TUTORIAL 4 FRACTURE, IMPACT, FRACTURE TOUGHNESS
TUTORIAL 4 FRACTURE, IMPACT, FRACTURE TOUGHNESS
Mechanical Failure ISSUES TO ADDRESS... • How do flaws in a material initiate failure? • How is fracture resistance quantified; how do different material classes compare? • How do we estimate the stress to fracture? • How do loading rate, loading history, and temperature affect the failure stress?
Ship-cyclic loading from waves waves. Adapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)
Computer chip-cyclic thermal loading. loading Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.)
Hip implant-cyclic loading from walking walking. Adapted from Fig. 22.26(b), Callister 7e. Chapter 8 - 2
FRACTURE MODES
Some materials will deform p plastically y before they y fracture they y are called ductile materials. Others will fracture after elastic deformation, they are called brittle materials.
Ductile fracture
bolt
Brittle fracture
strain
Example: Failure of a Pipe • Ductile failure:
--one piece p --large deformation
• Brittle failure:
--many pieces --small deformation Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., 1987. Used with permission.
Chapter 8 - 4
DUCTILE FRACTURE Crack initiation
Mechanism (a) Necking due to localization of plastic deformation (b) microvoid formation (fracture initiation) (c) microvoid coalescence to form a crack (d) crack propagation accompanied by plastic deformation (e) final shear fracture at 45o to tensile direction (shear lips) (f) crack can be stable (sustained for some time and leads to failure only when stress increases.
cup MICRO FEATURES
cone Crack propagation
Final shear fracture
BRITTLE FRACTURE
Crack initiation and propagation with no plastic deformation (prior or during) during). Fracture surface flat, Crack propagates rapidly normal to tensile axis. Brittle fracture surface is shiny. MICRO FEATURES
MACRO FEATURES
intergranular
Brittle fracture surface has characteristic Macro-pattern indicating the origin of the crack and this helps failure f analysis process.
4340 steel
transgranular
radial ridges emanating from fracture origin
1080 steel chevrons marks which point back to fracture origin
Intergranular crack showing grains
Transgranular crack : cleavage. Repeated b ki off atomic breaking i bonds along specific crystallographic planes.
IMPACT TESTING Tensile test determines the behavior of the material when it is subjected to slow rate of deformation (10-4-10-2 / s) Impact test determines the behavior when the material is subjected to sudden stress (impact) i.e. very rapid rate of deformation (103/s). Impact test evaluates material material’ss brittleness under sudden loading. loading Impact test is one of the older tests designed for materials testing. Measure impact energy from the difference in initial and final heights of a pendulum that strikes the specimen and breaks it.
Can also be unnotched
h0 hf
IMPACT TEST MEASURES: 1. IMPACT TOUGHNESS: The energy (J) absorbed by the fracture of the specimen (plastic yielding and creation of surface energy of crack). It is different from tensile toughness (J/cm3) determined from area under the curve of true stress-strain curve in uniaxial tensile tests. 2 DUCTILE TO BRITTLE TRANSITION TEMPERATURE (DBTT) 2.
C
B
A
3. NOTCH SENSITIVITY p in an impact p test and comparing. p g If the material is not notch Measured byy runningg notched and un-notched specimens sensitive the difference will be minimal.
9
10
11
Stress Intensity Factor, KI
σ
σma x
σ
σ
K
I
= fσ
πa
units : psi in .
where, a = flaw size (1/2 the full length for internal flaws)
σ = applied stress
f = geometry factor
If you do not k know the th geometry factor
FRACTURE TOUGHNESS, KIC Æ material property
K C = fσ
C
πa
Plane strain fracture toughness,
Computing Brittle Fracture Stress, σc
Brittle Brittle fracture stress ( σC ) depends on the fracture toughness (KC), the size (a) of pre-existing cracks or flaws and f the geometry factor (f=1 for internal flaws and 1.12 for surface flaws). F t Fracture stress, t σc
If KC and a are fixed fracture stress for brittle fracture is determined
σ c = K C / f πa
Computing Critical Flaw Size, ac, for Brittle Catastrophic Fracture A A material t i l can th thus b be d ductile til or b brittle ittl d depending di upon th the size i off cracks k or flaws which are present in the sample. The condition for brittle behaviour.
1 ⎛⎜ K C aC ≥ π ⎜⎝ fσ appl
⎞ ⎟ ⎟ ⎠
2
If applied li d stress t σappl andd fracture f t toughness, KC are fixed, design involves a maximum allowable crack size
where ac is maximum allowable flaw size (or critical size to propagate crack).
