ASSIGNMENT 10: LAB REPORT: METAL FATIGUE LAB
Date of Lab: 13 November 2008 Date of Submission: 3 December 2008
by
_______________________________________ Sreyes Kadapala
[email protected]
Submitted to: Dr. Richard Theis Department of Humanities and Communications College of Arts and Sciences
In Partial Fulfillment Of the Requirements Of COM 221.04 Technical Report Writing Fall 2008
Embry-Riddle Aeronautical University Prescott, Arizona
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ABSTRACT Structures such as bridges, buildings, aircraft, automobiles, and machines are under constant loading of forces and stresses. Therefore, in the world of engineering, study of material properties (fatigue, fatigue life, and fracture) of metals is a critical subject. An experiment was conducted on November 13, 2008 where three (3) different types of paper clips in sets of 20 were used to test the fatigue life of the metal. The paper clips were categorized as small silver, small brass and large silver, according to their size and color. The experiment was performed by cyclically bending the inner section of each clip to a certain angle (45°, 90°, 90 °, 135°,180°) and relapsing that inner section back to its original position (i.e., parallel to the outer section), until the clip broke. The purpose of this experiment was to study the strength of the material and the characteristics of fatigue. Fatigue failure of a paper clip dep ends on the angle of bending of the inner portion compared to the outer portion, and the external dimensions of the paper clip. This lab report elaborates on o n the basic concepts of metal fatigue, the lab experimental procedures, results of the lab experiment, and analysis of the results of the lab experiment. This report found that, for all paper clips, there is an inverse relationship between the angle of deflection and the number of cycles to failure. However, the experiment was found to be prone to errors due to inconsistency in the bending angle and the magnitude of force applied by the bender on the paper clip. The report recommends that the experiment be repeated with an increased level of control over the magnitude of force applied to attain usable data, measure the bending angles accurately, and avoid human error. The report concludes by listing a critical graph w hich establishes a relation between the bending angle and the cycles required by the metal to break.
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TABLE OF CONTENTS CON TENTS ABSTRACT......................................................................................................................iii TABLE OF CONTENTS..................................................................................................iv LIST OF TABLES..............................................................................................................v LIST OF FIGURES............................................................................................................v LIST OF EQUATIONS....................................................................................................vii LIST OF SYMBOLS.......................................................................................................viii LIST OF ABBREVIATIONS/ACRONYMS....................................................................ix ACKNOWLEDGEMENTS................................................................................................x 1.0 INTRODUCTION.........................................................................................................1 1.1 Research Topic...........................................................................................................1 1.2 Background Information............................................................................................1 1.3 Justification................................................................................................................1 1.4 Research Problem......................................................................................................1 1.5 Purpose Statement......................................................................................................1 1.6 Textual Overview......................................................................................................2 2.0 THEORY.......................................................................................................................3 1.1 Technical Definitions.................................................................................................3 1.2 Theoretical Principles................................................................................................3 1.3 Expected Results........................................................................................................4 1.4 Equations....................................................................................................................5 1.5 Justification................................................................................................................6 3.0 APPARATUS AND PROCEDURES...........................................................................7 1.6 Apparatus...................................................................................................................7 1.7 Procedures................................................................................................................12 4.0 RESULTS AND DISCUSSION..................................................................................19 1.8 Data..........................................................................................................................19 1.9 Graphical Representation of Data............................................................................21 1.10 Commentary on Data.............................................................................................24 5.0 CONCLUSIONS AND RECOMMENDATIONS......................................................25 1.11 Purpose...................................................................................................................25 5.2 Procedures................................................................................................................25 1.12 Key Results............................................................................................................25 5.4 Conclusions.............................................................................................................26 6.5 Recommendations....................................................................................................26 6.0 REFERENCES............................................................................................................27 7.0 ATTRIBUTIONS........................................................................................................28 8.0 APPENDIX I: SAMPLE CALCULATIONS..............................................................31 8.1 Average weight of one paper clip...........................................................................31 8.2 Average of cycles of failure....................................................................................32 9.0 APPENDIX II: RAW DATA.......................................................................................33 10.0 APPENDIX III: DATA SHEET................................................................................42
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LIST OF TABLES
Table 2.1: Predicted Number of Cycles to Failure..............................................................4 Table 4.1.1: Average Cycles to Failure (Small silver).......................................................20 Table 4.1.2: Average Cycles to Failure (Small brass).......................................................20 Table 4.1.3: Average Cycles to Failure (Small brass).......................................................21 Table 8.1: Team 1 Raw Data for Sample Calculation of Average....................................31
LIST OF FIGURES
