Int J Fract (2009) 155:143–153 DOI 10.1007/s10704-009-9336-5 ORIGINAL PAPER Families of asymptotic tensile crack tip stress fields in elastic-perfectly plastic single crystals Swapnil Patil · R. Narasimhan · Raja K. Mishra Received: 12 August 2008 / Accepted: 16 March 2009 / Published online: 3 April 2009 © Springer Science+Business Media B.V. 2009 Abstract In this work, two families of asymptotic near-tip stress fields are constructed in an elastic-ideally plastic FCC single crystal under mode I plane strain conditions. A crack is taken to lie on the (010) plane and its front is aligned along the [ 101] direction. Finite element analysis is first used to systematically exam- ine the stress distributions corresponding to different constraint levels. The general framework developed by Rice (Mech Mater 6:317–335, 1987) and Drugan (J Mech Phys Solids 49:2155–2176, 2001) is then adopted to generate low triaxiality solutions by intro- ducing an elastic sector near the crack tip. The two fami- lies of stress fields are parameterized by the normalized opening stress (τ A 22 /τ o ) prevailing in the plastic sector in front of the tip and by the coordinates of a point where elastic unloading commences in stress space. It is found that the angular stress variations obtained from the ana- lytical solutions show good agreement with finite ele- ment analysis. Keywords Asymptotic analysis · Elastic–plastic crack tip fields · FCC single crystals · Finite elements S. Patil · R. Narasimhan (B ) Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India e-mail: narasi@mecheng.iisc.ernet.in R. K. Mishra General Motors Corporation, 30500 Mound Rd., Warren, MI 48090, USA 1 Introduction The study of crack tip fields in single crystals is impor- tant in order to understand the physics of fracture in these materials as well as in polycrystalline solids (for example, transgranular fracture). In this context, it must be noted that when the crack opening displacement is much less than the grain size, the crack tip fields are contained within a single grain. Further, some key structural components are being fabricated in single crystal form. For example, blades in high pressure tur- bines of jet engines are made of single crystals of Nickel -based superalloys. Therefore, to ensure the structural integrity of such components, it is necessary to under- stand and characterize the stress and deformation fields present near a crack tip in a single crystal. Rice (1987) proposed an asymptotic solution for the crack tip stress field in ductile single crystals under mode-I, plane strain conditions within small strain, ideal plasticity framework. His analysis considered the case of a crack on the (010) plane with the crack front along [10 ¯ 1] direction for FCC and BCC crystals. The motivation for considering these crack orientations is because they have been frequently observed to occur in experimental studies on fracture of ductile single crystals (see, Neumann 1974a, b; Garrett and Knott 1975). The solution of Rice (1987) consists of sectors of constant stress, with concentrated kink and slip shear deformation on the sector boundaries. In particular, it suggests that a kink shear band should form at 90 ◦ to the crack line, while slip shear bands should occur at 123