Hyperelastic effects in brittle materials failure
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Hyperelastic effects in brittle materials failure Markus J. Buehler1, Farid F. Abraham2 and Huajian Gao1 Max Planck Institute for Metals Research, 70569 Stuttgart, Germany 2 IBM Almaden Research Center, San Jose, CA 95120-6099, USA 1
ABSTRACT A fact that has been neglected in most theories of brittle fracture is that the elasticity of a solid clearly depends on its state of deformation. Metals will weaken, or soften, and polymers stiffen as the strain approaches the state of materials failure. It is only for infinitesimal deformation that the elastic moduli can be considered constant and the elasticity of the solid linear. We show by large-scale atomistic simulations that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of fracture and that linear theory is incapable of capturing all phenomena. We introduce a new concept of a characteristic length scale χ for the energy flux near the crack tip and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale. The new length scale χ, heretofore missing in the existing theories of dynamic fracture, helps to form a comprehensive picture of crack dynamics, explaining super-Rayleigh and supersonic fracture. We further address the stability of cracks, and show agreement of the Yoffe criterion with the dynamics of cracks in harmonic systems. We find that softening hyperelastic effects lead to a decrease in critical instability speed, and stiffening hyperelastic effects leads to an increase in critical speed. The main conclusion is that hyperelasticity plays a critical role in forming a complete picture of dynamic fracture. INTRODUCTION We show by large-scale atomistic simulation that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of brittle fracture. This is in contrast to many existing theories of dynamic fracture where the linear elastic behavior of solids is assumed sufficient to predict materials failure [1]. Some experiments [2-4] as well as many computer simulations [5, 6] have shown a significantly reduced crack propagation speed in comparison with the theoretical predictions. Such discrepancies between theories, experiment and simulations can not solely be attributed to the fact that real solids have imperfections, as similar discrepancies also appear in molecular-dynamics simulations of cracks traveling in perfect atomic lattices. It was recently proposed that hyperelastic effects at the crack tip play an important role in the dynamics of fracture [3, 7]. In contrast, it is not generally accepted that hyperelasticity should play a significant role in dynamic fracture. This is because the zone of large deformation is highly confined to the crack tip, so that the region where linear elastic theory does not hold is extremely small compared to the extensions of the specimen [1]. Here we use large-scale molecular-dynamics simulations [5, 8-10] in conjunction with continuum mechanics concepts [1] to
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