vi Figure 2.1: Typical Stress Cycles .......................................................................................4 Figure 3.1: Charles Leonard® Protractor............................................................................7 Figure 3.2: C-Thru®MR-12 Stainless Steel Ruler...............................................................7 Figure 3.3: Wal-Mart® Long Nosed Pliers.........................................................................8 Figure 3.4: Staples® Small Silver Paper Clips....................................................................8 Figure 3.5: Staples® Small Brass Paper Clips.....................................................................9 Each paper clip has a length of 3.20 cm, a width of 0.75 cm at the wide end, and a width of 0.70 cm at the narrow end...............................................................................................9 Figure 3.6: Staples® Large Silver Paper Clips ...................................................................9 Figure 3.7: Ohaus-Dial-O-Gram® Balance.......................................................................10 Figure 3.8: Kodak ®Easy Share z812IS Digital Camera....................................................10 Figure 3.9: Apple ® i-Phone With the Stopwatch.............................................................11 Figure 3.10: HB Number 2 Pencil.....................................................................................11 Figure 3.2.1: Twenty (20) Staples® Small Silver Paper Clips..........................................12 Figure 3.2.2: Twenty (20) Staples® Small Brass Paper Clips...........................................12 Figure 3.2.3: Twenty (20) Staples® Large Silver Paper Clips..........................................13 Figure 3.2.4: Loops of the Small Brass Paper Clip............................................................13 Figure 3.2.5: Loops of the Small Silver Paper Clip...........................................................13 Figure 3.2.6: Loops of the Large Silver Paper Clip...........................................................14 Figure 3.2.7: Weighing the 3 Different Paper Clips..........................................................14 Figure 3.2.8: Small Silver Paperclip at 45˚ Angle.............................................................15 Figure 3.2.9: Small Silver Paperclip at 90˚ Angle.............................................................16 Figure 3.2.10: Small Silver Paperclip at 135˚ Angle.........................................................16 Figure 3.2.11: Small Silver Paper Clip at 135˚ Angle.......................................................17 Figure 3.2.12: Small Silver Paper Clip Which Failed due to Fatigue.............. ..................17 Figure 4.2.2: 45º Bar Graph...............................................................................................21 Figure 4.2.3: 90º Bar Graph...............................................................................................22 Figure 4.2.4: 135º Bar Graph.............................................................................................23 Figure 4.2.5: 180º Bar Graph.............................................................................................23 Figure 5.3.6: Failure Comparison by Brand......................................................................25 Figure 7.1: Dr. Theis..........................................................................................................28 Figure 7.2: Jake Jacot.........................................................................................................28 Figure 7.3: Shyam Thota....................................................................................................29 Figure 7.4: Sreyes Kadapala..............................................................................................29 Figure 7.5: Team Members for the Experiment.................................................................29 Team 1 Raw Data ..............................................................................................................34 Team 2 Raw Data ..............................................................................................................36
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LIST OF EQUATIONS
Equation 2.4: Average Cycles to Failure.............................................................................5
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LIST OF SYMBOLS A ................................................................Area...............................................................in
2
F ...............................................................Force................................................................lb X .......................................................Average X n .................................................Value
Value.........................................................--
of the nth term....................................................--
l .........................................................Original n .......................................................Number
length........................................................in of terms.......................................................--
δ ...........................................................Elongation............................................................in ε ...............................................................Strain................................................................-θ .....................................................Angle
of Deflection..................................................deg
° .....................................................Angle
of Deflection..................................................deg
σ ...............................................................Stress..........................................................lb/in 2
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LIST OF ABBREVIATIONS/ACRONYMS B58.......................................................Building 58...........................................................-COM 221.04......................Technical Report Writing Section 4........................................-ERAU.............................Embry-Riddle Aeronautical University......................................-IT................................................Information Technology.................................................--
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ACKNOWLEDGEMENTS The author would like to thank several people for their guidance throughout the compilation and writing of this report: •
Dr. Richard Theis for his contributions throughout Fall 2008 semester and COM 221.04.
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Shyam Thota, Steven Colenso, Jake Jacot, and Praful Chowdri for their help and willingness to answer questions regarding formatting and content.
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INTRODUCTION
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Research Topic
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This lab report discusses and elaborates the lab experiment performed on November 13, 2008. The lab experiment’s focus was to introduce the topic of metal fatigue. When cyclic bending stresses are applied on metals, cracks are formed at various points on the surface of the metal. This cyclic application of bending stresses leads metals to fail or break. The breaking of metals due this cyclic application of stresses is known as metal fatigue. In this lab experiment, cyclic stresses are induced in paper clips by bending the paper clip’s inner surface at certain angles.
1.2
Background Information
In the world of engineering, metal fatigue is a critical concept as metals are used in buildings, bridges, and machines. Various types of metals are subjected to cyclic stresses and the cyclic stresses and forces over time. Therefore, the metal will eventually fail. This failure often costs millions of dollars and thousands of human being lives. For example, the Aloha Airlines’ airplane accident on April 28, 1988 was caused due to metal fatigue failure.
1.3
Justification
In the contemporary world, machines are dependent upon metals, and metals play a central role in the lives of people across the globe. However, machines have been improvised since late 1800s. Hence, increasing the risk of fatigue failure of machines comprised of metals. Engineers and scientists have been working on decreasing the factors causing metal fatigue.
1.4
Research Problem
The factors causing metal fatigue and theory behind metal fatigue are unknown to college students until their junior year. However, college students concur that metal fatigue is one of the reasons behind the breaking and cracking of metals. The initial hypothesis for the lab experiment was the small silver category of paper clips will take least number of cycles to be broken into two separate parts.
