Fracture in equiaxed two phase alloys: part ii. fracture in alloys with isolated plastic particles
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I.
INTRODUCTION
IN this paper we deal
with fracture in two phase equiaxed alloys consisting of plastically deforming inclusions which effectively toughen a brittle continuous matrix. The microstructures considered in this paper are mirror images of those discussed in the preceding pape r~ and require a different approach in discussing their fracture characteristics. For these types of materials, fracture is initiated by matrix cracking and is described in terms of microscopic characteristics of the "process zone ''2'3 which is a region behind the crack tip where unbroken plastically deforming particles, acting as unbroken ligaments, are surrounded by a matrix crack. The process zone model, in conjunction with Dugdale's 4 concept of cohesive forces at the crack tip, will be used to develop a basis for formulating a fracture description for these alloys. This development will also employ current ideas on the fracture mechanics of "toughened" ceramics.
II.
T H E O R E T I C A L CONSIDERATIONS
A. Microstructural Description An extensive description, in microstructural terms, of the alloys investigated is given in Reference 1. Present work is concerned with alloys consisting of - 2 7 to 50 vol pct and 73 to 100 vol pct of the elastic phase, the "ideal" microstructures of which are classified as Group II and Group IV Table I.
B. Fracture Description Alloys containing either a relatively small amount of plastically deforming inclusions imbedded in a brittle matrix or alloys with a continuous brittle phase will, in general, fracture in a macroscopically brittle manner. The resistance to fracture of these alloys is thus best described in terms of a fracture toughness parameter which should incorporate present views on fracture in toughened ceramics. Recent descriptions of fracture in toughened ceramics employ Kraft's concept of a process zone and elements of Dugdale's model of "cohesive forces" as starting points. The process zone is understood to be a region behind the crack tip which consists of deformed, but not yet fractured, plastic particles surrounded by a fractured brittle matrix (Figure l(a)). The unbroken particles act as a restraint on crack growth and thus can be considered as a crack closing force which contributes to increased fracture toughness. In extending considerations of fracture in these alloys, we will use the above model as a starting point and incorporate elements of Tardiff's 5 approach for fracture in brittle matrix-ductile fiber composites, Evans '6'7'8 description of
Microstructural Characteristics of Alloys Studied
Microstmctural Elastic Phase Volume Group Fraction Rangc (f) II 27 to 50 pet IV 73 to 100 pet R = particle radius a = tetrakaidecahedronedge length -l/R = averagefree center-to-centerdistance
Particle Type Plastic
a/R
-l/R
(Tr/6~/2(1-f)) v3
Plastic
(7"r/N/2(1-f)) ~/3
2.35(1-f) 1,3 2.83(1-f)-'3
M.A. PRZYSTUPA, formerly Graduate Research Assistant, Department of Metallurgical Engineering, Michigan Technological University, is now Postdoctoral Research Associate, Materia
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