An Anisotropic Damage Model for Ductile Metals

2002 ◽  
Author(s):  
Youssef Hammi ◽  
Mark F. Horstemeyer ◽  
Doug J. Bammann
Keyword(s):  
Damage Model ◽  
Ductile Damage ◽  
Damage Effect ◽  
Irreversible Processes ◽  
Plastic Strain Rate ◽  
Fracture Mechanisms ◽  
Anisotropic Damage ◽  
Strain Rate Tensor ◽  
State Variables ◽  
Rate Dependent

An anisotropic ductile damage description is motivated from fracture mechanisms and physical observations in Al-Si-Mg aluminum alloys with second phases. Ductile damage is induced by the classical process of nucleation of voids at inclusions, followed by their growth and coalescence. These mechanisms are related to different microstructural and length scale parameters like the fracture toughness, the void size, the intervoid ligament distance, etc. The classical thermodynamic constraints of irreversible processes with material state variables are used to model the tensorial damage evolution coupled to the Bammann-Chiesa-Johnson (BCJ) rate-dependent plasticity. The damage-plasticity coupling is based on the effective stress concept, assuming the total energy equivalence, and written through a deviatoric damage effect tensor on the deviatoric part and through the trace of the second rank damage tensor on the hydrostatic part. The damage rate tensor is additively decomposed into a nucleation rate tensor, a void growth rate scalar, and a coalescence rate tensor. The induced damage anisotropy is mainly driven by the nucleation, which evolves as a function of the absolute value of the plastic strain rate tensor. Finally, some experimental data of cast A356 aluminum alloy are correlated with predictive void-crack evolution to illustrate the applicability of the anisotropic damage model.

Enhanced CDM model accounting of stress triaxiality and Lode angle for ductile damage prediction in metal forming

2020 ◽  
pp. 105678952095804
Author(s):  
Kai Zhang ◽  
Houssem Badreddine ◽  
Naila Hfaiedh ◽  
Khemais Saanouni ◽  
Jianlin Liu
Keyword(s):  
Constitutive Equations ◽  
Damage Model ◽  
Stress Triaxiality ◽  
Ductile Damage ◽  
Irreversible Processes ◽  
State Variables ◽  
Damage Prediction ◽  
Proposed Model ◽  
Lode Angle ◽  
Fully Coupled

This paper deals with the prediction of ductile damage based on CDM approach fully coupled with advanced elastoplastic constitutive equations. This fully coupled damage model is developed based on the total energy equivalence assumption under the thermodynamics of irreversible processes framework with state variables. In this model, the damage evolution is enhanced by accounting for both stress triaxiality and Lode angle. The proposed constitutive equations are implemented into Finite Element (FE) code ABAQUS/Explicit through a user material subroutine (VUMAT). The material parameters are determined by the hybrid experimental-numerical method using various tensile and shear tests. Validation of the proposed model has been done using different tests of two aluminum alloys (Al6061-T6 and Al6014-T4). Through comparisons of numerical simulations with experimental results for different loading paths, the predictive capabilities of the proposed model have been shown. The model is found to be able to capture the initiation as well as propagation of macro-crack in sheet and bulk metals during their forming processes.

Non-Associative Finite Strain Plasticity Coupled With Anisotropic Ductile Damage for Metal Forming

2012 ◽  
Author(s):  
T. Dung Nguyen ◽  
Houssem Badreddine ◽  
Khémais Saanouni
Keyword(s):  
Strong Coupling ◽  
Constitutive Equations ◽  
Damage Mechanics ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Continuum Damage Mechanics ◽  
Ductile Damage ◽  
Damage Effect ◽  
Irreversible Processes ◽  
State Variables

This paper presents the formulation of an advanced mechanical model describing a wide class of anisotropic elastoplastic constitutive equations accounting for the strong coupling with the anisotropic ductile damage. This model is developed within the framework of thermodynamics of irreversible processes with state variables and the continuum damage mechanics. The plastic anisotropy is accounted for through a non-associative theory for which a plasticity yield criterion and the plastic potential are defined separately but considering the strong coupling between both phenomena. The damage anisotropy is defined by using a second rank tensor. The effect of damage on the mechanical fields (stress, hardening, plastic strain, etc…) is described by a fourth rank damage effect operator that is defined in the context of the hypothesis of total energy equivalence. A rotating frame formulation is used to fulfil the objectivity of the constitutive equations under finite transformation. Finally, in order to illustrate the predictive capabilities of the model, the parametric studies with some simple loading case are investigated and the results discussed on the light of the anisotropic character of the ductile damage and its interaction with the anisotropy of plastic flow.

