Crystal plasticity finite element simulations of the indentation test

Crystal plasticity finite element simulations of the indentation test

Karol Frydrych

Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland.



The goal of the paper is to report the successful simulations of the nanoindentation problem. The finite-strain isotropic elasto-plasticity and crystal elasto-plasticity models used for the simulations are described. The developed contact formulation describing the contact with rigid surface approximating pyramidal indenter is presented. Both tensile stress-strain and indentation load-penetration curves obtained with a single set of material parameters are presented to be in the satisfactory agreement with experimental data. It seems that such a result is presented for the first time

Cite as:

Frydrych, K., (2019). Crystal plasticity finite element simulations of the indentation test. Computer Methods in Materials Science, 19(2), 41-49.

Article (PDF):


Crystal plasticity, Indentation, Al 6061-T6, Nanoindentation, Vickers, Berkovich, CPFEM


Alcalá, J., Casals, O., Očenášek, J., 2008, Micromechanics of pyramidal indentation in fcc metals: Single crystal plasticity finite element analysis, J. Mech. Phys. Solids, 56(11), 3277-3303.

Alcalá, J., Esqué-de los Ojos, D., Očenášek, J., 2015, Extracting uniaxial responses of single crystals from sharp and spherical hardness measurements, Mech. Mater., 84, 100-113.

Ambriz, R., Chicot, D., Benseddiq, N., Mesmacque, G., De La Torre, S., 2011, Local mechanical properties of the 6061-T6 aluminium weld using micro-traction and instrumented indentation,
European Journal of Mechanics- A/Solids, 30(3), 307-315.

Arminjon, M., 1991, A regular form of the Schmid law. Application to the ambiguity problem, Textures and Microstructures, 14-18, 1121-1128.

Asaro, R.J., Needleman, A., 1985, Texture development and strain hardening in rate dependent polycrystals, Acta Metall., 33(6), 923-953.

Asaro, R.J., J., Rice, R., 1997, Strain localization in ductile crystals, J. Mech. Phys. Solids, 25, 309-338.

Berla, L.A., Allen, A.M., Han, S.M., Nix, W.D., 2010, A physically based model for indenter tip shape calibration for nanoindentation, J. Mater. Res., 25(4), 735-745.

Casals, Q., Forest, S., 2009, Finite element crystal plasticity analysis of spherical indentation in bulk single crystals and coatings, Comput. Mater. Sci., 45(3), 774-782.

Chang, H.-J., Fivel, M., Rodney, D., Verdier, M., 2010, Multiscale modelling of indentation in fcc metals: From atomic to continuum, Comptes Rendus Physique, 11(3-4), 285-292.

Eidel, B., 2011, Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (0 0 1) fcc single crystal, Acta Mater., 59(4), 1761-1771.

Frydrych, K., Kowalczyk-Gajewska, K., 2018, Grain refinement in the equal channel angular pressing process: simulations using the crystal plasticity finite element method, Model.
Simul. Mater. Sci. Eng., 26, 065015.

Frydrych, K., Kowalczyk-Gajewska, K., Prakash, A., 2019, On solution mapping and remeshing in crystal plasticity finite element simulations: Application to equal channel angular pressing, Model. Simul. Mater. Sci. Eng., 27, 075001.

Gambin, W., 1991, Plasticity of crystals with interacting slip systems, Enging. Trans., 39, 303-324.

Hill, R., Rice, J.R., 1972, Constitutive analysis of elastic–plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20, 401-413.

Hosemann, P., Vieh, C., Greco, R., Kabra, S., Valdez, J., Cappiello, M., Maloy, S., 2009, Nanoindentation on ion irradiated steels, J. Nucl. Mater., 389(2), 239-247.

Hosemann, P., Kiener, D., Wang, Y., Maloy, S.A., 2012, Issues to consider using nano indentation on shallow ion beam irradiated materials, J. Nucl. Mater., 425(1-3), 136-139.

Hure, J., El Shawish, S., Cizelj, L., Tanguy, B., 2016, Intergranular stress distributions in polycrystalline aggregates of irradiated stainless steel, J. Nucl. Mater., 476, 231-242.

Korelc, J., 1996, Symbolic approach in computational mechanics and its application to the enhanced strain method, PhD thesis, Department of Mechanics, TH Darmstadt.

Korelc, J., 1997, Automatic generation of finite-element code by simultaneous optimization of expressions, Theoretical Computer Science, 187(1-2), 231-248.

Korelc, J., 2002, Multi-language and multi-environment generation of nonlinear finite element codes, Eng. Comput., 18, 312-327.

Korelc, J., Wriggers, P., 2016, Automation of finite element methods, Springer, Basel.

Kowalczyk, K., Gambin, W., 2004, Model of plastic anisotropy evolution with texture-dependent yield surface, Int. J. Plast., 20, 19-54.

Kucharski, S., Jarząbek, D., 2014, Depth dependence of nanoindentation pile-up patterns in copper single crystals, Metall. Mater. Trans. A, 45(11), 4997-5008.

Kucharski, S., Stupkiewicz, S., Petryk, H., 2014, Surface pile-up patterns in indentation testing of Cu single crystals, Exper. Mech., 54(6), 957-969.

Lengiewicz, J., 2008, Analiza wrażliwości dla zagadnień kontaktowych z tarciem, PhD Thesis, IPPT PAN, Warszawa, (in Polish).

Lewandowski, M., Stupkiewicz, S., 2018, Size effects in wedge indentation predicted by a gradient-enhanced crystal- plasticity model, Int. J. Plast., 109, doi 10.1016/j.ijplas.2018.05.008

Li, L., Shen, L., Proust, G., Moy, C.K., Ranzi, G., 2013, Threedimensional crystal plasticity finite element simulation of nanoindentation on aluminium alloy 2024, Mater. Sci. Eng.: A, 579, 41-49.

