Theoretical Consideration on High Strain Rate Fragmentation of a Closed Vessel

Abstract

In the previous Report No. 1, the empirical equations were obtained, showing that the characteristic indices, q₀, q_m and β of the fragment weight distribution function, F(q)=1-exp[-(q/q_m)β] which is derived from the proposed fracture model, are the functions of fracture strain rate ε_f of a closed vessel wall. This paper gives the theoretical discussion on those equations, resulting in the following conclusions:
(1) The dependence of the fragment mean weight upon ε_f is well explained by the nucleation process.
(2) Generally, the total effective work to be required for fragmentation varies with the material even in the same loading condition. It is inferred that this comes from the existence of energy coefficient λ inherent to the material, which can be derived from the empirical equations. Theoretically, the λ-value, defined as the ratio of q_m^β to q₀^2/3, determines the interrelation between the indices, q₀, q_m and β, covering the range of 0<λ<0.872.
(3) All the values of q₀, q_m and β decrease with increasing ε_f. The value of fracture exponent β is in the range of 0<β<2/3.
In addition, two engineering cases are given as the examples of application of the fragmentation concept.