metal fatigue in paperclips

Technical Lab Report on Metal Fatigue in Different Brands of Paperclips at Different Orientations

Date of Submission: 14 December 2004

By

________________________________Harsh Menon

[email protected] ID: 1010682

Box#8275

Submitted to Dr. Angela BeckDepartment of Humanities/Communications

College of Arts and SciencesEmbry-Riddle Aeronautical University

In Partial FulfillmentOf the Requirements

Of

COM 221.03 Technical Report WritingFall 2004

Embry-Riddle Aeronautical UniversityPrescott, Arizona

ABSTRACT

An elementary analysis of metal fatigue was the primary purpose of the experiment performed on November 18, 2004. The experiment involved bending paperclips at four different orientations, i.e., 45o, 90o, 135o and 180o. Four (4) brands of paperclips were used for the experiment, i.e., A, B, C and, D. Brand A were standard size silver paper clips, Brand B were the same size paperclips with colored stripes on it. Brand C were small gold-colored paperclips, and Brand D were jumbo size gold colored paperclips. Sixteen (16) paperclips of each brand were given to four (4) groups of approximately six (6) students to perform the in-class experiment. The experimental results showed that irrespective of the dimensions of the paperclips, the greater the angle through which the paperclip was bent, the fewer the cycles required for fracture.

The theory behind fatigue is quite complicated and hence most of the analysis in fatigue uses statistical methods. In general, the total number of cycles for a metal to fracture is inversely proportional to the stress acting on that metal. This can be seen graphically by plotting the data obtained from the experiments. Even though errors existed during experimentation, the data remained reasonable. However, the data should not be used for any future papers or analyses and should be used only for qualitative comparisons. The paper suffers from experimental errors and probably manufacturing errors. A more accurate paper could probably be obtained by ensuring consistency while fracturing the paperclip and operators ensuring they don’t compromise on accuracy due to time constraints.

This lab report contains an in-depth section on the theory behind metal fatigue, the procedures that were used during experimentation, the results obtained from the experimental data, and the conclusions that evaluate the extent to which this experiment is accurate.

ABSTRACT.....................................................................................................i

LIST OF TABLES.........................................................................................iii

LIST OF FIGURES........................................................................................iv

LIST OF SYMBOLS.....................................................................................vi

LIST OF EQUATIONS................................................................................vii

1.0 INTRODUCTION................................................................................1

2.0 THEORY..............................................................................................4

3.0 APPARATUS AND PROCEDURES.................................................21

3.1 APPARATUS..................................................................................21

3.2 PROCEDURES...............................................................................24

4.0 RESULTS AND DISCUSSION.........................................................29

5.0 CONCLUSIONS AND RECOMMENDATIONS.............................33

6.0 REFERENCES....................................................................................34

7.0 ATTRIBUTIONS................................................................................36

8.0 APPENDIX A: SAMPLE CALCULATIONS...................................37

9.0 APPENDIX B: RAW DATA..............................................................40

LIST OF TABLES

TABLE 2.1: MODULUS OF ELASTICITY FOR METALS .....................................................12

TABLE 2.2: AISI TYPE 302 PROPERTIES ........................................................................17

TABLE 2.2: AISI TYPE 302 PROPERTIES, CONTD. .........................................................18

TABLE 2.3: VINYL ALLOY PROPERTIES ..........................................................................18

TABLE 2.3: VINYL ALLOY PROPERTIES, CONTD. ...........................................................19

Table 9.1: Raw Data Calculations..................................................................................40

LIST OF FIGURES FIGURE 1.1: WRECKAGE RECONSTRUCTION. ...................................................................1

FIGURE 1.2: CABIN FATIGUE. ............................................................................................2

FIGURE 1.3: FUSELAGE FAILURE. .....................................................................................2

FIGURE 2.1: STAGE I AND II CRACK GROWTH. ...............................................................6

FIGURE 2.2: INTRUSIONS AND EXTRUSIONS. .....................................................................7

FIGURE 2.3: HIGH PLASTIC STRESS CONCENTRATION. ...................................................7

FIGURE 2.4: FRACTURE MARKINGS. .................................................................................8

FIGURE 2.5: STRIATIONS. ...................................................................................................9

FIGURE 2.6: STRESSES. .......................................................................................................9

FIGURE 2.7: AXIAL STRESS VS. AXIAL STRAIN. .............................................................11

FIGURE 2.8: SHEAR STRESS VS. SHEAR STRAIN. ............................................................11

FIGURE 2.9: STRESS CYCLES. ..........................................................................................13

FIGURE 2.10: REPEATED STRESS CYCLE. .......................................................................14

FIGURE 2.11: S-N DIAGRAM. ...........................................................................................15

FIGURE 2.12: METALS S-N CURVES. ...............................................................................16

FIGURE 3.1: PROTRACTOR. ..............................................................................................21

FIGURE 3.2: RULER. .........................................................................................................21

FIGURE 3.3: BRAND A. .....................................................................................................22

FIGURE 3.4: BRAND A BOX. .............................................................................................22

FIGURE 3.5: BRAND B. .....................................................................................................22

FIGURE 3.6: BRAND B BOX. .............................................................................................23

FIGURE 3.7: BRAND C. .....................................................................................................23

FIGURE 3.8: BRAND D. .....................................................................................................24

FIGURE 3.9: BRAND D BOX. .............................................................................................24

FIGURE 3.10: SUPERVISOR. ..............................................................................................25

FIGURE 3.11: DATA TABLE. .............................................................................................25

FIGURE 3.12: SHEET WITH ANGLES. ...............................................................................26

FIGURE 3.13: PARTS OF THE PAPERCLIP. .......................................................................26

FIGURE 3.14: FRACTURED PAPERCLIP. ...........................................................................27

FIGURE 4.1: BRAND A PLOT. ...........................................................................................29

FIGURE 4.2: BRAND B PLOT. ...........................................................................................29

FIGURE 4.3: BRAND C PLOT. ...........................................................................................30

FIGURE 4.4: BRAND D PLOT. ...........................................................................................30

FIGURE 4.5: ALL BRANDS. ...............................................................................................31

