v.#m.#sglavo#–#unitn#–2011# toughening mechanisms · v.#m.#sglavo#–#unitn#–2011#...
TRANSCRIPT
V. M. SGLAVO – UNITN – 2011
mechanical strength
defects (c)
microstructure (KIC)
!
"f =KIC
# c
fabrication!
material & processing!
intreaction between defects and microstructure!
Brittle materials:!theoretical strength ≈ (≈10 GPa)
!
E10
failure stress ≈ (≈100 MPa)
!
E10
lack of inelastic deformations at crack tip ¢ limited KC o GC!
Toughening mechanisms
V. M. SGLAVO – UNITN – 2011
fracture mechanics � homogeneous and continuous solid
!
"f =KIC
# c
!
KI " KIC fracture
policrystalline material: (grains and grain boundaries)
c
c
!
G " GC
3
2
1
Path?!!Effect on GC?!!Toughening effects (increasing GC)?!4
microstructure
V. M. SGLAVO – UNITN – 2011
Transgranular and intergranular fracture
tilt
twist
GC increases (θ, φ ≈ 45°, ΔGC ≈ 30%) crack surface increases, too
fracture on clivage planes (transgranular)!
Fracture of brittle solid 2nd ed., B. R. Lawn, Cambridge Univ. Press, 1993
V. M. SGLAVO – UNITN – 2011
fracture along grain boundary (intergranular)!
!
G(" )G(0)
>GC bg
GC 0
=GC0 # $bg
GC 0
= 1#$bg
GC 0
= 1#$bg
2$
θ if θ = 90°, G(θ)/G(0) ≈ 0.25 ➠ γbg > 1.5 γ usually θ < 90° , γbg > γ (impurities)
GC increases with fracture surface (≈50%)
Other effects:!• Statistical rotation and deflections!• Intersections among deflections!• Residual stresses !
limited effect on GC!
V. M. SGLAVO – UNITN – 2011
Crack deflection
Composite materials!
4
3
1
2
!
GCcomp
GC matr
0.2 0.4
spheres
disks
bars
volumetric fraction
Problems:!• Intergranular fracture!
• Residual stresses!
V. M. SGLAVO – UNITN – 2011
KC1
K
c0.5 c00.5
σφ1
KC2
σφ2
KC constant! KC increases with c !
K
c0.5 c00.5
σφ1
KC (c)
σφ
stable growth!
σf depends on c σf independent
Toughening - mechanical strength
R-curve or T-curve effect
V. M. SGLAVO – UNITN – 2011
Toughening mechanisms
dislocations
microcracking
phase transformation
ductile particles
grain bridging
fibers
whiskers
ductile particles
(a) (b) (a) process zone (frontal wake) weakening of frontal zone material
σ
ε εT
σC !GC " 2#$C %T h
(b) bridging zone (bridged interface) closure stress (t)
!GC " 2# t(u)
0
u *$ du
V. M. SGLAVO – UNITN – 2011
Process zone mechanisms
Transformation toughening !
zirconia (ZrO2) allotropic phases: cubic (c), tetragonal (t), monoclinic (m)
martensitic transformation (MS ≈ 1200°C - 600°C) ΔV ≈ 4%, εij ≈ 1-7%
MS decreases with: • stabilizing oxides (MgO, CaO, Y2O3, CeO2) • (grain size)-1 • compressive stresses (matrix)
t phase can be !metastable at Tamb!
temperature
V. M. SGLAVO – UNITN – 2011
ZrO2 - Y2O3 system
tetragonal zirconia polycrystals (only t, g ≈ 0.5 - 2 µm)
partially stabilized zirconia (t in c, g ≈ 30 - 60 µm)
c
t
V. M. SGLAVO – UNITN – 2011
t m
Toughening mechanism
σ
ε
σχ
εΤ φ σr
V. M. SGLAVO – UNITN – 2011
!
"KC = 0.22 E1# $ %T & h
asymptotic fracture toughness:
t grains fraction
**
Journal of the American Ceramic Society, 1990
V. M. SGLAVO – UNITN – 2011
weak interface (Γi<Γf)
limited friction coefficient
strong interface (Γi>Γf)
high friction coefficient
!KC = " d # f
2
E $ E %T( )2 +4&i
R 1$ "( )'
( ) )
*
+ , ,
+2- " hp
2
R
asymptotic fracture toughness (long fibers):
fiber radius
fiber strength interface fracture toughness
differential deformation
friction stress pull-out length
1. Bridging by fibers or whiskers!
Journal of the American Ceramic Society, 1990
Bridging mechanisms
V. M. SGLAVO – UNITN – 2011
fundamental condition: intergranular fracture
2. By bridging grains !
Journal of the American Ceramic Society, 1990
V. M. SGLAVO – UNITN – 2011
α-SIALON
V. M. SGLAVO – UNITN – 2011
Si3N4
V. M. SGLAVO – UNITN – 2011
Al2O3 - SiCw
V. M. SGLAVO – UNITN – 2011
ΔKC > 0 (200 - 300%)
!
"KC =E G
1#$ 2 =
E %
6(1#$ 2)&W
LW
'
( )
*
+ ,
2
= - &WL
W
'
( )
*
+ ,
2
friction at grain boundary
fraction of “working” grains
grain pull-out
2R=W
L
u
pull-out stress: σ = 2 τ (L-u)/R = 4 τ (L-u)/W
energy for pull-out:
!
G = Vdx
L / 2"du
0
x#0
L / 2# =
16$ %W
LW
&
' (
)
* +
2