Novel in situ device for investigating the tensile and fatigue behaviors of bulk materialsZhichao Ma, Hongwei Zhao, Qinchao Li, Kaiting Wang, Xiaoqin Zhou, Xiaoli Hu, Hongbing Cheng, and Shuai Lu Citation: Review of Scientific Instruments 84, 045104 (2013); doi: 10.1063/1.4798545 View online: http://dx.doi.org/10.1063/1.4798545 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/84/4?ver=pdfcov Published by the AIP Publishing

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REVIEW OF SCIENTIFIC INSTRUMENTS 84, 045104 (2013)

Novel in situ device for investigating the tensile and fatigue behaviorsof bulk materials

Zhichao Ma, Hongwei Zhao, Qinchao Li, Kaiting Wang, Xiaoqin Zhou, Xiaoli Hu,Hongbing Cheng, and Shuai LuCollege of Mechanical Science and Engineering, Jilin University, Renmin Street 5988,Changchun 130025, China

(Received 26 August 2012; accepted 12 March 2013; published online 4 April 2013)

For investigating the static tensile and dynamic fatigue behaviors of bulk materials, a miniaturizeddevice with separate modular tensile and fatigue actuators was developed. The fatigue actuator pre-sented good compatibility with the tensile actuator and mainly consisted of a special flexure hingeand piezoelectric stack. In situ fatigue tests under scanning electron microscope or metallographicmicroscope could be carried out due to the miniaturized dimensions of the device. A displacementcorrection method of tensile actuator based on load sensor compliance was investigated, and the fea-sibility of the method was verified by the comparison tests with a commercial tensile instrument.The application of testing the storage and loss modulus as a function of frequency was explained,and the temperature rises of both the piezoelectric stack and specimen were obtained as a functionof frequency. Output characteristics of the fatigue actuator were also investigated. Additionally, thedischarge performance of piezoelectric stack based on various initial voltages and fatigue tests onC11000 copper was carried out. This paper shows a modularized example that combines a servomotor with a piezoelectric actuator attached to the specimen grip to realize the in situ fatigue tests.© 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4798545]

I. INTRODUCTION

Fatigue is an important structural failure phenomenonthat can be observed in many mechanical and electromechan-ical components, and has become a progressively significantresearch field.1, 2 It is stated that at least half of all servicefailures are attributed to the fatigue effects.1, 3 Furthermore,in situ fatigue tests under SEM or metallographic microscopeare an effective tool for investigating the development of crackinitiation, for the analysis of the mechanisms of crack growth,for the quantitative determination of small crack growth ratesas well as for the examination of interactions between fatiguecrack growth and the microstructure.4 According to variousdriving modes, traditional fatigue machines can be classifiedas mechanical type, electro-hydraulic servo type, and the elec-tromagnetic resonant type,5, 6 accordingly, adjustable speedmotor, hydraulic actuator, and electromagnetic exciter are thefrequently used actuators for generating the alternating load.However, these driving modes always lead to the high cost andstructural complexity of the fatigue system and become keyfactors for designing the fatigue system.7 Meanwhile, thesedriving methods encounter a series of problems, such as fric-tion and wear, and the backlash and clearance could not becompletely eliminated during the alternating motion.8, 9 Fur-thermore, during a certain time interval of the alternating mo-tion, via the observation of specimen under the microscopes,the micro mechanical behavior and fatigue damage mecha-nism of various materials could be deeply researched, so theminiaturized size of fatigue machines is also required. There-fore, for the fatigue actuators, the characteristics of high ac-curacy and compact structure both are required. Additionally,the fatigue test mode with wide range stress ratio R accordswith the actual working condition for many components.10, 11

