Theoretical estimates of the parameters of longitudinal undular bores in PMMA bars based on their measured initial speeds

TL;DR

This paper presents a theoretical approach to estimate parameters of undular bores in PMMA bars by analyzing measured initial wave speeds and strain rates, validated through experiments.

Contribution

It introduces a method to estimate undular bore parameters in PMMA using measured wave speeds and strain rates, based on analytical solutions of the Gardner equation.

Findings

Good semi-quantitative agreement between estimates and experimental data.

Strain rate and oscillation growth depend on pre-strain, post-strain, and cross section.

Analytical estimates effectively predict undular bore evolution in PMMA bars.

Abstract

We study the evolution of the longitudinal release wave that is generated by induced tensile fracture as it propagates through solid rectangular Polymethylmethacrylate (PMMA) bars of different constant cross section. High speed multi-point photoelasticity is used to register the strain wave. In all cases, oscillations develop at the bottom of the release wave that exhibit the qualitative features of an undular bore. The pre-strain, post-strain, strain rate of the release wave and the cross section dimensions determine the evolution of the oscillations. From the wave speed and strain rate close to the fracture site, we estimate the strain rate of the release wave as well as the growth of the amplitude and duration of the leading oscillation away from the fracture site on using formulae derived from the simple analytical solution [1] of the linearised Gardner equation (linearised near the pre-strain level at fracture), developed in our earlier work . Our estimates are then compared to experimental data, where qualitative and good semi-quantitative agreements are established.