Dynamic fracture of two nano-cracks in graded elastic half-plane

• Main Authors: Rangelov, Tsviatko, Dineva, Petia
• Format: Conference Proceeding
• Language: English
• Subjects: Boundary conditions; Boundary element method; Boundary integral method; Cracks; Fourier transforms; Fracture mechanics; Free surfaces; Functionally gradient materials; Integral equations; Material properties; Mathematical analysis; P waves; Stress concentration
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0040131

Dynamic fracture behavior of two nano-cracks in a functionally graded elastic isotropic half-plane under excitation of time-harmonic P-wave is studied. The applied approach is based on the non-hypersingular traction based boundary integral equation method for the graded bulk elastic isotropic solid extended with the non-classical boundary conditions and the localized constitutive law for the matrix-nano-crack interface within the framework of the Gurtin-Murdoch theory. The formulation allows for a quadratic variation of the material properties in depth. The boundary integral equation is treated by using the frequency dependent half-plane Green‘s function derived analytically by application of an appropriate functional transform, accompanied by a follow-up Fourier transform. The numerical solution provides stress-strain state at any point in the semi-infinite graded solid as well as the displacements from which the stress concentrations are determined. Simulations for two nano-cracks parallel to the free surface of the half-plane are presented and discussed. They reveal the sensitivity of the scattered wave field and dynamic stress concentration factors to the complex influence of nano-cracks interaction phenomena, existence of material gradient and surface elasticity effects. The verification and parametric study illustrate convincingly the applicability of the proposed mechanical model in material science of functional graded composites and in computational dynamic fracture mechanics.