Closure to “Contact Unloading Behaviors of Elastic-Power-Law Strain Hardening Material Considering Indenter Elasticity Effect” (Chen, C., Wang, Q., Wang, H., Ding, H., Hu, W., Xie, W., Weng, P., Jiang, L., and Yin, X., 2022, ASME J. Tribol., 144(12), p. 1

Abstract

First of all, thanks to Professor Itzhak Green for the interest in our research paper and providing some comments. The main comments by Professor Green focus on the definitions of some mechanical parameters at initial yield. We have read them in detail and will make explanations in the following: The first parameter is the initial yield indentation δY (Eq. (3) in our paper).In fact, the Poisson’s ratio υ of most common metals is about in the range of 0.28–0.35, such as aluminum (υ = 0.33), bronze (υ = 0.34), stainless steel (υ = 0.3), tungsten (υ = 0.28), iron (υ = 0.3), magnesium (υ = 0.35), etc. After calculation, in this range, the maximum error of δY between the formula suggested by Johnson [1] and the formula suggested by Green [2] is only 6.8% and for the certain Poisson’s ratio υ = 0.3, the error is 4.2%. It illustrates that, in this range, the effect of Poisson’s ratio on δY is limited. It also should be emphasized that, for all contact simulations in our paper, the Poisson’s ratio of elastic-plastic materials is a constant value of 0.3 (as clearly stated in Sec. 2.2). Selecting p0=ϑYσY,ϑY=1.1, which is also selected by Stronge [3] when υ = 0.3, is reasonable, because it is a simpler formula with a good accuracy for common metals.The second parameter is the initial yield stress σY (Eq. (6) in our paper).The authors should state that, in our paper, Ref. [40] in Sec. 2 clearly reported the same form of σY with Eq. (6). In our paper, the research objects are elastic sphere and elastic-plastic half-space. To ensure the purely elastic deformations of the spheres, the ratio of the sphere yield stress to the half-space yield stress should be larger than 2.5 as suggested by Tabor [4], and 2.0 as suggested by Larsson and Olsson [5]. For all contact cases in our paper, the ratio of the sphere yield stress to the half-space yield stress is larger than 3.5. It is obviously that the initial plastic deformation occurs in the elastic-plastic half-space and there is no plastic deformation in sphere during contact. As for the comment by Professor Green, the controversy in Eq. (6) is for the condition that when the yield stresses of the two contact bodies are relatively close and plastic deformation will occur in both contact bodies. It is related to the contact between to two elastic-plastic bodies, which is more complex problem and not involved in our paper. To the author’s knowledge, the contact between the two elastic-plastic bodies has not been fully understood yet. So, when the yield stress of the elastic sphere is much larger than that of the elastic-plastic half-space, Eq. (6) is reasonable.The third parameter is the usage of ratios such as E*/σY.This comment is related to the selection of σY and the effect of Poisson’s ratio on initial yield. The authors would like to reiterate two facts in our paper: (1) the effect of Poisson’s ratio on δY is limited to most common metals and for all contact cases, Poisson’s ratio of elastic-plastic materials is a constant value of 0.3; (2) the research objects are elastic sphere and elastic-plastic half-space, and the yield stress of the elastic sphere is much larger than that of the elastic-plastic half-space. Based on these two facts, the usage of ratios such as E*/σY in our paper is reasonable.