Mechanical Properties of Ceramics - ETH - NONMET · 2010-02-08 · Prof. L.J. Gauckler ETH Zürich,...
Transcript of Mechanical Properties of Ceramics - ETH - NONMET · 2010-02-08 · Prof. L.J. Gauckler ETH Zürich,...
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Materials Science & Technology
Materials Science II - 2010, Ceramic Materials, Chapter 6, Part 2
Mechanical Properties of Ceramics
Jakob Kübler
orMechanical Behavior of Brittle Materials
& Prof. L.J. Gauckler
1Kübler Empa-HPC, ETHZ MW-II Ceramics-6.2, 2010
Jakob Kübler Empa, Science & Technology
Lab for High Performance Ceramics Überlandstrasse 129, CH-8600 Dübendorf
+41-44-823 [email protected]
& Prof. L.J. Gauckler ETH Zürich, Materials Department
• Design relevant mechanical properties (≠ properties by technological tests)Fracture toughness, strength, creep, subcritical crack growth, …
What you already know and understand!
Repetition learning targets part 1
• All materials exhibit a natural defect populationdue to production. Defects differ in size, form and orientation.
• Mechanical stress at crack tip is by factors larger than stress calculated from macroscopically available cross section and average applied stress.
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
ρσσ a210max
σmax stress at crack tipσ0 nominal stressρt radius of curvature at crack tip
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• Brittle materials like ceramics can’t diminish stress superelevationat crack tip by plastic deformation.
⎠⎝ ρt pa ½ crack width
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• Griffith’s basic idea: Balance energy consumed in forming new surfaces ascrack propagates against elastic energy released.
• Griffith’s law: Failure occurs whenrate at which energy is released is greater than rate at which it is consumed.(if defect related stress peak ≥ theoretical strength)
Repetition learning targets part 1
Valid as long as only factor keeping crack from extending is creation of new surfaces.
(if defect related stress peak ≥ theoretical strength)
• with help of Irwin’s correlation: Failure occurs if Stress Intensity Factor ≥ Critical Stress Intensity Factor
Ec ⋅⋅≥⋅⋅ γπσ 2σ, c applied stress, depth of crack2, γ surfaces created, intrinsic surface energy of materialE Young’s modulus
YcK I ⋅⋅= σ KIc ,σc fracture toughness, critical applied stressd th f k Y f t
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• KIc is material specific and indicates how well it withstands the extension of a crack under stress. The higher KIc, the more difficult it is for a crack to advance.
• Y-factor predicts intensity and distribution of a stress field around a defect caused by an external load.
YcK cIc σ c, Y depth of crack, Y-factor
Aim of chapter & Learning targets 1. Introduction2. Stresses at a crack tip3. Griffith law4. KI and KIc
5 R
part
1C
rack
tip
th
lear
ning
ta
rget
s 1“Why mechanical testing …”
“Higher than you’d assume …”“Conditions for failure …”
“Stress intensity & critical stress intensity …”
g 2
“I i t h ”5. R-curve6. Properties7. Strength
8. Statistic9. Proof testing10. Fractography
part
2St
reng
tpa
rt 3
Stat
istic
s
lear
ning
targ
ets “Improving toughness …”
“Knowing what you measure …”“Just a value …”
lear
ning
ta
rget
s 3“Weibull, a name you’ll never should forget …”
“Make it or …”“Reading fracture surfaces …”
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11. Thermal shock12. Slow crack growth13. SPT diagrams14. Creep15. Failure maps
part
4Ti
me&
Tem
p
lear
ning
ta
rget
s 4
“Temperature, time and geometry …” “After several years …”
“Combining strength, lifetime & statistics …”“Temperature makes it move …”
“Finding your way …”
part 5 - Case Study: Lifetime of All-Ceramic Dental Bridges
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Definition of crack dimensions for today’s lecture≠ last weeks definition
(… just to stay flexible …)Attention:
In literature “c” and “a” are often used vise versa
2 c
a
σ
a
2 c → ∞
σare often used vise versa.
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σ σ
R-curve behavior
KIR
KIR
Increasing resistance against crack propagation
Crack growth Δa
KIR= KIc
KIR
Why this increase ?
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e.g. fracture toughness of a polycrystalline ceramic is significantly higher than that of a single crystals of the same composition, e.g. KIc of alumina
single-crystal ~ 2.2 MPa √mpolycrystal ~ 4 MPa √m
Crack extension isn’t characterized by a constant KIc anymore but by a KIR - Δa curve.
