Abstract
A concise review of one and three-dimensional theories of isotropic or anisotropic damage coupled constitutive equations of time-dependent elastic or inelastic materials is systematically presented. When damage is considered as isotropic phenomenon both phenomenologically-based damage-creep-plasticity models (Kachanov, Rabotnov, Hayhurst, Leckie, Kowalewski, Dunne, etc.) and unified irreversible thermodynamics formulation of coupled isotropic damage-thermoelastic-creep-plastic materials (Lemaitre and Chaboche, Mou and Han, Saanouni, Foster and Ben Hatira) are reported. In case when anisotropic nature of damage is described in frame of the continuum damage mechanics (CDM) approach, a concept of the fourth-rank damage effect tensor M is introduced in order to define the constitutive tensors of damaged materials, stiffness or compliance
in terms of those of virgin isotropic materials. Matrix representation of constitutive tensors is reviewed in case of energy based damage coupled constitutive model of elastic-brittle (Litewka, Murakami and Kamiya) or elastic-plastic engineering materials (Hayakawa and Murakami). Particular attention is paid to the orthotropic creep-damage model and its computer applications to the case of non-proportional loading conditions, when the objective damage rate is applied. A non-classical problem of thermo-damage coupling is developed, when the second-rank tensors of thermal conductivity
and radiation
in the extended heat transfer equation are defined for damaged material in terms of the damage tensor D.
The CDM based finite difference method (FDM) and finite element method (FEM) computer applications to the analysis and design of simple engineering structures under damage conditions are developed. Structures of uniform creep damage strength are examined from the point of view of maximum lifetime prediction when the equality and inequality constraints are imposed, and the thickness and initial prestressing are chosen as design variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Skrzypek J. and Ganczarski A.: Application of the orthotropic damage growth rule to variable principal directions, Int. J. Damage Mech., 7 (1998), pp. 180–206.
Kachanov L.M.: Time of the rupture process under creep conditions, lzv. AN SSR, Otd. Tekh. Nauk, 8 (1958), pp. 26–31.
Kachanov L.M.: Foundations of Fracture Mechanics, Nauka, Moscow, 1974, in Russian.
Rabotnov Ju.N.: Creep rupture, in: Proc. 12 Int. Congr. Appl. Mech., Stanford, Calif., 1968 pp. 342–349.
Martin J.B. and Leckie F.A.: J. Mech. Phys. Solids, 20 (1972), pp. 223.
Hayhurst D.R. and Leckie F.A.: The effect of creep constitutive and damage relationships upon rupture time of solid circular torsion bar, J. Mech. Phys. Solids, 21 (1973), pp. 431–446.
Leckie F.A. and Hayhurst D.R.: Creep rupture of structures, Proc. Roy. Soc. London, A 340 (1974), pp. 323–347.
Hayhurst D.R.: Creep rupture under multiaxial state of stress, J. Mech. Phys. Solids, 20 (1972), pp. 381–390.
Hayhurst D.R.: On the role of creep continuum damage in structural mechanics, in: Engineering Approaches to High Temperature Design (Edited by Wilshire and D. Owen ), Pineridge Press, Swansea, 1983.
Trgpczyriski W.A., Hayhurst D.R. and Leckie F.A.: Creep rupture of copper and aluminium under non—proportional loading, J. Mech. Phys. Solids, 29(1981), pp. 353374.
Lemaitre J. and Chaboche J.L.: A non—linear model of creep fatigue damage cumulation and interaction, in: Proc. of IUTAM Symp. Mechanics of Visco—Elastic Media and Bodies (Edited by J. Hult ), Springer, Gothenburg, Sweden, 1975 pp. 291–301.
Lemaitre J. and Chaboche J.L.: Aspect phenomenologique de la rapture per endommagement, J. de Méchanique applique, 2 (1978), pp. 317–365.
Lemaitre J. and Chaboche J.L.: Méchanique des Matériaux Solides, Dunod Publ., Paris, 1985.
Chaboche J.L.: Continuum damage mechanics: Part I: General concepts, Part II: Damage growth, crack initiation, and crack growth, J. Appl. Mech., 55 (1988), pp. 5971.
Dunne F.P.E. and Hayhurst D.R.: Continuum damage based constitutive eqaution for copper under high temperature creep and cyclic plasticity, Proc. R. Soc. Lond., A 437 (1992), pp. 545–566.
Dunne F.P.E. and Hayhurst D.R.: Modelling of combined high—temperature creep and cyclic plasticity in components using Continuum Damage Mechanics, Proc. R. Soc. Lond., A 437 (1992), pp. 567–589.
