Gurson-Tvergaard-Needleman Research Articles

A lower bound damage-based finite element simulation of stretch flange forming of Al–Mg alloys

Numerical simulation of stretch flange forming of Al–Mg sheet AA5182 was performed using the upper and lower bound constitutive models of Gurson–Tvergaard–Needleman (GTN) and Sun and Wang, respectively. Stress and strain-controlled nucleation rules are adopted for both models. The lower bound model of Sun and Wang has been extended to include the void coalescence criterion of Tvergaard and Needleman to form the so-called Sun–Tvergaard–Needleman (STN) model. Upper and lower bound formability predictions are combined to create a predictive formability band as actual formability lies between these limits. The resulting formability predictions are compared with experimental results and an appropriate void nucleation stress and strain suggested.

Numerical simulations of specimen size and mismatch effects in ductile crack growth – Part I: Tearing resistance and crack growth paths

The Gurson–Tvergaard–Needleman (GTN) model has been used for detailed numerical simulations of the effects of specimen size and yield stress mismatch on ductile crack growth behaviour in two different finite specimen geometries. For deep cracked bending specimens the crack growth resistance, expressed through the far-field J, increases as the specimen size is reduced, most strongly seen in case of low hardening. An opposite effect can be seen to some extent for shallow cracked specimens loaded in tension for low and intermediate hardening. For the yield stress mismatch cases low hardening and bend loading are found to promote crack growth deviation away from the initial crack plane.

A Micromechanical Model for Ductile Fracture of API X65

This paper presents a micro-mechanical model of ductile fracture for the API X65 steel, using the Gurson-Tvergaard-Needleman (GTN) model. Experimental tests and FE damage simulations using the GTN model are performed for smooth and notched tensile bars with three different notch radii, from which micromechanical parameters in the GTN model are calibrated. The calibrated micro-mechanical model is applied to quantify pre-strain effects on plastic deformation and fracture of the API X65 steel. Good agreements of the FE damage results with experimental data suggest confidence in the use of the proposed micro-mechanical model to simulate ductile failure of pipelines made of API X65 steels.

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.

Yield Functions for Porous Materials with Cubic Symmetry Using Different Definitions of Yield

AbstractPlastic yield criteria for porous ductile materials are explored numerically using the finite‐element technique. The cases of spherical voids arranged in simple cubic, body‐centred cubic and face‐centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple‐cubic and body‐centred cubic arrays – in contrast to the famous Gurson‐Tvergaard‐Needleman (GTN) formula – while there is no such dependence for face‐centred cubic arrays within the accuracy of the finite‐element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield‐function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body‐centred and face‐centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.

Damage-Based Finite Element Modeling of Stretch Flange Forming of Aluminium-Magnesium Alloy

The numerical simulation of the stretch flange forming operation of Al-Mg sheet AA5182 was conducted with an explicit finite element code, LS-DYNA. A Gurson-Tvergaard- Needleman (GTN)-based material model was used in the finite element calculation. A strain controlled void nucleation rule was adopted with void nucleating particle fraction measured directly from the as-received Al-Mg sheet. Parametric study was performed to examine the effect of void nucleation strain on the predicted onset of ductile fracture. Critical porosity levels determined through quantitative metallurgical analysis were adopted to predict the commencement of void coalescence in the GTN model. The numerical results were compared to the experimental ones and an applicable void nucleation strain was suggested.

Influence of Surface Defect Geometry on the Localization and Failure of AA6111 Sheet: Necking versus Shear

The influence of surface defect geometry on the localization and failure behaviour of AA6111 sheet has been investigated through experimentation and numerical modelling. A series of uniaxial tensile samples were produced with idealized top and bottom surface defects (i.e. grooves), located either symmetrically or asymmetrically on the opposing surfaces. The symmetric arrangement corresponds to the “groove-like” initial imperfection of the classical Marciniak- Kuczyński (M-K) model. Experimental results indicate that both the symmetry of the defects and their wavelength have a profound effect on the resulting mode of localization and failure as well as on the limit strains. Specifically, symmetric surface defects are seen to induce localization and failure through simple necking, whereas asymmetric defects tend to promote macroscopic, throughthickness shearing. Furthermore, asymmetric surface defect geometries are found to produce lower limit strains in the AA6111 sheet under study for defect wavelengths below about 1.5 mm, while the reverse is true when defect wavelengths are above 1.5 mm. Finite element method (FEM) modelling simulations are also presented, demonstrating that the experimentally-observed trends in localization and failure behaviour can be replicated using a mixed isotropic-kinematic hardening implementation of the Gurson-Tvergaard-Needleman (GTN) material model.

