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A ServoControlled Axial Fatigue Machine with Strain Rate Feedback forTesting Polymers and CompositesC. K. H. Dharan andA. D. ColvinCitation: Rev. Sci. Instrum. 44, 326 (1973); doi: 10.1063/1.1686120View online: http://dx.doi.org/10.1063/1.1686120View Table of Contents: http://rsi.aip.org/resource/1/RSINAK/v44/i3Published by theAmerican Institute of Physics.Additional information on Rev. Sci. Instrum.Journal Homepage: http://rsi.aip.orgJournal Information: http://rsi.aip.org/about/about_the_journalTop downloads: http://rsi.aip.org/features/most_downloaded

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TH E REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 44, NUMBER 3 MARCH 197

A Servo-ControUed Axial Fatigue Machine with Strain Rate Feedbackfor Testing Polymers and CompositesC. K. H. Dharan and A. D. Colvin

Ford Motor Company, Sc ientif ic Research Staff , Dearborn, Michigan 48121(Received 28 August 1972; and in fma1 form, 24 October 1972)An inexpensive servo-controlled electrohydraulic fatigue machine, capable of a maximum load of 22.2kN (5000 IbO and a maximum servo-controlled strain rate of 0.2 sec-I, is described. Its primarycapability is to perform load and strain-range controlled fatigue tests conducted at constant strain ratefeedback. In addition, the machine is capable of performing constant strain rate tensile tests andclosed loop stress relaxation tests. The results of some initial fatigue tests are presented.

I. INTRODUCTIONAn investigation into the fatigue behavior of polymers

and composites whose deformation and failure characteristics are significantly different from those of metalsrequires a test system which is capable of varying andcontrolling a wide range of test variables. I t is well known,for example, that fatigue tests on polymeric materials athigh frequencies ('" lS Hz) generally produce quitedifferent results from those conducted at low frequencies.The high-frequency fatigue failure is usually a function ofthe dissipative heating experienced by the viscoelasticpolymeric material rather than being governed by fatiguecrack growth processes as seen in metals. Cessna et al.have demonstrated this effect in constant-stroke flexuralfatigue tests of glass-reinforced and unfilled thermoplasticconducted at 20 Hz.l An infra-red sensor used to monitorspecimen surface temperatures during testing revealedtemperature rises as high as SOc. I t is becoming evidenttherefore, that data obtained from fatigue tests conductedon the high-speed testing machines (20-30 Hz) usuallyemployed for testing metals may be misleading.

Another factor to be considered in the design of a suitablefatigue test system concerns its adaptability to fracturemechanics. For this purpose, it should be possible toconduct fracture mechanics tests at constant cyclicdeformation. For viscoelastic materials, the system wouldthen provide an automatic compensation for any accumulated creep deformation so as to maintain the sameinitial conditions for fatigue crack propagation. Manycommercially available testing machines are generallycapable of cycling only between either fixed load limits orfixed strain limits. When creep occurs during cyclingbetween zero and a fixed tensile strain, such machines willtend to impose a compressive stress on the specimen toachieve the lower strain limit, thus altering the stressfield seen by a fatigue crack. Andrews has described oneiesign of a fatigue machine which automatically detectsand compensates for creep.2 This is done by means of amechanical over-ride device which may, however, belimited in the minimum creep strain it can detect.

The above factors were considered when an investigation326

into the fatigue behavior of composites was undertakenThe following specifications were set for the proposed tessystem: (1) To be able to apply axial tension or compression loads with a maximum load capacity of 22.2 kN(SOOO lbf); (2) to carry out fatigue tests under strain-ratcontrol in which either load or strain-range limits thcycle amplitude; (3) to operate at servo-controlledcross-head speeds up to a maximum of 8.SXlO-3 m/se(20 in./min); (4) to be able to also perform tension ancompression tests at constant strain rates (up to 0.2 sec l )

The requirement for constant strain rate feedback waincluded because of the well-known sensitivity to strairate that polymers and polymer-based composites exhibitI t is usual in other similar axial testing machines for thcycling frequency to be kept constant while load or strainfeedback is employed to establish the cycle limits.3 Whenload-limit cycling is done in such a s y s t ~ m , any change ithe total strain results in a change in the cyclic strain ratsince frequency is kept constant. However, it is strain ratthat is the more fundamental parameter to be controlleand not frequency. While this effect may be small fometals it can be significant for polymers and compositesThe requirement for constant strain-range or straindifference rather than strain limits during strain cyclingalso ensures that automatic compensation is provided fothe accumulated creep deformation of such materials.

