Fracture And Failure Of Ceramics Flashcards
What is the strength of a ceramic dependent on?
The largest flaw in its stressed region - irrespective of other flaws as long as they don’t interact
What stresses does an arch have?
Compressive stresses are transmitted through structure
Which stress is higher in ceramics? Compressive or tensile?
Compressive
What are the two broad ways of approaching fracture?
Energy and Stress Intensity
What type of fracture do we mainly deal with in ceramics?
Brittle
When does crack extension occur - ceramics approach?
When energy available for growth overcomes resistance of materials
Creation of a new surface requires energy so energy needed is surface energy + local deformation/rearrangements
What does quasi-static mean?
Kinetic energy is small
What is G and a in the energy approach of fracture?
G - Energy release rate
A - half crack length
When are G and Gc equal?
At fracture
In an energy approach, what does fracture only depend on?
The largest flaw - no time or other parameters
How can lab results be translated to service use?
Only parameter is flaw size so a small sample can be taken providing flaw is same as on larger application. Results can be scaled up.
Means you can test large applications like an aircraft wing or large structure and do destructive testing in a lab.
How do you determine a flaw size non-destructively?
Imaging:
Ultrasonic spectroscopy - porosity like a bubble or crack shows a flaw (rly good for bubbles in glass)
X-ray tomography - pass X-rays through and find defects (for materials that can’t use ultrasonic)
What are LEFM, EPFM and dynamic, viscoelastic and viscoplastic FM?
LEFM - No plastic deformation
EPFM - Considers some plastic deformation
Dynamic (high impact - stress applied very quickly), Viscoelastic and viscoplastic all have time as a variable
How does the fracture behaviour of metals change at high temperatures?
Changes from linear elastic or plastic to viscoplastic
Which fracture behaviour do polymers experience?
Viscoelastic, although below Tg there can be some linear elastic
How does high temperature affect ceramic fracture behaviour?
Changes from linear elastic to viscoplastic
Where is LEFM on a stress v toughness graph?
The initial proportional line
What are the main reasons we use ceramics?
High mechanical performance with high temperature capability
How does a stress strain graph compare between metals and ceramics and how do their Young’s modulus compare and why?
Metals - proportional stress and strain until yield strength, then increase to UTS then a decrease and cut off at failure strength (E = 35-350GPa)
Ceramics - proportional stress and strain (stress increases very quickly with little strain), then fractures with no warning (E = 100-1000GPa - high because of very strong atomic bonding)
Why are metals sometimes more favourable?
Easy to form, use, cast etc
What does an ideal brittle ceramic do?
Elastic deformation followed immediately by fracture
What did Orowan say about the energy put into a component to fracture?
If a component is to fracture, the mechanical strain energy put into it must be greater than the energy of the two new fracture surfaces formed
What is a in the ceramic theoretical stress equation?
Atomic spacing
What is the theoretical strength of a ceramic related to?
Modulus, surface energy, lattice spacing
High strength = high modulus, high surface energy, small lattice spacing
What is a rough theoretical value for a ceramic and how do actual experimental values compare? Why is there a difference?
30GPa compared to actually 1.5GPa - something isn’t accounted for in the theoretical equation
ENTER GRIFFITH lol
What is Griffith theory?
In reality, fracture begins at the inherent flaws in the material at stress concentrations. (If you score glass, it will cut along that line really easily)
What is the Griffith equation for stress and what does it mean?
Fracture stress = Sqrt (2Esurfaceenergy/pi*halfcracklength)
Must have enough surface energy to form the two new surfaces
What is the Inglis equation for stress?
Fracture stress = Sqrt (Esurfaceenergy/8halfcracklength)
For a ceramic to fracture, does the Inglis or Griffith criteria need to be met?
Both! Inglis is much smaller so when that is met, only one condition is, so minimum stress for cracks to propagate is Griffith stress.
What is the most important parameter in the Inglis and Griffith stress equations and why?
C - size of largest flaw
For a series of similar samples, E and surface energy will be the same so strength relies on size of flaw present in the stressed region of material.
Which ceramic would be stronger? One with lots of 1um flaws but one 100um flaw or one with lots of 10um flaws?
Stress is only dependent on the largest flaw present in the stressed region so although the A has smaller uniform flaws, the one larger flaw overrides it.
What is the theoretical ceramic fracture stress equation?
