Fracture and Toughening

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 X_c, low M_c, low M_e 3. then chain scission

4. voiding  crack  fracture



effect of MM (on strength)

 M = 6 – 8 M_e?

 MM should be much higher than M_e.

Ch 23 sl 2

Fig 23.4 p561

radical conc’n by ESR higher than e_y lower than e_f

Fig 23.5

Brittle fracture



theoretical (tensile) strength of solids (by Griffith)

  for interatomic separation pp557-558

 whiskers, s_uor s_f ≈ E/10

 polymer single crystals, s_u or s_f ≈ E/40



for (isotropic glassy unfilled) polymers,

 s_f < E/100 < s_theo

 E = 1 – 3 GPa, s_f < 100 MPa

 due to flaw [crack, notch, or inclusion], which cause

 stress concentration and

 plastic constraint

Ch 23 sl 3

s_t= tensile strength s_u = ultimate stress s_f = fracture stress s_c = craze stress s_u = s_f = s_c 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

s_f ∝ 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 s_f

 high s_f  other process than elastic

= plastic deformation at crack tip

 local yielding ~ still brittle fracture

 replacing 2g with G_c

 G_c = 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 > (EG_c)^½

 stress intensity factor K

 crack propagates when K reaches K_c

 K_c = critical stress intensity factor

= ‘fracture toughness’ [(파괴)강인성] [MPa m^1/2]



3 modes of fracture

Ch 23 sl 7

G_Ic

K_Ic G_IIc

K_IIc

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 s_y

s_u

e_y e_u

Ductile-brittle transition

 yield to ductile failure craze to brittle fracture

 Both s_y and s_c [s_b] 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 T_b = d-b transition Temp

Fig 23.18(a)

s_b = brittle stress = s_c



strain rate

 T_b increases as strain rate increases.



surface notch, crack, scratch

 notch brittleness [plastic constraint]

 notch  triaxial stress state ahead

 s_y   T_b 

Ch 23 sl 12

s_c s_y

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  s_s = 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,

]

 energy absorbed per unit area (J/m²) or unit length (J/m)

 energy rather than strength

 related to Gc

 but not this quantitative

 G_Ic (and K_Ic) 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

s_y s_u

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

 T_g

 yield strength



particle

 content [volume fraction]

 size

 size distribution

 T_g

 adhesion to matrix

 morphology

Ch 23 sl 21

Fig 23.25