Modeling of Anisotropic Damage for Ductile Materials in Metal Forming Processes

2002 ◽  
Author(s):  
Youssef Hammi ◽  
Mark F. Horstemeyer ◽  
Doug J. Bammann
Keyword(s):  
Metal Forming ◽  
Ductile Damage ◽  
Fracture Mechanisms ◽  
Anisotropic Damage ◽  
Ductile Metals ◽  
Explicit Finite Element ◽  
Microstructural Parameters ◽  
Fully Implicit ◽  
Rate Dependent ◽  
Second Phases

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 of each mechanism evolution 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 fully implicit scheme and implemented into a explicit finite element code. This implementation is used to predict damage during the forward axisymmetric extrusion of an aluminum bar. This example illustrates the applicability of the model to predict the initiation and the evolution of anisotropic damage in metal forming processes.

Anisotropic ductile damage fully coupled with anisotropic plastic flow: Modeling, experimental validation, and application to metal forming simulation

2014 ◽  
Vol 23 (8) ◽  
pp. 1211-1256 ◽  
Author(s):  
W Rajhi ◽  
K Saanouni ◽  
H Sidhom
Keyword(s):  
Plastic Flow ◽  
Metal Forming ◽  
Kinematic Hardening ◽  
Ductile Damage ◽  
Damage Effect ◽  
Anisotropic Damage ◽  
State Variables ◽  
Energy Equivalence ◽  
Anisotropic Plastic ◽  
Equivalence Assumption

The main goal of this paper is the modeling, numerical simulation, and experimental validation of the anisotropic ductile damage effects on initially anisotropic plastic flow with mixed (isotropic and kinematic) nonlinear hardening under large plastic strains for metal forming processes simulation. A symmetric second-rank damage tensor together with a symmetrized fourth-rank damage-effect tensor is used to describe the anisotropic ductile damage evolution and its effect on the large plastic flow with hardening. Following the concept of effective state variables in the framework of the total energy equivalence assumption, the “Murakami” fourth-rank damage-effect tensor is chosen to describe the anisotropic damage effect on the elastic-plastic behavior including the mixed hardening. The “Lemaitre” ductile anisotropic damage evolution relationships, where the principal directions of the damage rate tensor are governed by those of the plastic strain rate tensor, are used. As difference with the works cited above, the nonlinear mixed isotropic and kinematic hardening is taken into account considering the full and strong damage effects through the effective state variables deduced from the total energy equivalence assumption initially proposed by Saanouni et al. The non-associative plasticity theory is considered, and the “ Hill 1948 ” quadratic (equivalent) stress norm is used to describe the large plastic anisotropic flow accounting for mixed isotropic and kinematic hardening with anisotropic damage effects. The formulation is performed assuming finite plastic strains and small elastic strains through the so-called rotated frame formulation. The obtained model was implemented into ABAQUS/Explicit® FE software thanks to the user’s developed subroutine VUMAT. The numerical aspects related to the time discretization of the fully coupled anisotropic constitutive equations are carefully described. Finally and for the validation purpose, the model is identified using an appropriate experimental data base concerning the grade 316L stainless steel to simulate numerically some metal forming processes.

Modeling of Solder Fatigue Failure due to Ductile Damage

2010 ◽  
Vol 26 (4) ◽  
pp. N23-N27 ◽  
Author(s):  
K. Aluru ◽  
F.-L. Wen ◽  
Y.-L. Shen
Keyword(s):  
Numerical Study ◽  
Fatigue Cracks ◽  
Damage Model ◽  
Quantitative Information ◽  
Ductile Damage ◽  
Element Analysis ◽  
Cyclic Shear ◽  
Rate Dependent ◽  
Solder Fatigue ◽  
Temporal And Spatial

ABSTRACTA numerical study is undertaken to simulate failure of solder joint caused by cyclic shear deformation. A progressive ductile damage model is incorporated into the rate-dependent elastic-viscoplastic finite element analysis, resulting in the capability of simulating damage evolution and eventual failure through crack formation. It is demonstrated that quantitative information of fatigue life, as well as the temporal and spatial evolution of fatigue cracks, can be explicitly obtained.

