Strain energy release rate

About: Strain energy release rate is a research topic. Over the lifetime, 7130 publications have been published within this topic receiving 166781 citations.

Elementary engineering fracture mechanics

Abstract: I Principles.- 1 Summary of basic problems and concepts.- 1.1 Introduction.- 1.2 A crack in a structure.- 1.3 The stress at a crack tip.- 1.4 The Griffith criterion.- 1.5 The crack opening displacement criterion.- 1.6 Crack propagation.- 1.7 Closure.- 2 Mechanisms of fracture and crack growth.- 2.1 Introduction.- 2.2 Cleavage fracture.- 2.3 Ductile fracture.- 2.4 Fatigue cracking.- 2.5 Environment assisted cracking.- 2.6 Service failure analysis.- 3 The elastic crack-tip stress field.- 3.1 The Airy stress function.- 3.2 Complex stress functions.- 3.3 Solution to crack problems.- 3.4 The effect of finite size.- 3.5 Special cases.- 3.6 Elliptical cracks.- 3.7 Some useful expressions.- 4 The crack tip plastic zone.- 4.1 The Irwin plastic zone correction.- 4.2 The Dugdale approach.- 4.3 The shape of the plastic zone.- 4.4 Plane stress versus plane strain.- 4.5 Plastic constraint factor.- 4.6 The thickness effect.- 5 The energy principle.- 5.1 The energy release rate.- 5.2 The criterion for crack growth.- 5.3 The crack resistance (R curve).- 5.4 Compliance.- 5.5 The J integral.- 5.6 Tearing modulus.- 5.7 Stability.- 6 Dynamics and crack arrest.- 6.1 Crack speed and kinetic energy.- 6.2 The dynamic stress intensity and elastic energy release rate.- 6.3 Crack branching.- 6.4 The principles of crack arrest.- 6.5 Crack arrest in practice.- 6.6 Dynamic fracture toughness.- 7 Plane strain fracture toughness.- 7.1 The standard test.- 7.2 Size requirements.- 7.3 Non-linearity.- 7.4 Applicability.- 8 Plane stress and transitional behaviour.- 8.1 Introduction.- 8.2 An engineering concept of plane stress.- 8.3 The R curve concept.- 8.4 The thickness effect.- 8.5 Plane stress testing.- 8.6 Closure.- 9 Elastic-plastic fracture.- 9.1 Fracture beyond general yield.- 9.2 The crack tip opening displacement.- 9.3 The possible use of the CTOD criterion.- 9.4 Experimental determination of CTOd.- 9.5 Parameters affecting the critical CTOD.- 9.6 Limitations, fracture at general yield.- 9.7 Use of the J integral.- 9.8 Limitations of the J integral.- 9.9 Measurement of JIc and JR.- 9.10 Closure.- 10 Fatigue crack propagation.- 10.1 Introduction.- 10.2 Crack growth and the stress intensity factor.- 10.3 Factors affecting crack propagation.- 10.4 Variable amplitude service loading.- 10.5 Retardation models.- 10.6 Similitude.- 10.7 Small cracks.- 10.8 Closure.- 11 Fracture resistance of materials.- 11.1 Fracture criteria.- 11.2 Fatigue cracking criteria.- 11.3 The effect of alloying and second phase particles.- 11.4 Effect of processing, anisotropy.- 11.5 Effect of temperature.- 11.6 Closure.- II Applications.- 12 Fail-safety and damage tolerance.- 12.1 Introduction.- 12.2 Means to provide fail-safety.- 12.3 Required information for fracture mechanics approach.- 12.4 Closure.- 13 Determination of stress intensity factors.- 13.1 Introduction.- 13.2 Analytical and numerical methods.- 13.3 Finite element methods.- 13.4 Experimental methods.- 14 Practical problems.- 14.1 Introduction.- 14.2 Through cracks emanating from holes.- 14.3 Corner cracks at holes.- 14.4 Cracks approaching holes.- 14.5 Combined loading.- 14.6 Fatigue crack growth under mixed mode loading.- 14.7 Biaxial loading.- 14.8 Fracture toughness of weldments.- 14.9 Service failure analysis.- 15 Fracture of structures.- 15.1 Introduction.- 15.2 Pressure vessels and pipelines.- 15.3 "Leak-bcfore-break" criterion.- 15.4 Material selection.- 15.5 The use of the J integral for structural analysis.- 15.6 Collapse analysis.- 15.7 Accuracy of fracture calculations.- 16 Stiffened sheet structures.- 16.1 Introduction.- 16.2 Analysis.- 16.3 Fatigue crack propagation.- 16.4 Residual strength.- 16.5 The R curve and the residual strength of stiffened panels.- 16.6 Other analysis methods.- 16.7 Crack arrest.- 16.8 Closure.- 17 Prediction of fatigue crack growth.- 17.1 Introduction.- 17.2 The load spectrum.- 17.3 Approximation of the stress spectrum.- 17.4 Generation of a stress history.- 17.5 Crack growth integration.- 17.6 Accuracy of predictions.- 17.7 Safety factors.- Author index.

