,由应力分析得出试件剪应力在短对角面上达到最大,引起在此平面上分子链间滑动从而产生应变软化形成剪切屈服带;双剪切试件的破坏模式为与剪切面呈45°的斜面。     

An Improved Experimental Method for Determining the Workability Diagram

The workability diagram is often used for ductile fracture predictions in metal forming processes. Its determination requires the measurement of the strain to fracture in several tests in which the triaxiality ratio is supposed to be known and fixed throughout the process of deformation. One of such tests is the uniaxial tension test. In practice, however, it is very difficult (or even impossible) to keep the triaxiality ratio fixed in this test because of necking. It is shown in the present paper that the uniaxial tension test can be replaced with the collar test for obtaining a point of the workability diagram when the fracture criterion based on an average value of the triaxiality ratio is adopted. It is also shown that the collar test provides a more accurate prediction of the strain to fracture. The test carries out at quasi-static strain rates.     

Tension–torsion fracture experiments – Part II: Simulations with the extended Gurson model and a ductile fracture criterion based on plastic strain

An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing.     

基于应力三轴度和罗德参数的6061和7075铝合金材料断裂失效分析

分别对6061铝合金和7075铝合金材料的缺口圆棒试件和凹槽平板试件进行准静态拉伸试验,并采用ABAQUS软件对拉伸过程进行数值模拟。模拟结果与试验测试结果吻合很好,验证了有限元模型的合理性和可靠性。通过有限元模拟,分别给出了不同试件的应力三轴度和罗德参数随等效塑性应变的变化曲线以及两种材料的失效轨迹,并对它们进行了分析讨论。结果表明:形状相同、材料性质不同的试件,应力三轴度的演化规律不同;材料的失效应变受应力三轴度和罗德参数的影响,并且不同性质的材料对罗德参数的敏感性不同。     

镁合金MB2在高应力三轴度下的拉伸破坏行为研究

通过光滑试件及不同曲率半径缺口圆柱试件的拉伸试验,实现对镁合金MB2的单向及多向应力状态加载。结合数值模拟分析,研究了不同试件在拉伸加载过程中应力状态的变化。以应力三轴度为参数,给出了镁合金MB2等效破坏应变的变化规律,在应力三轴度-等效破坏应变空间建立了镁合金MB2的失效破坏准则。利用扫描电镜对试件断口形貌进行观察,分析了导致材料宏观延性变化的微观损伤机理,对不同应力状态下镁合金MB2的失效破坏行为做出了合理解释。     

Asymptotic character of mixed mode in plane deformation of crack in rubber-like material

The asymptotic stress and strain distribution near a crack tip in rubber-like materials is determined by finite element for in-plane mixed mode loading. For large strain, the crack tip field is always in a state of uniaxial tension. The shear load affects only the orientation of the deformed near tip field in the space. A good agreement is obtained between the theoretical and numerical results.     

Effect of stress-state and spacing on voids in a shear-field

Unit cell model analyses are carried out for a material with a periodic array of voids, subject to shear loading. Thus the focus is on ductile fracture in conditions of low stress triaxiality. It has been shown recently that voids in shear are flattened out to micro-cracks, which rotate and elongate until interaction with neighboring micro-cracks gives coalescence, so that the failure mechanism is very different from that under tensile loading. In the present studies the plane strain unit cell has fully periodic boundary conditions, so that any combination of the stress components in the overall average stress state can be prescribed. This also allows for studies of the effect of different initial void spacing in the two in-plane coordinate directions. The stress states considered are essentially simple shear, with various levels of tensile stresses or compressive stresses superposed, i.e. low positive stress triaxiality or even negative stress triaxiality. For high aspect ratio unit cells a clear localization band is found inside the cell, which actually represents several parallel bands, due to periodicity. In the materials represented by a low aspect ratio unit cell localization would also occur after that the maximum shear stress has been passed, but this is not shown when periodicity is enforced. The effect of superposed tensile or compressive stresses is found to be bigger for high aspect ratio unit cells than for low aspect ratios.     

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

The shear gage: For reliable shear modulus measurements of composite materials

A special strain gage called the shear gage was developed for composite materials testing with notched shear specimens. The shear-gage records the average shear strain across the entire test section between the notches of the losipescu and compact shear specimens rather than just sampling the shear strain over a small region in the center of the test section. Hence, the shear stress/strain response is obtained by dividing the average shear stress (load divided by the cross-sectional area between the notches) by the average shear strain. By placing gages on both faces of the specimen, accurate and repeatable shear-modulus measurements can be made without prior knowledge of the shear strain or stress distributions. This scheme essentially integrates the shear strain through the entire test section. Knowledge of other material properties is not required to accurately determine shear modulus values. The shear gage was tested on a variety of composite and isotropic materials resulting in more reliable shear modulus determination and less scatter than previously possible.     

A ductile damage criterion at various stress triaxialities

The paper discusses the effect of stress triaxiality on the onset and evolution of damage in ductile metals. A series of tests including shear tests and experiments on smooth and pre-notched tension specimens was carried out for a wide range of stress triaxialities. The underlying continuum damage model is based on kinematic definition of damage tensors. The modular structure of the approach is accomplished by the decomposition of strain rates into elastic, plastic and damage parts. Free energy functions with respect to fictitious undamaged configurations as well as damaged ones are introduced separately leading to elastic material laws which are affected by increasing damage. In addition, a macroscopic yield condition and a flow rule are used to adequately describe the plastic behavior. Numerical simulations of the experiments are performed and good correlation of tests and numerical results is achieved. Based on experimental and numerical data the damage criterion formulated in stress space is quantified. Different branches of this function are taken into account corresponding to different damage modes depending on stress triaxiality and Lode parameter. In addition, identification of material parameters is discussed in detail.     

Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials

The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed.In this paper, a correlation between Swift effects and the stress–strain behavior in uniaxial tension and compression is established. It is based on an elastic–plastic model that accounts for the combined influence of anisotropy and tension–compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains. In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31–Mg alloy confirm the correlation established in this work between tension–compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.     

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.