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Purpose Statement
The purpose of the lab report is to introduce metal fatigue to the reader of the report, display the results of the lab experiment conducted to the reader, and help the reader analyze the results of the conducted experiment.
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Textual Overview
This lab report was written for a reader without any scientific background, and the lab report provides the reader with basic background knowledge and principles to understand the conducted lab experiment. Initially, the lab report presents theoretical information about metal fatigue. Next, the experiment’s procedures are summarized, and the generated results are listed, analyzed, discussed, and explained in statements, tables and graphics. Finally, conclusions and recommendations were made and discussed.
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THEORY
1.1
Technical Definitions
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•
Angle of Deflection: The angle an object is deflected, or bent, from the equilibrium or starting position.
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Compression Stress: Stress that causes deformation in the direction of the applied load.
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Cycle: One cycle is defined as deforming the paper clip to the specified angle of deflection and then returning the paper clip to the equilibrium, or starting, position.
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Cycles to Failure: The total number of cycles a paper clip can withstand before reaching the point of fatigue (i.e., the paper clip breaks).
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Fatigue Point: The point at which metal becomes fatigued and can no longer support the load, or force, being applied. Force (Cyclic) Loading: Strength or power exerted upon a metal repeatedly at a constant rate. •
Metal Fatigue: The phenomenon leading to the fracture of a metal under cyclic forces, stresses or strains. •
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Tensile Stress: Force acting upon a small area within a surface plane.
Tensile Strain: Amount of elongation or compression that occurs in a metal at a given stress or load •
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1.2
Shear Stress: Stress that acts parallel to a surface.
Theoretical Principles
This section will educate the reader about the basic principles and concepts of metal fatigue. During the lab experiment, the paper clips were exposed to bending stresses in continuous cycles. Initially, when the cyclic forces were applied during the bending of the paper clip microscopic cracks begin to develop. As the cyclic loading was continued, these cracks were beginning to propagate until the metal is no longer able to carry the stress load, and consequently failed (Engineers Edge). During the application of cyclic bending stress, the metal undergoes tensile stress and compressive stress. Figure 2.1
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illustrates a metal under tension and compression:
Figure 2.1: Typical Stress Cycles (Engineers Edge, 2008) As illustrated in Figure 2.1, tensile stress is considered to be positive while compression stress is considered to be negative. The top two graphs depict a sinusoidal stress curve, and the bottom graph represents the stress cycle on an aircraft wing during flight (Engineers Edge).
1.3
Expected Results
The expected results of the experiment were that the metal paper clips being bent to a certain angle will eventually fail. Depending upon the frequency and intensity of the stress applied the number of cycles could differ. Due to the large silver paper clips being thicker and taller than the other two paper clips (i.e., small silver and small brass), the large silver will take more cycles, and more force will have to be applied to break the large silver clips while compared to the small silver and small brass paper clips. Team 1’s predictions for the number of cycles to failure for each of the four angles (45, 90,135,180) are depicted in Table 2.1, on the top of the following page:
Table 2.1: Predicted Number of Cycles to Failure
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Brand Small silver Small brass Large silver
= 45º
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= 90º 30 65 75
= 135º 20 30 40
= 180º 10 15 30
5 10 20
As depicted in Table 2.1, small silver and small brasses are expected to have similar fatigue points. Large silver is expected to have the highest cycles to failure due to the thicker composition of large silver paper clips.
1.4
Equations
Tensile stress ( σ or S) can be quantitatively defined as the force applied (F ) on the metal per unit area ( A) of the metal. This definition is described by the equation, σ
=
F
Equation 2.1
A
Tensile strain (ε) can be quantitatively defined as the change in the length (Δl ) of the metal per unit length (l ). This definition is described by the equation, ε=
Elongation Length
=
∆l
Equation 2.2
l
The average weight of one (1) paper clip can be calculated using the following equation: Avg. weight =
Total Weight of
20
paper clips
20
Equation 2.3
The total weight of twenty (20) paper clips is found using a weighing scale. A sample calculation is depicted in section 8.1 The average cycles to failure for a category of paper clips for either of the bending angles can be calculated using the following equation: Avg. cycles to failure =
Test #1(Cycles ) + Test # 2(Cycles ) + Test #3(Cycles ) + Test # 4(Cycles )+ Test #5( Cycles)
Equation 2.4
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Justification
By incorporating theoretical principles of fatigue, stress, and strain, the reader is ab le to develop the skills required to understand metal fatigue in structures of machines. The data of fatigue of a metal is vital for engineering or prototyping a machine. Whether the machine is an aircraft, car or even a small drill machine, fatigue failure occurs on every metal of the machine. To ensure the durability and long-life for the machine, the engineers first determine the fatigue strength data from experiments on the metal being used. Then the engineer manufactures the machine using the metals experimented and tested upon.