Combination of flexure hinge and piezoelectric stack,12

which could provide a smooth motion and a very fast re-sponse without encountering the problems mentioned above,has been widely adopted in applications of precise driving,such as instruments of nano-indentation tester, gyroscopes,accelerometers, electro-hydraulic servo valve, and nano ma-nipulators, etc.12–14 Piezoelectric stack could easily achievethe alternating motion with high frequency due to the spe-ciality of fast response. However, as the charge accumula-tion and temperature rise cannot be completely avoided, thepiezoelectric stack could not uninterruptedly output an alter-nating motion with a large effective stroke based on high fre-quency and significant preload. Moreover, for carrying outthe tensile fatigue test by piezoelectric actuator, the flexurehinge is required to ensure that a compressive load is actedon piezoelectric stack when the external tensile load applieson the flexure hinge. Therefore, the design of flexure hingebecomes key factor for determining the performance of thepiezoelectric driven fatigue actuator, the output displacement,and the stiffness of the flexure hinge are also required tomatch rationally.14, 15 Chen et al. developed a piezoelectricdriven fatigue test system for electronic packaging applica-tions and proposed a decoupled packaging failure experi-ment procedure for exploring the effects of individual con-trol parameters.16 Gama and Morikawa monitored the fatiguecrack growth in compact tension specimens by using piezo-electric sensors, and the application of piezoelectric driving infracture mechanics specimens has been demonstrated throughexperiments with compact tension (CT) specimens.17 Liuet al. developed a new accelerated fatigue testing techniquefor adhesive metal interfaces using piezoelectric actuators viadetailed finite element analyses of the crack driving forces.18

Mall investigated the integrity of the host graphite/epoxy

0034-6748/2013/84(4)/045104/8/$30.00 © 2013 American Institute of Physics84, 045104-1

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045104-2 Ma et al. Rev. Sci. Instrum. 84, 045104 (2013)

laminate as well as of the embedded active PZT (piezoceram-ics) sensor/actuator under monotonic and fatigue loads.19, 20

Kobayashi et al. proposed and demonstrated a new methodfor the fatigue test of PZT thin films for piezoelectric MEMS(Micro-electromechanical Systems) devices by using the self-sensitive piezoelectric micro cantilevers.21 Saito et al. inves-tigated a fatigue testing machine with piezoelectric ceramicactuator, and more than 100 μm of displacement could beoutput precisely to the specimen at a frequency of 50 Hz.22

However, those devices or testing methods rarely mentionedthe fatigue tests with wide range stress ratio, which accordswith the actual working condition for many components.

This paper describes a novel test device with dimensionsof 196 mm × 135 mm × 45 mm for in situ fatigue test, basedon separate modular tensile and fatigue actuators, the devicecould carry out the in situ fatigue tests with wide range stressratio. A modular displacement correction method of the ten-sile actuator was given and the feasibility of the correctionmethod was verified. The alternating motion performance ofthe fatigue actuator was investigated based on various testmodes, and the fatigue test on C11000 copper was carriedout based on various initial tensile preloads. The temperaturerise and discharge performance of the piezoelectric stack werealso investigated.

II. DESCRIPTION OF THE DEVICE

A. Tensile actuator

The prototype of the proposed device with specific di-mensions of 196 mm × 135 mm × 45 mm is shown inFig. 1(a). The tensile actuator mainly consisted of a servomotor (Maxon EC-max) with a high resolution encoder(MR1024), a two-stage worm gears reducer with total reduc-tion ratio of 1600, a S-type load sensor (BSS) with measure-ment range of 3000 N and resolution of 1 N, and a grating

FIG. 1. (a) Prototype of the proposed device with (b) a novel grip design and(c) illustration of the specimen’s dimensions.

sensor (Heidenhain) with measurement range of 100 mm andresolution of 1 μm. Integrating the servo motor, reducer withlarge reduction ratio, and ball-screw with lead of 1 mm, thetensile actuator could achieve quasi static loading mode withminimum loading rate of 10 nm/s. The ball-screw and wormgears could achieve self-locking function to facilitate the insitu observation as the device could momentarily stop dur-ing the test. Combing with the ball screw, a couple of lin-ear guides were adopted to realize the linear motion. Seenfrom Fig. 1(a), the deformation of load sensor was countedin the measured displacement of the grating sensor, this ar-rangement mode would lead to the relatively smaller calcu-lated elastic modulus, and affect the evaluation of material’sperformance. Therefore, it is necessary to obtain the load sen-sor compliance.

