Syllabus

Module I- Fundamentals of Linear Elastic Fracture Mechanics (8 hours)

Why Fracture Mechanics? Three Kinds of Fracture Mechanics Crack-Parallel Stresses and Tensorial Damage as Quasibrittle Fracture Basis Size Effect Type and Role of Material Randomness Applications of Size Effect in Structural Analysis and Design
Energy Release Rate and Fracture Energy General Form of Near-Tip and Far Fields of a Notch Stress Singularities and Energy Flux at a Sharp Crack Tip Westergaard’s Solution for Crack in Infinite Body Stress Intensity Factor, Near-Tip Field, and Remote Field Fracture Modes I, II, and III Irwin’s Relationship between Stress Intensity Factors and Energy Release Rate Rice’s J –Integral Numerical Calculation of Stress Intensity Factors Stress Intensity Factors for Typical Simple Geometries Calculation of Elastic Compliance and Deflection from Stress Intensity Factors Bimaterial Interfacial Cracks Comments on Anisotropic Materials and Three-Dimensional Singularities

Module II - Nonlinear Fracture Mechanics: Line Crack Idealization and Diffuse Crack Model (8 hours)

Types of Fracture Behavior and Nonlinear Zone Irwin’s Estimate of the Size of the Inelastic Zone Estimation of FPZ Size for Quasibrittle Materials Equivalent Linear Elastic Crack Model R-Curves Cohesive Crack Model Integral Equations of Mode I Cohesive Crack Model Eigenvalue Analysis of Peak Load and Size Effect

Module III - Nonlinear Fracture Mechanics: Diffuse Crack Model (6 hours)

Why Crack Band? Crack-Parallel Stress and Other Evidence Strain Localization, Mesh Sensitivity, and Localization Limiters Crack Band Model Nonlocal Integral and Gradient Models Discrete Computational Models Energetic Size Effect in Quasibrittle Fracture Nominal Structural Strength and Size Effect Power-Law Scaling in Absence of Characteristic Length Dimensional Analysis of Size Effect Second-Order Asymptotic Scaling Behavior at Small Size Limit Derivation of Size Effect Equations Using Equivalent LEFM Determination of R-Curve from Size Effect Analysis Size Effect Testing of Cohesive Law Parameters

Module IV - Probabilistic Theory of Quasibrittle Fracture (6 hours)

Weibull Statistics of Structural Strength Finite Weakest-Link Model of Strength Distribution of Quasibrittle Structures Mean Size Effect on Structural Strength Problem with Applying Three-Parameter Weibull Distribution Fishnet Statistics for Biomimetic, Architectured, Lattice and Some Particulate Materials Remark on Failure Probability of Concrete Specimens of Random Mean Strength in Large Database

Module V - Quasibrittle Size Effect Analysis in Practical Problems (8 hours)

Tensile Fracture Problems Tensile Fracture of Sea Ice Compression Fracture with Shear and Size Effects Tensile Fracture and Size Effect in Fiber Composites Bone Fracture and Size Effect Size Effect in Polymer Nanocomposites Interfacial Fracture of Metal-Composite Hybrid Joints Reliability of Polycrystalline Silicon MEMS Devices Analogy with Scaling of Small-Scale Yielding Fracture of Metals

To provide the fundamentals of fracture mechanics.

To understand damage propagation in concrete structures.

To model crack growth in concrete numerically.

To learn fundamentals of probabilistic fracture mechanics.
To understand size-effect in concrete structures.

Students will develop skills in fracture mechanics analysis.

Students will be able to model damage and crack growth in concrete structures.

Students will be able to formulate and analyse complex engineering problems using the first principles of fracture mechanics.

Students will be able to investigate structural failure caused by crack-growth.

Students will be able to use codal provisions developed using fracture mechanics concepts.

Zdenek P. Bazant, Jia-liang Le, and Marco Salviato, Quasibrittle fracture mechanics and size effect, Oxford University Press , 2022

Zdenek P. Bazant, and Jaime Planas, Fracture and Size Effect in Concrete and Other Quasibrittle materials, CRC Press , 1998

David Broek, Elementary Engineering Fracture Mechanics, Springer , 2012

Prashant Kumar, Elements of Fracture Mechanics, Mc Graw Hill Education , 2019

Engineering Fracture Mechanics

Theoretical and Applied Fracture Mechanics

International Journal of Fatigue

International Journal of Fracture