Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T23:35:34.006Z Has data issue: false hasContentIssue false

Numerical Analysis of Damage Thermo-Mechanical Models

Published online by Cambridge University Press:  21 July 2015

Hamdi Hentati*
Affiliation:
LASEM Laboratory, National School of Engineers of Sfax, University of Sfax, Tunisia
Ilyes Ben Naceur
Affiliation:
Unit of Mechanical Production and Materials, National School of Engineers of Sfax, University of Sfax, Tunisia
Wassila Bouzid
Affiliation:
Unit of Mechanical Production and Materials, National School of Engineers of Sfax, University of Sfax, Tunisia
Aref Maalej
Affiliation:
LASEM Laboratory, National School of Engineers of Sfax, University of Sfax, Tunisia
*
*Corresponding author. Email: [email protected] (H. Hentati)
Get access

Abstract

In this paper, we present numerical computational methods for solving the fracture problem in brittle and ductile materials with no prior knowledge of the topology of crack path. Moreover, these methods are capable of modeling the crack initiation. We perform numerical simulations of pieces of brittle material based on global approach and taken into account the thermal effect in crack propagation. On the other hand, we propose also a numerical method for solving the fracture problem in a ductile material based on elements deletion method and also using thermo-mechanical behavior and damage laws. In order to achieve the last purpose, we simulate the orthogonal cutting process.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Griffith, A., The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London, 221 (1921), pp. 163198.Google Scholar
[2]Bourdin, B., The Variational Approach to Fracture, PhD thesis, University Paris 13, 1998.Google Scholar
[3]Francfort, G. and Marigo, J. J., Vers une théorie énergétique de la rupture fragile, Comptes Rendus Mécanique, 330 (2002), pp. 225233.Google Scholar
[4]Bourdin, B., Francfort, G. and Marigo, J. J., Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, 48(4) (2000), pp. 797826.Google Scholar
[5]Bourdin, B., Francfort, G. and Marigo, J. J., The variational approach to fracture, J. Elasticity, 91 (2008), pp. 5148.Google Scholar
[6]Johnson, G. R. and Cook, W. H., A constitutive model and data for metals subjected to large strains, high strain rate, and temperatures, Proceedings of the 7th International Symposium on Ballistics, The Hague, Netherlands, pp. 541547, 1983.Google Scholar
[7]Kim, K. W., Lee, W. Y. and Sin, H. C., A finite element analysis of machining with the tool edge considered, J. Mater. Process. Tech., 86 (1999), pp. 4555.Google Scholar
[8]Ozel, T. and Zeren, E., Fe modelling of stresses induced by high speed machining with round cutting tools, 2005.Google Scholar
[9]Ozel, T. and Zeren, E., A methodology to determine work material flow stress and tool-chip interfacial friction properties by using analysis of machining, J. Manufact. Sci. Eng., 128 (2006), pp. 119129.Google Scholar
[10]Ozel, T., Modelling of hard machining: effect of insert edge preparation in cbn cutting tools, J. Mater. Process. Tech., 141 (2003), pp. 284293.Google Scholar
[11]Fassi, H., Bousshine, L., Chaaba, A. and Elharif, A., Numerical simulation of orthogonal cutting by incremental elastoplastic analysis and finite element method, J. Mater. Process. Tech., 141 (2003), pp. 181188.CrossRefGoogle Scholar
[12]Alcaraz, J. L., Lorenzo, I. and Lacalle, L. N., Thermomechanical analysis of a chip machining process, in: ABAQUS Users’ Conference, 2003.Google Scholar
[13]Bil, H., Kilic, S. E. and Tekkaya, A. E., A comparison of orthogonal cutting data from experiments with three different finite element models, Int. J. Machine. Tools Manufacture, 44 (2004), pp. 933944.Google Scholar
[14]Barge, M., Hamdi, H., Rech, J. and Bergheau, J. M., Numerical modelling of orthogonal cutting: influence of numerical parameters, J. Mater. Process. Tech., 164-165 (2005), pp. 11481153.Google Scholar
