. . . 1M B \ . V. .H. _, ; .N.._wmw. . a k XIII?! L I B R A R Y E Michigan Sm te University 5,,: ”Whig: *1“ ,. "-"" llllllllllllllllllllllllmll/HIHWWWI - - , :;__ x, This is to certify that the thesis entitled TEMPERATURE AND RISE TIME EFFECTS ON DYNAMIC STRAIN MEASUREMENT WITH RESISTANCE STRAIN GAGES presented by William James Bagaria has been accepted towards fulfillment 5 of the requirements for ~_P_i]_._[14__ degree in Mechanics Z . g; ' W ’\ ., A Major professor Date all/f Z’) Iq73 0-7 639 ABSTRACT TEMPERATURE AND RISE TIME EFFECTS ON DYNAMIC STRAIN MEASUREMENT WITH RESISTANCE STRAIN GAGES by William James Bagaria Strain pulses in a test specimen were measured over a temperature range -lOO to +300°F with foil and semi-conductor resistance strain gages. These tests were performed to determine if the gage-output rise time and amplitude change as a function of temperature. The existence of a con— stant that should be added to the theoretical rise times of resistance strain gages, as suggested by Koshiro 0i, was re-examined. The foil gages were type ED-DY—OBlCF—350, manufactured by Micro~ Measurements. The semi-conductor gages were type SPB3-06-12, manufac— tured by BLH Electronics, Inc. All gages were bonded to the test speci- men with a large-temperature-range epoxy adhesive. The test specimen was made from Ni-Span—C, Alloy 926E)manufactured by The International Nickel Company, Inc. This alloy exhibited a con- stant long wave velocity over the temperature range ~l00 to +300°F. This characteristic was necessary in order to eliminate temperature William James Bagaria effects in the dispersion of the strain pulse. "Long" rise time strain pulses were produced in the test specimen by a falling steel ball which impacted the end of the specimen. The rise times of these strain pulses were on the order of 7 usec. and the strain amplitudes were approximately 65 pin/in. A new type of apparatus was de- signed and constructed that would generate "short" rise time strain pulses. The strain pulses were produced by impacting the end of the test specimen with a short pendulum—type hammer. The rise times were on the order of 0.l3 to 2 usec. The strain amplitudes were approximately 500 uin/in. The results of the 7-usec. rise-time tests showed that the rise time and amplitude of the gage output do not change appreciably as a function of temperature. The results of the Z—usec. rise—time tests showed that the amplitude of the gage output was relatively independent of the test temperature but did exhibit a hysteresis effect. The rise times remained constant up to a temperature of 200°F, then started to increase. The rise times at 300°F were approximately TOO per cent larger than at room temperature. The results of the sub-microsecond rise time tests indicated that the theoretical rise time additive constant is 0.05 usec. or less. This is one-half the value that Bickle arrived at by re-evaluating Oi's data. An analytical study was conducted on the sub~microsecond results using Taylor's theoretical work. From this analysis it was hypothesized that the output rise times of resistance strain gages do not require an addi- tive constant. TEMPERATURE AND RISE TIME EFFECTS ON DYNAMIC STRAIN MEASUREMENT WITH RESISTANCE STRAIN GAGES by William James Bagaria A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Metallurgy, Mechanics and Materials Science I973 Copyright by WILLIAM JAMES BAGARIA I973 ACKNOWLEDGEMENTS I wish to acknowledge the assistance given to me by Dr. William Sharpe, Jr. It was he, as my major advisor, who suggested the research problem and helped me in the data acquisition. Thanks are due to the rest of my guidance committee, Dr. D. J. Montgomery, Dr. D. H. Y. Yen and Dr. J. S. Frame. My wife deserves special thanks for her continual encouragement and support; and my children, who had to share their father with his research. ii TABLE OF CONTENTS Page LIST OF TABLES .......................... v LIST OF FIGURES .......................... vi LIST OF SYMBOLS .......................... viii I. INTRODUCTION ......................... 1 l.l General Comments and Purpose .............. 1 1.2 Previous Studies of Strain Gage Dynamic Response. . . . 3 1.3 Investigation of Strain Wave Generation Methods . . . . 7 l.3.l Piezoelectric .................. 7 l.3.2 Gas Pressure .................. 8 l.3.3 Pulsed Radiation ........ A ........ 10 l.3.4 Mechanical ................... 11 1.3.5 Hammer—Type Apparatus .............. 13 l.4 Selection of Test Temperature Range .......... 14 2. TESTING APPARATUSES AND INSTRUMENTATION ............ 15 2.l Criteria for the Hammer—Type Apparatus ......... 15 2.2 Hammer—Type Apparatus ................. 15 2.2.1 General Discussion ............... 15 2.2.2 Detailed Description .............. 17 2.2.3 Instrumentation ................. 3g 2.3 Ball Drop Apparatus .................. 54 3. SELECTION OF SPECIMEN MATERIAL AND STRAIN GAGES ....... 55 3.l Selection of Test Specimen Material .......... 56 iii Page 3.1.1 Dispersion and Temperature Effects ....... 56 3.1.2 Test Specimen Material ............. 63 3.2 Selection of Strain Gages and Mounting Adhesive . . . . 70 4. EXPERIMENTAL PROCEDURE AND RESULTS .............. 73 4.1 Experimental Procedure ................. 73 4.1.1 Ball Drop Tests ................. 73 4.1.2 Hammer Tests .................. 75 4.2 Data Reduction ..................... 78 4.2.1 Data Measurement ................ 78 4.2.2 Foil-Gage Data-Reduction Equations ....... 79 4.2.3 Semi-Conductor Data-Reduction Equations ..... 81 4.3 Ball Drop, Temperature-Test Results .......... 83 4.4 Hammer, Temperature-Tests Results ooooooooooo 91 4.5 Hammer, Sub-Microsecond Rise—Time-Test Results ..... 103 5. CONCLUSIONS .......................... 110 APPENDIX A LIST OF MANUFACTURER'S ADDRESSES ----------- 112 APPENDIX B LAPPING, POLISHING AND SURFACE MEASUREMENT TECHNIQUES- 113 APPENDIX C COMPUTER PROGRAMS ................... 115 BIBLIOGRAPHY ............................ 123 iv LIST OF TABLES TABLE 1 Parts List for Figure 9 ................. TABLE 2 Long Wave Velocity .......... .......... Page 32 69 Figure 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. LIST OF FIGURES Test Specimen ........................ Test Specimen Assembly ................... Lapped Specimen Assembly .................. Hammer Assembly ....................... Specimen and Hammer Assemblies ............... Hammer Shaft Misalignment Due to Bearing Clearance ..... Hammer Drive Assembly .................... Transducer Assembly ..................... Exploded View of the Hammer System ............. Hammer and Specimen Assemblies Showing Laser Beam Slot . . . Cross-section, Heating-cooling and Specimen Assemblies . . . Heat-cooling and Test Specimen Assemblies .......... Overall View of Testing Equipment .............. Test Apparatus Inside Vacuum Chamber ............ Close-up View of the Test Apparatus ............. Strain Gage Potentiometer Circuit .............. Hammer Velocity Circuit ................... Typical Em and E6 Traces .................. Strain Signal Trigger Circuit ................ Hammer Velocity Trigger Circuit ............... oooooooooooooooooo Ball Drop Test Apparatus vi Page 18 20 22 23 26 27 29 31 33 34 36 37 38 4O 41 42 47 51 53 53 55 Figure 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. First Mode Phase and Group Velocities ............ Distortion of Wave Shape Due to Dispersion ......... Thermal Expansion Characteristic .............. Effect of Heat Treatment on Modulus of Elasticity ...... Typical Ball—Drop-Test Records --------------- Measurement of A6 and A for Ball Drop Tests ........ t Strain-Temperature Curves, Ball Drop Tests ......... Rise Time-Temperature Curves, Ball Drop Tests ........ Non-Uniform Impact Velocity ................. Strain Gage Location .................... Typical Foil Gage Hammer-Test Records ............ Typical Semi-Conductor Gage Hammer-Test Records ....... Measurement of Ae and At for Hammer Tests .......... Strain-Temperature Curves, Hammer Tests ........... Rise Time-Temperature Curves, Hammer Tests ......... Sub-Microsecond Rise Time Records .............. Wave-Form Studied by Taylor ................. Vii Page 59 62 65 67 85 87 88 90 93 93 97 98 99 100 102 104 106 LIST OF SYMBOLS radius of bar coupling capacitor input capacitor damping capacitor semi-conductor quadratic gage factor sinusoidal wave group velocity longitudinal long wavevelocity sinusoidal wave phase velocity th component in Fourier series phase velocity of n clearance between races of hammer bearings modulus of elasticity DC supply voltage voltage across strain gage output voltage specimen reference density at temperature Tr voltage proportional to hammer angular position voltage proportional to hammer angular velocity cut-off frequency oscilloscope horizontal—amplifier gain (seconds/division) oscilloscope vertical-amplifier gain (volts/division) room temperature gage factor for foil strain gages semi-conductor linear gage factor viii GF test temperature gage factor for foil strain gages circuit current ‘ constant that relates w to Em active gage length, length between hammer bearings mass of test specimen ballast resistor feed-back resistor strain gage resistance unbonded semi-conductor gage resistance measured at temperature TO unbonded semi-conductor gage resistance at 0°F unbonded semi-conductor gage resistance at test temperature test temperature temperature at which R0 was measured reference temperature of pr and Er time rise time partical displacement in x direction of bar specimen reference volume at temperature Tr thermal coefficient of resistance, linear term thermal coefficient of resistance, quadratic term coordinate along longitudinal axis of bar linear coefficient of thermal expansion volume coefficient of thermal expansion hammer shaft misalignment angle strain-amplitude oscilloscope-trace deflection (divisions) change in semi-conductor gage resistance due to bonding and thermal expansion ix change in strain gage resistance change in semi-conductor gage resistance due to bonding, thermal expansion and load