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R-curve behavior (3)
Polycrystalline material:as crack deflects along weak grain
Why is KIR increasing?a) Crack deflection at grain boundaries
as crack deflects along weak grain boundaries, Ktip is reduced, because stress is no longer normal to crack plan
Barsoum, p380
crack plan
( ) apptip KK 23cos θ=
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assuming Θavg = 45° → Ktip ~ 1.25 x single-crystal value
crack deflection accounts for some of the enhanced toughness, but not all
R-curve behavior (4)
b) Crack bridging 1
Toughening results from bridging of
deflection of crack front along / around rod-shaped particles
Why is KIR increasing?
g g g gthe crack surfaces behind crack tip by a strong reinforcing phase e.g.
Bridging ligaments generate closure f k f hi h d K
• elongated grains• continuous fibers• whiskers• particles (metal …)ligament bridging mechanism with no
interfacial debonding
undeflected crack front
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forces on crack face which reduce Ktip.
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R-curve behavior (5)
SiC whiskers in - glass- mullite- alumina
b) Crack bridging 3: example
lines: predictionpoints: experiments
Mineralogical name of only chemically stable intermediate phase in SiO2 - Al2O3 system. The natural mineral is rare, occurring on the Isle of Mull, west coast of Scotland.
What’s Mullite ?
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Crack bridging and pullout can yield substantially increased fracture toughness.
Si3N4F. Monteverde, A. Bellosi, S. Guicciardi, © ISTEC-CNR
R-curve behavior (6)
Fracture toughness of a “composite” due to elastic stretching of a partially debonded reinforcing phase at crack tip with no interfacial friction:
P. Becher, J.Am.Ceram.Soc.,
b) Crack bridging 2: amount of increase
⎟⎟⎞
⎜⎜⎛
⋅⋅⋅
+⋅= fcffI
EVrGEK
γσ 2
where: c, m, f , i composite, matrix, reinforcement, interfaceE, V, r Young’s modulus, volume fraction, radius of bridging ligament σ, G strength of reinforcement phase, toughness of unreinforced ligament γf/γi ratio of fracture energy of the bridging ligaments to that of
the reinforcement/matrix interface
74:255-269 (1991)⎟⎟⎠
⎜⎜⎝
+if
fmcIc EGEK
γσ
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i.e. fracture toughness is increased for • “high” reinforcement content, • “weak” reinforcement (increasing Ec/Ef ratio) and • “weak” reinforcement / matrix interfaces (increasing γf/γi ratio)
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R-curve behavior (7)
b) Crack bridging 4: amount of increase
Al2O3 & SiC-whisker composite
Data for calculationm: matrix ; f : whiskerEm 400 GPaKIc Al2O3 3 MPa √mEw 580 GPaσw 8’400 MPadf 1 μmlf 10 μmwhisker direction random-3Dinterface γf / γi 1, 25, 125
4
6
8
10
ite K
Ic [
MPa
√m
]'super strong' interface'strong' interface'weak' interface
γf γi(1 = super strong)
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0
2
4
0.0 0.1 0.2 0.3 0.4
volume fraction of SiC-whisker
com
posi
c) Transformation toughening
… if tetragonal particles are fine enough, then upon cooling from Tprocess , they can be constrained from transformation by surrounding matrix.
i i l
R-curve behavior (8)
martensitically transformed zirconia particle
original metastable tetragonalzirconia particle
compressive stress field around crack tip
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… very large toughness due to stress-induced transformation of metastable phase (tetragonal → monoclinic Zr) in vicinity of propagating crack.
zirconia particle
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t → m in pure undoped ZrO2 during cooling is a reversible martensitic transformation, associated with a volume change (4–5%). Dopants (yttria, ceria,
i l i t ) ll dd d t t bili th hi h t t t d/
R-curve behavior (9)
Surface grinding induces the martensitic transformation, which in turn creates compressive surface layers and a concomitant increase in strength.
Matensitically transformed
magnesia, calcia etc.) are usually added to stabilize the high temperature t and/or c-phase in the sintered microstructure.
