Showing papers in "International Journal of Damage Mechanics in 2004"

An Irreversible Thermodynamics Theory for Damage Mechanics of Solids

Abstract: The entropy production is a non-negative quantity based on irreversible thermodynamics and thus serves as a basis for the systematic description of the irreversible processes occurring in a solid. In this paper, a thermodynamic framework has been presented for damage mechanics of solid materials, where entropy production is used as the sole measure of damage evolution in the system. As a result, there is no need for physically meaningless empirical parameters to define a phenomenological damage potential surface or a Weibull function to trace damage evolution in solid continuum. In order to validate the model, predictions are compared with experimental results, which indicates that entropy production can be used as a damage evolution metric. The theory is founded on the basic premise that a solid continuum obeys the first and the second laws of thermodynamics.

An Interfacial Debonding Model for Particle-Reinforced Composites

Abstract: To simulate the evolution process of interfacial debonding between the matrix and reinforcing particles, and to further estimate its effect on the overall elastic behavior of particle-reinforced co...

Modeling of Glass Fracture Damage Using Continuum Damage Mechanics - Static Spherical Indentation

Abstract: The response of soda-lime glass subjected to the stress field induced by the static indentation of a spherical indenter is studied using continuum damage mechanics (CDM). An anisotropic damage tensor with linear damage evolution law is chosen to model the cracking damage. An axisymmetric finite element model is generated to simulate the static indentation process. The damage pattern and zone size are predicted for both the loading cycle and the unloading cycle, and the comparison between the predictions and the experimental results reported in the open literature serves as a validation of the CDM model and the modeling procedure.

An Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals with Planar Anisotropy

Abstract: The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix anisotropy including planar anisotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion (Liao et al., 1997) in terms of an average anisotropy parameter. Three fitting parameters are used in the closed-form anisotropic Gurson yield criterion to fit the results of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the closed-form anisotropic Gurson yield criterion unde...

Numerical Prediction of Ductile Damage in Metal Forming Processes Including Thermal Effects

Abstract: The paper is dedicated to the study of the multiphysical coupling in metal forming. Attention is paid to the coupling between thermal exchange, small strain elasticity, finite plasticity with nonlinear hardening, ductile damage, and contact with friction. The standard framework of the thermodynamics of irreversible processes with state variables is used to derive fully coupled thermo-elastoplastic constitutive equations accounting for mixed nonlinear hardening and ductile damage. The related numerical aspects concerning both the local integration scheme of the constitutive equations, as well as the global resolution strategies of the associated Initial and Boundary Value Problem (IBVP) are shortly discussed. For the local integration, an asymptotic iterative scheme is used together with a reduction in the number of the integrated constitutive equations. This model is implemented into ABAQUS/Std using the Umat and Umatht user subroutines. A special care is given to the exact calculation of the consistent stiffness matrix required by the Newton-Raphson implicit resolution strategy of the coupled mechanical and thermal IBVPs. Applications are made to simple examples and the interactions between hardening plasticity, ductile damage, and thermal fields are carefully analyzed.

A Synergistic Damage Mechanics Approach to Viscoelastic Response of Cracked Cross-ply Laminates:

Abstract: A synergistic damage mechanics approach, i.e., a combined continuum damage mechanics (CDM) and micromechanics approach, is developed to characterize the viscoelastic response of cross-ply laminates with transverse cracks. The approach relies upon a second-order tensor-based description of damage wherein the crack opening displacement appears as an explicit function. The time variation of this function is calculated by micromechanics and is inserted into the continuum damage formulation. The relaxation moduli calculated for fixed states of damage (transverse crack density) by this approach agree well with independently calculated values by a CDM approach and finite element model.

Damage identification for anisotropic sheet-metals using a non-local damage model

Abstract: A new damage model which takes account of void shape effect and anisotropy of the matrix material is integrated into the explicit finite element framework to predict the damage evolution which occurs under crash or stamping process. The void coalescence failure mechanism by internal necking is also considered by using a modified Thomason’s plastic limit-load model. An inverse method is developed to identify the material parameters by correlating experimental and numerical measurements with tensile tests on sheet-metal strips. The pathological mesh dependence has been overcome by a non-local approach where the evolution equation for the porosity is modified by an additional term containing a characteristic internal length. In this paper the evaluation of the Laplacian is based on a least square approximation of the internal state variable around each integration points. The presented formulation is applied to an Ni-based sheet-metal (INCO 718) and an aluminium alloy (AA 5182). The effectiveness of the nume...