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3.0
APPARATUS AND PROCEDURES
1.6
Apparatus
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The following equipment was used during the experiment: • •
One (1) data sheet constituting of two pages (provided by Dr. Theis)
One (1) 180° Charles Leonard® Protractor, as illustrated in Figure 3.1:
Figure 3.1: Charles Leonard® Protractor The protractor pictured in Figure 3.1 measures angles up to 180°. ®
One (1) C-Thru MR-12 stainless steel ruler with metric and English measurements as depicted in Figure 3.2: •
Figure 3.2: C-Thru MR-12 Stainless Steel Ruler The ruler depicted in Figure 3.2 measures up to thirty (30) centimeters or twelve (12) inches. The measuring device can measure accurately up to 1 mm or 1/16 in.
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One (1) set of Wal-Mart® Long Nosed Pliers, as illustrated in Figure 3.3 :
Figure 3.3: Wal-Mart® Long Nosed Pliers The Wal-Mart® Long Nosed Pliers are 6 inch in length and weigh 2.35 oz and are made in China. •
Twenty (20) Staples® small silver paper clips. Each paper clip has a length of 3.20 cm, a width of 0.70 cm at the wide end, and a width of 0.60 cm at the narrow end as illustrated in Figure 3.4:
Figure 3.4: Staples® Small Silver Paper Clips The Staples® small silver paper clips illustrated on the bottom of the previous page, in Figure 3.4, are made of galvanized steel and weigh 0.43 gram. The paper clips’ contour is elliptical in shape and consist of three (3) 180° turns at the ends.
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Twenty (20) Staples® small brass paper clips. The Staples® small brass paper clips are made of galvanized steel and weigh 0.43 grams. Figure 3.5 illustrates small brass clips: •
Figure 3.5: Staples® Small Brass Paper Clips
Each paper clip has a length of 3.20 cm, a width of 0.75 cm at the wide end, and a width of 0.70 cm at the narrow end. Twenty (20) Staples® large silver paper clips. The Staples® large silver paper clips are made of galvanized steel and weigh 1.40 grams as illustrated in Figure 3.6: •
Figure 3.6: Staples® Large Silver Paper Clips The paper clips illustrated in Figure 3.6, are elliptical in shape and consist of three (3) 180° turns. Each paper clip has a length of 4.80 cm, a width of 1.10 cm at the wide end, and a width of 0.80 cm at the narrow end.
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One (1) Ohaus-Dial-O-Gram® balance as depicted in 7:
Figure 3.7: Ohaus-Dial-O-Gram® Balance The balance pictured in 7, Ohaus-Dial-O-Gram® balance was used to measure the ® weight of the three different paper clips. The balance is manufactured by Ohaus , is accurate to 0.01 grams, and can measure up to 310 grams. •
®
One (1) Kodak Easy Share z812IS digital camera as depicted in Figure 3.8:
Figure 3.8: Kodak Easy Share z812IS Digital Camera (Source: http://www.kodak.com/) The digital camera depicted in Figure 3.8 was used to take digital pictures for ® pictorial reference. The digital camera is manufactured by Kodak and marketed as the “Easy Share z812IS.” The digital camera is 6.4 inches wide, 7.4 inches tall, 4.3 inches thick, and weighs 1.2 pounds. •
One (1) Apple® i-Phone was used as a stopwatch. Figure 3.9 depicts an i-Phone with the stopwatch application in use:
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Figure 3.9: Apple ® i-Phone With the Stopwatch (Source: www.apple.com) Figure 3.9 illustrates the i-Phone with two thousand nine hundred and fifty two (2952) minutes clocked. •
One (1) HB Number 2 pencil as illustrated in Figure 3.10:
Figure 3.10: HB Number 2 Pencil (Source: www.google.com) A HB Number 2 pencil is used for writing purposes such as exams, essays, and class room notes.
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Procedures
The lab experiment was performed on November 13th, 2008 in B58, room 102 at ERAU in Prescott, Arizona. The following procedures were used to complete the experiment: 1.0 Set of twenty (20) Staples® small silver paper clips were collected as depicted in Figure 3.2.1 :
Figure 3.2.1: Twenty (20) Staples® Small Silver Paper Clips 2.0 Set of twenty (20) Staples® small brass paper clips were collected as depicted in Figure 3.2.2 :
Figure 3.2.2: Twenty (20) Staples® Small Brass Paper Clips 3.0 Set of twenty (20) Staples® large silver paper clips were collected as depicted in Figure 3.2.3 , on the top of the following page:
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Figure 3.2.3: Twenty (20) Staples® Large Silver Paper Clips 4.0 The length and the width (inner loop and outer loop) of one (1) Staples® small brass ® paper clip were measured using the C-Thru MR-12 stainless steel ruler. Each paper clip consisted of two widths, the inner loop width and outer loop width. Figure 3.2.4, below, illustrates the inner and outer loops of the small brass paper clip. The measurements were recorded in the data sheet by the recorder. Outer Loop Inner Loop Figure 3.2.4: Loops of the Small Brass Paper Clip 5.0 The length and the width (inner loop and outer loop) of one (1) Staples® small silver ® paper clip were measured using the C-Thru MR-12 stainless steel ruler. Figure 3.2.5, below, illustrates the inner and outer loops of the small silver paper clip. The measurements were recorded in the data sheet by the recorder. Outer Loop Inner Loop
Figure 3.2.5: Loops of the Small Silver Paper Clip 6.0 The length and the width (inner loop and outer loop) of one (1) Staples® large silver ® paper clip were measured using the C-Thru MR-12 stainless steel ruler. Figure 3.2.6, below, illustrates the inner and outer loops of the large silver paper clip. The measurements were recorded in the data sheet by the recorder.
