Homogenization-based continuum plasticity-damage model for ductile failure of materials containing heterogeneities

This paper develops an accurate and computationally efficient homogenization-based continuum plasticity-damage (HCPD) model for macroscopic analysis of ductile failure in porous ductile materials containing brittle inclusions. Example of these materials are cast alloys such as aluminum and metal matrix composites. The overall framework of the HCPD model follows the structure of the anisotropic Gurson-Tvergaard-Needleman (GTN) type elasto-plasticity model for porous ductile materials. The HCPD model is assumed to be orthotropic in an evolving material principal coordinate system throughout the deformation history. The GTN model parameters are calibrated from homogenization of evolving variables in representative volume elements (RVE) of the microstructure containing inclusions and voids. Micromechanical analyses for this purpose are conducted by the locally enriched Voronoi cell finite element model (LE-VCFEM) [Hu, C., Ghosh, S., 2008. Locally enhanced Voronoi cell finite element model (LE-VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions. Int. J. Numer. Methods Eng. 76(12), 1955-1992]. The model also introduces a novel void nucleation criterion from micromechanical damage evolution due to combined inclusion and matrix cracking. The paper discusses methods for estimating RVE length scales in microstructures with non-uniform dispersions, as well as macroscopic characteristic length scales for non-local constitutive models. Comparison of results from the anisotropic HCPD model with homogenized micromechanics shows excellent agreement. The HCPD model has a huge efficiency advantage over micromechanics models. Hence, it is a very effective tool in predicting macroscopic damage in structures with direct reference to microstructural composition.     

Constitutive modeling of deformation and damage in superplastic materials

The superplastic deformation and cavitation damage characteristics of a modified aluminum alloy are investigated at a temperature range from 500 to 550°C. The baseline alloy is AA5083. Nominally this alloy contains about 4.5% Mg, 0.8% Mn, 0.2% Cr, 0.037% Si, 0.08% Fe and 0.025% Ti by weight. The experimental program consists of uniaxial tension tests and digital image analysis for measuring cavitation. The experiments reveal that evolution of damage is due to both nucleation and growth of voids. A viscoplastic model for describing deformation and damage in this alloy is developed based on a continuum mechanics framework. The model includes the effect of strain hardening, strain rate sensitivity, dynamic and static recovery, and nucleation and growth of voids. The model predictions compare well with the experimental results.     

Design of microstructure-sensitive properties in elasto-viscoplastic polycrystals using multi-scale homogenization

Evolution of properties during processing of materials depends on the underlying material microstructure. A finite element homogenization approach is presented for calculating the evolution of macro-scale properties during processing of microstructures. A mathematically rigorous sensitivity analysis of homogenization is presented that is used to identify optimal forging rates in processes that would lead to a desired microstructure response. Macro-scale parameters such as forging rates are linked with microstructure deformation using boundary conditions drawn from the theory of multi-scale homogenization. Homogenized stresses at the macro-scale are obtained through volume-averaging laws. A constitutive framework for thermo-elastic–viscoplastic response of single crystals is utilized along with a fully-implicit Lagrangian finite element algorithm for modelling microstructure evolution. The continuum sensitivity method (CSM) used for designing processes involves differentiation of the governing field equations of homogenization with respect to the processing parameters and development of the weak forms for the corresponding sensitivity equations that are solved using finite element analysis. The sensitivity of the deformation field within the microstructure is exactly defined and an averaging principle is developed to compute the sensitivity of homogenized stresses at the macro-scale due to perturbations in the process parameters. Computed sensitivities are used within a gradient-based optimization framework for controlling the response of the microstructure. Development of texture and stress–strain response in 2D and 3D FCC aluminum polycrystalline aggregates using the homogenization algorithm is compared with both Taylor-based simulations and published experimental results. Processing parameters that would lead to a desired equivalent stress–strain curve in a sample poly-crystalline microstructure are identified for single and two-stage loading using the design algorithm.     

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。     

Shape and topology sensitivity analysis and its application to structural design

The incremental sensitivity analysis associated with variation of structure material parameters, shape or topology variation is generally discussed by analyzing the evolution of potential and complementary energies, or arbitrary functionals of state fields. The concept of configuration and sensitivity generalized forces is used in presenting the sensitivity derivatives. The general reciprocity relations are derived for the case of potential or complementary energy variations. The topology variations in bar structures related to introduction of elements and introduction of inclusions and voids in plates are discussed, and the sensitivity forces are derived.     

