Lemaitre Ductile Damage Research Articles

Numerical investigation and experimental validation of Lemaitre ductile damage model for DC04 steel and application to deep drawing process

Numerical investigation and experimental validation of Lemaitre ductile damage model for DC04 steel and application to deep drawing process

Presenting an explicit step-by-step algorithm for lemaitre's ductile damage model with the crack closure effect in tensile-compressive loadings

Continuum damage mechanics (CDM) studies the deterioration of mechanical properties in materials that leads to material failure. The Lemaitre’s ductile damage model is known as a suitable criterion for damage growth in ductile materials. The standard Lemaitre’s model cannot accurately predict the damage growth in most of bulk metal forming processes with a combination of tension and compression loadings. In this paper, first, an explicit step-by-step algorithm of the Lemaitre’s ductile damage model conjugated with the crack closure effect in compressive loadings is provided and directly presented for the computational implementations. Then, employing the proposed algorithm, a user-defined material subroutine is developed and implemented. In the following, a few bulk metal forming processes under compressive loadings are numerically simulated. Finally, the numerical simulation results are compared with the prediction results of the standard model and also experimental tests. The comparison confirms the high precision of the modified model vs. the standard model. Hence, it is concluded that the modified Lemaitre’s model can truly predict the damage behavior of ductile materials in bulk metal forming processes with combined tensile and compressive loadings.

A simple and accurate method for numerically determining the Lemaitre’s damage parameter in ductile metals

Damage is a progressive physical process that results in fracture. Recently, study of damage and failure in materials, particularly ductile metals has been of great importance for mechanical and structural engineers. So far, numerous criteria have been presented to predict damage behavior in ductile metals, each criterion is known by its advantages, disadvantages, and accuracy. One of the most famous models has been proposed by Lemaitre which is an accurate model and requires only one parameter to attain damage behavior of materials. In this article, employing the Lemaitre's ductile damage criterion, a new explicit, simple, and quick method is suggested to numerically determine the Lemaitre's damage parameter and damage behavior of ductile metals. This approach is much easier and cheaper than former conventional experimental methods because only needs a simple standard tensile test. Accuracy of the current numerical approach is validated through the experimental tests such as the standard, single and double notched tensile tests, and also the Nakazima fracture test. The numerical simulation results show suitable accuracy together with negligible percentage of error and perfect correlation in comparison with the experimental results.

Damage modeling of unidirectional laminated composites

This work deals with the existence of representative volume element (RVE) for unidirectional laminated composites (with and without preexisting cracks). The RVE existence in elastic regime is studied employing periodic boundary conditions for uniaxial and shear loadings separately. RVE does exist in elastic regime for materials having discrete cracking. The numerical simulations for different sizes of RVE are performed keeping the fiber volume and crack volume fractions constant. It is observed that the elastic response is independent of RVE dimension. The RVE validity in softening regime is studied by Lemaitre ductile damage model within matrix phase.

Anisotropic effects in the compression beading of aluminum thin-walled tubes with rubber

The purpose of this paper is to study numerically the “elastomer-assisted compression beading” (EACB process). It consists of conventional compressing beading after a local bulging carried out by an elastomer material. A Finite Element Method (FEM) is introduced to predict where and when the damage can occur in the tube and to study the effects of anisotropy on the occurrence of failure by cracking in regions where damage is accumulated. An anisotropic elasto-plastic constitutive model with mixed non-linear isotropic/kinematic hardening fully coupled with Lemaitre's ductile damage is implemented in ABAQUS/Explicit software via VUMAT subroutine. The influence of anisotropy on the damage evolution is investigated in this study and results are compared with isotropic model.

A Procedure for Ductile Damage Parameters Identification by Micro Incremental Sheet Forming

Incremental sheet forming is an important process that allows versatile parts without specific tools [1]. The micro-incremental sheet forming process (μSPIF) is the miniaturization of the classical single point incremental sheet forming process (SPIF). After a brief presentation of the specific properties of the μSPIF process, the ability of this technique to identify the ductile damage properties of the material under severe deformation process is presented [2].μSPIF is then investigated as a method to identify the material parameters of a Lemaitre's ductile damage evolution law. The identification procedure is based on the comparison between numerical simulations of μSPIF tests [3] and experimental data [4]. The error function to be minimized is initially computed as a L2-norm of the error between numerical and experimental forming forces, then after extended by full field measurements.A parameter sensitivity analysis of the numerical model is performed. An identifiability method, based on that proposed by Richard et al. [5] for indentation tests is used to quantify the influence of each data and demonstrate the meaningful mechanical properties obtained.Different numerical tests (line tests, indentation tests, truncated shape, Meuwissen tests and Out-of-Plane testing procedure by T. Pottier [6]) are also investigated.

Numerical Prediction of the Forming Limit Diagrams of Thin Sheet Metal using SPIF Tests

Sheet metal formability is usually limited by the occurrence of damages evolution, leading to a localized necking failure. The Forming Limit Diagram (FLD) is widely used for characterizing the formability of metal sheets.This paper aims to predict numerically the forming limit diagram using the 3D simulations of the micro-Marciniak tests with different width. A conventional Lemaitre ductile damage model with isotropic hardening is used to predict the strain hardening and the necking point. The identification of the ductile damage model is first performed from micro-single point incremental forming tests using inverse finite element method. Then, the micro-forming limit curves in terms of strain and stress are plotted in the major/minor strain space and major/minor stress space, respectively. Finally, the effect of the initial grain size on the forming limit curves is investigated.

