3D-simulation of ductile crack growth

3D-simulation of ductile crack growth H. Baaser and D. Gross Institutfur Mechanik, Technische Universitdt Darmstadt, Hochschulstr. 1- 64289 Darmstadt, Germany Email: baaser® coulomb.mechanik. tu-darmstadt. de Abstract Based on GlJRSON's damage model a simulation of ductile crack growth in three-dimensional CT-specimens is presented. After de- scribing the 3D finite element formulation and some computational aspects related to the multiplicative split of the deformation gradi- ent and the integration of the constitutive equations, we discuss the regularisation method used involving a characteristic length. Several problems which occur while solving the global FE-problem, are men- tioned and are overcome by a new "node-skipping-technique". A computational example shows the efficiency of the method. 1 Damage Model The damage model proposed by GURSON in [5] and modified in [8] is based on the experimental obsevation, that ductile failure pro- cesses consist of the nucleation, the growth and the coalescence of microvoids. The volume fraction / of the voids is choosen as a damage parameter. The GURSON yield function considering this process may be written as $=( —) + 2fcrcc*h^.+(*/*)-1 = 0, (1) . 6&K where a^ = (^SijSijY^ is the equivalent stress, Sij = &ij — \a the stress de viator, /* the effective void volume fraction (see [8]), q^ — 1.5 a material parameter and <JM the current yield stress of the matrix material. Note that the yield function is reduced to the classical v. MiSES yield function, if /* vanishes. In this formulation the total strain increment e is related to the deformation velocity tensor d described in section 2.1, eqn. (7). As described there, it is assumed that the total strain increment can be Transactions on Modelling and Simulation vol 22, © 1999 WIT Press, www.witpress.com, ISSN 1743-355X

3D-simulation of ductile crack growth

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ductile cracks

cracking

3d finite element

nucleation

void volume fraction