LIST OF SYMBOLS

A Amplitude Ratio

E Young’s Modulus of Elasticity N/ m2

G Shear Modulus of Elasticity N/ m2

I Moment of Inertia m4

M Bending Moment N-m

P Axial Force N

Q First moment m3

R Stress Ratio

V Shear Force N

a Area m2

b Width m

n Total number of data

x Data value

Summation

Axial Stress N/ m2

τ Shear Stress N/ m2

ε Axial Strain

γ Shear Strain

’ Mean Area m2

¯ Mean value of a set of data

∆ Change

LIST OF EQUATIONS

= P/A Equation 2.1

Equation 2.2

Q=y’A’ Equation 2.3

Equation 2.4

Equation 2.5

Equation 2.6

Equation 2.7

a = ( max - min) / 2 Equation 2.8

Equation 2.9

Equation 2.10

Equation 2.11

Equation 2.12

Metal Fatigue 1 4/8/2023

1.0 INTRODUCTION

Fatigue is a phenomenon defined as progressive failure of a material due to cyclic loading (Lanning 2004). This phenomenon is commonly encountered in the power, nuclear and aircraft industry in components such as pressure vessels, water, gas and steam turbines, piping, turbo compressors and other mechanical structures. Fatigue reduces the lifetime of structures and can be compared to the fatigue that humans feel after physical exertion.

The study of metal fatigue dates back to the mid 19th-century when the railroad locomotive axles broke quite often (Encyclopedia Britannica 2004). Since then, considerable progress has been achieved in the field of solid mechanics and structural analysis. Engineers are now capable of predicting fatigue in metals and hence modify their design accordingly.

A study on metal fatigue is essential for the aspiring aerospace, mechanical or civil engineer because fatigue is a very common occurrence and a thorough understanding of the concept would expand the engineer’s ability to design safer structures. Fatigue failure was one of the main reasons why the de Havilland DH-106 Comet failed over Elba, Italy on January 10, 1954. A reconstruction of the fuselage and tail wreckage can be seen in Figure 1.1: Wreckage Reconstruction:

Figure 1.1: Wreckage Reconstruction.(Source: geocities.com 1999).

The primary probable reason for the crash is fatigue failure in the cabin, due to the low fatigue resistance of the cabin. All persons on board were killed. Signs of fatigue failure in the skin of the airplane at the starboard rear corner of a rear aerial window are shown in Figure 1.2: Cabin Fatigue:


Figure 1.2: Cabin Fatigue.(Source: geocities.com 1999).

A similar but more recent accident took place on 28 April 1988 with a Boeing 737-297. The Aloha Airlines Boeing was flying over Hilo and was at an altitude of 24000 feet when the lap joint of the fuselage failed and the upper lobe of the fuselage separated from the rest of the plane, as can be seen in Figure 1.3: Fuselage Failure:

Figure 1.3: Fuselage Failure.(Source: airdisaster.com).

Surprisingly, the airplane had a safe landing with only one fatality. The fatality was a cabin attendant who was blown out because of the decompression that resulted from the disintegration of the fuselage.

However, since the concept of metal fatigue is relatively new, it is generally applied primarily to mechanical macroscopic structures such as bridges and aircraft and not to comparatively smaller structures such as paper clips. Therefore, the purpose of this lab is to test the metal fatigue in four (4) different types of paper clips and four (4) different orientations, i.e., 45o, 90o, 135o, 180o.


This report will encapsulate the theory behind the experiment, the findings from the experiment, and the conclusions that can be drawn from the findings.


2.0 THEORY

2.1 Technical Definitions

The technical definitions in this section have been defined in order of their appearance in the theory section to assist the reader in their understanding of the text. They are as follows:

Fatigue: Fatigue is the phenomenon leading to fracture under repeated or cyclic stresses having a maximum value less than the tensile strength of the material. Fatigue fractures are progressive, beginning as minute cracks that grow under the action of the cyclic stress.

Tensile Strength: When a force is applied on a body, the force is applied either into the body or away from it. When the force is acting away from the body, the force is said to be a tensile force. When the force is acting into the body, the force is said to be a compressive force. Tensile strength is defined as how large a tensile force the body can withstand.

Load: A load is a force applied on an object, either along or perpendicular to the axis of the body. The load could be a tensile or compressive force.

Stress: Stress is defined as the intensity of the internal force on a specific plane or section (Helbling 2004). It is expressed as the force per unit area.

Stress Concentration: A stress concentration is an increase in local stress due to an abrupt change in cross-sectional geometry (Helbling 2004).

Localized Shear Plane: The localized shear plane is the microscopic plane along which the different particles of the body slide against each other.

Shear Stress: Shear stress is the stress caused by forces operating parallel to each other but in opposite directions.

Plasticity: Plasticity is the tendency of a loaded body to assume a deformed state other than its original state when the load is removed.

Slip: Slip is the process which allows plastic flow to occur in metals, where the crystal planes slide past one another. In practice, the force needed for the entire block of crystal to slide is very great, and so the movement occurs by dislocation motion along the slip planes, which requires much lower levels of stress (matter.org 2004).

Slip bands: Slip bands are the steps or terraces formed on the specimen surface when parts of the material slip relative to one another (matter.org 2004)


Intrusions and Extrusions: As slip bands move in and out of the body, they intersect the surface and produce deformations extending into or away from the surface. The deformations that extend into the surface are called intrusions and the deformations that extend away from the surface are called extrusions (matter.org 2004).

Fracture: Fracture is defined as the separation of an item into two or more parts (matter.org 2004).

Moment: A moment is a force acting at a distance from a point in a structure so as to cause a tendency of the structure to rotate about that point.

