Showing papers in "Journal of Applied Mechanics in 1957"

On the Stress Distribution at the Base of a Stationary Crack

Abstract: In an earlier paper it was suggested that a knowledge of the elastic-stress variation in the neighborhood of an angular corner of an infinite plate would perhaps be of value in analyzing the stress distribution at the base of a V-notch. As a part of a more general study, the specific case of a zero-angle notch, or crack, was carried out to supplement results obtained by other investigators. This paper includes remarks upon the antisymmetric, as well as symmetric, stress distribution, and the circumferential distribution of distortion strain-energy density. For the case of a symmetrical loading about the crack, it is shown that the energy density is not a maximum along the direction of the crack hut is one third higher at an angle ± cos^(-1) (1/3); i.e., approximately ±70 deg. It is shown that at the base of the crack in the direction of its prolongation, the principal stresses are equal, thus tending toward a state of (two-dimensional) hydrostatic tension. As the distance from the point of the crack increases, the distortion strain energy increases, suggesting the possibility of yielding ahead of the crack as well as ±70 deg to the sides. The maximum principal tension stress occurs on ±60 deg rays. For the antisymmetrical stress distribution the distortion strain energy is a relative maximum along the crack and 60 per cent lower ± 85 deg to the sides.

The Response of Mechanical Systems to Random Excitation

Abstract: : Mechanical systems are not always excited by a harmonic force of fixed frequency and amplitude. Often the excitation input is of random nature, and the response of the system displays no orderly trends. Instantaneous values and phase are meaningless in such cases, and the problem must be treated from a statistical approach. It is the purpose of the paper to outline such an approach as related to the dynamic response of structures.

A Photoelastic Study of Strain Waves Caused by Cavitation

Abstract: Ultra-high-speed photoelastic techniques have been applied to a study of the transient stresses and strains in a photoelastic plastic when subject to cavitation. A photocell, used to detect the transient strains, indicated that the time duration of the strains was about 2 microseconds. Using an ultra-high-speed motion picture camera, ultrasonic cavitation bubbles have been photographed collapsing on the surface of a photoelastic specimen, and the resulting strain wave in the solid has been photographed. The dynamic properties of a photoelastic material have been obtained in order to permit quantitative interpretation of the transients. This has indicated that the stresses due to cavitation may be as high as 2.8 x 10^5 psi. The photoelastic plastic, CR-39, was found to exhibit strain birefringence, and its strain-optic constant was found to be independent of the rate of loading.