Research Papers

A Nonlinear Damage Model of Hardening-Softening Materials

[+] Author and Article Information
M. Ganjiani

Department of Mechanical Engineering,
College of Engineering,
University of Tehran,
P.O. Box 11155-4563,
Tehran 1439957131, Iran
e-mail: ganjiani@ut.ac.ir

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 22, 2016; final manuscript received June 24, 2017; published online September 13, 2017. Assoc. Editor: Huiling Duan.

J. Eng. Mater. Technol 140(1), 011010 (Sep 13, 2017) (11 pages) Paper No: MATS-16-1233; doi: 10.1115/1.4037656 History: Received August 22, 2016; Revised June 24, 2017

In this paper, an elastoplastic-damage constitutive model is presented. The formulation is cast within the framework of continuum damage mechanics (CDM) by means of the internal variable theory of thermodynamics. The damage is assumed as a tensor type variable and its evolution is developed based on the energy equivalence hypothesis. In order to discriminate the plastic and damage deformation, two surfaces named as plastic and damage are introduced. The damage surface has been developed so that it can model the nonlinear variation of damage. The details of the model besides its implicit integration algorithm are presented. The model is implemented as a user-defined subroutine user-defined material (UMAT) in the abaqus/standard finite element program for numerical simulation purposes. In the regard of investigating the capability of model, the shear and tensile tests are experimentally conducted, and corresponding results are compared with those predicted numerically. These comparisons are also accomplished for several experiments available in the literature. Satisfactory agreement between experiments and numerical predictions provided by the model implies the capability of the model to predict the plastic deformation as well as damage evolution in the materials.