Torque: A torque is a moment which is along the axis of a body. It results in the formation of shear stresses in the body (Rabern 2004).

Bending Moment: Bending moment is a moment that causes bending behavior in the body resulting in the formation of axial stresses. It does not act along the axis of the body (Rabern 2004).

Neutral Axis: The neutral axis is the internal axis of a member in bending along which the strain is zero; on one side of the neutral axis the fibers are in tension, on the other side the fibers are in compression (matter.org 2004).

Strain: Strain is defined as a change in shape or size due to an applied force. (Helbling 2004).

Plastic Deformation: Permanent change in the shape of a material as a result of the application of an applied stress. The work done in deforming the sample is not recoverable (matter.org 2004).

Stress Cycle: A stress cycle is defined as cyclic application of loads on a body. The magnitude of the loads could be constant or time-variant.

2.2 Mechanism of Fatigue Failure

Fatigue failure has been observed to occur in three (3) stages:

1. Crack Initiation

This process occurs at the microscopic level. A single load does not produce a considerable effect on the crystalline structure of the metal, but cumulative loading results in formation of several micro cracks. Cracks start forming on the localized shear plane at or near high stress concentrations, such as holes, fillets or other discontinuities. The localized shear plane usually occurs at the surface or at the interface between the crystals of the metal. Crack initiation might take place at a single site or several sites, but in either case the initiation site is very small.


2. Propagation

In this stage, two (2) types of cracks are formed:

Stage I cracks: Stage I cracks are short cracks which propagate at 450 to the direction of the applied load, i.e., along the line of maximum shear stress. The crack tip plasticity depends on microscopic properties such as slip characteristics, grain size, orientation, and stress level. This is because the crack tip size is comparable to the microstructure of the material.

Stage II cracks: Stage I cracks traverse about two or three grain boundaries and usually becomes Stage II cracks. Stage II cracks are long cracks that propagate 900 to the plane in which the tensile load is applied. Their formation does not depend on the material microstructure as much as Stage I cracks, because the crack tip plastic region for Stage II cracks is much larger than the material microstructure.

Stage I and Stage II cracks are illustrated in Figure 2.1: Stage I and II Crack Growth:

Figure 2.1: Stage I and II Crack Growth.(Source: ncode.com 2004).

On closer observation of the development of a Stage I crack, the formation of persistent slip bands along the shear plane is noticed. The bands slip back and forth and produce intrusions and extrusions as can be seen in Figure 2.2: Intrusions and Extrusions on the next page.


Figure 2.2: Intrusions and Extrusions.(Source: ncode.com 2004).

The Stage I crack propagates in this manner until sufficient energy has been transferred to the adjacent grain and so on and so forth.

After crossing two or three grain boundaries in the direction of crack propagation, the physical nature of the crack is observed to have changed. The crack forms a macroscopic obstruction to the flow of stress and this results in the formation of a high stress concentration at the crack tip. This can be seen in Figure 2.3: High Plastic Stress Concentration:

Figure 2.3: High Plastic Stress Concentration.(Source: ncode.com 2004).


3. Final Rupture

As the propagation of the fatigue crack continues, the cross-sectional area of the part reduces until the part gets so weakened that complete fracture occurs with only one more load application. The part then fractures. Once a crack has formed or complete failure has occurred, the surface of a fatigue failure can be inspected. A bending or an axial fatigue failure generally leaves behind clamshell or beach markings as can be seen in Figure 2.4: Fracture Markings:

Figure 2.4: Fracture Markings.(Source: ncode.com 2004).


Within the beach lines are lines called striations. The striations in between the beach lines can be seen in Figure 2.5: Striations:

Figure 2.5: Striations.(Source: Meyer 1997).

The striations are similar to the rings on the cross-section of a tree. The only difference is that instead of representing a year of growth, the striations represent the extension of the crack during one loading cycle. In the event of a failure, there exists a final shear lip which is the last bit of material supporting the load before failure.

2.3 Fatigue Analysis

Before a fatigue analysis can be performed, it is essential to define the loads that are acting on the object. There are three common ways in which stresses may be applied – axial force, torque and by a bending moment as can be seen in Figure 2.6: Stresses:

Figure 2.6: Stresses.(Source: Meyer 1997).

(a) (b) (c)

(a) Stress due to an axial force, (b) Stress due to a torque, (c) Stress due to a bending moment.


An axial force produces an axial stress which is defined by Equation 2.1:

= P/aEquation 2.1

where is the axial stress, P is internal axial force in the beam, a is the cross-sectional area of the beam.

Torque produces a shear stress which is defined by Equation 2.2:

Equation 2.2

where is the shear stress, V is the internal shear force, Q is the first moment, Iz is moment of inertia about the z-axis and b is the cross-sectional width at the point of interest.

Q, the first moment is defined by Equation 2.3:

Q=y’a’ Equation 2.3

where a’ is the area on the cross-section above or below a distance ‘y’ from the neutral axis and y’ is the distance from the neutral axis to the centroid of a’.

Bending moment produces an axial stress which is defined by Equation 2.4:

Equation 2.4

where M is the internal bending moment, y is the distance from the neutral axis and Iz is moment of inertia about the z-axis.

Hooke’s Law states that stress is directly proportional to strain. Several experiments have been performed to analyze the relationship between and axial stress and axial strain. The plot of axial stress versus axial strain can be seen in Figure 2.7: Axial Stress vs. Axial Strain on the next page.


Figure 2.7: Axial Stress vs. Axial Strain.(Source: Horak 2004).

Figure 2.7: Axial Stress vs. Axial Strain, shows the different effects a body undergoes as greater stress is applied to it. Hooke’s Law can be stated as an equation in Equation 2.5:

Equation 2.5

where is the axial stress, E is Young’s modulus of elasticity and ε is the axial strain.

