Elastic and transport properties in polycrystals of cracked grains: Cross-property relations and microstructure

Submitted to : International Journal of Engineering Science LBNL- October 2, 2007 Elastic and Transport Properties in Polycrystals of Cracked Grains: Cross-Property Relations and Microstructure James G. Berryman 1, ∗ University of California, Lawrence Berkeley National Laboratory, 1 Cyclotron Road MS 90R1116, Berkeley, CA 94740, USA Abstract Some arguments of Bristow (1960) concerning the effects of cracks on elastic and transport (i.e., electrical or thermal conduction) properties of cold-worked metals are reexamined. The discussion is posed in terms of a modern understanding of bounds and estimates for physical properties of polycrystals — in contrast to Bristow’s approach using simple mixture theory. One type of specialized result emphasized here is the cross-property estimates and bounds that can be obtained using the methods presented. Our results ultimately agree with those of Bristow, i.e., confirming that microcracking is not likely to be the main cause of the observed elastic behavior of cold-worked metals. However, it also becomes clear that the mixture theory approach to the analysis is too simple and that crack-crack interactions are necessary for proper quantitative study of Bristow’s problem. JGBerryman@LBL.GOV