Acta Mech 215, 57–69 (2010) DOI 10.1007/s00707-010-0305-x Addis Kidane · Vijaya B. Chalivendra · Arun Shukla Thermo-mechanical stress fields and strain energy associated with a mixed-mode propagating crack Received: 9 October 2009 / Revised: 25 January 2010 / Published online: 14 April 2010 © Springer-Verlag 2010 Abstract Thermo-mechanical stress field equations are developed for a mixed-mode crack propagating at con- stant velocity in homogeneous and isotropic materials using an asymptotic approach along with displacement potentials. Asymptotic temperature field equations are first developed for steady state temperature conditions using insulated crack-face boundary conditions. These temperature field equations are later used to derive the first three terms of thermo-mechanical stress field equations for a steady state propagating mixed-mode crack. Using these thermo-mechanical stress fields, various components of the stresses are developed, and the effects of temperature on these stress components are discussed. Further, strain energy density and the circumferential stress criteria are employed to study the effect of temperature and the crack-tip velocity on crack growth direction. 1 Introduction In many practical engineering problems, the structures are subjected to thermo-mechanical loads. Under these thermo-mechanical loads, the cracks in these structures can initiate and cause catastrophic failure. The crack-tip initiation, rapid crack growth, crack branching and arrest are of significant importance to understand material’s failure under combined thermo-mechanical loads. In the classical studies of thermo-elastic crack problems, Sih [1] and Kassir and Bergman [2] investigated quasi-static stress fields for a crack in an infinite medium when it is subjected to special thermal loadings. Later, Wilson and Yu [3] employed finite element analysis and the J-inte- gral approach to determine crack-tip stress intensity factors for finite specimen geometries under thermal loads. In continuation of the above studies, Lee and Sim [4] determined mode-I thermal shock stress intensity fac- tors using Bueckner’ weight function method for a surface-cracked infinite strip under sudden conductive cooling. Using a general finite element model, Chen and Weng [5] investigated a coupled transient thermo- elastic problem for an edge-cracked plate without an inertia term. Katsareas et al. [6] determined shock stress A. Kidane (B ) Graduate Aeronautical Laboratories, Division of Engineering and Applied Science, California Institute of Technology, 1200 E California Blvd., Mail code 205-45, Pasadena, CA 91125, USA E-mail: addis@caltech.edu Tel.: 1-626-393-4534 Fax: 1-626-449-6359 V. B. Chalivendra Department of Mechanical Engineering, University of Massachusetts, North Dartmouth, MA 02747, USA A. Shukla Dynamic Photomechanics Laboratory, Department of Mechanical Engineering & Applied Mechanics, University of Rhode Island, Kingston, RI 02881, USA