the stress-strain relationship

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I have complete lap report, I need to do few changes, most of them grammar, the others are some calculations. I will upload all files of excel that include all data and graphs.

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APPENDIX C TECHNICAL WRITING STYLE In experimental reports, the most important factors are the actions performed, the results obtained, and their meaning. The person or persons doing the experiment are of secondary importance. Therefore, it has become standard practice to write technical reports in an “impersonal” style. Impersonal Writing Style How does one write impersonally? There are several techniques, not usually emphasized in English courses, which help the student to develop an impersonal “scientific or technical” style to his or her writing. The following guidelines will help you: a) Personal Pronouns Omitted The personal pronouns: I, you, he, she, they, and who, should never be used in scientific writing. For example: Incorrect We set the dial to zero. Correct The dial was set to zero. “It” (a neutral pronoun) can be used occasionally when following a short sentence. However, if the previous sentence is long or involved, restate the subject under discussion. Ex: The measuring apparatus was adjusted. It was then set to zero. The pronoun “one” (General for ‘A Person’) may be used occasionally. Ex: One needs to consider alternative theories. b) Passive instead of Active Voice The most commonly used method of making writing appear more impersonal is to change the sentence from the active to the passive voice. This is done by inverting the word order so that the noun which was the direct object becomes the subject. A form of the verb to be is added to the past participle of the verb. The sentence on the next page shows the preferred form. In the following examples, an “S” above the word denotes the subject, “V” the verb, and “D.O.” the direct object. The verb is also underlined to show the transformation from active to passive voice. (Active) Ex: S V D.O. He found a direct correlation as shown in …… C-1 (Passive) Ex: S V A direct correlation was found as shown in…… S V D.O. Ex: The assistant gave Dr. Wizard the readout. Inverted Word Order Difficulties In writing an experimental report, many of the sentences are inverted word order, that is, the verb appears before the subject. One must be careful to make the verb agree with the subject, and not some other word in the sentence: Ex: V. S. Is any one (subject) of the gyroscopes available for use? Ex: V. S. Throughout the manual appear frequent references (subject) to the J. of Mech. Engr. Ex: Accompanying the report were the index and two S. appendices (compound subject) Economy of Expression Technical or scientific style is short and direct. This style can be achieved by the following: a) Word Selection Generally, short words are easier to understand than long words. Only occasionally is a long technical term more precise and therefore to be preferred over short ones. b) Sentence Structure A Sentence is a group of words which expresses a complete thought. Long, involved sentences with many clauses are difficult to comprehend, while short single sentences, one after another, tend to be choppy. The solution is to alternate long and short sentences. This gives relief and variety to the reader while retaining comprehension. (Note: If this structuring is difficult for you in the beginning, then you should write many short sentences; include some longer sentences later as your skill develops). C-2 c) Paragraph Length A Paragraph is a group of sentences which expresses the development of one idea or subject. They are like punctuation. When the idea you are writing about changes, start a new paragraph. Many students tend to write all of their paragraphs the same length, either filling up the whole page, or changing topics with each sentence. Both are difficult for the reader to digest. Such writing takes away from the “flow” of the report. In general, paragraphs should vary from three to ten typewritten lines covering one idea. If they are longer or shorter, they may need to be rewritten to provide clarity. What Questions Should You Ask? Technical writing needs to be concrete and give the answers to several important questions. Basically in writing a report the writer should briefly answer the following questions: What object was experimented on? How many things were involved? (number) How long (or What size) were they? (measurements) What happened to the experimental sample? How was the change measured? (apparatus and units) Where is the experimental change most evident? (location) When did the sample alter? (time) Why are the experimental results important? How do these results relate to the presently held theory or theories? As you can see, the most important questions to answer in technical and scientific writing are: What, How, How long, or How