[15]Francfort, G. and Marigo, J. J., Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46 (1998), pp. 13191342.CrossRefGoogle Scholar
[16]Oleaga, G. E., On the path of a quasi static crack in mode iii, J. Elasticity, 76 (2004), pp. 163189.Google Scholar
[17]Amor, H., Marigo, J. J. and Maurini, C., Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, J. Mech. Phys. Solids, 57 (2009), pp. 12091229.Google Scholar
[18]Pham, K. and Marigo, J. J., Approche variationnelle de l’endommagement: I. les. concepts fondamentaux, Comptes Rendus Mécanique, 338 (2010), pp. 191198.Google Scholar
[19]Pham, K. and Marigo, J. J., Approche variationnelle de l’endommagement: Ii. les modèles à gradient, Comptes Rendus Mécanique, 338 (2010), pp. 199206.CrossRefGoogle Scholar
[20]Buliga, M., Energy minimizing brittle crack propagation, J. Elasticity, 52(3) (1998), pp. 201238.Google Scholar
[21]Charlotte, M., Francfort, G., Marigo, J. J. and Truskinovski, L., Revisiting brittle fracture as an energy minimization problem comparisons of griffith and barenblatt surface energy models, In: Symposium on Continuous Damage and Fracture, 2000.Google Scholar
[22]Ambrosio, L. and Tortorelli, V. M., Approximation of functionals depending on jumps by elliptic functionals via gamma-convergence, In: Commun. Pure Appl. Math., 43 (1990), pp. 9991036.Google Scholar
[23]Ambrosio, L. and Tortorelli, V. M., On the approximation of free discontinuity problems, In: Boll. Un. Mat. Ital., B(7)6(1) (1992), pp. 105123.Google Scholar
[24]Mumford, D. and Shah, J., Optimal approximations by piecewise smooth functions and associated variational problems, In: Commun. Pure Appl. Math., XLII (1989), pp. 577685.Google Scholar
[25]Jagla, E., Stable propagation of an ordered array of cracks during directional drying, Phys. Rev. E, 2002.Google Scholar
[26]Jenkins, D., Optimal spacing and penetration of cracks in a shrinking slab, Phys. Rev. E, 2005.Google Scholar
[27]Jiang, C. P., Wua, X. F., Li, J., Song, F., Shao, Y. F., Xu, X. H. and Yan, P., A study of the mechanism of formation and numerical simulations of crack patterns in ceramics subjected to thermal shock, Acta Mater., 60 (2012), pp. 45404550.Google Scholar
[28]Bourdin, B., Maurini, C. and Knepley, M., Numerical simulation of reservoir stimulation-a variational approach, In: PROCEEDINGS, Thirty-Sixth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, January 31-February 2, 2011.Google Scholar
[29]Gurson, A., Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rules for porous ductile media, J. Eng. Mat. Tech., 99 (1977), pp. 215.Google Scholar
[30]Tvergaard, V. and Needleman, A., Analysis of cup cone fracture in a round tensile bar, Acta Metall., 32 (1984), pp. 157169.Google Scholar
[31]Lemaitre, J., Course on Damage Mechanics, Springer, Second Edition, 1991.Google Scholar
[32]Lemiale, V., Meunier, S. and Picart, P., Etude experimentale et numerique du decoupage de toles en faible epaisseur, XV Congres de Mecanique, Nancy, Sept 2001, pp. 440.Google Scholar
[33]Umbrello, D., M’Saooubi, R. and Outeiro, J. C., The influence of johnson-cook material constants on finite element simulation of machining of aisi 316l steel, Int. J. Mach. Tool Manufacture, 47 (2007), pp. 462470.Google Scholar
[34]Guo, NY. B., A fem study on mechanisms of discontinuous chip formation in hard machining, J. Mater. Process. Tech., 155-156 (2004), pp. 13501356.CrossRefGoogle Scholar
[35]Lestriez, P., Modlisation Numerique du Couplage Thermo Mcanique Endommagement en Transformation Finies, Application la Mise en Forme, PhD thesis, 2003.Google Scholar
[36]Poizat, C., Campagna, L., Daridon, L., Ahzi, S., Husson, C. and Merle, L., Modeling and simulation of thin sheet blanking using damage and rupture criteria, Int. J. Form. Process., 8(1) (2005), pp. 2947.Google Scholar