MSE 230 Assignment 6 Fall 2013 due 10 3 10 4 Problems with an by them will not be graded but solutions will be provided problems 2 5 7 and 8 will be graded 1 A tensile stress is applied along the 001 in an aluminum single crystal a If slip initiates on the slip system 111 01 1 at a tensile stress of 7 8 MPa calculate the critical resolved shear stress b Briefly explain the difference between the applied stress the yield stress the shear stress and the critical resolved shear stress 2 a Calculate the Schmid factor for all possible slip systems for slip of a single crystal of a FCC metal pulled in the 121 Hint by using the dot product and noticing when cos and cos are zero you can save yourself some work b On which slip system s will slip occur first c If the critical resolved shear stress is 10 MPa what is the yield strength 3 In each of the following situations state the most important strengthening mechanism involved and briefly describe how that strengthening mechanism works a Adding 10 wt of nickel to copper increase the yield strength of copper by approximately 30 b Decreasing the thickness of a piece of steel by 20 using a rolling mill at room temperature results in a significant increase in yield strength approximately 40 c Polycrystalline FCC metals generally have a higher yield strength than single crystal FCC metals 4 A manufacturer s specification requires that a metal alloy have a minimum yield strength of 300 MPa and a minimum ductility of 25 elongation If you are allowed to cold work the metal to meet the specs which of the following metals alloys are candidates for usage copper brass 1040 steel see Fig 7 19 Explain why or why not for each metal 5 A brass rod 1 5 cm in diameter is deformed in tension reducing its diameter to 1 128 cm The data for brass in Fig 7 19 will be helpful in solving this problem a If the deformation process was performed in one step what was the yield stress of your brass after reduction b Again assuming one step what was the force applied to your specimen in N at the very end of the reduction process Assume you applied just enough force to make the material yield c If your deformation equipment is able to apply a force of 35 000 N to your specimen could you accomplish your deformation process in one step Please explain your answer d If you cannot accomplish your deformation process in one step what must you do to reduce the diameter of the brass rod to 1 128 cm No you can t afford to purchase a bigger machine 6 A sample of brass 60 Cu 40 Zn undergoes 30 cold work in a rolling mill and is subsequently placed in a heat treating furnace at 475 C Sketch a plot of dislocation density yaxis versus heat treating time x axis for the brass sample 7 You are working for an aerospace contractor building lightweight pressure vessels from beryllium metal 2 0 g cm3 K1c 4 MPa m y 155 MPa for rocket applications A x ray system used to search for cracks in pressure vessels can detect cracks as small as 0 1 mm in length You are asked if the system is good enough to detect all cracks that might result in rupture of the pressure vessel before plastic deformation can occur Provide a response with a calculation to back up your answer Assume Y 1 8 A researcher working on a batch of a ceramic material tested two sets of samples for fracture strength For one set of samples the specimens were tensile bars with a 10x10x100 mm3 tensile gauge section and another set were bend bars of similar size The average strength calculated for the bend bars was 40 higher than for the tensile specimens Why Bend testing of ceramics is covered in Chapter 12 9 of Callister 9 A plate of 304 stainless steel was specified by the manufacturer to be in a recrystallized condition which specifies that y 205 MPa and K1c 50 MPa m When loaded in uniaxial tension the plate fractured in a brittle manner with no evidence of plastic deformation Analysis of the fracture surface revealed that the flaw causing failure had a size a of 5 3 mm For all calculations below assume Y 1 a According to the data supplied above should the plate have failed in a brittle manner Use a calculation to support your answer b Calculate the minimum value for the yield stress that will result in brittle fracture of the stainless steel plate c Given your answer to part a do you believe that the stainless steel was in a recrystallized condition If you answered no how would you describe the condition of the stainless steel Briefly explain your answer d Aside from performing another tensile test what test or analysis could you perform on the fractured pieces to see if your hypothesis in part c was correct 10 A university located in the Midwest commissioned the design of a glass K1c 0 70 MPa m0 5 sculpture consisting of a large hanging I as shown in the figure on the next page An artist s 1 8 scale model of the sculpture did not fail even when artificially loaded to stresses simulating the hanging weight of the larger I yet the full size version failed immediately after it was hung Briefly explain how this could happen Fractu re 11 A cylindrical 1045 steel bar Figure 8 34 is subjected to repeated compression tension stress cycling along its axis If the load amplitude is 22 000 N 4950 lbf compute the minimum allowable bar diameter to ensure that fatigue failure will not occur Assume a factor of safety of 2 0 12 Three identical fatigue specimens denoted A B and C are fabricated from a nonferrous alloy Each is subjected to one of the maximum minimum stress cycles listed below the frequency is the same for all three tests Specimen A B C max MPa 450 400 340 min MPa 350 300 340 a Rank the fatigue lifetimes of these three specimens from the longest to the shortest b Now justify this ranking using a schematic S N plot
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