Gurson Damage Model Research Articles

Effects of superimposed hydrostatic pressure on fracture in sheet metals under tension

The effect of superimposed hydrostatic pressure on fracture in sheet metals under plane strain tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that the superimposed hydrostatic pressure p has no noticeable effect on necking but significantly increases the fracture strain due to the fact that a superimposed pressure delays or completely eliminates the nucleation, growth and coalescence of microvoids or microcracks. The experimentally observed transition of the fracture surface, from P-type mode under atmospheric pressure to C-type mode under high pressure, is numerically reproduced.

Effects of superimposed hydrostatic pressure on fracture in round bars under tension

The effect of superimposed hydrostatic pressure on fracture in round bars under tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that while the superimposed hydrostatic pressure has no noticeable effect on necking, it increases the fracture strain due to the fact that a superimposed pressure delays or completely eliminates the nucleation, growth and coalescence of microvoids or microcracks. The experimentally observed transition of the fracture surface, from the cup-cone mode under atmospheric pressure to a slant structure under high pressure, is numerically reproduced. It is numerically proved that the superimposed hydrostatic pressure has no effect on necking for a damage-free round bar under tension.

Transferability of the Gurson Damage Model Parameters with Charpy and Tensile Tests with Different Constrain Level

Little work has been published concerning the transferability of Gurson’s ductile damage model parameters in specimens tested at different strain rates and in the rolling direction of a Grade A ship plate steel. In order to investigate the transferability of the damage model parameters of Gurson’s model, tensile specimens with different constraint level and impact Charpy specimens were simulated to investigate the effect of the strain rate on the damage model parameters of Gurson model. The simulations were performed with the finite element program ABAQUS Explicit [1]. ABAQUS Explicit is ideally suited for the solution of complex nonlinear dynamic and quasi–static problems [2], especially those involving impact and other highly discontinuous events. ABAQUS Explicit supports not only stress–displacement analyses but also fully coupled transient dynamic temperature, displacement, acoustic and coupled acoustic–structural analyses. This makes the program very suitable for modelling fracture initiation and propagation. In ABAQUS Explicit, the element deletion technique is provided, so the damaged or dead elements are removed from the analysis once the failure criterion is locally reached. This simulates crack growth through the microstructure. It was found that the variation of the strain rate affects slightly the value of the damage model parameters of Gurson model.

Effects of superimposed hydrostatic pressure on sheet metal formability

The effect of superimposed hydrostatic pressure on sheet metal formability is studied analytically and numerically. A tensile sample of power-law hardening material under superimposed hydrostatic pressure is first analyzed using the classical isotropic plasticity theory. It is demonstrated that the superimposed hydrostatic pressure p lowers the true tensile stress level at yielding by the amount of p, while material work-hardening is independent of p. It is showed, based on the Considère criterion, that the superimposed hydrostatic pressure increases the uniform strain. The effect of superimposed hydrostatic pressure on sheet metal formability is further assessed by constructing the Forming Limit Diagram (FLD) based on the M-K approach. It is found that the superimposed pressure delays the initiation of necking for any strain path. The difference in predicted FLDs between the superimposed hydrostatic pressure and the stress component normal to the sheet plane is demonstrated. Finally, the effect of superimposed hydrostatic pressure on fracture in round bars under tension is studied numerically using the finite element method, based on the Gurson damage model. The experimentally observed transition of the fracture surface, from the cup-cone mode under atmospheric pressure to a slant structure under high pressure, is numerically reproduced.

Study of Damage Mechanism on Aluminum Alloy under Two Kinds of Stress States and FEM Simulation

In order to study the damage mechanism under different stress states of aluminum alloy components, two kinds of representative triaxial stress states were adopted, namely notch tensile and pure shear. The results of study showed: During the notch tensile test, stress triaxiality in the least transverse-section was relatively higher. With increasing applied stress, the volume fraction of the microvoid in notch root was increasing constantly. When microvoid volume fraction reached the critical value, the specimen fractured. During the pure shear test, stress triaxiality almost came up to zero, and there was almost no micro-void but localized shear bands within the specimen. The shear bands resulted from non-uniform deformation constantly under the shear stress. With stress concentrating, the cracks were produced in the shear bands and later coalesced. When the equivalent plastic strain reached the critical value, the specimen fractured. The modified Gurson damage model and the Johnson-Cook model were used to simulate the notch tensile and shear test respectively. Simulated engineering stress-strain curves fit the measured engineering stress-strain curves very well. In addition, the empirical damage evolution equation for the notch specimen was obtained from the experiment data and FEM simulations.

