Question1 [25 marks]
(a) Table Ql shows typical data for strength of copper alloys: pure copper, bronze (a solid
solution of tin or beryllium in copper) and brass (a solid solution of zinc in copper). Rank
the strengthening mechanisms (as indicated in the table) in order of effectiveness.
[2]
Table Ql. Strengthof a selectionof copperalloys.
Alloy
Process route Main strengthening mechanism
Yield
strength
(MPa)
Pure Cu
Cast
None
35
Bronze: Cu + 10% Sn Cast
Solid solution strengthening
200
Brass: Cu + 30% Zn Cast
Solid solution strengthening
90
Brass: Cu + 30% Zn Cold-rolled
Solid solution strengthening+
400
dislocation strengthening
Bronze: Cu + 2% Be Heat treated Precipitation strengthening
1000
(b) The yield strength oy of plain carbon steel is dependent on the grain sized, and the relation
can be described by the equation:
+ k~ Uy= <J0
where Oo and k are material constants. The yield strength of a plain carbon steel is 622 MPa
for a grain size of 180 µm and 663 MPa for a grain size of 22 µm.
(i) Calculate the yield strength of the steel for a grain size of llµm.
[10]
(ii) Explain briefly the physical significance of the Oa constant.
[1]
(iii) What methods can you recommend to ensure grain refinement of a plain carbon steel?
[2]
(c) The critical strength 6c of a plain carbon steel equals 900 MPa. Ultrasonic non-
destructive inspection of an axle made of this steel has revealed a microcrack
S0µm long (2a = S0µm). Is it safe to operate such an axel? Estimate with the aid
of Griffith's criterion:
where o-cis the critical stress required for propagation of the brittle crack;
ys is the energy of the new surface area per unit of area;
Eis Young's modulus
a is a half-length of a critical crack that will propagate spontaneously;
1t = 3,14;
if the following parameters apply:
I Iron
Oc, MPa
I 900
Ys, J/m 2
1,2
E, GPa
205
[10]
2