Fracture and Size Effect in Concrete and Other Quasibrittle Materials

TLDR: In this paper, the authors used the Weibull-type approach to measure the effect of size effect on structural strength of a crack and its size effect in terms of the number of cracks and the size of the cracks.

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