Abstract
Based on previous experimental results of the plastic dynamic analysis of metallic glasses upon compressive loading, a dynamical model is proposed. This model includes the sliding speed of shear bands in the plastically strained metallic glasses, the shear resistance of shear bands, the internal friction resulting from plastic deformation, and the influences from the testing machine. This model analysis quantitatively predicts that the loading rate can influence the transition of the plastic dynamics in metallic glasses from chaotic (low loading rate range) to stable behavior (high loading rate range), which is consistent with the previous experimental results on the compression tests of a Cu50Zr45Ti5 metallic glass. Moreover, we investigate the existence of a nonconstant periodic solution for plastic dynamical model of bulk metallic glasses by using Manásevich–Mawhin continuation theorem.
Highlights
In [1], Cheng et al investigate a plastic deformation and give the following model σp − kx − σf x′ πd2 4 Mx′′, (1)where σp is the loading stress of the shear bands, d is the sample diameter, x is the shear sliding displacement, M is the equal e ective mass, and it is the e ective inertia of the machine-sample system (MSS) when responding to the stress gradient and is an empirical parameter estimated to be of the order of 10–100 kg for a typical MSS
We establish a model considering the internal friction during the plastic deformation and investigate how the parameters influence the stability of the system
E increasing of the friction coefficient improves the resistance of the motion
Summary
In [1], Cheng et al investigate a plastic deformation and give the following model σp − kx − σf x′. We give the existence of upper and lower bounds of the periodic solution of this equation. If c weak repell; if c > (Aσf p)2), the equilibrium /(1 + p)2), there exists an unstable periodic orbit of system (11) from the equilibrium point E. is is subcritical bifurcation. I.e., ασ By f0Ains dinrocrneoavs–inHgoapbfobuitfuσrfc0.ation theorem (see [11], P. the equilibrium p)2/A, there exists an unstable periodic orbit of system (11) from the equilibrium point E. is is subcritical bifurcation. We prove the existence of a nonconstant ω-periodic solution for model (6) by applying Manasevich–Mawhin continuation theorem. We consider the following differential equation with a singularity of derivative: x′′ + Cx′ + g x′ + Kx e(t),.
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