Growth of Spheroidal Voids in Elastic‐plastic Solids

Abstract

The effect of void shape on the mechanical behaviour of an elastic-plastic solid containing an isotropic array of aligned axisymmetric voids is examined. The mechanical response of such a material is studied by means of finite element (FE) analyses of an elementary unit cell containing an isolated void. The void shape is found to have a strong influence on both void growth rate and coalescence strain. This effect is strongest for low stress triaxialities. The numerical results are compared with analytical models of void growth, but none of the examined models give any good predictions of the results obtained numerically. A simple modification of the classical Gurson model is suggested so as to give reasonable correspondence with numerical results. Finally, some practical considerations of void shape effects are given. NOMENCLATURE a, h = radial and axial semiaxes of a spheroidal void e , , e2 = eccentricities of spheroidal void and unit cell, respectively E = Young's modulus f = void volume fraction h =initial derivative of void aspect ratio with respect to mesoscopic effective strain F,, F3 = radial and axial loading on the cell model H' = uniaxial plastic hardening rate (= 86/88') k, , k, = spring rates Lo. H , = radius and half height of material unit cell n, N =hardening exponents qi. q2 =parameters for the Gurson model Q, = void growth magnification factor S, = mesoscopic (global) deviatoric stress tensor T = stress triaxiality factor (= Z,,/C,) x l , xj, xg = cylindrical coordinates u,, u3 = displacements of the edges of cell model W = void aspect ratio (= b/a) 8, =reference strain rate Ef, = average effective plastic strain rate in the matrix qe = mesoscopic (global) effective strain @ = plastic potential K, m2, ZH = variables in the Gologanu et al. model 8, E, 6, = uniaxial stress, strain and yield stress, respectively Ze, Zh = mesoscopic (global) effective and hystrostatic stress Zij, qi, = mesoscopic (global) stress and strain tensor uM = matrix flow stress (averaged) 8 = stress proportionality factor (= ,Ell/ ,E33)Currently with Hydro Raufoss

Anisotropic ductile fracture of Al 2024 alloys

“…For an initially oblate void (W 0 = 1/6), the cell collapses at a much lower effective strain compared to the same cell including a prolate cavity of the same volume. Note that this result is in agreement with the results in [12,31]. As a consequence, elongated voids, W 0 > 1, with respect to the main loading direction, weaken a material less and cause delayed fracture compared to oblate ones, if the initial void volume fraction is the same in both cases.…”

Void growth and coalescence in f.c.c. single crystals

“…As noted in Hutchinson [10], the application of void growth prediction based on the conventional plasticity to micron-sized voids is probably unjustified. In addition, earlier studies on the void growth in ductile medium [2,8,[11][12][13][14][15][16][17] assumed the surrounding matrix material to be isotropic. However, the strong anisotropic response of single crystals cannot be predicted by the conventional plasticity model [18].…”

“…Voids nucleated by matrix cavitation, cracking of the second phase and debonding at the interface between the matrix and the second phase are generally micron-or submicron-sized [1,[7][8][9]. As noted in Hutchinson [10], the application of void growth prediction based on the conventional plasticity to micron-sized voids is probably unjustified.…”

Recent Trends in the Development of Gurson’s Model

“…As indicated in Eqs. (37a) and (37b), the necessity of decreasing the value of q for increasing n had already been recognized by several authors (e.g., Koplik and Needleman [7], Søvik and Thaulow [33]). The effect of the stress triaxiality ratio T on the factor q, that is included in Eq.…”