Homework 10

INTRODUCTION:

For a solid body, stress indicates the strength of the material from which the body is made, while strain measures the deformation of the body under a force. Strain may be calculated by the following equation:

Where ε = strain (unitless)
l = final specimen length
l₀ = initial specimen length

Through tension and compression tests, the stress and strain can be related to each other and give insight into how much force a material can experience without undue deformation or failure. Once stress and strain data have been collected, they can be plotted to produce a stress-strain diagram. A sample stress-strain diagram is shown below.

Strain is plotted on the x-axis, and stress is plotted on the y-axis. There are four regions: the elastic region, yielding, strain hardening, and necking. For the elastic region, stress and strain can be related through Hooke’s law:

where σ is the stress in ksi, E is the Young’s modulus (a material-specific constant), and ε is the strain (unitless – often expressed as in/in).

In the yielding region, the stress is constant while the strain varies.

In the strain-hardening region, the stress and strain can be empirically related through Hollomon’s equation:

where ε is the strain, ε_EL is the strain at the elastic limit (a material-specific constant), and K and n are material-specific constants.

In the necking region, the cross-sectional area of the sample begins to decrease in a localized area. It is difficult to empirically relate stress and strain.

At the fracture stress, the material sample breaks.

An input data file called strain_tests.txt contains test results for 304 stainless steel samples. Each record line has two columns, where the first column is the final length of the sample and the second column is the initial length of the sample. The input file is comma delimited.

ASSIGNMENT:

Write a Python script that will read the required values from the input file into two one-dimensional arrays: one array for the initial length and one array for the final length. Calculate the strain based on the length values, and use this strain to calculate the stress. Store the strain and stress in arrays. Print the strain, the stress in ksi, and which regime the strain corresponds to, both to the screen and to an output data file called stress_strain.txt.

Most of your code will be in the main function; you will have an external function to verify the input file. Other functions are at your discretion – use your best coding judgment.

For this problem, use the following constants:

Young’s Modulus	28,000 ksi
Elastic Limit – Strain	0.001527 in/in
Yield Stress (stress in yielding region)	30 ksi
K	184.923 ksi
n	0.45

And use the following strain ranges for the regions:

Elastic Region	0 < x < 0.001527 in/in
Yielding	0.001527 < x < 0.002 in/in
Strain Hardening	0.002 < x < 0.5 in/in
Necking	0.5 < x < 0.58 in/in

Use Hooke’s law for the elastic region, constant stress for the yielding region, and Hollomon’s equation for the strain hardening region. For the necking region, note that the stress cannot be calculated.

Use the “Code Setup.py” template on Blackboard to write your code.

Your program output will look like the illustration shown below. Use your PC’s cursor to determine the horizontal and vertical spacing for the output format.

OUTPUT FORMAT:

*******************************************

STRESS AND STRAIN FOR 304 STAINLESS STEEL

Strain Stress Region

x.xxxxx xxx.x Elastic

x.xxxxx xxx.x Yielding

x.xxxxx xxx.x Strain Hardening

x.xxxxx N/A Necking

. . .

. . .

. . .

*******************************************

SUBMITTING ASSIGNMENTS:

Once you have your program working, exit the Python IDE that you are using. Make sure that your source program file name conforms to the following specifications:

sn_pn_first_last

where: sn is your section number (01, 02, 03, …)

pn is the program number (10)

first is your first name

last is your last name

An example for the ninth coding assignment would be 1_10_elmer_fudd.py.

Submission:

Submit both your handwritten problem-solving process and your Python source code using the Assignments button in Blackboard. Remember to submit your Python source program in Python 3 only, using code as demonstrated in class. No other format will be accepted.

If you make changes to your program and need to resubmit, rename the file such as 1_10_elmer_fudd_2.py or 1_10_elmer_fudd_3.py, etc. Then use the Assignments button in Blackboard to submit the new version. Only the most current submitted program version will be graded.

FILE PATHS:

Files on the grader’s computer and Dr. B.’s computer will be located at:
C:ENGR 200strain_tests.txt and C:ENGR 200stress_strain.txt