ME 180 Arizona Christian University Stress Strain Relationships and Behavior Matlab Stress-Strain Relationships and Behavior For Homework Assignment 3, us

ME 180 Arizona Christian University Stress Strain Relationships and Behavior Matlab Stress-Strain Relationships and Behavior

For Homework Assignment 3, use any method to solve the problems listed in the following document:

Homework Assignment 03 Chapter 5.pdf

ACTIONS

Use MATLAB to solve problems 1, 4, & 6. To complete your assignment, publish your code from problems 1, 4, & 6 to a PDF file, then upload to the link in this assignment.

A solution to a problem similar to Problem1 is shown in the MATLAB code (m-file) and published code (PDF file) found here:

ME180Example5_5Dowling4thSp20.m

ME180Example5_5Dowling4thSp20.pdf

ACTIONS

Solutions to problems similar to Problems 3 through 7 are found here:

Problem5.17ElasticDeformation.pdf

ACTIONS

Problem5.26ElasticDeformationRigidDie.pdf

ACTIONS ME180 Mechanical Properties of Materials
CSUS Department of Mechanical Engineering
Instructor: Homen
pathomen@csus.edu
Homework Assignment 3
Chapter 5: 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 = 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 stressstrain behavior as in (c).
3. Strains measured on the surface of a polycarbonate plastic part are as follows:
x = -0.0130, y =
0.0095 and
xy
= 0.0078
Estimate the in-plane stresses x, y, and xy, and the strain z 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 z =
yz = zx = 0).
4. Strains are measured on the surface of a mild steel part as follows: x = 190
and
y = -760
=
300
Estimate
the
in-plane
stresses
,
,
and
,
and
also
the
strain
normal
to
the
xy
x y
xy
z
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:
z = yz = zx = 0).
5. Strains are measured on the surface of a titanium alloy part as follows: x = 3800
y = 160
Estimate the in-plane stresses x, y, and xy, and also the strain z normal
and xy = 720
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: z = yz = zx = 0).
6. For the situation of Fig. 6 (below), where a rigid die prevents deformation in both the x- and ydirections, 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’ = z / z, 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 xand 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’ = x / x, and comment on the
value obtained.
Figure 7
Homework Assignment Completion, Publishing, & Submission Instructions: ME180 Mech Properties Materials – SECTIONS 01, 04
7/14/20, 11:45 PM
Homework Assignment Completion,
Publishing, & Submission Instructions
Homework Assignment Instructions
Homework assignments submitted for grading are to be solved using MATLAB computational
software. Solve all problems in a given assignment in one script file. You can generate your code
using the Editor (m-file) or using the Live Editor (mlx-file live script). When complete, publish the
file to a PDF document (see below for general instructions on publishing your code to a PDF file).
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. For submission,
upload your published PDF file. ALWAYS include your last name in the file name. For example,
for homework #1, my file to be uploaded would have the filename
“Homen_ME180_HwkAssgt01.pdf”. Follow this general format.
To publish your code from MATLAB, follow these general instructions:
Publishing an m-file from the EDITOR:
1. Click on the “PUBLISH” tab next to the “EDITOR” tab at the top of the MATLAB IDE.
2. Click on the pull down menu on the “Publish” Icon (should be the right-most icon on the tool
bar at the top of the IDE under the tabs).
3. In the pull down menu, select “Edit Publishing Options…”. The “Edit Configurations” window
will open.
4. In the “Output settings” area, click on the file type shown in the “Output file format” field (the
default is html–if you’ve never changed this, it should show as such). A pull down menu
appears from which you can choose the output file type.
5. Choose “pdf” to change the file type in the Output file format field to pdf.
6. In the “Output folder” field (just below the “Output file format” field), the filepath to the folder
where MATLAB will put your published pdf file by default is shown. The filepath shown is to
your working folder, but notice that MATLAB shows it will create a NEW folder called “html” at
the end of the filepath (notice the addition of “html” in the filepath). You can publish your file
https://csus.instructure.com/courses/64014/pages/homework-assignmen…tion-publishing-and-submission-instructions?module_item_id=2314267
Page 1 of 2
Homework Assignment Completion, Publishing, & Submission Instructions: ME180 Mech Properties Materials – SECTIONS 01, 04
7/14/20, 11:45 PM
the end of the filepath (notice the addition of “html” in the filepath). You can publish your file
and have MATLAB create that new folder to place it in if you wish. I, personally, like to have all