many, Where, When, and Why. By contrast, who is not an important question. Notice how many of these important questions are answered in this one brief sentence. (How many?) (What?) (How long?) Four samples of iron, varying in length from 2” to 10” were (What happened?) (What was done?) subjected to compressive axial loading while measurements (What change?) (Where located?) were made of the deflection at the midpoint of the metal bar. C-3 Common Pitfalls or Which Way is Up? The student who has finished an experiment has the tendency to talk to the reader as if he or she were in the room: “First we did this and then we walked over there to the apparatus which was held up by clamps. We wrote down the data from these dials which were compared to those theoretical results.” As you can see, it’s difficult for someone not looking over the experimenter’s shoulder to know what is going on. It is best to use such “pointer” words as first, then, this, that, there, which, up, down, etc., sparingly. Remember, in writing your report, write as though the reader (a manager or another engineer) was not in the room and has not seen the experiment. Agreement of Noun and Verb in a sentence S. V. Ex: Our chief trouble (subject) was (not were) the black flies that swarmed about us during the experiment. S. Ex: The black flies (subject) that swarmed about us V. during the experiment were (not was) our chief trouble. Ex: S. The material (subject) that was most interesting to me V. when I worked on my research paper was (not were) the books that included graphs and diagrams. When part of the sentence is singular and part plural, as in the first two examples,, the sentence usually sounds less awkward if the subject and verb are plural, as in the example #2. Singular and Plural Nouns A “singular” noun refers to one item, object or person only when used as the subject in a sentence, and takes a singular form of the verb in every tense; e.g., present, past, future perfect. C-4 The woman is at work; The teacher gave out the equations; The student will be graduating in a few years. A “plural noun refers to two or more items, objects or persons and takes a plural form of the verb to match it in number regardless of the tense of the verb. Regular nouns are made plural by adding “s” or “es” to the singular form. The students studied hard. Quarks have yet to be seen by experimenters. Irregular Singular and Plural Nouns Many foreign words coming into the English language, especially technical and scientific terms, are made plural in a manner other than adding “s” or “es”. Below are some of the common rules for forming plurals of these irregular nouns: General Rules. To form the plural from the Singular Foreign nouns ending in: “us” change to an “i” Ex: alumnus changes to alumni “um” or “on” generally change to an “a” Ex: stratum changes to strata; phenomenon alters to phenomena “a” change to “ae” Ex: alga becomes algae “x” or “ex” usually alter to “ces” or “ices” Ex: appendix changes to appendices vortex becomes vortices “eau” generally add “x” for the plural form Ex: the tableau changes to tableaux “is” alter to “es” or “ides” Ex: analysis becomes analyses C-5 iris changes to irides In table C-1 are listed frequently misspelled and misused scientific and technical words of use to engineering students. The first column lists the singular form of the noun and the second column presents the foreign or the original plural. The third column gives the American plural form to which many of these words are slowly changing. However, the foreign (original) plural form is generally preferred, except for those words in the table noted by an asterisk. Table C-1. Irregular Singular and Plural Nouns (Including Frequently used Technical and Scientific Terms) _________________________________________________________ Foreign Singular Foreign Plural American Plural alumna (f) alumnus (m) analysis apex apparatus appendix axis basis criterion datum erratum focus formula gauge hypothesis matrix maximum medium memorandum minimum momentum parenthesis phenomenon radius spectrum syllabus symposium synopsis synthesis thesis vortex alumnae alumni analyses apices apparati appendices axes bases criteria data errata foci formulae gauges hypotheses matrices maxima media memoranda minima momenta parentheses phenomena radii spectra syllabi symposia synopses syntheses theses vortices alumni* alumni apexes apparatus* appendixes criterions focuses formulas* gage(s) matrixes maximums mediums memorandums minimums momentums radiuses spectrums syllabuses symposiums vortexes In the above table, words designated by an asterisk “*” are preferred in current usage; otherwise, the foreign plural form is preferred. C-6 Two Plurals Some words have two plurals with different meaning. The one technical term you are likely to use is: Singular Plural #1 Plural #2 index indexes (in books) indices (in mathematics) One Item, Plural Meaning Nouns which describe a pair of things, such as a pair of pants, are