Finite Element Simulation of Spherical Indentation Experiments

Finite Element Simulation of Spherical Indentation Experiments

S. Syngellakis H. Habbab B.G. Mellor

Wessex Institute, UK

University of Southampton, UK

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The problem of indentation of ductile materials by ball indenters is, in this paper, addressed by numerical modelling. A finite element model is built using general purpose software. The axisymmetry of the problem is taken into account thus reducing its dimensionality. Particular attention is given to contact modelling as well as mesh design for optimal performance. The model is validated by comparing its predictions to the exact elastic solution as well as experimental measurements from elasto-plastic indentation tests. In the latter case, indenter imperfection is accounted for and mate rial input are stress-strain curves originating from tensile tests. The sensitivity of numerical results to indenter elasticity is investigated. The effect of friction and specimen creep during indentation on load-displacement predictions is also assessed.


creep, elasto-plastic deformation, finite element modelling, friction, spherical indentation


[1] Sneddon, I.N., The relation between load and penetration in the axisymmetric Bouss inesq problem for a punch of arbitrary profile. International Journal of Engineering Science, 3(47), pp. 47–57, 1965.

[2] Taljat, B., Zacharia, T. & Kosel, F., New analytical procedure to determine stress-strain curve from spherical indentation data. International Journal of Solids and Structures, 35(33), pp. 4411–4426, 1998.

[3] Cao, Y.P. & Lu, J., A new method to extract the plastic properties of metal materi als from an instrumental spherical indentation loading curve. Acta Materialia, 52, pp. 4023–4032, 2004.

[4] Habbab, H., Mellor, B.G. & Syngellakis, S., Post-yield characterisation of metals with significant pile-up through spherical indentations. Acta Materialia, 54, pp. 1965–1973, 2006.

[5] Zhao, M., Ogasawara, N., Chiba, N. & Chen X., A new approach to measure the elastic plastic properties of bulk materials using spherical indentation. Acta Materialia, 54(1), pp. 23–32, 2006.

[6] Lee, J.H., Kim, T. & Lee, H., A study on robust indentation techniques to evaluate elastic–plastic properties of metals. International Journal of Solids and Structures, 47, pp. 647–664, 2010.

[7] Donohue, B.R., Ambrus, A. & Kalidindi, S.R., Critical evaluation of the indentation data analyses methods for the extraction of isotropic uniaxial mechanical properties using finite element models. Acta Materialia, 60(9), pp. 3943–3952, 2012.

[8] Barbadikar, D.R., Ballal, A.R., Peshwe, D.R. & Mathew, M.D., Finite element analysis of deformation due to ball indentation and evaluation of tensile properties of tem pered P92 steel. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 46(8), pp. 3448–3459, 2015.

[9] Dean, J. & Clyne, T.W., Extraction of plasticity parameters from a single test using a spherical indenter and FEM modelling. Mechanics of Materials, 105, pp. 112–122, 2017.

[10] Yamamoto, T., Kurishita, H. & Matsui, H., Modeling of the cyclic ball indentation test for small specimens using the finite element method. Journal of Nuclear Materials, 271–272, pp. 440–444, 1999.

[11] Ma, L., Low, S.R. & Song, J., Finite-element modeling and experimental comparisons of the effects of deformable ball indenters on Rockwell B hardness tests. Journal of Testing and Evaluation, 31(6), pp. 514–523, 2003 

[12] Kogut, L. & Komvopoulos, K., Analysis of the spherical indentation cycle for elastic perfectly plastic solids. Journal of Materials Research, 19(12), pp. 3641–3653, 2004.

[13] Karthik, V., Visweswaran, P., Bhushan, A., Pawaskar, D.N., Kasiviswanathan, K.V., Jayakumar, T. & Raj, B., Finite element analysis of spherical indentation to study pile up/sink-in phenomena in steels and experimental validation. International Journal of Mechanical Sciences, 54(1), pp. 74–83, 2012.

[14] Available at:

[15] Available at:

[16] Wilks, J. & Wilks, E., Properties and Applications of Diamond, Butterworth Heineman: Oxford, 1991.

[17] Syngellakis, S., Habbab, H. & Mellor, B.G., Weld zone material characterisation based on spherical indentation data. International Journal of Computational Methods and Experimental Measurements, in print, 2017.

[18] Habbab, H., Post-yield characterisation of welds based on instrumented hardness tester data, PhD Thesis, University of Southampton, 2005.

[19] Chudoba, T. & Richter, F., Investigation of creep behaviour under load during indenta tion experiments and its influence on hardness and modulus results. Surface & Coatings Technology, 148(2–3), pp. 191–198, 2001.

[20] Pharr, G.M., Oliver, W.C. & Brotzen, F.R., On the generality of the relationship among contact stiffness, contact area, and elastic-modulus during indentation. Journal of Materials Research, 7(3), pp. 613–617, 1992.

[21] Oliver, W.C. & Pharr, G.M., An improved technique for determining hardness and elas tic modulus using load and displacement sensing indentation experiments. Journal of Materials Research, 7(6), pp. 1564–1583, 1992.