Cracks propagation and interaction in an orthotropic elastic material: Analytical and numerical methods

• Published in: Computational materials science Vol. 46; no. 3; pp. 687 - 693
• Main Authors: Sadowski, T., Marsavina, L., Peride, N., Craciun, E.-M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2009; Elsevier
• Subjects: Cauchy integrals; Crack closure integral; Exact sciences and technology; FRANC2D; Fundamental areas of phenomenology (including applications); Orthotropic elastic material; Physics; Plemelj’s formulas; Solid mechanics; Structural and continuum mechanics; Crack closure integral; Plemelj’s formulas; FRANC2D; Cauchy integrals; Orthotropic elastic material; Riemann problem; Epoxy resin; Elastic material; Boundary condition; Orthotropic material; Crack propagation; Finite element method; Stress distribution; Analytical method; Crack length; Aramid fiber; Numerical simulation; Crack tip; Mathematical model; Cauchy integral; Plemelj's formulas
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2009.06.006

An elastic orthotropic material containing a crack in Mode I is considered to formulate a new analytical model. The boundary conditions for the crack existence in the material lead to the solution of the homogeneous Riemann–Hilbert problems. The mathematical model was elaborated for a single and two collinear cracks of different lengths and distance for Mode I in order to investigate cracks interaction problem. Using the theory of Cauchy’s integral and the numerical analysis, the fields in the vicinity of the crack tips were determined. Finite Element Method was applied to compare the mathematical analytical solution and to determine the fields in the vicinity of the crack tips. The critical values of applied stress which caused cracks propagation were evaluated. The interaction of cracks in an orthotropic aramid-epoxy material was studied in details. Comparison of both approaches to crack propagation leads to the conclusion that the new analytical model is correct and can be applied to more complex cracks geometries, including inclined cracks.