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Metastable tetragonal zirconia particle
zirconia particle
if t i i l t t f ti i i d d ( l i 4% h
Shielding factor Ks
R.M.Mc. Meeking and A.G. Evans, J.Amer.Ceram.Soc., 63:242-246 (1982)
R-curve behavior (10)
… if constrain is lost, transformation is induced (volume expansion ~4% → shear strain up ~7%). Approaching crack front (= free surface) triggers transformation,
which in turn places zone ahead of crack tip in compression.
To extend crack into compressive zone extra energy is required → KIc and σ ↑
κ dimensionless constant (Δa/w = ∞ → κ = -0.215 depends on shape of zoneahead of crack tip)
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E Young’s modulusVf volume fraction of transformable phaseεT transformation strainw width of zone with transformed phaseΔa length of crack inside transformed zone
w = 5 μm ; E = 210 GPa ; Vf =0.92 ; εt = -0.07
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R-curve behavior (11)
PSZ: partially stabilized zirconiaCubic phase is less than totally stabilized by the addition of MgO, CaO, or Y2O3. Heat treatment needed to keep precipitates small enough so that they do not spontaneously transform within the cubic zirconia matrix.
Toughened zirconia-containing ceramics
TZP: tetragonal zirconia polycristal100% tetragonal phase and small amounts of yttria and other rare-earth additives. σb up to 2’000 MPa.
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ZTC: zirconia-toughened ceramicTetragonal or monoclinic zirconia particles finely dispersed in other ceramic matrices such as alumina, mullite, and spinel.
Residual compressive stresses
R-curve behavior (12)
Increasing resistance against crack propagation by design, e.g.
compressive residual stresses in laminates
L1
= σLoad - σCResσLayer
KIc = ( σ−|σC| ) • √a • Y
reduce actual stress in outer layer
L1
L2
L1
σσ
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How can compressive stresses be introduced into surfaces,e.g. in glass and ceramics?Glass: Rapid cooling of outer surfaces.Ceramic: CTE gradient from surface to core.
σ-σ+
9
4
6
C
R-curve behavior (13)
Laminates (2): CTE mismatch to introduce residual stresses
0
2
0 200 400 600 800 1000Temperature °C
Si3N4 + X% TiNSi3N4
CTE
10-6
/ o C
Si3N4+30% TiN
Si3N4
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Temperature C
• TiN particle addition in Si3N4 increases the CTE.• Si3N4 gives layers under compressive residual stress.• Si3N4 +TiN gives layer under tensile residual stress.
R-curve behavior (14)
Laminates (3): Design
• Strong boundary layer interfaces. • External layers under compressive stress.
Si3N4 + 30 % TiNSi3N4
1 mm
150 μm
600 μm
Si3N4
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1 mm
10 µmSi3N4 +TiN
Remark: “Joining” temperature ~1’100°C
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R-curve behavior (15)
Laminates (4): Apparent Fracture Toughness = toughness you will measure but isn’t solely material related
Si3N4 Si3N4+TiN
0.5mma
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• KIc-app increases with notch length towards interface in compressive layer• KIc-app decreases in tensile layer.• KIc-app more than three times KIc of Si3N4.
Notch length a [mm]
R-curve behavior (16)
Laminates (5): improved designMicro-layered laminates
(with external tensile layers)
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R-curve behavior (17)
Laminates (6): further improved designMicro-layered laminates
(with external compressive tensile layers)
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Suggested design and KIc app behaviour of micro-laminate design with layers of five different compositions.
KIc app as function of crack length of the 2nd micro-laminate design with external compressive layers superimposed onto WFA model.
Kuebler J., et.al., KEM 333 (2007) 117-126
Properties (FT1)
Test methods for determination of fracture toughness KIc (KIc → resistance displayed by a material to propagation of crack through it)
SEVNBSEPB
CNB IF
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SCF IS
Fracture toughness should be qualified with the conditions under which the test is performed (e.g. method, test conditions, crack
size, geometry, stress field, crack velocity).
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Properties (FT2)FSEVNB (and SEPB, SENB)
Single Edge V-Notched Beam(and Single Edge Precracked Beam, Single Edge Notched Beam)
( )with
aW
SSWB
FYaK M
Ic −Γ⋅−
=⋅⋅=α
σ
2
2/321max
)1(23
S2
S1
W a
NCSi3N4
Wa
and
M
=
+−+−
−−=Γ
α
αααααα 2
2
)1()1()35.168.049.3(326.19887.1
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Properties (FT3)
CNChevron Notched Beam F
not validd
not valid
F
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Y'm 3.08 5.00a0 8.33a02+ +( ) 1 0.007
S1 S2
W2-----------+⎩ ⎭⎨ ⎬⎧ ⎫=
'maxmIc Y
WBFK⋅
=
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Properties (FT4)
1 Knoop hardness indent 2 polished surface
SCFSurface Crack in Flexure
improve visibility
2c
a
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Ymax : larger of Ys and Yd
Properties (FT5)
8.0
√m] other methods, indiv. avg.