Dunne F.P.E. and Hayhurst D.R.: Efficient cycle jumping techniques for the modelling of materials and structures under cyclic mechanical and thermal loadings, Eur. J. Mech., A/Solids, 13 (1994), pp. 639–660.
Dunne F.P.E. and Hayhurst D.R.: Physically based temperature dependence of elastic—viscoplastic constitutive equations for copper between 20 and 500°C, Philosophical Mag., A 74 (1995), pp. 359–382.
Othman A.M., Hayhurst D.R. and Dyson B.F.: Skeletal point stresses in circumferentially notched tension bars undergoing tertiary creep modelled with physically based constitutive equations, Proc. R. Soc. London, 441 (1993), pp. 343–358.
Germain P., Nguyen Q.S. and Suquet P.: Continuum Thermodynamics, ASME J. Appl. Mech., 50 (1983), pp. 1010–1020.
Dufailly J. and Lemaitre J.: Modeling very low cycle fatigue, Int. J. Damage Mech., 4 (1995), pp. 153–170.
Mou Y.H. and Han R.P.S.: Damage evolution in ductile materials, Int. J. Damage Mech., 5 (1996), pp. 241–258.
Saanouni K., Forster C.H. and Hatira F. Ben: On the anelastic flow with damage, Int. J. Damage Mech., 3 (1994), pp. 140–169.
Davison L. and Stevens A.L.: Thermodynamical constitution of spalling elastic bodies, J. Appl. Phys., 44 (1973), pp. 668–674.
Kachanov L.M.: Introduction to Continuum Damage Mechanics, Martinus Nijhoff, The Netherlands, 1986.
Krajcinovic D. and Fonseka G.U.: The continuous damage theory of brittle materials, Part I and II: General theory, J. Appl. Mech., Trans ASME, 48 (1981), pp. 809–824.
Krajcinovic D.: Constitutive theory of damaging materials, J. Appl. Mech., Trans. ASME, 50 (1983), pp. 355–360.
Krajcinovic D.: Damage Mechanics, North Holland Series in Appl. Math. and Mech., Elsevier, Amsterdam, 1996.
Lubarda V.A. and Krajcinovic D.: Damage tensors and the crack density distribution, Int. J. Solids Struct., 30 (1993), pp. 2859–2877.
Rabotnov Ju.N.: Creep Problems in Structural Members, North-Holland, Amsterdam, 1969, engl. trans. by F.A. Leckie.
Vakulenko A.A. and Kachanov M. L.: Continuum theory of medium with cracks, lzv. A.N. SSSR, M.T.T., 4 (1971), pp. 159–166, in Russian.
Murakami S. and Ohno N.: A continuum theory of creep and creep damage, in: Creep in Structures (Edited by A. Ponter and D. Hayhurst ), Springer, Berlin, 1980 pp. 422–444.
Cordebois J.P. and Sidoroff F.: Damage induced elastic anisotropy, in: Col. EUROMECH 115, Villard de Lans, 1979 Also in Mechanical Behavior of Anisotropic Solids (Ed. Boehler, J. P. ), Martinus Nijhoff, Boston 1983, 761–774.
Cordebois J.P. and Sidoroff F.: Endommagement anisotrope an élasticité at plasticité, J. Méc. Théor. Appl., Numero Spécial, (1982), pp. 45–60.
Betten J.: Damage tensors in continuum mechanics, J. Méc. Théor. Appl., 1 (1983), pp. 13–32.
Betten J.: Application of tensor functions in continuum damage mechanics, Int. J. Damage Mech., 1 (1992), pp. 47–59.
Litewka A.: Effective material constants for orthotropically damaged elastic solid, Arch. Mech., 6 (1985), pp. 631–642.
Litewka A.: Analytical and experimental study of fracture of damaging solids, in: Proc. of IUTAM/ICM Symp. Yielding, Damage, and Failure of Anisotropic Solids (Edited by J. Boehler ), Mech. Eng. Publ, London, 1987 pp. 655–665.
Litewka A.: Creep rupture of metals under multi-axial state of stress, Arch. Mech., 41 (1989), pp. 3–23.
Murakami S.: Notion of continuum damage mechanics and its applications to anisotropic creep damage theory, J. Eng. Mater. Technol., 105 (1983), pp. 99–105.
Murakami S.: Failure Criterion of Structural Media, Balkema, 1986.
Murakami S.: Progress of continuum mechanics, JSME, Int. J., 30(1987), pp. 701–710.
Murakami S.: Mechanical modelling of material damage, J. Appl. Mech., Trans. ASME, 55 (1988), pp. 280–286.
