Formulation and Identification of Damage Kinetic Constitutive Equations
The damage kinetic constitutive equations are derived from the thermodynamics of irreversible process in which physical considerations and experimental results are introduced in order to choose the proper variables and the analytical forms of the potentia
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Jean Lemaitre Laboratoire de Mecanique et Technologie Universite Paris 6, Cachan, France
ABSTRACT Thc
damage
kinet.ic constitutive equations are derived from the of irreversible process in which physical considerations and rxperimental resull~ are introduced in order to choose the proper variables and the analytical forms of the potentials. A gPneral damage model is formulated and then applied to duclile dam~ge, low cycle fatigue, high cycle fatigue and creep damage in ordcr t.o identified particular kinetic laws to be introduced in :;tructure calr.ulations to predict the initiation and the growlh of crackr.. th~rmodynamics
CONTENTS 1. THE PHENOMENOLOGICAL THERMODYNAMICAL APPROACH 2. GENERAL FORMULATION
2.1. Phenomena and variables 2.1.1. Elasto-plasticity 2.1.2. Oamage 2. 1.3. Micro-plasticity 2.1.4. Thermal effects 2.2. Effective stress concept 2.2. 1. Definition 2.2.2. Principle of strain equivalence 2.2.3. Extension to quasi-unilateral conditions 2.3. Thermodynamic potential 2.3. 1. Formulation 2.3.2. State laws 2.3.3. Damage criterion 2.3.4. Rupture criterion 2.4. Potential of dissipation, general damage model 2.4.1. Dissipative variables 2.4.2. Normality rule
2.4.3. Properties of the potential of dissipation D. Krajcinovic et al. (eds.), Continuum Damage Mechanics Theory and Application © Springer-Verlag Wien 1987
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3. DUCTILE DAMAGE 3.1. Phenomenological aspects 3.1.1. Physical mechanisms 3.1.2. Micro-mechanics of void growth 3.1.3. Experimental measurements 3.2. Models 3.2.1. Formulation 3.2.2. Identification 3.3. Applications to ductile fracture 3.3.1. Strain condition to macro-crack initiation 3.3.2. Master curve of ductile fracture 4. LOW CYCLE FATIGUE DAMAGE 4.1. Phenomenological aspects 4.1.1. Physical mechanisms 4.1.2. Experimental measurements 4.2. Models 4.2.1. Formulation 4.2.2. Law of Manson-Coffin 4.2.3. Identification 4.3. Applications 4.3.1. Crack initiation 4.3.2. Fatigue crack growth 5. HIGH CYCLE FATIGUE DAMAGE 5.1. Phenomenological aspects 5.1.1. Physical mechanisms 5.1.2. Experimental measurements 5.2. Models 5.2. 1. Formulation 5.2.2. Woehler-Miner's law, Goodman's rule 5.2.3. Identification 5.3. Applications 6. CREEP DAMAGE 6.1. Phenomenological aspects 6.1.1. Physical mechanisms 6.1.2. Experimental measurements 6.2. Models 6.2. 1. Formulation 6.2.2. Kachanov's creep damage law 6.2.3. Identitication 6.3. Applications 6.3. 1. Creep fatigue interaction 6.3.2. Creep crack initiation and growth
Damagc Constitutive Equations
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THE PHENDHENDLDGICAL THERHDDYNAHICAL APPRDACH In the field of applied mechanics, damage constitutive equations are derived in view of structure calculations in order to predict the state of damage through the remaining life (the time or the number of cycles to initiation of a macro-crack) and the evolution crack at the structure scale (the so-called "local a of approach"). The main tool is then the mechanics of continuous variables principal the medid with stress and strain as [J. LEMAITRE-J.L. CHABOCHE, 1985]. The damage constitutive equatio
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