strain-rise-time oscilloscope-trace deflections (divisions) strain amplitude bonding and thermal expansion strain semi-conductor—gage strain due to bonding, thermal expansion and load hammer angular position sinusoidal wave-length Poisson's ratio bar/specimen density specimen reference density at temperature Tr standard deviation slope of the modulus of elasticity vs. temeprature curve hammer angular velocity frequency of fundamental Fourier component CHAPTER 1 INTRODUCTION 1.1 General Comments and Purpose Resistance strain gages are strain transducers consisting of a resis- tance element cemented to a backing material. The two most common types of resistance elements are made from metallic foils and from semi-conduc- tors. These gages are commercially available in many shapes and sizes. The associated strain-gage instrumentation is well developed and readily available. The gages are easily bonded onto most specimens that are to be tested. The above features have led to the increasing application of re- sistance strain gages. As the use of resistance strain gages becomes more wide-spread, the types of strain (static and dynamic) and the conditions under which they are measured are becoming more varied. Hence it is appropriate that re- search is conducted in the dynamic response of strain gages at room tem- perature. Before a gage can be used to measure dynamic strain, its dy- namic response must be determined. The dynamic response of a gage is de— termined ideally by subjecting the gage to a step-function strain wave. Two parameters then define the dynamic response, the rise time and ampli— tude of the output signal. The rise time is the time it takes the output signal amplitude to rise from 10 to 90 per cent of its steady-state or first peak value. The greatest single factor that has been hindering 1 ‘¥— __ 2 this research has been the generation of a strain pulse that approaches an ideal step-function. Extensive research has been conducted on the application of strain gages for the measurement of static strain at various temperatures. It has been determined that there are two basic effects produced on a gage by a temperature change. First, the gage resistance and sensitivity (gage factor) will change. This is due to the non-zero coefficient of thermal resistivity of the gage element. Second, the gage will experience a strain due to thermal expansion. This "apparent" strain arises from different coefficients of thermal expansion for the gage element and the test specimen material. The dependence of gage sensitivity and apparent strain on temperature is supplied by the gage manufacture. The measured strain amplitude can thus be analytically corrected for temperature effects. The apparent strain can also be corrected for by appropriate instrumenta— tion. Since these two temperature effects on gage output are independent of the type of strain being measured (static or dynamic), the same correc— tion made for temperature effects under static strain conditions should be made under dynamic strain conditions. One area that is becoming increasingly important is the measuring of dynamic strain at different test specimen temperatures. However, the effects of extreme environmental temperatures on the output of resistance strain gages when employed for the measurement of dynamic strain have not been investigated. When strain gages are to be used to measure dynamic strains at various specimen temperatures, two important parameters must be known: the rise time of the gage, and the effect of temperature on the gage output. Two additional problems arise which were not present when conducting dynamic tests at room temperature. First, the various test temperatures must not produce changes in the strain—generating fi 3 apparatus. If any changes occurred it would be difficult to separate the effects produced by changes in the test apparatus from those produced by any changes in the gage. Second, a test-specimen material must be chosen so that the material properties that affect a propagating wave do not change with temperature. The purpose of this experiment was to determine the temperature effects on the rise time and output amplitude of foil and semi—conductor resistance strain gages. In order to accomplish this purpOSe the strain gages were mounted on a test specimen such that they could be subjected to a propagating strain wave. It was necessary that the strain-wave rise time be short and that the strain-wave shape be reproducible over the test-temperature range. It was not necessary that the wave have a specific shape. The wave fronts had rise times on the order of l to 2 microseconds. The tests were carried out at environmental temperatures ranging from ~100 to +300°F. 1,2 Previous Studies of Strain Gage Dynamic Response The first studies on the dynamic response of the resistance strain gage were conducted by De Forest (1939).* The resistance strain gages that he used had just been developed by the Hamilton Standard Propellor Company and the Massachusetts Institute of Technology. These gages con— sisted of a resistance strip, made from bakelite resin impregnated with graphite, sandwiched between layers of pure insulating bakelite. The Sage length was one inch, the width was 0.25 inch, and the thickness was 0.015 inch. The amplifiers and oscillographs required to record the * Surnames followed by dates in parenthesis refer to Bibliography. 4 resistance strain gage signal had been developed the previous year. De Forest conducted tests on impacting bars. He compared his ex- perimental results with the theoretical results computed by Sears (1908). From this investigation he concluded that "progress is being made in the measurement of stresses which are propagated at the speed of sound, and that impact strains need no longer remain in the realm of conjecture.“ The magnetostrictive effects of wire strain gages were studied by Vigness (1956). This effect is the "self-generation" of a voltage by a ferromagnetic material. The magnetic domains in a ferromagnetic material can be aligned by repeated mechanical impact while the material is carry- ing a "large" electrical current. Once the domains are aligned, the material can self-generate a voltage when subjected to mechanical impact in the absense of an external voltage. Vigness "conditioned" strain gages made of various types of materials by subjecting them to different amplitude strain-pulses while they were carrying electrical currents of approximately 0.15 amp. This caused a preferential alignment of the gage material magnetic domains. When the gages without a supply current were subsequently subjected to dynamic strains they would generate a voltage. He found that gages made from strongly magnetostrictive materials, such as nickel, will self-generate voltages on the order of "several“ milli- volts. For materials such as isoelastic, which are "weakly" magneto— strictive, the self—generated voltages may be as large as one millivolt. Since typical outputs from strain-measuring systems range from 0.1 to 1000 millivolts, the above source of error can be appreciable for small- amplitude strain measurements. A theoretical investigation was conducted by Taylor (1966) in order to study the effects that gage length has on measurement of strain-wave 5 rise-time and amplitude. His basic premise was that the output of a finite length strain gage will be the average value of the strain that is within the length of the gage. Then he computed the rise time and amplitude errors as a function of the length of the strain~pulse leading edge and the strain-gage length. From this he derived "application de— sign charts" for use with resistance strain gages. with these charts, the rise time and amplitude outputs of the gage could be corrected. There are two limitations to the use of these charts. First, the ex— perimental strain-pulses must be of a similar shape as compared to the theoretical ones upon which the charts are based. Second, since his approach was theoretical, he neglected effects such as instrumentation circuit capacitance and inductance, skin conduction, magnetostriction, gage backing and cement properties. 0i (1966) devised a method by which an elastic step wave, that had a calculated rise time of 1.4 microseconds, could be produced in a test specimen. These step strain waves had rise times that were several times shorter than those used by previous investigators. For example, Cunning- ham and Goldsmith (1959) had reduced the rise time of strain waves to 7 microseconds and 10 microseconds in steel and aluminum bars respectively. Oi conducted tests on polyester-backed wire gages that had theoretical rise times of 0.16 and 0.48 microsecond. Linearly extrapolating his data and using the most conservative results, he determined that a gage has a rise time of less than 0.2 usec + 0.8 L/cO , 6 where L is the active gage length, and cois the long wave velocity of the test specimen material. The constant 0.8 arises from the definition of rise time. 0i felt it was "dangerous" to use the 0.2 microsecond value which was obtained by extrapolation of his data. His "moderate conclusion' was to estimate the rise time of a resistance strain gage as less than 0.5 usec + 0.8 L/C0 Dispersion, induced by Poisson's effect, will alter the rise time and amplitude of a propagating step wave and thus must be considered when using Oi's results. The rise time of the strain-wave in Oi's experiment was determined by a theoretical calculation based on crack-propagation theory. Then he compared the measured with the theoretical results. While he ”supposed" that the amplitude differences of the experimental results compared to the theoretical were partially due to the dispersion, he apparently considered that the rise times were not affected. Because of dispersion, it seems likely that the strain-wave initially had a shorter rise time than the theoretical one. Subsequently, dispersion probably increased the rise time of the strain—wave by the time it reached the gage location. Consideration of dispersion effects would then seem to