usually treated as plural. Common words and engineering terms are: calipers scales tongs dividers pliers tweezers pincers scissors shears Plural Form - singular Meaning Other nouns are plural in form, that is, they end in an “s” but are used as a singular word with a singular verb in a sentence. Ex: Aeronautics is studied by a large number of engineers. Scientific terms ending with “ics” are the most common type in this group. acoustics economics hydrostatics optics statics aeronautics electronics mathematics physics statistics dynamics harmonics mechanics pyrotechnics tactics Singular Words That May Fool You When words like series, portion, part, type are used as the subject of a sentence, they take a singular verb even when followed by a phrase with a plural noun. Ex: A series of panel discussions is scheduled for the conference. Ex: A large portion of the references is missing. Ex: The most interesting part of the expeditions was the discovery and identification of the prehistoric fossils. Ex: One type of management options includes participant teamwork in problem solving. C-7 LABORATORY REPORT CONTENT For almost all of the experiments, the laboratory reports should include the following (total of 20 points): • Title Page (0.5 points) • Table of Content (0.5 points) • Abstract (2 points) • List of Symbols and Units (2 points) • Theory (3 points) • Procedures and Experimental Setup (2 points, with colored pictures) • Sample Calculation and Error Analysis (3 points, Error Analysis may not exist for some experiments) • Results (2 points with Table of Results and/or Figures) • Discussion and Conclusion (4 points) • References (0.5 points, e.g. textbooks, journal papers. Do NOT reference Wikipedia.) • Appendix (0.5 points, raw data sheet and hand calculation) LABORATORY REPORT FORMAT • Use 1 ½ spacing for texts and equations. • For all texts and equations, you must use the font Times New Roman, font size 12. • For section titles, use Times New Roman, size 14 with boldface. • Use 1 inch left margin, and ¾ margin on all other sides (right, top, and bottom). • Use justification on both left and right margins. • All equations must be centered with equations number: (1), (2), (3) with right justification • Try to use present tense in writing your report. • For all pages, you should have headers/footers such that: o Upper left corner: EGME 306A o Upper right corner: Experiment name o Lower left corner: Your name o Lower right corner: Page # /Total pages • • • • • Title Page: o Please include: course number, course title, name of the experiment, your name, Group name, your lab partner’s names, date the report due date, submission date Abstract: o Abstract should be between ½ pages to ¾ pages. You should clearly state the objective of the experiment in the very first sentence. You must also briefly answer a) What was done? b) How was it done? c) What were your basic results? d) How is your result compare to that of theory and/or other sources? List of Symbols and Units: o You should clearly write variables, name of the variables, and units in three column format. Theory: o With books and other sources, you must provide background information that helps in analyzing your data. You should include theoretical information for all of the equations that you used in analyzing your data. Procedures and Experimental Setup: o Concisely describe procedures and setup in your own words (do not copy from lab 1 • • • • handouts). Number the procedure in chronological order. Please place a couple of colored photos to better illustrate your procedure of the experiment. Sample Calculations and Error Analysis: o “Number” the sample calculation that you are analyzing in chronological order. o This number should correspond to the number in the error analysis. Results: o Make sure you have titles, axis labels with units in all tables and figures. Discussion: o Explain how your results relate to the theory. Similarities and differences between your results and that of others can be used to confirm your conclusions. You must explain in detail some sources of error. If your result disagrees with the published source, try to explain possible sources of error. If it agrees, you must also explain how you obtained the accurate results. Conclusion: o For the concluding paragraph, you must discuss the most important overall result and explain what you have accomplished. Remember, this “Discussion and Conclusion” section weighs more than any other section for a good reason (4 points). 