Effects of material rate sensitivity and void nucleation on fracture initiation in a circumferentially cracked bar
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I.
INTRODUCTION
THE present study is aimed at providing a qualitative understanding of the nature of the crack tip stress and deformation fields in an axisymmetric fracture specimen. We examine the effect of material rate sensitivity and void nucleation and growth on fracture initiation. The analysis is motivated by the dynamic fracture experiments of Costin et af.l3l and Couque et al.[I) at Brown University. The accuracy of the method was initially assessed by Nakamura et al., [4) who carried out a small strain finite element analysis using a rate-independent Jzflow theory model of plasticity. They performed both static and dynamic calculations using the stress strain curves for 1020 hot rolled steel (HRS) steel described by Costin et al. 13l In the present analysis, we choose a rate-dependent version of Gurson's model (Gurson l2 ) and Pan et alyl) which allows for progressive microrupture through void nucleation and growth. The nucleation of voids is taken to be strain controlled. The material parameters are chosen to be representative of mild structural steel, and in order to facilitate comparison with detailed finite strain calculations of other fracture specimens, we take the values used by Tvergaard and Needleman l6l in their analysis of a Charpy specimen. Since in the experiment the applied pulse is long compared to the specimen geometry, we restrict attention to quasi-static analysis in the present study. However, rate effects are investigated by carrying out an analysis at 106 times the reference quasi-static strain rate. An outline of the remainder of the paper follows. In Section II, we describe the constitutive model and illustrate its behavior for the case of plane strain tension with different levels of triaxiality and strain rate. In the present paper, we confine ourselves to what is termed straincontrolled void nucleation. In this, it is assumed that voids
B. MORAN, Assistant Professor, is with the Department of Civil Engineering, Northwestern University, Evanston, IL 60208. R.J. ASARO, Professor, is with the Department of AMES, University of Califomia~San Diego, La Jolla CA 92093. C.F. SHIH, Professor, is with the Division of Engineering, Brown University, Providence, RI 02912. Manuscript submitted January 26, 1990. METALLURGICAL TRANSACTIONS A
nucleate over a range of critical plastic strains. Straincontrolled nucleation is used especially for the purpose of analyzing the experiments of Couque et al.11] In those experiments, it was noted that the kinematics of ductile rupture at the level of microvoid nucleation and growth were very similar for the quasi-static and dynamic tests. This suggested to us that a strain-controlled void nucleation model would be an appropriate starting point. A note on the finite element implementation is given in Section III. In Section IV, we discuss a finite strain implementation of the domain integral method for evaluating the J-integral along an axisymmetric crack front. The results of the finite element calculations are presented in Section V. We conclude with
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