Engineering Transactions, 63, 4, pp. 463-480, 2015
10.24423/engtrans.245.2015

Influence of Exponent in Damage Evolution Equation on the Accuracy of Damage Modelling in Brittle Materials

Piotr Mika
Cracow University of Technology
Poland

This paper analyses the influence of nonlinearity of the damage evolution equation that is introduced by exponent to the results obtained in the simulation of elastic-brittle material . Constitutive equation of linear-elastic medium with damages is described by the linear-tensorial function due to damage tensor. The nucleation and growth of microdamages are modelled using a two-parameter equation of damage evolution, in which the current level of damage is expressed by the principal values of Vakulenko-Kachanov and Murakami-Ohno damage tensors. The study examines a relationship between the time of the first macro crack appearance, principal values of damage tensor at the critical moment and the exponent adopted to the equation of damage evolution. The subjects of the analysis are changes in both the qualitative and quantitative variables characterizing the damage.
Keywords: continuum damage mechanics; damage evolution equation; damage tensor
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Lemaitre J., Chaboche J., Mechanics of Solid Materials, Cambridge University Press, New York, 1990.

Krajcinovic D., Damage Mechanics, Elsevier Science, North Holland, 1997.

Skrzypek J.J., Ganczarski A.W. (Eds), Anisotropic Behaviour of Damaged Materials, Springer-Verlag, Berlin, 2003.

Kattan P.I., Voyiadjis G.Z., Damage Mechanics with Finite Elements: Practical Applications with Computer Tools, Springer-Verlag, Berlin, 2002.

Murakami S., Continuum Damage Mechanics: A Continuum Mechanics Approach to the Analysis of Damage and Fracture, Springer, Dordrecht, Heidelberg, London, New York, Springer, 2012.

Lemaitre J., Desmorat R., Engineering Damage Mechanics, Springer, Berlin, 2005.

ABAQUS Theory and users manuals, ver. 6.11, Dassault Systèmes Simulia Corp., Providence, RI, USA

Ambroziak A., Identification and validation of damage parameters for elasto-viscoplastic Chaboche model, Eng. Trans., 55, 1, 3–28, 2007.

Madej J., Influence of damage on variations of material thermal properties, Eng. Trans., 51, 1, 25–46, 2003.

Hervé G., Gatuingt F., Ibrahimbegović A., On numerical implementation of a coupled rate dependent damage‐plasticity constitutive model for concrete in application to high‐rate dynamics, Eng. Comp., 22, 5–6, 583–604, 2005.

Rizzi E., Carol I., Secant stress/strain relations of orthotropic elastic damage with dual properties, Archives of Mechanics, 59, 2, 133–171, 2007.

Kachanov L.M., On time to rupture in creep conditions [in Russian], Izv. AN SSSR, OTN, 8, 26–31, 1958.

Voyiadjis G.Z, Kattan P.I., Yousef M.A., Some basic issues of isotropic and anisotropic continuum damage mechanics, [in:] Handbook of Damage Mechanics – Nano to Macro Scale for Materials and Structures, 3–42, 2014.

Murakami S., Ohno N., A continuum theory of creep and creep damage, [in:] Creep in Structures, A.R.S. Ponter and D.R. Hayhurst (Eds.), Springer, Berlin, 422–444, 1981.

Vakulenko A.A., Kachanov M.L., Continuum theory of medium with cracks [in Russian], Izv. A. N. SSSR, MTT, 59–166, 1971.

Lemaitre J., Damage modelling for prediction of plastic or creep fatigue failure in structures, Trans. 5th Int. Conf. SMiRT, Berlin, North-Holland, Amsterdam, L, L5/1b, 1–8, 1979.

Litewka A., Creep rupture of metals under multi-axial states of stress, Arch. Mech., 41, 3–23, 1989.

Murakami S., Notion of continuum damage mechanics and its application to anisotropic creep damage theory, J. Eng. Mat. Techn., 105, 2, 99–105, 1983.

Litewka A., Hult J., One parameter CDM model for creep rupture prediction, Eur. J. Mech. A, Solids, 8, 185–200, 1989.

Mika P., Modelling of shell structures with damage growth process [in Polish], Civ. & Env. Eng., 3, 58, II, 405–412, 2011.

Mika P., On interaction between damage growth and material stiffness in 3D structures, J. Theor. App. Mech., 37, 4, 755–778, 1999.




DOI: 10.24423/engtrans.245.2015