Yield criterion of porous materials subjected to complex stress states

Finite-element simulations are used to obtain many thousands of yield points for porous materials with arbitrary void-volume fractions with spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic three-dimensional arrays. Multi-axial stress states are explored. We show that the data may be fitted by a yield function which is similar to the Gurson–Tvergaard–Needleman (GTN) form, but which also depends on the determinant of the stress tensor, and all additional parameters may be expressed in terms of standard GTN-like parameters. The dependence of these parameters on the void-volume fraction is found.

Crack Extension at an Interface: Prediction of Fracture Toughness and Simulation of Crack Path Deviation

Ductile tearing of laser welded Al sheets is studied both experimentally and numerically. The mechanical behaviour and the microstructure of the various zones of the weld are characterised. Mechanical tests on compact tension (C(T))-specimen are carried out, with the position of the initial crack in the heat affected zone. Due to the asymmetry of the configuration, crack path deviation towards the softer fusion zone is observed. The topography of the non-planar fracture surface is measured using laser equipment. This work is focussed on the prediction of the fracture resistance and the simulation of crack path deviation for the respective configuration. The numerical simulations are based on two different models for ductile damage: the micromechanical Gurson–Tvergaard– Needleman (GTN) model and the phenomenological cohesive model. In the case of the GTN-model, the crack front may follow an arbitrary path. In contrast, the crack propagation direction for the cohesive model is prescribed by the morphology of the finite element mesh. The GTN-model is used to investigate crack path deviation and to derive limits for simplifications used together with the cohesive approach. The latter allows for a cost-efficient 2D simulation. Good agreement between experimental results and numerical simulations could be achieved in all cases

Modelling of the Charpy Impact Test in the DBTT Range

The finite element method was used in order to compute the energy balance and the stress-strain distribution in the Charpy V-notch specimen. Inertial effects were taken into account by a fully dynamic computation. It was shown that inertial oscillations are damped by viscoplasticity ahead the notch and vanish rapidly. 3D modelling is needed since large scale yielding and ductile crack growth occur. The ductile crack front is curved, which is important to account for in order to correctly describe the stress distribution in the specimen. Ductile crack growth in Charpy specimen was predicted by the GTN (Gurson-Tvergaard-Needleman) model. The GTN model allows a good failure prediction with strain rate and temperature independent damage parameters.

A penny-shaped cohesive crack model for material damage

A novel micromechanics based damage model is proposed to address failure mechanism of defected solids with randomly distributed penny-shaped cohesive micro-cracks (Barenblatt–Dugdale type). Energy release contribution to the material damage process is estimated in a representative volume element (RVE) under macro hydrostatic stress state. Macro-constitutive relations of RVE are derived via self-consistent homogenization scheme, and they are characterized by effective nonlinear elastic properties and a class of pressure sensitive plasticity which depends on crack opening volume fraction and Poisson’s ratio. Several distinguished features of the present model are compared with Gurson model and Gurson–Tvergaard–Needleman (GTN) model, showing that the proposed model can better capture material degradation and catastrophic failure due to cohesive micro-crack growth and coalescence.

Using incremental forming to calibrate a void nucleation model for automotive aluminum sheet alloys

A novel method for the quantification of void nucleation rates in sheet material is presented. An incremental sheet forming process is employed to create large regions of homogeneous deformation, such that material density changes can then be used to quantify the evolution of void volume fraction with applied strain. This technique is employed to calibrate the void nucleation behaviour of three automotive aluminum sheet alloys (AA5182, AA5754 and AA6111) for incorporation into finite element method models which employ the Gurson–Tvergaard–Needleman (GTN) constitutive softening equations.

