MEE 312 – Engineering Materials

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MEE 312 – Engineering Materials

Homework 6

Due Wednesday 15  in class


1)  Briefly (in a single phrase or short sentence) describe/define the following terms in your own words and, if relevant, include an example:


  1. Strain hardening f)    Residual stresses
  2. Cold working g)   Annealing
  3. Springback h)   Polygonized subgrain structure
  4. Frank-Read source i)    Recrystallization temperature
  5. Texture strengthening j)    Hot working



2)  Some of the key mechanical properties of 2024 aluminum alloy (AA), obtained from tensile testing (MatWeb), are shown below:

Mechanical Properties
Modulus of Elasticity 10,600 ksi
Yield strength 11 ksi
UTS 27 ksi


  1. Draw the engineering stress-strain curve for 2024 AA (qualitative). Annotate the stress-strain diagram with the mechanical properties above and their respective values.
  2. On the same stress-strain diagram, using a dashed line, construct the stress-strain curve (qualitative) for a 2024 AA that has been subjected to 50% cold work. Explain the following:
    1. Would you expect the modulus of elasticity (stiffness) to differ between the two curves? Why or why not?
    2. Would you expect the yield strength and UTS to be higher or lower for the cold-worked material and why?
  • Would you expect the ductility to be higher or lower for the cold-worked material and why?



3)  Metals with what type of crystal structure are least responsive/receptive to cold working?  Most responsive/receptive?





4)  Data from a tensile test conducted on a metallic specimen is provided in an MS Excel spreadsheet (tensile_raw.xlsx).

  1. a) Convert these “semi-raw” measurements to an engineering stress-strain curve and a true stress-strain curve. Plot both curves on the same set of axes.
  2. b) Briefly describe (in words) how you would determine the stiffness, yield strength, UTS, ductility, and toughness of the material (no need to go through the actual calculations).
  3. c) Determine the strain-hardening exponent n for the plastic portion of the stress-strain curve. What type of crystal structure do you think the metal has?  (Extra Credit)



5)  Are polycrystalline ceramics responsive to cold working?  Amorphous ceramics?  Thermoset polymers?  Thermoplastic polymers?  Why or why not?  If yes, is the strain hardening mechanism the same as in metals?



6)  Fill in the table below as it relates to the different stages of annealing:


Stage Recovery    
Change in microstructure   New grains nucleate Grains enlarge
Change in mechanical properties     Further reduction in strength, further increase in ductility
Temperature Below T_rc   Well above T_rc



7)  Reproduce Example 8-5 on pp. 289-290 of the textbook (7th ed.) in your own words.  (Don’t just copy things down without thoroughly understanding each step.)  What did you learn about the interplay between cold working and annealing in deformation processing?










8)  Consider the following material property data obtained experimentally as a material was progressing through the three different stages of annealing:


Annealing Temperature (C) Electrical Conductivity (ohm-1 cm-1) Yield Strength (MPa) Grain Size (µm)
400 3.04 E5 86 100
500 3.05 E5 85 100
600 3.36 E5 84 100
700 3.45 E5 83 98
800 3.46 E5 52 30
900 3.46 E5 47 31
1000 3.47 E5 44 70
1100 3.47 E5 42 120


  1. Estimate the recrystallization temperature? How do you know?
  2. Estimate the grain growth temperature? How do you know?
  3. Estimate a suitable temperature for a stress-relief anneal.
  4. Estimate a suitable temperature for hot working.



9)  For each of the qualities/characteristics below, list whether it corresponds to cold working (CW), hot working (HW), or both.


Reduces ductility                                                                    Suited to form & shape large parts


Provides good surface finish                                                 Reduces porosity


Deforms material above T_rc                                               Produces anisotropic behavior


Does not increase strength                                                   Increases strength


Deforms material below T_rc                                               Provides poor surface finish


Easier to control dimensional                                               Harder to control dimensional

accuracy                                                                                accuracy


Material continuously recrystallizes                                     Decreases stiffness (modulus of

during deformation                                                               elasticity)


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