Chapter 23 Fracture and Toughening

Fracture behavior Fracture testing Impact/Fatigue Toughening Failure or fracture Ch 23 sl 2

 failure [破碎, 破斷] ~ rupture by exceedingly large stress  fracture [破壞] ~ failure by crack propagation

 micromechanism of fracture Fig 23.4 p561  chain scission or slip? radical conc’n by ESR  Upon stress,

1. chain slip (against Xtal, Xlinking, entangle) higher than ey 2a. crazing/yielding or lower than ef 2b. chain scission (early)

when high Xc, low Mc, low Me 3. then chain scission 4. voiding  crack  fracture

 effect of MM (on strength) Fig 23.5  M = 6 – 8 Me?

 MM should be much higher than Me. Brittle fracture Ch 23 sl 3

 theoretical (tensile) strength of solids (by Griffith)

  for interatomic separation pp557-558

st = tensile strength  whiskers, su or sf ≈ E/10 su = ultimate stress sf = fracture stress  polymer single crystals, su or sf ≈ E/40 sc = craze stress  for (isotropic glassy unfilled) polymers, su = sf = sc if brittle

 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 4

 stress concentration  Ahead of crack tip, stress is

larger than the applied stress s0

s0

 circular crack [a=b], s = 3 s0

 crack-tip radius

Fig 23.6 p562 Fracture mechanics Ch 23 sl 5

 energy balance approach LEFM [linear elastic FM]  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

plane s plane e

PMMA PS

−½ sf ∝ a

Fig 23.7 Ch 23 sl 6

 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 Irwin’s modification of Griffith criterion

 Gc = critical strain energy release rate = ‘fracture energy’ [J/m2] plastic zone Ch 23 sl 7

 stress intensity factor approach ½ ½  fracture when s(pa) > (EGc)  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

GIc GIIc KIc KIIc Fracture testing Ch 23 sl 8

 specimen

Fig 23.8

double torsion

double cantilever beam single-edge notched tension

SEN-3PB Ch 23 sl 9

 load (f)  K Ductile fracture Ch 23 sl 10

 failure after general yielding

 fracture with large plastic zone

s brittle [취성] ductile [연성] su yield sy

elastomeric Fig 23.14

e ey eu Ductile-brittle transition Ch 23 sl 11

 yield to ductile failure s2 craze to brittle fracture D  Both sy and sc [sb] are dependent on temperature, strain rate, --.

 temperature s1 Tb = d-b transition Temp

yield craze Fig 23.18(a)

sb = brittle stress = sc high T, low de/dt low T, high de/dt Ch 23 sl 12

 strain rate

Fig 23.18(b) sy sc

de/dt

 Tb increases as strain rate increases.  surface notch, crack, scratch  notch brittleness [plastic constraint]  notch  triaxial stress state ahead

 sy   Tb  Ch 23 sl 13

 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 22 sl 14

 d-b transition with thickness of specimen  as thickness   plane stress [ductile] to plane strain [brittle] transition

plane s plane e Impact strength Ch 23 sl 15

 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 Fig 23.20  related to Gc

 but not this quantitative

 GIc (and KIc) are material properties: IS is not.  depends on geometry Charpy Izod Fatigue Ch 23 sl 16 s  Upon cyclic loading [oscillation], su  materials fail [fracture] at stress level sy well below they can withstand under static loading (usually YS or TS).  very common in metal

 S-N curve e  stress vs # of cycles to fracture Fig 23.22  fatigue strength or ‘endurance limit’

 fatigue crack propagation  Paris equation

 DK ∝ Ds  lower m for tough polymers? not really Fig 23.23  PS, PMMA, PC Toughening Ch 22 sl 17

 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 Toughening mechanisms Ch 23 sl 18

 deformation and rupture of rubber particles  relatively small increase in toughness

 crack pinning  increasing surface area  tortuous path Ch 23 sl 19

 multiple crazing  particles initiate and stop crazes  stress-whitening observed  HIPS

Fig 23.26

Fig 23.28 Ch 23 sl 20

 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 Factors governing toughness Ch 23 sl 21

 matrix  degree of crosslinking  entanglement density

 Tg  yield strength

 particle  content [volume fraction]  size  size distribution

 Tg  adhesion to matrix Fig 23.25  morphology