(Deformation and Fracture)

1
???? ??? ?? (Deformation and Fracture) ??? ?? ??
??
2
???? ??? ?? (Deformation and Fracture)
Stress vs. Strain curve
Stress (s) ????? ???? ? Strain (e) ?l /l
(??? ??/???? ??) Elongation ?l /lo Yield
Point Yield Strength Modulus Strength at
termination Elastic deformation -??? 5-10 vs
?? 0.1 Necking Cold drawing -??? ??? ?? ??
?? Stress hardening -???? ?? ??
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???? ??? ?? (Deformation and Fracture)

• Elastic deformation
• -???? ??? Bending, Straining
• -???? ??? ?? (a)
• -??? ?? ??? ?? (b)
• -??? ??? ??

• Plastic deformation
• -??? ??? ??? ???? ??.
• -????? ??? ????? ??? ??.
• -?? ???(sliding) lt ????(uncoiling) lt ??
  ??(folding)

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???? ??? ?? (Deformation and Fracture)
Maxwell Model
Spring s1 Ee1,e1 Dashpot s2 ? de2/dt, e2

• Elastic deformation
• -???? ??? Bending, Straining

(1)
(2)
(3),(4) -gt (2)
(3)
(4)

• Plastic deformation
• -??? ??? ??? ???? ??.
• -?? ???(sliding) lt ????(uncoiling) lt ??
  ??(folding)

5
???? ??? ?? (Deformation and Fracture)
Stress vs. Strain curve
ductile and Tough PE
ductile and weak PTFE
hard and Brittle PS

• Ductility
• Brittleness
• Toughness
• Strength

Strong and Tough PC
hard and Tough POM, GF reinforced
6
???? ??? ?? (Deformation and Fracture)
Dependence on temperature and rate
Temperature dependence
Compression -ductile failure
Brittle-Ductile transition, Tb
Tensile -brittle failure
7
???? ??? ?? (Deformation and Fracture)
Dependence on temperature and rate
Brittle-Ductile transition, Tb
?????? ??? ???? ?? ????? ???? ?? gtgt ?????? ?? ???
???? ?? ??? -PS, natural rubber Tg ??? Tg ??
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???? ??? ?? (Deformation and Fracture)
Dependence on temperature and rate
????? ?? ?? ?? -???, ??, ???? ????? ?? -? (flaw)
????
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???? ??? ?? (Deformation and Fracture)
Stress vs. Strain curve

• ????? ??? ???
• - s so K/Mn
• so ?? ?? ??
• ????? ???? ???
• -? ?o K/Mz
• -??, ???? ???, ?? ??(entanglement)? ???
• -??, ???, ????, ???, ????, ??? ??? ?? ??? ???

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???? ??? ?? (Deformation and Fracture)
Stress vs. Strain curve
-??, ??( crosslinking, vitrification), ???
(plasticizer), ???? (orientation), -??? ??????
?? -gt ??? ??? ?? ?? ?? ??? ????? ?? (void) ? ??
-gt ?? ???? (stress-concentration factor)
11
???? ??? ?? (Deformation and Fracture)
Stress vs. Strain curve

• ???, true stress, s F/A, sn F/Ao, Al AoLo
  (????)
• ? (l lo)/lo
• ??? ??, nominal stress
• sn F/Ao,
• sn s/(1 ?)

For stable Necking

• Necking due to stress hardening

12
???? ??? ?? (Deformation and Fracture)

• Plastic deformation (????)
• Yielding (??)
• crazing (????)

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???? ??? ?? (Deformation and Fracture)
Plastic deformaton - yielding, crazing
???? ?? ??? (shear band), ? ???? ??
14
???? ??? ?? (Deformation and Fracture)
Plastic deformation (????) - yielding
???? (chain segment) ? ?? ??