2 EGME 306A The Stress-Strain Relationship in Tension Title Page: Course Number: 13150 Course Title: EGME 306A-06 Name of the experiment: The Stress-Strain Relationship in Tension Group D My name: ADEL ALQATTAN Lap partner’s name: ALI KHAJAH, MAEFARJ ALHAJRI, NASSER ALBORAIKI Due date: 09/28/2018 submission date: 09/28/2018 ADEL ALQATTAN Page 1 of 20 EGME 306A The Stress-Strain Relationship in Tension Abstract: The goals in this experiment are to find out the mechanical properties of three different metallic mixture bars steel 1018, steel 1045 and aluminum (blue, red and green respectively), by using Tensile Testing Machine (MTS), and to get a chart for every sample describing the relationship between stress and strain. We began the experiment with the aluminum (green) bar. First, we start measuring the diameter by using a digital caliper, then the green bar is fixed in the Tensile Testing Machine (MTS). After the machine started, the bar undergoes high load tension which is increasing rapidly until it has reached the maximum point, then it decreased gradually until the bar broke. While the load is increasing, the computer is recording the data through the software assigned for experiment 1. The bar starts to elongate, and in the middle, it deformed and got thinner until it suddenly broke. After that, the same process was repeated for the blue and red bars. From the data collected through software, I wrote charts using Excel. With the data collected, I also managed to calculate the stress, strain and elastic modulus. According to the calculation of the elastic modulus, I calculated the error percentage. It appears that my calculations of the percentage error very close to zero. List of symbols and units: σ= P/A (1) ε=δ/L (2) σ=Eε (3) variables name of the variables units σ stress Psi (pound per square inch) P Load (force) lbs. (pound) A area In2 ε strain Dimensionless (in/in) δ elongation In (inch) L Original length In (inch) E Young’s Modulus Psi (pounds per square inch) ADEL ALQATTAN Page 2 of 20 EGME 306A The Stress-Strain Relationship in Tension Theory: According to professors Yong Seok Park’s lectures note, stress can be defined as the strength of a material per unit area, and the unit can be psi, N/mm2 or MPa. = F = stress A Also, the force is perpendicular to the area. When the force is parallel to the area, this causes shear stress. ADEL ALQATTAN Page 3 of 20 EGME 306A The Stress-Strain Relationship in Tension While the strain is defined as deformation over original length. And since normal strain is length over length, the unit of strain is dimensionless, but it frequently expressed in in/in or mm/mm. A Then, by understanding the stress and strain, someone called Young come up with an equation called Young’s Modulus or elastic modulus, which is the ration between stress and strain. The unit for the elastic modulus is psi. And by measuring the young’s modulus you can know the stiffness of a solid material. And from the graph below, from 1-2, you can see the young’s modulus. E=/ Some definitions procedures and experimental setup: 1- Making sure the Tensile Testing Machine is connecting to the computer. ADEL ALQATTAN Page 4 of 20 EGME 306A 2- Identify each bar, the green, blue and red. The Stress-Strain Relationship in Tension 3- Measuring the diameter for each bar by using the digital calipers, then repeat the process three times and take the smallest measurement. 4- Open the program which relate to experiment 1 and make sure everything set to zero. 5- Fix the bar in the upper jaw of the machine and over tighten it by using the T-handle, then switch the control to the handset by pressing the lock picture, then use the handset to lower the specimen to the other jaw and tighten it. Also, make sure that the upper and lower does not move and leave a quarter inch in top and bottom of the jaw frame. 6- Switch back the control this the computer by pressing the lock picture again. ADEL ALQATTAN Page 5 of 20 EGME 306A The Stress-Strain Relationship in Tension 7- Put the extensometer in the middle of the bar and secure it by using the wire clip. After the extensometer fixed to the bar, remove the safety pin. note: the safety pin keeps the blades of the extensometer 2 inch spacing. 8- Zero all the number the values of the load, crosshead and extensometer by right clicking each one of them and zero all of them. 9- Switch the control to the machine, and preload the sample by 10000 pounds the switch it back to the computer. 10- Before starting the experiment, ask professor to finally check you set up, then press the green arrow on the computer. 11- Once you have checked everything, press ok to begin the experiment. 12- Type the bar color, group number and sample diameter, then press ok to start the experiment. 13- Notice the change in the load, extensometer reading and the necking in the specimen after the load decrease. 14- After a while, you will see the specimen breaks. Then, remove the extensometer and do not forget to return the pin to its position. 15- Follow the instructions on the computer, then remove the specimen before clicking ok. 16- Collect the data, final length and cross-section diameter of the specimen. 17- Save the data of the sample and give it an appropriate name. 18- Follow the instructions to import the file to Excel. 19- Repeat the steps 1 through 18 with the ...
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TeacherSethGreg
School: University of Virginia

