1
• How is fracture resistance quantified? How do the fracture
resistances of the different material classes compare?
• How do we estimate the stress to fracture? 
• How do loading rate, loading history, and temperature 
affect the failure behavior of materials?
Ship-cyclic loading
from waves.
Computer chip-cyclic
thermal loading.
Hip implant-cyclic
It can be accomplished by understanding the mechanics of failure
modes and applying appropriate design principles.
Failure cost 
Failure causes: 
 
Fracture 
Fracture is the separation of a body into two or more
 pieces in response to an imposed stress
Steps in Fracture:
Depending on the ability of material to undergo plastic deformation
 before the fracture two fracture modes can be defined - ductile or
brittle. 
Extensive plastic deformation ahead of crack
Crack is “stable”: resists further extension
unless applied stress is increased
Brittle fracture - ceramics, ice, cold metals:
Relatively little plastic deformation
increase in applied stress
 
 
(a) Necking
(d) Crack propagation by shear deformation
(e) Fracture 
 
parabolic dimples from shear loading.
8
Distinctive pattern on the fracture surface: V-shaped “chevron”
markings point to the failure origin.
 
the crack in a fanlike pattern
 
 
along grain boundaries (grain boundaries are weakened
or embrittled by impurities segregation etc.)
 
Measured fracture strength is much lower than predicted by calculations
 based on atomic bond energies. This discrepancy is explained by the
 presence of flaws or cracks in the materials.
The flaws act as stress concentrators or stress raisers,
amplifying the stress at a given point.
The magnitude of amplification depends on crack
geometry and orientation.
hole through plate, and is oriented
 perpendicular to applied stress, the
maximum stress, at crack tip
where
length of internal crack
 
(1)
o
a
   t 
• Avoid sharp corners! s 
Neugebauer, Prod. Eng. 
1943.)
Stress Concentration 
Crack propagation 
Cracks with sharp tips propagate easier than cracks having blunt tips
2/1
2  
   s s 
 
γs = specific surface energy
When the tensile stress at the tip of crack exceeds the critical stress value
the crack propagates and results in fracture.
 
EXAMPLE PROBLEM 8.1 Page 244 
A relatively large plate of a glass is subjected to a tensile stress of 40
MPa. If the specific surface energy and modulus of elasticity for this
glass are 0.3 J/m2 and 69 GPa, respectively, determine the maximum
length of a surface flaw that is possible without fracture.
= 2
fracture when a crack is present.
 =    
and microstructure.
The magnitude of K  c  diminishes with increasing strain rate
and decreasing temperature.
strain hardening generally produces corresponding decrease
in K  c  . 
 K  c  normally increases with reduction in grain size as
composition and other microstructural variables are
maintained constant.
Two standard tests, the Charpy and Izod, measure the impact
energy (the energy required to fracture a test piece under an
impact load), also called the notch toughness 
 
 brittle - ductile-to-brittle transition. 
the impact energy needed for fracture drops suddenly over a
relatively narrow temperature range –  temperature of the ductile-to-
 brittle transition. 
dependence of the measured impact energy absorption
 
Low strength steels(BCC)  
   I  m   p   a   c    t    E   n   e   r  g   y
Temperature 
 
• Problem: Steels were used having DBTT’s just below
room temperature.
Design Strategy:
e.g., bridges, aircraft, machine components, automobiles,etc.. 
Fatigue 
 
than tensile or yield strengths of material under a static
load.
Fatigue
Estimated to causes 90% of all failures of metallic structures
Fatigue failure is brittle-like (relatively little plastic
deformation) - even in normally ductile materials. Thus
sudden and catastrophic!
initiation in the areas of stress concentration (near stress
raisers), incremental crack propagation, final catastrophic
failure.
 
Fatigue properties of a material (S-N curves) are tested in
rotating-bending tests in fatigue testing apparatus 
Result is commonly plotted as S (stress) vs. N (number of
cycles to failure)
Fatigue limit (endurance limit) occurs for some materials
(e.g. some Fe and Ti alloys). In this case, the S —  N curve
 becomes horizontal at large N, limiting stress level. The fatigue
limit is a maximum stress amplitude below which the material
never fails, no matter how large the number of cycles is.
For many steels,
Magnesium) S decreases continuously with N. In this
cases the fatigue properties are described by
Fatigue strength: stress at which
fracture occurs after a
107)
fail at a specified stress
level
of materials when subjected to a constant load or stress.
For metals it becomes important at a high temperature
(> 0.4 Tm). Examples: turbine blades, steam
generators, high pressure steam lines.
Creep
For details read the book pages 265-267
 
2. Primary/transient creep. Slope of strain vs. time
decreases with time: strain-hardening
Constant
failure:
separation, necking, etc. 
Stages of Creep
duration and the steady-state creep rate .
=  
applications e.g. nuclear power plant component.
Another parameter, especially important in short-life
creep situations, is time to rupture, or the rupture
lifetime, tr.. e.g., turbine blades in military aircraft and
rocket motor nozzles, etc….