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Fracture and Toughening

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(1)

Chapter 23

Fracture and Toughening

Fracture behavior

Fracture testing

Impact/Fatigue

Toughening

(2)

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

(3)

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

(4)

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

(5)

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]

(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

Gc = critical strain energy release rate

= ‘fracture energy’ [J/m2]

Ch 23 sl 6

Irwin’s modification of Griffith criterion

plastic zone

(7)

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

(8)

Fracture testing

specimen

Ch 23 sl 8

Fig 23.8

single-edge notched tension

SEN-3PB

double torsion

double cantilever beam

(9)

load (f)  K

Ch 23 sl 9

(10)

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

(11)

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

(12)

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)

(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 23 sl 13

(14)

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

(15)

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

(16)

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

(17)

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

(18)

Toughening mechanisms

deformation and rupture of rubber particles

relatively small

increase in toughness

crack pinning

increasing surface area

tortuous path

Ch 23 sl 18

(19)

multiple crazing

particles initiate and stop crazes

stress-whitening observed

HIPS

Ch 23 sl 19

Fig 23.28

Fig 23.26

(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

Ch 23 sl 20

(21)

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

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