金属凝固原理习题 2

Chap.1 H EAT FLOW IN SOLIDFICATION

1-3 A large slab of aluminum,25cm thick,is poured in a sand mold with no superheat.

(a)How long will it take for the slab to solidify?(Assume negligible resistance to heat flow at the mold-metal interface and within the solidity metal)

(b)Show schematically cooling curves for a thermocouple 6.25 cm form the surface and one at the center of the casting .(Remember,the solidified portion of the casting remains very close to M T until the casting is completely solid)

1-10 (a) A slab of iron,25 cm thick,is poured with no superheat into an iron mold.Calculate the solidification time assuming no mold-metal interface .

(b) How much longer is required for solidification of the slab in a sand mold ? Neglect resistance to flow within the solidified metal and at the mold-metal interface.

(c)What percentage error did you introduce in (b) by neglecting resistance to heat flow within the solidified metal?

1-14 You are to help design a vertical continuous-casting machine to make 8-in-thick low-carbon steel slabs.Casting speed to be aimed for is 100in/min.What is the minimum-height casting tower you must plan to build?

Chap.2 PLANE FRONT SOLIDIFICATION OF SINGLE-PHASE ALLOYS

2-1 A Ge-Ga ingot containing 10 ppm Ga is solidified at R=8*3

10-cm/s with negligible convection.Show schematically,the composition along the length of the fully solidified ingot,giving the initial composition and

lengths of the initial and final transient.Assume L D =5*510-2cm /s,k=0.1.

2-5 An Al-1%Cu alloy is normally solidified with 'k =k.The phase

diagram for this alloy is schematically as in Fig.2-3 with E C =33%Cu,SM C =5.65%Cu,M T =660℃，and E T =548℃.

(a) How much eutectic will be present in the finally solidified bar assuming no solid diffusion?

(b) At a solidification velocity of 310-cm/s,do you expect significant

diffusion in the solid?[Note:S D =0.29*RT e

120.31-2cm /s;R=1.99 cal/(mol)(°K).]

Chap.3 CELLULAR SOLIDIFICATION

3-2 An Al-1%Cu alloy is grown by normal freezing at 3*4

10-cm/s with convection completely suppressed.(The phase diagram for this alloy is as shown schematically in Fig.2-3,E C =33%Cu,SM C =5.65%Cu,

M T =660℃,E T =548℃,and constant k and l m ;L D =3*510-2cm /s.)

3-3 What thermal gradient would be required to maintain the plane front in Prob.3-2,according to the Mullins and Sekerka interface st ability criterion?(Assume the thermal conductivity of the solid is hal f that of the liquid;σ=1.2*610-cal/2

cm .The volumetric heat of fusion can be calculated from Appendix B.)