B. Grip design

For the plate specimen, it is understood that the simplegeometries allow easy and accurate measurement. Schematicof the grip design is shown in Fig. 1(b). For the alignment is-sue, the location relationship between the upper gripper andthe nether gripper was realized by a pair of groove and boss.Cushion block with various thicknesses was embedded insidethe upper gripper to meet the gripping of specimen with var-ious thicknesses. The widths of the specimen, groove, boss,and cushion block were the same, so the alignment issue wasachieved by the equal width constrain. Additionally, intensiveknurl was machined on the nether gripper and cushion blockto ensure the stability of gripping. Illustration of the speci-men’s dimensions is shown in Fig. 1(c).

C. Fatigue actuator

The fatigue actuator mainly consisted of a special flex-ure hinge and a piezoelectric stack. Schematic of the fatigueactuator is shown in Fig. 2. The actuator presented specificdimensions of 66 mm × 60 mm × 8 mm. The compatibilitywith tensile actuator was realized by a couple of positioningpins, which were assembled on the rigid part of the flexurehinge. Therefore, the fatigue actuator could not only workindependently but also combine with the tensile actuator tooutput tensile/fatigue combined loads. Besides, for the designof the flexure hinge, the piezoelectric stack must bear com-pressive load when the external tensile load Ft, provided bythe tensile actuator, applied on point A of the flexure hinge,a special groove was designed to achieve the function. Formachining the flexure hinge, material of 65Mn was selectedfor the characteristics of low elastic lag and fine fatigue resis-tance, etc. According to the international standard of ASTMA 29/A 29M-04,23 the allowable tensile strength of 65Mn is432 MPa and the fatigue limit σ−1 of 65Mn is 430 MPa, thecorner filleted type flexure hinge was also selected for the in-sensitivity to stress concentration. In this paper, thickness of1 mm and width of 8 mm was selected for machining the flex-ure hinge.

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045104-3 Ma et al. Rev. Sci. Instrum. 84, 045104 (2013)

FIG. 2. Model of the fatigue actuator.

III. CORRECTION OF TENSILE ACTUATOR

A. Displacement correction methodof tensile actuator

Considering the coaxial arrangement of the load sensorand specimen, the measurement veracity of specimen’s stressis depended on the accurate measurement of specimen’s crosssection area and the calibration result of load sensor obtainedfrom the sensor’s load-voltage relationship. Therefore, thespecimen’s strain is decisive to characterize the measurementveracity of the tensile actuator. As mentioned above, due tothe installation method of grating sensor, the deformation ofload sensor must be taken into consideration to calculate thespecimen’s actual deformation. Additionally, the deformationof the tensile actuator’s base and the grippers would also af-fect the measured displacement of grating sensor. Based onthe position relationship, the actual displacement of specimen�lS could be described as

�lS = �lD − �lB − �lL − 2�lG. (1)

Where �lD is the displacement measured by the gratingsensor, �lB, �lL, and �lG are the corresponding deformationsof the base, load sensor, and symmetrical grippers with re-spective stiffness coefficients Ki. Figure 3 shows the stiffnesscoefficients Ki of the load sensor, base, and grippers. The lin-early incremental deformation �lB + �lL + �lG and �lB+ �lL were obtained as a function of tensile load Ft by thelaser sensor (LK-G10) with resolution of 10 nm. The overallstiffness K, which affected the measured strain of the speci-men, could be defined as

1

K= 1

KB+L

+ 2

KG

, (2)

where KB+L is the stiffness of the combination of load sensorand base and is calculated as 3.493 N/μm, KG is the stiffnessof single gripper and is calculated as 55.556 N/μm. Corre-spondingly, the actual displacement of specimen �lS can befurther described as

�lS = �lD − Ft/K, (3)

FIG. 3. Tests of stiffness coefficients Ki of the load sensor, base, and grippersby using the laser sensor (LK-G10).

where K is calculated as 3.103 N/μm. Based on the displace-ment correction method, the engineering stress-strain curvesof A570 Gr. 33 steel were obtained by the proposed device,and the comparison tests with commercial tensile instrument(Instron 3345 model) with the same experimental conditionswere also carried out.

