MSE45_Homework6_2023

MSE45: Properties of Materials Homework 6 1 1. (20 pts.) a. (10 pts.) Compute the rate of some reaction that obeys Avrami kinetics, assuming that the constants n and k have values 2.0 and 5 x 10 -4 , respectively, for time expressed in seconds. b. (10 pts.) The kinetics of the austenite-to-pearlite transformation obeys the Avrami relationship. Using the fraction transformed-time data given here, determine the total time required for 95% of the austenite to transform to pearlite. Fraction Transformed Time (sec.) 0.2 280 0.6 425 2. (15 pts.) Using the isothermal transformation diagram for an iron–carbon alloy of eutectoid composition (Figure 10.22), specify the nature of the final microstructure (in terms of microconstituents present and approximate percentages of each) of a small specimen that has been subjected to the following time–temperature treatments. In each case assume that the specimen begins at 760°C (1400°F) and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure. a. (3 pts.) Cool rapidly to 350°C (660°F), hold for 10 3 s, then quench to room temperature. b. (3 pts.) Rapidly cool to 625°C (1160°F), hold for 10 s, then quench to room temperature. c. (3 pts.) Rapidly cool to 600°C (1110°F), hold for 4 s, rapidly cool to 450°C (840°F), hold for 10 s, then quench to room temperature. d. (3 pts.) Reheat the specimen in part (c) to 700°C (1290°F) for 20 h. e. (3 pts.) Cool rapidly to 665°C (1230°F), hold for 10 3 s, then quench to room temperature. 3. (12 pts.) Similar to the hypoeutectic cooling, hypoeutectoid cooling also results in two forms of α phase: primary α phase (aka proeutectoid ferrite) and laminar α phase (eutectoid ferrite) in pearlite. On the continuous cooling transformation diagram for a 0.35 wt% C iron–carbon alloy provided at the end, sketch and label continuous cooling curves that will yield the following microstructures: a. (4 pts.) Fine pearlite and proeutectoid ferrite b. (4 pts.) Martensite and proeutectoid ferrite c. (4 pts.) Martensite, fine pearlite, and proeutectoid ferrite **Please turn in this page as the last page of your homework*** 4. (11 pts.) An aluminum wire 10 m long must experience a voltage drop of less than 1.0 V when a current of 5 A passes through it. Using the data in Table 18.1, compute the minimum diameter of the wire. 5. (17 pts.) a. (5 pts.) Using the data in Table 18.1, compute the resistance of an aluminum wire 5 mm (0.20 in.) in diameter and 5 m (200 in.) in length. b. (4 pts.) What would be the current flow if the potential drop across the ends of the wire is 0.04 V? c. (4 pts.) What is the current density? d. (4 pts.) What is the magnitude of the electric field across the ends of the wire?