Hooke’s law is applicable only in the linear region of the stress-strain curve. As long as the body is in the linear region, it will return to its initial position after the applied force is removed. If the stress is continually increased, the object will ultimately fracture. The applied stress at which irreversible plastic deformation is first observed across the sample is called the yield stress. A similar diagram exists for shear stress versus shear strain and this can be seen in Figure 2.8: Shear Stress vs. Shear Strain:

Figure 2.8: Shear Stress vs. Shear Strain.(Source: physics.uwstout.edu 2004).


As can be seen in Figure 2.8: Shear Stress vs. Shear Strain, there exists primarily two regions: the linear region and the elastic region. As long as the body is in the linear elastic region, it will return to its original position after the applied force is removed. If the stress is continually increased, the object will ultimately fracture.

Hooke’s Law for shear stress and strain can be stated as in Equation 2.6:

Equation 2.6

where is the shear stress, G is the shear modulus of elasticity and γ is the shear strain.

Table 2.1: Modulus of Elasticity for Metals shows the values of the two constants for a few common metals on the next page.

Table 2.1: Modulus of Elasticity for Metals (Source: Pennsylvania State University 2004).

Material E (109 N/m2) G (109 N/m2)Aluminum 70.3 26.1Bismuth 31.9 12.0

Brass (70 Zn, 30 Cu) 100.6 37.3Cadmium 49.9 19.2Chromium 279.1 115.4

Copper 129.8 48.3Gold 78.0 27.0

Iron (soft) 211.4 81.6Iron (cast) 152.3 60.0

Lead 16.1 5.59Magnesium 44.7 17.3Nickel (soft) 199.5 76.0Nickel (hard) 219.2 83.9

Platinum 168.0 61.0Silver 82.7 30.3

Steel (mild) 211.9 82.2Steel (tool-hardened) 203.2 78.5

Steel (stainless) 215.3 83.9Tungsten Carbide 534.4 219.0

There are also three stress cycles by which loads may be applied to a body. These are described on the next page.

1. Reversed Stress Cycle: This type of stress cycle has an amplitude which is symmetric about the x axis. The maximum and minimum stresses are equal, but opposite in sign.


2. Repeated Stress Cycle: The repeated stress cycle is a sine wave that is asymmetric about the x axis. The maximum and minimum stresses are not equal and opposite in sign.

3. Irregular/Random Stress Cycle: This stress cycle does not follow any pattern and the maximum and minimum stresses might or might not have a clear relationship.

All three stress cycles can be seen in Figure 2.9: Stress Cycles:

Figure 2.9: Stress Cycles.(Source: Shield n.d.).

Out of all three types of stress cycles, the irregular loading is the most common stress cycle. Further structural analysis in this document is continued using the repeated stress cycle as the applied load.

In the structural analysis of an object subjected to a cyclic loading, the following terms are defined on the next page.

Stress range ( ): The stress range is defined as the algebraic difference between the maximum stress ( max) and the minimum stress ( min) in a cycle, as can be seen in Equation 2.7:


Equation 2.7

Stress Amplitude ( a): The stress amplitude is defined as one half of the stress range, as can be seen in Equation 2.8:

a = ( max - min) / 2 Equation 2.8

Mean Stress ( m): The mean stress is defined as the sum of the maximum stress (max) and the minimum stress ( min) in a cycle, divided by 2, as can be seen in

Equation 2.9:

Equation 2.9

These variables are illustrated in Figure 2.10: Repeated Stress Cycle:

Figure 2.10: Repeated Stress Cycle.(Source: Hollis 2004).

Besides these basic parameters, two more parameters have been defined which are used as representations of the mean stress applied to an object:

Stress ratio (R): The stress ratio is defined as the ratio of the minimum stress (min) to the maximum stress ( max), as can be seen in Equation 2.10 on the next page.

Equation 2.10

Amplitude ratio (A): The amplitude ratio is defined as the ratio of the stress amplitude to the mean stress, as can be seen in Equation 2.11 on the next page.


Equation 2.11

For fully reversed stress cycles, the stress ratio is -1 and the amplitude ratio is infinity. For repeated stress cycles, the stress ratio is 0 and the amplitude ratio is 1.

In order to produce data for useful fatigue designs, stress-life fatigue tests are carried out on several specimen at different amplitudes over a range of fatigue lives for identically prepared specimens. The test data are then plotted on either semi-log or log-log coordinates. The curve in these plots is referred to as an S-N curve or a Wohler curve. It is a plot of stress amplitude versus number of cycles, as can be seen in Figure 2.11: S-N Diagram which is an S-N curve plotted on a semi-log coordinates:

Figure 2.11: S-N Diagram.(Source: csme.ed.ac.uk 2000).

When the curve is plotted on log-log scales, it becomes linear. The portion of the curve with a negative slope is called the finite life region and the horizontal line is called the infinite life region. The point on the S-N curve at which the curve changes from a negative slope to a horizontal line is called the knee of the S-N curve and it represents the fatigue limit or the endurance limit.

The endurance limit is defined as the stress level below which a specimen will withstand cyclic stress indefinitely without exhibiting fatigue failure. Rigid, elastic, low damping


materials such as thermosetting plastics and some crystalline thermoplastics do not exhibit an endurance limit or a fatigue limit. Ferrous materials and titanium alloys display a horizontal asymptote for high cycles, while metals such as aluminum, copper and magnesium do not have a fatigue limit.

Fatigue strength depends on grain size, corrosion, frequency and vacuum. Further discussion on those topics is beyond the scope of this document. Figure 2.12: Metals S-N curves shows the S-N curves for several metals and metallic alloys:

Figure 2.12: Metals S-N curves.(Source: Jenkins 2000).

From the S-N curve, it is obvious that as the magnitude of the stress increases, the number of cycles to failure decrease. In the in-class experiment reported herein, as the angle by which the paper clip was bent increased, the torque applied to the paper clip also increased. Since the torque increased, the total shear force applied to the system and hence the total shear stress increased. Since the stress increased, fewer numbers of cycles were required to fracture the material. The hypothesis made prior to the experiment was


that larger the angle, fewer the number of cycles for the paperclip to fracture, irrespective of the dimensions of the paperclip.

