Method of theoretically calculating spherical stress wave field in linear-hardening materials under impact load

Abstract

Based on the linear hardening plastic constitutive model, the theoretical solution of the elastic-plastic spherical stress wave field under impact load is established. Firstly, the influence of the impact load unloading rate on the propagation of the spherical stress wave is analyzed, and three different types of propagation images are obtained. On this basis, the method of theoretically calculating the spherical wave equation in elastic stage, plastic loading stage and unloading stage is established separately, and the calculation scheme of particle displacement, particle velocity, stress and strain is given. Compared with the existing theoretical methods, this method takes into account the different propagation patterns of the stress waves under different unloading rates, and shows how to calculate the stress wave parameters in unloading stage, which is more applicable. This method is used to calculate the elastic-plastic spherical stress wave field under constant shock load and exponential attenuation shock load. The calculated results are in good agreement with those from the existing theoretical method and numerical simulation results in the elastic stage and also in the plastic loading stage. In the unloading stage, the existing theoretical method is no longer applicable, while the results obtained in this paper are in good agreement with the numerical simulation results, which verifies the correctness of the theoretical method.

An analytical method for the spherical stress wave equation in linear hardening materials

“…The physical model in this paper refers to reference [19], as shown in Figure 1. Consider an infinite solid medium with a spherical cavity.…”

“…Reference [19] analyzed the propagation of the elastic-plastic spherical stress waves under the physical model above and obtained three different types of stress wave propagating images, as shown in Figure 2. We will solve the wave equation analytically in this section according to Figure 2.…”

“…The results verify the correctness of the analytical method. The error of the analytical results is mainly caused by the simplification of the stress wave propagating [19]. In addition, there is a difference between the analytical method and the numerical method.…”

“…However, researchers pay less attention to the influence of plasticity. Wang et al [19] developed a study on the theoretical calculation method for the spherical stress wave field in linear hardening materials under impact load, and obtained three different types of stress wave propagating images by analyzing the effects of the unloading. But the specific solving method for the wave equation was not given.…”

“…But the specific solving method for the wave equation was not given. In this paper, we develop a study on the analytical method for the spherical stress wave equation using the travelling wave method on the basis of reference [19]. The elastic, unloading and plastically loading wave equations are solved, separately.…”