Characterization and Modeling of Aluminum Extrusion Damage Under Crash Loading

This paper studied the deformation and damage behaviors of aluminum-alloy under different loadings. A series of static and dynamic plate tension tests, notch tension tests and shear tests were carried out and were combined with the finite element model to acquire material parameters. This work demonstrated that damage behavior of aluminum-alloy depends strongly on stress triaxiality and cannot be modeled with simple damage models based on one constant fracture strain. A systematic investigation shows that the micromechanical Gurson damage model and phenomenological Johnson–Cook model can be used to simulate crash behavior of aluminum components. The tests on an aluminum component of extrusion under static loading were performed and simulated to validate the applicability of Gurson damage model. Since damage parameters depend on element size, the component calculation was performed with the calibrated parameters optimized with the element sizes.

Numerical investigation of ductile tearing in surface cracked pipes using line-springs

Accurate prediction of crack-driving force equations is important in any pipeline fracture assessment program. In highly ductile materials, such as pipeline steel, a considerable amount of stable crack growth can be tolerated before the failure of the structure. The existing methods use simplified analytical procedures to account for ductile tearing, and they often result in conservative critical crack sizes. Further, none of the published numerical tools for modelling crack growth is suitable for engineering applications. This work describes a simple method for simulating through-thickness ductile tearing in surface cracked pipes, using line-spring finite elements. The crack growth resistance curve is used to advance the crack front. The line-spring results are verified using crack growth simulations employing the Gurson damage model. Finally, a detailed parametric study is carried out to examine the effect of ductile tearing on crack driving force relationships in circumferentially surface cracked pipes. The results demonstrate that considering ductile tearing is important in fracture assessment procedures for pipelines.

Comparison between Lemaitre and Gurson damage models in crack growth simulation during blanking process

In this paper, the numerical results obtained by a finite element analysis in the case of sheet metal blanking process are compared with the experimental ones to verify the validity of Gurson and Lemaitre damage models in describing the initiation and propagation of cracks during the process evolution. The concept of continuum damage mechanics has been retained to describe the progressive damage accumulation into the sheet metal leading to the final rupture. During the analysis, the crack propagation is simulated by the propagation of a completely damaged area. The comparative study of the results obtained by simulations using different damage models and experimental ones, showed that Gurson damage model is not able to predict the fracture propagation path in a realistic way. Only Lemaı̂tre damage model gives good results.

Material behaviour law identification for the various zones of the spot-weld under quasi-static loadings

The aim of this paper is to predict by FE simulation the non-linear behaviour and rupture of spot-welded assemblies subjected to quasi-static loadings and to show the feasibility of numerical works. The three material zones of the spot-weld (metal base, melted zone and heat affected zone) are analysed and studied on a metal sheet assembly structured 0.7/0.7mm Experimental works based on tensile-shear, cross-tensile and peeling tests are done, as well as a numerical sensitivity analysis on the three material zones. Different fracture modes are put into evidence. A methodology to identify the material behaviour law of the MB, HAZ and MZ is proposed. The rupture of the spot-welded structure is simulated with the help of the Gurson damage model. The damage parameters of the MB and HAZ are identified through an inverse method on the basis of tensile-shear and cross-tensile tests. The numerical/experimental comparison on the various applied quasi-static loadings validates this methodology.

Crack analysis in ductile cylindrical shells using Gurson's model

Damage evolution in cracked cylindrical shells subjected to uniform pressure is numerically simulated using finite 3D-continuum elements. The ductile material behaviour of mild steel is described in terms of the Gurson damage model. To represent the stress and damage distribution across the wall thickness, three element layers normal to the shell surface were used. The description of finite plasticity is based on the multiplicative split of the deformation gradient. The numerical method is applied to investigate damage evolution, crack initiation and growth in a tube under pressure containing an axial and a circumferential through-crack.

The calculation of dynamic JR-curves from the finite element analysis of a Charpy test using a rate-dependent damage model

A two-dimensional analysis of the Charpy V-notch specimen subjected to impact loading, according to the standard DIN EN 10045-1, is carried out, using a transient explicit dynamic finite element program. An elastic-viscoplastic, temperature dependent, constitutive relation for a porous plastic solid based on the Gurson damage model is developed. Ductile fracture of the matrix material will be described by the nucleation and subsequent growth of voids to coalescence. An updated Lagrange–Jaumann formulation is employed accounting for large strain and rotation. The discretization is based on four-node plane strain solid elements with one Gauss point. The equations of motion are integrated numerically by an explicit integration algorithm utilising a lumped mass matrix. The predictions of the numerical analysis in terms of force deflection response, crack resistance behaviour and deformation energy absorbtion are compared with results from Charpy tests which were carried out according to the low-blow technique.

Damage and strain localisation during crack propagation in thin-walled shells

Based on the GURSON damage model a simulation of ductile crack growth in thin-walled shell structures is presented. The proposed Finite Element model for shells is based on a 5-parameter theory taking bending effect into acount. The problem of mesh dependence in strain softening materials is treated by a non-local regularisation of the damage evolution equation. As an example a cylindrical tube under internal pressure is considered. Results for the equivalent stress, the equivalent strain and the damage parameter are shown.