A model for the axisymmetric growth and coalescence of small internal voids in elastoplastic solids is proposed and assessed using void cell computations. Two contributions existing in the literature have been integrated into the enhanced model. The first is the model of Gologanu-Leblond-Devaux, extending the Gurson model to void shape effects. The second is the approach of Thomason for the onset of void coalescence. Each of these has been extended heuristically to account for strain hardening. In addition, a micromechanically-based simple constitutive model for the void coalescence stage is proposed to supplement the criterion for the onset of coalescence. The fully enhanced Gurson model depends on the flow properties of the material and the dimensional ratios of the void-cell representative volume element. Phenomenological parameters such as critical porosities are not employed in the enhanced model. It incorporates the effect of void shape, relative void spacing, strain hardening, and porosity. The effect of the relative void spacing on void coalescence, which has not yet been carefully addressed in the literature. has received special attention. Using cell model computations, accurate predictions through final fracture have been obtained for a wide range of porosity, void spacing, initial void shape, strain hardening, and stress triaxiality. These predictions have been used to assess the enhanced model. (C) 2000 Elsevier Science Ltd. All rights reserved.

An extended model for void growth and coalescence

Publisher Summary An important failure mechanism in ductile metals and their alloys is by growth and coalescence of microscopic voids. In structural materials, the voids nucleate at inclusions and second-phase particles by decohesion of the particle–matrix interface or by particle cracking. Void growth is driven by plastic deformation of the surrounding matrix. Early micromechanical treatments of this phenomenon considered the growth of isolated voids. Later, constitutive equations for porous ductile solids were developed based on homogenization theory. Among these, the most widely known model was developed by Gurson for spherical and cylindrical voids.

/pdf/ductile-fracture-by-void-growth-to-coalescence-3rgsgx2sfa.pdf

Ductile Fracture by Void Growth to Coalescence

An extended model for void growth and coalescence - application to anisotropic ductile fracture

The past 20 years have seen substantial work on the modeling of ductile damage and fracture. Several factors explain this interest. (i) There is a growing demand to provide tools which allow to increase the efficiency of structures (reduce weight, increase service temperature or load, etc.) while keeping or increasing safety. This goal is indeed first achieved by using better materials but also by improving design tools. Better tools have been provided which consist (ii) of material constitutive equations integrating a physically-based description of damage processes and (iii) of better numerical tools which allow to use the improved constitutive equations in structural computations which become more and more realistic. This article reviews the material constitutive equations and computational tools, which have been recently developed to simulate ductile rupture.

/pdf/continuum-models-of-ductile-fracture-a-review-35khqjinf0.pdf

Continuum Models of Ductile Fracture: A Review

The past 20 years have seen substantial work on the modeling ofductile damage and fracture Several factors explain this interest (i) There is agrowing demand to provide tools which allow to increase the efficiency of structures(reduce weight, increase service temperature or load, etc) while keeping or increasingsafety This goal is indeed first achieved by using better materials but also byimproving design tools Better tools have been provided which consist (ii) of materialconstitutive equations integrating a physically-based description of damage processesand (iii) of better numerical tools which allow to use the improved constitutiveequations in structural computations which become more and more realistic Thisarticle reviews the material constitutive equations and computational tools, whichhave been recently developed to simulate ductile ruptureKEY WORDS: ductile rupture, models, numerical simulation INTRODUCTION P REDICTIVE NUMERICAL SIMULATIONS of ductile fracture may be ofgreat interest in industrial situations for which full-scale experimentalapproaches are either too costly or even impracticable This is the case ofductile tearing of gas pipelines over several hundred meters, of crackpropagation in large nuclear vessels or of ductile tearing of aircraft fuselageFor such applications, simulations should predict crack paths, stability,stress states, etc Several techniques may be used to achieve these objectivesThe approach based on Rice (1968) J-integral is widely used for industrialapplications but suffers from various limitations: (i) It can only deal withpreexisting cracks and cannot be applied to model crack initiation and pro-pagation from a notch (ii) It is not a material intrinsic property asit stronglydepends on specimen geometry as experimentally shown in Sumpter and

