Research Papers

Evaluation of Elastoplasticity-Dependent Creep Property of Magnesium Alloy With Indentation Method: A Reverse Numerical Algorithm and Experimental Validation

[+] Author and Article Information
Shoichi Fujisawa

Department of Precision Mechanics,
Chuo University,
1-13-27 Kasuga, Bunkyo,
Tokyo 112-8551, Japan

Akio Yonezu

Department of Precision Mechanics,
Chuo University,
1-13-27 Kasuga, Bunkyo,
Tokyo 112-8551, Japan
e-mail: yonezu@mech.chuo-u.ac.jp

Masafumi Noda

Magnesium Division,
Gonda Metal Industry Co., Ltd.,
1-1-16 Miyashimo, Chuo,
Sagamihara, Kanagawa 252-0212, Japan

Baoxing Xu

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: bx4c@virginia.edu

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 20, 2016; final manuscript received August 29, 2016; published online February 1, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021004 (Feb 01, 2017) (9 pages) Paper No: MATS-16-1147; doi: 10.1115/1.4035280 History: Received May 20, 2016; Revised August 29, 2016

Magnesium (Mg) alloys have been widely used in automotive and aerospace industries due to its merits of exceptional lightweight, super strong specific strength, and high corrosion-resistance, where intermetallic compounds with a small volume are very critical to achieve these excellent performance. This study proposes a reverse analysis that can be employed to extract elastoplasticity-dependent creep property of commercial die-cast Mg alloys and their intermetallic compounds from instrumented indentation with two sharp indenters. First, the creep deformation that obeys the Norton's law (ε˙  = Aσn) is studied, and the parameters of A and n are determined from two indentation experiments conducted with different sharp indenters. Then, a numerical algorithm and dimensional function developed is extended to extract the elastoplasticity of various metallic materials by focusing on the loading stage of indentation experiments. By considering the full loading history with both linear increase and holding stages of loads, we propose a framework of reverse analysis to determine both elastoplasticity and creep properties simultaneously. Parallel indentation experiments on pure magnesium and aluminum and Mg alloys are performed, and the results agree well with the numerical predictions.