Damage mechanics characterization on the fatigue behaviour of a solder joint material

2001 ◽  
Vol 215 (8) ◽  
pp. 883-892 ◽  
Author(s):  
C. L. Chow ◽  
F Yang ◽  
H. E. Fang
Keyword(s):  
Solder Joint ◽  
Fatigue Damage ◽  
Damage Mechanics ◽  
Internal State ◽  
Damage Effect ◽  
Irreversible Processes ◽  
State Variables ◽  
Solder Material ◽  
Damage Initiation ◽  
Joint Material

This paper presents the first part of a comprehensive mechanics approach capable of predicting the integrity and reliability of solder joint material under fatigue loading without viscoplastic damage considerations. A separate report will be made to present the comprehensive damage model describing life prediction of the solder material under thermomechanical fatigue (TMF) loading. The method is based on the theory of damage mechanics, which makes possible a macroscopic description of the successive material deterioration caused by the presence of microcracks/voids in engineering materials. A damage mechanics model based on the thermodynamic theory of irreversible processes with internal state variables is proposed and used to provide a unified approach in characterizing the cyclic behaviour of a typical solder material. With the introduction of a damage effect tensor, the constitutive equations are derived to enable the formulation of a fatigue damage dissipative potential function and a fatigue damage criterion. The fatigue evolution is subsequently developed on the basis of the hypothesis that the overall damage is induced by the accumulation of fatigue and plastic damage. This damage mechanics approach offers a systematic and versatile means that is effective in modelling the entire process of material failure, ranging from damage initiation and propagation leading eventually to macrocrack initiation and growth. As the model takes into account the load history effect and the interaction between plasticity damage and fatigue damage, with the aid of a modified general-purpose finite element program, the method can readily be applied to estimate the fatigue life of solder joints under different loading conditions.

Application of an efficient anisotropic damage model to the prediction of the failure of metal forming processes

2019 ◽  
Vol 28 (10) ◽  
pp. 1556-1579 ◽  
Author(s):  
Ali Salehi Nasab ◽  
Mohammad Mashayekhi
Keyword(s):  
Constitutive Equations ◽  
Metal Forming ◽  
Kinematic Hardening ◽  
Ductile Damage ◽  
Irreversible Processes ◽  
Anisotropic Damage ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Integration Schemes ◽  
Return Mapping Algorithm

The main objective of this study is the numerical implementation of an advanced elastic–plastic model fully coupled with anisotropic ductile damage. The implemented formulation has been defined in the framework of thermodynamics of irreversible processes and a symmetric second-order tensor is adopted to describe the anisotropic damage state variable. After a summary of the main constitutive equations is given, the numerical integration of constitutive equations is performed using implicit and asymptotic integration schemes. Finite element simulation is performed using ABAQUS/Explicit software and the developed VUMAT subroutine. Next, the application of the developed model to T-shaped hydroforming of tubes and square-cup deep drawing metal forming processes is thoroughly discussed and failure onset zones due to anisotropic ductile damage growth are predicted and the results were consistent with the literature. Finally, by making an assumption that kinematic hardening can be ignored, an elastic predictor/plastic corrector algorithm requiring the solution of one equation is introduced. The assessment of the developed one-equation return-mapping algorithm is carried out by applying it to the simulation of the tensile test of a pre-notched bar. The Central Prossessing Unit time decreases noticeably using one-equation return mapping algorithm compared to the conventional return mapping algorithm and the numerical results are in good agreement with previous numerical simulations and experiments.

Validation of Modified Lemaitre’s Anisotropic Damage Model with the Cross Die Drawing Test

2011 ◽  
Vol 488-489 ◽  
pp. 49-52 ◽  
Author(s):  
M.S. Niazi ◽  
H. H. Wisselink ◽  
T. Meinders
Keyword(s):  
Strain Rate ◽  
Automotive Industry ◽  
Damage Model ◽  
Anisotropic Damage ◽  
Rate Dependency ◽  
Damage Models ◽  
Rate Dependent ◽  
Drawing Test ◽  
Dp Steels ◽  
The Cross

Dual Phase (DP) steels are widely replacing the traditional forming steels in automotive industry. Advanced damage models are required to accurately predict the formability of DP steels. In this work, Lemaitre’s anisotropic damage model has been slightly modified for sheet metal forming applications and for strain rate dependent materials. The damage evolution law is adapted to take into account the strain rate dependency and negative triaxialities. The damage parameters for pre-production DP600 steel were determined. The modified damage models (isotropic and anisotropic) were validated using the cross die drawing test. The anisotropic damage model predicts the crack direction more accurately.

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