• Yielding (??)
• -Tensile yielding, shear yielding
• -No volume change, shear yielding?? ? ??
• -Tensile yielding , smax so at ?0
• -Shear yielding, ?max so/2 at ? 45

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???? ??? ?? (Deformation and Fracture)
Plastic deformaton - yielding

• Mechanism of yielding
• ??? ?? ??? ?? ?? ?? ?? ?? ?? ?? ?? ??, ??.
• ??? ?? ??? ??? ?? ?? ?? -gt ???? ??
• ??? ??? ?? ??? ??? ??? ?? ??? ?? (potential
  energy well) ? ???? ?? -gt ? ????? ???? ??
• Criteria of Yielding
• -Tensile yielding, ????? ?? ??? ss ? ???? ?? ??
  (Tresca)
• 0.5 (s1 s2) ss where s1 gt s2 gt s3
• ??? ?? ?? , s1 st, s2 s3 0, ? s/2
• -Shear yielding, ?? ??? ?? ?? ?? (Von Mises)
• (s1 s2)2 (s1 s2)2 (s1 s2)2 ?? where
  s1 gt s2 gt s3
• ??? ?? ?? , s1 -s2, ? s /2 1/3

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???? ??? ?? (Deformation and Fracture)
Plastic deformation - yielding

• What does yielding mean?
• ????? ???? ???? ??, ??? ??? ??? ??? ???? ?? ????
  ????? ??? ????? ??? ?? ??? ??? ??? ?. ?? ????? ??
  
• ????? ??? ?? (crack)? ????. ??? ?? ??
  ????(stress concentration factor) ??
• ???? ?? (shear band), ??? ?? (disentanglement)
  or ?? (scission) ? ?? Micro-CRACK

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???? ??? ?? (Deformation and Fracture)
Plastic deformation Craze

• What does craze mean?
• ??? ??? ?? ??? ???? ?? plastic deformation
• ??????? ??? ?? ???? (void) ?? -gt ??? ?? -gt crack
• Fibril ???? ?? ??? ??? ???? ?? -gt craze -gt ??
  fibril? ?? -gt crack
• ?? ??
• ?? 0.1 1 um
• Shear yielding ? ??? ?? ???? ?? -gt ???? (Brittle
  fracture) ??

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???? ??? ?? (Deformation and Fracture)
Plastic deformation Craze

• What does craze mean?
• Craze ??? ???? ????? ?? ??
• ?? ?? ???? -gt shear yielding? craze?? ?? -gt
  Ductile failure
• ?? ??? ???? ?? ????
• ???, craze, shear stress ?
• ?? craze ??, ?? yielding ??

19
???? ??? ?? (Deformation and Fracture)
Plastic deformation Craze

• What does craze mean?
• Craze ?? 2.5nm , ??? ?? ?? ??
• ?? ??? ??? ?? ??? ??
• ? ??? ?? ?? ???, ?? ??
• 40 - 60? ???? ??? ??
• ?????? ?? 27 ???
• TEM??

20
???? ??? ?? (Deformation and Fracture)
Plastic deformation Craze

• How does craze grow (craze thickening) ?
• ???? ?? ?? (micro void) ?? -gt ??? ?? (repeated
  nucleation )
• Mniscus instibility? ?? ??, ??? ??? ??? ?? ??,
  ??? ??? ??? ???? ??, ???? ???? ???.
• Donald? Kramer? ?? ??? ??

• How does craze grow (craze thickening) ?
• ??? ??, ?? ??? ?? ??
• ??? ?? craze? ?? -gt ??
• Craze??? ?? ??? ?? shea band ?? , craze? ??

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???? ??? ?? (Deformation and Fracture)
Plastic deformation Craze

• How does craze grow (craze thickening) ?
• ?? fibrril? ?? ???? ??? ???
• Shear band? ?? -gt crack ??? ?
• Crack?? ??
• Inhomogeneous plastic yielding? ???? ???? (strain
  softening)? ??
• ????? ?? -gt CRAZE? ??
• CRACK? ??, ???? ?? ??
• -gt ??? ?? (Toughening)

