Viscoplastic model for rheonomic behaviour of shape-memory alloys with a power dependence for rheonomic strain speed | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 22 > №3 / 2017 / Pages: 378-401

Viscoplastic model for rheonomic behaviour of shape-memory alloys with a power dependence for rheonomic strain speed


For the description of experimentally observed rheonomic behavior of shape-memory alloys, the analogue of viscoplastic model with power dependence for rheonomic strain speed has been introduced. The proposal to introduce power dependence is justified by the evident nonlinear initial asymptotic of experimental creep diagram displaying after the spike in stress under the process of stress-controlled stepwise load. That was the reason behind the poor correspondence between the experiment results and the model curves, which were generated based on the linear models introduced in the early works. It has been proven that for any process, which might be conceptually split into subprocesses, where each of them is ether an active monotonic stress process, determined by a smooth and locally bounded stress function, or a stress and unload process which is not active at all internal points, under condition of power exponent where both n and (which is a Weibull’s function power parameter) are integers, the necessary and sufficient condition for the record of model constitutive equations without the non-analytical function to retrieve the positive part (going forwards, will be labeled as an angular bracket symbol) is the following: the difference between deformations in a limiting slow and in a limiting fast load stress process should not be negative, and it cannot decrease with the increase in stress load. The method of model calibration is offered with the use of a least squares approach and the experimental results from a process of stress-controlled stepwise load. Using the method proposed, the evaluation of model parameters was done under conditions where n =1 and n =3. All sets of parameters received were tested to meet the conditions for the use of model without the angular brackets and non-negativity of the final loads during the stress-relaxation process. It was determined that the model curves with n =3 and the experimental results have a much better consistency (in comparison to the model constructed without a power parameter, which is equivalent to the n =1 model) for the stress-controlled stepwise load process. The simulation results in terms of dimensional variables using the calibrated models for n =1 and n =3 for the monotone stress-controlled and strain-controlled load processes, stress relaxation process and stress-controlled stepwise load process were presented. Analytical form of solution was derived for the processes of stress-controlled stepwise load and stress relaxation. Investigated the cluster of stress reduction processes with the following load increase up to boundaries of an active process. For such processes, an analytical type of function was derived that allows determining dependency between the deformation level and stress applied.