CIVE.3100 ENGINEERING MATERIALS EXAM #2: METALS, DIFFUSION, PHASE DIAGRAMS, STRESS STRAIN DIAGRAMS, AND RULE OF MIXTURES Print Name: Section: Date:

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1 CIVE.3100 ENGINEERING MATERIALS EXAM #2: METALS, DIFFUSION, PHASE DIAGRAMS, STRESS STRAIN DIAGRAMS, AND RULE OF MIXTURES Print Name: Section: Date: You may NOT use the back of any page if additional workspace is needed. You may NOT use an equation sheet. Blank paper for additional workspace is available from the Instructor upon request. Any communication device found to be on during this exam will result in a grade of ZERO (0) for the student with the device. Questions (2 Points Each - 20 Points Total): 1. Write the equation for Fick s Second Law of Diffusion and detail the variables in this equation. 2 C s = Surface concentration of element in gas diffusing into the surface. C 0 = Initial uniform concentration of element in solid. C x = Concentration of element at distance x from surface at time t1. x = Distance from surface D = Diffusivity of solute t = time erf = Error Function 2. Write the equation for Gibb s Phase Rule and detail the variables in this equation. P + F = C + 2 P = Number of phases which coexist in a chosen system C = Number of Components in a System (element, compound, or solution) F = Degrees of Freedom (Number of variables (e.g. Pressure, Temperature, Composition) that can be changed independently without changing the state of the phase or phases) 3. Write the equation for the Lever Rule and detail the variables in this equation. Lever Rule: X l + X s = 1 X s = Wt fraction of Solid Phase X l = Wt fraction of Liquid Phase

2 4. In your own words, describe a binary isomorphous alloy system. Mixture of two (2) metals that are completely soluble in each other in liquid and solid state (i.e. Meet the Hume-Rothery Solid Solution Rules). 5. In your own words (or sketch), describe an edge dislocation. A line defect (dislocation) created by insertion of extra half planes of atoms 6. In your own words (or sketch), describe interstitial diffusion. Atoms move from one interstitial site (i.e. space) to another. 7. Write the Rule of Mixtures equation for isostress conditions and detail the variables in this equation. E = Elastic Modulus V = Volume Fraction f = Fiber m = Matrix 8. Write the Rule of Mixtures equation for isostrain conditions and detail the variables in this equation. E = Elastic Modulus V = Volume Fraction f = Fiber m = Matrix 9. In your own words (or sketch), describe a grain boundary. A planar defect formed in the narrow region between two grains. 10. In your own words, describe diffusion. Diffusion is a process by which matter is transported through other matter. CIVE Exam 2 Solution Page 2 of 7

3 Problems: (1 20 points, 2 30 points, 3 15 points, 4 15 points) NOTICE: You must detail your answers (i.e. show your work) for these four problems for full credit. You may use additional paper provided at the front desk if needed. Make sure you reference the problem number if you use an additional blank page(s). You may NOT use the back of pages. 1. The surface of a steel gear made of ASTM 1020 steel (0.20 wt % C) is to be gascarburized at 1000 C (1832 F). Calculate the time necessary to increase the carbon content to 0.60 wt % at in. below the surface of the gear. Assume the carbon content of the surface to be 1.00 wt %. D (C in steel) at 1000 C = m 2 /s. GIVEN: C s = 1.00%, C 0 = 0.20%, C x = 0.60%, D 1000 C = 2.98x -11 m 2 /s erf Interpolating from provided erf Table: z = t = 3.68x10 4 seconds = 10.2 hours CIVE Exam 2 Solution Page 3 of 7

4 2. You have been provided the tensile test results shown in Figure 1. The specimen was loaded to fracture. Using these results, determine the following: Young s Modulus. The Yield Stress at 0.2% offset. The Ultimate Tensile Stress. The percent elongation at fracture. ULT Y Stress () (MPa) Strain () (mm/mm) Figure 1. Tensile Test Results for Problem 2. fracture = 0.197% ANSWERS: E = 8400 MPa/0.001 = 8,400,000 MPa = 8.4 GPa. Y = 9500 MPa ULT = MPa fracture = 1.97% CIVE Exam 2 Solution Page 4 of 7

5 3. You are given the binary isomorphous copper-nickel phase diagram shown in Figure 2. For a 35 wt% Cu 65 wt % Ni alloy at a temperature of 1350 C, determine the following: The phases present. The weight percent of each phase. SOLUTION: w s = 61% w l = 72% w o = 65% Figure 2. The binary isomorphous copper-nickel phase diagram. %%. % %%. % CIVE Exam 2 Solution Page 5 of 7

6 4. You are reinforcing an existing precast concrete column between two floors in an existing structure by placing new concrete around the existing column. The exiting precast concrete column is 12 inches square. You plan to place new concrete around the existing concrete column in a 24 inch diameter circle. Figure 3 presents a cross-section of the composite column. Previous testing has determined the elastic modulus of the precast concrete to be 2,200 ksi and the modulus of elasticity of the new concrete to be 4,400 ksi. Determine the elastic modulus for the composite concrete column. 24 inch diameter new concrete column 12 inch square existing precast concrete column Figure 3. Composite Column Cross-section (NTS). A composite = r 2 = ( )(12 inches) 2 = in 2 A old = (12 inches) 2 = 144 in 2 A new = A composite - A old = in in 2 = in E composite = 3700 ksi CIVE Exam 2 Solution Page 6 of 7

7 EXTRA CREDIT: (5 points) What is the commonly used value of the elastic modulus of steel? Provide your answer in units of kips per square inch. 29,000 ksi USEFUL INFORMATION? E = mc 2 1 ft = 12 inches = m CIVE Exam 2 Solution Page 7 of 7