# Mechanical Metallurgy Questions and Answers – Fracture Types in Metal – 2

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This set of Mechanical Metallurgy Quiz focuses on “Fracture Types in Metal – 2”.

1. The theoretical cohesive strength of brittle material is approximately equal to ________
a) E
b) E/2
c) E/π
d) E/2π

Explanation: The approximation for the theoretical strength of brittle material is given as:
σmax=λE/2πao;
where σmax= theoretical cohesive strength
λ= Lattice wavelength of the curve
ao = lattice parameter
E = Young modulus.
So taking approximation that λ=2ao and substituting in the equation, we get
σmax = E/π

2. Determine the cohesive strength of glass fibre, if E = 90 GPa, Surface energy = 1.2 Jm-1/2 and a0=0.18 nm?
a) 29.5 GPa
b) 10 GPa
c) 24.5 GPa
d) 150 MPa

Explanation: The cohesive strength is equal to:
{Eϒs/ao}1/2
Where; ϒs=surface energy, ao=lattice parameter
90*109*1.2/0.18*10-9 = (600*1018)1/2
24.49*109 = 24.49 GPa.

3. The maximum stress on the tip of the crack of length 2c and radius of curvature of the tip ρt is given as ____
a) σmax=$$σ[1+2(\frac{c}{ρt})^{1/2}]$$
b) σmax=$$σ[1+(\frac{c}{ρt})^{1/2}]$$
c) σmax=$$σ[2(\frac{c}{ρt})^{1/2}]$$
d) σmax=$$σ[(\frac{c}{ρt})^{1/2}]$$

Explanation: The maximum stress on the tip of the crack of length 2c and radius of curvature of the tip ρt is given as;
σmax=$$σ[1+2(\frac{c}{ρt})^{1/2}]$$
This can be approximated as=$$2σ(\frac{c}{ρt})^{1/2}.$$

4. The fracture on the sharpest crack tip will be equal to $$(\frac{Eϒ_s}{4c})^{1/2}$$ .
a) True
b) False

Explanation: The maximum stress on the crack tip is given as:
σmax=$$σ[1+2(\frac{c}{ρt})^{1/2}]$$
$$2σ(\frac{c}{ρt})^{1/2}$$
Now substitute the value of σmax=$$(\frac{Eϒ_s}{a_o})^{1/2}$$
Equate both the equation:
σfracture=$$(\frac{Eϒ_ρ}{4ac})^{1/2}$$
The sharpest possible crack tip will be the one where the crack tip curvature is equal to the interatomic spacing
σfracture=$$(\frac{Eϒ}{4c})^{1/2}$$.

5. Calculate the fracture stress of brittle material with the following properties.
E=200GPa, Surface energy=1.2 Jm-2, c=0.5*103nm
a) 346.4 MPa
b) 648.9 MPa
c) 589.9 MPa
d) 5898.8 MPa

Explanation: The fracture stress will be equal to; σfracture=$$(\frac{Eϒ}{4c})^{1/2}$$
Substitute the values in the equation:
200*109*1.2/4*0.5*10-6
34.64*107
346.4 MPa.

6. The statement of Griffith theory of brittle fracture says that “A crack will propagate when the decrease in elastic strain energy is at least equal to the energy required to create the new surface”.
a) True
b) false

Explanation: The idea behind the Griffith theory is that every material contains micro-cracks and in the local region of crack tip, the stress concentration causes the stress value high enough to cross the theoretical fracture stress of the material.

7. Which of the following statement is correct?
a) Crack inside the material of length 2c and surface crack length c will have some impact in reducing the strength of the material
b) Crack inside the material of length c, and surface crack length 2c will have the same effect on reducing the strength of the material
c) Crack inside the material of length 4c and surface crack length c will have an equal impact in reducing the strength of the material
d) Crack inside the material of length c, and surface crack length 4c will have same impact in reducing the strength of the material

Explanation: Both the crack will have the same effect in reducing the strength of the material. 8. If the crack length inside the material is increased by 4 times. The fracture strength will ___________
a) decrease by 4 times
b) decrease by 2 times
c) increase by 4 times
d) increase by 2 times

Explanation: According to Griffiths theory;
$$σ=(\frac{2Eϒ}{πc})^{1/2}$$
Here c indicates the length of the crack.
So if the crack length in increase by 4 times, strength will reduce by the square root of 4 times. 2 times.

9. Griffith’s theory for a thick plate predicts the fracture as_________
a) $$σ=(\frac{2Eϒ}{(1-v)πc)})^{1/2}$$
b) $$σ=(\frac{2Eϒ}{πc})^{1/2}$$
c) $$σ=(\frac{2Eϒ}{πc})^{1/2}$$
d) $$σ=(\frac{2Eϒ(1-v)}{πc})^{1/2}$$

Explanation: For a thick plate the condition of plane strain applies so the fracture stress changes to;
$$σ=(\frac{2Eϒ}{(1-v)πc})^{1/2}$$

10. The sensitivity of the fracture of the brittle solid to surface condition has been termed as the ____________
a) Bauschinger effect
b) Doppler effect
c) Joffe effect
d) Polarity effect 