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Huang, Z. W. , Zhao, Y. H. , Hou, H. , and Han, P. D. , 2012, “ Electronic Structural, Elastic Properties and Thermodynamics of Mg17Al12, Mg2Si and Al2Y Phases From First-Principles Calculation,” Physica B, 407(7), pp. 1075–1081. [CrossRef]
Guomin, H. , Zhiqiang, H. , Luo, A. , Sachdev, A. K. , and Liu, B. , 2013, “ A Phase Field Model for Simulating the Precipitation of Multi-Variant β-Mg17Al12 in Mg-Al-Based Alloys,” Scrip. Mater., 68(9), pp. 691–694. [CrossRef]
Mahmudi, R. , and Moeendarbari, S. , 2013, “ Effects of Sn Additions on the Microstructure and Impression Creep Behavior of AZ91 Magnesium Alloy,” Mater. Sci. Eng. A, 566, pp. 30–39. [CrossRef]
Hiraia, K. , Somekawa, H. , Takigawa, Y. , and Higashi, K. , 2005, “ Effects of Ca and Sr Addition on Mechanical Properties of a Cast AZ91 Magnesium Alloy at Room and Elevated Temperature,” Mater. Sci. Eng. A, 403(1–2), pp. 276–280. [CrossRef]
Lin, L. , Wang, F. , Yang, L. , Chen, L. J. , Liu, Z. , and Wang, Y. M. , 2011, “ Microstructure Investigation and First-Principle Analysis of Die-Cast AZ91 Alloy With Calcium Addition,” Mater. Sci. Eng. A, 528(15), pp. 5283–5288. [CrossRef]
Hort, N. , Huang, Y. , and Kainer, K. U. , 2006, “ Intermetallics in Magnesium Alloys,” Adv. Eng. Mater., 8(4), pp. 235–240. [CrossRef]
Mu, M. , Zhi-min, Z. , Bao-Hong, Z. , and Jin, D. , 2012, “ Flow Behavior and Processing Maps of As-Cast and As-Homogenized AZ91 Alloy,” J. Alloys Compd., 513, pp. 112–117. [CrossRef]
Nagasekhar, A. V. , Cáceres, C. H. , and Kong, C. , 2010, “ 3D Characterization of Intermetallics in a High Pressure Die Cast Mg Alloy Using Focused Ion Beam Tomography,” Mater. Charcterization, 61(11), pp. 1035–1042. [CrossRef]
Ogasawara, N. , Chiba, N. , and Chen, X. , 2009, “ A Simple Framework of Spherical Indentation for Measuring Elastoplastic Properties,” Mech. Mater., 41(9), pp. 1025–1033. [CrossRef]
Yonezu, A. , Akimoto, H. , Fujisawa, S. , and Chen, X. , 2013, “ Spherical Indentation Method for Measuring Local Mechanical Properties of Welded Stainless Steel at High Temperature,” Mater. Des., 52, pp. 812–820. [CrossRef]
Xu, B. , Yue, Z. , and Chen, X. , 2010, “ Characterization of Strain Rate Sensitivity and Activation Volume Using the Indentation Relaxation Test,” J. Phys. D, 43(24), p. 245401. [CrossRef]
Dao, M. , Chollacoop, N. , VanVliet, K. J. , Venkatesh, T. A. , and Suresh, S. , 2001, “ Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation,” Acta Mater., 49(19), pp. 3899–3918. [CrossRef]
Toyama, H. , Niwa, M. , Xu, J. , and Yonezu, A. , 2015, “ Failure Assessment of a Hard Brittle Coating on a Ductile Substrate Subjected to Cyclic Contact Loading,” Eng. Failure Anal., 57, pp. 118–128. [CrossRef]
Samadi-Dooki, A. , Malekmotiei, L. , and Voyiadjis, G. Z. , 2016, “ Characterizing Shear Transformation Zones in Polycarbonate Using Nanoindentation,” Polymer, 82, pp. 238–245. [CrossRef]
Meza, L. R. , and Greer, J. R. , 2014, “ Mechanical Characterization of Hollow Ceramic Nanolattices,” J. Mater. Sci., 9(6), pp. 2496–2508. [CrossRef]
Xu, B. , and Chen, X. , 2010, “ Determining Engineering Stress–Strain Curve Directly From the Load–Depth Curve of Spherical Indentation Test,” J. Mater. Res., 25(12), pp. 2297–2307. [CrossRef]
Xu, B. , Eggler, G. , and Yue, Z. , 2007, “ A Numerical Procedure for Retrieving Material Creep Properties From Bending Creep Tests,” Acta Mater., 55(18), pp. 6275–6283. [CrossRef]
Liu, T. , Deng, Z. C. , and Lu, T. J. , 2007, “ Minimum Weights of Pressurized Hollow Sandwich Cylinders With Ultralight Cellular Cores,” Int. J. Solids Struct., 44(10), pp. 3231–3266. [CrossRef]
Deana, J. , Campbell, J. , Aldrich-Smith, G. , and Clyne, T. W. , 2014, “ A critical assessment of the “stable indenter velocity” method for obtaining the creep stress exponent from indentation data,” Acta Mater., 80, pp. 56–66. [CrossRef]
Nautiyal, P. , Jain, J. , and Agarwal, A. , 2015, “ A comparative study of indentation induced creep in pure magnesium and AZ61 alloy,” Mater. Sci. Eng. A, 630, pp. 131–138. [CrossRef]
Bucaille, J. L. , Stauss, S. , Felder, E. , and Michler, J. , 2003, “ Determination of Plastic Properties of Metals by Instrumented Indentation Using Different Sharp Indenters,” Acta Mater., 51(6), pp. 1663–1678. [CrossRef]
Oliver, W. C. , and Pharr, G. M. , 2004, “ Measurement of Hardness and Elastic Modulus by Instrumented Indentation: Advances in Understanding and Refinements to Methodology,” J. Mater. Res., 19(01), pp. 3–20. [CrossRef]
Inoue, N. , Yonezu, A. , Watanabe, Y. , Okamura, T. , Yoneda, K. , and Xu, B. , 2015, “ Prediction of Viscoplastic Properties of Polymeric Materials Using Sharp Indentation,” Comput. Mater. Sci., 110, pp. 321–330. [CrossRef]


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Fig. 2

Relationship between indentation creep depth and creep time and indentation curve

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Fig. 1

Microstructure of α-Mg and β-Mg17Al12 in die-cast magnesium alloy (AZ91D)

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Fig. 3

Two-dimensional axisymmetric FEM model of indentation test with triangle indenter and input creep parameter

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Fig. 4

Relationship between indentation creep depth and creep time by changing the creep parameter, n

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Fig. 5

Dimensionless function of pure Mg obtained by 115 deg triangle indenter

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Fig. 6

Relationship between h˙/E*nAhmax and n estimated by indentation creep test of Fig. 2

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Fig. 7

Dimensionless function of pure Mg obtained by 115 deg triangle indenter. This compares with n−h˙/E*nAhmax curve estimated by indentation creep test for pure Mg.

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Fig. 8

Relationship between creep parameter A and n for 115 deg and 100 deg triangle indenters

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Fig. 10

Relationship between indentation creep depth and creep time for β-phase

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Fig. 9

Relationship between indentation creep depth and creep time for α-phase

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Fig. 11

Relationship between C/E* and σr/E* for 115 deg and 100 deg triangle indenters

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Fig. 12

Comparison of σr/E* estimated by experiment and σr/E*—slope and intercept of n−h˙/E*nAhmax curve for 115 deg triangle indenter (A = 2.5 × 10−10)

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Fig. 13

Flowchart of estimation process

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Fig. 14

Comparison of estimated σr/E* with input ones for 115 deg and 100 deg triangle indenter experiments

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Fig. 15

Comparison of estimated creep parameter with input ones



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