Solve this and show all of the work. I want to see all of the formulas with all the calculations for every step. crit 'critSuppose the critical shear stress, T. for slip on the {110}/(111) slip systems of a BCC metal is50 MPa. Assuming the model below and a value of 3 for k, determine σ. for {200}/(100) slipsystems in this metal. Here he is the slip-plane spacing, 6 is the magnitude of the Burger's vectorfor the corresponding slip direction, and c, like k, is another material constant. (You do not need toknow the value of c to obtain a numerical value for T crit, {200}/(100) •hkldhklTom-ex cxp(-4)Т.crit=cXb

Solve this question step by step with full calculations.

Answered: crit ' crit Suppose the critical shear…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Assume k = 5 in the modelτ crit = c exp(−kd hkl / b) .(a) Determine the ratio ofτ crit for the {222}/<110> slip systems to that for the {110}/<111> slipsystems in a BCC metal.(b) Do the same for an FCC metal comparing the {220}/<111> and {111]/<110> slip systems;i.e., compute the ratioτ crit 220{ }/ 111 :τ crit 111{ }/ 110 .(c) Here the aim is to see the impact of confusing the preferred slip systems in BCC with thosein FCC metals. In principle, one would want to examine the ratiosτ crit 111{ }/ 110 :τ crit 110{ }/ 111andτ crit 110{ }/ 111 :τ crit 111{ }/ 110 for BCC and FCC metals, respectively; however, it is necessaryto consider {222} type planes for the BCC structure and {220} type planes for the FCCstructure. Why?
Consider a metal rod with a critical resolved shear stress of 40 MPa for a specific crystallographic plane (hkl). The angle between the normal to the plane and the applied force is 30 degrees, and the angle between the slip direction and the force is 15 degrees. Two force levels of F1 = 75 N and F2 = 40 N is applied. The cross-sectional area of the rod is 1 mm^(2). Will the slip initiate at the two force levels? Select one: a. F1: Yes, F2: No b. F1: No, F2: No OC. F1: Yes, F2: Yes Od. F1: No, F2: Yes
Consider a metal rod with a critical resolved shear stress of 40 MPa for a specific crystallographic plane (hkl). The angle between the normal to the plane and the applied force is 30 degrees, and the angle between the slip direction and the force is 15 degrees. Two force levels of F1 = 75 N and F2 = 40 N is applied. The cross-sectional area of the rod is 1 mm^(2). Will the slip initiate at the two force levels? Select one: O a. F1: Yes, F2: No O b. F1: Yes, F2: Yes O C. F1: No, F2: Yes d. F1: No, F2: No
If a rod of single-crystal copper (FCC) is pulled in tension in the [210] direction (i.e. force direction) at a tensile stress of 50 MPa, slip will occur in the [0 1 1] direction on the (1 1 -1) plane. Use this information to answer the following questions. Which of the following is the critical resolved shear stress on the slip plane in the slip direction? Group of answer choices 24.49 MPa 34.65 MPa 12.25 MPa 102 MPa
There is a table provided to help organize answers. In many BCC metals, there are more slip systems than those mentioned, but we will ignore them for this problem. Thank you
Consider an iron single crystal with CCC crystal structure oriented in such a way that a tensile stress is applied to the along one direction [010]. a) Calculate the shear stress resolved along a plane (110) and a direction when a tensile stress of 52 MPa is applied. The normal to the slip plane forms 45° with traction direction. the direction of slip forms 55º with the traction direction. b) If the slip occurs in one plane (110) and in one direction and the critical resolved shear stress is 30 MPa, calculate the magnitude of tensile stress that must be applied to initiate the flow.
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.
7-5
Consider a single crystal of silver oriented such that a tensile stress is applied along a [001] direction. If slip occurs on a (111) plane and in a 101 direction, and is initiated at an applied tensile stress of 1.1 MPa (160 psi), compute the critical resolved shear stress. i MPа
A BCC mono crystal is oriented such that the direction [001] is parallel to the direction of application of the effort. If the resolved shear stress in the direction of slip is 12,000 psi, determines the magnitude of the moment applied (and that is required) to cause slippage in the steering (110)
Consider an iron single crystal with CCC crystal structure oriented in such a way that a tensile stress is applied to the along one direction [010]. a) Calculate the shear stress resolved along a plane (110) and a direction [11] when a tensile stress of 52 MPa is applied. The normal to the slip plane foms 45° with traction direction. the direction of slip forms 55° with the traction direction. b) If the slip occurs in one plane (110) and in one direction [ī11] and the critical resolved shear stress is 30 MPa, calculate the magnitude of tensile stress that must be applied to initiate the flow.
Consider a single crystal of some hypothetical metal that has the FCC crystal structure and is oriented such that a tensile stress is applied along a [11 2] direction. If slip occurs on a ( 111) plane and in a [0 11] direction, and the crystal yields at a stress of 5.12 MPa, compute the critical resolved shear stress. CRITICAL RESOLVED SHEAR STRESS • CRITICAL RESOLVED SHEAR STRESS (T, THE MOST FAVORABLY ORIENTED SLIP SYSTEM WHEN SHEAR STRESS IS AT J: SLIP IN A SYSTEM STARTS ON CRSS THIS CRITICAL VALUE • MINIMUM SHEAR STRESS REQUIRED TO INITIATE SLIP • SINGLE CRYSTAL PLASTICALLY DEFORMS WHEN: T, > T, CRSS OR TR(max) =T CRSS 'R Tcrss (cos o cos A)max

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