1) One scenario that has been examined in the failure investigation of the Space Shuttle Columbia is the impact of a chunk of polyamide foam of mass of 1.211 kg, of dimensions of 0.508 m wide x 0.406 m long x 0.152 m tall, traveling at 457.3 m/s with a thermal heat-shielding tile, essentially composed of silica (SiO₂).

1. A) (4 pts.) Calculate the kinetic energy with which the polyamide foam hit the silica tile.

1. B) (7 pts.) Use your textbook to determine silica‘s modulus of elasticity (E), the yield stress (YS), the

ultimate tensile strength (UTS), percent elongation (the amount of strain multiplied by 100%) at

failure, the coefficient of thermal expansion (CTE), and the fracture toughness (also known as the

critical stress-intensity factor).  Use SI units.  Assume the worst case.

1. C) (6 pts.) Assume the ultimate compressive strength is equal to the ultimate tensile strength. Sketch the

stress-strain curve for silica along with the YS, UCS, MOE, RS, and the strain at the yield stress

and the strain at failure.

1. D) (7 pts.) Assume that the silica is highly efficient at transferring the load from the point of

impact and distributing the load equally over the whole tile (Cross-sectional area = .005 m² with a

thickness of 0.05 m).  Calculate the amount of energy in Joules that a silica tile would be capable

of absorbing without plastically deforming.

1. E) (1 pt.) Comparing your results of parts D and A, would the silica tile elastically absorb the impact?

1. F) (4 pts.) Compute the amount of plastic deformation that the silica tile can absorb.

1. G) (4 pts.) If the silica has a 1 mm crack from a previous incident, given the numbers from part

B, and assuming Y = 1, calculate the maximum amount of stress that the tile could take now.

Would you be safe using a shuttle tile with a 1 mm crack in it? Provide a brief explanation using

some of the quantities you have either looked up or have calculated.

2) (10 pts.) An ion gauge with a glass/metal interface (see photo) is heated under vacuum.  The interface heats up such that the glass side (“Glass, borosilicate (Pyrex)” in the accompanying tables) heats up from 298 K to 340 K, but the annealed “Super Invar” (under Miscellaneous Nonferrous Alloys” heats up only to 310 K.  Using Appendix B, determine a) the strain that the glass experiences, b) the strain that the Super Invar metal experiences, and c) the difference in strain (the strain across the interface between the two materials.  Do either the glass or the metal experience enough strain to be plastically deformed?  Do either the glass or the metal experience enough strain such that the glass/metal interface breaks?

3)  A) (5 pts.)  List a set of causes as to why your teeth might fail.

1. B) (5 pts.) Associate each cause from part A with one or more failure mechanisms in part B.

1. C) (5 pts.) What might you do to prevent premature tooth failure?

4)  You are part of a team designing a process and robots to mine the moon’s soil, do a very preliminary separation of such soil to separate aluminum-rich particles by size (Assume they will be smaller.) from other lunar soil, and then use a flying robot to transport the Al-rich particles to an aluminum refinery elsewhere on the moon’s surface.

1. A) (5 pts.) List a set of causes as to why your process and robots might fail.

1. B) (5 pts.) Associate each cause from part A with one or more failure mechanisms in part B.

1. C) (5 pts.) What might you do to prevent premature failure of any part of the lunar mining and refining?

5)  Some fish can live at depths of 5000 meters.  Assume gravity is 9.81 m/s².  Assume fish and human        bone have a yield stress of 100 MPa, a modulus of elasticity of 1500 MPa, and a Poisson’s ratio of

0.3.  Assume the density of salt water and bone are 1025 kg/m³ and 1900 kg/m³, respectively.

1. A) (3 pts.) Calculate the bulk modulus of the fish.

1. B) (3 pts.) Calculate the volumetric strain on the fish at a depth of 5000 meters.

1. C) (3 pts.) Assuming (incorrectly) that the fish is isotropic, calculate the amount of stress on the fish, and determine whether or not the fish bone is plastically deformed.

1. D) (3 pts.) Calculate the shear modulus of the fish bone.

6) (15 pts.) You have prepared a molybdenum nitride by cooling a 6 wt. % N/94% Mo mixture infinitely slowly.  A) Sketch what the material will look like after that infinitely slow cooling.  B) What is undesirable about the material in part A? C) Thoroughly describe a process, being specific about temperatures and endpoints (but not exact times), to best remediate the problem described in parts A and B.