The metal used to make paperclips was assumed to be AISI Type 302 Stainless Steel tested at 21oC. The properties of the steel are enumerated in Table 2.2: AISI Type 302 Properties:

Table 2.2: AISI Type 302 Properties (Source: matweb.com 2003).

Physical Properties Metric English Comments

Density 7.86 g/cc 0.284 lb/in³

Mechanical Properties

Tensile Strength, Ultimate 585 MPa 84800 psi

Tensile Strength, Yield 255 MPa 37000 psi at 0.2% offset

Elongation at Break 57 % 57 % in 50 mm

Modulus of Elasticity 193 GPa 28000 ksi

Poisson's Ratio 0.25 0.25 Calculated

Shear Modulus 77.2 GPa 11200 ksi

Electrical Properties

Electrical Resistivity 7.2e-005 ohm-cm 7.2e-005 ohm-cm at 20°C, 0.000078 Ohm-cm at 100°C,

0.000086 Ohm-cm at 200°C, 0.0001 Ohm-

cm at 400°C

Magnetic Permeability 1.008 1.008 at RT

Thermal Properties

CTE, linear 20°C 17.2 µm/m-°C 9.56 µin/in-°F from from 0-100°C

CTE, linear 250°C 17.8 µm/m-°C 9.89 µin/in-°F at 0-315°C (32-600°F)

CTE, linear 500°C 18.4 µm/m-°C 10.2 µin/in-°F at 0-540°C, 18.7 µm/m-C at 0-650°C

http://matweb.com/search/GetUnits.asp?convertfrom=5&value=18.4



http://matweb.com/search/GetUnits.asp?convertfrom=116&value=7.2e-005


http://matweb.com/search/GetUnits.asp?convertfrom=45&value=193





Thermal Properties

Heat Capacity

Metric

0.5 J/g-°C

English

0.12 BTU/lb-°F

Comments

from 0-100°C (32-212°F)

Thermal Conductivity 16.2 W/m-K 112 BTU-in/hr-ft²-°F

at 100°C (212°F), 21.5 W/m-K at 500°C

(930°F)

Melting Point 1400 – 1420 °C 2550 - 2590 °F

Solidus 1400 °C 2550 °F

Liquidus 1420 °C 2590 °F

Maximum Service Temperature, Air

870 °C 1600 °F Intermittent Service

Maximum Service Temperature, Air

925 °C 1700 °F Continuous Service

The vinyl-coated metal used to make Brand B paperclips was assumed to have properties similar to that of PolyOne Geon® HTX™ M6210 Vinyl Alloy, which are listed in Table 2.3: Vinyl Alloy Properties:

Table 2.3: Vinyl Alloy Properties (Source: matweb.com 2003).

Physical PropertiesMetric English Comments

Specific Gravity 1.28 g/cc 0.0462 lb/in³ ASTM D792

Linear Mold Shrinkage 0.002 - 0.005 cm/cm

0.002 - 0.005 in/in

ASTM D955

Spiral Flow 94 cm 37 in


Hardness, Shore D 79 79 Instantaneous; ASTM D2240

Tensile Strength, Yield 40 MPa 5800 psi Type 1 - Rigids, 2

in/min; ASTM D638

Elongation at Break 61 % 61 % Type 1 - Rigids, 2

in/min; ASTM D638

Tensile Modulus 2.22 GPa 322 ksi Type 1 - Rigids, 2

in/min; ASTM

Table 2.2: AISI Type 302 Properties (Source: matweb.com 2003), Contd.












D638

Flexural Modulus 2.45 GPa 355 ksi ASTM D790


Flexural Strength

Metric

73.8 MPa

English

10700 psi

Comments

ASTM D790

Izod Impact, Notched 0.534 J/cm 1 ft-lb/in Method A, Injection

Molded, 0.125 in bars, 32°F (0°C); ASTM

D256

Izod Impact, Notched 3.74 J/cm 7 ft-lb/in Method A, Injection

Molded, 0.125 in bars, 73°F

(23°C); ASTM D256

Thermal Properties

Deflection Temperature at 0.46 MPa (66 psi)

76.1 °C 169 °F Unannealed, 0.250 in bars;

ASTM D648


82.8 °C 181 °F Annealed, 0.250 in bars;

ASTM D648


72.2 °C 162 °F Unannealed, 0.250 in bars;

ASTM D648


82.2 °C 180 °F Annealed, 0.250 in bars;

ASTM D648

UL RTI, Electrical 50 °C 122 °F UL 746

UL RTI, Mechanical with Impact 50 °C 122 °F UL 746

UL RTI, Mechanical without Impact 50 °C 122 °F UL 746

Flammability, UL94 V-0 V-0 All Colors; 0.058 in.

Flammability, UL94 V-0 V-0 5VA, All Colors; 0.061

in.

Flammability, UL94 V-0 V-0 All Colors; 0.059 in.

Table 2.3: Vinyl Alloy Properties (Source: matweb.com 2003), Contd.













Flammability, UL94 V-0 V-0 5VA, All Colors; 0.059in

2.4 Statistical Analysis

The data obtained from experimental results needs to be conveyed to others in a manner in which the data is easily understood by others. Statistics is a very powerful tool to express what graphs and data mean. The most commonly used term in statistics is the mean or average, and it is calculated using Equation 2.12:

Equation 2.12

where is the mean value, is the sum of all the data values and n is the number of observations in the data set.


3.0 APPARATUS AND PROCEDURES

3.1 APPARATUS

The following equipment was used during the experiment:

One (1) protractor, as shown in Figure 3.1: Protractor:

Figure 3.1: Protractor.

One (1) 30 in. Hawker Pacific Aerospace© Ruler, as can be seen in Figure 3.2: Ruler:

Figure 3.2: Ruler.

