In the case of rigid/perfectly plastic material, the velocity fields in the vicinity of maximum friction surfaces must be describable by nondifferentiable functions. In particular, the equivalent strain rate follows an inverse square root rule near such surfaces and, therefore, approaches infinity at the surface. Because the equivalent strain rate is involved in many evolution equations for material properties, its behavior near the maximum friction surfaces should lead to high gradients in the material properties near the surface, which is confirmed by experiment. To quantitatively describe the evolution of material properties in the vicinity of surfaces with high friction, the concept of strain rate intensity factor can be adopted.
An Approach to Predicting Evolution of Material Properties Near Surfaces With High Friction in Metal Forming
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Alexandrov, S. "An Approach to Predicting Evolution of Material Properties Near Surfaces With High Friction in Metal Forming." Proceedings of the World Tribology Congress III. World Tribology Congress III, Volume 1. Washington, D.C., USA. September 12–16, 2005. pp. 817-818. ASME. https://doi.org/10.1115/WTC2005-63296
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