Fracture and Failure Theory

1
Fracture and Failure Theory
2
Defining Failure

• Failure can be defined in a variety of ways
• Unable to perform the to a given criteria
• Fracture
• Yielding

3
Failure of Structural Materials

• Yielding is often considered impending failure
• The deformations associated with yield provide a
  warning
• The service life is effectively ended if a
  materials yields under service, in most cases.

4
Tresca Yield Criterion

• Ductile Materials
• Assumes slip occurs during yielding
• yielding begins when max. shear stress reaches
  the shear stress obtained in a simple tension
  test at yield
• tmax (s1 s2)/2

5
Tension in x and y directions
t
s
sx
sy
6
Tension in x and y directions
t
s
sx
sy
7
von Mises Yield Criterion

• Separates hydrostatic pressure from distortion
  stresses
• Bases on Energy of distortion is equal to energy
  of distortion at yield of a simple tension test

8
Comparison of Theories
9
Surface Energy and Fracture

• Energy required to generate new surfaces
• Griffith crack theory
• Crack will propagate if elastic strain energy is
  equal to energy of newly created surface

10
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Real Distribution
r
r
2a
Plastic Zone
?
11
Stress Intensity
?

• The Stress Intensity Factor is a constant that
  defines the stress distribution near a crack

r
r
2a
r distance from crack tip.
?
12
Fracture Toughness, KIc

• Fracture toughness, KIc
• Material property
• Used to predict the crack size that can be
  tolerated
• sc KIc/(pa)1/2
• KIc increases with thickness
• KIc decreases with temperature increase

13
Stress Concentrations
?

• Stress risers occur at discontinuities
• SCF is related to hole shape and size

smax
save
r
r
2a
?