Fracture and Size Effect in Concrete and Other Quasibrittle Materials

Abstract: Why Fracture Mechanics? Historical Perspective Reasons for Fracture Mechanics Approach Sources of Size Effect on Structural Strength Quantification of Fracture Mechanics Size Effect Experimental Evidence for Size Effect Essentials of LEFM Energy Release Rate and Fracture Energy LEFM and Stress Intensity Factor Size Effect in Plasticity and in LEFM Determination of LEFM Parameters Setting Up Solutions from Closed-Form Expressions Approximate Energy-Based Methods Numerical and Experimental Procedures to Obtain KI and G Experimental Determination of KIc and Gf Calculation of Displacements from KI-Expressions Advanced Aspects of LEFM Complex Variable Formulation of Plane Elasticity Problems Plane Crack Problems and Westergaard's Stress Function The General Near Tip Fields Path-Independent Contour Integrals Mixed Mode Fracture Criteria Equivalent Elastic Cracks and R-Curves Variability of Apparent Fracture Toughness for Concrete Types of Fracture Behavior and Nonlinear Zone The Equivalent Elastic Crack Concept Fracture Toughness Determination Based on Equivalent Crack Concepts Two Parameter Model of Jenq and Shah R-Curves Stability Analysis in the R-Curve Approach Determination of Fracture Properties from Size Effect Size Effect in Equivalent Elastic Crack Approximations Size Effect Law in Relation to Fracture Characteristics Size Effect Method: Detailed Experimental Procedures Determination of R-Curve from Size Effect Cohesive Crack Models Basic Concepts in Cohesive Crack Model Cohesive Crack Models Applied to Concrete Experimental Determination of Cohesive Crack Properties Pseudo-Boundary-Integral Methods for Mode I Crack Growth Boundary-Integral Methods for Mode I Crack Growth Crack Band Models and Smeared Cracking Strain Localization in the Series Coupling Model Localization of Strain in a Softening Bar Basic Concepts in Crack Band Models Uniaxial Softening Models Simple Triaxial Strain-Softening Models for Smeared Cracking Crack Band Models and Smeared Cracking Comparison of Crack Band and Cohesive Crack Approaches Advanced Size Effect Analysis Size Effect Law Refinements Size Effect in Notched Structures Based on Cohesive Crack Models Size Effect on the Modulus of Rupture of Concrete Compressing Splitting Tests of Tensile Strength Compression Failure Due to Propagation of Splitting Crack Band Scaling of Fracture of Sea Ice Brittleness and Size Effect in Structural Design General Aspects of Size Effect and Brittleness in Concrete Structures Diagonal Shear Failure of Beams Fracturing Truss Model for Shear Failure of Beams Reinforced Beams in Flexure and Minimum Reinforcement Other Structures Effect of Time, Environment, and Fatigue Phenomenology of Time-Dependent Fracture Activation Energy Theory and Rate Processes Some Applications of the Rate Process Theory to Concrete Fracture Linear Viscoelastic Fracture Mechanics Rate-Dependent R-Curve Model with Creep Time-Dependent Cohesive Crack and Crack Band Models Introduction to Fatigue Fracture and Its Size Dependence Statistical Theory of Size Effect and Fracture Process Review of Classical Weibull Theory Statistical Size Effect Due to Random Strength Basic Criticisms of Classical Weibull-Type Approach Handling of Stress Singularity in Weibull-Type Approach Approximate Equations for Statistical Size Effect Another View: Crack Growth in an Elastic Random Medium Fractal Approach to Fracture and Size Effect Nonlocal Continuum Modeling of Damage Localization Basic Concepts in Nonlocal Approaches Triaxial Nonlocal Models and Applications Nonlocal Model Based on Micromechanics of Crack Interactions Material Models for Damage and Failure Microplane Model Calibration by Test Data, Verification, and Properties of Microplane Model Nonlocal Adaptation of Microplane Model or Other Constitutive Models Particle and Lattice Models Tangential Stiffness Tensor via Solution of a Body with Many Growing Cracks References Index

Adhesion of spheres : the JKR-DMT transition using a dugdale model

Abstract: In the Johnson-Kendall-Roberts (JKR) approximation, adhesion forces outside the area of contact are neglected and elastic stresses at the edge of the contact are infinite, as in linear elastic fracture mechanics. On the other hand, in the Derjaguin-Muller-Toporov (DMT) approximation, the adhesion forces are taken into account, but the profile is assumed to be Hertzian, as if adhesion forces Could not deform the surfaces. To avoid self consistent numerical calculations based on a specific interaction model (Lennard-Jones potential for example) we have used a Dugdale model, which allows analytical solutions. The adhesion forces are assumed to have a constant value σO, the theoretical stress, over a length d at the crack tip. This internal loading acting in the air gap (the external crack) leads to a stress intensity factor Km, which is cancelled with the stress intensity factor KI due to the external loading. This cancellation suppresses the stress singularities, ensures the continuity of stresses, and fixes the radius c and the crack opening displacement δt. The energy release rate G is computed by the J-integral and the equilibrium is given by G = w. The equilibrium curves a(P), a(δ), and P(σ), the adherence forces at fixed load or fixed grips, the profiles, and the stress distributions can therefore be drawn as a function of a single parameter λ. When λ increases from zero to infinity there is a continuous transition from the DMT approximation to the JKR approximation. Furthermore the value of G for the DMT approximation is derived. It is shown that it is not physically consistent to have tensile stresses in the area of contact and no adhesion forces outside or no tensile stresses in the area of contact and adhesion forces outside. In the JKR approximation the distribution of adhesion forces is reduced to a singular stress at r = a+. The total attraction force outside the contact being zero, the integral of stresses in the contact is equal to the applied load P and negative applied loads are supported by the elastic restoring forces. In the DMT approximation the adhesion stresses tend toward zero to have a continuity with the stress at r = a−, but their integral is finite and the total attraction force outside the contact is 2πwR. In the area of contact the distribution of stresses is Hertzian, and their integral is P + 27πwR. Negative applied loads are sustained by adhesion forces outside the contact.