Modified Gurson Model Research Articles

A macroscopic viscoelastic viscoplastic constitutive model for porous polymers under multiaxial loading conditions

A macroscopic constitutive model, the Porous Eindhoven Glass Polymer (Porous EGP) model, is presented to describe the deformation behavior of cavitated rubber toughened polymers under multiaxial loading conditions. It is shown that the proposed macroscopic constitutive model is able to describe the non-linear pre-yield regime, strain rate dependence, post-yield behavior (strain softening and hardening) and void evolution for loading conditions ranging from shear to equi-triaxial (pure triaxial) tension and compression. The Porous EGP model is a combination of a well established non-linear viscoelastic viscoplastic model, the Eindhoven Glassy Polymer (EGP) model, and the modified Gurson model. The Gurson model is adopted to determine the equivalent stress and plastic rate of deformation tensor making it depending on the void volume fraction, deviatoric and hydrostatic stress. The macroscopic constitutive model is developed based on the response of realistic 3D representative volume elements (RVEs) containing randomly positioned mono-disperse inclusions. The constitutive behavior of the matrix phase in this full-field model is described by the EGP model, and the cavitated inclusions are idealized as voids. Their response is studied for a range of void volume fractions, multiaxial loading conditions, strain rates and thermodynamic states. The yield behavior of the heterogeneous material depends non-linearly on the macroscopic hydrostatic stress. This response is well captured with the proposed macroscopic constitutive model.

Experimental and computational analysis of the in situ tensile deformation of 2D honeycomb lattice structures in Ni single crystals

A ~12 μm thick film of single crystal Ni was shaped with a focused ion beam (FIB) instrument to form a set of tensile samples with hexagonal holes of sides ~3 μm long and ~2.5 μm thick arranged in a honeycomb lattice structure. The plane normal of the film was <001> and the tensile axis was parallel to <100>. The samples were then tested in tension in situ inside a scanning electron microscope. The tensile properties, viz., yield strength and peak strength observed in the lattice sample, were higher than those of a standard sample by about 30%, while the strain to fracture decreased drastically. Finite element (FE) modelling, utilising size effect corrections and the modified Gurson model, was performed to elucidate the response of the microlattice, and it was found that the changes in the mechanical properties could be explained by the stress distribution around the hexagonal holes and localised sample size effects. These models were corroborated by observations of the crystal orientation using electron backscatter diffraction (EBSD) maps. The assumption of void formation as a mechanism of failure in the Gurson model was validated experimentally by transmission electron microscopy, which showed nano-voids in the thin bands formed by localised slip.

Gurson-based modelling of ductile damage and failure during cyclic loading processes at large deformation

Purpose is the formulation, numerical implementation, identification and application of a material model for ductile damage and failure during cyclic and non-proportional loading. The authors combined a hyperelasticity-based elasto-plastic model for non-linear isotropic as well as kinematic hardening with a modified Gurson model. Evolution strategy helped identify the model parameters for the high-strength steel 10MnMoNi5-5. The simulation of ductile failure in fracture mechanics specimens verified the model with respect to cyclic loading at two temperatures. The simulation of additional fracture mechanics applications validated the model as to the development of residual stresses at the crack tip under cyclic loads.

Modified Gurson Model to Describe Non-linear Compressive Behaviour of Polyurethane Foam with Considering Density Effect

Polyurethane Foam(PUF), a outstanding thermal insulation material, is used for various structures as being composed with other materials. These days, PUF composed with glass fiber, Reinforced PUF(R-PUF), is used for a insulation system of LNG Carrier and performs function of not only the thermal insulation but also a structural member for compressive loads like a sloshing load. As PUF is a porous material made by mixing and foaming, mechanical properties depend on volume fraction of voids which is a dominant parameter on density. Thus, In this study, density is considered as the effect parameter on mechanical properties of Polyurethane Foam, and mechanical behavior for compression of the material is described by using modified Gurson damage model.

Parametric Study of Edge Crack of Silicon Steel Strip in Cold Rolling based on a Shear Modified GTN Damage Model

Edge cracking is a commonly observed phenomenon during the cold rolling process of the silicon steel strip which may cause the rupture of strip and reduce the product quality and productivity. In this work, the damage behavior and edge cracking of steel strip in cold rolling is analyzed based on a shear modified Gurson model. Taguchi experimental design method is used to analyze the effects of reduction ratio, roll diameter, tension, friction coefficient on the initiation and propagation of edge cracks. The analysis results reveal that the possibility of edge crack for silicon steel increases with the increasing of reduction ratio, tension, friction coefficient and the decrease of roll diameter.

