Stress concentration

Abstract: A method is presented in which fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened. This assumption may be regarded as a way of expressing the energy adsorption GC in the energy balance approach, but it is also in agreement with results of tension tests. As a demonstration the method has been applied to the bending of an unreinforced beam, which has led to an explanation of the difference between bending strength and tensile strength, and of the variation in bending strength with beam depth.

Abstract: Preface 1. Introduction and overview Part I. Cyclic Deformation and Fatigue Crack Initiation: 2. Cyclic deformation in ductile single crystals 3. Cyclic deformation in polycrystalline ductile solids 4. Fatigue crack initiation in ductile solids 5. Cyclic deformation and crack initiation in brittle solids 6. Cyclic deformation and crack initiation in noncrystalline solids Part II. Total-Life Approaches: 7. Stress-life approach 8. Strain-life approach Part III. Damage-Tolerant Approach: 9. Fracture mechanics and its implications for fatigue 10. Fatigue crack growth in ductile solids 11. Fatigue crack growth in brittle solids 12. Fatigue crack growth in noncrystalline solids Part IV. Advanced Topics: 13. Contact fatigue: sliding, rolling and fretting 14. Retardation and transients in fatigue crack growth 15. Small fatigue cracks 16. Environmental interactions: corrosion-fatigue and creep-fatigue Appendix References Indexes.

Abstract: D istributions of stress occurring at the tip of a crack in a tension field are presented for both plane stress and plane strain. A total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used. For applied stress sufficiently low such that the plastic zone is very small relative to the crack length, the dominant singularity can be completely determined with the aid of a path-independent line integral recently given by rice (1967). The amplitude of the tensile stress singularity ahead of the crack is found to be larger in plane strain than in plane stress.

Abstract: In an earlier paper it was suggested that a knowledge of the elastic-stress variation in the neighborhood of an angular corner of an infinite plate would perhaps be of value in analyzing the stress distribution at the base of a V-notch. As a part of a more general study, the specific case of a zero-angle notch, or crack, was carried out to supplement results obtained by other investigators. This paper includes remarks upon the antisymmetric, as well as symmetric, stress distribution, and the circumferential distribution of distortion strain-energy density. For the case of a symmetrical loading about the crack, it is shown that the energy density is not a maximum along the direction of the crack hut is one third higher at an angle ± cos^(-1) (1/3); i.e., approximately ±70 deg. It is shown that at the base of the crack in the direction of its prolongation, the principal stresses are equal, thus tending toward a state of (two-dimensional) hydrostatic tension. As the distance from the point of the crack increases, the distortion strain energy increases, suggesting the possibility of yielding ahead of the crack as well as ±70 deg to the sides. The maximum principal tension stress occurs on ±60 deg rays. For the antisymmetrical stress distribution the distortion strain energy is a relative maximum along the crack and 60 per cent lower ± 85 deg to the sides.

Abstract: 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.