indicate that the original 0.2 additive constant arrived at by Di might be conservative. Oi's work was re-evaluated by Bickle (1970). He first considered the 0.5 microsecond additive constant. Bickle felt that a 0.3 microsecond "safety factor" should not have been added to the rise time, since 0.2 microsecond "represents actual experimental results." He examined the effect of Oi's instrumentation system on the measured rise time. Bickle 7 concluded that the rise time of a strain gage is less than: 0.1 usec + 0.8 L/CO Next, Bickle considered the 0.8 L/c0 term. By making a coordinate-system transformation, he derived a closed-form analytical expression which yielded the input to the resistance strain gage based on the output. The use of this analytical method for resistance strain gage data reduction eliminates the 0.8 L/c0 term from the rise time expression. Bickle, then conducted an experiment which verified his analytical results. l;§_ An Investigation of Strain-Wave Generation Methods 1.3.1 Piezoelectric Piezoelectric materials have been used to generate sinusoidal stress (strain) waves in various substances. For example, they have been used to generate sonar waves in water and resonate standing waves in the "horns" of ultrasonic welders and drills. Stuetzer (1967) analyzed the transient behavior of thin piezoelectric elements. One of the many configurations and applications that he de- scribed was the use of a thin piezoelectric element as a mechanical pulse generator. The operating principle was as follows. A thin piezoelectric element was bonded between the ends of two "long" cylinders. A transient electrical voltage was applied across the faces of the piezoelectric ele— ment. When the voltage was applied by means of an "open—circuit opera— tion," a stress wave traveled into each of the cylinders. The waves were identical rectangular stress pulses traveling in oppositewco Logger .m weaned ceww mcwxwuca uwmsm mcwpomccoocmch mcwcam m>wco _m:owmc0h comm pcaoz Luau Eco: emv_oz z_nsmmm< m>eco 30 pre-load, the impact velocity of the hammer could be set to the desired value. The worm gear was rotated by a flexible shaft that passed through the vacuum chamber. A plunger passed through the vacuum chamber. The plunger performed two functions. First, when it was pushed, it disengaged the sear from the index gear. This allowed the torsional spring to drive the hammer which resulted in the hammer impacting the specimen. Second, when the plunger contacted the sear, it completed an electrical circuit. This circuit provided the trigger for the hammer velocity recording instrumentation. The transducer assembly is shown in Figure 8. This assembly mounted on the hammer assembly as shown in Figure 5. The transducer assembly coupled an angular potentiometer to the hammer shaft. The output of the potentiometer was a voltage proportional to the hammer angular position. This voltage was differentiated electronically, which resulted in a volt— age proportional to the angular velocity of the hammer. This voltage was then recorded. A calibration constant along with the voltage record was used to determine the hammer angular impact velocity. Figure 9 shows an exploded view of the hammer assembly, the hammer drive assembly, and the transducer assembly. Table 1 is a list of parts for Figure 9. Figure 10 shows the hammer and specimen assemblies ready to be joined. A 0.01 x 0.25-inch slot on the underside of the hammer holder provided a path for a laser beam. The laser beam was directed into the vacuum cham— ber and through the slot. A photodiode was placed at the beam-exit-end of the slot. The diode was included in an electronic circuit with an operation amplifier (op-amp). With the hammer in a raised position the laser beam could illuminate the diode. This resulted in a voltage output 31 Angular Potentiometer s3) / T' Figure 8. Transducer Assembly Shaft Coupling Mounting Bracket \ 32 cow—o: >FnEmmm< w>wce pczoz cmom comm peso: cmmw Eco: cmww Eco: Apmmsz Eco: o“ meccqm chowmcoo mcwpmmcv QEMFU mcem cmcwwpmm m>mmpm Ammcwcmmn pcmsm acccowccoochCF any cow cmwccmu m we ucm mecz Eco: mzu com mcwcmmn m we mpomv m>wmpm Poms: Eco: mmcwcmmm “cmzm mccpomccoocmch comm mewxoucH o» umcopmwc pcmcm meccumccoocmch mcccnm m>wca cocmcoc cmumEOTHCmpom cm_:mc< pmxomcm macpcsoz cmposowpcwuom cm_:m:< m:w_a=ou mmcccmwm wcmcm cwEEm: :_a cmEEm: pcwcm cmsgm: cease: cmu_oz cease: mEmz ecea a eczmcc coc omen mecee ._ e_eec "va-LnkONooow consaz “can 34 popm Emmm .63.. 9.265 3:9:me 55.50% EB cmEEm: .oc acemcc 35 from the op—amp. When the hammer contacted the specimen, the laser beam was interrupted. This resulted in a zero voltage output from the op—amp. The laser beam along with the diode circuit provided a trigger source for the strain recording instrumentation. A cross sectional view of the heating-cooling assembly as it was fitted to the specimen assembly is shown in Figure 11. A hollow specimen support located the test specimen relative to the holder while the potting compound cured. During testing the hollow portion of the support acted as an exit passage for the heating-cooling fluid. An inlet tube passed through a tee- fitting and the specimen support into the hollow section of the test speci- men. The tee-fitting separated the fluid inlet and outlet. The inlet tube, specimen support and specimen thus acted like a coaxial counter—flow heat- exchanger. The thermocouple determined when the test specimen was at the desired test temperature. Figure 12 shows the test specimen and heat- cooling assemblies. Note that the instrumented test specimen was pressed out of the holder and is still encased in the potting compound. An overall view of the testing system and instrumentation is shown in Figure 13. A cruved insulated duct passed through the support tripod. This duct carried the heating-cooling fluid to the test apparatus. The heating fluid was air heated by a heat gun. The heat-gun fan provided a positive pressure to the inlet of the duct. A vacuum system provided a negative pressure at the outlet of the heating-cooling assembly. The air was heated by an electrical resistance element. The specimen temperature was controlled by varying the air flow rate and by cycling the heating element on and off. Cold air could not be used for the cooling fluid. This was tried, but the water vapor in the air froze inside the heating-cooling assembly block- ing the air flow. 36 mmwpnemmm< cmewomam new mcwpoooumcwpmoz .:0wpoomummocu cmvpo: cmerooam pmpwso nw:_c mcwpoooumceumo: cmewomam pmmh /////////// / war % ///// /////> ///::_. uczoasou mcwppoa ucoaazm cmewowam .__ ecemcc amps? ova—u mac—oooumcwpmmz mecepcc-eee. T TM 1 3:332 .823on pump can 9580.353: .3 9.33... 38 «29533 9:38. we 33> 5985 m_ eczmcc 39 Subsequently, cold nitrogen was used as the cooling fluid. This was supplied by a reservoir of liquid-nitrogen. The vacuum at the heating: cooling assembly outlet would cause gaseous nitrogen to boil off from the liquid-nitrogen. By adjusting the vacuum level, the boil-off rate was controlled. This resulted in an adjustable flow rate of cold nitrogen through the system. The flow rate then determined the specimen tempera— ture. Figure 14 shows the test apparatus as seen through the vacuum cham- ber. Figure 15 shows a close-up view of the test apparatus. The vacuum bell-jar is removed for clarity. 2.2.3 Instrumentation Resistance strain gages change resistance when they are subjected to a strain. A potentiometer circuit converted the resistance change into a voltage change. Calibration factors then determined the strain from the voltage change. The potentiometer circuit is shown in Figure 16. A ballast resistor, Rb’ is in series with the strain gage, Rg. For any fixed supply voltage, Eb’ the maximum sensitivity of the circuit will oCcur when Rb = R9. The coupling capacitor, CC, prevents the passage of direct current to the re- cording instrument. Thus, this circuit will only respond to dynamic strains or the dynamic component of combined strains. By Ohm's law the current in the circuit is I = Eb/(Rb + R9) (3") consmsu Ezzom> mvwmcH mspmcmaa< pmwk .w— mczmwc 40 a) b) C) d) e) f) rack and pinion system for rotating the hammer to a raised position plunger beneath the sear with wiring for the velocity- signal trigger-circuit flexible shaft (curves through 90°) for adjusting the drive spring pre—load mirror (black rectangular holder angled at 45°), to direct the laser beam through the slot in the hammer holder hammer holder with hammer in a slightly raised position angular potentiometer with wiring for the velocity signal circuit photodiode (black rectangular housing) with wiring for the strain-signal trigger—circuit Figure 15. Close—up View of the Test Apparatus 42 —————4>- Rb c .