Three-dimensional micromechanical models were developed to study the damage by void growth in ductile materials. Special emphasis is given to the influence of the spatial arrangement of the voids. Therefore, periodical void arrays of cubic primitive, body centered cubic and hexagonal structure are investigated by analyzing representative unit cells. The isotropic behaviour of the matrix material is modelled using either v. Mises plasticity or the modified Gurson-Tvergaard constitutive law. The cell models are analyzed by the large strain finite element method under monotonic loading while keeping the stress triaxiality constant. The obtained mesoscopic deformation response and the void growth of the unit cells show a high dependence on the value of triaxiality. The spatial arrangement has only a weak influence on the deformation behaviour, whereas the type and onset of the plastic collapse behaviour are strongly affected. The parameters of the Gurson-Tvergaard model can be calibrated to the cell model results even for large porosity, emphasizing its usefulness and justifying its broad applicability.

Three-dimensional cell model analyses of void growth in ductile materials

Compared with conventional fracture mechanics concepts, constitutive equations which account for local damage of the material have the advantage that the corresponding material parameters for ductile fracture can be transferred between different specimen geometries. They will hence be able to describe the physical effect of constraint on the tearing resistance in a natural way. The paper shows the capabilities of the GURSON model in predicting J R -curves for different specimen geometries under static and dynamic loading with one set of material parameters. It is shown how these parameters can be determined from the numerical simulation of simple tensile tests. Problems and open questions are discussed and perspectives for future applications are given.

Application of the Gurson model to ductile tearing resistance

Dynamic tensile tests and instrumented impact tests with Charpy-V-notch specimens and precracked Charpy specimens (SENB) are performed and simulated. Two strain-rate dependent micromechanical models based on the modified Gurson flow function are compared by simulating different dynamically loaded specimens. One purpose of the study is to investigate the influence of strain rate on the parameters of the micromechanical models and thus to check the applicability of these models for dynamic loading. Another purpose is to find out the relation between the micromechanical approach and conventional fracture mechanics. The results indicate that the critical void volume fraction f c and the characteristic length l c are practically independent of strain rate and specimen geometry. The deformation and fracture behavior of the Charpy-V and SENB specimens can be well calculated with the parameters determined from a dynamic tensile test and a static fracture mechanics test. The tunneling of the crack in the interior of the Charpy specimen is predicted in a satisfactory way by a three-dimensional analysis with the strain-rate dependent Gurson model.

Application of Micromechanical Models to the Analysis of Ductile Fracture Under Dynamic Loading

Different micromechanical material models were applied to simulate ductile fracture and creep damage. Ductile fracture behaviour of different specimens was analysed by using the modified Gurson model which is based on physical descriptions of micromechanisms of ductile fracture characterized by nucleation, growth and coalescence of voids. Due to the transferability of micromechanical parameters between different geometries and loading situations this model has been used to extend the fracture mechanics data base of an irradiated weld material. In contrast to the J-integral concepts the modified Gurson model can be employed to assess the initiation and propagation behaviour of a crack at the interface of two different materials like ferrite and austenite, with large gradients of the properties at the fusion line. A new material model for creep damage is a combination of the Rodin and Parks model and the viscoplastic model of Robinson. It contains a strain controlled evolution law for the damage parameter ρ. The material parameters were fitted to different creep curves. The application of the model to different specimens shows a good agreement between the predictions and the experiments.

Dong-Zhi Sun

Papers

Three-dimensional cell model analyses of void growth in ductile materials

Application of the Gurson model to ductile tearing resistance

Application of Micromechanical Models to the Analysis of Ductile Fracture Under Dynamic Loading

Development and application of micromechanical material models for ductile fracture and creep damage

Characterization and modeling of damage behavior of a casting aluminum wheel considering inhomogeneity of microstructure and microdefects