Chow C.L. and Lu T.J.: An analytical and experimental study of mixed-mode ductile fracture under nonproportional loading, Int. J. Damage Mech., 1 (1992), pp. 191–236.
Chaboche J.L.: Development of continuum damage mechanics for elastic solids sustaining anisotropic and unilateral damage, Int. J. Damage Mech., 2(1993), pp. 311–329.
Chaboche J.L.: Thermodynamically founded CDM models for creep and other conditions, in: Creep and Damage in Materials and Structures (Edited by H. Altenbach and J. Skrzypek), Advanced School No. 187, Udine, Sept. 7–11, 1998, Springer Vienna, 1999.
Murakami S. and Kamiya K.: Constitutive and damage evolution equations of elastic—brittle materials based on irreversible thermodynamics, Int. J. Solids Struct., 39 (1997), pp. 473–486.
Hayakawa K. and Murakami S.: Thermodynamical modeling of elastic—plastic damage and experimental validation of damage potential, Int. J. Damage Mech., 6 (1997), pp. 333–362.
Hayakawa K. and Murakami S.: Space of damage conjugate force and damage potential of elastic–plastic damage materials, in: Damage Mechanics in Engineering Materials (Edited by G. Z. Voyiadjis, J.-W. Ju and J.-L. Chaboche ), Elsevier Science, Amsterdam, 1998 pp. 27–44.
Skrzypek J. and Ganczarski A.: Modeling of damage effect on heat transfer in time–dependent non–homogeneous solids, J. Thermal Stresses, 21 (1998), pp. 205–231.
Skrzypek J. and Ganczarski A.: Modeling of Material Damage and Failure of Structures, Springer, Berlin–Heidelberg, 1999.
Leckie F.A. and Onat E.T.: Tensorial nature of damage measuring internal variables, in: Proc. of IUTAM Symp. Physical Non–linearities in Structural Analysis (Edited by J. HuIt and J. Lemaitre ), Springer, Berlin, 1981.
Chaboche J.L.: Le concept de contraine appliqué à l’élasticité et la viscoplasticité en présence d’un endommagement anisotrope, in: Mechanical Behaviour of Anisotropic Solids (Edited by J. Boehler), Col. EUROMECH 115, Grenoble 1979, Editions du CNRS No. 295, Paris, 1982 pp. 737–760.
Simo J.C. and Ju J.W.: Strain– and stress–based continuum damage models. I — Formulation, Il — Computational aspects, Int. J. Solids Struct., 23(1987), pp. 821–869.
Krajcinovic D.: Damage mechanics, Mech. Mater., 8 (1989), pp. 117–197.
Chen X.F. and Chow C.L.: On damage strain energy release rate Y, Int. J. Damage Mech., 4 (1995), pp. 251–236.
Voyiadjis G.Z. and Park T.: Anisotropic damage for the characterization of the onset of macro–crack initiation in metals, Int. J. Damage Mech., 5 (1996), pp. 68–92.
Voyiadjis G.Z. and Park T.: Kinematics of large elastoplastic damage deformation, in: Damage Mechanics in Engineering Materials (Edited by G. Voyiadjis, J.-W. Ju and J.-L. Chaboche ), Elsevier Science, Amsterdam, 1998 pp. 45–64.
Qi W. and Bertram A.: Anisotropic creep damage modeling of single crystal super-alloys, Techn. Mechanik, 17 (1997), pp. 313–332.
Zheng Q.-S. and Betten J.: On damage effective stress and equivalence hypothesis, Int. J. Damage Mech., 5 (1996), pp. 219–240.
Taher S.F., Baluch M.H. and Al-Gadhib A.H.: Towards a canonical elastoplastic damage model, Eng. Fracture Mechanics, 48 (1994), pp. 151–166.
Robinson E.L.: Effect of temperature variation on the long time rupture strength of steel, Trans. ASME, 74 (1952), pp. 777–780.
Chrzanowski M. and Madej J.: Construction of the failure curves based on the damage parameter concept, Mech. Teor. Stos., 4 (1980), pp. 587–601, (in Polish).
Chaboche J.L.: Une Loi Différentielle d’Endommagement de Fatigue avec Cumulation non Linéaire, Revue Française de Mecanique, (1974), pp. 50–51, english trans. in: Annales de I’IBTP, HS 39, (1977).
Othman A.M. and Hayhurst D.R.: Multi–axial creep rupture of a model structure using a two–parameter material model, Int. J. Mech. Sci., 32 (1990), pp. 35–48.
Kowalewski Z.L., Hayhurst D.R. and Dyson B.F.: Mechanisms–based creep constitutive equations for an aluminium alloy, J. Strain Analysis, 29 (1994), pp. 309–316.