Attached.

EGME 306A

The Stress-Strain Relationship in Tension

Title Page:
Course Number: 13150
Course Title: EGME 306A-06
Name of the experiment: The Stress-Strain Relationship in Tension
Group D
My name: ADEL ALQATTAN
Lap partner’s name: ALI KHAJAH, MAEFARJ ALHAJRI, NASSER ALBORAIKI
Due date: 09/28/2018
submission date: 09/28/2018

ADEL ALQATTAN

Page 1 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Table of Contents
Abstract: ...............................................................................................................................................................3
List of symbols and units:.....................................................................................................................................4
Theory: .................................................................................................................................................................5
Procedures and experimental setup:...................................................................................................................7
Sample Calculations and Error Analysis: ..............................................................................................................8
Green sample: ..................................................................................................................................................8
Blue sample ......................................................................................................................................................9
Red sample:......................................................................................................................................................9
Results: .............................................................................................................................................................. 11
Green sample: ............................................................................................................................................... 11
Blue sample:.................................................................................................................................................. 12
Red sample.................................................................................................................................................... 13
Discussion: ........................................................................................................................................................ 14
Conclusion: ........................................................................................................................................................ 15
References: ....................................................................................................................................................... 16
Appendix: .......................................................................................................................................................... 17

ADEL ALQATTAN

Page 2 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Abstract:
The goals of these experiment are to find out the mechanical properties of three different metallic
mixture bars steel 1018, steel 1045 and aluminum (blue, red and green respectively), by using
Tensile Testing Machine (MTS), and to get a chart for every sample describing the relationship
between stress and strain. The experiment begins with the aluminum (green) bar where its diameter
is measured using a digital caliper. The bar is fixed in the Tensile Testing Machine (MTS). The
machine is started and the bar undergoes tension which increases rapidly until it has reached the
maximum point and gradually decreases until the bar broke. Data is recorded by a software as the
load is increased. The breaking of the bar is proceeded by elongation and deformation in the middle.
The same process was repeated for the blue and red bars. From the data collected through software
charts and graphs are drawn using Excel. The stress, strain and elastic modulus are also calculated
from the data obtained. Calculation of the elastic modulus is compared with the Theatrical values to
obtain the percentage errors.

ADEL ALQATTAN

Page 3 of 21

EGME 306A

The Stress-Strain Relationship in Tension

List of symbols and units:
σ= P/A (1)
ε=δ/L (2)
σ=Eε (3)
Symbol

Variables

units

σ

stress

Psi (pound per square inch)

P

Load (force)

lbs. (pound)

A

area

In2

ε

strain

Dimensionless (in/in)

δ

elongation

In (inch)

L

Original length

In (inch)

E

Young’s Modulus

Psi (pounds per square inch)

ADEL ALQATTAN

Page 4 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Theory:
Stress can be defined as force per unit area of a material. The units of stress are pounds square inch
(psi), Newton per millimeter square (N/mm2) or Mega Pascal (MPa). It is defined by the formula:
𝑆𝑡𝑟𝑒𝑠𝑠, 𝜎 =

𝐹
𝐴

Figure 1

The direction of force is perpendicular to the area as it can be seen in figure 1. Shear stress is caused
when the force is parallel to the area as shown in figure 2. Shear stress is given by the formula:
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠, Ƭ =

𝐹
𝐴

Figure 2

ADEL ALQATTAN

Page 5 of 21

EGME 306A

The Stress-Strain Relationship in Tension

While the strain is defined as deformation over original length. And since normal strain is length
over length, the unit of strain is dimensionless, but it frequently expressed in in/in or mm/mm.

A

Then, by understanding the stress and strain, someone called Young come up with an equation called
Young’s Modulus or elastic modulus, which is the ration between stress and strain. The unit for the
elastic modulus is psi. And by measuring the young’s modulus you can know the stiffness of a solid
material. And from the graph below, from 1-2, you can see the young’s modulus. E=/

Some definitions

ADEL ALQATTAN

Page 6 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Procedures and experimental setup:
1. The Tensile Testing Machine was connected to the computer and the bars were identified as
the green, blue and red bar.
2. The diameter of each bar was measured three times using the digital calipers and the small

measurements taken.
3. The program related to experiment 1 was opened ensuring everything was set to zero.
4. The bar in the upper jaw of the machine was fixed and over tightened using the T-handle.
The control was switched to the handset by pressing the lock picture, then the handset used to
lower the specimen to the other jaw and tightened. The upper and lower jaw were ensured to
be fixed and a quarter inch left in the top and bottom of the jaw frame.

5. The control was switched back by pressing the lock picture. The extensimeter was put in the
middle of the bar and secured by using the wire clip then the safety pin was removed.

