Chapter 23
Fracture and Toughening
Fracture behavior
Fracture testing
Impact/Fatigue
Toughening
Failure or fracture
failure [破碎, 破斷] ~ rupture by exceedingly large stress
fracture [破壞] ~ failure by crack propagation
micromechanism of fracture
chain scission or slip?
Upon stress,
1. chain slip (against Xtal, Xlinking, entangle) 2a. crazing/yielding or
2b. chain scission (early)
when high Xc, low Mc, low Me 3. then chain scission
4. voiding crack fracture
effect of MM (on strength)
M = 6 – 8 Me?
MM should be much higher than Me.
Ch 23 sl 2
Fig 23.4 p561
radical conc’n by ESR higher than ey lower than ef
Fig 23.5
Brittle fracture
theoretical (tensile) strength of solids (by Griffith)
for interatomic separation pp557-558
whiskers, suor sf ≈ E/10
polymer single crystals, su or sf ≈ E/40
for (isotropic glassy unfilled) polymers,
sf < E/100 < stheo
E = 1 – 3 GPa, sf < 100 MPa
due to flaw [crack, notch, or inclusion], which cause
stress concentration and
plastic constraint
Ch 23 sl 3
st= tensile strength su = ultimate stress sf = fracture stress sc = craze stress su = sf = sc if brittle
stress concentration
Ahead of crack tip, stress is
larger than the applied stress s0
circular crack [a=b], s = 3 s0
crack-tip radius
Ch 23 sl 4
s0
Fig 23.6 p562
Fracture mechanics
energy balance approach
specimen with crack length 2a
Crack grows when
released (elastic) strain energy by stress [s2pa2/2E]
is greater than created surface energy [4ag]
Griffith (brittle) fracture criterion
Ch 23 sl 5
plane s plane e
Fig 23.7
PMMA PS
sf ∝ a−½
LEFM [linear elastic FM]
energy balance approach (cont’d)
for polymers
g from exp’t = ~ 1 J/m2
g from Griffith criterion = ~ 1,000 J/m2
high g high sf
high sf other process than elastic
= plastic deformation at crack tip
local yielding ~ still brittle fracture
replacing 2g with Gc
Gc = critical strain energy release rate
= ‘fracture energy’ [J/m2]
Ch 23 sl 6
Irwin’s modification of Griffith criterion
plastic zone
stress intensity factor approach
fracture when s(pa)½ > (EGc)½
stress intensity factor K
crack propagates when K reaches Kc
Kc = critical stress intensity factor
= ‘fracture toughness’ [(파괴)강인성] [MPa m1/2]
3 modes of fracture
Ch 23 sl 7
GIc
KIc GIIc
KIIc
Fracture testing
specimen
Ch 23 sl 8
Fig 23.8
single-edge notched tension
SEN-3PB
double torsion
double cantilever beam
load (f) K
Ch 23 sl 9
Ductile fracture
failure after general yielding
fracture with large plastic zone
Ch 23 sl 10
Fig 23.14 e
s
brittle [취성] ductile [연성]
yield
elastomeric sy
su
ey eu
Ductile-brittle transition
yield to ductile failure craze to brittle fracture
Both sy and sc [sb] are
dependent on temperature, strain rate, --.
temperature
Ch 23 sl 11
D s2
s1
yield craze
high T, low de/dt low T, high de/dt Tb = d-b transition Temp
Fig 23.18(a)
sb = brittle stress = sc
strain rate
Tb increases as strain rate increases.
surface notch, crack, scratch
notch brittleness [plastic constraint]
notch triaxial stress state ahead
sy Tb
Ch 23 sl 12
sc sy
de/dt
Fig 23.18(b)
plastic constraint
Ahead of crack tip, there exists triaxial stress state.
s1 > 0 (applied), s2 and s3 > 0 (due to crack)
triaxiality yield at higher stress ss = s1 – s3
plastic deformation constrained
craze rather than yield brittle fracture
Ch 23 sl 13
d-b transition with thickness of specimen
as thickness
plane stress [ductile] to plane strain [brittle] transition
Ch 22 sl 14
plane e plane s
Impact strength
testing method
flexed beam impact test
Charpy, Izod
falling weight impact test
tensile impact test
impact strength [IS,
충격강도]
energy absorbed per unit area (J/m2) or unit length (J/m)
energy rather than strength
related to Gc
but not this quantitative
GIc (and KIc) are material properties:
IS is not. depends on geometry
Ch 23 sl 15
Charpy Izod
Fig 23.20
Fatigue
Upon cyclic loading [oscillation],
materials fail [fracture] at stress level well below they can withstand
under static loading (usually YS or TS).
very common in metal
S-N curve
stress vs # of cycles to fracture
fatigue strength or ‘endurance limit’
fatigue crack propagation
Paris equation
DK ∝ Ds
lower m for tough polymers? not really
PS, PMMA, PC
Ch 23 sl 16
e s
sy su
Fig 23.22
Fig 23.23
Toughening
dream: strength of steel with resilience of rubber
goal: enhancing the ability to resist crack propagation
toughening = introducing 2nd phase that
enlarge the volume of energy absorption, or
limit the crack growth by increasing # of site of crazing or yielding
methods
rubber toughening
large energy absorption, modulus drop
HIPS, ABS, toughened epoxy, etc
thermoplastic toughening
small energy absorption, no modulus drop
PC/ABS, PC/PBT, Nylon/PPO, etc
Ch 22 sl 17
Toughening mechanisms
deformation and rupture of rubber particles
relatively small
increase in toughness
crack pinning
increasing surface area
tortuous path
Ch 23 sl 18
multiple crazing
particles initiate and stop crazes
stress-whitening observed
HIPS
Ch 23 sl 19
Fig 23.28
Fig 23.26
cavitation and shear yielding
particles debond or cavitate
removing triaxiality
removing hydrostatic component
inducing yielding of matrix
necking observed
toughened PVC
crazing and shear yielding
whitening and necking
ABS
Ch 23 sl 20
Factors governing toughness
matrix
degree of crosslinking
entanglement density
Tg
yield strength
particle
content [volume fraction]
size
size distribution
Tg
adhesion to matrix
morphology
Ch 23 sl 21
Fig 23.25