4(a) Derive the approximate plastic zone size for mode-| plane stress and plane strain

condition. Given principal stresses and local stresses at the crack tip are the same. (3)
4(0) What is the basis on which J integral approach is followed? (3)
4(c) What are the limitations in following S-N curve? (3)

56) Derive the relationship between C TOD and KI Note that crack opening v
along load direction is given below (5)

1 72 (a? — x2}?

v=—j—
201+۲

where, 8 is the modulus of rigidity, a is semi crack length and v is Poission's ratio
and x =0 at the middle of the crack.

How fatigue crack initiates on a smooth surface? For a nucleation life of 1 0 * cycles
corresponding to a crack length for a crack length of 40 mm, the ratio of AK to square
5(0) root of radius of curvature of crack root is measured as 1500MPa. If crack root radius

is 2.5mm, what is the (Kmax - Kmin)? (4)

6 (೩) Write down the expression for SIF at minor and major axes of an elliptical crack (3)

6(b) Explain the fracture surface formation under plane stress and plane strain for mode ‏اج‎ (3)

6 (0) Draw plastic zone shape under plane stress and plane strain for mode - | loading (3)
Part-C

7 (a) How using single end notch beam CTODc is determined? (6)

7 (b) An infinite plate with a centre crack is subjected to a constant amplitude fatigue load
with omax — 120MPa and omn = 12MPa. Calculate the life of the component if initial
crack length is 2.6mm and KIC = 901/08. The Paris law constants are C=6.0 x 10 MPa nil
2 and m=3. Arrive at the formula used. (6)

8 (a) The test configuration for KIC gives conservative estimate. Justify the approach. (4)

8 (b) What is the condition for a crack arrest? Give three practical examples when crack
arrest

Occurs?. (4)

8 (c) Explain the behaviour of fatigue crack closure.What modification is required for Paris
law? । (4)
9 (a) Draw a Chevron notch and write down its advantages of for Kic test? (4)
9 (b) Explain the behavior of multiple branch cracking during dynamic (4)

instability. 9 (c) Bring out the significance of overload pulse on retarded crack

(4)
growth.