SEVNB; G P AvgAlumina-999
Why those differences?
Fracture toughness values measured with various test methods in comparison with SEVNB values
4.0
6.0
Tou
ghne
ss [
MPa
√ SEVNB; G.P.Avg.SEVNB; G.P.Std.Dev.
5/4)
6/5) 5)) o ) 10/5
)
N2 5) H2O 1/5)
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0.0
2.0
Method (Participant / Number of Specimens)
Frac
. T
SEPB
(25
SEPB
(26
SCF
(10/
5
CN
(8/5
)
SCF
(9/4
)
SCF+
halo
(10/
5SC
F-N
2 (1
SEV
NB
-N (1/
SEV
NB
-H (1
J. Kübler, ASTM STP 1409, 2002
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Properties (FT6)Development of Vickers indentation cracks
����������� ����
Vickers - IFIndentation Fracture
KIc 0.032H a EH----⎝ ⎠
⎛ ⎞
12---
ca--⎝ ⎠
⎛ ⎞
12---
=����� ������
����� ��������
���� �������
H⎝ ⎠ a⎝ ⎠H = F/2a (hardness)only valid if c/a > 2.5
F
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����� �������� �����
���������
plastic deformation !!
Properties (FT7)
Example: Micro-Hardness (… plasticity …)
Si3N4 – 05
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Scanning Probe Microscope
Optical Glass BK7, HV-1N
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Strength (1)
Determination of design relevantstrength properties
☺Creep
Relation betweencreep rate and
load.
Crack growth /Lifetime
static dynamicRelation betweendefect size and
strength.
Relation between strength and probability of
Fracturetoughness Strength
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Relation between crackgrowth speed and stress
intensity factor.
KIc
failure.
Strength (2)
Strength of ceramics; evolution
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Strength (3)
Advantage• simple (fixation of sample,
simulation of environment, …)cheap (sample jig )
Bend test
• cheap (sample, jig, …)• universal (strength, fracture
toughness, Young’s modulus, fatigue, …)
• sensitive to surface defects
Disadvantage• small volume tested
t di t th f t
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• stress gradient therefore not valid by plastic deformation
WM B
B=σ
Strength (4)
3- vs. 4-pt-bending
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Strength (5)
P: load at failure r ΔP = 0.2 %b, h: size (3x4 mm) r Δb, r Δh = 0.07 %d: o/i rolls (10 mm) r Δd = 1.0 %
(calculated from tolerances of test jig)
Example: 4-Pt-bending strength @ elevated temperature
Measurement uncertainty
( ) 2
3:,,,hb
dPdhbP⋅
⋅⋅=σ
( j g)
Relative measurement uncertainty:% 1 2 %
Relevant factors, e.g.:• σf ≥ 100 MPa / ≥1’000 MPa Δe1 > ± 2.7 % / < ± 0.3 %• Δl jig (T related) Δe2 ~ ± 3.0 %
h ti @ f Δ 5 0 %
∑ Δ+∑ Δ⋅⎟⎟⎠
⎞⎜⎜⎝
⎛=Δ
==
m
mj
n
ninxx
i
exfdxdy
11
2
)...1(
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Δσ% ≤ 1.2 % • chem. reaction @ surface Δe3 ~ ± 5.0 %Remark:• Considering uncertainty of TC ± 2.0 °C, registration equipment• Not considered: test speed variation, surface quality, rel. humidity
Bending strength "Real" relative measurement uncertainty ≥ 100 MPa ± 1.2 % + 2.7 % + 3.0 % + 5.0 % = 11.9 %
≥ 1000 MPa ± 1.2 % + 0.3 % + 3.0 % + 5.0 % = 9.5 %
Strength (6)
Scatter of mechanical strength
f(σc)
Dispersion density of the strength measured on a series of components
σc1 σcσc2σc ( )∫ =
∞
01cc σσ df
34Kübler Empa-HPC, ETHZ MW-II Ceramics-6.2, 2010
( )∫=<<2
121 )(
c
cccccc
σ
σσσσσσ dfP
( )∫=c
ccc
σ
σσσ0
)( dfF
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Strength (7)
Dispersion of the largest (failure relevant) defects and failure strengths
h(a) 1-F(σc)h(a)
H(a)
f(σc)( c)
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… large “largest” defect→ low strength …
a σc
… small “largest” defect→ high strength …
Strength (8)
Strength of a ceramic component …
… is defined by a combination of• critical stress intensity factor• size of critical defect• position of critical defect• stress and stress direction the crack sees
failure relevant defect
largest,but not failure relevant defect
A large number of small defects present in a component are loaded too, but aren’t responsible for catastrophic failure
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stress and stress direction the crack sees
… therefore it’s difficult to predict the strength of a component !