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Outer Loop
Figure 3.2.6: Loops of the Large Silver Paper Clip 7.0 All the twenty (20) small silver paper clips were placed on the Ohaus-Dial-O-Gram® Balance and were weighed as illustrated in Figure 3.2.7 : Measurement Scale
Paper Clips on the scale
Figure 3.2.7: Weighing the 3 Different Paper Clips 7.1
The weight of the twenty (20) Staples® small silver paper clips was divided by 20 to get the average weight of one (1) small silver paper clip (for further explanation refer to section 8.1). The average weight of one (1) small silver paper clip was recorded in the data sheet by the recorder. 8.0 All the twenty (20) Staples® large silver paper clips were placed on the Ohaus-DialO-Gram® Balance and were weighed in a similar procedure used for weighing the small silver paper clips. Figure 3.2.7 illustrates the weighing of the twenty (20) large silver paper clips similar to the weighing of small silver paper clips.
8.1
The weight of the twenty (20) Staples® large silver paper clips was divided by 20 to get the average weight of one (1) large silver paper clip ( for further explanation refer to section 8.1). The average weight of one (1) large silver paper clip was recorded in
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the data sheet by the recorder. 9.0 All the twenty (20) Staples® small brass paper clips were placed on the Ohaus-DialO-Gram® Balance and were weighed in a similar procedure used for weighing the small silver paper clips. Figure 3.2.7 illustrates the weighing of the twenty (20) small brass paper clips similar to the weighing of small silver paper clips. 9.1
The weight of the twenty (20) Staples® small brass paper clips was divided by 20 to get the average weight of one (1) small brass paper clip (for further explanation refer to section 8.1). The average weight of one (1) small brass paper clip was recorded in the data sheet by the recorder. 10.0 The Staples® small silver paper clip was placed on the sheet of angles as illustrated below in Figure 3.2.8. The inner loop of the paper clip was placed parallel to the horizontal line (zero degrees). The top stem of the paper clip was bent back (i.e., till 45°) and forth (i.e., back to the original position) until the paper clip broke.
10.1
The small silver paper clip was placed on the sheet. The first angle was 45°. The paper clip was bent up to 45°, repeatedly using the Wal-Mart® Long Nosed Pliers, as depicted in Figure 3.2.8, below. The number of cycles (one cycle is the bending of the stem to 45° and then back to its original position at zero degrees) w as counted and recorded in the data sheet. This step was repeated five (5) times. Metal piece being bent up to 45° with the help of the pliers
Figure 3.2.8: Small Silver Paperclip at 45˚ Angle 10.2
Another small silver paper clip was placed on the sheet of angles. The second angle was 90°. The paper clip was bent up to 90°, repeatedly using the Wal-Mart® Long Nosed Pliers, as depicted in Figure 3.2.9, on the following page. The number of cycles (one cycle is the bending of the stem to 90° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5)
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times.
Metal piece being bent up to 90° with the help of the pliers
Figure 3.2.9: Small Silver Paperclip at 90˚ Angle 10.3
Another small silver paper clip was placed on the sheet of angles. The third angle was 135°. The paper clip was bent up to 135°, repeatedly using the Wal-Mart® Long Nosed Pliers, as illustrated in Figure 3.2.10 , below. The number of cycles (one cycle was the bending of the stem to 135° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times.
Metal piece being bent up to 135° with the help of the pliers
Figure 3.2.10: Small Silver Paperclip at 135˚ Angle 10.4
Another small silver paper clip was placed on the sheet of angles. The forth angle was 180 °. The paper clip was bent up to 180°, repeatedly Wal-Mart® Long Nosed Pliers, as depicted in Figure 3.2.11 , on the following page. The number of cycles (one
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cycle was the bending of the stem to 180° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times.