B. Feasibility of the correction method based onstress-strain curve

The feasibility of displacement correction method mainlyaims at the measurement veracity of the specimen’s stress-strain relationship. The adopted material for verifying the dis-placement correction method was A570 Gr. 33 steel, whichaccords with ASTM A36/A36M-08.24 The adopted commer-cial tensile instrument (Instron 3345 model) is a compact me-chanical instrument for tensile and compression tests withmaximum load of 5000 N. According to Eq. (3), the cor-rected stress-strain curves of A570 Gr. 33 steel obtainedby the self-made device are shown in Fig. 4. Seen fromthe curves, the corrected curve presented an improvementof calculated elastic modulus and a decrease of calculated

FIG. 4. Comparison results between the raw curve and the reference curveof A570 Gr. 33 steel.

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045104-4 Ma et al. Rev. Sci. Instrum. 84, 045104 (2013)

TABLE I. Parameters comparison results of A570 Gr. 33 steel between thecommercial instrument and the self-made device.

Self-made platform Commercial instrument

E (GPa) σ b (MPa) δ (%) E (GPa) σ b (MPa) δ (%)

Mean 201.56 396.86 22.53 205.06 397.73 21.47

elongation. Furthermore, the mechanical parameters of A570Gr. 33 steel obtained by each instrument are shown in Table I,the average value of the corrected elastic modulus E of201.56 GPa, the average value of the corrected tensile strengthσ b of 396.86 MPa, and the average value of the correctedelongation δ of about 22.53% were obtained by the self-madedevice. For commercial tensile instrument, these parametersshowed corresponding values of 205.06 GPa, 397.73 MPa,and 21.47%, respectively. Therefore, all the corrected pa-rameters were close to the experimental results obtained bycommercial tensile instrument, which preliminarily indicatesthe feasibility of the displacement correction method.

IV. EXPERIMENTS AND DISCUSSIONS

A. Principles of the fatigue test

As mentioned above, the tensile preload was providedby the tensile actuator, which integrated the functions ofquasi static loading and load/displacement measurement ofthe specimen. For providing the preload, control parameterssuch as displacement rate and load rate were set by the soft-ware. Then the control command of square-wave signal wascreated from the motion control card and sent to the servomotor (Maxon Ec-max). The measured load and displacementsignals were collected by the A/D card (ART-PCI 8602) andsent to the computer. Comparing the measured value withthe setting value, error value was obtained and then sent tothe servo controller. Repeat the process mentioned above un-til the measured value equals to the setting value. Further-more, the analog signal of load or displacement could be se-lected as feedback sources for precisely closed loop control,and pulse/direction mode was selected for driving the servomotor.

The fatigue tests could be carried out with a given fre-quency, and the alternating voltage applied on the piezo-electric stack was provided by arbitrary waveform generator(RIGOL AFG 3000C) and amplified by piezoelectric power(BOSHI HPV). For carrying out the in situ fatigue test, dur-ing the interval of the alternating motion with a certain num-ber of cycles N, the metallographic microscope or SEM couldcapture the images of specimen when the device momentarilystopped before imaging. Due to the miniaturized size, it is notdifficult for the proposed device to realize the compatibilitywith metallographic microscope or SEM. The time intervalduring the alternating motion could facilitate the charge re-lease and temperature reduction of the piezoelectric stack aswell as capture the images of specimen, the scheme by adopt-ing piezoelectric actuator to realize in situ fatigue test couldbe feasible. The oscilloscope (RIGOL DS1052) was used toobserve the waveform applied on the piezoelectric stack, and

FIG. 5. Schematic diagram of the fatigue test system integrating the temper-ature probes.

the schematic diagram of the fatigue test system is shown inFig. 5.

B. Tests of complex modulus and temperature rise

For many viscous-elastic materials, during the fatiguetests, the material’s deformation response presents a certainhysteresis compared with the load response.11 When carry-ing out the fatigue test with sinusoidal signal, the strain re-sponse, and stress response of material could be, respectively,described as

ε(t) = ε0 sin(2πf t), (4)

σ (t) = σ0 sin(2πf t + δ). (5)

Equations (4) and (5) were set up as a strain control mea-surement with the phase angle δ measured in the stress, and ftis the test frequency, σ 0 is the material’s initial stress, and ε0

is the material’s initial strain, so the complex modulus E∗ canbe given as

E∗ = σ (t)

