An alternating technique for evaluating weight functions for 3-D surface flaws in finite solid bodies

An efficient method, based on the Schwarz–Neumann alternating technique, is presented for computing weight functions of a general solid (3-D as well as 2-D), with embedded or surface-flaw configurations. The total rate of change of the crack-opening displacements, due to simple perturbations of crack-dimension characteristics, is conveniently decomposed into the infinite-domain and boundary-correction parts. The former is determined from available analytical solutions of ideal-shaped cracks, whereas the latter is computed numerically by imposing nil boundary-traction requirements for the displacement field corresponding to the weight functions. Numerical examples, with solutions for 3-D weighted-average and local stress intensity factors, indicate that the proposed method is very accurate and efficient.     

Repulsive Flux Pinning Force in NbTi/Nb Superconductor/Superconductor Multilayers

Flux pinning characteristics have been investigated for the Nb _x Ti_100-x /Nb(x = 65, 50 and 28) and Nb ₂₈ Ti ₇₂/Nb ₆₅ Ti ₃₅ superconductor(S)/superconductor(S^′) multilayers. The maximum of the pinning force F _{p⊥ max} perpendicular to the layer plane as a function of the structure modulation length λ has a peak in the quasi-two-dimensional region (λ～20 nm). The maximum. values of the F _{p⊥ max} versus λ curve are proportional to the difference of the GL coherence length (ξ _GL ) between the superconductive sublayers S and S^′. The results suggest that the large F _{p⊥ max} in the S/S^′ multilayer is caused by the repulsive pinning force due to Nb layers with larger ξ _GL .