22
???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• Crack? ?? ? ???? ?? ??? ?? ?? -gt ??? ?? ??
  (failure criterion)
• ??? ?? (energy balance approach) crackt ??? ??
  ????? ??? crack ??? ???? ??? ?? ???, ?? ??, ????
  (fracture toughness) ?? ?? ??? ?? ?? (critical
  strain release rate) Gc
• ?? ?? ?? (Stress intensity approach) ??? ??? ??
  ??? ?? ??, ??? ??? ?? ??, ???? (fracture
  toughness) ????? ???? (critical stress
  intensity factor), Kc

• How does fracture?
• crack ?? -gt ?? ?????? ??
• Crack? ?? ??? ????? ??? ??,?? ??? ?? ?? -gt ????
• Fracure mechanics -gt ?? ??? ???, ????? ??? ??
  ????, ??? ??? ?? ??? crack??? ??? ??? ??

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???? ??? ?? (Deformation and Fracture)
Polymer Fracture
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???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ??? ?? (energy balance approach) , Griffith
• ??? ??? ?? ?? ??? ?? -gt ??? ?? ?? ??? ?? ??
• ??? ??? -gt ????? ?? ?? (strain energy)
• ?????? ?? -gt ?????? ??
• -gt ??? ??
• Crack??? ?? ????? gt ????? ?? ???? ??? ??? ??
• ??? ?? ?? ?? ????? (Elastic strain energy), Uel
• Uel ?s2a2/E where ????(plane stress) E
  (Youngs modulus), ?? ??(plane strain) E/(1-?2),
  ?Poission ratio
• Crack??? ???????, Us 4a?s, ?s ??? ?? ???

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???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ??? ?? (energy balance approach)
• Utotal Uel Us
• ?s2a2 / E 4a?s,
• Crack? da ??? ???? ??? ????? ?? dUtotal/da lt 0
• ?? ??, s br ? (2 ?sE/ ?a)1/2
• ????? ??? ??? ?? ??
• s br vs. a-1/2 ? ?? ?s ??? ????? ?? ?? ?. PMMA,
  PS 103-104 J/m2 gtgt ?? 1000 ?
• Van der Waals??? ?? 2? ??? ??, ??? ?? ?? ??? ??
  -gt ?? ??? ??? ??? ???? ??, ??? ??? ?? ??, ?? ???
  ????? ????, ?????? ??, ?p ??

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???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ??? ?? (energy balance approach)
• Van der Waals??? ?? 2? ??? ??, ??? ?? ?? ??? ??
  -gt ?? ??? ??? ??? ???? ??, ??? ??? ?? ??, ?? ???
  ????? ????, ?????? ??, ?p ??
• s br ? (2 ?p E/ ?a)1/2
• Irwin, 2 ?p Gc, ?? ??? ????(critical energy
  release rate), ??? ?? ???
• s br ? (Gc E/ ?a)1/2
• Gc, critical energy release rate, frature energy
  ?
• Gc ???? ????? ?? ??? ?? ??? ??, ?????
  ????? ???? ??? (J/m2)
• ???? (Inherent flaws) ?? ????? ????? ??? ?????
  ??
• ex. PS ???? gt PMMA, PS ? ? craze

27
???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ?? ?? ?? (Stress intensity approach) ??? ??? ??
  ??? ?? ??, ??? ??? ?? ??, ???? (fracture
  toughness) ????? ???? (critical stress
  intensity factor), Kc
• ????? ??? ???? a ?? ??? ???? ????? ???? a? ??
• ?? s? ??? ?? ??, s12 , ??? 1, ?? ?? 2, r crack
  ????? ?? , vector r, ?sms ???? ?? ?? ??
• ?????? K? ?? ??? ??? Kc ??? ?? ?? , ?? ?? ??? ??
• sbr Kc / (?a)1/2

28
???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ?? ?? ?? (Stress intensity approach) ??? ??? ??
  ??? ?? ??, ??? ??? ?? ??, ???? (fracture
  toughness) ????? ???? (critical stress
  intensity factor), Kc
• ????? ??? ???? a ?? ??? ???? ????? ???? a? ??
• ?? s? ??? ?? ??, s12 , ??? 1, ?? ?? 2, r crack
  ????? ?? , vector r, ?sms ???? ?? ?? ??
• ?????? K? ?? ??? ??? Kc ??? ?? ?? , ?? ?? ??? ??
• sbr Kc / (?a)1/2
• Gc Kc2 / E
• K -gt Kc vs. G-gt Gc