Numerical prediction of springback and ductile damage in rubber-pad forming process of aluminum sheet metal

Rubber forming is a sheet metal forming process using flexible punch or die. In this paper, finite element method is introduced to analyze rubber-pad forming process of aluminum sheet metal. An elasto-plastic constitutive model with J2 yield criterion and mixed non-linear isotropic/kinematic hardening coupled with Lemaitre's ductile damage has been adopted during flexible forming operation. To model rubber material, a Mooney-Rivlin theory is used in the finite element simulation. A stamping of aluminum sheet metal with soft punch is simulated. A fully coupled elasto-plastic damage model is implemented in ABAQUS/Standard software via UMAT subroutine to study the effect of some key process parameters like hardness of rubber, type of rubber on the variation of the thickness, the springback and damage of aluminum sheet metal.

Using the finite cell method to predict crack initiation in ductile materials

In this paper, the Finite Cell Method (FCM) is used to predict the crack evolution in ductile materials under small strains and nonlinear isotropic hardening conditions. The FCM is the result of combining the p-version finite element and fictitious domain methods, and has been shown to be effective in solving problems with complicated geometries for which the meshing procedure can be quite expensive. The crack evolution is introduced to the constitutive equations by using the simplified Lemaitre ductile damage model. The performance of the method is verified by means of two numerical examples in both 2D and 3D problems.

Damage driven crack initiation and propagation in ductile metals using XFEM

Originally Continuum Damage Mechanics and Fracture Mechanics evolved separately. However, when it comes to ductile fracture, an unified approach is quite beneficial for an accurate modelling of this phenomenon. Ductile materials may undergo moderate to large plastic deformations and internal degradation phenomena which are well described by continuum theories. Nevertheless in the final stages of failure, a discontinuous methodology is essential to represent surface decohesion and macro-crack propagation. In this work, XFEM is combined with the Lemaitre ductile damage model in a way that crack initiation and propagation are governed by the evolution of damage. The model was built under a finite strain assumption and a non-local integral formulation is applied to avoid pathological mesh dependence. The efficiency of the proposed methodology is evaluated through various numerical examples.

Numerical Prediction of Forming Limit in Hemispherical Punch Bulging by Lemaitre's Ductile Damage Model

Prediction of sheet metal forming limits or analysis of forming failures is a very sensitive problem for design engineers of sheet forming industries. In this paper, first, damage behaviour of St14 steel (DIN 1623) is studied in order to be used in complex forming conditions with the goal of reducing the number of costly trials. Mechanical properties and Lemaitre's ductile damage parameters of the material are determined by using standard tensile and Vickers micro-hardness tests. A fully coupled elastic-plastic-damage model is developed and implemented into an explicit code. Using this model, damage propagation and crack initiation, and ductile fracture behaviour of hemispherical punch bulging process are predicted. The model can quickly predict both deformation and damage behaviour of the part because of using plane stress algorithm, which is valid for thin sheet metals. Experiments are also carried out to validate the results. Comparison of the numerical and experimental results shows good adaptation. Hence, it is concluded that finite element analysis in conjunction with continuum damage mechanics can be used as a reliable tool to predict ductile damage and forming limit in sheet metal forming processes.

Ductile crack growth based on damage criterion: Experimental and numerical studies

The continuum mechanical simulation of the microstructural damage process is important in the study of ductile fracture mechanics. In this paper, the continuum damage mechanics framework for ductile materials developed by Lemaitre has been validated experimentally and numerically for A533-B1 alloy steel under triaxial stress conditions. An experimental procedure to identify the damage parameters was established and the experimental calibrated damage parameters were then used in a finite element model. A fully coupled constitutive elastic–plastic-damage model has been developed and implemented inside the ABAQUS implicit FEA code. The model is based on a simplified Lemaitre ductile damage model whose return mapping stage requires the solution of only one scalar non-linear equation. A local crack growth criterion based on the critical damage parameter was proposed; the validity of this criterion was examined by comparing the simulation with the experimental results on standard three point bending (3PB) test. The critical load at crack growth initiation and the fracture toughness, J Ic, has also been predicted from the simulation. These numerically predicted values compared favourably with those obtained from experiments.

Finite element prediction of ductile fracture in sheet metal forming processes

In this contribution, Lemaitre's ductile damage model is coupled with Hill's orthotropic plasticity criterion. The coupling between damaging and material behaviour is accounted for within the framework of Continuum Damage Mechanics (CDM). The resulting constitutive equations are implemented in the Abaqus/Explicit code, for the prediction of fracture onset in sheet metal forming processes. The damage evolution law takes into account the important effect of micro-crack closure, which dramatically decreases the rate of damage growth under compressive paths.

A fast, one‐equation integration algorithm for the Lemaitre ductile damage model

AbstractThis paper introduces an elastic predictor/return mapping integration algorithm for a simplified version of the Lemaitre ductile damage model, whose return mapping stage requires the solution of only one scalar non‐linear equation. The simplified damage model differs from its original counterpart only in that it excludes kinematic hardening. It can be used to predict ductile damage growth whenever load reversal is absent or negligible—a condition met in a vast number of practical engineering applications. The one‐equation integration scheme proves highly efficient in the finite element solution of typical boundary value problems, requiring computation times comparable to those observed in classical von Mises implementations. This is in sharp contrast to the previously proposed implementations of the original model whose return mapping may require, in the most general case, the solution of a system of 14 coupled algebraic equations. For completeness, a closed formula for the corresponding consistent tangent operator is presented. The performance of the algorithm is illustrated by means of a numerical example. Copyright © 2002 John Wiley & Sons, Ltd.