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I.

INTRODUCTION

T H E presence of inclusions and second-phase particles limits the ductility of structural metals. Voids nucleated by decohesion or by cracking of second-phase particles grow and coalesce to form the fracture surface, l~-41 Particles which are softer than or have strength comparable to the matrix material frequently are deformed during forming operations such as forging or rolling. Voids nucleated from severely flattened particles behave with a crack-like character when stressed in particular orientations. This leads to anisotropy in the fracture behavior as evidenced by tension tests on specimens cut from various orientations in rolled plate. The ductility of specimens tested in the through-thickness direction is less than the ductility of those tested in the longitudinal or long transverse directions. Experiments on steels containing sulfide inclusions t5'6] have shown that, for metals which fail by microvoid coalescence, this anisotropy in ductility is due largely to the anisotropy of the inclusions in the plate. Many analytical and numerical models have been employed to study void nucleation and growth and its relation to ductility. Most of these models deal with initially spherical voids. Analytical and finite element models which have examined initially spheroidal and elliptical voids indicate that the void shape alters void growth r a t e s . [7'8'91 In light of these results, modifications to the Gurson r~~ constitutive relation were proposed which account for void shape effects on void growth for proportional strain histories, tlq The modified constitutive model was used in bifurcation analyses similar to those of Yamamoto [121 and Saje, Pan, and Needleman [131to illustrate the shape effects on ductility. In the present study, the effect of void shape on void growth rates and ductility was examined using finite eleR. B E C K E R , Senior Engineer, R.E. SMELSER, Scientific Associate, and O. R I C H M O N D , Corporate Fellow, are with the Alumin u m C o m p a n y of America, Alcoa Center, P A 15069. E.J. A P P L E B Y is the Director of Information Services at Saint Vincent College, Latrobe, PA 15650. Manuscript submitted June 1, 1981. METALLURGICAL TRANSACTIONS A

ment models of arrays of initially spheroidal voids. These analyses continued the previous work of Appleby, Smelser, and Richmond. L14] The material characterization and void morphology were taken from the uniaxial tension experiments of Speich and Spitzig. tSl For those experiments, axisymmetric specimens were cut from cross-rolled plate with the tensile axis coinciding with the through-thickness direction of the plates. Since approximately equal reductions were taken in each of the cross-rolling directions, the shape of the deformed inclusions was approximately an oblate spheroid with the short semiaxis in the tensile direction. This permitted modeling the inclusions as axisymmetric. The present model assumed that the voids nucleated at the inclusions at the outset of deformation. The loading conditions applied to the models s