ADEL ALQATTAN

Page 7 of 21

EGME 306A

The Stress-Strain Relationship in Tension

6. All the number values of the load, crosshead and extensometer were set to zero by right
clicking each one of them.
7. The control was switched to the machines and the sample preloaded by 10,000 pounds before
switching it back to the computer.
8. The setup was checked by the professor to ensure everything was okay and the ok button was
pressed to begin the experiment. The bar color, group number and sample diameter were
inputted before the experiment began.
9. The change in the load, extensometer reading and the necking in the specimen after the load
decreased was noted.
10. The extensometer was removed after the specimen breaks and the specimen was removed
before clicking ok.
11. The final length and cross-section diameter of the specimen were recorded and saved using
an appropriate name. The results were then exported to excel.
12. The steps 1 through 11 were repeated with the other two samples.

Sample Calculations and Error Analysis:
Green sample:
𝑆𝑡𝑟𝑒𝑠𝑠, 𝜎 =

𝐹
49.35
=𝜋
= 584.0494028 𝑝𝑠𝑖
2
𝐴
𝑥
0.328
4

𝑆𝑡𝑟𝑎𝑖𝑛, 𝜀 =

𝛿 0.00009
=
= 4.5𝑥10−5 𝑖𝑛/𝑖𝑛
𝐿
2

Young Modulus of elasticity = 21,877,708.83Psi
Theoretical young modulus= 10,000,000psi
%𝐸𝑟𝑟𝑜𝑟 =
ADEL ALQATTAN

21,877,708.83 − 10,000,000
= 118.78%
10,000,000
Page 8 of 21

EGME 306A

The Stress-Strain Relationship in Tension
% 𝐴𝑟𝑒𝑎 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = 100 𝑥

=

𝑑օ2 − 𝑑𝑓 2
𝑑օ2

0.08449627601 − 0.04227327075
𝑋 100 = 49.97%
0.08449627601

Blue sample:
𝑆𝑡𝑟𝑒𝑠𝑠, 𝜎 =

𝐹
68.704
=𝜋
= 1774.950284 𝑝𝑠𝑖
2
𝐴
𝑥
0.222
4

𝑆𝑡𝑟𝑎𝑖𝑛, 𝜀 =

𝛿 0.00007
=
= 3.5𝑥10−5 𝑖𝑛/𝑖𝑛
𝐿
2

Young Modulus of elasticity = 64,100,935.35psi
Theoretical young modulus= 29,700,000psi
%𝐸𝑟𝑟𝑜𝑟 =

64,100,935.35 − 29700000
= 115.83%
29700000

Ultimate strength = 235,000psi
Published values = 63,800
%𝐸𝑟𝑟𝑜𝑟 =

235000 − 63,800
= 268.34%
63,800

Yield strength = 170,000
Published values = 53,700
%𝐸𝑟𝑟𝑜𝑟 =

170000 − 53700
= 216.57%
53700

𝑑օ2 − 𝑑𝑓 2
% 𝐴𝑟𝑒𝑎 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = 100 𝑥
𝑑օ2
=

0.03870756308 − 0.03397946614
𝑥100 = 12.21%
0.03870756308

Red sample:
𝑆𝑡𝑟𝑒𝑠𝑠, 𝜎 =

ADEL ALQATTAN

𝐹
63.271
=𝜋
= 1080.909971 𝑝𝑠𝑖
2
𝐴
𝑥
0.273
4

Page 9 of 21

EGME 306A

The Stress-Strain Relationship in Tension
𝑆𝑡𝑟𝑎𝑖𝑛, 𝜀 =

𝛿 0.00007
=
= 3.5𝑥10−5 𝑖𝑛/𝑖𝑛
𝐿
2

Young Modulus of elasticity = 43,300,815.82
Theoretical young modulus= 29,900,000
%𝐸𝑟𝑟𝑜𝑟 =

43,300,815.82 − 29900000
= 44.82%
29900000

Ultimate strength = 213,000psi
Published values = 81,900
%𝐸𝑟𝑟𝑜𝑟 =

213000 − 81900
= 205.49%
63,800

%𝐸𝑟𝑟𝑜𝑟 =

197000 − 45000
= 337.78%
45000

Yield strength = 197,000
Published values = 45,000

𝑑օ2 − 𝑑𝑓 2
% 𝐴𝑟𝑒𝑎 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = 100 𝑥
𝑑օ2
=