of my published files in the same folder as my MATLAB files–the working folder. To do this,
select and delete the additional “html” in the default filepath. Now the filepath is to your
working folder.
7. Click the “Publish” button at the bottom of the “Edit Configurations” window to publish your
document.
Note: if you are “re-publishing” the same m-file, MATLAB does not overwrite the existing PDF file
in your output folder (I don’t think it will even publish). You must delete the existing published PDF
file first (easiest to right click on the pdf file in your working folder area in your MATLAB IDE, then
choose “Delete” from the pull down menu). Then simply publish your m-file again.
You can, if you so desire, save the specified output file format and output folder to a default setting
of your choice. You’ll find the two buttons to do that just above the “Output settings” area in the
“Edit Configurations” window.
If you want your published PDF file to be formatted properly with a Table of Contents, and the
text/comments at the top of each problem section to look different from the comments embedded
in your code, pay attention to how you are “sectioning” and “titling” your m-file. Whatever you put
at the very top of your m-file following a double percent “%%” AND a space will output as the
giant, Bolded Title of your published document. Just below that first line, begin with a single
percent “%” AND a space, and those comments will be formatted into a subtitle/single paragraph
in black text. Begin each problem with “%%” AND a space to split your m-file into sections. The
first line in each section will become a formatted Bolded title for that problem in the published
PDF file. MATLAB will also create a “Table of Contents” showing page numbers for each “section”
(or problem) to show at the beginning of your published PDF file just below the main title of the
document and the subtitle (I usually put my name in the subtitle). The resulting published PDF file
should be a nicely formatted, well-organized document.
Publishing an mlx-file from the Live Editor:
If you are working in the Live Editor with an mlx-file, to publish, simply click on the pull down arrow
on the “Save” button in the “File” area of the toolbar, and select “Export to PDF…” from the pull
down menu. You can choose where to save that file as you normally would using the “Save as…”
function. Note that the Live Editor “pre-formats” your script file and it will publish it as it appears in
the Live Editor. Very cool.
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Page 2 of 2
ME180 Example Problem 5.5 (Dowling 4th Ed.)
Prof Homen
%
%
%
%
%
%
At 500° C, a silica glass has an elastic modulus of E = 50 GPa and a
tensile viscosity of ? = 1000 GPa·s. Assuming that the elastic,
steady-state creep model of Fig. 5.5(a) applies, determine the
response to a stress of 30 MPa maintained for 5 minutes and then
removed. Plot both strain versus time and stress versus strain for
a total time interval of 10 minutes.
clc
clear
% Governing equation: epstotal = epselastic + epsplastic
% = (sig/E) + (sig/eta)*t
% Steady state creep, sig, eta = constant
sig = 30000000; % Pa
eta = 1000000000000; % Pa-sec
% Elastic Modulus given:
E = 50000000000; % Pa
% For plots, all each time block straight lines (no non-linear
hardening)
% Strain vs time plot, 5 points: t=0, t=0, t=5min, t=5min, t=10min
t = [0 0 5 5 10];
% tsec = 60*t
% Strain at t=0 =0 (point 1)
eps1 = 0;
% Initial elastic strain, time independent (point 2):
eps2 = sig/E; % initial elastic, unitless strain (point 2)
% Creep strain at t = 5 minutes, st st: eps3 = (sig/eta)*t:
epscreep = (sig/eta)*t(3)*60; % unitless, *60 to convert to minutes
% Total strain at point 3 = initial elastic + creep
eps3 = eps2 + epscreep;
% Remove load at t=5 min, point 4, recover elastic strain:
% Creep strain post removal = eps3 – eps2
eps4 = eps3 – eps2;
% Strain remains constant after load removal (permanent creep strain)
% Strain at point 5 (10 minutes) = strain at point 4
eps5 = eps4;
% Create strain vector for plotting:
eps = [eps1 eps2 eps3 eps4 eps5];
% Plot strain vs time:
figure(1);
plot(t,eps,’-r’);
hold on;
plot(t,eps,’*k’,”MarkerSize”,12);
grid on;
title(‘Strain vs Time’);
xlabel(‘time, t (minutes)’);
1
ylabel(‘strain, eps’);
hold off
% Plot stress vs time
% Stress vector:
% pt1=0,pt2=sig,pt3=sig,pt4=0,pt5=0
sigvec = [0 sig sig 0 0]/1000000; %MPa
figure(2);
plot(eps,sigvec,’r-‘);
hold on;
plot(eps,sigvec,’*k’,”MarkerSize”,12);
grid on
title(‘Stress vs Strain’);
xlabel(‘strain, eps’);
ylabel(‘stress, MPa’);
2
Published with MATLAB® R2019b
3
x
x
y
y
xy
z
E
yz
xy
z
zx
z
x
y
(a) Determine the stresses in the x- and y-directions, the strain in the z-direction, and the
volumetric strain.
(b) Evaluate the ratio of stress to strain for the z-direction, E’ = z/ z, and comment on the value
obtained.
E
x
y
x
x
y
E
y
x
y

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