Lecture

Fracture Mechanics: Cohesive Zone Model

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In course

ME-437: Advanced solid mechanics

Description

This lecture covers the concept of crack-tip energy dissipation in brittle materials, the generalization for ductile materials, and the analysis of the cohesive zone model for fracture. It explains the determination of small-scale yielding, the length scales in the cohesive zone model, and the stress fields near a crack tip. The lecture also discusses the hierarchy of length scales in small-scale yielding and provides solutions to the center-crack problem using complex variable analysis. Additionally, it explores the dominance of the singular field near crack tips and presents atomistic results on stress fields ahead of cracks of various sizes.

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Related concepts (28)

Fracture mechanics

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip.

Fracture

Fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band or dislocation. Brittle fractures occur without any apparent deformation before fracture.

Strength of materials

The field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.

Ductility

Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile stress before failure. Ductility is an important consideration in engineering and manufacturing. It defines a material's suitability for certain manufacturing operations (such as cold working) and its capacity to absorb mechanical overload.

Fracture toughness

In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. A component's thickness affects the constraint conditions at the tip of a crack with thin components having plane stress conditions and thick components having plane strain conditions. Plane strain conditions give the lowest fracture toughness value which is a material property.

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Fracture Mechanics: Cohesive Zone Modeling

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Fracture Mechanics: Introduction and Crack Growth Analysis

Covers the basics of fracture mechanics, including crack shape and growth analysis.

Crack Tip Plasticity in Materials

Explores crack tip plasticity in materials, emphasizing the importance of the plastic zone in crack resistance.

Crack Growth: Stress Intensity and Fracture Mechanics