Metal piece being bent up to 180° with the help of the pliers
Figure 3.2.11: Small Silver Paper Clip at 135˚ Angle 10.5
Figure 3.2.12 displays a failed small silver paper clip:
Point where the paper clip breaks
Figure 3.2.12: Small Silver Paper Clip Which Failed due to Fatigue 11.0 The Staples® small brass paper clip was placed on the sheet of angles as illustrated in Figure 3.2.8 (similar to the placement of small silver paper clips). The inner loop of the paper clip was placed parallel to the horizontal line (zero degrees). The top stem of the paper clip was bent back (i.e., till 45°) and forth (i.e., back to the original position at zero degrees) until the paper clip broke. 11.1
The small brass paper clip was placed on the sheet. The first angle was 45°. The paper clip was bent up to 45°, repeatedly using the Wal-Mart® Long Nosed Pliers, similar to the silver paper clips as depicted in Figure 3.2.8 (similar to the placement of small silver paper clips). The number of cycles (one cycle is the bending of the stem to
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45° and then back to its original position at zero degrees) was counted and recorded in the data sheet. This step was repeated five (5) times. 11.2
Another small brass paper clip was placed on the sheet of angles. The second angle was 90°. The paper clip was bent up to 90°, repeatedly using the Wal-Mart® Long Nosed Pliers, similar to the silver paper clips as depicted in Figure 3.2.9 (similar to the placement of small silver paper clips). The number of cycles (one cycle is the bending of the stem to 90° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times.
11.3
Another small brass paper clip was placed on the sheet of angles. The third angle was 135°. The paper clip was bent up to 135°, repeatedly using the Wal-Mart® Long Nosed Pliers, similar to the silver paper clips as depicted in Figure 3.2.10 (similar to the placement of small silver paper clips). The number of cycles (one cycle was the bending of the stem to 135° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times.
11.4
Another small brass paper clip was placed on the sheet of angles. The forth angle was 180 °. The paper clip was bent up to 180°, repeatedly Wal-Mart® Long Nosed Pliers, similar to the silver paper clips as illustrated in Figure 3.2.11 (similar to the placement of small silver paper clips). The number of cycles (one cycle was the bending of the stem to 180° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times. 12.0 The Staples® large silver paper clip is placed on the sheet of angles, in such a way that the paper clip is parallel to the horizontal line of the angles diagram. The top stem of the paper clip is bent back and forth until the stem breaks.
12.1
The large silver paper clip was placed on the sheet. The first angle was 45°. The paper clip was bent up to 45°, repeatedly using the Wal-Mart® Long Nosed Pliers, similar to the silver paper clips as illustrated in Figure 3.2.8 (similar to the placement of small silver paper clips). The number of cycles (one cycle is the bending of the stem to 45° and then back to its original position at zero degrees) was counted and recorded in the data sheet. This step was repeated five (5) times.
12.2
Another large silver paper clip was placed on the sheet of angles. The second angle was 90°. The paper clip was bent up to 90°, repeatedly using the Wal-Mart® Long Nosed Pliers, as similar to the silver paper clips as depicted in Figure 3.2.9 (similar to the placement of small silver paper clips). The number of cycles (one cycle is the bending of the stem to 90° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times.
12.3
Another large silver paper clip was placed on the sheet of angles. The third angle was 135°. The paper clip was bent up to 135°, repeatedly using the Wal-Mart® Long Nosed Pliers, similar to the silver paper clips as illustrated in Figure 3.2.10 (similar to the placement of small silver paper clips). The number of cycles (one cycle was the
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bending of the stem to 135° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times. 12.4 Another large silver paper clip was placed on the sheet of angles. The forth angle was 180 °. The paper clip was bent up to 180°, repeatedly Wal-Mart® Long Nosed Pliers, similar to the silver paper clips as depicted in Figure 3.2.11 (similar to the placement of small silver paper clips). The number of cycles (one cycle was the bending of the stem to 180° and then back to its original position at zero degrees) were counted and recorded in the data sheet. This step was repeated five (5) times. ®
13.0
The pictures of the apparatus were taken using the Kodak Easy Share z812IS digital camera (the camera is illustrated in Figure 3.10).
14.0
The experiment area was cleaned by up ensuring that every piece of the broken paper clips was disposed.
15.0
The completed data sheet was submitted to the class instructor for review, and comparison with the other groups’ data sheets.
4.0
RESULTS AND DISCUSSION
1.8
Data
Each team collected and recorded data from the lab experiment which was conducted on November 13, 2008. The instructor allowed each team to have the data recorded by the remaining three teams to generate accurate results. However, the lab experiment was found to be prone to errors, and the generated results were constantly inconsistent. The inconsistency was due to the irregularity in the bending angle and cyclic force and stresses applied at the point of application.
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Table 4.1.1 depicts the average number of cycles to failure in reference to the angle of deflection for small silver paper clips. Averages are depicted for both individual team data and for the entire data set given by the instructor. Table 4.1.1: Average Cycles to Failure (Small silver) Team
Size
1
Small
2
Small
3 4
Small Small
Brand Silver Silver Silver Silver
Average
Small
Silver
= 45º 71.8 55.6 34.2 278.6 110.05
= 90º 18.6 22.6 10.8 26 19.5
= 135º 13.2 8.8 7.2 17.4 8.98
= 180º 3.4 7.4 3 4.8 11.65
Table indicates that with an increased angle of deflection, the number of cycles to failure decreased as predicted by the team. Table 4.1.2 depicts the average number of cycles to failure for small brass paper clips: Table 4.1.2: Average Cycles to Failure (Small brass) Team
Size
1 2
Small Small
3 4
Small Small
Brand Brass Brass Brass Brass
Average
Small
Brass
= 45º 52.8 105.6 15.4 146.4 80.05
= 90º 19.6 20.8 9.6 12 15.5
= 135º 8.4 12.6 8 8 9.25
= 180º 8 5 4 5.4 5.6
Table 4.1.2 indicates that with an increased angle of deflection, the number of cycles to failure decreased as predicted by the team.
