EMA 4223                                                                              January 2007

Mechanical Behavior of Materials                                       Example Test 1A

 

Name ________________________                                      UFID # _________________

 

Each question is worth 20 points.

 

1.      The unit cell of the CsCl   is shown in the accompanying figure.  The radius of Cs+ is 0.169 nm and that of Cl- is 0.181nm.  Determine the theoretical cleavage stress for CsCl loaded in tension along [100] if the surface energy is 0.1 J/m2 and E[100] is 49 GPa.  State any assumptions you have to make to perform the calculation.

 

 

 

 

 

 

2.   For a copper BCC crystal structure determine the theoretical shear strength. The copper atom has a radius of 0.128 nm, the Young’s modulus in <111> is 192 GPa, in  <100> is 67 GPa,  and the shear modulus is 30.8 GPa.

 

 

 

 

 

 

 

 

 

3. You are a materials engineer who is called upon to design the cantilever beam for an atomic force microscope.  (Attached to the end of this beam will be a silicon or silicon nitride tip during surface measurements.)  The design requirements are that the beam must sustain a force, F, of  0.1 N  at the tip end without deflecting more than d (d =1 mm) and that the weight of the structure is minimized.  Assume that the beam has a square cross section.  The deflection of the beam (ignoring self weight) is:

 

                  d = 4 l3 F / (E t4)

 

where l is the length ( 2 mm) of the unsupported beam, E is the elastic modulus and t is the thickness.   

[The moment of inertia of a beam with square cross section is t4/12. The density,  r = M/V,  where M is the mass and V [=l t2]is the volume of the solid]

Develop a Figure of Merit for this beam so that the desired material can be selected for use.  Show the methodology based on principles learned in class.  Show all work!

 

 

 

 

 

 

 

 

 

4.   For the CaTiO3 structure calculate the angle between (a) the [100] and [111] and between (b) the [111] and [112] directions, respectively.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.   (a)  Describe the differences between melting temperature and the glass transition temperature in terms of specific volume, temperature and the transition between liquid and solid.  You may use a graph of specific volume versus temperature as a visual aid.

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) List in order of melting temperature or glass transition temperature, i.e., highest to lowest, between an inorganic glass, an organic glass, covalent crystalline solid,  metallic solid and ionic solid.  Indicate which temperature applies to which.