REFINEMENTS OF SHEAR-LAG MODEL AND ITS APPLICATIONS

Since it was developed by Cox [Cox, H.L., 1952. The elasticity and str ength of paper and other fibrous materials. Br. J. Appl. Phys. 3, 72-7 9.], the shear-lag model (SLM) or fiber-loading theory has been widely used by material scientists and structural geologists as a powerful a nalytical method for analyzing mechanical interactions between hard an d soft phases (layers) in composites and two-phase rocks. We found tha t several approximations in previous mechanical derivations of the mod el can be improved in terms of mechanical equilibrium and boundary con ditions. Our refinements make the model more rigorous and elaborate. A pplications of the improved model include: (1) prediction of the axial tensile stress in strong inclusions embedded in a continuous weak mat rix, and consequently interpretation of extension fracture boudinage; (2) modeling of the distribution of shear stresses in the weak matrix surrounding the strong inclusions and, accordingly, interpretation of the variations of dislocation density and of recrystallized grain size in composites and polyphase rocks; and (3) prediction of mechanical p roperties of industrial composites and two-phase rocks. The analytical results of the improved model agree approximately with those obtained from both experimental investigations and numerical calculations.