General Analytical Solutions for Dynamic Load-Carrying Capacity of Brittle Materials Under an Arbitrary Incident Stress Wave

Abstract

In this study, two general solutions for the dynamic tensile load-carrying capacity of brittle materials subject to an arbitrary incident stress wave in the form of Fourier integrals are derived. In order to verify the general solutions, we reduce them to three particular solutions, respectively, i.e., trapezoidal pulse, quadratic pulse and cubic pulse. It is found that all of them can well capture the experimental trends in the previous studies. In between, the first two particular solutions can exactly accord with the two previous analytical solutions under the same boundary conditions, respectively. Therefore, for arbitrary tensile boundary pulses, the dynamic tensile strength of the brittle materials can be calculated from static parameters and characteristics of external loading. This study improves the credibility of the previous works that working on deriving the dynamic load-carrying capacity through analytical methods, and thus, consolidate their theoretical foundation. Meanwhile, on basis of the general solution, the relation between the dynamic tensile load-carrying capacity and strain rate can be further deduced by combining static parameters, hence, it could be inappropriate to claim the strain rate effect on tensile strength as an intrinsic material property anymore. In addition, we found that the process to obtain an explicit analytical solution becomes increasingly difficult with the increased complexity of waveform for an incident pulse, or even no explicit solution can be obtained.