Microelastic wave field signatures and their implications for microstructure identification

This work combines closed-form and computational analyses to elucidate the dynamic properties, termed signatures, of waves propagating through solids defined by the theory of elasticity with microstructure and the potential of such properties to identify microstructure evolution over a material’s lifetime. First, the study presents analytical dispersion relations and frequency-dependent velocities of waves propagating in microelastic solids. A detailed parametric analysis of the results show that elastic solids with microstructure recover traditional gradient elasticity under certain conditions but demonstrate a higher degree of flexibility in adapting to observed wave forms across a wide frequency spectrum. In addition, a set of simulations demonstrates the ability of the model to quantify the presence of damage, just another type of microstructure, through fitting of the model parameters, especially the one associated with the characteristic length scale of the underlying microstructure, to an explicit geometric representation of voids in different damage states.     

An Examination of Anisotropic Void Evolution in Aluminum Alloy 7075

This paper investigates the anisotropy of void evolution and its relation with ductility in the high strength rolled aluminum alloy 7075-T7351. Smooth tension specimens are extracted from three principal material orientations, i.e. rolling (R), transverse (T), and short transverse (S). The mechanical behavior of these specimens is characterized and the varying ductility in the three orientations is clearly observed. Electron Backscattered Diffraction (EBSD), optical microscopy, and Scanning Electron Microscopy (SEM) are employed to characterize the grain structure and the size, location, and chemical composition of the intermetallic particles. In-situ X-ray Tomography (XCT) experiments are performed to obtain tomographic images of the specimens at critical loading steps. The radiographs acquired during the tensile test are then reconstructed and examined through quantitative analysis to partition particles and voids. These tomographic images enable us to visualize void evolution as the specimens are loaded along material orientations. The tomographic images clearly illustrate anisotropy in the void evolution and highlight the importance of local coalescence in developing 1D and 2D void structures prior to global coalescence. Fractography confirms tomography. These findings motivate model forms with appropriate internal variables to adequately describe the dominant mechanisms which govern anisotropic void evolution.     

Experimental study and modeling of damage of Al alloys using tensor theory

This article presents and evaluates experiments for the characterization and modeling of damage of structural aluminum and aluminum–magnesium alloys. Tensile tests were performed for specimens with artificial defects (voids) represented by different arrangements of pre-drilled micro-holes. The corresponding stress–strain curves were experimentally obtained. Plastic dilatation and deviatoric strain were determined both for the local zones with artificial defects and directly for meso-elements (i.e., material cells with artificial defects). A symmetric second-rank order tensor of damage was applied for a quantitative estimate of the material damage connected with the volume fraction and shape of micro-defects. The definition of this tensor is physically motivated, since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume fraction and shape of micro-defects, respectively. Such a representation of damage kinetics allows us to use two integral measures for the calculation of damage in deformed materials. The first measure determines damage related to an increase in void volume fraction (i.e., plastic dilatation). A critical amount of plastic dilatation corresponds to the moment of macro-fracture of the deformed metal. By means of experimental analysis, we can determine the function of plastic dilatation which depends on the strain accumulated by material particles under various stress and temperature-rate conditions of forming. The second measure accounts for the deviatoric strain of meso-elements, and is related to the change in their shapes. The critical deformation of ellipsoidal voids corresponds to the onset of their coalescence and to the formation of large cavernous defects. The second measure is considered as a criterion of micro-destruction due to formation of cavities in the deformed material. Based on the experimental data, some numerical modeling is realized for the investigated Al alloys to taken a change in stress triaxiality into account. It shows that a change in triaxiality toward smaller values results in an appreciable decrease of damage induced by strain. Both damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques.     

Damage evolution of ductile material under impact loading

Nucleation, growth and coalescence of micro-voids result in the fracture of materials. Most mathematical models neglect nucleation and introduce initial damage, assuming it as a material constant. However, the original damage, which is formed during material working, is a material constant. The initial damage is a model parameter and depends on the load. Apparently, the predictability of such a model is poor.This paper made comparison and analysis of the four classical void growth models and showed their similarities. At the beginning of damage evolution, all the models follow a linear relationship in the form , where c is the size of micro voids and k is a parameter which relates the material and loading condition. With the concept of statistical micro-damage and the assumption of uniform void radius for new voids, a damage evolution equation was deduced based on the above void growth model. With this equation the effects of nucleation and growth at the beginning of the damage stage on the whole process of damage evolution can be calculated. The transition time from the nucleation dominant phase to the growth dominant phase can be determined. When the transition time is applied to the damage failure model of ductile material proposed by Johnson, the initial damage (f₀), a model parameter in the original model, can also be determined. The results of the derived damage evolution equation agree well with the previous research results.     

