Assumption for description of material deformation

We assume for the mathematical description of material deformation under dynamic impact (Zukas et al., 1992):

1. The state of the stress over the cross-sectional area is one-dimensional and uniaxial.

2. The state of the stress at any instant is homogenous and in equilibrium over the entire composite specimen.

3. Transverse strain, lateral inertia, and body forces are negligible.

4. Frictions with the interfaces bar-sample are negligible.

A wave is dispersive if it changes shape (through components which travel at different velocities). Issues rated to the effect of dispersion in a SHPB at a high strain rate are worthy of verification because composite materials undergo elastic deformation under dynamic or non-uniform loading conditions, making it possible for the pulse to change in amplitude and duration during transmission through the specimen. Since the calculated axial stress in the specimen depends linearly on the axial strain on the output bar, wave dispersion would result in underestimating the strength of the specimen.

Using longer bars and a short specimen minimizes the effect of non-uniform stress and non­equilibrium within the specimen used in this study. Since the time to traverse the specimen is short compared to the duration of the wave, equilibrium within the specimen is satisfied by the possible multiple reflections, (Ravichandran & Subbash, 1994). Thus, stress will be homogenous within the specimen, satisfying assumption (3). Transverse strain, lateral inertia, and body forces are all negligible since the rise time condition is satisfied and the impact is parallel to the longitudinal direction. Validity of the SHPB for application to the dynamic behaviour of materials is well documented (Zhao & Gary, 1996), (Follansbee & Frantz, 1983).