Abstract
This research program was conducted to study the effects of acoustic-impedance mismatch between materials in a layered elastic solid on the amplitudes of the head waves generated at the interface as a stress wave develops and propagates in one of the layers. Dynamic photoelasticity methods were employed. The isochromatic-fringe patterns used for analysis were recorded with a Cranz-Schardin multiple-spark camera operating at a framing rate of approximately 188,000 exposures per second. Acoustic-impedance ratios from a low of 1.7∶1 to a high of 17.4∶1 were studied. Small charges of lead azide were used to generate the original dilatational (P 1) wave.
Results of the study confirm the existence of all waves predicted by theory except for theP 1 P 1 waves reflected from the free surface and from the interface near the source in the low-impedance layer. In the region near the explosive detonation, the head waves are important since they have significant magnitudes for certain impedance ratios and they appear to attenuate at a rate much lower than the rate associated with the incidentP 1 wave or the reflectedP 1 S 1 waves.
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Abbreviations
- C L :
-
acoustic wave velocity in a plate\(\sqrt {E/\rho (1 - v^2 )}\)
- C 0 :
-
acoustic-wave velocity in a\(bar = \sqrt {E/\rho }\)
- C P1 ;C P2 :
-
velocities of dilatational wavesP 1 in photoelastic material andP 2 in high-impedance material
- C S1 ;C S2 :
-
velocities of distortional wavesS 1 in photoelastic material andS 2 in high-impedance material
- d :
-
depth of explosion from free surface distance from explosion to interface [Fig. 1(a)]}
- \(f_\sigma ^\prime\) :
-
dynamic photoelastic-fringe constant
- I L :
-
acoustic impedance for plates =C L ρ
- I 0 :
-
acoustic impedance for bars=C 0 ρ
- N :
-
photoelastic-fringe order
- P 1 :
-
incident dilatational wave in photoelastic material
- P 1 P 1 :
-
reflected dilatational wave from free surface of photoelastic material
- P 1 S 1 :
-
reflected distortional wave in photoelastic material
- P 1 S 2 :
-
refracted distortional wave in high-impedance material
- P 1 P 2 :
-
refracted dilational wave in high-impedance material
- P 1 P 2 P 1,P 1 P 2 S 1 P 1 P 2 S 2,P 1 S 2 P 1 P 1 S 2 S 1}:
-
dilatational head waves as defined in Figs. 1 and 2
- \(\alpha _1 , \beta _1\) :
-
angles of incidence and reflection in material 1
- \(\alpha _2 , \beta _2\) :
-
angles of refraction in material 2
- ν:
-
Poisson’s ratio
- ρ:
-
mass density
- σ:
-
normal stress
- E :
-
modulus of elasticity
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Burger, C.P., Riley, W.F. Effects of impedance mismatch on the strength of waves in layered solids. Experimental Mechanics 14, 129–137 (1974). https://doi.org/10.1007/BF02322835
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DOI: https://doi.org/10.1007/BF02322835