Statistical aspects of cleavage fracture in steel
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I.
INTRODUCTION
THE cleavage fracture of steel has been rationalized as a phenomenon dictated by the brittle extension of cracked carbides into the ferrite matrix, within the elastic/plastic stress field of a major crack. 1,2 This premise is based on extensive work on notched bend bars which indicates that the extension of cracked carbides into the ferrite matrix dictates failure. 2 Circumstances which permit the subsequent stable growth of the cleavage crack can be conjectured (Appendix), but will be neglected for present purposes. The cracked carbides that dictate the failure of notched specimens are considered to be located near the elastic/plastic interface, where the principal tensile stress is a maximum. The stress at this location, at the failure instability, defines an effective cleavage strength, S. This cleavage strength is usually invariant with temperature ~ for slip initiated cleavage (at least, in the temperature range amenable to measurements) and decreases with increase in carbide size, 2 r (as, S ~ r-l/2). Application of cleavage concepts derived from notched beam test to the extension of sharp cracks to determine K~c has recognized that the rapid gradient in stress near the crack tip must influence the cleavage condition. Specifically, a realization that the peak tensile stress near the tip, 6- > S (Figure 1), has led to the definition by Ritchie, Knott, and Rice ~ (RKR) of a critical distance, xc, at which the crack tip stress reaches the cleavage stress. However, a consistent microstructural significance has not yet been attached to this critical distance.* It has subsequently been *The original proposaP that xc is some c o n s t a n t multiple of the grain diameter is not fully consistent with subsequent observations. 2-6 Rather, the grain size multiple varies between materials.
proposed that xc is dictated by weakest link statistical strength considerations related to the carbide size and spacing distribution within the variable crack tip field. 7"8'9 However, a comprehensive weakest link model of this process has not been developed. The intent of the present paper is to develop a quantitative weakest link cleavage fracture model, based on concepts of crack growth from cracked carbides. The model provides a rationale for the existence of a critical distance (related primarily to the size and spacing A.G. EVANS is Professor of Ceramic Engineering, Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720. Manuscript submitted November 19, 1982.
METALLURGICAL TRANSACTIONS A
distribution of cracked carbides) and predicts trends in toughness with material properties that appear to agree with available measurements.
II.
GENERAL CONSIDERATIONS
In general, cleavage fracture may involve one, or more, subcritical cracking event in a zone around the major crack. Plastic deformation firstly initiates stable cracks in certain carbides,4' sodue to the development of stress concentrations. The stress concentrations can be induced either by discrete deforma
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