Kowalewski Z.L., Lin J. and Hayhurst D.R.: Experimental and theoretical evaluation of a high–accuracy uni–axial creep testpiece with slit extensometers ridges, Int. J. Mech. Sci., 36 (1994), pp. 751–769.
Hayhurst D.R.: Material data bases and mechanisms–based constitutive equations for use in design, in: Creep and Damage in Materials and Structures (Edited by H. Altenbach and J. Skrzypek), Advanced School No. 187, Udine, Sept. 7–11, 1998, Springer Vienna, 1999.
Rides M., Cocks A.C. and Hayhurst D.R.: The elastic response of damaged materials, J. Appl. Mech., 56 (1989), pp. 493–498.
Johnson A.E., Henderson J. and Mathur V.D.: Combined stress creep fracture of commercial copper at 250°, The Engineer, 24 (1956), pp. 261–265.
Johnson A.E., Henderson J. and Khan B.: Complex-stress creep, relaxation and fracture of metallic alloys, HMSO, Edinbourgh, 1962.
Chaboche J.L. and Rousselier G.: On the plastic and viscoplastic constitutive equations–P.1: Rules developed with internal variable concept, P.2: Application of internal variable concepts to the 316 stainless steel, J. Pressure Vessel Technol, 105 (1983), pp. 153–164.
Lemaitre J.: A continuum damage mechanics model for ductile fracture, ASME J. Engng. Mat. and Technology, 107 (1985), pp. 83–89.
Lemaitre J.: Formulation and identification of damage kinetic constitutive equations, in: Continuum damage mechanics — theory and application (Edited by D. Krajcinovic and J. Lemaitre), CISM Courses and Lectures, 295, Springer, Berlin, 1987 pp. 37–89.
Broberg H.: Damage measures in creep deformation and rupture, Swedish Solid Mechanics Report, 8 (1974), pp. 100–104.
Chow C.L. and Wang L.: An anisotropic theory of elasticity for continuum damage mechanics, Int. J. Fracture, 33 (1987), pp. 3–16.
Chow C.L. and Wang L.: An anisotropic theory of continuum damage mechanics for ductile materials, Eng. Fract. Mech., 27 (1987), pp. 547–558.
Voyiadjis G.Z. and Kattan P.I.: A plasticity–damage theory for large deformation of solids, Part I: Theoretical formulation, Int. J. Eng. Sci., 30 (1992), pp. 1089–1108.
Chaboche J.L., Lesne P.M. and Moire J.F.: Continuum damage mechanics, anisotropy and damage deactivation for brittle materials like concrete and ceramic composites, Int. J. Damage Mech., 4 (1995), pp. 5–22.
Ganczarski A. and Skrzypek J.: Effect of initial prestressing on the optimal design of plates with respect to orthotropic brittle rupture, Arch. Mech., 46 (1994), pp. 463–483.
Litewka A. and Hult J.: One parameter CDM model for creep rupture prediction, Eur. J. Mech., A/Solids, 8 (1989), pp. 185–200.
Gallagher R.H.: Fully stressed design, in: Optimal Structural Design (Edited by R. Gallagher and O. Zienkiewicz ), John Willey, New York, 1973 pp. 19–23.
Zyczkowski M.: Optimal structural design in rheology, J. Appl. Mech., 38(1971), pp. 39–46, proc. 12 Int. Cong. Theor. Appl. Mech., Standford 1968.
Zyczkowski M.: Optimal structural design under creep conditions (1), Appl. Mech. Reviews, 41 (1988), pp. 453–461.
Zyczkowski M.: Problems of structural optimization under creep conditions, in: Proc. of IUTAM Symp. Creep in Structures IV, 1990 (Edited by M. Zyczkowski ), Springer, Berlin, 1991 pp. 519–530.
Zyczkowski M.: Optimal structural design under creep conditions (2), Appl. Mech. Reviews, 49 (1996), pp. 433–446.
Hayhurst D.R., Dimmer P.R. and Chernuka M.W.: Estimates of the creep rupture lifetimes of structures using the finite element methods, J. Mech. Phys. Solids, 23 (1975), pp. 335–355.
Hayhurst D.R., Dimmer P.R. and Morrison C.J.: Development of continuum damage in the creep rupture of notched bars, Phil. Trans. R. Soc. London, A 311 (1984), pp. 103–129.
Saanouni K., Chaboche J.L. and Bathias C.: On the creep crack growth prediction by a non—local damage formulation, Eur. J. Mech., A/Solids, 8 (1986), pp. 677–691.