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Table 4.1.3 depicts the average number of cycles to failure for large silver paper clips: Table 4.1.3: Average Cycles to Failure (Small brass) Team
Size
1
Large
2
Large
3 4
Large Large
Brand Silver Silver Silver Silver
Average
Large
Silver
= 45º 44.8 75.6 26.4 183.6 82.6
= 90º 13.6 13.6 12 11.2 12.6
= 135º 5.4 6.4 6.2 4.6 5.65
= 180º 1.8 2.6 1.6 2.6 8.6
Table 4.1.3 indicates with an increased angle of deflection, the number of cycles to failure decreased as predicted by the team. An observation was made by the team that the averages for large silver clips are higher than the averages for either small silver or small brass paper clips.
1.9
Graphical Representation of Data
Figure 4.2.2 depicts the number of cycles to failure for each brand of paper clip for an angle of forty five (45) degrees (θ =45º):
Figure 4.2.2: 45 º Bar Graph As seen in Figure 4.2.2, most of the data is relatively inconsistent. If a general trend line would be drawn, then the line would not be linear as expected. There is an obvious distinction between data points for separate teams.
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Figure 4.2.3 illustrates the number of cycles to failure for each brand of paper clip for an angle of ninety (90) degrees (θ =90º):
Figure 4.2.3: 90 º Bar Graph As seen in Figure 4.2.3, small silver generally has a larger number of cycles to failure than small brass or large silver. The data is n ot suitable for comparing small brass to large silver.
Figure 4.2.4 , on the top following page, depicts the number of cycles to failure for each brand of paper clip for an angle of one hundred and thirty five (135) degrees (θ =135º):
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Figure 4.2.4: 135 º Bar Graph As illustrated in Figure 4.2.4, there is a separation of data when comparing brands. However, the data is inconsistent because for some data point’s small brass has the best endurance, yet for data points 15 to 20, small brass fails in the shortest number of ben ds.
Figure 4.2.5 depicts the number of cycles to failure for each brand of paper clip for an angle of one hundred and eight (180) degrees (θ =180º):
Figure 4.2.5: 180 º Bar Graph
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As seen, on the bottom of the pervious page, in Figure 4.2.5, small silver paper clips are generally consistent for θ =180º. However, the data for small brass and large silver do not allow for conclusions to be drawn.
1.10 Commentary on Data Although general trends could be established, the data obtained from each team was not consistent enough to draw specific conclusions. Howe ver, the number of cycles to failure was inversely proportional to the angle of deflection (i.e., as the angle of deflection increased, the number of cycles to failure decreased regardless of the type of paper clip). The inconsistency in data is most likely due to a number of factors such as the following: a) The various methods used by each team to bend the paper clips, b) The differences in magnitude of the force applied to bend the paper clips, c) The speed at which the paper clips were bent, and d) The time elapsed between each cycle (i.e., the time interval when one cycle was completed and another cycle was started). All of these factors could be controlled by establishing specific instructions and creating a controlled experiment. The data obtained was rendered as inappropriate for scientific purposes since the data generated was constantly inconsistent.
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CONCLUSIONS AND RECOMMENDATIONS
1.11 Purpose This experiment served two purposes: a) The experiment introduced the topic of metal fatigue to readers and allowed the readers to draw conclusions from experimental data, and b) The experiment allowed students to write a technical lab report in preparation for future classes.
5.2
Procedures
From each of the three brands of paper clips, twenty paper clips were collected, measured and weighed. The paper clips were then bent to a specified angle of deflection until the paper clips experienced fatigue failure. Data was recorded for each paper clip, and the cumulative data from each team was compiled and distributed to the other three teams.
1.12 Key Results The general trend of the data depicted that the number of cycles to failure for each paper clip was essentially independent of its physical characteristics. When related to the angle of deflection, however, a very clear relationship emerged: the number of cycles to failure for a paper clip was inversely dependent on the angle of deflection (i.e., as the angle of deflection increased, the number of cycles to failure decreased). This relationship is illustrated in Figure 5.3.6:
Figure 5.3.6: Failure Comparison by Brand
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As illustrated on the bottom of the previous p age, in Figure 5.3.6, an increase in the angle of deflection resulted in a decrease in the number of cycles to failure for all paper clips, regardless of brand.
5.4
Conclusions
The lab report explained the procedures and the results of the lab experiment which was conducted on November 13, 2008. This experiment tries to describe the relation between the cycles of failure and the bending angle for the three categories of paper clips (i.e., small silver, small brass, and large silver). As explained in the section 4.0 Results, the breaking of metal (paper clips in this case), was dependent on the bending angle and the force applied. The initial hypothesis was found to be incorrect. The small silver and small brass paper clips failed much earlier than the large silver paper clips at high bending angles. It was also observed that paper clips (metal) undergo fatigue failure after a finite number of cycles for any bending angle. This study predicts that metals could break due to finite or infinite number of cyclic forces or stresses being applied on them.
