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MME 467 Ceramics for Advanced Applications

Lecture 08

Fracture Toughness and Toughening Mechanisms Ref: Richerson, Modern Ceramic Engineering, Ch17, Marcel Dekker, 1992

Prof. A. K. M. Bazlur Rashid Department of MME, BUET, Dhaka

Topics to discuss....

1. Fundamentals of fracture mechanics 2. Fracture toughness

3. Needs for toughening

4. Principles of toughening

4. Toughening mechanisms

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Introduction

² Ceramic components in most cases fail by unstable propagation of flaws (pores, cracks or inclusions).

� Ceramic materials lack a mechanism to relieve the stress build up at the tip of flaws.

� The observed large scatter in strength is due to the scatter of flaw size in a component.

� This makes them notch-sensitive, and consequently their strength will depend on the combination of applied stress and flaw size.

² The flaws in ceramics act as stress concentrators and failure occurs at an applied stress which is much lower than the theoretical stress.

² Fracture mechanics deals with crack surface displacement and the stresses at the tip of the crack.

Fracture mechanics: Fundamentals

Presence of microscopic flaws (cracks, voids, notches, etc.) acts as stress concentrator and amplify the applied stress at the crack tip.

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à For a long crack oriented perpendicular to the applied stress, the maximum stress near the crack tip is:

σm ≈ 2 σ0 a ρt

½

σ0 = applied external stress a = half length of crack (internal flaw)

(full length for surface flaw) ρt = radius of curvature of crack tip

 Crack propagates when the applied stress exceeds to a certain critical value σC.

2Eγs πa

½ σC = γs = specific surface energy, J/m2

² The stress concentration at a crack tip is denoted by the stress intensity factor, K, which depends on

u the applied load v size of crack w geometry of component

Stress intensity factor

KI , KII , and KIII

The subscripts I, II and III refer the mode of direction of applied load with respect to the position of crack I – open mode where load is perpendicular to the crack (as in tensile or bend test); most frequently encountered for ceramic materials; II – shearing mode; III – sliding mode.

² The stress intensity factor :

a ρt

½ K = ≈ 2

σm σ0

² K varies from one system to another, but when it reaches the critical value, KC , it will remain constant for the material, regardless of the crack or load type.

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² The higher the fracture toughness, the more difficult it is to initiate and propagate a crack.

Fracture toughness

² The fracture toughness indicates the amount of energy that can be absorbed by the material ahead of an internal flaws

KIC = Yσy (πa)½ Y = dimensionless constant, which

depends on specimen geometry and manner of load application

σy = yield stress of defect-free material

Fracture Toughness KIc (MPa√m) Fracture Toughness KIc (MPa√m)

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Fracture toughness of selected ceramics

Ceramics E, GPa KIC , MPa m1/2

Al2O3 390 2.0 – 6.0 MgO 250 – 300 2.5 ZrO2 (cubic) 220 3.0 – 3.6 ZrO2 (partially stabilised) 190 3.0 – 15.0 SiC (single crystal) 460 3.7 Si3N4 (hot pressed) 300 – 330 3.0 – 10.0 WC 450 – 650 6.0 – 20.0 SiO2 (fused) 72 0.80

� Condition for crack propagation:

σC ≥ KIC Fracture toughness Depends on material, temperature, environment, and rate of loading

Stress intensity factor Depends on applied stress, crack length, and component geometry

Need for toughening of ceramics

� Thus, ceramics are brittle and susceptible to catastrophic failure due to two reasons: 1. the ease of crack initiation

ß due to a high degree of stress concentration of an applied load at very small microstructural or surface flaws

2. the ease of crack propagation ß due to the low fracture toughness of most ceramic materials

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� So, if we are to avoid this brittle fracture, the challenge is to build into the ceramic microstructure mechanisms that either

1. allow the material to withstand the concentration of stored energy at the crack tip, or

2. to delocalise (spread out) the energy.