Liu Y., Murakami S. and Kanagawa Y.: Mesh—dependence and stress singularity in finite element analysis of creep crack growth by Continuum Damage Mechanics, Eur. J. Mech. A/Solids, 13 (1994), pp. 395–417.
Murakami S., Kawai M. and Rong H.: Finite element analysis of creep crack growth by a local approach, Int. J. Mech. Sci., 30 (1988), pp. 491–502.
Murakami S. and Liu Y.: Mesh—dependence in local approach to creep fracture, Int. J. Damage Mech., 4 (1995), pp. 230–250.
Skrzypek J., Kuna-Ciskal H. and Ganczarski A.: On CDM modelling of pre— and post—critical failure modes in the elastic—brittle structures, in: Beiträge zur Festschrift zum 60 Geburstag von Prof. Dr.—Ing. Peter Gummert, Mechanik, Berlin, 1998 pp. 203–228.
Skrzypek J., Kuna-Ciskal H. and Ganczarski A.: Continuum damage mechanics modeling of creep—damage and elastic—damage—fracture in materials and structures, in: Proc. Workshop on Modeling Damage, Localization and Fracture Process in engineering Materials, Kazimierz Dolny, 1999 (to be published).
Ganczarski A. and Skrzypek J.: Optimal prestressing and design of rotating disks against brittle rupture under unsteady creep conditions, Eng. Trans., 37 (1989), pp. 627–649, (in Polish).
Ganczarski A. and Skrzypek J.: On optimal design of disks with respect to creep rupture, in: Proc. of IUTAM Symp. Creep in Structures (Edited by M. Zyczkowski ), Cracow, 1990 pp. 571–577.
Ganczarski A. and Skrzypek J.: Optimal shape of prestressed disks against brittle rupture under unsteady creep conditions, Struct. Optim., 4 (1992), pp. 47–54.
Ganczarski A. and Skrzypek J.: Optimal design of rotationally symmetric disks in thermo—damage coupling conditions, Techn. Mechanik, 17 (1997), pp. 365–378.
Skrzypek J.J.: Plasticity and Creep, Theory, Examples, and Problems, Begell House — CRC Press, Boca Raton, 1993, ed. R. B. Hetnarski.
Skrzypek J. and Egner W.: On the optimality of disks of uniform creep strength against brittle rupture, Eng. Opt., 21 (1993), pp. 243–264.
Egner W. and Skrzypek J.: Effect of pre-loading damage on the net—lifetime of optimally prestressed rotating disks, Arch. Appl. Mech., 64 (1994), pp. 447–456.
Ganczarski A. and Skrzypek J.: Axisymmetric plates optimally designed against brittle rupture, in: Proc. World Congr. on Optimal Design of Structural Systems, Structural Optimization 93 (Edited by J. Herskovits ), Rio de Janeiro 1993, 1993 pp. 197–204.
Ganczarski A. and Skrzypek J.: Brittle-rupture mechanisms of axisymmetric plates subject to creep under surface and thermal loadings, in: Proc. of SMIRT-12 (Edited by K. Kussmaul ), Edited by K. 1993, 1993 pp. 263–268.
Ganczarski A., Freindl L. and Skrzypek J.: Orthotropic brittle rupture of Reissner’s prestressed plates, in: Proc. 5 Int. Conf. On Computational Plasticity (Edited by D. Owen, E. O. Nate and E. Hinton ), Barcelona, 1997 pp. 1904–1909.
Ganczarski A. and Skrzypek J.: Concept of thermo—damage coupling in continuum damage mechanics, in: Proc. First Int. Symp. Thermal Stresses ‘85 (Edited by R. Hetnarski and N. Noda ), Hamamatsu, Japan, Act City, 1995 pp. 83–86.
Ganczarski A. and Skrzypek J.: Modeling of damage effect of heat transfer in solids, in: Proc. Second Int. Symp. Thermal Stresses ‘87 (Edited by R. Hetnarski and N. Noda ), Rochester, NY, 1997 pp. 213–216.
Holman J.P.: Heat Transfer, McGraw-Hill, 1990.
Odqvist F.K.G.: Mathematical Theory of Creep and Creep Rupture, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1966.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Wien
About this paper
Cite this paper
Skrzypek, J.J. (1999). Material Damage Models for Creep Failure Analysis and Design of Structures. In: Altenbach, H., Skrzypek, J.J. (eds) Creep and Damage in Materials and Structures. International Centre for Mechanical Sciences, vol 399. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2506-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2506-9_3
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83321-6
Online ISBN: 978-3-7091-2506-9
eBook Packages: Springer Book Archive