• Square cross-section specimens tested in compression SHPB experience stress concentrations and shear stresses at the corners due to geometric mismatch and lateral inertia • Characteristic transfer length (L t ) over which stress concentrations and shear stresses vanish is derived based on shear lag theory • Finite element simulations and SHPB experiments on Al6061 specimens validate the characteristic stress transfer length from the theory • Number of wave transits needed for specimen end forces to equilibrate for square shaped specimens (n = 12 to 18) studied are 3X higher than cylindrical specimens (n = 4 to 6) • Considering stress-strain-strain rate uniformity, optimal specimen aspect ratio is found to be L s /W s = sqrt(1+ν) = 1.14 for a Poisson’s ratio of 0.30. Performing both split Hopkinson pressure bar (SHPB) experiments and finite element simulations, this study investigates the effect of specimen length on dynamic force equilibrium, stress uniformity, and stress concentrations in square cross-section test specimens. While geometric mismatch at the load introduction induces axial stress concentrations, friction at the bar-specimen interfaces and lateral inertia due to Poisson’s ratio (ν) effects induce shear stresses, resulting in complex multi-axial stress states near the specimen ends and delayed force equilibrium. A semi-analytical formulation based on composite material shear lag theory is employed to estimate a characteristic transfer length L t = W s 1 + υ 4 over which the axial stress concentrations and shear stresses vanish from corners in a compression SHPB square cross-section specimen of width, W s . The transfer length formula is combined with FE and SHPB experimental measurements to determine a critical specimen length, L scrit = 2L t and associated aspect ratio L s c r i t W s = 1 + υ 2 . These findings are validated by performing SHPB FE simulations and experiments for plastically deforming Al6061 specimens of three different lengths, L s ∼ L scrit , 2L scrit and 3.5L scrit (L s /W s ∼ 0.47, 1.18 and 2) and a width of 12.7 mm. The critical stress transfer length predicted by the FE models and estimated from experimental digital image correlation (DIC) displacements match the analytical predictions. The number of wave transits, n, needed for specimen end forces to equilibrate in square shaped specimens ranges from 12 ≤ n ≤ 18 and are 3X higher than what’s reported in the literature (n = 4 to 6) for cylindrical specimens. For L s L scrit , average stresses and strains estimated using the classical SHPB equations represents the actual/expected material response reasonably well. When using strains measured via DIC, the estimated stress-strain response matches the actual/expected material response for L s ≥ L scrit . Considering stress-strain-strain rate uniformity, the optimal specimen length is shown to be L s ∼ 2L scrit resulting in an optimal aspect ratio of L s /W s = 2L scrit /W s = sqrt(1+ν) = 1.14 for a Poisson’s ratio of 0.30.
Sockalingam et al. (Fri,) studied this question.