No abstract

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 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 high dependence on the value of triaxiality. The spatial arrangement has only 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 ce ll model results even for large porosity, emphasizing its usefulness and justifying its broad applicability

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 JR-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.

Two damage models were implemented into the finite element program ADINA to study the correlation between microscopical damage and macroscopical material failure. In the first model, based on the Gurson yield function the nucleation, growth and the coalescence of voids were incorporated into the constitutive relations. In the second model the void growth was determined according to the Rice and Tracey model using the von Mises yield function, and material failure was simulated by eliminating the elements where the critical void growth ratio was exceeded. The numerical results for the local and global behaviour of the specimens were compared with experiments. The generality of the damage parameters was checked by investigating several specimen geometries. Both damage models deliver qualitatively consistent results with regard to the influence of the stress triaxiality on the void growth and on the beginning of the material failure. However, the Gurson model gives a more accurate numerical simulation because the damage development and the stress drop continue after the onset of void coalescence while the critical void growth model causes less convergence problems in the simulation of large crack extension. The J,-curve was estimated on the basis of both models. NOMENCLATURE a = crack length Aa = crack extension Ad = change of diameter B, D = coefficients for void nucleation E = elastic modulus E, = current tangent modulus cF, = equivalent plastic strain tN = mean strain for void nucleation f = void volume fraction f , = critical void volume fraction at void coalescence ff = void volume fraction at rupture f N = volume fraction of void forming particles fa = initial void volume fraction f,, = coefficient for void coalescence G = shear modulus J = J-integral K =bulk modulus tij = strain tensor q , = coefficient in Gurson yield condition R = void radius R, = initial void radius p = notch radius S , = standard deviation ue = equivalent stress u . = Cauchy stress tensor 8: = Jaumann stress rate tensor urn = flow stress of the material uy = yield stress of the material u, = maximum principal stress ukk,3 = mean stress 20 I 202 D.-Z. SUN et al.

The ductile fracture behavior of different specimens is analyzed by continuum damage-mechanics techniques. A model introduced by Gurson and modified by Needleman and Tvergaard has been implemented in the finite element program package, ADINA. The damage parameters of the model are measured and calculated from smooth tension tests, and the characteristic material distance is estimated from compact tension experiments. A steel, ASTM A710, and a weld metal for the steel, ASTM A508, are investigated. The damage parameters determined from the smooth bars are used to predict the deformation and fracture behavior of notched round bars and of sidegrooved compact specimens. For the weld metal, a side-grooved WOL-X-specimen is also simulated. In every case, a satisfactory agreement of prediction and experiment is observed. In order to investigate the influence of the stress state (constraint) in cracked specimens, a series of numerical computations of different specimen geometries and loading situations is performed utilizing the same set of parameters of the ASTM A710 steel. The slopes of the predicted J-resistance curves increase with increasing ratio of tension versus bending load and with decreasing relative crack length.