Ling, C., Tanguy, B., Besson, J., Forest, S., Latourte, F., 2017, Void growth and coalescence in triaxial stress fields in irradiated fcc single crystals, J. Nucl. Mater., 492, 157-170.

Liu, M., Lu, C., Tieu, K., Yu, H., 2014, Numerical comparison between berkovich and conical nano-indentations: Mechanical behaviour and micro-texture evolution, Mater. Sci. Eng.
A, 619, 57-65.

Liu, M., Lu, C., Tieu, K., Peng, C.T., Kong, C., 2015, A combined experimental-numerical approach for determining mechanical properties of aluminum subjects to nanoindentation, Scientific reports, 5, 15072.

Liu, M., Lu, C., Tieu, K., Zhou, K., Peng, C.T., 2016, Indentation analysis of mechanical behaviour of torsion-processed single-crystal copper by crystal plasticity finite-element method modelling, Philosophical Magazine, 96(3), 261-273.

Liu, Y., Wang, B., Yoshino, M., Roy, S., Lu, H., Komanduri, R., 2005, Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper
at mesoscale, J. Mech. Phys. Solids, 53 (12), 2718-2741.

Liu, Y., Varghese, S., Ma, J., Yoshino, M., Lu, H., Komanduri, R., 2008, Orientation effects in nanoindentation of single crystal copper, Int. J. Plast., 24(11),1990-2015.

Mandel, J., 1971, Plasticité classique et viscoplasticité, CISM course No. 97. Springer, Wien.

Nie, J., Liu, Y., Xie, Q., Liu, Z., 2018, Study on the irradiation effect of mechanical properties of RPV steels using crystal plasticity model, Nuclear Engineering and Technology, 2018.

Petryk, H., Stupkiewicz, S., Kucharski, S., 2017, On direct estimation of hardening exponent in crystal plasticity from the spherical indentation test, Int. J. Solids Struct., 112, 209-221.

Renner, E., Gaillard, Y., Richard, F., Amiot, F., Delobelle, P., 2016,. Sensitivity of the residual topography to single crystal plasticity parameters in Berkovich nanoindentation on FCC nickel, Int. J. Plast., 77, 118-140.

Ryś, M. , 2016, Constitutive modelling of damage evolution and martensitic transformation in 316l stainless steel, Acta Mechanica et Automatica, 10(2), 125-132.

Ryś, M., Skoczeń, B., 2017, Coupled constitutive model of damage affected two-phase continuum, Mech. Mater., 115, 1-15.

Saleh, M., Zaidi, Z., Ionescu, M., Hurt, C., Short, K., Daniels, J., Munroe, P., Edwards, L., Bhattacharyya, D., 2016, Relationship between damage and hardness profiles in ion irradiated
SS316 using nanoindentation–Experiments and modelling, Int. J. Plast., 86, 151-169

Skoczeń, B., Ustrzycka, A., 2015, Radiation Damage Evolution in Ductile Materials, Springer International Publishing, Cham, 397-411.

Skoczeń, B., Ustrzycka, A., 2016, Kinetics of evolution of radiation induced micro-damage in ductile materials subjected to time-dependent stresses, Int. J. Plast., 80, 86-110.

Stupkiewicz, S., Lengiewicz, J., Korelc, J., 2010, Sensitivity analysis for frictional contact problems in the augmented Lagrangian formulation, Computer Methods in Applied Mechanics and Engineering, 199(33-36), 2165-2176.

Thomas Jr., J.F., 1968, Third-order elastic constants of aluminum, Physical Review, 175(3), 955.

Torres-Torres, D., Muñoz-Saldaña, J., Gutierrez-Ladron-de Guevara, L., Hurtado-Macías, A., Swain, M., 2010, Geometry and bluntness tip effects on elastic–plastic behaviour during
nanoindentation of fused silica: experimental and FE simulation, Model. Simul. Mater. Sci. Eng., 18(7), 075006.

Wang, Q., Cochrane, C., Skippon, T., Wang, Z., Abdolvand, H., Daymond, M.R., 2019, Orientation-dependent irradiation hardening in pure Zr studied by nanoindentation, electron microscopies, and crystal plasticity finite element modeling, Int. J. Plast., 124, 133-154.;

Wang, Y., Raabe, D., Klüber, C., Roters, F., 2004 Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals, Acta Mater., 52(8), 2229-2238.

Wang, Z., Zhang, J., ul Hassan, H., Zhang, J., Yan, Y., Hartmaier, A., Sun, T., 2018, Coupled effect of crystallographic orientation and indenter geometry on nanoindentation of single crystalline copper, Int. J. Mech. Sci., 148, 531-539.

Xiao, X., Chen, L., Yu, L., Duan, H., 2019a, Modelling nano-indentation of ion-irradiated FCC single crystals by straingradient crystal plasticity theory, Int. J. Plast., 116, 216-231.

Xiao, X., Terentyev, D., Bakaev, A., Zinovev, A., Dubinko, A., Zhurkin, E., 2019b, Crystal plasticity finite element method simulation for the nano-indentation of plasma-exposed tungsten, J. Nucl. Mater., 518, 334-341.

Yao, W., You, J., 2017, Berkovich nanoindentation study of monocrystalline tungsten: a crystal plasticity study of surface pile-up deformation, Philosophical Magazine, 97(17), 1418-1435.

Zambaldi, C., Raabe, D., 2010, Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation, Acta Mater., 58(9), 3516-3530.

Zambaldi, C., Yang, Y., Bieler, T.R., Raabe, D., 2012, Orientation informed nanoindentation of α-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip, J. Mater. Res., 27(1), 356-367.