University of California, Berkeley

Lab 7: Fatigue TestingScout Heid

Date Submitted: November 2, 2015Date Performed: November 9, 2015Lab Section: Lab 101 Monday 8-10amLab GSI: Sayna Ebrahimi

AbstractThe objective of this lab was to perform stress-control fatigue testing under different stressamplitudes and compare the experimental results with the theoretical results derivedthrough equations. We put our specimen through an Instron R.R Moore high-speedrotating beam fatigue testing apparatus to measure the number of cycles to failure underdifferent applied loads. We then plotted the data and used S-N curves to compare theunnotched, notched, and experimental data. We primarily used a macroscopic, total life,stress-based approach to study the fatigue failure of each specimen, which allowed us todetermine the accuracy of our equations. We then took images of the fracture surface andanalyzed how the crack growth was affected by the loading conditions. The results showedthat the low cycle stress predictions by the theoretical notch S-N curve differed greatlyfrom that of the experimental data; however, the predictions were relatively accurate athigh cycles. The images of the specimen after fracture also implied that an increase instress amplitude resulted in a rougher fracture surface and unstable crack propagation.This along with lacking data points and preexisting imperfections could be the cause of theerror between the theoretical data, and the experimental data.

IntroductionIn this lab we analyzed material fatigue infour specimen and performed common fatigueanalysis techniques to understand the effectsof different stress amplitude. Fatigue is atype of failure that occurs under cyclical load-ing conditions, but can occur at levels be-low the ultimate tensile strength derived fromstatic loading. It can also occur at stresslevels below the monotonic yield strength.This carries significant importance becausethis means that failure can occur in materialsunder normal, every day stresses. Engineersmust consider the conditions at which theirproducts and materials will be used in orderto avoid unexpected and potentially catas-trophic premature failure.

The two main approaches used to ana-lyzing fatigue failure are macroscopic or mi-croscopic analysis. We focused primarilyon using the stress-based macroscopic ap-proach and utilized stress life curves to pre-dict how different stress amplitudes undercyclical loading would affect the notched testspecimen. We generated the experimental S-N curve for AISI 1045 Steel by using an In-stron R.R Moor high-speed rotating beam fa-tigue testing apparatus to measure the num-ber of cycles to failure for different appliedloads.We plotted the S-N curve based on ex-perimental data and used linear approxima-tion methods to compare it with a theoreticalcurve generated by the sample’s geometricaland material properties.

We also looked at microscopic images ofeach specimen’s fracture surface to analyzefatigue properties under different stressamplitudes. The surface features provide alot of information about how the materialfractured, which can give insight as to whyour experimental results differed from ourtheoretical solution. The same images werethen compared to a specimen that under-went the Charpy impact test to visualize the

similarities and differences between fatiguefailure and other types of failure.

Theory

Fatigue consists of three main stages: crackinitiation, crack growth, and fatigue life.Since the majority of the process is dom-inated by crack initiation (Ni) and crackgrowth (Ng), fracture is neglected and fatiguelife (Nf ) of the material is characterized bythe equation Nf = Ni + Ng; however fatiguelife is also dependent on the type of materialused. Brittle material will be controlled bycrack initiation, whereas a ductile material iscontrolled by crack growth [1].

The three main approaches to fatigue anal-ysis are stress-based approach, strain-basedapproach, and fracture mechanics approach.The first two are considered macroscopic ap-proaches because in these cases, the fatiguelife is directly related to a global driving forceof fatigue, such as stress or strain amplifica-tion. Conversely the third approach is clas-sified as microscopic because the fatigue lifeis obtained in terms of local driving force,such as stress intensity factor range. Themacroscopic and microscopic approaches alsofall under the Total Life and Damage Toler-ant methods respectively. Similar to macro-scopic, Total Life assumes the device is de-fect free and âœlifeâ is based on initiationand propagation of flaws. This differs fromthe Damage Tolerant, which assumes all ma-terials have innate initial flaws and âœlifeâ isbased on propagation. For this lab, we willbe using the macroscopic approaches, specif-ically the stress-based approach [2].