↑ direction⊕ position),,,,( ⊕↑= ccKf Iccomponent σσσ a, a
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Strength (9)
… during fabrication of component:• always: powder agglomerates• friction when pressing• powder sedimentation when casting (slurry)
Sources for defects …
• always: cracks and pores from sintering
… during usage of component:• corrosion, pitting• subcritical crack growth, creep • friction, scratches• stress peaks (impact, …)
(in ductile materials e g in fcc-metals stress peaks can be reduced
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(in ductile materials, e.g. in fcc metals, stress peaks can be reduced by plastic deformation at RT due to 5 independent plains for sliding)
→ ceramic materials are very brittle - they fail without warning even at elevated temperatures (KIc is between 1 MPa √m and 20 MPa √m)
→ increase of toughness in ceramics has to happen in a different way than over sliding and plastic deformation
Strength (10)
Toughness ↔ defect size ↔ strength
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~ 1 : 10’000 (!!)
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Strength (11)
1) increase σc by reducing ac, e.g. by improved processing
Two strategiesto improve σc and KIc 2) increase KIc by increasing
fracture energy, e.g. by crack bridging, transformation t h itoughening
σ c(M
Pa)
100’000
10’000
1’000
)log(loglog21log YKa Iccc −+⋅−=σ
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σ
1 10 100 1’000
critical defect size (μm)
1 000
Strength (12)
• in ceramics strength controlling defects have a size of a few μm up to a few 100 μm
• failure relevant is the largest volumeor surface defect under stress
Summary
or surface defect under stress
• ceramic materials don’t have a single strength value
• identical components will not fail at onereproducible strength value (= strength value distribution)
• When is the density of defects smallNever …
nsity
of d
efec
ts
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• When is the density of defects small enough so that we can be absolutely sure that no defect with a critical size is present ?
Statistical data is needed!The strength of ceramics is described by the Weibull statistics - see part 3.
defect size
den
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What you should know and understand, now! Learning targets part 2
Improving toughness …• Fracture toughness is related to the work required to extend a crack and is
determined by the details of the crack propagation process. It can be enhanced by increasing the energy required to extend the crack.
• Ceramics with R-curve behavior:- degradation in strength with increasing flaw size is less severe- reliability increases (some recent evidence shows that thermal shock resistance increases)
• Only for the fracture of the most brittle solids is the fracture toughness simply related to surface energy.
• Crack deflection, crack bridging, martensitic transformation (next to others) (and design) are mechanisms that enhance KIc app.
Know what you measure
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Know what you measure …• Fracture toughness values measured with different test methods may differ.• Bend test: - universal (e.g. strength, fracture toughness)
- sensitive to surface defects- only a small volume is tested- value σ3Pt test > value σ4PT test- specimen sees stress gradient (not valid by plastic deformation)
Learning targets part 2
Strength is “just a value” …• All components have defects due to fabrication and usage• The strength controlling defects in ceramic components have a size of a few μm up
to a few 100 μm• The strength of a component is defined by a combination of
i i l i i f- critical stress intensity factor - size of critical defect- position of critical defect- stress and stress direction the crack sees
• Identical components will not fail at one reproducible strength value = strength value distribution
• Ceramic materials fail without warning even at elevated temperatures KIc is between 1 MPa √m and 20 MPa √m
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• The aim is always to improve both- σc by reducing ac , e.g. by improved processing- KIc by increasing fracture energy, e.g. crack bridging, transformation toughening …
• The strength of ceramics must be described by statistics