6.5
Recommendations
There are limitations while conducting undergraduate college experiments. The procedures used for performing the experiment could have been altered to minimize errors. The factors affecting the inaccuracy of the results are human error, unknown material composition, and inconsistent bending angle. To ensure accurate results, the experimenters must make sure of the following: a) The bending angle should be the same for every cycle of bending. b) The experimenters could use a device which applies constant force on the paper clip for every cycle. c) Each category of paper clips were tested five (5) times for each angle (45°, 90°, 135°, 180°), which could be insufficient to make any conclusions. Hence, more number of tests were to be conducted. In addition to the experimenters’ precautions, a lab monitor could assist the students in conducting the experiment.
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REFERENCES
Engineers Edge (2000). Fatigue – Strength (Mechanics) of Materials. Engineers Edge. Retrieved November 28, 2008, from http://www.engineersedge.com/material_science.
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ATTRIBUTIONS
Person
Task
Dr. Richard Theis
Setup, Experiment
Jake Jacot
Bender
Shyam Thota
Recorder, Timer
Sreyes Kadapala
Photographer
Figure 7.1, Figure 7.2 , Figure 7.3, and Figure 7.4 display the images of the conductors of the lab experiment on November 13, 2008, and the professor who guided the experimenters to conduct the experiment:
Figure 7.1: Dr. Theis Dr. Theis was responsible for the setup of the experiment.
Figure 7.2: Jake Jacot Jake Jacot was responsible for the bending of the paper clips.
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Figure 7.3: Shyam Thota Shyam Thota was responsible for the recording and timing the results.
Figure 7.4: Sreyes Kadapala Sreyes Kadapala was responsible for the photographs which w ere to be taken of the experiment. Figure 7.5, illustrates an image of the team which conducted the lab experiment on November 13, 2008
Figure 7.5: Team Members for the Experiment In Figure 7.5 from left to right in order: Jake Jacot, Shyam Thota, and Sreyes Kadapala.
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Staples® is a registered trademark of Staples Inc. USA. Ohaus® is a registered trademark of Ohaus Corporation USA. Wal-Mart® is a registered trademark of Wal-Mart America Inc. USA. Charles Leonard® is a registered trademark of Charles Leonard Inc. USA Kodak® is a registered trademark of Kodak USA. Apple® is a registered trademark of Apple Inc. USA. ®
C-Thru is a registered trademark of C-Thru Inc. USA.
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APPENDIX I: SAMPLE CALCULATIONS
In order to accurately compare the data of one team to the data of another team, an average value was needed. To calculate the average, Table 8.1 was used. A sample calculation for calculating the average number of cycles to failure is depicted in Table 8.1:
Table 8.1: Team 1 Raw Data for Sample Calculation of Average Size
Brand
Small
A A A A A
Test #
= 90º 1 2 3 4 5
50 40 50 20 30
The data in column four of Table8.1 was added together to calculate the sum of the values: 50 + 40 + 50 + 20 + 30 = 190 The sum of data values in column four of Table8.1 was then divided by the total number of data values (5) as illustrated below: 190 / 5 = 38 The average of the sample data is found to be 38.
8.1 Average weight of one paper clip The average weight of one (1) paper clip for the small silver category was calculated as follows: The total weight is of twenty (20) Staples® small silver paper clips was measured u sing Ohaus-Dial-O-Gram® Balance, and the total weight was measured 8.3 grams. Avg. weight =
Totalweight 20
=
8.3 g 20
= 0.43g
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8.2 Average of cycles of failure The average of cycles to failure for the Staples® small silver paper clips for bending angle of 45° after five (5) tests was calculated as follows: Avg. of cycles to failure = cycles to failure in each attempt / number of attempts. For example, the calculation done below is an average of small silver paper clips bent at an angle of 45° for five (5) cycles. Avg. of cycles to failure =
94 + 100 + 94 + 77 + 120 5
=
485 5
= 97
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APPENDIX II: RAW DATA
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SCANNED IN DATA SHEET FOR TEAM 1 (PAGE 1)
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SCANNED IN DATA SHEET FOR TEAM 2 (PAGE 1)
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SCANNED IN DATA SHEET FOR TEAM 3 (PAGE 1)
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SCANNED IN DATA SHEET FOR TEAM 4 (PAGE 1)
Team 4 (Couch, Mueller, Cummings, Freienmuth)
Size Small
Small
Large
Brand A A A A A B B B B B C C
Test # 1 2 3 4 5 1 2 3 4 5 1 2
= 45º 91 550 513 26 213 205 120 138 49 220 182 231
= 90º 29 21 23 26 31 14 13 9 17 7 2 28
= 135º 17 26 10 11 23 14 9 5 6 6 2 3
= 180º 3 6 4 5 6 3 6 8 5 5 1 6
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10.0 APPENDIX III: DATA SHEET
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Data Sheet Page 1
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Data Sheet Page 2
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