Analysis of interface cracks in adhesively bonded lap shear joints, part 4

Conservation laws of elasticity for nonhomogeneous materials were developed and were used to study the crack behavior in adhesively bonded lap shear joints. By using these laws and the fundamental relationships in fracture mechanics of interface cracks, the problem is reduced to a pair of linear algebraic equations, and stress intensity solutions can be determined directly by information extracted from the far field. The numerical results obtained show that: (1) in the lap-shear joint with a given adherend, the opening-mode stress intensity factor, (K sub 1) is always larger than that of the shearing-mode (K sub 2); (2) (K sub 1) is not sensitive to adherent thickness abut (K sub 2) increases rapidly with increasing thickness; and (3) (K sub 1) and (K sub 2) increase simultaneously as the interfacial crack length increases

Analysis of cracks emanating from a circular hole in unidirectional fiber reinforced composites, part 2

An analytical method is developed for cracks emanating from a circular hole in an off-axis unidirectional fiber-reinforced composite. The method which is formulated by using conservation laws of elasticity and fundamental relationships in anisotropic fracture mechanics, provides a convenient and accurate means to examine the complicated crack behavior, when used in conjunction with a suitable numerical scheme such as the finite element method. The formulation is eventually reduced to a system of linear algebraic equations of mixed-mode stress intensity factors. Fracture parameters, describing crack-tip deformation and fracture in the composite, are obtained explicitly. Effects of material anisotropy and crack/hole geometry are examined also. Of particular interest are the energy release rates associated with crack extension; their values are evaluated for various cases. Results show that mixed-mode stress intensity factors and energy release rates associated with the cracks emanating from a hole change very appreciably with fiber orientation in the composite. K sub 1 and G increase monotonically with increasing theta; but K sub 2 reaches its maximum at theta = 45 deg, and then decreases gradually as theta increases further

A Note on ODEs from Mirror Symmetry

We give close formulas for the counting functions of rational curves on complete intersection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the instanton corrected Yukawa coupling.Comment: 24 pages using harvma