Materials Science and Engineering (MECH317) Midterm Exam (Spring, 2013) Time allowed for 120 minutes and attempt four questions. 1. For CsCl structure, atomic radius of ions is 0.17nm, 0.18nm. Electronegativities of ions are X Cs =0.7, X Cl =3.0 and atomic weights of Cs and Cl atoms are 132.9 g/mol, 35.5 g/mol respectively. Avogadro’s number is 6 x 10 23 . Answer the following questions. [30 pts] (a) What crystal structure would you predict? [10 pts] (b) What is the ionic percentage? [10 pts] (c) Calculate the theoretical density of CsCl. [10 pts] 2. For a linear polymer molecule, the total chain length L depends on the bond length between chain atoms d, the total number of bonds in the molecule N, and the angle between adjacent backbone chain atoms θ, as follows: L = Nd sin u 2 | \ | . | (2.1) Furthermore, the average end-to-end distance for a series of polymer molecules r in Fig. 2a is equal to r = d N (2.2) A linear polyethylene has a number-average molecular weight of 300,000 g/mol; compute average values of L and r for this material. Here, the atomic weights of carbon and hydrogen is 12.01 g/mol and 1.008 g/mol respectively, and geometric parameters are d=0.154 mm and θ=109° for polyethylene as shown in Fig. 2b. [20 pts] Fig. 2a Schematics of a single polymer chain molecule Fig. 2b Structure of polyethylene 3. When a uniaxial force applied to a cylinder of a pure metal single crystal, resolved shear stress will produced on a slip system. Answer the following questions. [25 pts] (a) Describe how to define the slip system, i.e. slip plane and slip direction of the single crystal, and calculate the resolved shear stress from Fig. 3a. [10 pts] (b) Copper (Cu) has the FCC crystal structure (Fig. 3b), and the resolved shear stress acts on the (111) and [011] slip system of a unit cell. Calculate the resolved shear stress if a stress of 1.1 MPa is applied in the [001] direction of a unit cell. [10 pts] (c) Define the critical resolved stress and explain how to predict the yield stress from the critical resolved stress. [5 pts] Uniaxial force F Cross sectional area A s l i p d i r e c t i o n F A F s l i p d i r e c t i o n F A F z y x Fig. 3a Schematics of a slip system with uniaxial force Fig. 3b FCC unit cell 4. A famous scientist J.E. Gordon mentioned “The worst sin in an engineering material is not lack of strength or lack of stiffness, desirable as these properties are, but lack of toughness, that is to say, lack of resistance to the propagation of cracks. Before one can start arguing about how tough materials ought to be, one must be able to measure how tough they are.” Answer the questions below. [25 pts] (1) Differentiate the process of a product design based on strength, stiffness and toughness, and suggest a specific example of a product design based on toughness including material selections, design criteria and any technical/practical issues to consider. [15 pts] (2) Propose any two test methods to evaluate the toughness of a material, and explain how the toughness can be measured by proposed test methods. [10 pts]