水介质条件下7075合金扭转复合微动磨损特性研究

在新型扭转复合微动试验机上,以7075合金平面/GCr15钢球配副为研究对象,研究水介质对7075合金扭转复合微动磨损行为的影响.在微动动力学特性分析的基础上结合磨痕形貌微观分析,研究水介质环境下7075合金扭转复合微动的磨损机理.结果表明：水介质对扭转复合微动运行和损伤机制存在显著影响,水介质明显地改变了微动运行区域;相比干态,在部分滑移区和混合区,水介质下的剥层现象更加明显,水介质加速了微动损伤.在滑移区,磨损机制主要转变为以磨粒磨损为主,湿润的磨屑能有效降低表面摩擦系数和减缓微动损伤;而单一的水介质会加剧材料的磨损.此外,水介质和干态微动环境中不同倾斜角度下的磨损体积均与累积耗散能分别呈不同的线性关系.     

A multi-length scale sensitivity analysis for the control of texture-dependent properties in deformation processing

Material property evolution during processing is governed by the evolution of the underlying microstructure. We present an efficient technique for tailoring texture development and thus, optimizing properties in forming processes involving polycrystalline materials. The deformation process simulator allows simulation of texture formation using a continuum representation of the orientation distribution function. An efficient multi-scale sensitivity analysis technique is then introduced that allows computation of the sensitivity of microstructure field variables such as slip resistances and texture with respect to perturbations in macro-scale forming parameters such as forging rates, die shapes and preform shapes. These sensitivities are used within a gradient-based optimization framework for computational design of material property distribution during metal forming processes. Effectiveness of the developed computational scheme is demonstrated through computationally intensive examples that address control of properties such as Young’s modulus, strength and magnetic hysteresis loss in finished products.     

Porous materials with two populations of voids under internal pressure: II. Growth and coalescence of voids

This study is devoted to the mechanical behaviour of polycrystalline materials with two populations of voids, small spherical voids located inside the grains and larger spheroidal voids located at the grain boundaries. In part I of the work, instantaneous effective stress–strain relations were derived for fixed microstructure. In this second part, the evolution of the microstructure is addressed. Differential equations governing the evolution of the microstructural parameters in terms of the applied loading are derived and their integration in time is discussed. Void growth results in a global softening of the stress–strain response of the material. A simple model for the prediction of void coalescence is proposed which can serve to predict the overall ductility of polycrystalline porous materials under the combined action of thermal dilatation and internal pressure in the voids.     

Influences of initial porosity,stress triaxiality and Lode parameter on plastic deformation and ductile fracture

Local mechanical properties in aluminum cast components are inhomogeneous as a consequence of spatial distribution of microstructure,e.g.,porosity,inclusions,grain size and arm spacing of secondary dendrites.In this work,the effect of porosity is investigated.Cast components contain voids with different sizes,forms,orientations and distributions.This is approximated by a porosity distribution in the following.The aim of this paper is to investigate the influence of initial porosity,stress triaxiality and Lode parameter on plastic deformation and ductile fracture.A micromechanical model with a spherical void located at the center of the matrix material,called the representative volume element(RVE),is developed.Fully periodic boundary conditions are applied to the RVE and the values of stress triaxiality and Lode parameter are kept constant during the entire course of loading.For this purpose,a multi-point constraint(MPC)user subroutine is developed to prescribe the loading.The results of the RVE model are used to establish the constitutive equations and to further investigate the influences of initial porosity,stress triaxiality and Lode parameter on elastic constant,plastic deformation and ductile fracture of an aluminum die casting alloy.     

In situ 3D Synchrotron Laminography Assessment of Edge Fracture in Dual-Phase Steels: Quantitative and Numerical Analysis

The mechanical performance of automotive structures made of advanced high strength steels (AHSS) is often seen reduced by the presence of cut edges. An attempt is made to assess and quantify the initial damage state and the damage evolution during mechanical testing of a punched edge and a machined edge via a recently developed 3D imaging technique called synchrotron radiation computed laminography. This technique allows us to observe damage in regions of interest in thin sheet-like objects at micrometer resolution. In terms of new experimental mechanics, steel sheets having sizes and mechanical boundary conditions of engineering relevance can be tested for the first time with in situ 3D damage observation and quantification. It is found for the investigated DP600 steel that the fracture zone of the punched edge is rough and that needle-shape voids at the surface and in the bulk follow ferrite-martensite flow lines. During mechanical in situ testing the needle voids grow from the fracture zone surface and coalesce with the sheared zone. In contrast, during in situ mechanical testing of a machined edge the damage starts away from the edge (～800μm) where substantial necking has occurred. Three-dimensional image analysis was performed to quantify the initial damage and its evolution. These data can be used as input and validation data for micromechanical damage models. To interpret the experimental findings in terms of mechanical fields, combined surface digital image correlation and 3D finite element analysis were carried out using an elasto-plastic constitutive law of the investigated DP steel. The stress triaxiality and the accumulated plastic strain were calculated in order to understand the influence of the edge profile and the hardening of the cutting-affected zone on the mechanical fields.     