______ c Ttb \I e ll T '1" R E0 9 l Eb : Circuit Supply Voltage (DC) I Circuit Current Rb : Ballast Resistor Rg : Strain Gage (Unstrained Resistance) CC Coupling Capacitor Eo Output Voltage Figure 16. Strain Gage Potentiometer Circuit 43 and the voltage across the gage is l'T'l ll IR . (2-2) Substituting Eq. (2-1) into Eq. (2—2), gives the voltage across the strain gage as = R + R 59 EbRg/( b 9) Applying a strain to the gage changes the gage resistance to R9 + ARg . The current then becomes 2 2-3 I Eb/(Rb + R9 + ARg) , ( ) and the voltage across the gage becomes e , (2-4) Eg + AEg I(Rg + ARg) Substituting Eq. (2-3) into Eq. (2-4) gives the new voltage across the aeas g g Eb(R + ARg) Eg + AEg =(R +gR + AR ) b 9 9 (2-5) Successive algebraic operations on Eq. (2-5) give EbRg(' + ARg/Rg) g ‘ in, + Rg)<1 + gag/(Rb + Rgl) E + AE 9 EbRg(l + ARg/Rg) [1 - (ARg/(Rb + Rg)) R + Rg b 44 2 3 + (erg/(Rb + Rg>> — (ARg/(Rb + Rgll + ...] E R =_b__q_ _2 2 Rb+Rg [l + ARgRb/Rg(Rb + Rg) ARg Rb/Rg(Rb + R9) + AR 3R /R (R + R )3 - ...] . (2-6) gbgb g The first term on the right hand side of Eq. (2-6) is Eg which is the DC component of the voltage across R9. The remaining terms are then the dynamic component of the voltage across the gage. Since the coupling ca- pacitor will only pass the dynamic component of the voltage, we have as the circuit output voltage m ll AE . (2-7) Thus Eqs. (2-6) and (2-7) give E R AR - b b _g_ 2 E - 1 - AR R + R + AR R + R r g /( b g) g /( b g 2 )2 ° (Rb + Rg) - ...] (2-8) Typical foil strain gages subjected to elastic strains have the following values: R9 = 1200 or 3500 AR 29 g< Therefore, the higher order terms in Eq. (2-8) can be neglected. This re- sults in an error in Eoof less than one per cent. The output voltage for 45 foil gages is then (2-9) 2 ° (Rb + Rg) Typical semi-conductor strain gages subjected to elastic strains have the following values: R9 = 1209 or 3509 ARg < 100 Therefore, third-order and higher terms in Eq. (2-8) can be neglected. This results in an error in E0 of less than 1/5 per cent. The output voltage for semi-conductor gages is then E EbRbARg 0 _ [1 - ARg/(Rg + Rbll . (2—10) (Rb + Rg)2 The potentiometer circuit output voltage was displayed on a Tektronix, type 555, oscilloscope with a type 1A1 vertical amplifier. An oscillo- scope camera provided a permanent record of the signal. The input impedance of the oscilloscope was approximately one Mn . This value was much greater than the strain gage resistance. Therefore, the effect of the oscilloscope impedance on the output of the potentiometer circuit was negligible. The vertical gain of the oscilloscope was cali- brated using a known amplitude square wave. It was also necessary to determine the rise time of the total strain instrumentation system. The expected rise time of the strain-pulse was on the order of 0.1 microsecond. If the instrumentation system rise time was about 0.1 microsecond or larger, the recorded rise time would be of the 46 system and not of the strain gage. The rise time of the oscilloscope/ vertical amplifier combination was 0.01 microsecond. This value was obtained from the specific ations of the oscilloscope, Thus, the oscillo- scope had the capability of measuring a voltage signal with a rise time of 0.1 microsecond. A Tektronix, type 114, pulse generator was used as the source of a known rise time square-wave voltage. The rise time of the square wave was 0.01 usec. The square wave was applied across the strain gage and displayed on the oscilloscope. The total strain instrumentation system rise time was found to be 0.02 microsecond. This value was sufficiently smaller than 0.1 microsecond to insure fidelity in the recording of a 0.1-microsecond rise-time output from the strain gage. The angular potentiometer connected to the hammer shaft provides a voltage output, Ee’ proportional to the hammer angular displacement. An electronic circuit was designed and built in order to determine the ham- mer angular velocity. The output voltage, Em, of this circuit is propor— tional to the hammer angular velocity. This circuit is shown in Figure 17. A six-volt battery supplied power to the potentiometer. The poten— tiometer output was the simultaneous input to two devices: the first channel of a dual-trace oscilloscope, and the differentiator circuit. The differentiator op-amp supply was a Model 5382, Dual Power Supply, f 15VDC @ 100 ma, manufactured by Analog Devices, Inc. The output from the differentiator circuit was the input to a low-pass filter. The filter was a Model 335R, Variable Filter, manufactured by Krohn-Hite. The out— put from the low-pass filter was the input to the second channel of the dual-trace oscilloscope. The angular potentiometer and filter output voltages were recorded using a Tektronix, type 564, storage oscilloscope 47 cmzom use no w .fi capped -mmmq-304 pwzocwu wioo~w> cmEEo: .Np mczmwc a: .1 .1: w. in .4 Apaasm “ .+ _ “1.4* I “ Fill c 71.111” _ \Vl _ :Em- _ _ 1 \j _ co . _ .5, _ _ : _ _/ N r1, ..L eceecco coeeceeececcco 'F l l / l ._._....__l / _l _ _ _ _ _ _ _ _l .L I. II I pcmgm cmEEm; op empomccoo powccoo occur—m .cmpmsorpcmuoe cm_:mc< 48 and a Tektronix, type 3A3, dual-trace vertical—amplifier. An oscillo— scope camera was used to provide permanent records of the signals. It was necessary to determine the following velocity circuit para- meters: a) input capacitor, C], b) feed—back resistor, R1, c) damping capacitor, C2 , d) low-pass-filter cut-off frequency,'fC Standard practice when using a uA74l op-amp with a t 15 VDC power supply is to choose Rf = 0.1 Mo . Experimentally, C1 was selected as luf. These values of R1; and C1 enabled the op-amp to operate below its saturation level. This would assure that distortion of the output sig- nal due to saturation would not occur. The damping capacitor, C2’ is necessary to reduce the noise on the output of the differentiator. Caution must be exercised in selecting C2. A large value would reduce the desired output signal along with the noise. The largest value found for C2 that did not affect the output signal was 0.01uf. However, this value did not completely eliminate the noise. The low-pass filter was used to further reduce the noise. As with the damping capacitor, the filter could also reduce the desired output signal. A cut-off frequency, fc, of 200 Hz was experimentally selected. The angular velocity, w, of the hammer was determined from the equa- tions of the differentiator circuit. The output voltage, Em, of the circuit as a function of the input voltage, E9’ is 49 Em = - RfC](dE”/dt) Rearranging gives dEO at“ : ' 5,,/ch1 Then the angular velocity of the hammer is U) = - KELO/RfC] 3 where K is a constant to be determined. The impact velocity occurs when Em reaches a maximum value, since the hammer is continually accelerating until impact. Therefore, /R C . (2-11) w impact : ' KEu max f 1 Now, it is necessary to determine the constant K. When the hammer When the hammer is is in contact with the specimen, E6 = — Ea max indexed to a raised position, through an angle e, E0 = 0. The resulting equation for K is K = - e/E max For this experiment it was determined that K = - 0.78rad/volt . (2-12) 50 Substituting Eq. (2—12) into Eq. (2—11) gives C . (2-13) = 0'78Ew lmax/Rf 1 w impact The impact velocity is then calculated from the maximum recorded value of Em with the use of Eq. (2—13). A value of w Iimpact calculated from Eq. (2-13) was compared with a value of w obtained by graphically limpact differentiating a typical Em record. The agreement of these velocities showed that the values of C2 and fC were satisfactory. Figure 18 shows typical Em and E6 traces. The bottom trace, Eo’ showed that the hammer rotated from the indexed position to the impact position in approximately 15 milliseconds. The reversed portion of the curve, approximately 28 milliseconds in duration, shows the rebound of the hammer. After rebound the hammer remains at rest as shown by the straight remaining-poriton of the curve. The t0p trace, Em, reaches a maximum value at the same time that the E6 trace shows that impact has occurred. After impact the Em trace becomes negative then positive showing the hammer rebound velocity. The hammer velocity then becomes zero as shown by the straight remaining-portion of the trace. It can be seen that the Em trace is not the precise differential of the E6 trace after impact has occurred. This is due to three of the parameters of the velocity circuit: the op-amp "slew" rate; the damping capacitor, C2; and the low-pass filter cut—off frequency, fc. The combined effect of these three parameters was to reduce the rate at which the differentiator cir- cuit can respond to its input signal. However, since the E6 voltage changes slowly before impact in comparison with the reversal of velocity after impact, the differentiator does give the true value of E0 max - 51 -——e4 }Er—— 10 msec ————————5>- t Top Trace: Em vs. time Bottom Trace: Ee vs. time Figure 18. Typical Em and E6 Traces 52 The circuit, which triggered the type 555 oscilloscope in order to record the strain signal, is shown in Figure 19. This circuit is based * on one shown in the Silicon Photodetector Design Manual, published by United Detector Technology. A laser beam from a continuous wave He - Ne, 4-milliwatt-output laser passed through the slot in the hammer holder and illuminated the photodiode. The photodiode was a type PIN-040A, manufac— tured by United Detector Technology. The op-amp was a Tektronix, type 0. The values for Rf and Eb were experimentally determined. The values selected were Rf = 1M0 and Eb = 6V. With the hammer in a raised posi- tion, the beam illuminated the diode and E0 = 70V. With the hammer in contact with the specimen, the beam was blocked and E0 = 0. The output voltage, E0, was then used as the input to the type 555, oscilloscope, delayed-trigger, circuit. This allowed the starting time of the oscillo- scope trace to be adjusted. The trace starting time could be set with t 0.1 microsecond. This tolerance was necessary since the time period available for recording a tenths of microsecond rise time strain signal was about 0.6 microsecond. The type 564 oscilloscope which recorded the hammer angle and veloc— ity signals was triggered by the circuit shown in Figure 20. The sear engaged the indexing gear to hold the hammer in a raised position. When the plunger disengaged the sear from the indexing gear, the electrical circuit was completed. The resulting voltage, E0, was then used as the input to the type 564, oscilloscope, trigger circuit. The temperature was monitored on a standard thermocouple millivolt potentiometer. * Manuals, Catalogs and Bulletins are listed in the Bibliography under manufacturer's name. Laser Beam Op-amp Si'Photodiode 1,, C' i 11 — _ *— - - Figure 19. Strain Signal Trigger Circuit lz/x-Sear [_ V O I: ‘1 I g” Plunger ' lo \ :1]: 11. = J 6 V Figure 20. Hammer Velocity Trigger Circuit 54 2.3 Ball—Drpp Apparatus A ball-drop test fixture was constructed for the purpose of conduct- ing two types of tests. One test was to determine the strain gage output for less severe dynamic strain conditions. The strain-pulse amplitudes would be lower than the ones produced by the hammer-type apparatus. The strain pulse rise times would be on the order of 7 to 10 microseconds. The tempera- ture range would be -100 to +300°F. The second test was to verify the published test specimen material- properties data. The long wave velocity was measured in the temperature range of -100 to +300°F. The ball-drop test fixture is shown in Figure 21. A 5/16-inch dia- meter ball dropped through a four-foot guide tube onto the end of the test specimen. The test specimen was 1/2 inch in diameter and 9 1/2 inches long. Two strain gages and one thermocouple were mounted on the specimen. The specimen was contained in an environmental chamber to control the specimen temperature. The trigger, strain and temperature instrumentation were the same as described in section 2.2.2. 