MATEC Web Conf.
Volume 80, 2016NUMIFORM 2016: The 12th International Conference on Numerical Methods in Industrial Forming Processes
|Number of page(s)||8|
|Section||MS11: Advances in Forming Simulation. A Symposium in Honor of Professor J.L. Chenot|
|Published online||24 October 2016|
Elastic-plastic transition: A universal law
Research and Innovation Center, Ford Motor Company, Michigan, 48131, United States
2 Department of Materials Science and Engineering, The Ohio State University, Columbus, 43210, United States
3 School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, China
a Corresponding author: email@example.com
Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following:
There is no significant linear elastic region; the proportional limit is ~0 MPa when measured with sufficient sensitivity.
Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the “modulus reduction rate.”The corresponding equation captures ~80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation.
Most interestingly, the transitional behavior for all alloys follows a “Universal Law” requiring no fit parameters. The law depends only upon the strength of the material and its Young’s modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures ~90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply.
The practical and theoretical implications of these results are discussed. The results provide a simple path to significantly improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.
© The Authors, published by EDP Sciences, 2016
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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