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Bonora, N. , Majzoobi, G. , and Khademi, E. , 2014, “ Numerical Implementation of a New Coupled Cyclic Plasticity and Continum Damage Model,” Comput. Mater. Sci., 81, pp. 538–547. [CrossRef]
Soyarslan, C. , and Tekkaya, A. E. , 2010, “ A Damage Coupled Orthotropic Finite Plasticity Model for Sheet Metal Forming: CDM Approach,” Comput. Mater. Sci., 48(1), pp. 150–165. [CrossRef]
Gurson, A. L. , 1977, “ Continuum Theory of Ductile Rupture by Void Nucleation and Growth—Part I: Yield Criteria and Flow Rules for Porous Ductile Media,” ASME J. Eng. Mater. Technol., 99(1), pp. 2–15. [CrossRef]
Lemaitre, J. , 1985, “ A Continuous Damage Mechanics Model for Ductile Fracture,” ASME J. Eng. Mater. Technol., 107(1), pp. 83–89. [CrossRef]
Abu Al-Rub, R. K. , and Kim, S. M. , 2010, “ Computational Applications of a Coupled Plasticity-Damage Constitutive Model for Simulating Plain Concrete Fracture,” Eng. Fract. Mech., 77(10), pp. 1577–1603. [CrossRef]
Cicekli, U. , Voyiadjis, G. Z. , and Abu Al-Rub, R. K. , 2007, “ A Plasticity and Anisotropic Damage Model for Plain Concrete,” Int. J. Plast., 23(10–11), pp. 1874–1900. [CrossRef]
Voyiadjis, G. Z. , Taqieddin, Z. N. , and Kattan, P. I. , 2009, “ Theoretical Formulation of a Coupled Elastic-Plastic Anisotropic Damage Model for Concrete Using the Strain Energy Equivalence Concept,” Int. J. Damage Mech., 18(7), pp. 603–638. [CrossRef]
Voyiadjis, G. Z. , Taqieddin, Z. N. , and Kattan, P. I. , 2008, “ Anisotropic Damage-Plasticity Model for Concrete,” Int. J. Plast., 24(10), pp. 1946–1965. [CrossRef]
Brünig, M. , 2006, “ Continuum Framework for the Rate-Dependent Behavior of Anisotropically Damaged Ductile Metals,” Acta Mech., 186(1), pp. 37–53. [CrossRef]
Rodin, G. J. , 2000, “ Continuum Damage Mechanics and Creep Life Analysis,” ASME J. Appl. Mech., 67(1), pp. 193–196. [CrossRef]
Bonora, N. , 1997, “ A Nonlinear CDM Model for Ductile Failure,” Eng. Fract. Mech., 58(1), pp. 11–28. [CrossRef]
Chow, C. L. , and Yang, X. J. , 2004, “ A Generalized Mixed Isotropic-Kinematic Hardening Plastic Model Coupled With Anisotropic Damage for Sheet Metal Forming,” Int. J. Damage Mech., 13(1), pp. 81–101. [CrossRef]
Ganjiani, M. , Naghdabadi, R. , and Asghari, M. , 2012, “ An Elastoplastic Damage-Induced Anisotropic Constitutive Model at Finite Strains,” Int. J. Damage Mech., 22(4), pp. 499–529.
Ganjiani, M. , 2013, “ Identification of Damage Parameters and Plastic Properties of an Anisotropic Damage Model by Micro-Hardness Measurements,” Int. J. Damage Mech., 22(8), pp. 1089–1108.
Nguyen, G. D. , Korsunsky, A. M. , and Belnoue, J. P.-H. , 2015, “ A Nonlocal Coupled Damage-Plasticity Model for the Analysis of Ductile Failure,” Int. J. Plast., 64, pp. 56–75. [CrossRef]
Voyiadjis, G. Z. , and Park, T. , 1997, “ Anisotropic Damage Effect Tensors for the Symmetrization of the Effective Stress Tensor,” ASME J. Appl. Mech., 64(1), pp. 106–110. [CrossRef]
Park, T. , and Voyiadjis, G. Z. , 1998, “ Kinematic Description of Damage,” ASME J. Appl. Mech., 65(1), pp. 93–98. [CrossRef]
Wang, T.-J. , 1992, “ Unified CDM Model and Local Criterion for Ductile Fracture—II: Ductile Fracture Local Criterion Based on the CDM Model,” Eng. Fract. Mech., 42(1), pp. 185–193. [CrossRef]
Chandrakanth, S. , and Pandey, P. C. , 1993, “ A New Ductile Damage Evolution Model,” Int. J. Fract., 60(4), pp. R73–R76. http://www.nptel.ac.in/courses/105108072/mod06/hyperlink-7.pdf
Chandrakanth, S. , and Pandey, P. C. , 1995, “ An Isotropic Damage Model for Ductile Material,” Eng. Fract. Mech., 50(4), pp. 457–465. [CrossRef]
Thakkar, B. K. , and Pandey, P. C. , 2007, “ A High-Order Isotropic Continuum Damage Evolution Model,” Int. J. Damage Mech., 16(4), pp. 403–426. [CrossRef]
Kumar, M. , and Dixit, P. , 2014, “ A Nonlinear Ductile Damage Growth Law,” Int. J. Damage Mech., 24(7), pp. 1070–1085.
Chow, C. L. , and Wang, J. , 1987, “ An Anisotropic Theory of Continuum Damage Mechanics for Ductile Fracture,” Eng. Fract. Mech., 27(5), pp. 547–558. [CrossRef]
Gao, X. , Zhang, T. , Zhou, J. , Graham, S. M. , Hayden, M. , and Roe, C. , 2011, “ On Stress-State Dependent Plasticity Modeling: Significance of the Hydrostatic Stress, the Third Invariant of Stress Deviator and the Non-Associated Flow Rule,” Int. J. Plast., 27(2), pp. 217–231. [CrossRef]
Bonora, N. , Gentile, D. , and Pirondi, A. , 2004, “ Identification of the Parameters of a Nonlinear Continuum Damage Mechanics Model for Ductile Failure in Metals,” J. Strain Anal. Eng. Des., 39(6), pp. 639–651. [CrossRef]
