MSE 3004 Spring Semester 2011
Problem-Set #7 - Solutions
1) Determine the Eigenvalues and Eigenvectors for the following matrix:
3 1 1
A = 2 4 2
1 1 3
Eigenvectors:
2) Textbook, #3.36 (The following stresses were measured on a metal specimen: 11
= 94 MPa,
MSE 3004 Mechanical Behavior of Materials
Spring 2011
Homework Set # 1 - Solutions
1) What does it mean, if a material is isotropic? If it is homogeneous? Are all
homogeneous materials isotropic or are all isotropic materials homogeneous?
Note that there
MSE 3004 Mechanical Behavior of Materials
Spring 2011
Homework Set # 2 Solutions
1) Consider a thin-wall tube, capped at each end and loaded under internal pressure. Calculate
the ratio of the axial strain to the hoop strain, assuming that the deformation
MSE 3004 Mechanical Behavior of Materials
Spring 2011
Homework Set # 5: Solutions
1) An aluminum single crystal is subjected to a tensile stress of x = 250 kPa parallel to x =
[100] and a compressive stress of y = -50 kPa parallel to y = [010] with all ot
MSE 3004 Mechanical Behavior of Materials
Spring 2011
Homework Set # 6: Solutions
1) The stress tensor values at a point P in a material is given by the array
5 7 0
= 7 0 2 .
0 2 4
Determine the stress vector on the plane at P whose equation is 4x +
MSE 3004 Spring Semester 2011
Problem-Set #8 - Solutions
1) (a) Determine the mean pressure (one third of the trace of the stress tensor), expressed
in units of Gb/r for an edge dislocations. At what value (this being the angle between
the Burgers vector
MSE 3004 Mechanical Behavior of Materials
Spring 2011
Homework Set # 4 Solutions
1) (a) Determine the indices for the directions shown below:
(i) [ 1 11] ; (ii) [012]; (iii) [ 3 20] ; (iv) [2 2 1 ]
(b) Indicate in a plot the following directions for a cub
MSE 3004 Mechanical Behavior of Materials
Spring 2011
Homework Set # 3 - Solutions
1) Textbook # 3.1
From = K n we obtain ln ( ) = ln(K ) + n ln ( ) . A plot of the two data points in a log-log
format yields the value for n as the slope of a linear fit.
T