Sixteen (16) Staples© Brand A small silver paperclips, as can be seen in Figure 3.3: Brand A on the next page.


Figure 3.3: Brand A.

The paperclips shown in Figure 3.3: Brand A, are silver in color. They have a length of 3.2 cm, a width (wide) of 0.7 cm, and a width (narrow) of 0.6cm. They have a smooth surface and no ridges.

One (1) Staples© Box containing the silver paperclips as can be seen in Figure 3.4: Brand A Box:

Figure 3.4: Brand A Box.

The box is red in color and held 100 paperclips. It has a flap which can be opened and closed.

Sixteen (16) Staples© Brand B striped and colored paperclips, as can be seen in Figure 3.5: Brand B:

Figure 3.5: Brand B.


As shown in Figure 3.5: Brand B, the paperclips are wrapped in plastic. They have a length of 3.3 cm, a width (wide) of 0.9 cm, and a width (narrow) of 0.8 cm. They have a smooth surface and no ridges.

One (1) Staples© Transparent Box containing the striped and colored paperclips as can be seen in Figure 3.6: Brand B Box:

Figure 3.6: Brand B Box.

The box has a red label and the rest is made of transparent plastic. It contained 100 striped and colored paperclips.

Sixteen (16) Staples© Brand C gold-colored paperclips, as can be seen in Figure 3.7: Brand C:

Figure 3.7: Brand C.

As shown in Figure 3.7: Brand B, the paperclips have a gold-colored paint coating. They have a length of 3.2 cm, a width (wide) of 0.8 cm, and a width (narrow) of 0.6 cm. They have a smooth surface and no ridges.


One (1) Staples© Transparent Box containing the gold colored paperclips. The box has a red label and the rest is made of transparent plastic. It contained 100 gold colored paperclips.

Sixteen (16) Staples© Brand D jumbo gold colored paperclips, as can be seen in Figure 3.8: Brand D:

Figure 3.8: Brand D.

As shown in Figure 3.8: Brand D, the paperclips are bigger than the others. They have a length of 4.9 cm, a width (wide) of 1.0 cm, and a width (narrow) of 0.9 cm. They have a smooth surface and no ridges.

One (1) Staples© Transparent Box containing the jumbo gold-colored paperclips as can be seen in Figure 3.9: Brand D Box:

Figure 3.9: Brand D Box.

The box has a red label and the rest is made of transparent plastic. It contained 100 striped and jumbo gold-colored paperclips.

3.2 PROCEDURES

The procedures that were used for the experiment, which was completed on November 18, 2004 at Embry-Riddle Aeronautical University are described on the next page.


1.0 The class was divided into four (4) teams with an average of six (6) students per team for the experiment.

2.0 Each team member was assigned a role for the experiment, i.e., recorder, operator and, photographer.

3.0 Sixteen (16) paper clips of each brand, i.e., A, B, C and D, were distributed to each of the four (4) groups by the supervisor, Dr. Patrick McElwain, who is shown in Figure 3.10: Supervisor:

Figure 3.10: Supervisor.

Figure 3.2.1: Supervisor.

4.0 A lab data sheet was handed out which required the teams to fill in a rich description of each brand of paper clip, the type of ruler used, and the dimensions of each brand of paper clip. It also had a table which required the group to fill in the number of cycles it took for each type of paper clip to fail at 45o, 90o, 135o and 180o, with four (4) sets of data for each angle. The data table can be seen in Figure 3.11: Data Table:


Figure 3.11: Data Table.

5.0 The 30 in. Hawker Pacific Aerospace© Ruler and the protractor were used to draw all the angles on a separate sheet of paper as is shown in Figure 3.12: Sheet with Angles:

Figure 3.12: Sheet with Angles.

6.0 A certain brand paperclip was clasped between the index finger and thumb of the left hand, by placing the index finger on the top of the paperclip and the thumb at the bottom of the paperclip. The different parts of the paperclip can be seen in Figure 3.13: Parts of the Paperclip:

Figure 3.13: Parts of the Paperclip.

7.0 The paperclip was placed in a vertical orientation over the sheet of paper with all the angles on it.


8.0 The paperclip was bent in the following manner:

8.1 The big pin was clasped in its original position using the left thumb and index finger.

8.2 The small pin was held at point H using the right index finger with the thumb providing support at the bottom of the paperclip.

8.3 The small pin was pulled back by 45o until the pin was coincident with the 45o line on the sheet of paper.

8.4 The small pin was then pushed back by the same fingers as mentioned in step 8.2 to its original position.

8.5 Steps 8.1 to 8.4 were repeated and this was referenced to be one cycle.

8.6 The operator(s) counted the cycles aloud to commit it to memory.

9.0 Steps 8.1 – 8.6 were repeated until the paperclip failed at the point of bending which is point A.

10.0 Once the paperclip failed, a picture of the failed paperclip was taken as can be seen in Figure 3.14: Fractured Paperclip:

Figure 3.14: Fractured Paperclip.

11.0 The number of cycles required for the paperclip to fail was recorded on the data sheet.

12.0 Steps 6.0 to 11.0 were repeated for all the other angles of the chosen brand, i.e., 90o, 135o and 180o.


13.0 Steps 6.0 to 12.0 were repeated for all the other brands at all the other angles.

14.0 The recorded data was submitted to the supervisor once all experimentation had concluded.

15.0 Any excess paperclips were turned in to the supervisor for future use.

16.0 Broken paper clips were discarded in the dust bin in the classroom.

17.0 The data collected from the experiment was then placed in a Microsoft Excel Worksheet.

18.0 The data from each group was placed in a different section and the averages were calculated.

19.0 The data was also used to calculate a correlation coefficient between the data.

20.0 The average number of cycles for each brand were plotted against the four (4) angles in four (4) separate plots.

21.0 The four (4) plots were then combined into one (1) single plot to identify the difference between the data for all the separate brands.