ε(t)=σ0

ε0(cos δ + i sin δ)=E′ + iE′′, (6)

where E′ is the material’s storage modulus and representsthe real component of complex modulus E∗, E′′ is the ma-terial’s loss modulus and represents the imaginary componentof complex modulus E∗. As mentioned above, the proposeddevice integrated the load sensor and grating sensor, and thedisplacement correction method was verified to be feasible,therefore, the device could real-timely record the specimen’sload and displacement as a function of time, and could be usedto obtain storage and loss modulus as a function of frequency.Furthermore, seen from Fig. 5, two probe type temperaturesensors were, respectively, tied on the surfaces of specimenand piezoelectric stack and were kept in real time contact withthe surfaces. During the temperature rise tests, the peak volt-age of the given sinusoidal signal was set as 100 V, the ini-tial load of the specimen was set as 500 N, the material forcarrying out the test was C11000 copper, the chemical com-position of C11000 copper determined by atomic absorptionspectroscopy is shown in Table II. With each certain num-ber of cycles N of 2.5 × 104, the temperature rises of the

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045104-5 Ma et al. Rev. Sci. Instrum. 84, 045104 (2013)

TABLE II. Alloy composition (wt. %) of C11000 copper determined byatomic absorption spectroscopy.

CuAg Sn Zn Fe Ni Sb As

99.93 0.002 0.005 0.004 0.004 0.002 0.002

specimen and piezoelectric stack under various test frequen-cies were obtained and shown in Fig. 6. For the specimen,when the test frequency increased to 300 Hz, the specimendid not present obvious change of temperature as a function offrequency, the fluctuation of temperature showed in Fig. 6(a)was mainly caused by the measurement accuracy of the tem-perature sensor, so under the given test frequency and initialload, the C11000 copper did not present significant viscousdeformation. For the piezoelectric stack as shown in Fig. 6(b),when the test frequency increased to 300 Hz and the numberof cycles N increased to 105, the temperature rise of piezo-electric stack was close to 3.6 ◦C. Considering the charge ac-cumulation and temperature rise of piezoelectric stack, if 105

was set as the certain number of cycles N before each time in-terval during the in situ fatigue test, it could not only facilitatethe charge release and temperature reduction but also providea sufficiently large number of cycles of the applied stress tocause the fatigue failure.

FIG. 6. Temperature rise of the specimen and piezoelectric stack as a func-tion of test frequency.

FIG. 7. Constitute system for testing the output characteristics of the fatigueactuator.

C. Output characteristics of the fatigue actuator

The output characteristic of the fatigue actuator wastested based on static and dynamic voltages. The constitutesystem for testing the output characteristics of the fatigue ac-tuator is shown in Fig. 7. The size of the piezoelectric stack(PST-HD) was 10 mm × 10 mm × 40 mm, and the lasersensor (LK-G10) was also adopted to measure the displace-ment output of the fatigue actuator. During the tests, variousstatic voltages with initial values of 0 V, 40 V, and 80 V were,respectively, applied, on this basis, an analog sinusoidal sig-nal with peak value of 20 V was also applied on the piezo-electric stack. Figure 8 shows the alternating motion perfor-mance of the fatigue actuator based on the various appliedvoltages, every single displacement waveform output by thefatigue actuator manifested sinusoidal trajectory, based on thesinusoidal signal and the initial static voltage of 0 V, a dis-placement amplitude of about 4.1 μm was obtained, when theinitial static voltages increased to 40 V and 80 V, respectively,the corresponding displacement amplitude of about 4.7 μmand 10.5 μm was also obtained, the nonlinearity increment ofdisplacement responses was mainly caused by the hysteresis

FIG. 8. Alternating motion performance of the fatigue actuator based on var-ious initial voltages.