Stress based analysis utilizes semi-logstress-life (S-N) plots to characterize the ma-terial, where stress amplitude is denoted by Sand Cycles of Failure is denoted by N. Since,the S-N approach does not work well with lowcycle fatigue of less than 103 cycles, we lookat the finite and infinite fatigue life between

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103 and 106 cycles. The two main stress am-plitudes are: stress at 100 cycles (Sf ) andendurance limit stress (Se). The stress am-plitude and number of fatigue cycles in thisregion follow the power-law relationship [1]:

σ = A ∗N bf (1)

With the alternate form

σ = σ′f ∗ (2Nf)b (2)

Where A and b are intrinsic fatigue parame-ters of the material. We will be using Sf =0.9 ∗ Su and endurance limit Se = 0.5 ∗ Su,where Su is the ultimate tensile strength.

It is important to note that the stress am-plitude remains constant as cycles to failureincreases, which implies that too low of astress will never fatigue the material. We usestress based approach because we expect thesteel to fracture at relatively high cycles.

The strain based approach inspects boththe elastic and plastic deformation. The fa-tigue life is dominated by plastic strain duringlow cycles and elastic strain at high cycles;therefore, this approach is more accurate atlow-cycle fatigue.

The tests we conducted used notches toconcentrate the stress at a specified locationon the specimen. It will cause crack initiationto occur at the surface discontinuity, allowingfor a controlled experiment. This is a com-mon method for fatigue testing [3]. The en-durance limit is modified for the notch spec-imen based on the equation:

Se =mt ∗md ∗ms ∗mo ∗ Se

′

Kf(3)

Where the m constants are factors basedon sample geometry, Se′ is the original en-durance limit, and Kf is the modified fatigue

intensity factor based on notch size. Kf iscalculated using the equation:

Kf = 1 + q ∗ (Kt − 1) (4)

Where q is the notch sensitivity factor andKt

is the stress concentration factor We willapply these formulae and methods to gener-ate theoretical S-N curves for theoretical un-notched, notched specimen, and then com-pare them with the S-N curve generated fromthe experimental data. These plots will helpus analyze the effects of stress amplitude onthe material and its fatigue failure properties.

Experimental ProcedureWe will be testing straight shank specimensconsisting of AISI 1045 steel with a notch ofradius 0.047 in. machined into the middle ofeach shank. The tests will be performed us-ing an Instron R.R Moor high-speed rotatingbeam fatigue testing apparatus, shown in Fig-ure 1, running at 6000 RPM. The weights ap-ply a constant bending moment on the speci-men, which result in compressive stress on thetop and tensile stress on the bottom. Duringa one half revolution, the stress is reversedfrom compression or tension to the other,and a complete revolution the test specimenpasses through a complete cycle of flexturestress [4]. The main operation RPM range is500 to 10,000 RPM, with a speed stability of±2%. Further specification can be found inAppendix A.

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Figure 1: Machine used for testing cyclesuntil fracture. [4]

We conducted 4 tests and varied the weightof each specimen (9lbs, 10lbs, 11.5lbs, 13lbs).After each test we measured the number ofcycles before fracture and analyzed the frac-ture surface of each specimen. The momentarm was fixed at 4 inches for all samples.

Testing Procedure:

1. Load the specimen on the machineby attaching the end collets and thenscrewing them into the larger loadingharness, specimen holders.

2. Connect the loading harness to themotor shaft and set up the weight panassemblies on the machine, starting witha minimum weight of 9lb

3. Set up the rotation speed to 50%(6000rpm)

4. Turn on the power entry module5. Press the âœmotor onâ button to start

the motor6. Once it reaches a steady-state speed

(approximately 200 cycles), gently loadthe additional weight desired for thespecific experiment onto the weight panand reset the revolution counter.

7. Once the specimen has failed (frac-tured), record the number of cyclesshown by the revolution counter.

8. Turn off the power entry module, unloadthe loading harness and weight panassemblies, and dismount the failedspecimen

9. Repeat the above steps for each fatiguespecimen for different testing conditions.

ResultsWe performed the previously stated experi-mental procedure on 4 samples. We calcu-lated the stress amplitude of each using theequation:

σa =1

K∗ M ∗D/2

I=

1

Kf∗ 16WL

π ∗D3(5)

Where Kf is the fatigue intensity factor, W isthe load applied, L is moment arm distance,ad D is the minimum diameter of cylindri-cal fatigue specimen. Using the the materialgeometry and charts in Appendix B, we esti-mated Kt to be 1.65 and q = .78. Pluggingthese values into Equation 4, we got Kf to be1.507. Table 1 shows the weight, Cycles toFailure, and Stress Amplitude for each spec-imen.

Test Weight(lbs)

Cycles toFailure

StressAmplitude

1 9 130977 298.932 10 102086 332.153 11.5 45490 381.984 13 20886 431.80

Table 1: Properties of each test specimen

The data indicates that increasing the appliedweight decreases the cycles to failure and in-creases the stress amplitude.