Thermo-mechanical response of tension panels under intense rapid heating

The temperature dependence of the fracture strength of 7075-T6 aluminum alloy was determined under rapid heating (0.02–.50 sec) conditions by exposing thin-section specimens to intense surface irradiation while under constant tensile load. When combined with a numerical thermal analysis and an appropriate limit analysis, these data enabled accurate prediction of the heating time required to produce ductile fracture in spot irradiated tension panels. The transient heat transfer model employed in the computations incorporated material removal due to melting, temperature-dependent material properties, and convection/radiation losses.     

升温热冲击环境下超高温陶瓷材料抗热震性能的热-损伤模型

在现有的抗热震理论基础上考虑到超高温陶瓷材料热物理性能对温度的敏感性及损伤在其使役历程中随温度的演化,建立了适用于升温服役环境下表征超高温陶瓷材料抗热震性能的热-损伤模型。该模型考虑了微裂纹尺寸、密度、热冲击环境温度等因素对材料抗热震性能的影响。利用此模型研究了超高温陶瓷材料在升温服役环境下损伤以微裂纹形核规律演化时对其抗热震性能的影响。从理论上验证了基于材料微结构设计思想在制备超高温陶瓷材料时,引进一定密度一定尺寸的微裂纹并控制其随温度演化规律以形核方式进行,既可以使材料保持较高的强度又能大幅度提升材料的抗热震性能。     

Small surface and corner crack propagation in aluminum and steel alloys

The purpose of the investigation reported here was to examine experimentally the transition behavior of a short crack in detail using surface-crack measurements with a traveling microscope and micromeasurements obtained by scanning-electron microscopy (SEM). The cyclic growth and transition of initial part-through cracks into through the thickness flaws are documented through experiments by using compact-type specimens fabricated from 7075-T6 aluminum, 2024-T3 aluminum, and mild-steel material, with a keyhole notch. Paper was presented at the 1986 SEM Fall Conference on Experimental Mechanics held in Keystone, CO on November 2–5.     

Void growth and coalescence in anisotropic plastic solids

Large strain finite element calculations of unit cells subjected to triaxial axisymmetric loadings are presented for plastically orthotropic materials containing a periodic distribution of aligned spheroidal voids. The spatial distribution of voids and the plastic flow properties of the matrix are assumed to respect transverse isotropy about the axis of symmetry of the imposed loading so that a two-dimensional axisymmetric analysis is adequate. The parameters varied pertain to load triaxiality, matrix anisotropy, initial porosity and initial void shape so as to include the limiting case of penny-shaped cracks. Attention is focussed on comparing the individual and coupled effects of void shape and material anisotropy on the effective stress–strain response and on the evolution of microstructural variables. In addition, the effect of matrix anisotropy on the mode of plastic flow localization is discussed. From the results, two distinct regimes of behavior are identified: (i) at high triaxialities, the effect of material anisotropy is found to be persistent, unlike that of initial void shape and (ii) at moderate triaxialities the influence of void shape is found to depend strongly on matrix anisotropy. The findings are interpreted in light of recent, microscopically informed models of porous metal plasticity. Conversely, observations are made in relation to the relevance of these results in the development and calibration of a broader set of continuum damage mechanics models.     

泡沫铝率相关性能的有限元模拟

构建了三维随机分布球形泡孔模型,模拟开、闭孔混合结构泡沫铝材料的微细观结构,并通过有限元方法计算了10~104 s-1应变率范围内、孔隙率35%~65%泡沫铝材料的率相关性以及应变率和相对密度变化对泡沫铝动态压缩力学性能的影响。研究表明:中、低应变率下,泡沫铝材料率相关性能主要取决于基体材料的应变率敏感性;高应变率下,泡沫铝材料率相关性能受基体材料的应变率敏感性以及微结构惯性联合作用,且相对密度较低泡沫铝材料的微结构惯性效应更显著。