4.0 RESULTS AND DISCUSSION

The data obtained from the in-class experiments were entered into a Microsoft Excel Worksheet and the average number of cycles was plotted against the angle for each brand. These graphs can be seen in Figure 4.1: Brand A Plot, Figure 4.2: Brand B Plot, Figure 4.3: Brand C Plot, Figure 4.4: Brand D Plot and Figure 4.5: All Brands:

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Figure 4.1: Brand A Plot.

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Figure 4.2: Brand B Plot.


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Figure 4.3: Brand C Plot.

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Figure 4.4: Brand D Plot.


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Figure 4.5: All Brands.

As can be seen from these five graphs, a greater number of cycles are required for the metal to fracture at smaller angles. This is in accordance with the hypothesis that was made prior to the experiment and reported in 2.0: Theory.

The five graphs were expected to be similar to the S-N curves discussed in 2.0: Theory. Most of the graphs had the same general shape as can be seen in Figure 2.11: S-N Diagram and Figure 2.12: Metals S-N Curves. The graph for Brand B however had an anomaly, as it took a lot of cycles to fracture at 135o. This is an unexpected result that could possibly be due to operator errors, manufacturing inconsistencies or both.

Another expected result that can be seen from Figure 4.5: All Brands is that Brand D took the least number of cycles to fracture. Since Brand D had the largest dimensions, the expected result was that it would take the most number of cycles to fracture. However, the experimental results were contrary to the expected results. This error could most probably be attributed to the inaccuracy of the operators. However, defective industrial manufacturing could also be a cause for error and should not be ruled out.

The other deviation from expected results was based on material properties. As can be seen from Table 2.2: AISI Type 302 Properties in 2.0: Theory, the metal used to make the paperclip has a high tensile strength of 585 MPa, which means that the metal will not break until it experiences a stress of 585 MPa. Since the paperclip fractured only due to mechanical forces, the thermal and electrical properties of the metal are not important for this analysis and can be safely neglected.


However, out of the four different brands of paperclips, not all were made of the same metal. Brand B paperclips were vinyl-coated metal clips.

As can be seen from Table 2.3: Vinyl Alloy Properties in 2.0: Theory, the vinyl-coated has a lower tensile strength of only 40MPa, as compared to 585MPa. Therefore, if the same forces are applied to the four brands of metals, Brand B should take the least number of cycles to fracture. However, Figure 4.5: All Brands says otherwise, with Brand B taking the most number of cycles to fracture. There are several probable reasons for this unexpected behavior. Some of the reasons are that there might have been manufacturing errors. Another possibility is that the student operators might have miscounted or bent the paperclip through inaccurate angles. There is also a possibility that the assumed metal did not match the properties of the metal that was used during the in-class experiment.

.


5.0 CONCLUSIONS AND RECOMMENDATIONS

This lab was an attempt to study metal fatigue by performing a simple experiment involving bending paperclips. Four (4) different brands of paperclips were distributed to four (4) teams on November 18, 2004. The teams were given instructions to bend the different brands of paperclips at four (4) pre-defined orientations: 45o, 90o, 135o and 180o. The results were tabulated in a data sheet containing the number of cycles of loading placed on each brand of paperclip at each orientation.

As mentioned in 4.0: Results and Discussion, a fewer number of cycles were required to fracture the paperclips at higher angles, irrespective of the brand. This conclusion can be drawn from the information provided in 3.0: Theory, where the S-N curves show that the greater the stress, the fewer the cycles. Since the stress is greater at greater angles, it follows that the paperclips should take a fewer number of cycles to fracture at higher angles. This is an intuitive theory and is of critical importance in the real world as shown in 1.0: Introduction.

However, as is the case with most labs, there were limitations. Several procedures performed during the in-class experiment were susceptible to errors. More accurate results could have been obtained had the students been given an extra hour. The time constraints made it difficult for the students to repeat any fatigue cycle, in the event of a mishap of any kind, especially if their fatigue cycle was at 45o. If the students had been provided with pliers or a similar useful tool for fracturing the paperclip, then more accurate data could have been obtained in the same period of time.

The students also compromised on their accuracy and used approximations to estimate the angle by which they had bent the paperclip. This source of error could be rectified if the students were provided with a sheet of paper each, with all the separate angles marked on them.

Furthermore, since the four separate groups were allowed to work independently without any rigid instructions, there is a possibility that inconsistencies might arise in data, due to individual or group misinterpretations of data, or merely due to gross errors. If the students had been provided with a clear rigid set of instructions, there would be less room for errors. Also if the proctor had been supervising the method of bending used by each group and corrected the students when and if they made errors, greater accuracy could be achieved.

Overall, the experiment was not a complete failure. Even though there were errors during the experiment, the results did not seem too deviant from the expected theoretical results. The findings in 4.0: Results and Discussion are not accurate data and suffer from errors. However, they are satisfactory for a qualitative analysis of the effect of metal fatigue at different orientations in paperclips of different brands.


6.0 REFERENCES

(2003). AISI type 302 stainless steel, tested at 210C. Retrieved December 11, 2004 from matweb.com: Materials Property Database.

(2003). PolyOne Geon® HTX™ M6210 Vinyl Alloy. Retrieved December 11, 2004 from matweb.com: Materials Property Database.

(2004). Accident synopsis 04281988. Retrieved December 6, 2004 from airdisaster.com Accident Database.

(2004). Fatigue engineering: An introduction. Retrieved December 4, 2004, from <http://www.ncode.com/page.asp?section=00010001000100130022>.

(2004). Matter. Retrieved December 13, 2004 from the University of Liverpool website: <http://www.matter.org.uk/>.

Fatigue Encyclopædia Britannica. Retrieved December 9, 2004, from Encyclopædia Britannica Premium Service. <http://www.britannica.com/eb/article?tocId=9033819>.

Helbling, J. (2004, December 5). [Personal Communication].

