Chapter 3 Rubber Elasticity

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.

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