Numerical Study of the Effect of Materials’ Plastic Behavior on Equibiaxial Residual Stress Measurement Using Indentation

Document Type : Research Paper


1 department of mechanical engineering, faculty of engineering, university of zanjan, zanjan, iran

2 University of Zanjan


Indentation is a new method for estimating residual stress. The plastic behavior of the materials under study can affect indentation parameters and, thus, influences the results of residual stress measurement. In this paper, the effect of yield stress and work-hardening exponent on the accuracy of residual stress measurements in steels and aluminums was studied.
Results showed that, for materials with a low strain-hardening exponent and yield strain, Lee’s model is applicable; for materials with relatively high amounts of strain-hardening exponent and yield strain, Wang’s model is more accurate; and for materials with a medium range of strain-hardening exponent and yield strain all three models can be applied. It was also found that the stresses being tensile or compressive can affect the accuracy of the calculated results for each model. The applicable range of each model is represented in the article.


Main Subjects

[1] Xiao, L., Ye, D., and Chen, C., "A Further Study on Representative Models for Calculating the Residual Stress Based on the Instrumented Indentation Technique", Comp. Mater. Sci. Vol. 82,  pp. 476-482, (2014).
[2] Tsui, T.Y., Oliver ,W.C., and Pharr, G.M., "Influences of Stress on the Measurement of Mechanical Properties using Nanoindentation: Part I. Experimental Studies in an Aluminum Alloy", J. Mater. Research, Vol. 11, No. 03, pp. 752-759, (1996).
 [3]  Bolshakov, A., Oliver ,W.C., and Pharr, G.M., "Influences of Stress on the Measurement of Mechanical Properties using Nanoindentation: Part II. Finite Element Simulations", J. Mater. Research, Vol. 11, No. 03, pp. 760-768, (1996).
[4]   Suresh, S., and Giannakopoulos, A.E., "A New Method for Estimating Residual Stresses by Instrumented Sharp Indentation", Acta Mater. Vol. 46, No. 16, pp. 5755-5767, (1998).
[5] Carlsson, S., and Larsson, P.L., "On the Determination of Residual Stress and Strain Fields by Sharp Indentation Testing.: Part I: Theoretical and Numerical Analysis", Acta Mater. Vol. 49, No. 12, pp. 2179-2191, (2001).
[6] Lee, Y.H., and Kwon, D., "Measurement of Residual-stress Effect by Nanoindentation on Elastically Strained (1 0 0) W", Scripta Mater. Vol. 49, No. 5, pp. 459-465, (2003).
[7] Wang, Q., Ozaki, K., Ishikawa, H., Nakano, S., and Ogiso, H., "Indentation Method to Measure the Residual Stress Induced by Ion Implantation", Nucl. Instrum. Methods Phys. Res. B, Vol. 242, No. 1–2, pp. 88-92, (2006).
[8] Bocciarelli, M., and Maier, G., "Indentation and Imprint Mapping Method for Identification of Residual Stresses", Comp. Mater. Sci. Vol. 39, No. 2, pp. 381-392, (2007).
[9] Huber, N., and Heerens, J., "On the Effect of a General Residual Stress State on Indentation and Hardness Testing", Acta Mater. Vol. 56, No. 20, pp. 6205-6213, (2008).
[10] Heerens, J., Mubarok, F., and Huber, N., "Influence of Specimen Preparation, Microstructure Anisotropy, and Residual Stresses on Stress–strain Curves of Rolled Al2024 T351 as Derived from Spherical Indentation Tests", J. Mater. Research,Vol. 24, No. 3, pp. 907-917, (2011).
[11] Rydin, A., and Larsson, P.L., "On the Correlation between Residual Stresses and Global Indentation Quantities: Equi-Biaxial Stress Field", Tribol. Lett. Vol. 47, No. 1, pp. 31-42, (2012).
[12] Lee, J.H., Lee, H., Hyun, H.C., and Kim, M., "Numerical Approaches and Experimental Verification of the Conical Indentation Techniques for Residual Stress Evaluation", J. Mater. Research, Vol. 25, No. 11, pp. 2212-2223, (2011).
[13] Rickhey, F., Lee, J.H., and Lee, H., "A Contact Size-independent Approach to the Estimation of Biaxial Residual Stresses by Knoop Indentation", Mater. Des., Vol. 84, pp. 300-312, (2015).
[14] Ahn, H.J., Kim, J.h., Xu, H., Lee, J., Kim, J.Y., Kim, Y.C., and Kwon, D., "Directionality of Residual Stress Evaluated by Instrumented Indentation Testing using Wedge Indenter", Met. Mater. Int., Vol. 23, No. 3, pp. 465-472, (2017).
[15] Yonezu, A., Kusano, R., Hiyoshi, T., and Chen, X., "A Method to Estimate Residual Stress in Austenitic Stainless Steel using a Microindentation Test", J. Mater. Eng. Perform. Vol. 24, No. 1, pp. 362-372, (2015).
[16] Ding, Y., and Chromik, R.R., "Relationship between Indentation Plastic Zone Size and Residual Stresses in Plastically Deformed Fe", Mater. Sci. Eng A Struct. Mater. Vol.  696, pp. 1-9, (2017).
[17] Pham, T.H., and Kim, S.E., "Determination of Equi-biaxial Residual Stress and Plastic Properties in Structural Steel using Instrumented Indentation", Mater. Sci. Eng. Struct. Mater(A). Vol. 688, pp. 352-363, (2017).
[18] H Faisal, N., and Ahmed, R., "A Review of Patented Methodologies in Instrumented Indentation Residual Stress Measurements", Recent Pat. Mech. Eng. Vol. 4, No. 2, pp. 138-152, (2011).
[19] Fischer-Cripps, A., "Nanoindentation", Springer, New York, pp. 21-37, (2011).
[20] Fischer-Cripps, A.C., "Nanoindentation", Springer, New York, pp. 105-117, (2011)
[21] Yan, J., Karlsson, A.M., and Chen, X., "Determining Plastic Properties of a Material with Residual Stress by using Conical Indentation", Int. J. Solids Struct. Vol. 44, No. 11, pp. 3720-3737, (2007).