Introduction to Fracture Mechanics
1
Introduction to Fracture Mechanics
From Suresh: Fatigue of Materials
INTRODUCTION
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.
2
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
approach and a more rigorous mechanics approach.
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
3

The surface energy of the crack system is
2
1
'
v
E
E


sS
aBW

4

Plane strain
where γ
S
is the free surface energy per unit surface area.
The total system energy is then given by
.4
'
22
SSP
aB
E
Ba
WWU







7
a

As the second derivative, d
2
U/da
2
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
p
s




8
,
a


F
w
10
the work done by the external forces.

F
Irwin (1956) proposed an approach for the
characterization of the driving force for fracture in
cracked bodies, which is conceptually equivalent to
that of the Griffith model.