Abstract
In relation to the dynamic tests of materials, the approach to solve the viscoelastic wave propagations in a one dimensional viscoelastic rod was summarized. By conducting Laplace transform, the governing partial differential equations were transformed to ordinary differential equations for the image functions, which were solved analytically with suitable boundary equations. Inversely transforming these image functions gives the results of the stress, velocity, and strain in the bar. Two wave problems occurred in split Hopkinson pressure bar (SHPB) tests are analyzed: 1) the problem of evaluating the internal stress distributions in a viscoelastic specimen; and 2) the problem of stress wave propagations in a viscoelastic bar. Both problems were solved numerically by way of numerical inverse Laplace transform. For the first problem, the special case when the specimen is pure elastic was solved analytically, giving the exact solution to the problem of elastic wave propagation in a sandwich elastic media.
Highlights
Split Hopkinson Pressure Bar (SHPB, known as Kolsky bar) test technique is widely used in the dynamic material properties tests under strainrate 102–104 s−1
The exact analysis of SHPB experimental results is based on the two basic assumptions: one-dimensional stress wave propagation in the bar, the uniform stress/strain of the specimen along the length direction
The differential equation of the image function σ (x, s) gives the result of the stress based on the Eqs. (7)–(10): d 2 σdx2
Summary
Split Hopkinson Pressure Bar (SHPB, known as Kolsky bar) test technique is widely used in the dynamic material properties tests under strainrate 102–104 s−1. While the specimen is viscoelastic material, the key of the problem is summed up in solving the viscoelastic wave propagation. The first method is a finite difference method, solving the wave problem by the compatibility relationships along the characteristic lines [1,2,3]. The latter method is a analytical method by way of Fourier series. Laplace transform as a kind of common integral transform, can be used for the solving the wave propagation problems of SHPB or specimen. By conducting Laplace transform, we analyzed the viscoelastic wave propagation rule of short specimens in the SHPB experiment
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