Bonora, N. , Gentile, D. , Pirondi, A. , and Newaz, G. , 2005, “ Ductile Damage Evolution Under Triaxial State of Stress: Theory and Experiments,” Int. J. Plast., 21(5), pp. 981–1007. [CrossRef]
Hayakawa, K. , and Murakami, S. , 1997, “ Thermodynamical Modeling of Elastic-Plastic Damage and Experimental Validation of Damage Potential,” Int. J. Damage Mech., 6(4), pp. 333–363. [CrossRef]
Hayakawa, K. , and Murakami, S. , 1998, “ Space of Damage Conjugate Force and Damage Potential of Elastic-Plastic-Damage Materials,” Stud. Appl. Mech., 46, pp. 27–44. [CrossRef]
Murakami, S. , Hayakawa, K. , and Liu, Y. , 1998, “ Damage Evolution and Damage Surface of Elastic-Plastic-Damage Materials Under Multiaxial Loading,” Int. J. Damage Mech., 7(2), p. 103. [CrossRef]
Brünig, M. , 2003, “ An Anisotropic Ductile Damage Model Based on Irreversible Thermodynamics,” Int. J. Plast., 19(10), pp. 1679–1713. [CrossRef]
Brünig, M. , Gerke, S. , and Brenner, D. , 2015, “ Experiments and Numerical Simulations on Stress-State-Dependence of Ductile Damage Criteria,” Inelastic Behavior of Materials and Structures Under Monotonic and Cyclic Loading, Springer, Cham, Switzerland, pp. 17–33. [CrossRef]
Chow, C. L. , and Wang, J. , 1988, “ Ductile Fracture Characterization With an Anisotropic Continuum Damage Theory,” Eng. Fract. Mech., 30(5), pp. 547–563. [CrossRef]
Bielski, J. , Skrzypek, J. J. , and Kuna-Ciskal, H. , 2006, “ Implementation of a Model of Coupled Elastic-Plastic Unilateral Damage Material to Finite Element Code,” Int. J. Damage Mech., 15(1), pp. 5–39. [CrossRef]
Sidoroff, F. , 1981, “ Description of Anisotropic Damage Application to Elasticity,” Physical Non-Linearities in Structural Analysis, Springer, Berlin, pp. 237–244. [CrossRef]
Truesdell, C. , and Noll, W. , 2004, “ The Non-Linear Field Theories of Mechanics,” The Non-Linear Field Theories of Mechanics, Springer, Berlin, pp. 1–579.
Simo, J. C. , and Hughes, T. J. R. , 1998, Computational Inelasticity, Vol. 7, Springer-Verlag, New York.
Belytschko, T. , Liu, W. K. , Moran, B. , and Elkhodary, K. , 2014, Nonlinear Finite Elements for Continua and Structures, 2nd ed., Wiley, Chichester, UK.
Murakami, S. , 2012, Continuum Damage Mechanics: A Continuum Mechanics Approach to the Analysis of Damage and Fracture, Vol. 185, Springer Science & Business Media, Dordrecht, The Netherlands.
de Souza Neto, E. A. , Peric, D. , and Owen, D. R. J. , 2011, Computational Methods for Plasticity: Theory and Applications, Wiley, Chichester, UK.
Le Roy, G. , Embury, J. D. , Edwards, G. , and Ashby, M. F. , 1981, “ A Model of Ductile Fracture Based on the Nucleation and Growth of Voids,” Acta Metall., 29(8), pp. 1509–1522. [CrossRef]
Mkaddem, A. , Gassara, F. , and Hambli, R. , 2006, “ A New Procedure Using the Microhardness Technique for Sheet Material Damage Characterisation,” J. Mater. Process. Technol., 178(1–3), pp. 111–118. [CrossRef]


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Fig. 1

Dimensions of the specimen used in the tensile test (mm)

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Fig. 4

The parameter η as the slop of the line In D˙2/D˙1 versus ε1 for aluminum 2024-T3 [14]

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Fig. 7

Deformed shear specimen of aluminum 2024-T3. Distribution of: (a) stress, (b) effective plastic strain, (c) accumulated damage, and (d) experiment.

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Fig. 3

The experimental and simulated tensile data for aluminum 2024-T3 [14]: (a) stress–strain and (b) damage-strain curves

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Fig. 5

Four types of meshing used for the shear simulation: (a) 152, (b) 316, (c) 504, and (d) 602 elements

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Fig. 6

Load–displacement curve of shear specimen

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Fig. 8

Predicted results compared with experimental data in tensile test for aluminum 2024-T3 [23]: (a) stress–strain, (b) damage-strain, and (c) determination of parameter η

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Fig. 9

Comparison between the predicted results and experimental data via (a) stress–strain and (b) damage-strain curves

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Fig. 2

The specimen of shear test (dimensions are in millimeters)



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