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I.

INTRODUCTION

THE ductile fracture process of metals has been well established[1,2,3] as divided into three stages: (1) nucleation of microvoids, (2) growth of microvoids, and (3) link-up of microvoids. Any factor that provides resistance or assistance in each stage may also have an influence on toughness and ductility. From the microstructural viewpoint, secondphase particles play an important role on the fracture process. They are classified as (1) inclusions; (2) intermediate particles (or dispersoids); and (3) precipitates depending on their size. Inclusions are the most important factor among the three types of dispersed phase affecting toughness and ductility. Their influence on ductility was studied by Edelson and Baldwin[4] by using powder metallurgy to produce different copper dispersion alloys in which the variation of fracture strain with volume fraction was obtained. An equation for particle cracking stress and an equation for the relationship between fracture strain and volume fraction were derived by Gurland and Plateau[5] in studying the ductile rupture of Al-13Si alloy, Armco iron, and a pearlitic steel. The fracture of cementite particles in a spheroidized 1.05 pct C steel was also studied by Gurland.[6] Fiber-loading and dislocation pileup mechanisms were used in accounting for the influence of shape and orientation of particles on particle cracking. A model for ductile rupture was developed by Hahn and Rosenfield.[1] A relationship, KlC } f21/6, was derived to coordinate with existing data for high-strength steels and aluminum alloys. Regarding the general behavior relating to particle cracking, several features may be summarized, as follows:[1,6] (1) the stress required for particle cracking decreases as particle size increases; (2) the cracking of particles seldom occurs before yielding, but it occurs after the onset of plastic deformation;

JIEN-WEI YEH, Professor, is with the Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu, 30043 Taiwan, Republic of China. WEN-PIN LIU, Associate Professor, is with the Department of Mechanical Engineering, Chengshiu Junior College of Technology and Commerce, Kaoshung, 83305 Taiwan, Republic of China. Manuscript submitted April 15, 1996. 3558—VOLUME 27A, NOVEMBER 1996

(3) the number of particles cracked increases as the strain or stress increases; (4) most of the cleavage planes tend to be perpendicular to the tensile axis; and (5) longish particles crack more easily than spherical particles. As for the crack-initiation theory for particles, many models have been proposed.[5,7–17] However, the basis of each theory was different. These models could be grouped into three categories: (1) stress criterion, (2) strain criterion, and (3) energy criterion. Furthermore, they differ in their mechanics. That is, some models derived cracking equations in continuum mechanics, and other models derived cracking equations in dislocation theory. Under such a variety, most theories are not consistent with each other in terms of their r