V.#M.#SGLAVO#–#UNITN#–2011# Toughening mechanisms · V.#M.#SGLAVO#–#UNITN#–2011# Transgranular and intergranular fracture tilt twist G C increases (θ, φ ≈ 45°, ΔG C

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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


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


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


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!


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!


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


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


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


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


t m

Toughening mechanism

σ

ε

σχ

εΤ φ σr


!

"KC = 0.22 E1# $ %T & h

asymptotic fracture toughness:

t grains fraction

**

Journal of the American Ceramic Society, 1990


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!


Bridging mechanisms


fundamental condition: intergranular fracture

2. By bridging grains !



α-SIALON


Si3N4


Al2O3 - SiCw


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

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V.#M.#SGLAVO#–#UNITN#–2011# Toughening mechanisms · V.#M.#SGLAVO#–#UNITN#–2011# Transgranular and intergranular fracture tilt twist G C increases (θ, φ ≈ 45°, ΔG C