A transgranular fatigue crack growth model based on restricted slip reversibility
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I.
INTRODUCTION
E A R L Y theoretical models for fatigue c r a c k growth were developed on the basis o f continuum mechanics principles in w h i c h the analysis o f crack-tip plasticity was coupled with critical damage criteria to formulate c r a c k growth rate equations, tl'2m These damage criteria were defined in terms o f either accumulated plastic work (hysteresis energy), accumulated plastic deformation (fracture strain), or a balance o f total energy input into the system. These continuum mechanics models were not derived on the basis o f the underlying physics o f the deformation and fracture processes. Weertman t4j considered the plastic blunting process and related crack growth rate to the crack-tip opening displacement by taking into account the effect o f geometrical factors ahead o f the crack tip. Yokobori and co-workers tSm used dislocation dynamics to determine the n u m b e r o f dislocations emitted from the c r a c k tip, which provide the required cracktip opening displacement. Taylor and KnotttT~ and Gerberich e t a l .18~ also used dislocation dynamics concepts to assume the proportionality between the c r a c k growth rate and the near-crack-tip strain range o r dislocation group velocity. However, the boundary o f slip activity, w h i c h is an important factor in controlling the rate o f c r a c k growth, was not considered in these dislocation models. The role o f slip processes in inducing fatigue damage ( c r a c k initiation and propagation) has long been recognized. 19,1°,m Particularly, the slip reversal has been found to be responsible for sharpening the vertex o f the crack, t~2~ The alternating forward slip and slip reversal processes also lead to the formation o f striations during fatigue crack X.J. WU, formerly Graduate Student, Department of Mechanical Engineering, University of Ottawa, is Visiting Fellow, Structures and Materials Laboratory, Institute for Aerospace Research, National Research Council of Canada. A.K. KOUL, Senior Research Officer, is with the Structures and Materials Laboratory, Institute for Aerospace Research, National Research Council of Canada, Ottawa, ON, Canada K1A OR6. A.S. KRAUSZ, Emiratus Professor, is with the Department of Mechanical Engineering, University of Ottawa, Ottawa, ON, Canada KIN 6N5. Manuscript submitted June 1 5 , 1992. METALLURGICAL TRANSACTIONS A
propagation. This concept is consistent with experimental observations and explains many essential features o f fatigue fracture, t~2,~3,14] These considerations were further extended by Fong and Tromans r~5,16] to a restricted slip reversibility (RSR) m o d e l for depicting the events at a propagating c r a c k tip, as shown schematically in Figure 1. The m o d e l explains transgranular c r a c k propagation events as follows. (1) Upon loading, slip systems on two favorably oriented slip planes S1 and $2 are activated. (2) Forward slip occurs solely on S1 during the rising load cycle, producing a slip step o f length 11. (3) During the decreasing load cycle, an increment o f slip revers
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