Approximate Model of the Necking Behaviour and Application to the Void Growth Prediction

Abstract: Stress distributions at the minimum cross section of axisymmetric specimens undergoing necking are determined using an approximate method recently developed by the authors. This method is briefly presented, then applied to experimental data from tensile tests of ductile metals, available in the literature. The stress triaxiality distributions across the necked section so evaluated are used to predict the void growth according to the model by Rice and Tracey. The resulting damage evolution as well as the above stress and triaxiality distributions are finally compared with results from finite element simulations as well as with experimental damage measurements.

A Generalized Mixed Isotropic-kinematic Hardening Plastic Model Coupled with Anisotropic Damage for Sheet Metal Forming

Abstract: The paper presents a generalized mixed isotropic-kinematic hardening plastic model coupled with anisotropic damage for sheet metal forming. A nonlinear anisotropic kinematic hardening is developed. For the predication of limit strains at localized necking in stamping under complex strain history, the model and its associated damage criterion for localized necking are established and implemented into LS-DYNA3D by compiling it as a user subroutine. The finite element simulation of LS-DYNA3D based on the present model is carried out. The location of localized necking for sheet metal forming has been successfully identified.

Modeling of Anisotropic Damage for Ductile Materials in Metal Forming Processes

Abstract: The primary goal of this study is to model the anisotropic effect of ductile damage in metal forming processes. To represent the ductile metals, an anisotropic ductile plasticity/damage formulation is considered within the framework of continuum mechanics. The formulation is motivated from fracture mechanisms and physical observations in Al–Si–Mg aluminum alloys with second phases. The ductile damage mechanisms are represented by the classical ductile process of nucleation of voids at inclusions, followed by their growth and coalescence. Functions associated with each mechanism are related to different microstructural parameters. The damage, represented by a second rank tensor, is coupled to the Bammann–Chiesa–Johnson (BCJ) rate-dependent plasticity using the effective stress concept. The constitutive equations are integrated using a trapezoidal implicit scheme and implemented into an explicit finite element code. This implementation is used to predict damage during the forward axisymmetric extrusion of a...

Coupling Effects of Hardening and Damage on Necking and Bursting Conditions in Sheet Metal Forming

Abstract: New materials are appearing for sheet metal components. Their use in automotive industry require careful analysis of the influence of initial and induced properties on the formability and risks of failure during the process. The proposed approach is based on experimental investigations, mechanical modelling and FE simulations to analyse the effects of hardening and damage on the development of necking, bursting and fracture in sheet metal forming.First, the proposed study focuses on stainless steel sheet metal parts obtained by rolling at different reduction ratios. A new method has been developed to identify the initial elastic modulus from vibration tests on plates and beams. Next conventional tensile tests are used to characterise the initial hardening effect on hardening laws.Then, plastic deformations directly related to stamping conditions are imposed to the specimens. The elastic properties are measured again after unloading from vibrations tests to notice the effect of induced hardening related to...

Mechanical Implications of High Current Densities in Flip-chip Solder Joints

Abstract: We studied the electromigration damage to flip-chip solder joints of eutectic Sn/Pb under current stressing at room temperature with a current density of 1.3 × 104 A/cm2. The height of the solder joints was 100 μm. The mass accumulation near the anode side and the void nucleation near the cathode were observed during current stressing. In the preliminary experiment, the surface marker movement technique was used to measure the atomic flux driven by electromigration and to calculate the product of effective charge number and diffusivity (D × Z*) of the solder. Subsequent experiments revealed that the presence of thermomigration due to joule heating makes the extraction of the product of effective charge number and diffusivity erroneous when using marker movement technique.

