Fe Calculations of J-integral in a Constrained Elastomeric Disc with Crack Surface Pressures and Isothermal Loads

In this study, we performed linear and nonlinear FE (Finite Element) analyses to compute J-integrals for a centrally perforated star-shaped disc, which was made of an elastomeric material, under crack surface pressures and isothermal loads. Deformations of the disc were constrained by a circular steel ring enclosing the disc. Different crack sizes were assumed to exist in the front of the star-shaped notches. For the linear analysis, material compressibility was modeled with Poisson's varying form 0.48 to 0.4999. In addition, with the presence of the crack surface pressure, the J-integral was modified by including an additional line integral. Numerical studies show that the value of the J-integral increases with the increase of the crack length, reaches a maximum value at 1in. of crack length, and then decreases gradually. Both linear and nonlinear analyses agree qualitatively but differ quantitatively. It is also found that values of the J-integral strongly depend upon the material compressibility. INTRODUCTION Defects such as voids and cracks may form in elastomeric materials due to the manufacturing, handling or ageing. To ensure the integrity and reliability for such structural components, fracture toughness should be ascertained so that the onset of the crack growth can be determined based on the fracture resistance of the material. The J-integral is a measure of the fracture toughness, and commonly used as a criterion to determine the maximum operating loads for a given preexisting defect. Most elastomeric materials such as rubbers and solid propellants exhibit mechanical behavior that remain nonlinearly elastic at large strains and have very little compressibility, and hence these materials are often referred to as fully or nearly incompressible. When these elastomers are loaded in a highly confined state, even a small change in the compressibility can result in dramatic difference of stress distributions. For example, Schapery [1] conducted an experiment for a circular polymeric disk under the hydrostatic tension, and showed that a small change in Poisson’s ratio could alter the stress distribution significantly. Many investigations have been conducted to determine the relationship between the crack-tip stress and strain fields and the energy release rate for rubber-like materials. Thomas [2] was the first to study this relationship experimentally. He found that the average strain energy density in a sheet of rubber was uniquely related to the energy release rate regardless of the specimen type. Thomas’s conclusion had been validated later by Andrews [3] and Knauss [4]. Andrews used a microscopic, photoelastic technique to quantify the strain fields around the crack tip whereas Knauss used a printed-grid technique. Morman et al. [5] also gave an analytical solution relating the energy release rate to the crack tip radius. Rice’s development of the J-integral [6] gave a mathematical argument to characterize the local stress-strain field around a crack front. The J-integral was found to be equivalent to the energy release rate and independent of the path contours. Based on the J-integral, several pathindependent integrals have been proposed for more general elastic-plastic problems by including non-proportional loading and unloading, thermal strains, and material inhomogeneity. A review about the limitations and salient features of these integrals can be found in Kim and Orange’s work [7]. Note that Rice‘s original form of the J-integral is valid even for the nonlinear elastic materials. The problem of a crack in an infinite, thin, and incompressible sheet subjected to a biaxial tension at infinity was studied, within the framework of nonlinear elasticity for a Neo-Hookean material, by Wong and Shield [8], and Chang [9] generalized the J-integral for nonlinear elastic materials with finite strains. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE JUN 2004 2. REPORT TYPE 3. DATES COVERED 4. TITLE AND SUBTITLE FE Calculations of J-Integrals in a Constrained Elastomeric Disk with Crack Surface Pressure and Isothermal Load 5a. CONTRACT NUMBER