Crack closure

About: Crack closure is a research topic. Over the lifetime, 28157 publications have been published within this topic receiving 588158 citations.

Plane strain deformation near a crack tip in a power-law hardening material

Abstract: C rack-tip strain singularities are investigated with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field of an elastic material (or elastic/plastic material treated by a deformation theory). It is argued that the product of stress and strain exhibits a singularity varying inversely with distance from the tip in all materials. Corresponding near crack tip stress and strain fields are obtained for the plane straining of an incompressible elastic/plastic material hardening according to a power law. A noteworthy feature of the solution is the rapid rise of triaxial stress concentration above the flow stress with increasing values of the hardening exponent. Results are presented graphically for a range of hardening exponents, and the interpretation of the solution is aided by a discussion of analogous results in the better understood anti-plane strain case.

Singular behaviour at the end of a tensile crack in a hardening material

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.

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

Numerical simulations of fast crack growth in brittle solids

Abstract: Dynamic crack growth is analysed numerically for a plane strain block with an initial central crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on crack branching, and the effect of an inhomogeneity in strength, as in crack growth along or up to an interface. The effect of cohesive surface orientation on crack path is also explored, and for a range of orientations zigzag crack growth precedes crack branching. Finer mesh calculations are carried out where crack growth is confined to the initial crack plane. The crack accelerates and then grows at a constant speed that, for high impact velocities, can exceed the Rayleigh wave speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of crack growth is not constrained. The crack speed reaches about 45% of the Rayleigh wave speed, then the crack speed begins to oscillate and crack branching at an angle of about 29° from the initial crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast crack growth in brittle solids.