The influence of iron content on the bendability of AA6111 sheet

The effect of iron (Fe) level on the bendability of three Fe-variants of AA6111 sheet (i.e. 0.06, 0.26 and 0.68 wt.% Fe) is investigated using an instrumented cantilever bend test (CBT) apparatus. The tests are also simulated in a finite element method (FEM) model which employs a isotropic–kinematic hardening version of the Gurson–Tvergaard–Needleman (GTN) constitutive softening equations. Experimentally, increasing Fe content level is found to decrease bendability. This trend is attributed to an increasing volume fraction of void-nucleating particles, particularly within first-order clusters, and is demonstrated by a series of GTN-based FEM model predictions.

Prediction of ductile fracture initiation using micromechanical analysis

In the paper ductile fracture initiation analysis of low-alloyed ferritic steel has been made by application of two micromechanical models: the Rice–Tracey void growth model and the Gurson–Tvergaard–Needleman (GTN) model. The aim of the study was to analyse transferability of micromechanical parameters determined on specimens without initial crack to pre-cracked specimens. A significant part of the research has been carried out through participation in the round robin project organised by the European Structural Integrity Society (ESIS). Tensile tests have been performed on cylindrical smooth specimens and CT specimens. Critical values of micromechanical parameters determined on smooth specimen for both applied models, have been used for prediction of the crack growth initiation in CT specimen. Modelling of the first phase of ductile fracture––void nucleation––has been carried out using quantitative metallographic analysis of non-metallic inclusion content in tested steel. For determination of critical values of model parameters corresponding to ductile fracture initiation a simple procedure has been applied based on a combination of experimental and numerical results. Evaluated J-integral values corresponding to onset of crack growth, J i, are in good agreement with experimental result and both models have proved to be suitable for determination of the ductile fracture initiation in tested steel. The effect of FE size at a crack tip on J i-value has been particularly analysed: it has been established that the calculation with FE size corresponding to the mean free path λ between inclusions in steel gives results that are in accordance with the experimental ones.

The co-operative role of voids and shear bands in strain localization during bending

The use of kinematic hardening is known to promote shear band formation as a result of increased yield surface curvature. Hence, the implementation of kinematic hardening in a Gurson-type model facilitates the combined effect of shear bands and voids on strain localization behaviour. An alternative formulation of the kinematic hardening Gurson–Tvergaard–Needleman (GTN) constitutive softening equations is presented herein. The resulting equations are implemented as a user material subroutine (umat) in the commercial finite element code LS-DYNA and the implementation is verified against published results. A numerical study is used to establish the role of various GTN parameters in the development of macroscopic shear localization during bending.

Void coalescence within periodic clusters of particles

The effect of particle clustering on void damage rates in a ductile material under triaxial loading conditions is examined using three-dimensional finite element analysis. An infinite material containing a regular distribution of clustered particles is modelled using a unit cell approach. Three discrete particles are introduced into each unit cell while a secondary population of small particles within the surrounding matrix is represented using the Gurson–Tvergaard–Needleman (GTN) constitutive equations. Deformation strain states characteristic of sheet metal forming are considered; that is, deep drawing, plane strain and biaxial stretching. Uniaxial tensile stress states with varying levels of superimposed hydrostatic tension are also examined. The orientation of a particle cluster with respect to the direction of major principal loading is shown to significantly influence failure strains. Coalescence of voids within a first-order particle cluster (consisting of three particles) is a stable event while collapse of inter-cluster ligaments leads to imminent material collapse through void-sheeting.

The Gurson-Tvergaard-Needleman-model for rate and temperature-dependent materials with isotropic and kinematic hardening

Based on the upper bound solution of cell models under dynamic or creep loading conditions, the Gurson-Tvergaard-Needleman (GTN) constitutive law of ductile fracture for rate and temperature-dependent materials with isotropic and kinematic hardening has been established. Two additional parameters, which account for the influences of strain rate, inertia and the average distance between voids, have been introduced in the GTN yield criterion. 2D and 3D analysis has been performed for different metals. It can be concluded that the GTN model is a powerful tool for crack growth analysis.