Principles of toughening

� The inherent brittleness due to flaw sensitivity and low fracture toughness provide a challenge to achieve reliability of ceramics in structural applications.

� The common toughening mechanisms:

1. Modulus transfer 2. Pre-stressing 3. Crack deflection or impediment 4. Crack bridging 5. Fibre pull out 6. Crack shielding

Toughening mechanisms

� A variety of approaches have been used to enhance their fracture toughness and resistance to fracture.

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I. Modulus Transfer

� Use of high elastic modulus fibres in a low elastic modulus matrix.

Examples: glass/carbon fibre reinforced polymer boron/silicon fibre reinforced metal carbon fibre reinforced concrete

� Factors controlling the degree of toughening: 1. Modulus difference between fibres and matrix, and fibres strength 2. Volume fraction of fibre and architecture of fibre distribution 3. Length of fibre 4. Interfacial bond between fibres and matrix

© The stress applied to the material is “transferred” from the matrix to the fibres, so that the high-modulus, high-strength fibres carry the load.

Fig. 1: Strength improvement of Al-alloys by reinforcement with unidirectional SiC fibres

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II. Pre-stressing

� Involves placing a portion of ceramic under a residual compressive stress. © Tensile fracture will only occur after a large enough applied

load exceeds the compressive prestress and the build up tensile stress becomes large enough to initiate a crack at a critical flaw

� Methods of developing compressive prestress: 1. By placing the surface in compression

ß Done by (1) quenching, (2) ion exchanging, or by (3) layering

2. By using fibres ß Done by (1) the fibres elastically stressed in tension before

applying the matrix, or by (2) utilising a thermal mismatch between the fibre and the matrix

III. Crack Deflection or Impediment

� Fracture toughness is strongly affected by the microstructure of ceramics and by the path that a crack follows as it propagates through the material.

1. Crack following a planar, smooth path (as in single crystal or glass) ß the new surface produced is a minimum, resulting low fracture energy or

the fracture toughness

2. Crack following differently orientated grains and grain boundary (as in polycrystalline ceramics)

ß crack follows some weak grain boundaries, and fractured through some weak grains

ß the new surface generated as the crack propagates is greater, resulting high fracture toughness.

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Fig. 2b: Schematic of crack deflection mechanism at grain boundaries

Fig. 2a: Microstructure-controlled crack deflection

app3

tip K 2θcos K ⎟⎠⎞

⎜⎝⎛=

� Reduction of stress intensity at the crack tip:

Ktip = stress intensity at crack tip Kapp = applied stress intensity θ = angle of deflection

� For an average θ value of 45o, KIC increases by about 1.25 times above the single crystal value.

Example: Single crystal, KIC = 0.3-2.0 MPa.m1/2 Glass KIC = 1.0 Equiaxed polycrystalline ceramics KIC = 2.0- 4.0

� Methods of increasing the crack deflection or impediment 1. controlled grain boundary phase, 2. multimodal grain structure, 3. elongated or fibrous grain structure, and 4. dispersing foreign particles, plates, whiskers, or chopped fibres

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Fig. 3: Predicted relative change in fracture toughness versus shape of dispersed particles.

For 0.5 vol.% particles spherical particle KIC increases by a factor of 2 disc-shaped particle KIC increases by a factor of 3 rod-shaped particle KIC increases by a factor of 4

For 20 vol.% SiC whiskers added MoSi2 composites θ increases from 7.2 to 13 deg Toughness increases from 5.3 to 8.3 MPa m1/2 (about 50 %)

IV. Crack Bridging

� Toughening results from bridging of the crack surface behind the crack tip by a strong reinforcing phase.

� It is a major toughening mechanism for ceramics reinforced with long fibres

Fig. 4: Increase in fracture toughness by the bridging of cracks by long fibres.

