Determination of the Loading Mode Dependence of the Proportionality Parameter for the Tearing Energy of Embedded Flaws i
In this paper, the relationship between the tearing energy and the far-field cracking energy density (CED) is evaluated for an embedded penny-shaped flaw in a 3D elastomer body under a range of loading modes. A 3D finite element model of the system is use
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Determination of the Loading Mode Dependence of the Proportionality Parameter for the Tearing Energy of Embedded Flaws in Elastomers Under Multiaxial Deformations R. J. Windslow, T. W. Hohenberger, and J. J. C. Busfield
Contents 1 Introduction 2 Material Model 3 FEA Model Development 4 FEA Results 5 Discussion 6 Conclusions References
Abstract In this paper, the relationship between the tearing energy and the far-field cracking energy density (CED) is evaluated for an embedded penny-shaped flaw in a 3D elastomer body under a range of loading modes. A 3D finite element model of the system is used to develop a computational-based fracture mechanics approach which is used to evaluate the tearing energy at the crack in different multiaxial loading states. By analysing the tearing energy’s relationship to the far-field CED, the proportionality parameter in the CED formulation is found to be a function of stretch and biaxiality. Using a definition of biaxiality that gives a unique value for each
R. J. Windslow Schlumberger, Ltd., Rosharon, TX, USA T. W. Hohenberger and J. J. C. Busfield (*) Queen Mary University of London, School of Engineering and Materials Science, London, UK e-mail: j.busfi[email protected]
R. J. Windslow et al.
loading mode, the proportionality parameter becomes a linear function of stretch and biaxiality. Tearing energies predicted through the resulting equation show excellent agreement to those calculated computationally. Keyword Biaxiality · Cracking energy density · Elastomer · Fracture · Multiaxial · Tearing energy
1 Introduction Researchers during the early twentieth century suggested that stress concentrations at flaws were the root cause of fracture. However, analytical modelling found that the maximum stress of an elliptical crack approached infinity (a physical impossibility) as the radius of the crack tip tended towards zero [1]. To overcome this problem, Griffith proposed evaluating the local energy field at the crack tip rather than the more complex stress field [2]. Griffith’s premise was that the release of strain energy as a crack propagated was equivalent to the surface energy required to form the new fracture surfaces. Therefore, a crack would only propagate if the resulting release of strain energy was in excess of the surface energy requirements to create the new faces. This proved successful for brittle materials but did not translate to elastomers as dissipative effects caused the released strain energy to significantly exceed the surface energy. Realising the issue, Rivlin and Thomas extended Griffith’s approach to make it more applicable to elastomers and other polymers [3]. This was achieved by introducing a critical energy release rate, above which the crack would grow independent of the test piece geometry. The critical energy release rate, or tearing energy, T, is equivalent to the rate of change in strain energy, U, of the sample, divided by the increase in area of one of the newly formed fracture surfaces, A. Under the assumption that the sample was held at constant length, l, the en
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