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Symmetry breaking and other nonlinear elastic responses of metallic glasses subject to uniaxial loading
Topologically disordered metallic glasses (MGs) are known for exceedingly high elastic limit (2%â€“3%) and large local deformation at the onset of yielding in the form of shear banding. However, the manifestation of the large elastic deformation has not been taken into consideration in understanding the overall mechanical responses. By applying a finite deformation theory to initially isotropic solids under uniaxial loading, we investigate the nonlinear elastic behavior and its effects on mechanical properties. We take bulk metallic glass (BMG) Zr52.5Ti5Cu17.9Ni14.6Al10 as an example which is the only system by far with the experimentally measured nonlinear elastic constants up to the fourth order available for our theory. We show that the uniaxial loading breaks the isotropic symmetry of the MG and makes it transversely isotropic. We also predict the strain dependence of Poisson's ratio, Young's modulus, and anisotropic coefficients of the amorphous solids. Our work also gives the first estimate of the theoretical stress-strain relations and the elastic stability conditions under uniaxial loading from which we obtain the maximum tensile and compressive strengths and intrinsic deformation modes at the corresponding maximum stresses. Although depicting ideal scenarios, the theoretical results provide a useful reference for understanding mechanical response of MGs at large deformation.