Use of a modified Gurson model for the failure behaviour of the clinched joint on Al6061 sheet

ABSTRACTThis paper discusses the ductile fracture behaviour of the clinched joint on Alloy 6061 sheets. Failure behaviour of the clinched joint is associated with the nucleation, growth and coalescence of voids within the microstructure. Various corrections to the original Gurson model are proposed to allow for instability and final fracture of the material. This paper is concerned with the application of the modified Gurson–Tvergaard–Needleman damage developed by Ken Nahshon and Zhenyu Xue. The results of the tension tests are compared with those of numerical analysis to obtain the initial void volume fraction f0 and the shear damage coefficients kw. The modified Gurson–Tvergaard–Needleman model is used to describe the failure behaviour and the shear strength of the clinched joint. Good agreement is shown between the experiment results and the numerical results on the location of fracture and the maximum failure load.

Implementation and Validation of a Gurson Damage Model Modified for Shear Loading: Effect of Void Growth Rate and Mesh Size on the Predicted Behavior

The optimization of automotive security components requires good knowledge of the material state after fabrication, particularly with respect to damage that may have been done to the material by the manufacturing process. To achieve this, numerical simulation of the fabrication process is often undertaken. However, classical continuum damage models, like the Gurson [3] model, are not appropriate for the simulation of the blanking by punching operation because the material damage is primarily the result of shear stresses. This work is focused on the use and validation of a modified Gurson type damage model capable of modeling this process, which has recently been proposed by Nahshan [7]. After a brief description of the modification, the implementation and the validation of the modified Gurson model is detailed. A comparison between the original Gurson model and the modified model is presented in order to highlight the importance of the modification for a pure shear stress state and to show that the two models are equivalent for a purely hydrostatic stress state. It is also shown that the results from the modified model are dependent on the finite element mesh size.

APPLICATION OF DAMAGE MODEL WITH MATERIAL FLOW EVALUATION TO HIGH TEMPERATURE COMPRESSION PROCESSES

Mechanisms of ductile failure in a compression process are studied, based on micro-structural considerations, with analytical and experimental investigations performed on a cylindrical specimen. Geometrical softening is able to occur by void if the shear band is generated inside of materials. The original Gurson model is used to analyze tensile deformation, and a modified Gurson model is proposed, which incorporates damage accumulation under shear and compression. This modified Gurson model is also applied to the void closure of sintered material under compression loading. However, the compressed materials must be considered in both the void nucleation and closure, because the void is nucleated and closed at a specific angle. The results of individual analyses of nucleation and closure do not agree with observations, but the analysis considered here, of both the nucleation and closure of a void, corresponds well with experimental results.

The Effect of Random Voids in the Modified Gurson Model

The porous plasticity model (usually referred to as the Gurson–Tvergaard–Needleman model or modified Gurson model) has been widely used in the study of microvoid-induced ductile fracture. In this paper, we studied the effects of random voids on the porous plasticity model. Finite-element simulations were conducted to study a copper/tin/copper joint bar under uniaxial tension using the commercial finite-element package ABAQUS. A randomly distributed initial void volume fraction with different types of distribution was introduced, and the effects of this randomness on the crack path and macroscopic stress–strain behavior were studied. It was found that consideration of the random voids is able to capture more detailed and localized deformation features, such as different crack paths and different ultimate tensile strengths, and meanwhile does not change the macroscopic stress–strain behavior. It seems that the random voids are able to qualitatively explain the scattered observations in experiments while keeping the macroscopic measurements consistent.

Strength analysis of metallic bonded joints containing defects

Finite element simulation has been utilized to study the overall strength of metallic single lap joints with defects in their adhesive layers. Three types of defects are taken into account respectively, which are local debonding, weak bonding and void. For the first two types of defects, a developed numerical method using the cohesive zone model modified by user-defined subroutines is carried out as to consider the influences of the defect size and location. Furthermore, a modified-Gurson model is employed to simulate the adhesive layer with voids, considering the influence of the void size. The results show that the overall strength of the joints diminishes as the defect size is increased. Especially, the adhesive fracture properties and the size of the weak bonding region have combined influences on the strength of the joints.

A Yield Criterion for Pressure-Sensitive Materials

Following the modified Gurson model in meso-mechanics, the models with spherical holes are established by the assumption which the matrix meets the two-parameter elliptic yield condition. The macroscopic stress expression which contains micro structure parameters and the material equation of yield surface are given by the upper bound theorem of plastic limit analysis. The parameters of the matrix material and damage(porosity) which impact on macroscopic yield surface equation are discussed. These works provide theory foundations for material damage and design.