This paper describes the details of the machine that waconstructed and its operating characteristics.

II. DESCRIPTION OF TEST SYSTEMA. Load Frame and Hydraulic System

The machine consists essentially of a rigid four-pillaloading frame with a hydraulic servo-actuator mounted athe top. Figure 1 shows the setup. The over-all size of thmachine (1.09 m high) is small enough to permit it to btable mounted as shown. I t is also possible to mount thframe in a horizontal position on the table if so desirefor convenience in microscopic observation of the specimeduring testing. The calculated over-all stiffness of thframe is approximately 3.SX108 N/m (2X106 lbf/in.).

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AXIAL FATIGUE MACHINE 327The servo-actuator used was designed by Moog, Inc.

(Model 1725 H) and was originally meant for use in amissile system. As a surplus item it was inexpensive andyet its specifications made it quite suitable for use in thisapplication:Maximum oil pressureLoad capacityMaximum piston velocityMaximum strokeOver-all length

20.7 X 10 6 N/m2 (3000 Ibf/in.2)44.5 kN (10000 lbf)0.38 m/sec0.076 m0.43 m

A pressure transducer and a potentiometric displacementtransducer, both of which may be used for feedbackcontrol, are built into the servo-actuator. However, becauseof the higher accuracy and stability that was desired inthis application, these transducers were not used.

A Vickers hydraulic power package provides oil at amaximum pressure of 13.8X106 N/m2 (2000 Ibf/in2.) andmaximum flow rate of 1.26XlO-4 m3/sec (2 gpm). Anaccumulator is used to reduce line pressure fluctuations.

Both grips that are attached to the servo-actuator andthe load cell are self-aligning. In addition, the mid-spansupport (Fig. 1) can be adjusted to align the piston withthe load axis. Using sheet specimens of materials that arebirefringent, it is easy to check for any misalignment byviewing the specimen through a polarizer in polarizedlight.

B. Instrumentation and Control SystemLoad measurement is done by a Lebow load cell (modelNo. 3132-5K) which has a maximum load capacity of

I.09m

TABLE

SERVO-ACTUATOR4 COLUMN LOAD FRAME

CONTROL SIGNALMID SPAN SUPPORT

CLIP GAGE EXTENSOMETER

TO SERVO CONTROLLER

COMMANDSIGNAL

FIG. 1. Schematic and block diagram of the test system.

- 1 2 F = = = ~ ____-16

-2 0

z -2 4



328 C. K. H. D H A R A N AND A. D. COLVIN+15V ILoad Zerol-15V

100 k, . .-__ 11-'-'.00=2__ ..,

100

-15V22 k

UNMARKED DIODES IN4005RESISTANCES IN OHMSCAPACITANCES IN ,. F

eter which are integrated with the control circuitry in onepackage.4 Altogether eight operational amplifiers areemployed. Amplifier 1 amplifies the load signal for displayand for use as low and high load limits to reverse thehydraulic ram. The feedback load resistor is chosen tocalibrate the load cell at 2220 N/V (500 Ibf/V). Calibrationis done by plotting the voltage output against calibratedweights suspended from the load cell mounted in a fixtureor by using a shunt calibration resistor.

Amplifier 2, which acts as a comparator, has a squarewave output whose polarity changes when a limit isreached. When the ram is pulling (in zero to tensioncycling) the limit may be a load or a displacement; whenrelaxing, it is some minimum load. The displacementsignal from the clip gauge extensometer or the LVDT is

1N400522M

IN4005

1M 303M 10M 22M

IOUTPUTIl iN.

OUTPUTMAX.

FIG. 4. Peak storage circuit for high-frequency fatigue tests.

10k

rs;;;:l~FIG. 3. Servo-controller and transducer signaconditioning circuit diagram.

amplified by amplifiers 3 and 4. The low level output of theclip gauge requires both amplifiers while the high output othe LVDT requires only amplifier 4. Calibration is variedby the 14k n variable feedback resistor. Clip gauge calibration is done by using an rnstron calibrating micrometer

Amplifier 5 is an inverter used to give the negative of thedisplacement signal which is used as an input for amplifie7. The last minimum displacement signal is rememberedby amplifier 6 which is set up as a peak detector. Amplifie7 sums the displacement signal at any time and thenegative of the minimum displacement (as noted above)The result is the output of amplifier 7 and represents thstrain of the sample during the last cycle.Amplifier 8 (Analog Devices PsOlB) is the servo-valvecontrol amplifier. It s low leakage current, 10 pA, allow

1.0 10 100 1000SLOPE AO.IUSTMENT SETTING

FIG. 5. System frequency response. The slope adjustment setting iin arbitrary units proportional to the desired strain rate.




