Analytical modeling of stiffness reduction in symmetric and balanced laminates due to cracks in 90 degrees layers

Stiffness reduction in [S,90(n)](s) symmetric laminates, containing orthotr opic sub-laminates (S) and cracked 90 degrees layer, is analyzed. Closed-fo rm expressions relating stiffness changes to the transverse crack density a re derived. They contain only material properties, laminate geometry and a stress-perturbation function that is proportional to the normalized average crack-opening displacement. Stress-distribution models [shear lag, based o n variational approach, and finite-element analysis (FEA)] are adopted for the [S,90(n)](s) configurations and used to calculate the stress-perturbati on function. Predictions are compared with experimental data for [+/- theta , 90(4)](s) theta = 0, 15, 30, 40 glass-fiber/epoxy-resin laminates. Genera lly the FEA model slightly underestimates stiffness reduction whereas both of the variational models used lead to similar results, slightly lower than experimental. Even the shear-lag model may be successfully used if the she ar-lag parameter is first obtained from fitting test results for cross-pip laminate of the same material. (C) 1999 Elsevier Science Ltd. All rights re served.