Dynamic failure prediction of cross-rolled beryllium sheets subjected to vibration loads

Abstract

The principal objective of this investigation is to develop and verify a numerical method for prediction of failure for cross-rolled beryllium sheet structures that are subjected to vibration loads. To this end, complementary laboratory experiments and numerical simulations are carried out on glass and beryllium plates. A-total of five glass and nine beryllium specimens with various length-to-width ratios aretested to failure. Energy is imparted to each plate in the form of sinusoidal base excitationby means of a shaker table. Amplitude of excitation at the resonant frequency is continuously increased until the specimen fails; the amplitude is increased from zero to a target maximum within a period of 15 seconds. A high-speed data acquisition system is used to obtain time-history data from transducers attached to each specimen. Strain gages and an accelerometer are attached to the plate and a point on the excitation fixture, respectively. Laboratory tests were conducted at the Vibrations and Control Laboratory of Texas A&M University and at NASA Johnson Space Center. As a precursor to experiments with beryllium, a series of glass specimens were tested in the laboratory and numerically simulated. These plates were clamped by a specially designed fixture at the center of the length to form a double cantilever. Effective length and width dimensions of each specimen vary from 114.3 x 10.0 min (4.5 x 0.4 in.) to 114.3 x 114.3 mm (4.5 x 4.5 in.). AU glass specimens were approximately 2.24 nun (0.088 in.) in thickness. In contrast to the structural symmetry of the glass plates, 2.54-mm (0.1-in.) thick beryllium specimens were clamped only at one end to form a single cantilever. A steel mass was added to the end of each plate in order to decrease its natural frequency, and thereby reduce the acceleration level required to fail the specimen at resonance. Three sets of specimens (each set consisting of three equal size plates) were excited to failure. Two other specimens were also tested to gain additional information. Specimen length and width dimensions vary from I 1 4.3 x 25.4 mm (4.5 x 1.0 in.) to 114.3 x 114.3 mm (4.5 x 4.5 in.). Frequencies of excitation ranged from 71 Hz to 96 Hz. Tsai-Wu failure models for regular annealed glass and cross-rolled beryllium SR200 sheet material are incorporated into a commercial finite element code by means of a specially written subroutine. A failure criterion that is a function of three in-plane components of stress is compared with the stress level at each integration point in the finite element model. A comparison between stress at a point and the failure envelope is made at each incremental load. Failure is predicted to occur when the state of stress at one or more points in the material exceeds those stresses that satisfy the failure criterion. Because each specimen was excited at the first fundamental mode, maximum stresses occurred at the support. Tensile failure stresses of approximately 551,6 Mpa (80,000 psi) were obtained from the beryllium plate experiments. These stresses compare well with stresses obtained by other investigators using static loads. By visual inspection, it is determined that the failure of all specimens is brittle. Numerical models show good agreement with experimentally measured quantities. Using the developed failure models, the primary failure stresses for each plate are predicted to within an average of seven percent of the actual failure stress.