AUTOMATED CALIBRATION OF A VOID CLOSURE MODEL FOR HIGH-TEMPERATURE DEFORMATION

The so-called Gurson model is a well-established micromechanical model of the ductile fracture of porous materials, where the mechanism is void nucleation, growth and coalescence. Although the Gurson model, and particularly its modified form developed by Tvergaard and Needleman, is widely used, its application to void closure has received relatively little attention. The first objective of the current work is to explore the applicability of the Gurson model to void closure. The fixed parameters characterizing the modified Gurson model are not universal and must be calibrated for a particular material, typically by trial and error fitting of finite element (FE) simulations to experimental data. However, the trial and error approach is expensive and time consuming (one test generally corresponds to only one triaxiality level). A novel approach has been developed in the present work to identify the void closure model parameters using a nongradient based optimization search method (pattern search method). Rather than using experimental data for void closure, a series of finite element analyses, one of a representative volume element (RVE) containing a spherical void, and another with an equivalent cell of Gurson–Tvergaard (GT) material, has been performed. Both models have parametric characterizations, enabling simulations under different triaxialities and initial void volume fractions. The numerical results of the discrete void RVE and the GT cell can then be compared and model parameters identified. The new automated method was applied using material properties obtained from high temperature tensile testing of Telby plus steel at 900°C and 1100°C, temperatures in the range of those experienced during a typical steel rolling process. The effect of strain rate on void closure is also investigated using this approach for Telby plus steel.

Use of a modified Gurson model approach for the simulation of ductile fracture by growth and coalescence of microvoids under low, medium and high stress triaxiality loadings

Abstract In the paper the modified Gurson model is developed for the simulation of damage growth and ductile fracture under low, medium and high stress triaxiality loadings. A new coalescence criterion is introduced based on a simple assumption that singular value of the effective stress triggers the coalescence of microvoids in materials. According to the introduced approach the void coalescence described by means of the modified Gurson model is not only determined by the so-called critical, constant void volume fraction but also by the stress triaxiality ratio. Computational simulations have been carried out for Al 2024–T351 aluminum specimens. In order to find some improvements of micromechanical damage models, two different approaches have been compared for modeling the shear driven microvoid coalescence under low stress triaxiality loadings.

Ductile shear failure or plug failure of spot welds modelled by modified Gurson model

For resistance spot welded shear-lab specimens, interfacial failure under ductile shearing or ductile plug failure are analyzed numerically, using a shear modified Gurson model. The interfacial shear failure occurs under very low stress triaxiality, where the original Gurson model would predict void nucleation and very limited void growth. Void coalescence would therefore be largely postponed. However, using the shear modification of the Gurson model, recently introduced by Nahshon and Hutchinson (2008) [1], failure prediction is possible at zero or even negative mean stress. Since, this shear modification has too large effect in some cases where the stress triaxiality is rather high, an extension is proposed in the present study to better represent the damage development at moderate to high stress triaxiality, which is known to be well described by the Gurson model. Failure prediction and tensile response curves for an interfacial shear failure or a ductile plug failure, are here compared when using either the original Gurson model, the shear modified model, or the extension to the shear modified model. The suggested extension makes it possible to use the shear modified model as a simple way of accounting for damage development under low triaxiality shearing, without further increasing the damage rate in regions of moderate to high stress triaxiality.

Yield Criteria for Pressure-Sensitive Materials Based on Meso-Mechanical Analysis

Investigation on mechanical properties of rock, soil and powder metallurgy is an important subject in study of damage constitutive models. These materials contain micro-voids (such as defects, inclusions and cracks) and perform pressure sensitivity. Unlike metal materials, hydrostatic pressure can influence plastic yield of these materials. Following the modified Gurson model in meso-mechanics and considering the meso-compressibility, this paper focuses on plastic limit analysis of micro-deformation mechanism of these materials. The two-independent-parameters criterion is taken as matrix yield function and spherical voids as the represent unit cell. The macroscopic stress and strain rate related to micro structure parameters are derived via upper-bound theorem. Then the macroscopic yield function (containing micro structure parameters) is established. Finally, the properties of macroscopic yield surfaces are studied by setting different values of these micro parameters. This paper provides theory foundations for materials damage and design.