AXIAL FAT IGUE MACHINE 329Ne&140,.----------------------------------,

9080 'Q2070 :!

:::>60 i040 enen30 ..0:I-20 enUJ

IOOr- - - - - - -I-

FIG. 6. Results of some fatigue tests i 80conducted on a unidirectional glass fiber- :Jl 60epoxy composite. II!Iii 40UJ

10 ..JinZ10 7

20ffiI- O ~ I - - - ~ - - - ~ ~ - - - ~ - - - - ~ . - - - ~ ~ - - - ~ - - - ~ ..I-

very low strain rates to be achieved. I t compares the timederivative of the strain signal with the constant (squarewave) output of amplifier 2 and drives the coil of theservovalve.

The diodes on the input to amplifier 2 choose the largerof the stress or strain signal as the proper limit for reversingthe load. Varying the displacement gain determines whichlimit is used. A low displacement gain insures that theload limit will prevail while a high disp lacement gain makesdisplacement the limit. A portion of the square waveoutput of amplifier 2 is used to determine the step size ofthe load or displacement desired.

c. Data RecordingDepending upon the nature of the test being performed,

an X-V plotter (Hewlett-Packard 7035 B), a two-penstrip-chart recorder (Hewlett-Packard 7100 B), and a dualbeam storage oscilloscope (Tektronix 5031) are used torecord the stress and the strain. A peak storage circuit(Fig. 4) was constructed to enable the use of the lowresponse strip-chart recorder for continuously recordingthe progress of high-cycle (and therefore high-frequency)fatigue tests of long duration. The circuit consists ofseparate charging circuits for the maximum and minimumcyclic peaks and a variable shunting resistor which servesto control the recovery between successive peaks. Bysetting a low chart speed on the recorder and using thepeak storage circuit, a complete history of the maximumand minimum loads or displacements is obtained from thetraces of the two pens. In the load limit mode, for example,TABLE I. Approximate cost of machine components (costs for designing and debugging the control circuit are not included).

Load frameGripsServo-actuator (Moog, Inc.-model 1725H)Hydraulic power package and fittings(Vickers Division, Sperry Rand Corp.)ExtensometersLoad cellControl circuit(including transduc er conditioningcircuits, peak storage circuit,and counter)

Cost$1000.00300.00400.001300.00400.00500.00600.00

$4500.00

NUMBER OF STRESS REVERSALS (2.NF CYCLES)

the average apparent modulus can be monitored continuously in this manner by recording displacements.The X - Y plotter and the storage oscilloscope may beused for recording hysteresis loops and stress-strain

curves. The number of elapsed cycles are recorded by anelectromechanical counter which is driven by a countingsignal that is taken from the 12 V square wave outpuof amplifier 2 and amplified in current. The countingsystem performs satisfactorily at frequencies up to 25 Hz.

D. PerformanceSystem response is best evaluated by determining themotion of the system as a function of the desired strain

rate which is directly proportional to the setting of theslope potentiometer shown in Fig. 3. This forms part othe input circuit to amplifier 8. In Fig. 5, the response othe system in terms of the measured strain rate is shownas a function of the slope potentiometer adjustment setting(in arbitrary units proportional to the desired strain rate)The measurements show that the system has a maximumusable crosshead velocity of about 8.S X 10-3 m/sec(corresponding to a maximum strain rate of 0.2 sect)beyond which the response is nonlinear. Figure 5 is theequivalent of a frequency response study. Display of thefrequency response in the conventional manner of plottingan amplitude ratio vs frequency is meaningless here sincethe frequency response depends upon the cyclic amplitudechosen. The measurements as plotted in Fig. 5, howeverillustrate the response of the system independent oamplitude and in terms of the feedback control variableviz., strain rate.

