Simulation-Visualization of Wave Propagation in a
Unidirectional Graphite/Epoxy Composites

R.D. Kriz, Associate Professor
Department of Engineering Science and Mechanics
Director, Laboratory for Scientific Visual Analysis
Virginia Polytechnic Institute and State University
Blacksburg, Virginia

Within the past ten years there has been a renewed interest in numerical simulation of stress wave propagation because of the availability of fast super computers with large memory capabilities. Only recently have a few investigators applied these simulations to problems where elastic anisotropy was included as a major factor. The massive output of results from these simulations, together with the added complexity of coupled phenomena that uniquely exist for a given anisotropy, defies intuition. To grasp the physical significance of these numerical simulations requires visual data analysis in an animated format.

Merkulov and Yakovlev where the first to experimentally-visually demonstrate the influence of elastic anisotropy on the energy propagation deviation by the use of Schlieren. This technique is applicable only for transparent media such as Quartz. For anisotropic media that is opaque we study the influence of anisotropy on this energy deviation by using a simulation- visualization technique. First we show how to experimentally measure this energy deviation in an opaque graphite-epoxy material by lateral movement of the receiving transducer at the outer boundary. With a full field simulation and visualization we can also study the physics of these phenomena in the interior. An interactive visual tool was developed to study how degradation in either the fiber (graphite) component or matrix (epoxy) component could be used to measure preferential component degradation in a unidirectional composite. With full field simulation results it is possible to study the shear and longitudinal components of QL and QT waves in a finite element mesh [Kriz- Heyliger, 89]. With a higher density finite difference mesh we can more accurately observe continuity of propagating waves but fail to differentiate between shear and logintudinal components [Kriz-Gary, 90]. Recently we have shown that changing the fiber orientation can lead to a mode transition of shear and longitudinal components of these waves at a fiber orientation of 51 degrees [Kriz-Vandenbossche, 95]. We provide a schematic of our full field simulation that will help us interpret the full field animation where we observe the propagation of an two cycle pulse emanating from the lower boundary. Note that the energy bifurcates into faster moving QL and a slower moving QT components where the reflected QL component reflects back towards the original transmission location without generating another QT wave. Also note that the difference of the QL and QT wavelengths.

We can use this idea to preferentially launching either a QL or QT wave at the boundary. We demonstrated this numerically by launching only the QL wave for theta of 50 degrees. This same data set was used to create a SIGgraph89 video ( (32Mb) / wave.mpg (24Mb)).

Animated sequences of gray scale images were used to observe the deformation fields at various values of theta to characterize the total acoustic response of unidirectional graphite/epoxy: 1) before mode transition (theta less than 50 degrees), 2) near mode transtion (theta=50 degrees), and after mode transition (theta greater than 51 degrees). Here both QL and QT waves are launched as continuous sinusoidal waves over a finite aperature. Theta: 10, 20, 30, 40, 50, 60.

Numerical simulations are closer to real wave propagation then stress wave theory. Stress wave theory is developed with the assumption that the waves are of infinite extent and propagate in a semi-infinite medium. The numerical simulation, like any real stress wave, must have bounds, and therefore includes the effects of reflection, diffraction, beam-spreading, and surface waves. These effects are easily seen in all of these numerical simulations.

Kriz, R.D. and Heyliger, P.R., "Finite Element Model of Stress Wave Topology in Unidirectional Graphite/Epoxy: Wave Velocities and Flux Deviations,"Review of Progress in Quantitative Nondestructive Evaluation, Vol.8A, Plenum Publishing Corp., pg 141-148, 1989.

Kriz, R.D. and Gary J.M., "Numerical Simulation and Visualization Models of Stress Wave propagation in Graphite/Epoxy Composites,"Review of Progress in Quantitative Nondestructive Evaluation, Vol.9, Plenum Publishing Corp., pg 125-132, 1990.

Vandenbossche, B. and Kriz, R.D.,and Oshima, T." Stress Wave Displacement Polarizations and Attenuation in Unidirectional Composites: Theory and Experiment,"J. Research In Nondestructive Evaluation, Vol. 8, No. 2, pp. 101-123, 1996.

Created by Ron Kriz,

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