Failure prediction of beryllium cross-rolled sheets by incorporating closure of cubic polynomial tensor

Abstract

Thin beryllium sheets are known to fail catastrophically when deformed by out-of-plane loadings. Primary objective of this study is to approach the overall problem of failure prediction from a macroscopic point of view. Principal components are (1) development of a higher-order failure criteria, (2) experimental evaluation of strength parameters for cross-rolled beryllium sheet, (3) incorporation of failure criterion into a finite element code, (4) comparison of experimental and numerical results, and (5) application of the criterion to failure loadings for beryllium structures. By supplementing and modifying failure criteria suggested by previous investigators, a multi-dimensional failure surface is proposed for thin beryllium structures. The new criterion is represented by a failure surface in six-dimensional stress space. For simplicity, the criterion is formulated exclusively for orthotropic materials. The proposed criterion calls for a number of uniaxial, biaxial, and triaxial experiments. Results from these tests provide the required strength parameters for the cubic criterion. For a general, three-dimensional, orthotropic material fifteen tests are required. Through-thickness material variations for cross-rolled beryllium sheet are experimentally verified via ultrasonic techniques. Through-thickness elastic moduli range from 296.5 GPa (43.0 x 10^3 ksi) at the neutral axis to 533.7 GPa (77.4 x 10^3 ksi) near the outer surfaces of the plate. A variety of experiments and loading situations establish the credibility of the criterion and the constitutive laws suggested for SR-200 beryllium sheets. These include a plate-plug arrangement under a complex state of stress and clamped plates with an out-of-plane point load at the center, in addition to the numerical predictions for most of the experiments performed for determining the failure coefficients. Failure results for the plate-plug and clamped plate tests are accurate to within 2%. Failure prediction is automated by incorporating the criterion into a commercial finite element package, thereby providing a design and evaluation tool. Numerous fringe plots display numerical displacement, strain, and stress distributions that result from simulation of the laboratory experiments for 2.54-mm (0.10-in.) thick beryllium sheet structures. Comparison of experimental and numerical results suggests that the numerical model is more than adequate for the analysis of SR-200 beryllium structures.