55 maumcaaa<.ummh aoco ——mm cmpmsowpcmpoa _ m_a:oooscmsp r11 ._N eczmcc ///////A/n 1H ’,///// momma cwmcpm .._._..———__.—... .___._ .5- mQOUWOFFwomo i. pesocwu commwce .muowuouosa ease macaw L7/2/'/z/zzg/ Ppmm LirL 111: mpazoooscmch 1|. cmswumam “mop 4 L143 \l//51\1|flflflflmwwmm11# . consmcu Focucoo wczeecmasw» CHAPTER 3 SELECTION OF SPECIMEN MATERIAL AND STRAIN GAGES 3.1 Selection of Test Specimen Material It has been noted that dispersion effects alter the rise time and amplitude of a step-wave as it travels along a specimen. If the dis- persion effects are not recognized, this alteration of a step-wave might be attributed to the strain gage and/or the instrumentation system. In addition to a consideration of dispersion in a specimen, the effect that specimen temperature has on dispersion must be studied. When the effects of dispersion on traveling step-waves and the effects of temperature on dispersion are known, then a test specimen material can be chosen. 3.1.1 Dispersion and Temperature Effects Davies (1948) thoroughly studied the Hopkinson pressure bar. He compared traveling wave properties as predicted by three theories. These were the elementary one-dimensional wave theory, the Pochhammer-Chree theory, and the Love theory. The Love theory will not be considered in this paper. The elementary one—dimensional wave equation is 56 57 32u(x,t) : 2 32u(x,t) 2 CO 2 - (3'1 ) at 8x _ 1/2 Co - (E/b) (3-2) The only parameters considered in the one-dimensional theory are time, t, distance along the bar, x, partical displacement, u, bar density, p, and elastic modulus, E. This theory indicates that strain waves will travel along the bar at a velocity of co. This theory does not include any parameters related to the shape of the wave. This means that if a wave is composed of sine waves with various wave lengths, all of the waves will travel with the same velocity. Thus the phase velocity, cp, 0 Since these waves travel along the bar without shape change, they are and the group velocity cg, between the sine waves are equal to c . called distortionless. The general Pochhammer-Chree equations are exact for waves propaga— ting in a circular cross section bar of infinite length. (see Love (1934), page 288, or Kolsky (1963), page 54). .The boundary conditions at free ends of a finite length bar cannot be satisfied exactly for these equa- tions, (see Love§201). Thus these equations cannot be solved in closed form for most test situations. This implies that specific dispersion effects cannot be determined for a particular test. Davies devised a method by which general dispersion effects could be studied. He 58 considered an infinite length bar that had a periodic initial displace- ment along its length. This allowed him to numerically solve for the first three roots of the Pochhammer—Chree frequency equations and to write the periodic initial-displacement in terms of a Fourier series. The frequence equations are given in Love, page 289, and Kolsky, page 57. The roots were then plotted with cp/cO as a function of a/A and v = 0.29. Here cp is the phase velocity of sinusoidal waves traveling in the bar, a is the bar radius, A is the sinusoidal wave-length and v is Poisson's ratio. The first root corresponds to the first longitudinal mode and is shown in Figure 22. The sinusoidal-wave group velocity, non-dimen- sionalized using co, is given by The curve of cg/c0 as a function of a/A was calculated by differentiating the cp/cO curve and using Eq. (3—3). This curve is also shown in Figure 22. It can be seen from Figure 22, that cp/cO = l and cg/cO = 1 only in the limit when a/A becomes zero (this is the reason that cO is called the long wave velocity). Thus the general theory indicates that the propaga- tion velocity of sinusoidal waves is a function of A, a, v, E and 0. Whereas according to the one-dimensional theory the propagation velocity of sinusoidal waves is only dependent on E and p. Therefore, the general 59 One-Dimen51onal Theory ___,_..__ cp/c0 and cg/c0 c /co Pochhammer-Chree Theory p -————— cg/cO 1.]_____ —-«].I 1.0 .9 \J 00 O Figure 22. First Mode Phase and Group Velocities 60 equations imply that for any arbitrary wave that is resolvable into Fourier components, the relative phase of these components will vary with distance traveled. Dispersion will in general occur and any wave that is comprised of more than one sinusoidal component will suffer distortion as it travels along the bar. Having determined the behavior of cp/c0 and cg/co, Davies then used the phase and group velocities along with Fourier's theorem to determine the dispersion effects on periodic waves. He considered a "trapezium- shaped" periodic wave and wrote the Fourier series for this wave. The th n component of the Fourier series at a distance x from the origin was of the form 8n 532} [0030“: - X/Cpn) - 14,3 9 (3-4) where cpn is the phase velocity of the nth component and x/cpn is the time it takes this component to travel the distance x. In order to evaluate the terms given by (3-4) it is necessary to evaluate the cpn corresponding to the values of nwo. From the relationship between fre- quency and wave length for sinusoidal waves, Davies derived the following equation. C a 0 =2r—Efl— . (3-5) CO A The quantity on the right hand side of this equation can be evaluated from Figure 22. Then a curve of cpn/cO as a function aan/co can be plotted. This curve then gives the value of cpn corresponding to a given 61 n when a and c0 are known. Thus using the curve of cp/cO as a function of anmo/cO and the Fourier series, Davies determined the distortion of the ”trapezium-shaped" wave as it traveled along the bar. These results are plotted in Figure 23, from Davies' paper. This plot shows, that as the "trapezium-shaped" wave traveled along the bar, the slope of the wave decreased, the amplitude increased, and superimposed sinusoidal-type oscillations appeared. Thus the rise time of a step-wave would increase, the amplitude would change and the shape would become distorted as the wave travels along the bar. Davies concluded that two parameters greatly affect the distortion of a traveling wave: the radius of the bar and the distance that the wave travels. The assumption is made that the material property variables do not change along the bar. Therefore, when the dynamic response of a strain gage is to be studied by subjecting the gage to a traveling step— wave, the test specimen diameter should be as small as practical and the gage should be located as near to the source of the step-wave as possible. The effects that test temperature have on dispersion can now be con— sidered. The test specimen and apparatus were designed to minimize ther- mal gradients. Also the specimen temperature did not change during a test. Thus it can be assumed that temperature did not have a functional dependency on x or t. In Eq. (3-1), u is only a function of x and t with E and p considered as constants. The only way that temperature can be considered in this equation is to let E and p be functions of temperature, since the temperature is not a function of x or t. For these conditions, co is a constant for any given temperature. The temperature effect on the solutions of Eq. (3—1) can be seen to be only a change in the velocity co. Thus temperature changes do not affect the wave shapes which are 62 cowmcwammo op mzo mnmcm m>m3 co cowpcopmmo .mm mczmwc Auwmav p LTIIIIIII cmv com, omm_ come oe~_ ONN_ oomc Aev Dom owe owe oee owe ooe - :u/ _l _, _ c .a 4, _ c a _ g _ fl _ _ _ l\\ 1/ ..ll\...\/ _o.o . / V. / \A , IIIN. / eeceecem 33.8.5.6me \ 4 «JV. \ 1 3853.5: , ..c 3.x? / \ illso. / . \ ..|_m. // c c ., s L .. u n l . Eu com u x Ac:u mczpmcmaswp . :wocpm cow h d — — omp «AF Air Hi Addy mcawmcmasmh pmmp cop om . a . mama couozncouimEmm AV .mm deemed. 1P «1- db- cu- k cowpme>mo vcmvceum memem mco QM aaew ccoc no Lac ,6“ (uoissaddwog ‘ui/ui 9_01) apnsildwv uiedis 89 It appears that when the large deviations are considered, the measured strain-pulse amplitudes remain fairly constant over the temperature range. The theoretical rise time of a resistance strain gage is given by 1 tR = cO/L . (4-19) The length, L, of the foil gage was 0.031 inch and of the semi—conductor gage 0.06 inch. The long wave velocity, c0, of the test specimen mater- 5 ial was 1.85 x 10 inches per second. Thus the theoretical rise times for the foil and semi-conductor gages are tR foil = 0.134 microsecond and tR semi-conductor = 0.259 microsecond The foil and semi-conductor strain—pulse rise times as a function of temperature are plotted in Figure 29. The two curves are plotted separat- ely for clarity. The plotted data points are the average of the increas- ing and decreasing temperature tests. The vertical bars indicate the standard deviation of the data at each test temperature. The large dev— iation was caused by slight plastic deformation of the test specimen from each impact. The average room temperature rise time of about 7 micro— seconds for both gages was about 35 times greater than the theoretical rise time . Thus there should not be any significant difference in the 9O mpmmk aocoi_~mm .mm>c:u mcspmcmaemp . meek mmwm .mm mcsmwd AcoV mcspmcmasm» amok oom omm oom omp ooP om w om- mop- ..m.m s. . c . . 2. J/Illlllllllms\\\\\\\\ -.m.n -_e ,.. P so.w mmmw couozvcooiwemm 4 f .m.m 1r « w w « w w A 1.1 m.@ 19 1H1 A4uLIOoN .