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045104-6 Ma et al. Rev. Sci. Instrum. 84, 045104 (2013)

FIG. 9. Hysteresis tests of the fatigue actuator based on static and dynamicvoltages.

of the fatigue actuator. The output displacement response as afunction of voltage is shown in Fig. 9, the static voltages wereapplied with stepping mode and each step was set as 5 V, themaximum input voltage was 100 V. As the voltage increased,the output displacement presented certain nonlinearity, whenthe voltage decreased from 100 V to 0 V, the trajectory ofoutput displacement did not follow the loading phase, and thehysteresis was calculated as about 0.1248. For the displace-ment response as a function of dynamic voltage, a sinusoidalvoltage with peak value of 100 V was applied on the piezo-electric stack, and the displacement response approximatelyaccorded with the output displacement under static voltage.Additionally, when the total voltage increased to 100 V, thefatigue actuator could achieve maximum output displacementof about 30 μm, which also accorded with conclusion shownin Fig. 8.

Furthermore, based on constant initial voltage andpreload, the effective stroke le of the fatigue actuator as afunction of test frequency was also investigated. Schematicfor calculating the effective stroke le of the fatigue actuator isshown in Fig. 10, the effective stroke le based on various exci-tation frequencies could be defined as the difference betweenthe maximum displacement lmax and minimum displacementlmin of the fatigue actuator, therefore, le could be described as

le = lmax − lmin. (7)

FIG. 10. Schematic for calculating the effective stroke of the fatigue actuator.

FIG. 11. Displacement responses of the fatigue actuator based on variousexcitation frequencies.

During the test, the initial preload was provided by thetensile actuator and set as 500 N, the applied sinusoidal volt-age with peak value of 100 V was also set. Seen from Fig. 11,when the applied excitation frequency was 10 Hz, the max-imum output displacement of the fatigue actuator lmax couldachieve about 30 μm, and the minimum output displacementlmin was about 2 μm, the effective stroke of the fatigue actu-ator le was calculated as 28 μm. Correspondingly, when theexcitation frequency increased to 50 Hz, the maximum out-put displacement and effective stroke of the fatigue actuatorwere, respectively, obtained as 30 μm and 24 μm. The ef-fective stroke of the fatigue actuator le gradually decreasedas the excitation frequency increased, this was mainly causedby the insufficient response rate of the flexure hinge as wellas the charge accumulation and temperature rise of piezoelec-tric stack. Additionally, when the test frequency increased to100 Hz, the effective stroke of fatigue actuator le was onlyabout 8 μm.

D. Voltage decay of the piezoelectric stack

Since the charge accumulation would weaken the effec-tive stroke of piezoelectric stack, and a certain time inter-val during the alternating motion could not only facilitatethe charge release but also accord with the requirement ofin situ fatigue test, although the adopted piezoelectric power(BOSHI HPV) integrated an accelerating discharge module, arational time interval range should be confirmed. Seen fromFig. 12, initial voltages of 20 V, 50 V, and 80 V were, re-spectively, applied on the piezoelectric stack, the oscilloscope(RIGOL DS1052) was used to observe the voltage decay.When shut off the power supply, the residual voltage insidepiezoelectric stack decreased rapidly, as time increased, thespeed of voltage decay trended to slow. Specifically, whenthe initial voltage was 80 V, the residual voltage decreasedto 1.2 V within 30 s. Therefore, a certain time interval ofat least 30 s was required to facilitate the charge release forthe in situ fatigue test. Via exponential curve fitting, the volt-age decay could be considered as exponential decay, and the

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045104-7 Ma et al. Rev. Sci. Instrum. 84, 045104 (2013)

FIG. 12. Voltage attenuation of the piezoelectric stack based on various ini-tial voltages.

relationship between residual voltage U and time t could be,respectively, described as U1 = 80e−0.2489t, U2 = 50e−0.1502t,and U3 = 20e−0.1303t with corresponding initial voltages of20 V, 50 V, and 80 V. Equation (8) was given for describingthe decay speed of residual voltages inside the piezoelectricstack with various initial voltages:

λ= − dU/dt

U (t), (8)

where U(t) is the residual voltage at time t, and λ is the decayconstant that describes the speed of voltage decay, so Eq. (8)could describe the probability of voltage decay within unittime. Seen from Fig. 12, the variations of decay constantswere, respectively, calculated as 0.2489, 0.1502, and 0.1303with corresponding initial voltages of 80 V, 50 V, and 20 V,the decay constants presented a rising tendency as the initialvoltage increased. Therefore, within the same time range, thedecay speed of residual voltages inside the piezoelectric stackwas faster when the initial voltage was higher.

