Int J Fract (2011) 167:281–287 DOI 10.1007/s10704-010-9556-8 © Springer Science+Business Media B.V. 2010 LETTERS IN FRACTURE AND MICROMECHANICS 123 CROSS-PROPERTY CONNECTION BETWEEN WORK-HARDENING COEFFICIENT AND ELECTRICAL RESISTIVITY OF STAINLESS STEEL DURING PLASTIC DEFORMATION David Dominguez and Igor Sevostianov Department of Mechanical Engineering, New Mexico State University, Las Cruces, NM 88001, USA e-mail: igor@nmsu.edu Abstract. Present paper focuses on the cross-property connection between the changes in electrical resistivity and work hardening coefficient in the process of plastic deformation. The possibility of the cross-property connection is provided by the fact that both quantities are governed by the same parameter - growth of the dislocation density caused by the applied stresses. Experimental measurements on stainless steel 304 are in a good agreement with analytical estimates. Keywords: cross-property connection, plasticity, work-hardening, electrical resistivity, dislocation density. 1. Introduction. Present paper focuses on the cross-property connection between the growth in electrical resistivity and decrease in work hardening coefficient in the process of plastic deformation of stainless steel under quasi-static loading. Generally, cross-property connections link variations in different physical properties caused by microstructural changes in materials. Their importance for inhomogeneous materials has been pointed out by Berryman and Milton (1988) and was particularly emphasized by Gibiansky and Torquato (1995). Research on cross-property connections split on three main lines: (1) variational cross-property bounds; (2) explicit analytically derived cross-property connections; and (3) phenomenologically observed cross-property connections. The general approach to establishing various cross-property correlations was outlined by Milton (1997). His results were substantially advanced by Gibiansky and Torquato (1995, 1996a,b), who narrowed them under additional restrictions on the composite microgeometry and on the properties of constituents. Explicit connections between elastic and conductive properties have been first derived and experimentally verified for materials with randomly oriented microcracks by Bristow (1960). General case of anisotropic heterogeneous materials was addressed by Sevostianov and Kachanov (2002) and specified for various materials in works of Sevostianov (2003), Sevostianov et al (2006), Sevostianov and Sabina (2007) (see review of Sevostianov and Kachanov, 2008 for detailed literature review). The possibility of such connections is rooted in similarity between microstructural parameters governing different physical properties (Kachanov and Sevostianov, 2005).