% villlllli .0 n. o. .u .0 Jiliiiiiiiiin . A .o .o wwm.c .H fl. fled cowpmw>mo wcmucmum mammm mco H“ cm.m some case no (spuooas 9_01) awry asiu F'—'Tw_firfil 91 measured rise times of the strain pulses due to the two different gage lengths. The average rise time as a function of temperature varied by about 10 per cent for the semi-conductor gage and by about 5 per cent for the foil gage. The maximum standard deviation was about t 15 per cent for the semi—conductor gage and about I 8 per cent for the foil gage. Within the deviation Of the data, the measured strain-pulse rise times appear to remain constant over the test temperature range. 4.4 Hammer, Temperature-Test Results The purpose of these hammer tests was to determine the temperature effects on the strain-gage output when the gages were subjected to "high“ amplitude "short" rise time strain pulses. The strain pulses for these tests had amplitudes Of approximately 450 microinches per inch and rise times of approximately 2 microseconds. The amplitude of the strain pulse produced in the test specimen by the hammer impact could not be approximated by the one-dimensional wave propagation theory, due to the shor-pendulum geometry. The impact velocity was neither uniform across nor perpendicular to the specimen impact face, as can be seen by examining the impact velocity vector and the hammer geo- metry. The tangential velocity vector, V, of a rotating object is where 0 is the angular velocity vector and F is the position vector to v. If T max’ the angular velocity vector at impact, is substituted for A, the v becomes the impact velocity vector, v impact' The hammer 8 geometry is shown in Figure 30. Also shown are the position vectors to the inside and outside of the specimen and their associated tangential velocity vectors 9, and to. This figure shows that the position vector 92 Figure 30. Non-Uniform Impact Velocity --Foil Gage #2 Semi-Conductor Gage #1 Foil Gage #1 Semi-Conductor Gage #2 Center Line of Hammer Pivot-Axis Figure 31. Strain Gage Location 93 F does not lie in the impact plane and does not have a uniform length across the specimen face. Therefore, 6 is not uniform across impact and not perpendicular to the specimen impact face. This results in a two- dimensional velocity initial condition. Thus the one-dimensional wave theory cannot be used to approximate the strain pulse amplitude for these tests. Figure 31 shows an end view of the test specimen and the gage loca— tions. Since each gage is on a different part Of the specimen circum- ference and the impact velocity varies across the diameter Of the speci- men, each gage would experience a different strain amplitude and possibly a different wave shape. Another factor that would influence the strain amplitude around the specimen circumference is the mis-alignment between the hammer and specimen impact faces. The impact velocity would be the highest at the time when impact first occurs. The specimen and hammer would make contact at a certain point (due to mis-alignment) the deform until both faces were entirely in contact. As the area of contact in- creases the hammer velocity would decrease. Thus the impact velocity across the specimen would also vary due to the mis-alignment. This is another reason why the strain amplitude would not be uniform around the specimen circumference. The fact that each gage might not experience the same amplitude and shape strain pulse does not influence these tests. The only requirements imposed on the strain pulse by these tests are short rise times, elastic amplitudes and repeatability over the test temperature range. The repeatability criteria, however, does require that m be the same for all tests. max These tests were conducted using 2 microseconds rather than 94 sub-microsecond rise times because Of an unexpected problem that arose. The test specimen was made from Ni-Span-C and the hammer was made from 7075T6 aluminum. Because Of the ingot size and expense Of Ni-Span-C, the hammer could not be made from this material. The test specimen was ther~ mally isolated from the rest of the apparatus by the potting compound. This also caused the specimen to be electrically isolated. When the ham- mer impacted the specimen an electrical transient appeared on the strain signal. The transient was approximately 5 millivolts high and 0.1 micro- second long. It appeared approximately 0.2 microsecond before the strain signal. This would indicate that at the instant of hammer impact a volt- age was being induced (possibly due to the dissimilar metals) across the specimen into the strain gage potentiometer circuit. The existence of a voltage potential between the hammer and specimen at impact was also in- dicated by the appearance of the hammer impact face after about 30 im— pacts. The face would lose its highly polished reflective surface and would become blackish-gray in color. Measurements taken of the discolor- ed face indicated that the surface finish had deteriorated from 3-5 to 15-20 rms microinches. Thus it appeared that the hammer-impact-face sur- face finish was being degraded by an electrical arcing phenomenon. The specimen was then electrically grounded to the hammer. The electrical transient was no longer visible on the strain signal. However, the re— polished hammer face still deteriorated to about 10-15 rms microinches surface finish. The surface finish would stabilize at this value after about 40 to 50 impacts. During the degradation Of the surface finish the strain pulse rise time would increase from a sub—microsecond value to about 2 microseconds. Once the surface finish stabilized, the rise time also stabilized. Since the hammer would experience several hundred 95 impacts during the temperature tests, these tests were conducted after the rise times had stabilized at about 2 microseconds. Another type of problem was encountered. When the foil strain gages were subjected to the short rise time strain pulses, the solder, which joined the lead wire to the gage solder tab, would unbond from the tab. In order Unalleviate this problem, the minimum amount of solder for a good electrical/mechanical connection was used and the potentiometer cir— cuit voltage, Eb’ was reduced. The reduced voltage reduced the gage cur-1 rent, thus reducing the electrical-resistance heating Of the gage and solder joint. The values of Eb finally chosen were 2 to 4 volts. At all temperatures, some tests were performed with Eb = 2 volts in order to com— pare the strain records as the 'tests were being conducted. The higher voltage was mainly used at the lower temperatures because of the ' improved heat transfer rate from the gage to the specimen. Even with these precautions the solder joint of fOil gage number two (see Fig- ure 31) failed at the 150°F tests. NO problems were encountered with foil gage number one and this gage was used for all Of the temperature tests. While the reduction in Eb did not influence the performance of the gage, just the solder joint, it did proportionally reduce the output, E0, from the potentiometer'isircuit. This is one of the reasons that the amplitudes of the oscillosc0pe records for the foil gage are small (about two divisions). The other reason that these traces are small was due to the required band width on the oscilloscope vertical amplifier. In order for the amplifier to respond to a one microsecond rise time signal the band width had to be approximately 410%: or greater. This large band width reduces the gain available from any type of amplifier and thus the available oscilloscope trace deflection. 96 Two semi-conductor gages were bonded to the specimen so that there would be a "back-up" gage in the event that one gage failed. However, the semi-conductor gages did not experience any failure since the lead wires were welded to the gage by the manufacturer. All of the tempera- ture tests were conducted using semi-conductor gage number one (see Fig- ure 31). The average hammer angular velocity was 74.6 f 3% radians per second for all tests. Thus the average magnitudes Of v0 and 9, were 146.6 f 3% and 138.3 f 3% inches per second respectively. Typical records of oscilloscope traces for three test temperatures are shown in Figures 32 and 33. The records in Figure 32 are for the foil gage and those in Figure 33 are for the semi-conductor gage. The time scale reads from left to right and compressive strain is indicated by a positive going trace. It can be seen that the wave shapes are different for each type of gage. This is attributed to the different locations of the gages on the specimen as discussed above. However, for each gage, the wave shape remained essentially the same as the test tem— perature was changed. The diagram of Figure 34 shows how the trace am— plitude and rise time were measured. The foil and semi-conductor strain- pulse-amplitudes as a function of temperature are plotted in Figure 35. The curves are plotted separately and the vertical bars that indicate the standard deviation are omitted for clarity. The average value for the standard deviation at each test point was 16 microinches/inch for the foil gage and 7 microinches/inch for the semi-conductor gage. The arrow- heads on the curves indicate the direction of temperature change between tests. The room temperature amplitude for the foil gage was 520 micro— inches/inch and 444 microinches/inch for the semi-conductor gage. This 97 compression Figure 32. Foil Hammer-Test-Records compression Figure 33. 98 Semi-Conductor Hammer-Test-Records 99 50(t) 1A ' Strain Pulse Trace / A 1 A 0.8A€ E Y t “X K ./ >1; 1 1‘ At 1 0.1 A Figure 34. Measurement of A8 and At for Hammer Tests 3mg cease: . 85.3 232853 1. Emcpm .mm 859“. AcoV oczumcmasme meh oom. omm com omp oo_ om a q a :c\:w1 m u cocpww>mo ucmcceum mamwm mco wmmcw>< mono couozvcouuwsom AV 100 1.. 