第五章 二元相图和合金的凝固 Chapter 5 Binary Phase Diagrams and
The Solidification of Alloys
作业1：An Al-5%Cu ingot is unidirectionally solidified under the conditions of no diffusion in the solid, complete diffusion in the liquid, and local equilibrium at the interface, so that the scheil equation applies. Cs?KC0?1?fS?K?1 CL?C0?1?fS?K?1
(a) Calculate the composition of the liquid when the ingot is 50 percent solid. What is the average composition of the solid?
(b) What is the interface temperature at this point?
(c) How much eutectic and second phase θ will have formed when the ingot is completely solidified?
(d) Plot the composition profile in the solidified ingot.
Solution:
?Z?C0k0?1??C?L?(a) CL?S?k0k0k0?1?Z??C0?1???L?k0?1660℃
548℃ 5.65 33
Al-Cu系： k0?CS?5.65?0.17
CL33CL?5%??0.5?5.65?133?8.9%
5%
CS0?C0k0?0.85
Al
Cu%
CS?CLk0?1.5%
1CS0?CS?1.2% 2660?548(b) TL?TA?mCL?660??8.9%?932.7K?659.7℃
33C0.5 T?TA?m0?660?3.4??650℃
K0.17CS0???(c) 当CL?33%, CS?5.65%时，发生共晶转变。
33%?5%??1?f?0
k?1?1?f??k?133
05f?1?k0?133?0.9 5??0 (d)
Cu
33.2 0.1 5.65 0.85 0 fS
1.0
作业2.：After being slowly cooled from the austenite region, a simple iron-carbon steel exhibits a microstructure consisting of 40 percent pearlite and 60 percent ferrite.
(a). Estimate the carbon concentration of the steel.
(b). Describe the equilibrium microstructure that would be obtained if the steel were heated to 730℃ and held there for a long period of time.
(c). What would be the equilibrium structure of this steel if it were heated to 850℃? (d) Make sketches of all of these microstructures. Solution:
(a). Suppose the carbon concentration of this steel is X,
then 40%P?x?0.0218?100%
0.77?0.0218 x?0.4??0.77?0.0218??0.0218?0.32% （b）Ferrite +Austenite (c) Austenite (d)
作业3：Al-Cu合金相图如图所示，设分配系数k和液相线斜率均为常数，试求：
（a）含1%Cu固溶体进行缓慢的正常凝固，当凝固分数为50%时所凝固出的固体成分； （b）经过一次区域熔化后在x?5处的固体成分，取l?0.5；
（c）测得铸件的凝固速度R?3?10?4cm/s，温度梯度G?30℃/cm，扩散系数
D?3?10?5cm2/s时，合金凝固时能保持平面界面的最大含Cu量。
解：
?Z?（a）CS?C0k0?1???L? k0?k0?15.655.65?1?1%???0.5?33?0.286%
33CS5.65??0.17 CL335.65?5kZ??0????5.65??（b）CS?C0?1??1?k0??eL??0.01?1??1??e33?0.5??0.85%
33?????? m?660?548?3.4
33%（c）成分无过冷时的临界点：
GmC01?k0?? RDk0k0GD303?10?5?0.17C0??????18%
Rm1?k03?10?43.4??1?0.17?
作业4： 1) 用冷却曲线表示50%的Pb-Sn合金的平衡结晶过程，画出室温平衡组织示意
图，标上各组织组成物；
2） 计算该合金室温组织中组成相的相对重量； 3） 计算该合金室温组织组成物的相对重量；
4） 指出该合金系室温组织中含βⅡ最多的合金组成物；
5） 指出该合金系室温组织中共晶体最多和最少的合金成分或成分范围。
解答：
T 1）
t A
tB
L 1
L→α 1
β
α 2 L→α+β 2 97.5 19 61.9
α . . .. βⅡ
2) 室温组成相： ?%?98?50?100%?48.97%
98?0.02 ?%?1??%?51% 3) 共晶T：?????%?50?19?100%?72%
61.9?19 ?'初%?1??????%?28% 室温：?初%??'初%?98?19?100%?22.57%
98?0.02 βⅡ%=?'初%??初%?5.43% 4）含βⅡ最多成分为19%Sn.
5) 含共晶体最多成分为 61.9%Sn。
最少成分：C%<19%, C%>97.5S
作业5：将Fe-Fe3C相图的液、固相线近似为直线，试分析含碳0.4%合金在100cm长的水平圆模中顺序凝固结束时，沿棒长度方向的组织与成分分布。并求出各组织的长度，假定凝固过程中固相无扩散，液相成分完全混合且界面为平直面。 解：k0??0.09?0.17 0.53k0??1Cs??Z??k0??0.4%?1???L?
当Cs??0.09%时，
Z?0.29 即29cm为δ，剩余长度为1-0.29=0.71 Lk0??2.11?0.49 4.3k0??1?Z?Cs??k0??0.53?1???L?
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