Studies on Micro- to Macroscopic Mechanical Behavior of Porous Polymer under Compaction

The 2D extended homogenization model based on molecular chain network theory is employed to investigate the micro-to macroscopic mechanical behavior of polymer with randomly distributed voids under macroscopic compaction. A parametric study is performed to quantify the effect of the volume fraction of voids and the macroscopic stress triaxiality of loading conditions on the compaction behavior of porous polymer. The results suggest that the onset of localized shear band at the ligament between voids leads to the macroscopic yield of porous polymer. Furthermore, the microscopic localized shear deformation behavior is promoted in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which results in the early appearance of the macroscopic yield. After the macroscopic yield, a remarkable strain hardening is shown in the macroscopic response of porous polymer under high macroscopic stress triaxiality loading condition, which is due to the onset and propagation of a large number of shear bands at the ligaments between voids. On the other hand, microscopic buckling develops at the narrowest ligament in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which leads to the relative low macroscopic deformation resistance. Furthermore, to develop the macroscopic constitutive model of polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, a modified Gurson model is proposed which takes account of microscopic buckling and gives a good agreement with the unit cell computational results.

A modified Gurson model and its application to punch-out experiments

Recent experimental evidence has reiterated that ductile fracture is a strong function of stress triaxiality. Under high stress triaxiality loading, failure occurs as a result of void growth and subsequent necking of inter-void ligaments while under low stress triaxiality failure is driven by shear localization of plastic strain in these ligaments due to void rotation and distortion. The original Gurson model is unable to capture localization and fracture for low triaxiality, shear-dominated deformations unless void nucleation is invoked. A phenomenological modification to the Gurson model that incorporates damage accumulation under shearing has been proposed. Here we further extend the model and develop the corresponding numerical implementation method. Several benchmark tests are performed in order to verify the code. Finally, the model is utilized to model quasi-static punch-out experiments on DH36 steel. It is shown that the proposed modified Gurson model, in contrast to the original model, is able to capture the through-thickness development of cracks as well as the punch response. Thus, the computational fracture approaches based on the modified Gurson model may be applied to shear-dominated failures.

Effect of a shear modified Gurson model on damage development in a FSW tensile specimen

For a friction stir welded aluminum plate the resistance to ductile failure is studied by analyzing tensile test specimens cut out across the weldline. As the stress triaxiality is rather low in these tests, the Gurson material model is not expected to give a very accurate description of the void growth to coalescence. A recently proposed modified version of the Gurson model is used, in which an extra term in the damage evolution law allows for the prediction of failure even at zero or negative values of the mean stress. This modification of the Gurson model is purely phenomenological, such that the damage parameter does not really represent the void volume fraction. Various amounts of the additional damage evolution are compared with predictions of the original Gurson model. The analyses are carried out for different yield stress profiles transverse to the weld and for different specimen widths. It is found that the modification does provide additional damage development in the friction stir weld, which may help to fit experimental data. But the suggested modification depends strongly on the overall stress state, and may have a too strong effect in some cases where the stress triaxiality is rather high.

On yield criteria in plasticity coupled with damage

The coupling of elasto-plasticity and damage is still the subject of many papers, namely in the construction of evolution laws for internal parameters. In this paper we propose to partly overcome some difficulties by using the only basic fact that a plastic-damaged body is made up of two physical constituents, namely the matrix material and the micro-defects. The elasto-plastic matrix material is the resisting skeleton connecting the elements of the body and the micro-defects bring their own contributions to reversible and irreversible strains. Naturally strong couplings exist between the stress states of the body and the matrix material. These considerations will lead to generalisations and new formulations of the so-called equivalence principles and a new equivalence principle will be proposed. Finally, concerning the irreversible strains due to both plasticity of the matrix and growing of micro-defects, we will prove that yield conditions must be used simultaneously on the body as well as on the matrix, leading to some non-smooth resultant yield-damage surface. The modified Gurson model for porous material is then analysed in order to illustrate this last point. In this paper, large strains are considered, but time-dependant plasticity and thermal effects are excluded.

A simplified canonical form algorithm with application to porous metal plasticity

AbstractA canonical form for the representation of material constitutive equations within standard finite element codes has been developed which is deceptive in its simplicity. Substitution of different equation systems is trivial and a consistent material Jacobian may be obtained automatically. The process is essentially numerical and does not involve the difficult algebraic manipulation associated with more traditional approaches. It is nevertheless exact because partial derivatives are derived analytically and simple because calculation of these derivatives is the only algebraic manipulation required. The remainder of the process is generic. In this paper, the algorithm is simplified further. A much more detailed and transparent explanation of the key to the method is given, namely calculation of the consistent Jacobian. A trivial modification also extends the method to plane stress. The original algorithm was validated for a simple material model. The new form is used to implement the significantly more difficult modified Gurson model for porous metal plasticity with hydrostatic yield dependence. It is tested for single element cases involving total collapse and also used to simulate necking of a notched cylindrical bar. Copyright © 2005 John Wiley &amp; Sons, Ltd.