E. Tensile fatigue tests on C11000 copper based onvarious stress ratios

C11000 copper and strain control mode were adopted forcarrying out the tensile fatigue tests. At room temperature,tensile fatigue stress response of C11000 copper at variousdeformation stages was shown in Fig. 13, the applied alter-nating stress presented a cycle stress amplitude σ r of 22 MPaand frequency of 20 Hz, and the initial tensile stresses for car-rying out the fatigue tests were, respectively, set as 265 MPa,456 MPa, and 291 MPa, which, respectively, correspondedwith the specimen’s elastic deformation stage, hardening de-formation stage, and necking deformation stage. Seen fromFig. 13, the specimen underwent cyclic hardening at variousdeformation stages. Additionally, the mean stress σ a of thespecimen presented a certain decrease as a function of timeat each deformation stage, and the decrease of mean stressσ a also gradually aggravated as the tensile strain ε increased.Specially, at the elastic deformation stage, decrease of meanstress σ a was not significant, while, at the necking deforma-

FIG. 13. Tensile fatigue stress response of C11000 copper at various defor-mation stages.

tion stage, the mean stress σ a decreased from 291 MPa to264 MPa within 350 s. The decrease of mean stress might becaused by the stress relaxation of the specimen.

The tensile actuator could also carry out the stress re-laxation tests during arbitrary loading stages due to the self-locking function. To investigate the decrease of mean stress ofthe specimen, tensile stress relaxation curves at various defor-mation stages were obtained and shown in Fig. 14. The initialstresses for the stress relaxation tests were identical with theinitial mean stresses during the fatigue tests. When stoppedthe servo motor, the stress also presented a certain decreasewith various degrees. Specifically, at the elastic deformationstage, the decrease of stress was about 1 MPa with testingtime of 160 s, the slight decrease of stress in the elastic rangewas mainly caused by the insufficient contact stiffness andtransmission clearances of the ball-screw and worm gears, asthey were the parts to achieve the self-locking function of thetensile actuator. At the necking deformation stage, the decre-ment was about 23 MPa with testing time of 350 s. Therefore,the tensile stress decrease behavior during the stress relax-ation tests presented the similar principles compared with themean stresses decrease behavior during the fatigue tests, andthe decrease of mean stress caused by the stress relaxation ofthe specimen was basically verified.

FIG. 14. Tensile stress relaxation curves at various deformation stages.

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045104-8 Ma et al. Rev. Sci. Instrum. 84, 045104 (2013)

V. CONCLUSIONS

A miniaturized device that integrates tensile and fatigueactuators with dimensions of 196 mm × 135 mm × 45 mmis developed based on modular idea. The device can be usedto investigate the static tensile and dynamic fatigue behaviorsof bulk materials. For the tensile actuator, a displacement cor-rection method based on the load sensor compliance is given,the feasibility of the method is carried out on A570 Gr. 33steel and is verified to present an improvement of calculatedelastic modulus and a decrease of calculated elongation, thecorrection parameters are also compared with the parame-ters obtained by commercial tensile instrument (Instron 3345model). The fatigue actuator is consisted of a special flexurehinge and piezoelectric stack, combined with the tensile actu-ator, the device could carry out the in situ fatigue tests underSEM or metallographic microscope due to the miniaturizeddimensions. Principles of the fatigue test are introduced, andthe application of testing the storage and loss modulus as afunction of frequency is also explained, as the device couldreal-timely record the specimen’s load and displacement asa function of time. Two probe type temperature sensors areused to test the temperature rise of the specimen and piezo-electric stack, when the test frequency increases to 300 Hzand the number of cycles N increases to 105, the temperaturerise of piezoelectric stack is close to 3.6 ◦C. Based on constanttest frequency, output characteristic of the fatigue actuator istested as a function of initial voltage, a maximum output dis-placement of about 30 μm is obtained when the applied volt-age achieved 100 V. Also, based on constant initial voltage of100 V and preload of 500 N, effective stroke of the fatigue ac-tuator is also investigated as a function of test frequency, whenthe test frequency increases to 50 Hz, the effective strokeof the fatigue actuator is obtained as 24 μm. For investigatingthe discharge performance of piezoelectric stack, variation ofdecay constants was obtained based on exponential curve fit-ting. The charge accumulation and temperature rise of piezo-electric stack could be solved as a time interval of at least 30 sduring the in situ fatigue test is set to facilitate the charge re-lease and temperature reduction of the piezoelectric stack aswell as to capture the images of specimen. Finally, fatigue teston C11000 copper based on various initial tensile stresses iscarried out, and the decrease of mean stress is mainly causedby the stress relaxation of the specimen.

