Stability of a Propagating Interphase Boundary in a Thermoplastic Material

The propagation of interphase boundaries in oneand two-dimensional deformations of solids that can undergo phase transformations has been studied by, amongst others, James [12], Hutchinson and Neale [11], Coleman [6], Fager and Bassani [7], and Tugcu and Neale [20, 21]. Many of these studies have been motivated by the experimental observations on the cold-drawing of polymer fibers and membranes. These works have examined the existence and properties of a steady-state solution characterized by a steadily propagating interphase boundary that divides the body into two uniform or nearly uniform deformed regions. This phenomenon is somewhat similar to the directional solidification process studied by Mullins and Sekerka [18], Langer [16], and Godreche [10] where a moving planar interface separates the solid and liquid regions. For this case a planar interface can become morphologically unstable and then develop into a cellular or dendritic pattern. We note that detailed experimental observations on the morphology of a propagating interphase boundary in two-dimensional deformations of solids undergoing phase transformations has not been reported. Here we use Mullins and Sekerka's method to study analytically the morphological stability of a planar propagating interphase boundary in phase-transforming thermoplastic solids deformed in antiplane shear. For a thermoelastic solid deformed in antiplane shear, Fried [9] has investigated the relationship between the morphological stability of the planar interface and the "kinetic functions" proposed by Knowles [15] and Abeyaratne and Knowles [1].