ADEL ALQATTAN

0.05853493972 − 0.03698361412
𝑋 100 = 36.82%
0.05853493972

Page 10 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Results:
Green sample:

Stress -Strain Curve over the elastic range
90000
80000

Stress (δ)

70000
60000
50000
40000
30000
20000
y = 2E+07x + 702.7
R² = 0.9999

10000
0
0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

Strain (ε)

Stress -Strain Curve over entire region
120000

Ultimate
strength

Stress (δ)

100000
80000

Yield point

60000

Propotion limit

40000

Breaking
point

20000

Elastic region
0
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Strain (ε)

Young Modulus of elasticity = 21,877,708.83Psi
Table 1

Before the stick breaks After the stick breaks
Average diameter (in) 0.328

0.232

Area (in2)

0.04227327075

Highest load
ADEL ALQATTAN

0.08449627601

3875.768 lbs.
Page 11 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Highest length

0.13698

Blue sample:

Stress- Strain curve over the elastic range
160000
140000

Stress (δ)

120000
100000
80000
60000
40000
y = 6E+07x + 101.51
R² = 0.9999

20000
0
0

0.0005

0.001

0.0015

0.002

0.0025

Strain (ε)

Stress- Strain curve over the entire range
250000

Ultimate
Strenght

Stress (δ)

200000
150000

Yield point

100000

Propotion limit

50000

Elastic region

Breaking point

0
0

0.02

0.04

0.06

0.08

0.1

Strain (ε)

Young Modulus of elasticity = 64,100,935.35psi
Table 2

Before the stick breaks After the stick breaks
Average diameter (in) 0.222

0.208

Area (in2)

0.03397946614

ADEL ALQATTAN

0.03870756308

Page 12 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Highest load

5360.745 lbs.

Highest length

0.03344in

Red sample:

Stress-strain curve over elastic range
90000
y = 4E+07x + 1413.1
R² = 0.998

80000

Stress (δ)

70000
60000
50000
40000
30000
20000
10000
0
0

0.0005

0.001

0.0015

0.002

0.0025

Strain (ε)

Stress- Strain curve over entire range
250000

Ultimate strenght

Stress (δ)

200000
150000

Yield Point
100000

Propotion limit
50000

Elastic region

Elastic region
0
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Strain (ε)

Young Modulus of elasticity = 43,300,815.82
Table 3

Before the stick breaks After the stick breaks

ADEL ALQATTAN

Page 13 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Average diameter (in) 0.273

0.217

Area (in2)

0.03698361412

0.005853493972

Highest Load

7696.145 lbs.

Highest Length

0.06945 in

Fracture surface of each sample:

Discussion:
Table 4

%Errors

Green bar

Blue bar

Red bar

Young’s Modulus

118.78%

115.83%

44.82%

268.34%

205.49%

Ultimate Strength

ADEL ALQATTAN

Page 14 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Yield Strength
Area

49.97%

216.57%

337.78%

12.21%

36.82%

The table shows the percentage errors of young’s modulus, Ultimate strength, Yield Strength, and
the percentage area change for the green, blue and red bars. The blue and the red bars are the 1018
Steel and 1045 steel respectively. The percentage errors are very high for the green bar and the red
bar when the experimental young’s modulus is compared with the published values. The red bar
shows some close precession to the young’s modulus. The Ultimate strength and the Yield strength
shows a large deviation from the published values. The percentage change in area is low for the blue
bar and high for the red and green bars. This means the cross-sectional area of the blue bar was less
affected during the experiment. The errors of the experiment are summarized in table 4. After the
experiment, the blue fracture surface is seen to be the smallest in diameter and is more prominent,
while the green and red are hollower and bigger in diameter. In general, all the specimens are
pointed and sharp.

Conclusion:
Through the tensile test, and by applying immense pulling force, it was proven that different metals
have different levels of stiffness. Through this experiment, we can know the properties of different
metals in order to pick the correct specimen for certain designs and safety precautions. Also, from
the charts and graphs we can understand how long each specimen takes to break, and depending on
the original shape of the specimen, the measurements can be different. However, the results of the
experiment showed a large deviation from those of the published values.

