EMA 4223 April 2007

Mechanical Behavior Example Test 4

Name ___________________________ UFID # ____________________

[Each Question is worth 20 points unless noted otherwise.]

1. (a) Sketch creep curves for a typical metal, polymer and ceramic. Indicate the temperature of each relative to a critical temperature, i.e., T_M or T_g. Place these curves on the same graph in relative proportion to each material.

(b) On the creep deformation map shown below, fill in the appropriate regions with the appropriate titles. Assume typical behavior for a polycrystalline material of a ceramic or metal.

2. A cylindrical specimen creeps at a constant rate during 10,000 hours when it is subjected to a constant load of 1000 N. The initial diameter and length of the specimen are 10 and 200 mm, respectively, and the creep rate is 10^-7 h^-1. Find:

(a) The length of the specimen after 10,000 hours.

(b) The true and engineering strains after 10,000 hours.

(c) The true and engineering stresses after 10,000 hours.

Show all work!

3. (a) You are asked to select a material which will resist power-law (dislocation) creep. Which criteria would you use (based on what you have learned in class)?

(b) You are asked to select a material that will resist diffusional flow. Which criteria would you use (based on what you have learned in class)?

(c) You are asked to select a material that will resist creep in polymeric materials. Which criteria would you use (based on what you have learned in class)?

4. An amorphous polymer has a glass transition temperature of 100°C. A creep modulus of 1 GPa was measured after 1 hour at 75 °C. Using the Williams-Landel-Ferry expression, determine the time required to reach this modulus at 85°C. The WLF equation is: ln a_T = - C₁(T-T_s) / (C₂ + T – T_s). If the reference temperature is T_g, then C₁ = 17.5 and C₂ = 52 °K. If the reference temperature is taken about 50°C above T_g, then C₁ = 20.4 and C₂ = 101.6°K.

5. Consider a bolt which is tightened onto a rigid component so that the initial stress in its shank is s_i. The length of the shank must remain constant, i.e., the total strain, e_tot, remains constant. Creep strain can replace elastic strain, causing the stress to relax, i.e., e_tot = e_elastic + e_creep. Derive an expression for the relaxation time in terms of the initial stress and the elastic modulus based on power law creep. Relaxation time is arbitrarily defined as the time taken for the stress to relax to half its original value.

Assume e_creep = B sⁿ.

6. EXTRA CREDIT (a) [5 points] Much of creep behavior relies on an Arrehnius-type relationship which includes its dependence on the exponential term, e ^{– Q/RT}. Why is the symbol for the exponential term named “e”? [It is not because it stands for exponential.]

(b) 10 points – Who are the authors of your text book?