Theoretical stress = Sqrt (E*surface energy/lattice spacing)
What is the most common flaw present and how much does it affect strength? Why aren’t ceramics usually 100% density?
Porosity - 5% gives 20-30% less strength
Achieving 100% density requires very high temperatures, so very high energy usage and very high manufacturing costs
How does the shape of a pore affect strength?
Angular pores have higher stress concentration than spherical or near-spherical
How does effective flaw size change with grain size?
If surrounding grains are small, the effective flaw size is much larger in comparison
How is critical flaw size affected by surrounding grain sizes?
Small surrounding grains reduces the critical flaw size
How does the distance of a pore from the surface affect the strength?
If a pore is closer to surface, the bridge of material separating it from surface may break first resulting in a critical flaw which is the size of the pore plus the length of the bridge.
What are pore clusters sand how do they affect strength?
If pores are close, the material bridges in between them can break first, linking the pores and producing a much larger, potentially critical flaw.
What are inclusions and how do they affect strength of ceramics?
Contaminations from ceramics processing
Effect is similar to pores - angular are much worse
Thermal expansion of inclusions and matrix have a big effect - if they differ then heating and cooling can cause cracking as they expand differently.
Elastic modulus differences of inclusions and matrix also can result in formation of cracks when a stress is applied.
What are the stress equations for 3 and 4 point bending?
3 Point stress = 3PL / 2bd^2
4 Point stress = 3Pa / b*d^2
P = downward force (add both for the 4 point)
L = open length between fixed points
a = distance from edge to load points
How does accuracy and stress compare between 3 point, 4 point and tensile tests?
3 point is unlikely to find largest flaw perfectly at centre (so test would show stress is higher as it hasn’t found the flaw)
4 point are more accurate
Tensile is the most accurate as almost entire thing is under stress so largest flaw will be stressed (so test would find stress to be lowest as it will most likely find flaw)
If tensile tests are more accurate, why don’t we only use tensile testing?
- Preparing samples is much more expensive than for 3 or 4 point bends - must be accurate and machined rather than just a rod
- Requires very special grips that minimise unwanted stresses on the ceramic - high cost
Why does 3 point bend testing get used more than 4 point?
- 4 point requires aligning specimen perfectly so takes longer than 3 point.
- 3 point gives larger stress values so is a good incentive to use it (even though its more inaccurate).
What is the effect of temperature on HPSN and RBSN ceramic strength?
Hot Pressed Silicon Nitride - sintered with glassy additives (zero porosity) - higher strength at low temps but rapidly decreases at higher temps below RBSN
Reaction Bonded Silicon Nitride - prepared from metal nitridation (porous) - lower strength but doesn’t vary much across a range of temps
Graph shows the effect of temp so should denote the usage
What are the advantages of using ceramics?
High stiffness, strength, corrosion resistance, hardness, wear resistance and low density
What property do ceramics not posses?
Fracture toughness (very brittle)
What is the equation for mode 1 stress intensity factor K1?
K1 = Yappliedstressc^0.5
Y is a dimensionless term defined by crack configuration and loading geometry
C is half the crack length
As fracture toughness doubles, critical flaw size quadruples
This increases reliability as chance of getting a flaw that size reduces
What are the ways of increasing reliability of a component?
Reduce flaw size by improving processing
Increase toughness by microstructural design or additives like Zirconia
Why might there be significant variation in fracture strength for a ceramic?
Because it depends on the probability of a critical flaw existing and this probability varies between specimens
Why does fracture strength increase with a smaller specimen size?
Probability of a critical flaw existing decreases
What does a sketch of the stress distribution ahead of a crack tip look like and why?
Max stress at crack tip, which reduces exponentially as distance from crack tip increases
Near the crack tip, the stress is really high because of the sudden change in geometry leading to a localised stress concentration.
As you get further from the crack tip, the material responds with plastic deformation which redistributes the stress and the chains relax.
What factors determine if a ceramic will deform or fracture?
Fracture toughness - higher - more resistant to fracture and will deform
Strength - ability to withstand stresses without permanent deformation or fracture - higher strength are more likely to fracture
Microstructure - porosity, impurities, grain size all effect it
Stress intensity
Loading rate - rapid can lead to brittle fracture while slow can allow for energy dissipation and plastic deformation
Temperature
