1. Fracture mechanics Subjects of interest Introduction/ objectives
Stress intensity factor
Determination of fracture toughness
Fracture toughness and design
Plasticity correction
Crack opening displacement
R curve
Probabilistic aspects of fracture mechanics

2. Crack and stress intensity approach
The unit of KI is MPam

3. Stresses near and tip of the crack

4. Loading types
In all loading1/r singularity may occur at the tip of the crack. K (stress intensity factor) and fij (dimensionless shape correction factor) depend on laoding type and shape geomety. (i,j=1,3)
There are three ways of applying a force to enable a crack to propagate:
Mode I fracture : opening mode(a tensile stress normal to the plane of the crack).
Mode II fracture : sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack).
Mode III fracture : Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front)

5. Cauchy stress around a crack tip and Stress Intensity Factors
Crack deformation mode.
K value can be evaluated using standard mathematical
approaches,
Mode I: tension,
opening
Mode II: In plane shear,
sliding
Mode III: Out of plane
shear, tearing

6. ac : is the critical crack length in an infinite plate
Stress intensity factor K can be described as fracture toughness KIC of materials (material resistance to crack propagation) under conditions of
Brittle fracture
In the presence of sharp crack
Under critical tensile loading
KIC : is the critical stress intensity factor for plane strain
condition in mode I failure.
ac : is the critical crack length in an infinite plate
app : is the applied stress
LEFM- Linear Elastic Fracture Mechanics
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7. Stress intensity factor types in a plate including crack
Mode I and Mode II calculations of a plate subjected to tension. (Mixed Mode Loading)

8. Stresses in the systems with crack
When the crack at the center of a plate the stress and stress intensity factors terms can be given as :
: Shape correction factor
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9. Center crack in an infinite plate subjected to tension
Stress Intensity Factor Aprroach K : h 2a b P
where w = 2b

10. Types of Stress:
Plane stress problem : the stress in z direction becomes zero.
z = xz = yz = 0,
Plane strain problem : the strain in z direction becomes zero
xz = yz = 0 and
z =  (x + y).

11. Geometries of Fracture
Center crack and finite plate:
Stress intensity factor
infinite plate:

12. Single sided notch, subjected to stress
Stress intensity factor
One-sided cracked plate
if( a
w) semi infinite plate β=1.12

13. Stress intensity factor
Double-sided notch :
Stress intensity factor
a) if( a
w) semi infinite plate β=1.12 b)
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14. Stress intensity factors Y wrt a/w ratio

15. Eliptic Crack

16. Semi Eliptic Surface crack

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