Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Textbook Question
Chapter 6.13, Problem 15KCP
(a) Why does slip in metals usually take place on the densest-packed planes? (b) Why does slip in metals usually take place in the closest-packed directions?
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Chapter 6 Solutions
Foundations of Materials Science and Engineering
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- 1. There are three slip systems on a FCC octahedral plane, i.e. one of the {111} planes. Assume a2 MPa tensile stress is applied along the [100] direction of a gold single crystal, whose criticalresolved shear stress is 0.91 MPa at room temperature. Demonstrate quantitatively thatmeasurable slip will not occur on any of the three slip systems containing the (111) plane as aresult of this applied tensile stress. (Hint: Schmid’s law) 2. Identify the Burgers vector (using vector notation) of a screw dislocation that can cross-slipbetween (111) and (111) planes of an FCC crystal (Hint: Use Weiss zone law). 3. Why are dislocations not considered thermodynamic equilibrium defects like vacancies?Explain by describing the relative interplay between entropy and enthalpy affecting the Gibbsfree energy of the dislocations-containing material system.arrow_forwardA single crystal of iron (BCC) is pulled along [123]. Which is the first slip system to operate? Use {110}<111> slip systems. Hint: Use Schmid’s law to solve the problem. Also, you need to use Weiss zone law to identify the slip systems Please follow the approach as shown below. In BCC, there are six non-duplicating planes of {110} type: (011), (101), (110), (1-10), (01-1), and (10-1). You need to use then the appropriate single slip directions under <111> family of directions to get the valid slip system combinations (twelve of them). Note that there are more than one possible single slip directions under <111> family of directions. So, you definitely need the zone law to ascertain which slip direction(s) satisfy in relation to each possible slip plane (as given above) and then only you can find out the 12 independent slip systems of {110}<111> type. Then you can apply Schmid's law to solve the problem.arrow_forwardA single crystal of aluminum is loaded under a stress state such that ơ11 = 250 kPa, 022 = 50 kPa , o33 = 10 kPa and T23 = T 31 = T 12 = 0 Assume that slip occurred on the (111) plane in the [1 -1 0] direction and only on this slip system. What is the shear stress on this slip system?arrow_forward
- A single-crystal rod of FCC nickel is oriented with the [001] direction parallel to the rod axis. a. Identify the type of slip system involved in the plastic flow of nickel. b. How many such slip systems are in a position to be activated at the same time when the load is applied parallel to this crystallographic direction? c. What is the Schmid factor for this slip system? (The angles between the {100} and {110} and {100} and {111} planes are 45 and 54.7°, respectively.)arrow_forward3) The strength of a titanium piece is found to be 65,000 psi when the grain size is 17 x10-6 m and 82,000 psi when the grain size is 0.8 x10 m. What would be the 9- (a) Constants in the Hall-Petch equation Strength of this titanium piece when the grain size is reduced to 0.2 x10 m. (9)arrow_forwardDerive all possible slip systems in a face centered cubic unit cell. (Remember slip systems consist of close packed planes in close packed directions) (a) List all the possible permutation of slip systems. (b) How many slip systems do you have if you discounted redundant planes? List all of them. (Explain how you determined that the planes were redundant) (c) How many slip systems do you have if you also discounted negatives of slip directions? List all of them. (d) Out of the remaining slip systems, how many of them are valid? List all the valid slip systems and explain your answer either mathematically or graphically. (e) Draw all the independent slip systems that you get from the problem before.arrow_forward
- An FCC crystal is pulled in tension along the [100] direction. (a) Determine the Schmid factor for all slip systems. (b) Identify the slip system(s) that would be activated first. (c) What is the tensile stress under which this crystal will flow plastically? (t. = 50 MPa)arrow_forwardSlip Systems 1. One slip system for the BCC crystal structure is {110}(111). In a manner similar to Figure 7.6b, sketch a {110} -type plane for the BCC structure, representing atom positions with circles. Now, using arrows, indicate two different (111) slip directions within this plane. E D (a) Figure 7.6 B A D E F (b)arrow_forwardA single crystal of silver is oriented so that the (111) slip plane is perpendicular to an applied stress of 50 MPa. List the slip systems composed of close-packed planes and directions that may be activated due to this applied stress.arrow_forward
- a) Sketch and label tensile stress-strain curves for a typical BCC and FCC metal and explain the salient differences from a slip system perspective Explain the Fick’s two laws of diffusion and discuss their common uses. What atomic factors govern the extent of solid solubility?arrow_forwardWhat is a solid solution? In general, what is its implication on the mechanical behavior of metals (i.e., increase or decrease in strength)?arrow_forwardHelp me pleasearrow_forward
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