© These bridging ligaments can be whiskers, continuous fibres, or elongated or ductile grains

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V. Whisker and Fibre Pullout

� Composites that exhibit whisker or fibre debonding and frictional sliding have pull out contribution to toughness.

� Part of energy is spent to friction as fibre, particle, or grain slides against each adjacent microstructural features, which effectively increase fracture toughness.

� Pullout often accompanied bridging.

� Toughening by fibre pullout is proportional to 1. the fibre content 2. fibre strength, and 3. fibre radius

and inversely proportional to 1. fibre-matrix interfacial shear strength

Fig. 5: Fibre pullout and debonding in fibre reinforced ceramic matrix composites

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VII. Crack Shielding

� Stress-induced microstructural changes result in a reduction in stress at the crack tip.

� The effect occurs in a zone around the crack tip and extending back along the crack.

� The extent of the zone affects the degree of stress shielding at the crack tip.

� Methods so far have been identified: 1. microcracking 2. ductile zone 3. transformation zone.

Transformation toughening

� A very powerful mechanism of toughening can occur in a few ceramic materials which undergo a type of martensitic transformation. Example: 1. Zirconia (ZrO2)

2. Hafnia (HfO2) 3. Dicalcium silicate (Ca2SiO4)

� In these materials, the martensitic phase transformation occurs on cooling from a high temperature and results in a volume increase.

� The martensitic nature of the transformation is important

© the transformation can occur quickly enough to affect the behaviour of a running crack.

© not normally thermally activated transformations, don’t need diffusion and can occur instantaneously.

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� In zirconia, for example © it goes through a spontaneous athermal martensitic phase

transformation at about 1150 C from high temperature tetragonal form to room temperature monoclinic form

© the transformation will induce about a 6 % volume increase and 7 % shear distortion, which in turn place the zone ahead of the crack front in compression

� Factors that triggers the transformation of finely dispersed tetragonal zirconia phases in a matrix: 1. the approaching crack front (being a free surface) 2. surface grinding or abrading

� By controlling (1)  the composition (2)  grain size (3)  the heat treatment cycle

zirconia can be maintained in its metastable tetragonal phase at room temperature.

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� Ahead of a crack in a brittle material, the accumulation of stress relieves the constraint preventing the transformation.

© This creates a region ahead of the crack where transformation is possible

� After transformation in the stress field, the particles are now in their stable state and form a transformed zone on either side of the crack.

Compressive stress field around crack tip

Original untransformed metastable tetragonal

zirconia particle

Martensitically transformed monoclinic zirconia particle

Fig. 6: Transformation zone ahead and around the crack tip

Size of transformation zone

� Transformation occurs in the region ahead of the crack where the critical stress for transformation σt is reached.

� The critical stress depends on the average particle size of the metastable particles.

© with small particle sizes, the critical stress will be large (lots of constraint from matrix) and the width of the transformation zone will be narrow. Limited toughening.

© if the particles are too large, the critical stress will be small or zero (very little constraint from matrix); they may transform spontaneously even in the absence of a crack. Limited or no toughening.

� The ideal microstructure has all the metastable particles at the same size, just below the spontaneous transformation size. This will give the biggest possible transformed zone around the crack.

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� Transformation toughening that works so well at ambient temperatures – mainly due to the tetragonal phase – is ineffective at elevated temperatures.

© Increasing the temperature reduces the driving force for transformation and consequently the extent of the transformed zone, leading to less tough materials

� Pure ZrO2 does not have transformation-toughening behaviour.

© Additives such as CaO, MgO, Y2O3, CeO2, and rare earth oxides are required to stabilise such behaviour.

© Too much additions fully stabilises the ZrO2 in a cubic crystal structure, which also does not have transformation-toughening behaviour.

Peak of curve – maximum tetragonal phase Left of peak – monoclinic phase increases Right of peak – cubic phase increases

Fig. 7: Fracture toughness versus composition for transformation toughened zirconia materials

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Next Class

Lecture 09

Examples of Toughened Ceramics 1