Fracture Toughness Metals/ Alloys
Graphite/ Ceramics/ Semicond
Polymers
100
K Icc (MPa · m0.5 )
70 60 50 40 30
C-C(|| fibers) 1 Steels Ti alloys Al alloys Mg alloys
Based on data in Table B5, C lli t 7 Callister 7e.
20
Al/Al oxide(sf) 2 Y2 O 3 /ZrO 2 (p) 4 C/C( fibers) 1 Al oxid/SiC(w) 3 Si nitr/SiC(w) 5 Al oxid/ZrO 2 (p) 4 Glass/SiC(w) 6
10 7 6 5 4
Diamond Si carbide Al oxide Si nitride
PET PP
3
PVC
2
1 0.7 0.6 0.5
Composites/ fibers
PC
Si crystal Glass -soda Concrete
PS Polyester
Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook 1 Handbook, Vol. Vol 21 21, ASM Int Int., Materials Park, OH (2001) p. 606. 2. (55 vol%) Courtesy J. Cornie, MMC, Inc., Waltham, MA. 3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics, Vol. 7, Plenum Press (1986). pp. 61-73. 4. Courtesy CoorsTek, Golden, CO. 5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/85-22011/2, ORNL, 1992. 6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc Vol. Proc., Vol 7 (1986) pp pp. 978 978-82. 82
Glass 6 Chapter 8 - 15
Engineering Design • Great, we can design to prevent brittle behavior • Things still fail – Creep – Fatigue • Next time!
Chapter 8 - 16
Loading Rate • Increased loading rate...
-- increases σy and TS -- decreases %EL
An increased rate gives less time for dislocations to move past obstacles.
• Why?
σ σy
TS
ε larger
TS
ε smaller
σy ε Chapter 8 - 17
Engineering Fracture Design • Avoid sharp corners! σ σo max Stress Conc Conc. Factor Factor, K t = σ w σmax r,
o
2.5
h
fillet
2.0
increasing
w/h
radius Adapted from Fig. 8.2W(c), Callister 6e. (Fi 8 (Fig. 8.2W(c) 2W( ) iis ffrom G G.H. H Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)
1.5
1.0 0
0.5
1.0
r/h
sharper h fill fillett radius di Chapter 8 - 18
Mechanical Failure ISSUES TO ADDRESS... • How do flaws in a material initiate failure? • How is fracture resistance quantified; how do different material classes compare? • How do we estimate the stress to fracture? • How do loading rate, loading history, and temperature affect the failure stress?
Ship-cyclic loading from waves waves. Adapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)
Computer chip-cyclic thermal loading. loading Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.)
Hip implant-cyclic loading from walking walking. Adapted from Fig. 22.26(b), Callister 7e. Chapter 8 - 2
FRACTURE MODES
Some materials will deform p plastically y before they y fracture they y are called ductile materials. Others will fracture after elastic deformation, they are called brittle materials.
Ductile fracture
bolt
Brittle fracture
strain
Example: Failure of a Pipe • Ductile failure:
--one piece p --large deformation
• Brittle failure:
--many pieces --small deformation Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., 1987. Used with permission.
Chapter 8 - 4
DUCTILE FRACTURE Crack initiation
Mechanism (a) Necking due to localization of plastic deformation (b) microvoid formation (fracture initiation) (c) microvoid coalescence to form a crack (d) crack propagation accompanied by plastic deformation (e) final shear fracture at 45o to tensile direction (shear lips) (f) crack can be stable (sustained for some time and leads to failure only when stress increases.
cup MICRO FEATURES
cone Crack propagation
Final shear fracture
BRITTLE FRACTURE
Crack initiation and propagation with no plastic deformation (prior or during) during). Fracture surface flat, Crack propagates rapidly normal to tensile axis. Brittle fracture surface is shiny. MICRO FEATURES
MACRO FEATURES
intergranular
Brittle fracture surface has characteristic Macro-pattern indicating the origin of the crack and this helps failure f analysis process.
4340 steel
transgranular
radial ridges emanating from fracture origin
1080 steel chevrons marks which point back to fracture origin
Intergranular crack showing grains
Transgranular crack : cleavage. Repeated b ki off atomic breaking i bonds along specific crystallographic planes.