This paper shows a modularized example that combines aservo motor with a piezoelectric actuator attached to the spec-imen grip to realize the in situ fatigue tests.

ACKNOWLEDGMENTS

This research is funded by the National Natural Sci-ence Foundation of China (NSFC) (Grant Nos. 50905073,51275198, and 51105163), Special Projects for Developmentof National Major Scientific Instruments and Equipments(Grant No. 2012YQ030075), National Hi-tech Research andDevelopment Program of China (863 Program) (Grant No.2012AA041206), Key Projects of Science and TechnologyDevelopment Plan of Jilin Province (Grant No. 20110307),and Graduate Innovation Fund of Jilin University (Grant No.20121084).

1M. Ohring, Reliability and Failure of Electronic Materials and Devices(Academic, New York, 1998), p. 539.

2T. Hua, H. M. Xie, X. Feng, X. Wang, J. M. Zhang, P. W. Chen, and Q. M.Zhang, Rev. Sci. Instrum. 80, 126108 (2009).

3J. Maity, S. Kumar, and A. Bhattacharyya, Steel. Res. Int. 82, 866(2011).

4L. Smiltneek, S. R. Shinde, and D. W. Hoeppner, Rev. Sci. Instrum. 77,015104 (2006).

5C. Bathias, Int. J. Fatigue 28, 1438 (2006).6H. J. Kim, S. K. Choi, S. H. Kang, and K. H. Oh, Rev. Sci. Instrum. 79,115101 (2008).

7S. Eve, N. Huber, O. Kraft, A. Last, D. Rabus, and M. Schlagenhof, Rev.Sci. Instrum. 77, 103902 (2006).

8K. Shinohara and Q. Yu, Int. J. Fatigue 33, 1221 (2011).9H. K. Oh, J. Mater. Process. Technol. 54, 365 (1995).

10H. Wang, T. A. Cooper, H. T. Lin, and A. A. Wereszczak, J. Appl. Phys.108, 084107 (2010).

11J. S. Park, P. Revesz, A. Kazimirov, and M. P. Miller, Rev. Sci. Instrum. 78,023910 (2007).

12B. J. Pokines and E. Garcis, Smart Mater. Struct. 7, 105 (1998).13A. A. Elmustafa and M. G. Lagally, Precis. Eng. 25, 77 (2001).14H. Huang, H. W. Zhao, Z. C. Ma, L. L. Hu, J. Yang, G. Q. Shi, C. X. Ni,

and Z. L. Pei, J. Manuf. Syst. 31, 76 (2012).15H. W. Ma, S. M. Yao, L. Q. Wang, and Z. Zhi, Sens. Actuators, A 132, 730

(2006).16K. S. Chen, B. Z. Chen, and C. C. Huang, IEEE Trans. Compon. Packag.

Technol. 29, 841 (2006).17A. L. Gama and S. R. K. Morikawa, Exp. Mech. 48, 247 (2008).18M. Liu, K. H. Hsia, and J. K. Shang, J. Intell. Mater. Syst. Struct. 16, 557

(2005).19S. Mall and T. L. Hsu, Smart Mater. Struct. 9, 78 (2000).20S. Mall, Smart Mater. Struct. 11, 527 (2002).21T. Kobayashi, R. Maeda, and T. Itoh, J. Micromech. Microeng. 18, 115007

(2008).22S. Saito, K. Kikuchi, Y. Onishi, and T. Nishino, J. Nucl. Mater. 307–311,

1609 (2002).23ASTM A 29/A 29M-04. Standard specification for steel bars, carbon and

alloy, hot-wrought, general requirements (Ref. 1) (2011).24ASTM A36/A36M-08. Standard specification for carbon structural steel

(2003).

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