The lowest setting of the slope potentiometer corresponds to zero strain rate, i.e., a fixed position of thecrosshead. This setting may be used for closed-loop stressrelaxation experiments in which the strain is kept at acerta in fixed level and the stress monitored.Figure 6 illustrates the results of some low-cycle fatiguetests conducted on a unidirectional glass fiber-epoxycomposite.E. Cost

The costs of building the machine using the componentdescribed above are very low when compared with asimilar commercial electrohydraulic system (Table I)




330 C. K. H. D H A R A N AND A. D. COLVINRead-out devices have not been included in the costsince requirements usually vary with the investigator.The costs include all assembly labor costs but do notinclude costs for designing and debugging the controlcircuit.

TH E REVIEW OF SCIENTIFIC INSTRUMENTS

lL. C. Cessna, J. A. Levens, and J. B. Thomson, Polym. Eng.Sci. 9, 339 (1969).2E. H. Andrews, in Fatigue in Polymers, edited by W. E.Brown, (Interscience, Ne w York, 1968), Vol. 4, p. 237.3K. Jerram, J. Phys. E 3, 477 (1970)."The LM 201 operationa l amplifiers are manufactured byNational Semiconductor Corp., Santa Clara, Calif.

VOLUME 44. NUMBER 3 MARCH 1973

Optical Fiber Breaking Stress Distributions Obtained by a CantileverMethod

M. J. SaundersBell Laboratories, Norcross, Georgia 30071(Received 27 October 1972; and in final form, 20 November 1972)

A description is given of a cantilever apparatus to determine the mechanical strength and elastic modulusof optical fibers. This test method overcomes the problem of fiber breakage in the jaws of tensile machines.Young's modulus, the breaking stress distribution, and values of the breaking radius of curvature and strainare presented for fused quartz fibers.INTRODUCTION

There is currently an increased interest in fiber opticscommunication systems. Aside from questions of fiberlosses, splicing techniques, pulse spreading and the availabili ty of devices, the mechanical strength of the individualfibers is an important consideration. I t is well known thatthe breaking stress of a particular fiber depends on a number of variables such as temperature, humidity, glasscomposition, and most importantly, the state of the fibersurface. Consequentiy, the mechanical strength of a particular type of fiber must be characterized by a breakingstress distribution function.This paper describes a cantilever apparatus to obtain,relatively quickly, the breaking stress statistics of glassfibers. Young's modulus and the radius of curvature atwhich the fiber breaks are obtained, and the breakingstress is calculated from these two quantities and the fiberdiameter. This method of testing overcomes the problemof fiber breakage in the jaws of the standard tensile testingmachines. Approximately 10 breaking stress determinations can be made on a fiber of 7.5 cm length. Breakingstress distributions are presented for fused quartz fibersmade at Bell Laboratories. Values of Young's modulusand the radius of curvature and strain at which the fiberbreaks are also presented.Methods other than tensile exist for the determinationof the breaking stress of glass fibers, and these should bementioned. Reinkober1 described a method in which afiber, clamped across two knife edges, supports a smallcontainer. Water is slowly poured into the container untilthe fiber breaks. Joffe and Walther wrapped a fiber, inhelical fashion, around a tapered cylinder until the fiberbroke. The breaking radius of curvature of the fiber could

be determined by noting the position of the fiber on thecylinder. The breaking stress could then be determined iYoung's modulus were known. Lastly, Piggott3 describeda three point bend testing apparatus in which a fiber ilaid across a span about 0.1 cm in length and a blade deflects the middle of the fiber until breakage occurs. Ameasurement of the depression of the fiber when it breakpermits one to calculate the radius of curvature at thecenter of the fiber, from which the breaking stress can beobtained if Young's modulus is known. In this apparatusthe results are dependent upon the coefficients of frictionbetween the fiber and the supports although, for fiberdeflection to span length ratios less than about 0.4, theradius of curvature is independent of the friction coefficientThe effective gauge length for this apparatus is about 0.01cm and is the smallest of all the methods examined. 4 Assuch, the intrinsic strength of glass fibers (the strength inthe absence of surface flaws) can be closely approximatedby the use of this equipment.

I. THEORY OF THE HORIZONTALCANTILEVER METHODThe fiber to be tested is clamped over a knife edge andvertically acting loads are applied to the end of the fibe

until breakage occurs. The maximum stress in the fibeoccurs at the knife edge and, under the assumption of purebending, the tensile stress at which the fiber breaks igiven by

u=Ed/2R, (1where E is Young's modulus, d is the diameter of the fiberand R is the radius of curvature at the knife edge. At anyfiber cross section, the lower part is in compression, theupper part is in tension, and the maximum tensile stres

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