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University of Ontario Institute of Technology

Department of Auto, Mech. And manuf. Engineering

Manufacturing and Operation Processes (MANE 3190)

Mid-term Examination

Student name

Student # October 8, 2013

CLOSED BOOK EXAM

PLEASE ANSWER ALL QUESTIONS Question 1 (10 Marks)

a- A solid cylindrical specimen 100 mm high is compressed to a final height of 40 mm in two steps between frictionless platens; after the first step, the cylinder is 70 mm high. Calculate the

engineering strain and the true strain for both steps compare them, and comment on your

observations. (5 Marks)

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b- Assume that the specimen in problem (b) has an initial diameter of 80 mm and is made of 1100-O aluminum. Determine the load required for each step. (5 Marks)

(Note that for 1100-O aluminum, K=180 MPa and n=0.020)

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Question 2 (7 Marks)

a- If e is the engineering strain, is the engineering stress show that the true stress can be represented by: (5 Marks)

b- For an alloy, the following true stresses produce the corresponding plastic true strains, prior to necking: (5 Marks)

True Stress (MPa) True Strain

280 0.177

324 0.259

If the material that behaves according to the equation = K n (MPa) and on the basis of the above information, compute the engineering stress necessary to produce an engineering strain of 0.25.

-----------1

-----------2 From 1 and 2:

n= 0.383 & K=543

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Question 3 (10 Marks)

a- Explain how the modulus of resilience of a material changes, as it is strain-hardened:

1. For an elastic, perfectly plastic material. (3 Marks)

Modulus of Resilience = Y2/2E

For elastic, perfectly plastic material the yield stress and modulus of elasticity are const. The modulus of

resilience remains const.

2. For an elastic, linearly strain-hardening material. (3 Marks)

Modulus of Resilience = Y2/2E

For elastic linearly strain-hardening material, the yield stress increases as it is cold worked while the

modulus of elasticity remains const. thus, the modulus of resilience increases as the amount of cold work

increases.

b- If you remove the layer of material ad from the part shown in the figure, using grinding, which way will the specimen

curve? Answer with drawing only Note that: layers od and ef have tensile residual stress while layers

ad and oe have compressive residual stress. (4 Marks)