Abstract
The scope of the present article is the study of the fracture initiation from initial spherical flaws in incompressible propellant materials. Using a constitutive law, derived from the neo-Hookean strain energy function, one may deduce the relation between the radial pressure applied at infinity and the corresponding extension ratio, at the surface of the cavity. An equation which defines the critical extension ratio for a given value of a parameter, κ, was derived and the corresponding critical load, pc, is related to the critical cavity extension ratio. Plots for the extension ratio and normalized pressure were provided solving the appropriate equation derived from the analysis. The failure of the cavity is associated with the incremental energy transfer at a constant critical stress between the applied work, internal strain energy and surface energy. The influence of the surface energy on the radial deformation of an initially intact sphere is presented and it turns out that a characteristic cavitation phenomenon occurs instead of the bifurcation. A mathematical formula is derived for the pressure, per unit current area, which is valid for a general form of incompressible elastic strain energy function. Using the derived formula one may deduce the relation between the radial pressure and the corresponding extension ratio at the surface of the cavity. In an incompressible material of given modulus and surface energy it is proved that a critical field stress exists at which a small internal cavity may grow in size where the significant quantities are the radial and tangential strains.
Highlights
The scope of the present article is the study of the fracture initiation from initial spherical flaws in incompressible propellant materials
The microstructural damage and fracture processes associated with the fracture-toughness behavior of a polymer-matrix composite solid rocket-propellant material have been studied [1]
Experiments have been performed on poker chip type of sample, using the acoustic emission technique, to evaluate the cavitation process in rubber materials [2]
Summary
The microstructural damage and fracture processes associated with the fracture-toughness behavior of a polymer-matrix composite solid rocket-propellant material have been studied [1]. Failure of the cavity will be associated with incremental energy transfers at some constant critical stress pc between applied work, internal strain energy, and surface energy. Considerations similar to those used by Griffith [13] will be employed, but in addition finite strains will be permitted because of our desired application to rubbery incompressible media. A plot of the surface traction stretch relation for an initially intact incompressible neo-Hookean sphere, for various values of S is shown in Fig. 2 (see ref. [16])
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.