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Mid-Term Exam: ENGR 2220U: 40734 Section 2; Fall 2008 Time allowed - 70 minutes Q 1 (7 marks) a) What do we mean by the term crystalline materials? They are solid materials where atoms, ions or molecules are characterized by a periodic and repeating three-dimensional array. b) How will you describe a unit cell of a crystalline structure? The unit cell has a periodic and repeating three-dimensional array c) How will you calculate the atomic packing factor of SC structure? Show all steps. APF
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   Mid-Term Exam: ENGR 2220U: 40734 Section 2; Fall 2008 Time allowed - 70 minutes   Q 1 (7 marks) a)   What do we mean by the term crystalline materials? They are solid materials where atoms, ions or molecules are characterized by a  periodic and repeating three-dimensional array.  b)   How will you describe a unit cell of a crystalline structure? The unit cell has a periodic and repeating three-dimensional array  c)   How will you calculate the atomic packing factor of SC structure? Show all steps. APF = Vs/Vc = [(4/3) П  (0.5a) 3 ]/ [a 3 ] = 0.52 Q 2 (6 marks) a)   What is the difference between polymorphism and allotropy? Allotropy refers mainly to elemental solids while polymorphism can refer to any material.  b)   Give one example of each. Allotropy: diamond Polymorphism: silica c)   Mechanical properties in crystals depend upon direction. Explain why many polycrystalline materials in general have isotropic properties. In polycrystalline materials, the orientation of the individual grains is random. Each grain can be anistropic  but a material made up of grain aggregate behaves isotropically. Q 3 (7 marks) a)   How do impurity atoms affect the yield strength of alloys and why? They improve the yield strength. Adding impurities result in the formation of a second phase that might be stronger mechanically than the initial phase.  b)   Can you explain this affect by discussing the structure of common glass? Cations present in the silicates help in bonding the SiO 4  tetrahedra together. c) Briefly explain why small-angle grain boundaries are not as effective in interfering with the slip process (movement of dislocations) as are high-angle grain boundaries. Grain boundaries are barriers to slip. The strength of these barriers increases with increasing angle of misorientation which itself gets larger as the angle of grain boundary increases.   Mid-Term Exam: ENGR 2220U: 40734 Section 2; Fall 2008 Time allowed - 70 minutes   Q 4 (10 marks) What kind of structures would the following ceramics form? a) CsBr, b) MnI 2   CsBr Coordination# = r  cation/ r  anion = 0.170/0.196 = 0.867 which is between 0.732 and 1 Therefore, it is a cubic (CsCl) structure MnI 2 : Coordination# = r  cation/ r  anion = 0.067/0.220 = 0.305 which is between 0.225 and 0.414 Therefore, it is a ZnS structure. Q 5 (10 marks) In a tensile test of a metal single crystal, it is oriented such that the normal to the slip plane is at an angle of 55 °  with the tensile axis. Three possible slip directions make angles of 22 ° , 43 ° , and 75 °  with the same tensile axis. a) Which of these three slip directions is most favored?  b) If the plastic deformation begins at a tensile stress of 2.2 MPa, determine the critical resolved shear stress for this metal. a)   Slip is favored when the value of cos φ  cos λ   is maximum (largest cos λ   here.) So that direction is: Cos (22 ° ) = 0.92 Cos (43 ° ) = 0.73 Cos (75 ° ) = 0.258 22 °  slip direction  b) = 2.2 MPa Cos (55 ° ) Cos (22 ° ) = 1.17 MPa   Mid-Term Exam: ENGR 2220U: 40734 Section 2; Fall 2008 Time allowed - 70 minutes   Q 6 (15 marks) A cylindrical bar of metal having a diameter of 18.8 mm and a length of 198 mm is deformed elastically in tension with a force of 49,400 N. Given that the elastic modulus and Poisson's ratio of the metal are 67.1 GPa and 0.34, respectively, determine the following: (a) The amount by which this specimen will elongate (in mm) in the direction of the applied stress. (b) The change in diameter of the specimen (in mm). Indicate an increase in diameter with a positive number and a decrease with a negative number. a) Combining Hooke's law - i.e., with the definition of stress for a cylindrical specimen--i.e., and also incorporating the expression for longitudinal strain--i.e., we get the following: Then solving for the change in length, Δ l , leads to and, for this problem, the following value for Δ l : = 0.525 x 10 -3  m = 0.525 mm   Mid-Term Exam: ENGR 2220U: 40734 Section 2; Fall 2008 Time allowed - 70 minutes   (b) When the definition for Poisson's ratio--i.e., is combined with the expression for transverse strain, and longitudinal strain, The following equation results: and, finally solving for the change in diameter, Δ d  , leads to which, for this problem, yields the following value for Δ d  : = - 0.0169 mm  Q 7 (15 marks) An iron-carbon alloy containing 0.55wt% C is exposed to an oxygen rich and virtually carbon-free atmosphere at 1325 K (1052 ºC). Under these conditions the carbon diffuses from the alloy and reacts with the oxygen at the surface, that is, the concentration of carbon at the surface position is maintained essentially at 0 wt% C. (This process of carbon depletion is termed as decarburization.) At what position will the carbon concentration be 0.25 wt% after a 10-h treatment? The value of D at 1325K is 4.3 x 10 -11  m 2 /s.
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