Effects of Grain Boundary Sliding on Microstructural Evolution and Damage Accumulation in Tin-Lead Alloy

Abstract: Experiments on the eutectic tin-lead (Sn-Pb) alloys were conducted to study the effects of grain boundary sliding on the deformation and damage processes at the microscopic level. The primary objective is to gain mechanistic undersanding of solder joint reliability in microelectronic packaging. Bulk specimens were subjected to relatively fast deformations of tension, compression, and bending, for the purposes of examining the pure mechanical effect without the influence of diffusion-related phenomena. Grain realignment and phase redistribution were characterized by microscopy and microhardness indentation. A micromechanical model is proposed to elucidate the observed microstructural changes and progressive damage. This study illustrates the significance of damage in the form of microscopic heterogeneity caused by grain boundary sliding. It also illustrates the possibility of mechanically induced phase coarsening in actual solder joints. High-frequency cyclic shear tests on Sn-Pb solder joints showed damag...

Constitutive Model for Sn–Pb Solder under Fatigue Loading

Abstract: The paper presents a constitutive model for Sn–Pb solder which captures the response of this complex material subject to a variety of load paths including fatigue loading. Internal state variables are established to characterize grain coarsening and material degradation observed experimentally. A damagecoupled viscoplastic constitutive model is formulated to take into account the effects of temperature and loading rates on mechanical response. The influence of fatigue loading frequency or strain rate, hold time, and temperature on mechanical behavior and fatigue life for 63Sn–37Pb solder alloy is examined. The fatigue failure predictions are compared with those obtained experimentally and found to be satisfactory.

The Fluid-filled Spherical Cavity in a Damage-susceptible Poroelastic Medium:

Abstract: This paper examines the problem of fluid pressure development in a fluid-filled spherical cavity located in an extended fluid-saturated poroelastic medium susceptible to damage. The evolution of damage introduces alterations in both the hydraulic conductivity and skeletal elasticity properties of the poroelastic solid. The paper examines the fluid-filled spherical cavity problem with a view to establishing the influence of the stress state-dependent damage on the amplification and decay of the fluid pressure in the spherical cavity. Sufficient computational results are available to aid the development of certain generalized conclusions relating to the influence of damage on the behaviour of encapsulated fluid domains.

Notes on Damage Effect Tensors of Two-Scalar Variables

Abstract: The aim of this paper is the presentation of notes concerning the two-scalar damage effect tensors by Chow as well as the formulation of conditions of thermodynamic admissibility of such tensors and the verification of known-in-literature damage effect tensors from the point of view of the derived conditions.

Phenomenological Modeling of the Stress-Stretch Behavior of EPDM Rubber with Loading-rate and Damage Effects:

Abstract: This paper formulates a phenomenological continuum model, which includes the idealized Mullins effect and loading-rate effects, for the stress-stretch behavior of ethylene-propylene-diene terpolymer (EPDM). This proposed model is based on Ogden and Roxburgh's pseudoelasticity theory and a hyperelastic form of strain-energy function describing the Mullins effect. Based on experimental results, the loading-rate effects are introduced into this model by replacing the material parameters with an exponential formation as a function of loading rate. The loading rate has effects only on the material parameters and the degree of damage in a specimen is only dependent on the maximum stretch ratio it experiences. It is demonstrated that this model provides a good agreement with the experimental results on EPDM stress-stretch behavior over a wide range of stretching rates.

A Multilevel Superelement Technique for Damage Analysis

Abstract: A multilevel superelement technique is applied to model the effects of circular voids on the effective elastic properties of a porous material. A twodimensional representative volume element with a circular void in its center is initially modeled by a superelement. A thin plate of porous material with a macrocircular hole in the center is constructed with this superelement. The finite element computation is then conducted to estimate the effective Young’s modulus, Poisson’s ratio, and the shear modulus of the material using the ABAQUS code for different void sizes. The values of the isotropic damage variables, DE and DG, under various degree of damage are hence determined. These values are compared with those calculated by using a conventional micromechanics damage model. A new isotropic damage model is proposed based on the results of this analysis. To demonstrate the applicability of this damage model, an example case of a notched cylindrical bar under tensile loading is investigated.