ME180 Mechanical Properties of Materials
CSUS Department of Mechanical Engineering
Instructor: Homen
pathomen@csus.edu
All Homework Assignments
Homework assignments submitted for grading are to be solved using MATLAB computational
software. You may solve all problems in one assignment in one script file. When complete, publish
the file to a pdf document. Be sure to use plenty of comments in your work. This is for your benefit
as well as the grader’s benefit. Plots should be correctly formatted with a plot title and axes titles,
with correct units (always). Your published file should show all of the results (answers) neatly
organized and labeled with proper units (always). It is best to use the fprintf function for this.
Upload BOTH your script file (.m) AND your published pdf file to the appropriate upload link on
Moodle. ONLY .m and .pdf files will be accepted. DO NOT UPLOAD ZIPPED FOLDERS CONTAINING
YOUR SOLUTION FILES – SUBMIT THE SCRIPT AND .pdf FILES SEPARATELY.
ALWAYS include your last name in the file name. For example, for homework #1 my two files to be
uploaded would have filenames “Homen_ME180_Hwk01.m” and “Homen_ME180_Hwk01.pdf”.
Homework 3
Stress‐Strain Relationships and Behavior
1. At 550°C, a silica glass has an elastic modulus of E = 60 GPa and a tensile viscosity of η = 10,000
GPa·s. Assuming that the elastic, steady‐state creep model of Fig. 5.5(a) (Dowling, 2013, 2019;
figure shown below) applies, determine the response to a stress of 100 MPa maintained for 5
minutes and then removed. Plot both strain versus time and stress versus strain for a total time
of 10 minutes.
Figure 5.5
Rheological models with time‐dependent behavior and stress‐time step responses
From Dowling, 2019 (Pearson)
2. A polymer is used for shrink‐on banding to keep cardboard boxes from popping open during
shipment of merchandise. The tension in the banding is observed to have dropped to 90% of its
initial value after 3 months. Estimate how long it will take for the tension to drop to 50% of its
original value. The polymer may be assumed to behave according to an elastic, steady‐state
creep model, as in Fig. 5.6 (Dowling, 2013, 2016; figure shown below).
Figure 5.6
Figure 5.6: Relaxation under constant strain for a model
with steady‐state creep and elastic behavior. The step in
strain (a) causes stress‐time behavior as in (b), and stress‐
strain behavior as in (c).
3. Strains are measured on the surface of a polycarbonate plastic part as follows: εx = ‐0.0130, εy =
0.0095, and γxy = 0.0078. Estimate the in‐plane stresses σx, σy, and τxy, and also the strain εz
normal to the surface. (Assume that the gages were bonded to the polymer when there was no
load on the part, that there has been no yielding, and that no loading is applied directly to the
surface, so that σz = τyz = τzx = 0).
4. Strains are measured on the surface of a mild steel part as follows: εx = 190 με, εy = ‐760 με, and
γxy = 300 με. Estimate the in‐plane stresses σx, σy, and τxy, and also the strain εz normal to the
surface. (Assume that the gages were bonded to the metal when there was no load on the part,
that there has been no yielding, and that no loading is applied directly to the surface, so that:
σz = τyz = τzx = 0).
5. Strains are measured on the surface of a titanium alloy part as follows: εx = 3800 με, εy = 160
με, and γxy = 720 με. Estimate the in‐plane stresses σx, σy, and τxy, and also the strain εz normal
to the surface. (Assume that the gages were bonded to the metal when there was no load on the
part, that there has been no yielding, and that no loading is applied directly to the surface, so
that: σz = τyz = τzx = 0).
6. For the situation of Fig. 6 (below), where a rigid die prevents deformation in both the x‐ and y‐
directions, the material is an ABS plastic, and the stress in the z‐direction is 30 MPa
compression.
a. Determine the stresses in the x‐ and y‐directions and the strain in the z‐direction.
b. Evaluate the ratio of stress to strain for the z‐direction, E’ = σz / εz, and comment on the
value obtained.
Figure 6
7. For the situation of Fig. 7 (below), where rigid walls prevent deformation in the z‐direction, the
material is an aluminum alloy, and equal compressive stresses of 100 MPa are applied in the x‐
and y‐directions.
a. Determine the stress in the z‐direction, the strains in the x‐ and y‐directions, and the
volumetric strain.
b. Evaluate the ratio of stress to strain for the x‐direction, E’ = σx / εx, and comment on the
value obtained.
Figure 7