FRACTURE MECHANICSPresented by

Muhammad Shahid BS (hons) 4th semester

Institute OF chemistry,University of the Punjab

Overview

Brittle & Ductile Fracture

Modes of Failure

Energy Release Rate & Crack Resistance

Crack Growth

Stress Intensity Factor

parameters

Applications of Fractures Mechanics

Fracture means the cracking or breaking of a hard object or material.

What is fracture?

Breakingof

Materials

High sulphur in material

Cold waters

Welding instead of riveting

Continuity of the structure

Applied stress

Microcracks

Factors affecting fracture

Thermal expansion Quality of surfacesMagnitude of stress

Brittle deformation: it occurs (in rocks) when a rock breaks or fractures due to stress. This happens in high pressure but low temperature environments

Elastic deformation: An object can bend or flex temporarily and will “ spring back" to its original shape, but at some point it will also fail.

Ductile deformation: Any strain is irreversible and the rock deforms readily (Think taffy puller). Often in a single fault all three forms of deformation take place in that order as depth increases.

Brittle & Ductile Fracture

• Ductile materials - extensive plastic deformation and energy absorption (“toughness”) before fracture

• Brittle materials - little plastic deformation and low energy absorption before fracture

What is 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.

Fracture mechanics is based on the implicit assumption that there exists a crack in a work component.

It is the study of flaws and cracks in materials.

Mostly deals with crack growth.

Importance of Fracture mechanics

In modern materials science, fracture mechanics is an important tool in improving the mechanical performance of mechanical components. It applies the physics of stress and strain, in particular the theories of elasticity and plasticity, to the microscopic crystallographic defect found in real materials.

Fractography is widely used with fracture mechanics to understand the causes of failures and also verify the theoretical failure predictions with real life failures.

Fracture propagation

Crack

Due to internal pressure a crack occurs in metal plate…

CRACK INITIATION

Physically, cracks initiate from; An imperfection

An already existing crack

A damaged (locally weakened) area

A failure analysis must include; Stress analysis

Failure criterion

Three Modes of Fracture

Mode I denotes a symmetric opening (opening or tension mode) Mode II denotes an antisymmetric separation (In-plane shear

mode) Mode III denotes an antisymmetric separation (out-of-plane shear

or tearing mode) Crack growth usually takes place in mode I or close to it. The crack “adjusts” itself such that the load is perpendicular to the

crack faces.

Parameters of Fracture Mechanics

J-Integral

Energy-Release Rate

Stress-Intensity Factor

T-Stress

Material Force

C*-Integral

Energy Release Rate and J-Integral

The strain energy release rate (or simply energy release rate) is the energy consumed during fracture per unit of newly created fracture surface area. This quantity is central to fracture mechanics because the energy that must be supplied to a crack tip for it to grow must be balanced by the amount of energy dissipated due to the formation of new surfaces and other dissipative processes such as plasticity.

Strain energy release rate

where   is the potential energy available for crack growth,   is the work associated with any external forces acting, and   is the crack area (crack length for two-dimensional problems). The units of   are J/m2. where   is the potential energy available for crack growth,

Where U is the potential energy available for crack growth, and V is the work associated with any external forces acting and A is the crack area. The units of G are J/m2.

The energy release rate failure criterion states that a crack will grow when the available energy release rate G  is greater than or equal to a critical value Gc.

G >=Gc

The quantity Gc is the fracture energy and is considered to be a material property which is independent of the applied loads and the geometry of the body

Stress Intensity Factor

The stress intensity factor K  is used in fracture mechanics to predict the stress state ("stress intensity") near the tip of a crack caused by a remote load or applied stresses.

Stress Intensity Factor is a quantity determined analytically and varies as a function of the crack configuration and the external loads are applied

Critical stress intensity factor is independent of the crack geometry and loading and may be regarded as a material constant.

T-Stress

T- Stress is the stress acting parallel to the crack faces

Unlike J-integral, it can have both negative and positive values

Positive T-stress values promotes fracture, where negative T-stress values results in larger plastic zones

The J-integral represents a way to calculate the  strain energy release rate or work (energy) per unit fracture surface area, in a material.

Crack growth becomes a concern when structural components are operated at high temperatures i.e Nuclear Industry

Applications of Fracture Mechanics

Fracture mechanics can be used in different major areas:

(i) designing

(ii) material selection and alloy development

(iii) determining the significance of defects.

(iv) monitoring , control, and failure analysis. 

Cont.…

Many large complex structures such as bridges, ships, buildings, aircraft and pressure vessels can have crack like imperfections, sharp notches and discontinuities of various kinds. Using fracture mechanics an engineer can quantitatively establish allowable stress levels and inspection requirements to design against the occurrence of fractures in such structures.in addition fracture mechanics is also used to analyze the growth of small cracks to critical size by loading or by stress cracking. therefore fracture mechanics techniques have several advantages and offer the designer a method of quantitative design to prevent fracture in structures.

THANK YOU!