Three-dimensional singular stress/residual stress fields at crack/anticrack fronts in monoclinic plates under antiplane shear loading Reaz A. Chaudhuri ⇑ Department of Materials Science and Engineering, 122 S. Central Campus Dr., Room 304, University of Utah, Salt lake City, UT 84112-0560, United States article info Article history: Received 9 September 2010 Received in revised form 27 November 2011 Accepted 9 December 2011 Keywords: Three-dimensional eigenfunction Stress intensity factor Stress singularity coefficient Monoclinic Crack front Crack deviation Anticrack Energy release rate Residual stress abstract A recently developed eigenfunction expansion technique, based in part on separation of the thickness-variable, is first developed to derive three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness crack/anticrack weakening/ reinforcing an infinite monoclinic plate, of finite thickness and subjected to far-field anti- plane shear loading. Crack/anticrack-face boundary conditions and those that are pre- scribed on the top and bottom (free or fixed) surfaces of the anisotropic (monoclinic) plate are exactly satisfied. Five different through-thickness crack/anticrack-face boundary conditions are considered: (i) slit crack, (ii) anticrack or perfectly bonded rigid inclusion, (iii) transversely rigid inclusion (longitudinal slip permitted), (iv) rigid inclusion in part perfectly bonded, the remainder with slip, and (v) rigid inclusion located alongside a crack. The three-dimensional stress intensity factor for a center-crack, and stress singularity coef- ficients for/on a center-anticrack are then derived by incorporating an extension of the Stroh type approach in the present analysis. Through-thickness distribution of stress inten- sity factor and stress singularity coefficient for a crack and an anticrack, respectively, is also presented. Additionally, singular residual stress fields in the vicinity of the fronts of these cracks, anticracks and similar discontinuities are also discussed. Hitherto unavailable expressions for three-dimensional energy release and absorption rates for center-cracks and anticracks are derived by using Irwin’s crack closure and Eshelby’s eigenstrain approach, respectively. A heretofore unavailable expression for the energy release rate on the super-rigid inclusion is derived, using an approach which is analogous, in a reverse sense, to Irwin’s crack closure method. Finally, a new mode III crack deflection/bifurcation criterion is also derived. The crack deviation under antiplane shear loading is strongly correlated with the elastic stiffness constant, c 45 , of the monoclinic single crystal or off-axis composite lamina concerned. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Monoclinic materials occupy an important place in terms of both geological occurrences as well as modern materials technology. Important classes of geological materials with monoclinic symmetry include orthoclase and sanidine classes of alkali feldspars, barium feldspars and hornblende (a complex inosilicate series of minerals), while important synthetic monoclinic materials include anthracene (coal tar byproduct), naphthalene, tartaric acid as well as its salt, potassium tart- arate [1,2]. In addition, off-axis smeared-out unidirectional continuous fiber reinforced composite laminas are modeled as monoclinic materials. 0013-7944/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2011.12.003 ⇑ Tel.: +1 801 581 6282; fax: +1 801 581 4816. E-mail address: r.chaudhuri@utah.edu Engineering Fracture Mechanics 87 (2012) 16–35 Contents lists available at SciVerse ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech