Introduction to Fracture Mechanics phần 1 ppsx

Introduction to Fracture Mechanics Introduction to Fracture Mechanics From Suresh: Fatigue of Materials... Importance of Fracture Mechanics :  All real materials contain defects: unders

Introduction to Fracture Mechanics Introduction to Fracture Mechanics

From Suresh: Fatigue of Materials

Importance of Fracture Mechanics :

 All real materials contain defects: understand

the influence of these defects on the strength of the material Defect-tolerant design philosophy

the material Defect-tolerant design philosophy

 Relevance for Fatigue: understand the initiation

and growth of fatigue cracks

We will use two approaches, an energy-based

Key Idea : Griffith (1921) postulated that for unit crack extension to occur under the influence of the

applied stress, the decrease in potential energy of

Griffith Fracture Theory

Introduction

applied stress, the decrease in potential energy of

the system, by virtue of the displacement of the

outer boundaries and the change in the stored elastic

energy, must equal the increase in surface energy

due to crack extension

Consider the center-cracked plate shown below The in-plane dimensions of the plate are large compared to the crack length

Using the results of Inglis (1913) Griffith found that

the net change in potential energy of the plate caused

by the introduction of the crack is:

'

2 2

E

B

a

WP  





E 

= E Plane stress

The surface energy of the crack system is

2

1

'

v

E E





s

S aB

W  4 

Plane strain

The total system energy is then given by

.

4 '

2 2

S S

E

B

a W

W

Griffith noted that the critical condition for the onset

of crack growth is:

2

a dW

dW

where A=2aB is the crack area and dA denotes an

incremental increase in the crack area

Thus the stress required to initiate fracture is:

.

'

2

a



a



As the second derivative, d2U/da2 is negative, the

above equilibrium condition gives rise to unstable

crack propagation This applies for brittle materials;

it must be modified for ductile materials such as metals

Orowan (1952) extended Griffith’s brittle fracture

concept to metals by simply adding a term representing

plastic energy dissipation The resultant expression

for fracture initiation is

,

) (

'

2E  s  p

a

p

s

where is the plastic work per unit area of surface  p

.





Energy Release Rate Crack Driving Force

Consider an elastic plate with an edge crack of length

as shown below:

,

a

The total mechanical potential energy of a cracked elastic body is given by the general expression

F

where is the stored elastic strain energy and is  wF

the work done by the external forces. F

Irwin (1956) proposed an approach for the

characterization of the driving force for fracture in