Micro-plasticity constitutive model taking account of size effects for pure aluminum by microindentation

Abstract

The macro-plasticity power function constitutive model (MPFCM), the modified macroplasticity power function constitutive model (MMPFCM) and the micro-plasticity constitutive model (MCM) taking the material intrinsic length were established to characterize the microindentation size effects of pure aluminum, respectively. The experimental results indicated MPFCM only determined precisely in the great indentation load. While a modified one named MMPFCM was subsequently established taking account of the parameters variation with the increase of indentation depth. The conventional dimensional analysis method was employed to determine the strength coefficient K and the strain hardening exponent n of this modified model. And then MCM taking account of size effects was proposed based on the Taylor dislocation model. The firstorder steepest gradient descent method was adopted to obtain the material intrinsic length for the geometrically necessary dislocations. The parameters of MCM were identified by using the UMAT subroutine of ABAQUS software. The average absolute relative error of MCM is relatively lower than that of the macro-one. Although the precision of the modified one is also high, the applied scope is limited, only for the microindentation material. In addition, the intrinsic length 5.09 μm of pure aluminum is also obtained based on the strain gradient theory.

Keywords

constitutive model / size effects / pure aluminum; microindentation

References

[1] Fleck NA, Muller GM, Ashby MF, . Strain Gradient Plasticity: Theory and Experiment [J]. Acta. Metall. Mater., 1994, 42: 475-487.

[2] Fleck NA, Hutchinson JW A Reformulation of Strain Gradient Plasticity [J]. J. Mech. Phys. Solids, 2001, 49: 2 245-2 271.

[3] Zhu HX, Karihaloo BL Size-dependent Bending of Thin Metallic Films [J]. Int. J. Plasticity, 2008, 24: 991-1 007.

[4] Zbib HM, Aifantis EC Size Effects and Length Scales in Gradient Plasticity and Dislocation Dynamics[J]. Scripta Mater., 2003, 48: 155-160.

[5] Gao H, Huang Y, Nix WD, . Mechanism-based Strain Gradient Plasticity-I. Theory [J]. J. Mech. Phys. Solids, 1999, 47: 1 239-1 263.

[6] Huang Y, Gao H, Nix WD, . Mechanism-based Strain Gradient Plasticity-II. Analysis [J]. J. Mech. Phys. Solids, 2000, 48: 99-128.

[7] Huang Y, Xue Z, Gao H, . A Study of Micro-Indentation Hardness Tests by Mechanism-based Strain Gradient Plasticity [J]. J. Mech. Phys. Solids, 2000, 15: 1786-1796.

[8] Al-Rub RKA, Voyiadjis GZ A Direct Finite Element Implementation of the Gradient-dependent Theory [J]. Int. J. Numer. Meth. Eng., 2005, 63: 603-629.

[9] Begley MR, Hutchinson JW The Mechanics of Size-dependent Indentation [J]. J. Mech. Phys. Solids, 1998, 46: 2049-2068.

[10] Al-Rub RKA, Voyiadjis GZ Analytical and Experimental Determination of the Material Intrinsic Length Scale of Strain Gradient Plasticity Theory from Micro- and Nano-indentation Experiments [J]. Int. J. Plasticity, 2004, 20: 1 139-1 182.

[11] Lee J, Lee C, Kim B Reverse Analysis of Nano-indentation Using Different Representative Strains and Residual Indentation Profiles [J]. Mater. Design, 2009, 30: 3 395-3 404.

[12] Li M, Chen WM, Liang NG, . A Numerical Study of Indentation Using Indenters of Different Geometry[J]. J. Mater. Res., 2004, 19: 73-78.

[13] Gouldstone A, Chollacoop N, Dao M, . Indentation across Size Scales and Disciplines: Recent Developments in Experimentation and Modeling[J]. Acta Mater., 2007, 55: 4 015-4 039.

[14] Oliver WC, Pharr GM Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments [J]. J. Mater. Res., 1992, 7: 1 564-1 583.

[15] Oliver WC, Pharr GM Measurement of Hardness and Elastic Modulus by Instrumented Indentation: Advances in Understanding and Refi nements to Methodology [J]. J. Mater. Res., 2004, 19: 3-20.

[16] Luo J, Lin J A Study on the Determination of Plastic Properties of Metals by Instrumented Indentation Using Two Sharp Indenters [J]. Int. J. Solids Struct., 2007, 44: 5 803-5 817.

[17] Dao M, Chollacoop N, Van VKJ, . Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation [J]. Acta Mater., 2001, 49: 3 899-3 918.

[18] Abdella K, Thannon RA, Mehri AI, . Inversion of Three-stage Stress-Strain Relation for Stainless Steel in Tension and Compression [J]. J. Constr. Steel Res., 2011, 67: 826-832.

[19] Jiang WG, Yan C, Qu SX Friction Effect on Micro-indentation Measurement with Different Indenters [J]. Chinese Quarterly of Mechanics, 2010, 31: 236-242 (in Chinese).

[20] Mandal S, Rakesh V, Sivaprasad PV, . Constitutive Equations to Predict High Temperature Flow Stress in a Ti-modifi ed Austenitic Stainless Steel [J]. Mater. Sci. Eng. A, 2009, 500: 114-121.