Answer:
grain diameter is
Explanation:
i) Lower yield point =230MPa when grain diameter is mm
ii) Lower yield point =275MPa when grain diameter is mm
The relation between yield stress and grain size is
-----1
This is the Hall–Petch equation
where Yp is the yield stress,
a is a materials constant
b is the strengthening coefficient (material specific)
and d is the average grain diameter
therefore (i) can be represented as
-----2
And ii) represented as
------3
Further simplifying since = 10
And = 12. 91
We have that eqn 2 and 3 becomes respectively
Solving the simultaneous eqns 4 and 5
Eqn 5 – eqn 4 gives
Therefore b = 15.46
Substituting the value of b in eqn 4 we have that
Therefore a becomes 230 -154.6 = 75.4
a=75.4
Eqn 1 now becones
-----6
Therefore for a yield point of 310, eqn 6 becomes