A Course on Damage Mechanics

by Jean Lemaitre, H. Lippmann (Foreword by)

Overview

This second, corrected and enlarged edition teaches macroscopic modeling for the design, processing, testing, and control of mechanical components in engineering, and also includes the damage of interfaces and statistical damage analysis with microdefects. The first chapter deals with the phenomenology of damage, while the second couples damage to strains before going on to cover the three-dimensional situation. Chapter 3 is devoted to kinetic laws of damage evolution used by the author to unify many models, and the book is rounded off with several methods for predicting crack initiation. Detailed calculations and many exercises help students to apply the powerful techniques to practical problems in engineering.

Product Details

ISBN-13:	9783540609803
Publisher:	Springer Berlin Heidelberg
Publication date:	06/14/1996
Edition description:	2nd rev. and enlarged ed.
Pages:	228
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

1 Phenomenological Aspects of Damage.- 1.1 Physical Nature of the Solid State and Damage.- 1.1.1 Atoms, Elasticity and Damage.- 1.1.2 Slips, Plasticity and Irreversible Strains.- 1.1.3 Scale of the Phenomena of Strain and Damage.- 1.1.4 Different Manifestations of Damage.- 1.1.5 Exercise on Micrographic Observations.- 1.2 Mechanical Representation of Damage.- 1.2.1 One-Dimensional Surface Damage Variable.- 1.2.2 Effective Stress Concept.- 1.2.3 Strain Equivalence Principle.- 1.2.4 Coupling Between Strains and Damage; Rupture Criterion; Damage Threshold.- 1.2.5 Exercise on the Micromechanics of the Effective Damage Area.- 1.3 Measurement of Damage.- 1.3.1 Direct Measurements.- 1.3.2 Variation of the Elasticity Modulus.- 1.3.3 Variation of the Microhardness.- 1.3.4 Other Methods.- 1.3.5 Exercise on Measurement of Damage by the Stress Amplitude Drop.- 2 Thermodynamics and Micromechanics of Damage.- 2.1 Three-Dimensional Analysis of Isotropic Damage.- 2.1.1 Thermodynamical Variables, State Potential.- 2.1.2 Damage Equivalent Stress Criterion.- 2.1.3 Potential of Dissipation.- 2.1.4 Strain-Damage Coupled Constitutive Equations.- 2.1.5 Exercise on the Identification of Material Parameters.- 2.2 Analysis of Anisotropic Damage.- 2.2.1 Geometrical Definition of a Second-Order Damage Tensor.- 2.2.2 Thermodynamical Definition of a Fourth-Order Damage Tensor.- 2.2.3 Energetic Definition of a Double Scalar Variable.- 2.2.4 Exercise on Anisotropic Damage in Proportional Loading.- 2.3 Micromechanics of Damage.- 2.3.1 Brittle Isotropie Damage.- 2.3.2 Ductile Isotropie Damage.- 2.3.3 Anisotropie Damage.- 2.3.4 Microcrack Closure Effect, Unilateral Conditions.- 2.3.5 Damage Localization and Instability.- 2.3.6 Exercise on the Fiber Bundle System.- 3 Kinetic Laws of Damage Evolution.- 3.1 Unified Formulation of Damage Laws.- 3.1.1 General Properties and Formulation.- 3.1.2 Stored Energy Damage Threshold.- 3.1.3 Three-Dimensional Rupture Criterion.- 3.1.4 Case of Elastic-Perfectly Plastic and Damageable Materials.- 3.1.5 Identification of the Material Parameters.- 3.1.6 Exercise on Identification by a Low Cycle Test.- 3.2 Brittle Damage of Metals, Ceramics, Composites and Concrete.- 3.2.1 Pure Brittle Damage.- 3.2.2 Quasi-brittle Damage.- 3.2.3 Exercise on the Influence of the Triaxiality on Rupture.- 3.3 Ductile and Creep Damage of Metals and Polymers.- 3.3.1 Ductile Damage.- 3.3.2 Exercises on the Fracture Limits in Metal Forming.- 3.3.3 Creep Damage.- 3.3.4 Exercise on Isochronous Creep Damage Curves.- 3.4 Fatigue Damage.- 3.4.1 Low Cycle Fatigue.- 3.4.2 Exercise on Creep Fatigue Interaction.- 3.4.3 High Cycle Fatigue.- 3.4.4 Exercise on Damage Accumulation.- 3.5 Damage of Interfaces.- 3.5.1 Continuity of the Stress and Strain Vectors.- 3.5.2 Strain Surface Energy Release Rate.- 3.5.3 Kinetic Law of Debonding Damage Evolution.- 3.5.4 Simplified Model.- 3.5.5 Exercise on a Debonding Criterion for Interfaces.- 3.6 Table of Material Parameters.- 4 Analysis of Crack Initiation in Structures.- 4.1 Stress-Strain Analysis.- 4.1.1 Stress Concentrations.- 4.1.2 Neuter’s Method.- 4.1.3 Finite Element Method.- 4.1.4 Exercise on the Stress Concentration Near a Hole.- 4.2 Uncoupled Analysis of Crack Initiation.- 4.2.1 Determination of the Critical Point(s).- 4.2.2 Integration of the Kinetic Damage Law.- 4.2.3 Exercise on Fatigue Crack Initiation Near a Hole.- 4.3 Locally Coupled Analysis.- 4.3.1 Localization of Damage.- 4.3.2 Postprocessing of Damage Growth.- 4.3.3 Description and Listing of the Postprocessor DAMAGE 90.- 4.3.4 Exercises Using the DAMAGE 90 Postprocessor.- 4.4 Fully Coupled Analysis.- 4.4.1 Initial Strain Hardening and Damage.- 4.4.2 Example of a Calculation Using the Finite Element Method.- 4.4.3 Growth of Damaged Zones and Macrocracks.- 4.4.4 Exercise on Damage Zone at a Crack Tip.- 4.5 Statistical Analysis with Microdefects.- 4.5.1 Initial Defects.- 4.5.2 Case of Brittle Materials.- 4.5.3 Case of Quasi Brittle Materials.- 4.5.4 Case of Ductile Materials.- 4.5.5 Volume Effect.- 4.5.6 Effect of Stress Heterogeneity.- 4.5.7 Exercise on Bending Fatigue of a Beam.- History of International Damage Mechanics Conferences.- Authors and Subject Index.