Hollis, P. (2004). Fatigue failure theories. Retrieved December 4, 2004 from Florida State University website: < http://www.eng.fsu.edu/~hollis/eml3018c-s04/Chapter6-a.doc>.

Horak, E. (2004) Stress strain period .Retrieved December 13, 2004 from University of Pretoria website: <http://www.up.ac.za/academic/civil/divisions/swk213/StressStrainPeriod8.pdf>.

Jenkins, M. (2000). Time dependent behavior: cyclic fatigue. Rertieved December 6, 2004 from University of Washington website: <www.me.washington.edu/~jenkinsm/me354/notes/chap9.pdf>.

Lanning, D. (2004, December 9). [Personal communication].

Meyer, C. (1997 July). Experimental fatigue. Retrieved December 4, 2004 from Virginia Institute of Technology website: <http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/exper/meyer/www/meyer.html>.

Ministry of Transport and Civil Aviation. (1955 February). Official accident report of Comet I G-ALYP. Retrieved December 6, 2004, from<http://www.geocities.com/CapeCanaveral/Lab/8803/fcogalyp.htm#galyp>.


Rabern, D. (2004, December 9). [Personal Communication].

Shield, C. (n.d.). Fatigue. Retrieved December 4, 2004 from Carnegie Mellon University website: <http://www.ce.umn.edu/classes/fall04/ce4401/4_Fatigue_Lecture.pdf>.


7.0 ATTRIBUTIONS

Person TaskDr. Patrick McElwain Proctor

Daniel Lacore OperatorBrian Pollock Data RecorderHarsh Menon Operator

Shreyank Muralidhara PhotographerIan Wells Operator

Staples© is a registered trademark of Staples USA, Incorporated.


8.0 APPENDIX A: SAMPLE CALCULATIONS

Brand A

Average Number of Cycles to Failure at 45o:

= (168+198+163+170+112+139+122+174+55+73+49+49+58+45+44+54)/16= 104.56


= (50+55+62+32+34+34+36+50+26+30+33+26+100+50+23+63)/16=44.00


= (15+13+20+10+9+14+13+16+5+5+11+10+13+7+13+10)/16=11.50


= (6+5+4+4+3+5+4+7+4+3+6+6+6+10+15+6)/16=5.88

Brand B


= (202+218+208+222+56+70+75+92+137+143+137+178+48+38+54+37)/16=119.69


= (76+149+151+60+48+24+25+27+30+24+24+25+31+37+33+34)/16=49.88


= (45+55+144+260+19+16+17+21+9+7+9+17+11+13+18+18)/16=42.44



= (15+11+17+20+13+18+11+7+9+8+10+8+19+9+6+6)/16=11.69

Brand C


= (125+120+113+100+66+146+79+111+100+133+82+112+68+98+60+66)/16

=98.69


= (36+34+38+42+73+30+38+30+37+37+31+45+46+26+31+21)/16=37.19


= (19+16+22+39+10+7+23+21+23+26+24+33+16+24+19+30)/16=22.00


= (6+9+20+4+4+8+5+4+3+8+10+7+11+20+5+25)/16=9.31

Brand D


= (192+103+94+109+55+59+53+47+128+129+123+167+33+24+28+29)/16=85.81


= (37+11+43+48+31+21+35+21+13+11+16+15+26+18+18+20)/16=24.00


= (11+4+10+5+17+13+14+18+7+5+4+10+10+6+5+11)/16=9.38



= (3+5+6+3+7+4+3+4+5+8+5+3+3+4+7+1)/16=4.44


9.0 APPENDIX B: RAW DATA

Table 9.1: Raw Data Calculations.

Group 1

Group 2

Brand Test 45º 90º 135º 180º Brand Test 45º 90º 135º 180ºA 1 168 50 15 6 A 1 112 34 9 3A 2 198 55 13 5 A 2 139 34 14 5A 3 163 62 20 4 A 3 122 36 13 4A 4 170 32 10 4 A 4 174 50 16 7B 1 202 76 45 15 B 1 56 48 19 13B 2 218 149 55 11 B 2 70 24 16 18B 3 208 151 144 17 B 3 75 25 17 11B 4 222 60 260 20 B 4 92 27 21 7C 1 125 36 19 6 C 1 66 73 10 4C 2 120 34 16 9 C 2 146 30 7 8C 3 113 38 22 20 C 3 79 38 23 5C 4 100 42 39 4 C 4 111 30 21 4D 1 192 37 11 3 D 1 55 31 17 7D 2 103 11 4 5 D 2 59 21 13 4D 3 94 43 10 6 D 3 53 35 14 3D 4 109 48 5 3 D 4 47 21 18 4

Group 3

Group 4

Brand Test 45º 90º 135º 180º Brand Test 45º 90º 135º 180ºA 1 55 26 5 4 A 1 58 100 13 6A 2 73 30 5 3 A 2 45 50 7 10A 3 49 33 11 6 A 3 44 23 13 15A 4 49 26 10 6 A 4 54 63 10 6B 1 137 30 9 9 B 1 48 31 11 19B 2 143 24 7 8 B 2 38 37 13 9B 3 137 24 9 10 B 3 54 33 18 6B 4 178 25 17 8 B 4 37 34 18 6C 1 100 37 23 3 C 1 68 46 16 11C 2 133 37 26 8 C 2 98 26 24 20C 3 82 31 24 10 C 3 60 31 19 5C 4 112 45 33 7 C 4 66 21 30 25D 1 128 13 7 5 D 1 33 26 10 3D 2 129 11 5 8 D 2 24 18 6 4D 3 123 16 4 5 D 3 28 18 5 7D 4 167 15 10 3 D 4 29 20 11 1

metal fatigue in paperclips

Documents

microsoft excel worksheet

materials property database

official accident report

vinyl alloy properties

ii crack growth

riddle aeronautical university

irregular random stress cycle

reversed stress cycle