1 qt- ‘— c-ll— ~— unq— - Havoc pmmp meuwcH mmpmowvcm + mmcmgo wcaumcmaemk co :o_pomcwo 305m meow: zocc< omm\umc wa o.e~ n mpwooFm> uoeaEH cepsmc< cease: cw\:w: m— u cowumw>mo ucmvcmpm msm_m wco ommcm>< some Feed no oops ‘- , oom r 00¢ . oom A Leoom ooe .oom .ooo econ l/Ul 9_01) apniiidwv “£9443 (uoissaudwog ‘u 101 difference is attributed to the different locations of the gages on the specimen. Both curves exhibit a loop which is similar to the hysteresis effect seen in many types of instrumentation systems. This hysteresis effect is at times also seen when resistance strain gages are used to measure static strains at various temperatures. In static strain mea— surement this effect is due to a viscoelastic behavior of the gage back- ing material and the mounting adhesive. Since for these tests the stan- dard deviation for each gage is not large enough to account for the am- plitude differences at each temperature, it seems that the hysteresis effect must be attributed to the backing material and adhesive acting viscoelastically. Other than the hysteretic behavior, the strain am- plitudes do not seem to deviate seriously from the room temperature values. The foil and semi-conductor strain-pulse rise times as a function of temperature are plotted in Figure 36. The average values for the stan— dard deviation at each test point was 0.6 microsecond for the foil gage and 0.1 microsecond for the semi-conductor gage. Since the rise time did not exhibit a hysteresis effect larger than the standard deviation, the plotted data points are the average of the increasing and decreasing tem— perature tests. . The average room temperature rise times of about 2 micro- seconds is approximately 14 times greater than the theoretical rise time Of the foil gage and about 7 times greater than the theoretical rise time of the semi-conductor gage. Thus a difference Of about 14 per cent might be expected between the rise times of the foil and semi—conductor gages. However, the standard deviations Of the data apparently masks this difference. It can be seen in Figure 36 that the rise times Of both gage outputs mumme cmeamx .mm>c:u mcspmcmasmp . meek mmwm .mm mczmcd Acav mczpmchEmH pmmh «Jr—- 1 mmm\nmc & xpcoo_m> pomnEH ce_:mc< cmesm: cowumw>mo ucmucmpm «Emwm mco mmmcm>< mmew copoancouécmm 4 :owpme>mo mcmucmpm mamwm mco mmecm>< 88 :0... O 00—1 TO.— ._ 1m.¢ (Spuooas 9_0[) awll 9548 103 exhibit a sharp increase above a temperature Of 200°F. This character- istic could also be attributed to a viscoelastic behavior of the gage backing and adhesive materials. Since the pulse duration of approxi- mately 20 microseconds was much longer than the pulse rise time, the backing and adhesive materials would have enough time in order to attain and transmit to the gage element the maximum amplitude of the strain pulse. This behavior would have to be taken into account when resist— ance strain gages are used to measure microsecond rise time strain pulses at specimen temperatures above 200°F. 4.5 Hammer, Sub-Microsecond Rise-Time-Test Results The ability of the hammer apparatus to produce sub-microsecond rise time strain pulses was used to investigate whether the rise time Of a resistance strain gage includes an additive constant. New gages (two 0.031 inch long foil and one 0.06 inch long semi- conductor types) were mounted on a test specimen. This was done because it was felt that the gages used in the temperature tests might have changed their room temperature properties due to being subjected to various temperatures and to large numbers of strain pulses. The hammer and specimen holder surfaces were refinished and the apparatus reassem— bled. The test specimen was subjected ha 26 impacts. Two of the oscillOSCOpe records are shown in Figure 37. The oscilloscope traces were dim because the trace was swept across the screen at a rate of 0.1 microsecond per division. Therefore, the oscilloscope records had to be rephotographed in order to enhance the traces. The average measured rise time for the 0.031 inch long foil gages was 0.18 microsecond. This was 0.046 microsecond greater than the 0.134 104 Foil Gage 5|..- 1 l ’ r :0... compression 0.1 usec 74° F Semi-Conductor Gage time Figure 37. Foil and Semi-Conductor Sub-Microsecond Rise Time Test-Results 105 microsecond theoretical value. It was 0.054 microsecond less than the 0.1 microsecond additive constant Bickel arrived at by re—evaluating Oi's data. Since the actual rise time of the strain pulse was unknown, the 0.046 microsecond difference is not necessarily a characteristic Of the gage. However, if there is an additive constant associated with foil gages, it can be said to be no greater than 0.046 microsecond . The average measured rise time for the 0.06 inch long semi-conductor gage was 0.31 microsecond. This was 0.051 microsecond greater than the 0.259 microsecond theoretical value. Since 0i did not investigate semi— conductor gages, the 0.051 microsecond difference cannot be compared to the 0.1 microsecond additive constant arrived at by Bickel. As above the 0.051 microsecond difference is not necessarily a characteristic of the gage. A hypothesis about the rise time additive constant may be formulated by considering the results from the theoretical study by Taylor (1966) and the combined results from the foil and semi-conductor tests. One of the strain pulse shapes that Taylor investigated was a ”linear ramp rise" up to a constant level, then the constant level was "maintained indefinitely relative to the time of rise.“ This wave form is shown in Figure 38. The constant level amplitude is A and the length Of the rise portion is b. For a gage of length L the output amplitude of the gage is S where S = ARg/Rg and is given by Taylor as 2 A(GF)/2Lb , 0: xt EL (4-21) S ==xt and Figure 38. 106 Wave—Form Studied by Taylor If 107 s = Aéfigl- [2xt(b + L) — xt2 - 52 - L2] , bixtfb + L . (4-22) In this equation, xt is the "distance Of progression of the hnpressed strain wave form into the gage length." The 10 per cent amplitude Of the gage output is then found by multiplying Eq. (4—21) by 0.1 and the 90 per cent value by multiplying Eq. (4—22) by 0.9. Performing these Operations gives 1 xt 10% = 0.447 (bL) ’2 (4-23) and 1 2 xt 190% = (b + L) - 0.446 (bL) / . (4—24) In arriving at Eqs. (4~22) and (4-23) it is noted that S/A(GF) = 1 The 10 to 90 per cent rise time Of the gage output signal is then given by tR = (Xt 190% ' Xt 110%)/°o (4‘25) Substituting Eqs. (4-23) and (4—24) into Eq. (4-25) gives tR = [b + L - 0.894 (bL)'/2]/cO . (4-25) 108 Now if it is assumed that the strain pulse produced by the hammer apparatus has the same shape as the one shown in Figure 38, then Eq. (4-26) can be solved in terms of b by using the foil gage data. This is done by letting tR = 0.18 microsecond = 0.031 inch and c0 = 1.85 x 105 inches/second The result is b = 0.292 inch The theoretical riSe time Of the strain pulse based on the rise time of the foil gage output can then be determined from Figure 9 in Taylor's paper. In order to use this figure the value of a = b/L must be calcu- lated. For the foil gage, L = 0.031 inch; thus a foil = 0.934 Then theoretical rise time Of the strain pulse was then determined to be t, = 0.127 microsecond . (4-27) The theoretical output of the semi-conductor gage to this strain pulse can now be determined. For the semi-conductor gage we have L = 0.06 inch thus 109 a 1semi—conductor : 0'482 ’ (4‘28) Using Eqs. (4—27) and (4~28) and Taylor's Figure 9, the theoretical rise time Of the semi-conductor gage output for the type of strain pulse shown in Figure 38 is found to be tR = 0.28 microsecond . (4-29) The theoretical rise time of the semi—conductor gage as given in Eq. (4-29) compares reasonably well with the measured rise time of 0.31 microsecond. Better agreement might have been achieved if the leading edge Of the theoretical strain pulse had less abrupt slope changes as probably occurred in the tests. Also the semieconductor gage might have been subjected to a slightly different rise time due to its being loca- ted at a different position on the specimen than the foil gage. The above calculations are based on a gage rise time given by tR = 0.8L/cO Since these theoretical calculations did not include an additive constant and they agreed well with the experimental results, it may be hypothesized that there is no additive constant associated with the rise time Of re- sistance strain gages. CHAPTER 5 CONCLUSIONS Foil and semi-conductor resistance strain gages were subjected to strain pulses over a temperature range of -100 to +300°F. The foil gages were type ED-DY—O3lCF-350, manufactured by Micro-Measurements. The semi- conductor gages were type SP83-06-12, manufactured by BLH Electronics, Inc. The gage elements were made of isoelastic and P-type silicon. Two types of strain pulses were used for these tests. One type of pulse was approximately a half-sine wave with a peak amplitude of 65 microinches/ inch and a rise time of 7 microseconds. The second type Of pulse was approximately a ramp function. The maximum amplitude of this pulse was 450 microinches/inch with a 2 microseconds rise time. The rise times and amplitudes of the gage outputs were unaffected by temperature for the tests using the longer type pulse. When the gages were subjected to the shorter ramp type pulse, the output amplitudes were essentially unaffected by temperature. However, the output amplitudes did exhibit a hysteresis loop. This hysteresis effect is attributed to a viscoelastic behavior of the gage backing and bonding materials. The rise time Of the output remained independent Of temperature up to a value Of 200°F. Above this temperature, the rise time showed a marked increase. The rise time at 300°F was 100 per cent greater than the room temperature value. This increase at the high 110 lll temperatures is also attributed to a viscoelastic behavior of the gage backing and bonding materials. This increase in the rise time of the output with increasing temperature would have to be taken into account when using resistance strain gages above 200°F. It was found that the gage circuit supply voltage had to be re- duced when the foil gages were subjected to the 2 microseconds rise time pulse. This was to prevent the solder joints, which attached the lead wires to the gage solder tabs, from unbonding. The constant added to the rise time of the gage output which was suggested by Di was re-examined. Since the rise time of the strain pulse was not known, the conclusion reached was that the additive constant is 0.05 microsecond or less. However, using the theoretical work of Taylor it was hypothesized that there is no additive constant associated with the rise time of the output from resistance strain gages. APPENDICES 10. 