Figure 2 describes the theoretical S-Ncurve for AISI 1045 Steel for an unnotched

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sample. In order to use Equation 2 to ex-press the curve we utilize the ultimate tensilestrength is 700 MPa, which we then use tocalculate Sf and S ′

e. We calculated b and σ′f

using the following formula [5]:

b =log(S ′

e)− log(Sf )

log(106)− log(103)(6)

σ′f =

S′

(106)b(7)

Figure 2: S-N curve for an AISI 1045 Steelunnotched sample

Figure 3 illustrates the theoretical S-N curvefor 1045 Steel with a notched sample. Wecalculate the modified endurance limit usingequation 3. Using this new Se to replace S ′

e

in Equations 6 and 7, new b and sigma′f con-stants are determined.

Figure 3: S-N curve for AISI 1045 Steelnotched sample

Figure 4 is a S-N curve based on the exper-imental data found in Table 1. In order tocalculate Stress Amplitude we perform a lin-ear fit using MATLAB’s polyfit tool on thelogarithm of stress amplitude and cycle data.The results can be used to solve for the con-stants A and b in Equation 8, a rearrangedversion of Equation 2.

log(σa) = b ∗ log(Nf ) + log(A) (8)

σ′f can be found using the equation [5]:

σ′f =

A

2b(9)

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Figure 4: S-N plot of Experimental Datawith notch

Table 2 contains the significant points on anS-N curve, Se and Sf , as well as the constantsb and σf

DataType σ′

f b Se

(MPa)Se

(MPa)Unnotched 1134.0 -0.0851 350 593.9Notched 2054.5 -0.1711 193.2 559.5

Experimental 3311.8 -0.1904 381.98209.2 779.2Table 2: Significant variables and their

values for plotting the specified S-N curves

Appendix C contains images of each spec-imen’s unique fracture surface. It also in-cludes an image of non-heat treated sampleof AISI 1045 from Charpy Impact Testing.The Charpy specimen is very smooth relativeto the fatigue testing samples.

Discussion

The four specimen tested imply that an in-crease in applied weight will decrease thenumber of cycles until fracture, which alsocorrelates to an increase in stress amplitude.This allows us to generate an S-N curve andcompare it to the theoretical S-N curves de-rived from known equations. When lookingat the two theoretical curves, we see that thepredicted Se and Sf for the notched curve are

below that of the unnotched. Interestingly,the difference in endurance limit at high cycleis much higher than that of Sf at high cycle.This is probably a result of a steeper curve,which is the consequence of a larger b (inabsolute value) in the theoretical notch case;therefore, this causes failure to occur withinless cycles and a lower Se. Our data calcula-tions further support this trend because theconcentrated stress that results from notch-ing matches the larger stress amplitude in thenotch curve.

The experimental data has a similar re-lationship with the theoretical unnotched S-N curve, except for the stress at 1000 cy-cles. It differs greatly with our predicted S-Ncurve as well. Even though our endurancelimit and b constant are within a 10% differ-ence, the stress at 1000 cycles differs by a sur-prising 28.2%. It is significantly higher thanthe value predicted by the theoretical notchcurve, and even surpasses the ultimate tensilestrength. We can deduct from this substan-tial difference that the predicted values de-rived from the equation are fairly inaccurateat low cycles; however, our equations are rela-tively accurate at predicting fatigue behaviorat higher cycles.

A few possible causes for these discrepan-cies between the theoretical S-N curve and ex-perimental S-N curve are pre-existing cracksor imperfections, lack of data points, and theeffect of stress amplitude at higher cycles.Any cracks that existed prior to testing couldaffect where crack growth begins and the rateat which crack propagation occurs. Since, ourtheoretical values are predicted in an ideal en-vironment, any imperfections in the materialwill change the prediction. Another possiblecause is the lack of data points to fit the linearapproximation along, especially at the begin-ning and end of the curve, could result in aninaccurate S-N plot. Due to time constraintswe were unable to perform further tests, buttaking more data points distributed along the

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entire region will probably yield a more accu-rate S-N curve.

