Elastic wave scattering in semi-crystalline polymers

An exact analysis is carried out to examine the scattering of progressive longitudinal (P) and shear (S) waves in semi-crystalline polymers with spherulitic pattern. A simplified mathematical model is constructed which considers the interaction of the elastic waves with an anisotropic spherical spherulite with radially aligned microstructural composition, embedded within a bulk isotropic polyethylene surrounding. The representative spherulite is appropriately modeled by an effective spherically isotropic medium. Separation of variables in conjunction with Frobenius power series method is employed to obtain an exact solution. Numerical calculations reveal the important effect of degree of crystallinity on the P- and S-wave scattering cross sections for a moderately wide range of incident wave frequencies. The presented solution is of interest in nondestructive evaluation of crystalline polymers. It can provide a valuable benchmark for comparison to other solutions obtained by strictly numerical or experimental techniques.