Abstract
To better describe its constitutive relation, we need a new constitutive equation for an important nonlinear elastic material, Mn-Cu damping alloy. In this work, we studied the nonlinear and hysteretic characteristics of the stress-strain curve of the M2052 alloy with the uniaxial cyclic tensile test with constant strain rate. The strain rate and amplitude correlations of M2052 resembled those of nonlinear viscoelastic material. Therefore, we created a new constitutive equation for the M2052 damping alloy by modifying the fractional Maxwell model, and we used the genetic algorithm to carry out numerical fitting with MATLAB. By comparing with the experimental data, we confirmed that the new constitutive equation could accurately depict the nonlinear constitutive relation and hysteretic property of the damping alloy. Taken together, this new constitutive equation for Mn-Cu damping alloy based on the fractional Maxwell model can serve as an effective tool for further studies of the constitutive relation of the Mn-Cu damping alloys.
Highlights
Mn-Cu damping alloy is a typical twin-damping alloy
In view of the existing study about nonlinear constitutive relation of Mn-Cu damping alloy being less, and that it should not be treated as linear elastic material, this study chose M2052 damping alloy as the research object, through uniaxial cyclic tensile test under constant strain rate to analysis its nonlinear constitutive relation and hysteretic characteristics
We can get the following conclusions: 1. Through uniaxial cyclic tensile test with constant strain rate, it is concluded that Mn-Cu damping alloy can be considered as a viscoelastic material
Summary
Mn-Cu damping alloy is a typical twin-damping alloy. In the 1940s, Zener [1] first developed. Based on the measured data of energy storage modulus and loss factor of the damping alloy in the frequency domain, they developed a three-parameter constitutive relation model of the damping alloy. Mn-Cu damping alloy and SMA are twin damping alloys, but the first one do not have the shape memory effect and superelastic effect of the second one, so their constitutive relations are different It can be seen from literature [11,12,13] that the constitutive relationship of damping alloy can be well described by treating the damping alloy as a viscoelastic material. The fractional Maxwell model can describe the nonlinear damping properties of materials within a wide frequency. We simulated the nonlinear constitutive relationship of damping alloy and compared with curves
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