WAVE PROPAGATION IN A LAYERED MODEL DUE TO POINT SOURCE LOADING IN A HIGH‐IMPEDANCE MEDIUM

Geophysics ◽  
1971 ◽  
Vol 36 (3) ◽  
pp. 517-532 ◽  
Author(s):  
I. M. Daniel ◽  
R. L. Marino
Keyword(s):  
Wave Propagation ◽  
Point Source ◽  
Explosive Loading ◽  
Isochromatic Fringe ◽  
Layered Model ◽  
High Impedance ◽  
Impedance Ratio ◽  
Fringe Patterns ◽  
Refracted Waves ◽  
Attenuation Characteristics

Dynamic photoelastic techniques were used to study the incident, reflected, and refracted waves in a layered model. The model, consisting of two birefringent layers with an impedance ratio of 2.2:1, was subjected to point source explosive loading in the high‐impedance medium. The isochromatic fringe patterns were photographed with a Cranz‐Schardin multiple spark camera operating at a rate of 200,000 frames per second. Propagation and attenuation characteristics of waves in both layers were studied.

A PHOTOELASTIC ANALYSIS OF STRESS WAVE PROPAGATION IN A LAYERED MODEL

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 881-899 ◽  
Author(s):  
W. F. Riley ◽  
J. W. Dally
Keyword(s):  
Wave Propagation ◽  
Dynamic State ◽  
Lead Azide ◽  
Stress Wave Propagation ◽  
Principal Stresses ◽  
Individual Values ◽  
Isochromatic Fringe ◽  
Fringe Patterns ◽  
The Individual ◽  
Explosive Detonation

Dynamic photoelasticity was used to study some fundamental aspects of wave propagation in layered media and to obtain information on the dynamic state of stress associated with the various waves generated by a point source explosion. Columbia Resin CR‐39 and aluminum were used to obtain a model with an acoustical impedance‐mismatch between layers of 6 to 1. A Cranz‐Schardin multiple spark camera, operating at approximately 200,000 frames per second, was used to record the dynamic isochromatic fringe patterns associated with the propagating stress waves. Small charges of lead azide were used to explosively load the models. Six different wave types were clearly identified. In the region near the explosive detonation, the predominant waves were the incident [Formula: see text] wave and the reflected [Formula: see text] waves from the interface and the free boundary. In regions away from the explosive detonation the headwaves ([Formula: see text], [Formula: see text], and [Formula: see text]) dominate since their rate of attenuation is much lower than the rate associated with the incident dilatational or the reflected shear waves. The data obtained in the form of isochromatic fringe patterns were converted to individual values of the principal stresses in several instances. The methods developed for this separation are applicable whenever the dilatational or distortional waves occur alone. The separation method requires no auxiliary data other than the isochromatic fringe orders and yields dynamic displacement data in addition to the individual values of the principal stresses.

scholarly journals Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

2020 ◽  
pp. 237-249
Author(s):  
L. V Stepanova
Keyword(s):  
Series Expansion ◽  
Digital Image ◽  
Power Series Expansion ◽  
Crack Tip ◽  
Higher Order ◽  
Accurate Estimation ◽  
Principal Stresses ◽  
Isochromatic Fringe ◽  
Higher Order Terms ◽  
Fringe Patterns

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

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