IMPACT TESTING Tensile test determines the behavior of the material when it is subjected to slow rate of deformation (10-4-10-2 / s) Impact test determines the behavior when the material is subjected to sudden stress (impact) i.e. very rapid rate of deformation (103/s). Impact test evaluates material material’ss brittleness under sudden loading. loading Impact test is one of the older tests designed for materials testing. Measure impact energy from the difference in initial and final heights of a pendulum that strikes the specimen and breaks it.
Can also be unnotched
h0 hf
IMPACT TEST MEASURES: 1. IMPACT TOUGHNESS: The energy (J) absorbed by the fracture of the specimen (plastic yielding and creation of surface energy of crack). It is different from tensile toughness (J/cm3) determined from area under the curve of true stress-strain curve in uniaxial tensile tests. 2 DUCTILE TO BRITTLE TRANSITION TEMPERATURE (DBTT) 2.
C
B
A
3. NOTCH SENSITIVITY p in an impact p test and comparing. p g If the material is not notch Measured byy runningg notched and un-notched specimens sensitive the difference will be minimal.
9
10
11
Stress Intensity Factor, KI
σ
σma x
σ
σ
K
I
= fσ
πa
units : psi in .
where, a = flaw size (1/2 the full length for internal flaws)
σ = applied stress
f = geometry factor
If you do not k know the th geometry factor
FRACTURE TOUGHNESS, KIC Æ material property
K C = fσ
C
πa
Plane strain fracture toughness,
Computing Brittle Fracture Stress, σc
Brittle Brittle fracture stress ( σC ) depends on the fracture toughness (KC), the size (a) of pre-existing cracks or flaws and f the geometry factor (f=1 for internal flaws and 1.12 for surface flaws). F t Fracture stress, t σc
If KC and a are fixed fracture stress for brittle fracture is determined
σ c = K C / f πa
Computing Critical Flaw Size, ac, for Brittle Catastrophic Fracture A A material t i l can th thus b be d ductile til or b brittle ittl d depending di upon th the size i off cracks k or flaws which are present in the sample. The condition for brittle behaviour.
1 ⎛⎜ K C aC ≥ π ⎜⎝ fσ appl
⎞ ⎟ ⎟ ⎠
2
If applied li d stress t σappl andd fracture f t toughness, KC are fixed, design involves a maximum allowable crack size
where ac is maximum allowable flaw size (or critical size to propagate crack).
Fracture Toughness Metals/ Alloys
Graphite/ Ceramics/ Semicond
Polymers
100
K Icc (MPa · m0.5 )
70 60 50 40 30
C-C(|| fibers) 1 Steels Ti alloys Al alloys Mg alloys
Based on data in Table B5, C lli t 7 Callister 7e.
20
Al/Al oxide(sf) 2 Y2 O 3 /ZrO 2 (p) 4 C/C( fibers) 1 Al oxid/SiC(w) 3 Si nitr/SiC(w) 5 Al oxid/ZrO 2 (p) 4 Glass/SiC(w) 6
10 7 6 5 4
Diamond Si carbide Al oxide Si nitride
PET PP
3
PVC
2
1 0.7 0.6 0.5
Composites/ fibers
PC
Si crystal Glass -soda Concrete
PS Polyester
Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook 1 Handbook, Vol. Vol 21 21, ASM Int Int., Materials Park, OH (2001) p. 606. 2. (55 vol%) Courtesy J. Cornie, MMC, Inc., Waltham, MA. 3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics, Vol. 7, Plenum Press (1986). pp. 61-73. 4. Courtesy CoorsTek, Golden, CO. 5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/85-22011/2, ORNL, 1992. 6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc Vol. Proc., Vol 7 (1986) pp pp. 978 978-82. 82
Glass 6 Chapter 8 - 15
Engineering Design • Great, we can design to prevent brittle behavior • Things still fail – Creep – Fatigue • Next time!
Chapter 8 - 16
Loading Rate • Increased loading rate...
-- increases σy and TS -- decreases %EL
An increased rate gives less time for dislocations to move past obstacles.
• Why?
σ σy
TS
ε larger
TS
ε smaller
σy ε Chapter 8 - 17
Engineering Fracture Design • Avoid sharp corners! σ σo max Stress Conc Conc. Factor Factor, K t = σ w σmax r,
o
2.5
h
fillet
2.0
increasing
w/h
radius Adapted from Fig. 8.2W(c), Callister 6e. (Fi 8 (Fig. 8.2W(c) 2W( ) iis ffrom G G.H. H Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)
1.5
1.0 0
0.5
1.0
r/h
sharper h fill fillett radius di Chapter 8 - 18
