Size effect of cohesive delamination fracture triggered by sandwich skin wrinkling

Because the observed size effect follows neither the strength theory nor the linear elastic fracture mechanics, the delamination fracture of laminate-foam sandwiches under uniform bending moment is treated by the cohesive crack model. Both two-dimensional geometrically nonlinear finite element analysis and one-dimensional representation of skin (or facesheet) as a beam on elastic-softening foundation are used. The use of the latter is made possible by realizing that the effective elastic foundation stiffness depends on the ratio of the critical wavelength of periodic skin wrinkles to the foam core thickness, and a simple description of the transition from shortwave to longwave wrinkling is obtained by asymptotic matching. Good agreement between both approaches is achieved. Skin imperfections (considered proportional to the the first eigenmode of wrinkling), are shown to lead to strong size dependence of the nominal strength. For large imperfections, the strength reduction due to size effect can reach 50%. Dents from impact, though not the same as imperfections, might be expected to cause as a similar size effect. Using proper dimensionless variables, numerical simulations of cohesive delamination fracture covering the entire practical range are performed. Their fitting, heeding the shortwave and longwave asymptotics, leads to an approximate imperfection-dependent size effect law of asymptotic matching type. Strong size effect on postpeak energy absorption, important for impact analysis, is also demonstrated. Finally, discrepancies among various existing formulas for critical stress at periodic elastic wrinkling are explained by their applicability to different special cases in the shortwave-longwave transition.