29
???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ??????? ?? ??
• r (crack ????? ??) -gt 0 , ?? ??? ?? ?? ? ,
• ??? ???? ??? ????, ?? ???
• ?? ?? ?? (plane stress) ??? ?? ?? ??? ?? ?? ??
  ?? s33 0
• ?? ?? ?? (plane strain) ??? ??? ?? ??? ?? ?? ??
  ?? ?33 0
• ?? ?? ?? (plane stress) gt ?? ?? ?? (plane
  strain) ?? ????? ??

30
???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ?? ?? ?? (Stress intensity approach) ??? ??? ??
  ??? ?? ??, ??? ??? ?? ??, ???? (fracture
  toughness) ????? ???? (critical stress
  intensity factor), Kc
• ??? ?? -gt Kc ?? ??? -gt ?? -gt ??? ??

31
???? ??? ?? (Deformation and Fracture)
Polymer Fracture

• ????? ??
• Gc ? Kc ??? ????? ??, ??? ????? ??, ?? (linear
  elastic)
• ?? ??? ?? ??? ??? ?? ??, ??? crack? ?? ????
• DT (double torsion) ??? ?? ??, ??? ??
• DCB(double canti-lever beam) ????? ??????? ??
• SEN (single edge notched) ?? ?? ??

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???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• ???(Toughness) ??? ???? ??? ?? ??? ??? ???
• ??? (Intrinsic) ???, ???(extrinsic) ???
• ?? ??? ??? ????? ?? ??

33
???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• ?? ???? ???? -gt ???? crazing? ????? ???? ?? -gt
  Rubber Toughning
• ?????? ??? ?? (??, ????) ?? -gt ?? ??(crack
  shielding)? ?? ????? ??
• 1? ?? ???? ???? ?? ?? ?? (crack briding), ?????
  ??? ??? ??(welt)?? 2? ??? ???
• ?? ??????? ???? ??? -gt ???? ??? ?? ??, ?? ??

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???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• ??? ??? ???? ??, ????, ????? ??
• ABS, HIPS ??? ??? ??? ??
• ???? ??? ?? ?? ??
• ?? ???? ???? -gt ???? ?? ???? (multi-crazing)?
  ????? ???? ?? -gt Rubber Toughening
• Stress-strain curve
• -PS brittle, HIPS yielding, ductile behavior

35
???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• RTPMMA (Rubber toughened PMMA)
• -35 ?? ?? ??

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???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• CTBN(carboxyl terminated butadiene rubber) /Epoxy
• -????? ??? (phase separation) -gt ?????? ?????
  ?? -gt ????? (interfacial adhesion) ??
• ??? ?? -gt ????? ??
• -gt ??? ??

37
???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• Rubber Toughening Mechanism
• ??? (cavitation)
• ???? ????? ?? ?? (Interfacial failure )
• ???? ?? ???? (multi-crazing)? ????? ???? (Plastic
  deformation)
• ??? ??????(unsaturated Polyester)? ?? ??? ?? ??
  ??? -gt ???? ??? ?? crazing?? ?? ??? ???

38
???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• TEM?? ??? HIPS??? crazing
• ???? ??, ???? ??, ???? ? ????? ?? ?.
• Occluded particle
• ?? ??(Stress whitening)

39
???? ??? ?? (Deformation and Fracture)
Polymer Toughening
TEM?? ??? RTPMMA ( core-shell??) Crazing? ??
shear band? ?? ??? -gt ?? ????? ???? ??
40
???? ??? ?? (Deformation and Fracture)
Polymer Toughening

• ?????? ??? ?? (??, ????) ?? -gt ?? ??(crack
  shielding)? ?? ????? ??
• ????? ?? ??? ?? ?? -gt ???? ?? ??
• 1? ?? ???? ???? ?? ?? ?? (crack briding), ?????
  ??? ??? ??(welt)?? 2? ??? ???
• ??? ???, ????? ???