Finally, the images in Appendix C indicatethat higher stress amplitudes at high cyclecan result in premature fracture, before fullcrack propagation can take place. The 10%error in endurance limit, which is a propertyat high cycle, could be a result of the fastercrack growth and unstable crack propagation,especially near the fracture point. The im-ages in Appendix C show that for 9 lbs, thefracture surface has only 1 small rough circle;however, as the applied weight increases, thefracture surface has larger rough circles nearthe center. Fracture surface in Appendix C.3has a significant fracture mark at the cen-ter, suggesting that fracture occurred beforecrack propagation occurred through the en-tire specimen cross-section. The outer re-gions of the cross-section are subjected tohigher stress than the inner regions, imply-ing higher stress intensity and much fastercrack growth. This property is best seenin Appendix C.4, which exhibits roughnessalong the edges of fracture. The specimenwith higher applied stress amplitudes seemto have rougher edges than those with lowerstress amplitudes. This makes sense becausea higher applied load increases the stress onthe sample and forces the sample to fracturein a more chaotic manner; however it is im-portant to note that all the specimen do showsome crack growth. Even though stress am-plitude stabilizes at high cycles, the behaviorat lower cycles around 1000 seem to be ableto vary greatly.

All four specimen have little similaritieswith the smooth fracture surface of the nonheated Charpy impact test sample. The maincause most likely lies in the difference be-tween the instantaneous fracture caused byimpact fracture testing and the high cycle fa-tigue testing we performed in lab. The signif-icant plastic deformation, especially aroundthe edges, implies that the fatigue specimen

resisted fracture in a ductile manner, com-pared the flat brittle fracture illustrated inAppendix C.5. The culmination of all three ofthese factors probably added up and resultedin a significant difference between the theo-retical S-N model and the S-N model fromexperimental data.

ConclusionIn this lab we studied the fatigue behaviorof AISI 1045 steel and performed basic fa-tigue analysis on the 4 notched specimen.Fatigue failure occurs as a result of cyclicloading at levels below the ultimate tensilestrength of the material. The cyclic loadingcauses crack growth and crack propagationto develop until the sample fractures. Weused the macroscopic stress based approachand S-N curves to model the fatigue behaviorusing an R.R Moore Instron machine, whichrepeatedly stresses the sample in tension andcompression though rotations until fracture.Our data shows that increasing the appliedweight increases the stress amplitude, andconsequently caused the material to fail inless cycles. The stress amplitudes predictedby the theoretical S-N curve was relativleyaccurate at high cycles, but differed greatlyat low cycles. As discussed in the previoussection, this can be a result of may factors,including pre-existing imperfections, insuffi-cient data, and the chaotic crack propagationat high stress amplitudes. Although the S-Ncurve may become more stable near fracture,the crack initiation stress can vary. We cansee from the comparison with the Charpy Im-pact test sample that materials behave in sig-nificantly different manner when subjected tocyclical loading, and that it is why it is im-portant to consider fatigue properties.

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References1. K. Komvopoulos, Mechanical Testing of Engineering Materials, 2nd edn (San Diego,

CA: University Readers, 2011).

2. Dr. Norhayati Ahmad, Mechanical Failure-Fatigue (WordPress) Originally retrievedfrom https://materialsection.files.wordpress.com/2011/02/4-1fatigue.pdf on 11-8-2015

3. ASM International, Elements of Metallurgy and Engineering Alloys - Fa-tigue (ASM International, Materials Park, OH, 2008) Originally retrieved fromhttp://www.asminternational.org/documents/10192/1849770/05224G Chapter14.pdfon 11-8-2015

4. Instron, R. R. Moore Rotating Beam Fatigue Testing System (Indus-trial Products Group, Grove City, PA, 2007) Originally retrieved fromhttps://depts.washington.edu/mstlab/equip pics/pod rrmoore rev6 0807.pdf on11-8-2015

5. N. E. Dowling, Mechanical Behavior of Materials, 3rd edn (Upper Saddle River, NJ:Prentice Hall, 2007)

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1 Appendix

1.1 Appendix A

Appendix A Instron R.R Moore machine specifications

1.2 Appendix B.1

Appendix B.1: Plot for estiamting Notch sensitivity q

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1.3 Appendix B.2

Appendix B.2: Plot for estimating Kt

1.4 Appendix C.1

Appendix C.1: Fracture surface with 9lbs applied force

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1.5 Appendix C.2

Appendix C.2: Fracture surface with 10lbs applied force

1.6 Appendix C.3

Appendix C.3: Fracture surface with 11.5lbs applied force

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1.7 Appendix C.4

Appendix C.4: Fracture surface with 13lbs applied force

1.8 Appendix C.5

Appendix C.5: Fracture surface of non-heat treated AISI 1045 steel

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