11. 12. 13. 14. APPENDIX A LIST OF MANUFACTURER'S ADDRESSES Analog Devices, Inc., Cambridge, Massachusetts. Bendix, Industrial Metrology Division, Dayton, Ohio. BLH Electronics, Inc., Subsidiary of Baldwin-Lima-Hamilton Corporation, Waltham, Massachusetts 02154. Crane Packing Company, Lapmaster Division, 6400 Oakton Street, Morton Grove, Illinois. Dexter Corporation, Hysol Division, Orlean, New York & Los Angeles, California. Dow Chemical Company, Midland, Michigan 48640. Hamilton Watch Company, Precision Metals Division, Lancaster, Pennsylvania 17604. International Nickel Company, Huntington Alloy Products Division, Huntington, West Virginia 25720. Krohn-Hite, Cambridge, Massachusetts. Micro—Measurements, a division of Vishay Intertechnology Inc., 38905 Chase Road, Romulus, Michigan 48174. Pfizer and Company, Inc., Minerals, Pigments, and Metals Division, 260 Columbia Street, Adams, Massachusetts 01220. Poly-Paks Inc., South Lynnfield, Massachusetts 01940. Tektronix, Inc., P.0. Box 500, Beaverton, Oregon 97005 United Dector TechnOlOgy, 1732 let Street, Santa Monica, California, 90404. 112 APPENDIX B LAPPING, POLISHING AND SURFACE MEASUREMENT TECHNIQUES The specimen in the specimen holder and the hammer in the hammer holder were lapped with a LapmasteHE)12 lapping machine manufactured by Crane Packing Company. This machine had a 12 inches in diameter cast iron lap. Up to three parts could be lapped simultaneously. The lapping abrasive was Lapmaster #1800. The abrasive consisted of aluminum oxide particles. The average particle size was 18.5 microns. The oil-based abrasive-vehicle was Lapmaster #5-001-0-0009. An oil based vehicle was necessary for two reasons. First, water would rust the lap. Second, aluminum oxide in water will react with aluminum. This would have prevented the achievement Of a smooth surface- Weights were placed on the parts during lapping. The weights were sized in order to exert a pressure of approximately 0.35 pound per square inch over the surface being lapped. This resulted in a material removal rate of approximately 24 microinches per minute. The lapping Operation was followed by two hand polishing operations. First, the parts were polished with a one micron particle size aluminum oxide abrasive in the oil based vehicle. A cast iron hand lap plate covered with a polishing cloth made from a denim type material was used for this operation. Second, the parts were polished with a 1/3 micron particle size aluminum oxide abrasive in the Oil based vehicle. For this 113 114 operation the hand lap plate was covered with a polishing cloth made from a synthetic velvet-type material. After final polishing the parts were cleaned in a ultrasonic cleaner. The finished surfaces of the parts were checked for flatness by an optical technique. A Lapmaster optical flat was placed on the polished surface. A 6510 A wave length red light was used to illuminate the polished surface through the optical flat. Interference fringes are thus produced by the polished surface and the optical flat. The curvature of these fringes was used to determine the flatness Of the part. For a de— tailed description Of this method see the Crane Packing Company Bulletin NO. L-404-6. If the surfaces were not flat within one-half wave length, the lapping, polishing and cleaning Operations were repeated. The surface finish was measured using a profilometer. This is a de- vice which moves a "tracing head" over the surface to be measured and automatically gives a readout in rms microinches. The profilometer, type- 08 Model 18, and tracing head, type MA, were manufactured by Bendix, Industrial Metrology Division. APPENDIX C COMPUTER PROGRAMS This appendix contains the print-outs of the four principal com- puter programs used for reduction of the test data. The programing language was Time Sharing Fortran IV. The programs were run on an IBM 360 computer. The use of individual programs is shown by the comment statement on line 2 of each program. The line numbers are indi- cated by a L followed by a number on the left hand side of the print" out. 115 1.0001 t.¢¢dz L.9043 L .0004 L.¢¢bs L.hd¢6 L.fi¢d7 L.hh¢8 L.fMflg L.h¢13 L.fldII 373.39. :9. H \j ‘EDCQ‘S. NHH ‘SLCDOO 521 822 823 524 ¢25 n26 Pf—F'F'F'F'F’F‘I— r _ O O 0 O 0 O i—l-F' ‘9. N \l QQQQE‘SE‘QERQ 028 -529 939 -031 REQ‘Q‘Q ‘Q‘G. WW J4 N .834 035 535 , 38 039 a - CADRE ‘3. U4 \l 841 7542 043 T137319. ‘8. J? ‘8. - I 3‘8. 3'4? U14? 046 947 F'F’F'F—F'F—F'F‘r'f—F'i—l—l—I—i—l—F'i—l— 00......0.......... 33.5833 116 /d08 CO C 090 619 62¢ 19 20 30 11X,'RISE TIME SEMI-COMO BALL DROP DATA REDUCTION DIMENSION DSTCSD),GSTC50),EBGCSD),DPTC50),CT(SO) 1,5(5h),Ricsh) wRITE(6,6np) FORMATC'TEST TEMPERATURE (one F)') wRITEC6,hId) FORMATC1x,'Avo ONE SIGMA') WRITEC6,620) FORMATCBX,'ClN/IN)',8X,'STRAIN',6X,'(SFC)', 17x,'RISE TIME'//) READCS) N,TEMP,cr,c2,RO,To,Rc IFCN)990,999,2¢ 00 3d 1:1,N READCS) DSTCI),GST(I),EUG(I),DPT(I),CT(I) CONTINUE EN=N SUME=W.U SUMRT=¢.0 SSDE=0.0 SSORT=d.n X=1.fl-¢.20400283T0+h.¢499923319332 R00=ROIX ROTT=ROO“(1.fl-¢.W¢UWDZ8”TEMP+U.09000233TEMP TOR=TO+459.65 TTR=TEMP+459.65 As=ROTixc23 AP=CEBGCI)312¢.¢)/<(12¢.A+Ro>““3) BR=-(Ebc(1)“120.h)/((12¢.9+Rc)“"2) CR=DEG RADR=SQRTCBR"“2-H.03AR3CR) 0R=(-oR-RA0R)/(2.¢“AR) c=ROTT—(OR+RG) RAD=SQRT(B”“2-A.D”A”C) ET=(-B+RAD)/C2.0”A) ECI)=ET-Es SUME=SUME+ECI) AVGE=SUME/EN STRAIM',bx,'ONE SIGMA Avc', 332) 52 53 55 57 S8 59 55¢ 63¢ 6hfi 999 /DATA lEND 117 RTCI)=DPTCI)”GT(I) SUMRT=SUMRT+RT(I) AVGRT=SUMPT/EN CONTINUE DO 55¢ 1:1,N OEE=(E(I)-AVGE)”*2 SSDE=SSDE+DEE SOEstRTCSSOE/END DERTzCRTCID-AVGRT)**2 SSDRT=SSDRT+DERT SDRT=SQPTCSSDRTIEN) CONTINUE WRITEC6,63fl> TEMP FORMATCIX,El3.S) WRITEC6,6ufl) AVGE,SDE,AVGRT,SDRT FORMATCIX,4EI3.5/) GO TO IN STOP ENO 118 L.flfl¢1 /dnB CO I.¢fifl2 C SEMI—COMO HAMMER-DATA PEOUCTION I.¢¢¢3 DIMENSION OSTCSS),O§T(5O),Emacs”),nnT(5O) L.fl¢flu I,OT(5fl),Dw<5fl>,CST65fl),Euccsd),OPTcsfi) l.fiflfl5 2,w(5fl),VC5¢) L.fiflfl6 WPITEC6,6Wfl) L.%¢¢7 Gfifi FORMATC'TEST TEMPEPATUPE (DEC F)') L.fl¢fl8 WRITE(6,61fl) 1.¢flfi9 61M FORMATCIX,'AVG STRAIN ONE SIOMA AVG EIOE' L.flfi1fl 1,1x,'TIME ONE SIGMA AVG IMP VEL ONE',Ix, I.¢¢11 2'SIGMA MEAN IMP VEL') L.fl¢12 WRITEC6,62fl) L.fl¢13 62w FORMATCSX,'CIN/IN)',8X,'STPAIN',6X,'(SECD',7X, L.n¢1u I'RISE TIME (RAD/$EC) IMP VEL',SX, L.flfl15 2'(IN/SEc)'//) L.¢n16 1H READCS) N,TEMP,GF,C2,RO,TO,RC L.¢¢17 IFCN)999,999,2¢ L.fl¢18 Zfl OO 3“ I=I,N fl¢19 READCS) DSTCI),GST(I),EBC(I),DPT(I) L L flzfi READCS) GTCI),ON(I),ON(I) L ¢21 3P CONTINUE L ¢22 EN=N L ¢23 SUME=¢.¢ L fiZfi SUMRT:¢.¢ L fl25 SUMN=¢.¢ L ¢26 SSOE:¢.¢ L fi27 SSDRTzn.n L 628 ssnv:fi.¢ $29 x=I.a-fl.PgflagzngO+n,gmnanzsxrnxnz H3” ROO=PO/x “31 R0TT=R00“(1.fl-fl.flflfiflfl28xTEMP+fl,fldflflfi233TFMpxxg) ‘3. VJ VJ U3u fl36 ¢37 ' ' :9. \N N TOR=TO+H59.65 TTR:TEMP+459.65 AS=ROTT3C2“(TOR/TTR)“"2 Bs=ROTTficP3cTOR/TTR) CS=ROTT-RG RADS=5OPTCBSK*2-u.OXASKCS) ES=C—BS+RADS)/(2.¢”AS) AzROTTxczchOP/TTR3332 B=ROTT“GF“(TOR/TTR) DO sflw I=1,N DEG=-DSTCI)”GSTCI) AR=CEBGCI)“12¢.fl)/((12¢.fi+RG)““3) - Pun BRz—(EBGCI)“12¢.fl)/((12fl.¢+RG)““2) L fins CR=DEG L,fi¢46 RADRzSQRTCkafiz-u.flxAR3CR) OR:(-BP-PADR)/(2.63AR) C=ROTT-CDR+RG) ('1' () 1:311:13 UTva :0 H21 '. '. L L L “518.133.513.321. U1 KN 56 U“! U1 56 \n \l 58 OK” a“) O 0 O O . O O O O O F‘F‘I‘T‘T‘F’F‘F’F’f— mom wmI—a i..- . . . C5 .5? .1 aaaa‘a‘a‘aa‘a‘a Vac-x U 6 667 668 669 676 ‘3. \3 H 672 673 6711 3333133331 676 f— 1— 7— i— :- T- '— - 1.1- 1— 1— ”" .. O O O O O O O O O O O O O O O O O O 0 71—77-73" 566 556 636 666 999 /DATA /END 119 RAD=SORT(B““2-H.H“A"C) ET=C~B+PAD)/(2.6*A) ECI)=ET—ES SUME=SUME+E(I) AVCEzSUME/EN RTCID=DRTCI)“CT(I) SUMRTZSUMRT+RT(I) AVGRT=SUMRT/EN EK=(6.78539816) ENCI)=DNCI)“GN(I) WCI)=EK”EWCI)/6.1 SUMN:SUMN+N(I) AVGw=SUMleN AVGVzAVGw31.813 V(I)=N(I)“1.813 CONTINUE DO 556 1:1,N DEE=CECID~AVGED337 SSDE: SSDE+DEE SOE: -SOPT(SSDE/EN) DEPT: (PT(1)- AVGRT) SSDPT: SSDRT+DERT SORT: SQPTCSSDPT/EN) DEV: AVCST,SDST,AVCRT,SDRT 666 FORMATC1X,9E13.5/) GO TO 16 999 STOP END /[)ATA IEND 121 I.6661 /UOB CO L.6662 C POIL HAMMER-DATA REDUCTION L.6663 DIMENSION DSTC56),CST(56),FBCC56),DRT(S6) L.6664 1,GT(S6),DNCS6),CN(56),DEC(56),ST(56),PT(56) L.6665 2,Ew(56),wcs6),v(s6) L.6666 WRITEC6,666) L.6667 666 FORMATC'TEST TEMPERATURE (DEG FD') L.6668 WRITEC6,616) L.6669 616 PORMATCIX,'AVC STRAIN ONE SICNA AVC RISF' L.6616 1,1x,'TIME ONE SIGMA AVC IMP VEL CNP',IX, L.6611 2'SICMA MEAN IMP VEL') L.6612 WRITEC6,626) L.6613 626 FORMATC3X,'(IN/IN)',8X,ISTRAIN',6x,'(SEC)',7x, L.6619 l'RISE TIME (RAD/SEC) IMP VEL',5x, L.6615 2'CIN/SEc)'//) L.6616 16 READCS) N,TEMP,GF L.6617 IPCN>999,999,26 L.6618 26 DO 36 I=1,N 1.6619 READCS) DSTCI),GST(I),EBG(I),DRTCI),GT(I) L.6626 READCS) EBTCI),Dw(I),Cw(I) L.6621 36 CONTINUE L.6622 EN:N L.6623 SUMST=6.6 L.6624 SUMRT:6.6 L.6625 SUMw=6.6 L.6626 SSDS=6.6 L.6627 SSDRT=6.6 L.6628 SSDv=6.6 L.6629 CFT=CFxc-6.6659466+6.66611996 TEMP L.6636 1-6.66666646623 TEMP “2) L.6631 CCFT:CFT+CF L.6632 DO 566 I=I,N L.6633 DEGCI)=—DSTCI)”GST(I) L.6639 STCI)=C9.6“DEG(I))/(EBGCI>366ET> L.6635 SUMST=SUMST+STCID ‘ L.6636 AVCSTzSUMST/EN L.6637 RTCI)=DRT(I)“GTCI) L.6638 SUMRT=SUMRT+RT(I) L.6639 AVCRT=SUMRT/EN L.6666 EK=C6.78539816) L.6691 EWCID=DWCI)“GWCI) L.6692 NCI)=EK“ENCI)/6.1 I.6669 SUMw=SUMw+w(I) L.6699 AVGw=SUMW/EN L.6695 VCI)=N(I)*1.813 L.6696 AVGV=AVGW31.813 L.6697 S66 CONTINUE L.6648 DO 556 I=1,N L.6699 DES=CST(I)—AVGST)“”2 L.6656 L.6651 L.6652 L.6653 L.6659 L.6655 L.6656 L.6657 L.6658 L.6659 L.6666 L.6661 L.6662 L.6663 L.6669 L.6665 L.6666 L.6667 L.6668 L.6669 556 636 122 SSDS:SSDS+DES SDSTstRTCSSDS/EN) DERT=CRTCID~AVCRT)“”2 SSDRT:SSDRT+DERT SDRTzSORTCSSDRT/EN) DEV=(V(I)-AVGV)““2 SSDV=SSDV+DEV SDv:SORTCSSDV/EN) SDw=SDV/1.813 CONTINUE WRITEC6,636) TEMP FORMATCIX,EI$.5) WRITEC6,646) AVCST,SDST,AVCPT,SDRT 1,AVGw,SDw,AVGV 666 FORMATCIX,7E13.5/) 999 /DATA /EMD GO TO U1 STOP END BIBLIOGRAPHY BIBLIOGRAPHY Becker, E. 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