Material Damage Models for Creep Failure Analysis and Design of Structures
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 p
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J.J. Skrzypek Cracow University of Technology, Cracow, Poland
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. ln 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 A or .A- 1 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 problern of thermo-damage coupling is developed, when the second-rank tensors of thermal conductivity L and radiation f 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. H. Altenbach et al. (eds.), Creep and Damage in Materials and Structures © Springer-Verlag Wien 1999
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J.J. Skrzypek
DAMAGE VARIABLES AND CDM EQUIVALENCE PRINCIPLES
1.1. State of darnage and darnage variables State of material darnage is identified as the existence of distributed microvoids, microcavities or microcracks in a volume of a material. Irreversible time-dependent microprocesses, when the microdefects nucleation, growth and coalescence cause a progressive degradation of the physical and thermomechanical properties through reduction of strength, elasticity modulae, microhardness, ultrasonic wave speed, heat conductivity, etc., is called the darnage evolution. When the continuum darnage mechanics CDM method is used the true distribution of microdeffects, their size, density and orientation, is homogenized by a selection of the set of internal variables of different nature, scalar D, vector Da" secend-rank tensor D, fourth-rank tensor :6, etc., that me
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