Fracture in Equiaxed Two Phase Alloys: Part I. Fracture in Alloys with Isolated Elastic Particles
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I.
INTRODUCTION
E X T E N S I V E studies have established the microscopic features of fracture initiation and propagation in two phase alloys composed of one plastically deforming phase and another phase that deforms only elastically or when both phases deform plastically, but to different degrees, up to fracture.I-17 These descriptions are incomplete in the sense that alloy fracture characteristics cannot be predicted a priori from the mechanical properties of the individual phases and their respective volume fractions. For alloys consisting of isolated elastically deforming inclusions imbedded in a plastically deforming matrix, fracture initiates by inclusion fracture2'6'7 or inclusion-matrix inteffacial decohesion, 5'9'18-24 and Rice and Johnson's (RJ) 25 theory of ductile fracture appears suitable for describing fracture in such alloys. They predict that fracture occurs when the extent of the heavily deformed zone at the crack tip (which can be a fractured or decohered particle in the case of a tensile test) attains a critical size which is related to the distance between the crack tip and adjacent fractured or decohered particles. Although this description was developed essentially for alloys containing a small volume fraction of elastic inclusions, Przystupa, Stout, and Courtney (PSC) have recently s h o w n 26 that it can be extended to alloys containing a fairly high volume fraction of elastic phase as well. For materials consisting of plastic inclusions dispersed in an elastic matrix, fracture initiates by matrix cracking. However, the description of fracture in such alloys is not as fully developed as the converse case discussed above. Recent efforts have concentrated on describing fracture in terms of the microscopic characteristics of the "process zone," which is a region behind the crack tip where unbroken plastically deforming inclusions are surrounded by a matrix crack. 27'2s The main difficulties associated with this description are related to accurate modeling of the inclusion deformation and inclusion-matrix decohesion or inclusion fracture in the process zone and to ascertaining how this "two stage" fracture process affects the fracture toughness of such alloys. This and the following paper develop a comprehensive description of the fracture process in equiaxed alloys conM.A. PRZYSTUPA, formerly Graduate Research Assistant, Department of Metallurgical Engineering, Michigan Technological University, is now Postdoctoral Research Associate, Materials Science and Engineering Department, University of California, Los Angeles, CA 90024. T.H. COURTNEY, Professor, is with the Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931. Manuscnpt submitted September 30, 1980.
sisting of isolated elastic inclusions imbedded in a plastically deforming matrix and vice-versa. This description will be complemented by comparison of predicted and experimentally measured fracture toughnesses over a wide range of volume fractions of the two phases. This paper is concerned wit
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