9. Consider a metal rod, whose grain size can be adjusted by different processing techniques.The graph below shows how the yield stress changes with grain size d; the x-axis islogarithmic.The curve reaches a limiting value of 60 MPa as indicated by the horizontal dashed line on the y-axis,for very large grain sizes. Also, you are given the information that at d = 25 microns (vertical dashedline), the yield stress is 100 MPa.Using this information, what will be the yield stress at d = 5 microns? Select the closest numericalvalue.Use the Hall-Petch relation in working out your answer.Yield stress (MPa)●●228882S1301201101006010⁰10¹10²Grain size d (microns)132.4 MPa149.4 MPa165.2 MPa156.3 MPa10

The Hall Petch equation is given by the formula.σ=σ0+k/dDetermine the constant (k) based on the…

Answered: The curve reaches a limiting value of…

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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4. The mechanical properties of a given titanium alloy (Ti-6Al-4V) are E = 114 GPa, σy = 880 MPa and Kic = 75 MPa√m. What is the approximate plastic zone size? How large must a part be made if we want to test its K₁ using LEFM?
You are given three metal test samples, with the same chemical composition and differing grain sizes: A: 5.0, B: 10.0 and C: 20.0 microns. Samples A and B have been tested and have yield stresses of 142.4 MPa and 135.8 MPa (all numbers are rounded off to the 1st decimal point). Based on this information, which of the following values do you think will be the closest to the yield stress of Sample C? In calculating the answer, use the Hall-Petch relation between yield stress of a metal o vield and the grain size of the metal d, which is Oyield = 00 + kd¬1/2 where k and og are constants. (This question has only one correct answer) а. 100.6 MPa b. 131.1 MPa С. 152.4 MPa O d. 115.8 MPa е. 128.1 MPa
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(2) Consider a homogeneous structure made out of metal subjected to homogeneous boundary conditions t = σn. For o corresponding to uniaxial, biaxial and shear stress state, calculate the stress at which the material yields.
1. A part made of Aluminum 6061-T6 has a yield strength = 400 MPa. For each stress state below, draw all 3 Mohr's circles, find the principal stresses, and calculate the safety factor against yield using both the distortion-energy (von Mises) and maximum shear stress (Tresca) criterions. (If relevant) A clearly labeled diagram (or diagrams) clearly pertaining to your analysis with a coordinate system and relevant labels. Final answer with appropriate units and significant figures. You can use the fprintf() command in MATLAB to format numerical results A 2-3 sentence reflection on your answer. Does it make sense? Why or why not? What are some implications?
What would be the compressive stress in MPa developed in the silica glass furnace tube constrained in the way illustrated in the figure if it were heated to 1000C?
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1. For the stress-strain curve shown below, please estimate the properties indicated. (a) Fracture Strain Please do your work on a separate sheet of paper, and put your answers in the boxes on the right. Be sure to include the proper symbol and units. Stress Strain 70 60 50 Stress (ksi) 240 30 20 10 70 0 0.000 60 50 Stress (ksi) 40 20 10 KULL 0 0.000 0.010 0.050 0.100 Strain (in/in) Stress Strain 0.020 0.030 Strain (in/in) 0.040 0.150 0.050 (b) Ultimate Tensile Stress (c) Fracture Stress (d) Proportional Limit (e) Elastic Modulus (1) Yield Stress (g) Tensile Toughness (Modulus of Toughness) (h) Modulus of Resilience
Suppose that o2 = 70 MPa. (Figure 1) 15 MPa O x Part B Determine the normal stress that acts on the element with orientation = -11.6°. Express your answer to three significant figures and include the appropriate units. 02 = Part C Oy = Part D μА Value Determine the normal stress oy that acts on the element with orientation = -11.6 ⁰. Express your answer to three significant figures and include the appropriate units. Tz'y' = Value Units μA Value Units Determine the shear stress Ta'y that acts on the element with orientation = -11.6°. Express your answer to three significant figures and include the appropriate units. ? Units ? ?
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Draw two schematic graphs using pencil showing a typical stress-strain curve for aluminum. The first graph should show engineering stress vs engineering strain, and the second graph should show true stress vs true strain. Label the showing: (i) elastic modulus (ii) proportional limit (iii) yield stress (iv)yield strain (v) fracture stress (vi) fracture strain on each graph. You may showboth graphs on one plot. Explain the difference between engineering stress and true stress.

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