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I.

INTRODUCTION

IN recent years, it has been recognized that microscopic changes in the geometry of cracks in an engineering material can play an important role in governing its macroscopic resistance to cyclic fracture. Even for Mode I fatigue cracks loaded in purely uniaxial far-field cyclic tension, pronounced mixed-mode displacements can exist in the near-tip region due to deflections in crack path arising from various mechanical, microstructural, and environmental factors (for a detailed description, see Reference 1). Deviations of the crack from the Mode I growth plane lead to alterations in the effective stress intensity, apparent propagation rates, and the extent of crack closure. Although such mixed-mode crack advance plays a significant role in influencing the growth characteristics of nominally Mode I fatigue cracks, the mechanics and mechanisms of deflection processes and their effects on overall growth rates have not received detailed quantitative treatments. The theoretical analysis of crack deflection processes is a complex problem. In the last few years, independent theoretical studies have provided mutually-consistent local stress intensity calculations for some idealized deflection geometries, such as those involving a single kink or a fork at the tip of an infinitely long elastic crack. 2'3'4 Many uncertainties still exist in the understanding of the mechanics of nonplanar cracks with more complex geometries typically encountered in the fracture of solids. However, valuable insight into the influence of crack deflection on the mechanisms of failure can be gained by exploring the applications of existing analyses to some idealized cases of crack deflection, which are physically realistic within a limited scope of practical situations. Models of deflection processes in fracture now span many diverse applications including the toughening of ceramics, 5 microstructurally influenced quasistatic fracture in aluminum, 6 variable amplitude fatigue, 1'7 and microstructural effects on fatigue crack growth.l'7-9 In cyclic fracture, the phenomenon of crack deflection 1 also influences the reduction in effective stress intensity due

S. SURESH is Assistant Professor, Division of Engineering, Brown University, Providence, RI 02912. Manuscript submitted March 19, 1984.

METALLURGICAL TRANSACTIONS A

to fracture surface mismatch (arising from the kinematic irreversibility of deformation and displacements) during the unloading portion of the fatigue cycle.l~4 To date, theoretical models have not been attempted to justify the observed crack growth behavior based on the interaction of crack deflection and deformation processes. The objective of this paper is to present simple quantitative analyses of the changes in fatigue crack growth characteristics which stem from the combined influence of deflections in crack path and relative shear between the fracture surfaces resulting in premature contact.

II.

MODEL FOR TILTED CRACKS

In order to understand the effects of deflections and crack face contact on fatigue cr