FAILURE MODES and
MATERIALS PROPERTIES
MECH2300 - Materials Lecture 10
R. W. Truss
Materials Engineering
R.Truss@uq.edu.au
COMPONENT FAILURE MODES
examples:
• Excessive Elastic
deformation
• Plastic deformation
– High stress/short
term
– Low stress/long
term/high
temperature
• Brittle fracture
– Static load
– Fatigue
• Wear
• Corrosion /
degradation
• etc
Failure Mode
Material Property
------------------------------------------------------Elastic deformation
Plastic deformation
Brittle fracture
Wear
Corrosion
Degradation
Modulus (E)
Yield strength (σy)
Creep resistance
Fracture toughness (K1c, G1c)
Fatigue crack propagation
hardness, fracture toughness
half cell potential, etc
UV stability, etc.
COMPONENT FAILURES
• Structures lectures → stresses on
component
• stresses cause response in component that
may lead to failure
(failure = cease to perform design function)
Component failures
• Important to match failure mode to
material property used in design
• mode may change with conditions
Ductile and Brittle Fracture
Ductile fracture
- substantial bulk plastic
deformation of sample
brittle fracture
- little bulk deformation
failure is often sudden
and catastrophic
Toughness
Defn :
Toughness - energy required to cause failure/fracture
Failure modes change with conditions
eg Charpy energy v Temp
Measured by:
1) Area under stress
strain curve to failure
2) Impact
energy
(Charpy/Izod)
3) Fracture mechanics (see later)
Example:
brittle failure
of welded
ships
Ductile/ brittle transition
Depends on:
• alloy composition
• bcc or fcc metals
(transition at much higher
temperatures in bcc
metals)
• Presence of notches
Corrected fig.
Brittle
fracture likely
Ductile fracture
likely
1/T
Ductile / Brittle transition in Polymers
As a function of temperature or rate
• Ductile at high temperatures or slow rates
• Brittle at high rates or low temperatures
Ductile/Brittle transition in Polymers
As a function of time under load
Example: failure modes in HDPE Pipes
Short term failures - ductile
Long term failures - Brittle
• time to failure increases with decreasing load
• design pressure decreases as design failure time increases
But
• type of failure changes with time
• Caused by different time dependency of ductile and brittle
failure modes
Toughness: fracture mechanics approach
Basis of Fracture Mechanics
• all materials are imperfect
i.e. they contain flaws or small cracks
• these cracks can grow to cause brittle fracture
• cracks propagate only when specific energy or
stress conditions met
Stress, σ, at point near tip of a crack
y
σx= {K /√πr} fx (θ)
σy
σx
σy= {K /√πr} fy (θ)
τxy
r
σz= {K /√πr} fz (θ)
σz
θ
crack
r - distance from crack tip
θ - angle from the plane of the crack
z
Design against Brittle Fracture
Brittle fracture occurs when
K1c = Yσf (πa)1/2
• Fracture toughness, K1c, fixed from
materials selection
• stress, σ, from design
• Flaw size, a, from non destructive
testing or inspection
x
• stress near crack tip described by term K
– stress intensity factor
• crack begins to grow at critical value of K,
K1c (fracture toughness)
K1c = Yσf (πa)1/2
Y = geometry term a = crack length
For internal notch of length 2a, in a infinite sheet,
Y=1
For a surface notch of length a, Y~ 1.12
Case study:
Failure of a loaded bolt
Possible failure modes:
• Yield
• Brittle fracture
• Corrosion
• Elastic deformation
• Creep
• ???
D
d
Will the bolt deform and yield or
undergo brittle fracture when loaded
with an axial load P
D
• Yield governed by
yield stress, σy
• Brittle fracture
related to fracture
toughness, K1c
d
For Brittle fracture:
K1c D3/2 / Pf = 1.72 D/d –1.27
where Pf is load at fracture
For yield/ductile failure:
σy = Py / 3.14 x10-4 (based on inner diameter)
where Py is the load to yield
Failure loads in bolt
Load for Yield Load for Brittle
fracture (kN)
(kN)
81.7
242.6
Tool steel
817
(hardened & tempered)
High strength alloy
459
steel
Bolt thread can act as flaw
Stress Intensity Factor for circumferential notch in a
rod (bolt thread is approximately this geometry) is
given to ~1% accuracy by
K1 D3/2 / P = 1.72 D/d –1.27
for 0.5 < d/D < 0.8,
where D is diameter of rod; d is diameter of notched
region; P is tensile load on rod.
{cf K1c = Yσf (πa)1/2}
Steel properties
for bolt with D = 25 mm , d = 20mm
(D,d in ‘m’)
K1c = Pf *222.6
Medium carbon steel
Brittle fracture of bolt
98.8
440
Medium carbon steel
Yield stress Fracture Toughness
MPa
MPam 1/2
260
54
Tool steel
2600
(hardened & tempered)
High strength alloy
1460
steel
22
98
brittle fracture stress as a
statistical quantity
• materials contain distribution of flaws
• K1c is a material property - invariant
(for given conditions)
• measured brittle failure stress must
change with flaw size
• distribution of failure stresses
Design stress depends on
acceptable failure rate
Mean failure stress
50% fail
Stress for
10% failure
Wiebull Modulus
probability of failure
F = f (σ, V)
σ = applied stress
V = volume under
stress
f ailur e st r ess
m
⎛ σ −σt ⎞
⎟ dV}
F =1−exp{−∫ ⎜
σ
⎝
0 ⎠
V
σt is stress below which the probability
of failure is zero
σ0 is a normalising parameter
m is the Wiebull modulus
how do you select design stress?
• based on some probability of failure
• stress at which there is 10% chance of
failure
Wiebull modulus
measure of strength variation
high m - narrow distribution in failure
stress
low m - wide distribution of failure
stress
note : for many ceramics and glasses
5 < m < 20
question
if I measure the tensile strength of a
ceramic in 3pt bending, 4 pt bending
and in tension
σf (3pt) > σf (4pt) > σf (tension)
WHY IS IT SO?