Transcript AND = ME 240: Introduction to Engineering Materials

ME 240: Introduction to Engineering Materials
CHAPTER 8
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
FRAC
The Fundamentals
Fracture = separation of body into two or more pieces due to
application of static stress
Tensile,
Compressive
Shear or torsional
Lets talk about the tensile loading of materials
Modes of fracture
Chapter 8. Failure
DUCTILE
BRITTLE
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ME 240: Introduction to Engineering Materials
Back to the The tensile test
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Ductile fracture in copper
nucleating around inclusions
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Cup and Cone fracture
Chapter 8. Failure
Brittle fracture
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ME 240: Introduction to Engineering Materials
Transgranular vs. intergranular fracture
(cleavage fracture)
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Professor Inglis (1913)
The birth of the term
‘’stress concentration’’
Large structures
Stress trajectories
y
x
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Griffith (1920) – application of Inglis to cracks and defects
~ 100 microns
in diameter
Bent to a strain of 7.5%
i.e. 5000MPa.
Normal strength of glass = 100-200MPa.
HE PROVED HIS POINT!!
Crack-free silica (glass) fiber
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Ellipse
2b
But radius of curvature =  t = b2/a
For circular hole
Chapter 8. Failure
Stress concentration factor
b= a = r  Kt = 1 + 2 (1/1)1/2) = 3
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ME 240: Introduction to Engineering Materials
Stress concentration factor
vs.
Specimen Geometry/configuration
So what happens if a crack intersects a hole?
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Griffith and his Energy criterion
Crack propagates when favorable, i.e. system reduces its total energy

Relaxed material behind crack
=
Elastic strain energy released
Crack having surface energy (s)
G
 2 a
a
 Gc  2  R  constant
E
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
What about ductile materials
But for v. ductile materials p >>> s
Define the strain energy release rate Gc
(IRWIN)
Hence
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Modes of fracture
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Stress intensity factor
AND
Chapter 8. Failure
=
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ME 240: Introduction to Engineering Materials
What about ductile materials  consider y (i.e. y means direction not yield)
Plastic zone
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Plane strain fracture toughness
Chapter 8. Failure
To be plane strain
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Design using fracture mechanics
Example:
Compare the critical flaw sizes in the following metals subjected to
tensile stress 1500MPa and K = 1.12 a.
KIc (MPa.m1/2)
Critical flaw size (microns)
Al
250
7000
Steel
50
280
Zirconia(ZrO2)
2
0.45
Toughened Zirconia
12
16
SOLUTION
Where Y = 1.12. Substitute values
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
This problem asks us to determine whether or not the 4340 steel alloy specimen will
fracture when exposed to a stress of 1030 MPa, given the values of KIc, Y, and the
largest value of a in the material.
This requires that we solve for  from Equation (8.7). Thus
c
Therefore, fracture will not occur because this specimen will tolerate a stress of 1380 MPa
(199,500 psi) before fracture, which is greater than the applied stress of 1030 MPa (150,000
psi).
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
IMPACT TESTING
Tensile test vs. real life failures
Impact energy measured
or notch toughness
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
How do we specify a
ductile-brittle transition
temperature (DBTT)??
Also HCP
Not all materials exhibit DBTT
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
FATIGUE
Failure under repeated cyclic loading
Definitions
Mean stress
Range of stress
Stress amplitude
For Reversed cycle fatigue
R = -1
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
How do you practically make these fatigue measurements ?
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Endurance limit or Fatigue limit vs. fatigue life
e.g. steels
& Ti Alloys
e.g. Al
e.g. 35-60% of TS
High cycle
vs.
low cycle fatigue
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
How does a fatigue crack form and propagate?
STAGE II 
Nf = Ni + Np
Initiation Propagation
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ME 240: Introduction to Engineering Materials
Beachmarks
Chapter 8. Failure
Striations
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
One of failure analysis goals = prediction of fatigue life of component
knowing service constraint and conducting Lab tests
Ignores crack initiation
and fracture times
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ME 240: Introduction to Engineering Materials
Can make extrapolations
To obtain log A
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
QUESTION
Eqn. 8.26
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Other effects:
a) Mean stress
b)stress concentrations
c) Surface treatments
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ME 240: Introduction to Engineering Materials
CREEP
Time dependent and permanent deformation of materials
when subjected to load or stress (significant at T = 0.4Tm)
 = f (T, t, )
Lead pipes deforming
under their own weight
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Effect of temperature and stress
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Chapter 8. Failure
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ME 240: Introduction to Engineering Materials
Data extrapolation methods – e.g. prolonged exposures (years)
Perform creep tests in excess of T and shorter time but at same stress level
Chapter 8. Failure
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