ADEL ALQATTAN

Page 15 of 21

EGME 306A

The Stress-Strain Relationship in Tension

References:
Theory
Information and some pictures from Professor Yong Seok Park lectures note in EGME 331. He is a
professor in California State University, Fullerton.
Digital caliper picture
https://www.midwayusa.com/product/1012741342/hornady-digital-caliper-6-stainless-steel
Extensometer picture
http://www.instron.us/en-us/products/testing-accessories/extensometers
Picture of MTS from lap manual
https://moodle-2018-2019.fullerton.edu/mod/resource/view.php?id=908040
Steel 1018 (Blue) reference value
https://www.azom.com/article.aspx?ArticleID=6115
Steel 1045 (Red) reference value
http://www.matweb.com/search/datasheet_print.aspx?matguid=193434cf42e343fab880e1dabdb143b
a
Aluminum 1100 (green) reference value
https://www.amesweb.info/Materials/Modulus-of-Elasticity-Metals.aspx

ADEL ALQATTAN

Page 16 of 21

EGME 306A

The Stress-Strain Relationship in Tension

Appendix:

ADEL ALQATTAN

Page 17 of 21

EGME 306A

ADEL ALQATTAN

The Stress-Strain Relationship in Tension

Page 18 of 21

EGME 306A

ADEL ALQATTAN

The Stress-Strain Relationship in Tension

Page 19 of 21

EGME 306A

ADEL ALQATTAN

The Stress-Strain Relationship in Tension

Page 20 of 21

EGME 306A

ADEL ALQATTAN

The Stress-Strain Relationship in Tension

Page 21 of 21


64,100,935.35
Test Method
Sample I. D.
Specimen Number
Load (lbf)

14000

stress (psi)

12000
10000
8000
6000
4000
2000
0
0

exp-1 Tensile with Extensometer.msm
Sample109.mss
2

before
Time (s)
Crosshead (in)
Extensometer (in)
strain ε (in/in)
68.704
0.9
0
0.00007
3.5E-05
126.495
1.7
0.001
0.00012
184.564
2.5
0.001
0.00016
Stress
vs.
Strain
Blue
stick
243.622
3.3
0.002
0.00021
300.304
4.1
0.002
0.00027
339.242
4.9
0.002
0.00028
367.638
5.7
0.003
0.00029
y = 6.5
6E+07x
393.453
0.003
0.00033
417.126
7.3
0.004
0.00034
439.051
8.1
0.004
0.00037
462.511
8.9
0.004
0.00038
0.00019
483.59
9.7
0.005
0.00039
506.091
10.5
0.005
0.00042
0.000020.000040.000060.00008 0.0001 0.000120.000140.000160.00018 0.0002
528.518
11.3
0.006
0.00044
strain (in/in)
550.392
12.1
0.006
0.00045
572.378
12.9
0.006
0.00046
593.571
13.7
0.007
0.00048
614.444
14.5
0.007
0.00049
633.449
15.3
0.008
0.0005
652.656
16.1
0.008
0.00053
672.783
16.9
0.008
0.00054
0.00027
690.66
17.7
0.009
0.00055
708.457
18.5
0.009
0.00057
726.748
19.3
0.01
0.00059
743.621
20.1
0.01
0.0006
762.827
20.9
0.01
0.00062
779.018
21.7
0.011
0.00062
796.401
22.5
0.011
0.00064
814.757
23.3
0.012
0.00064
832.357
24.1
0.012
0.00066
850.254
24.9
0.012
0.00068
0.00034
867.305
25.7
0.013
0.00069
885.604
26.5
0.013
0.0007
904.503
27.3
0.014
0.00073
923.472
28.1
0.014
0.00073
942.123
28.9
0.014
0.00075
962.087
29.7
0.015
0.00077
980.073
30.5
0.015
0.00077
1000.258
31.3
0.016
0.0008
1019.012
32.1
0.016
0.00083
1038.334
32.9
0.016
0.00082
0.00041

1058.373
1077.382
1097.115
1116.482
1135.339
1156.213
1175.654
1194.355
1215.399
1233.817
1254.455
1274.785
1293.962
1315.454
1334.984
1357.118
1375.746
1397.835
1417.047
1438.022
1456.447
1478.095
1496.468
1517.726
1537.918
1557.783
1578.78
1599.12
1619.49
1641.285
1659.70...

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Anonymous
Excellent job

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