Scholars' Mine. Missouri University of Science and Technology. Maher Kassar. Wei-wen Yu Missouri University of Science and Technology,

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Miouri Univerity of Science and Technology Scholar' Mine Center for Cold-Formed Steel Structure Library Wei-Wen Yu Center for Cold-Formed Steel Structure 8-1-1989 Deign of automotive tructural

edu Follow thi and additional work at: http://cholarmine.mt.

1 Miouri Univerity of Science and Technology Scholar' Mine Center for Cold-Formed Steel Structure Library Wei-Wen Yu Center for Cold-Formed Steel Structure Deign of automotive tructural component uing high trength heet teel the effect of train rate on compreive mechanical propertie of heet teel Maher Kaar Wei-wen Yu Miouri Univerity of Science and Technology, Follow thi and additional work at: Part of the Structural Engineering Common Recommended Citation Kaar, Maher and Yu, Wei-wen, "Deign of automotive tructural component uing high trength heet teel the effect of train rate on compreive mechanical propertie of heet teel" (1989). Center for Cold-Formed Steel Structure Library Thi Report - Technical i brought to you for free and open acce by Scholar' Mine. t ha been accepted for incluion in Center for Cold-Formed Steel Structure Library by an authorized adminitrator of Scholar' Mine. Thi work i protected by U. S. Copyright Law. Unauthorized ue including reproduction for reditribution require the permiion of the copyright holder. For more information, pleae contact cholarmine@mt.edu.

2 Civil Engineering Study 89-4 Structural Serie Twelfth Progre Report DESGN OF AUTOMOTVE STRUCTURAL COMPONENTS USNG HGH STRENGTH SHEET STEELS THE EFFECT OF STRAN RATE ON COMPRESSVE MECHANCAL PROPERTES OF SHEET STEELS by Maher Kaar Reearch Aitant Wei-Wen Yu Project Director A Reearch Project Sponored by the American ron and Steel ntitute Augut 1989 Department of Civil Engineering Univerity of Miouri-Rolla Rolla, Miouri

3 ii TABLE OF CONTENTS Page LST OF TABLES LST OF FGURES iv vii. NTRODUCTON REVEW OF LTERATURE A. GENERAL... 3 B. DYNAMC TESTNG FOR VAROUS STRAN RATES... 4 C. EFFECT OF STRAN RATE ON COMPRESSVE MECHANCAL PROPERTES a. Steel... 5 b. Aluminum EXPERMENTAL PROGRAM 10 A. MATERALS 10 B. COMPRESSON TESTS. ' ASTM Specification Specimen Equipment Procedure... 13

4 iii TABLE OF CONTENTS (Cont.) Page C. RESULTS Stre-Strain Curve Mechanical Propertie a. Proportional Limit 15 b. Yield Strength or Yield Point D. DSCUSSON Mechanical Propertie a. Yield Strength or Yield Point b. Proportional Limit Strain-Rate Senitivity Prediction of Yield Strength in Compreion for High Strain Rate V. ADDTONAL EVALUATON FOR THE TENSLE TEST DATA PRESENTED N THE ELEVENTH PROGRESS REPORT V. CONCLUSONS 22 ACKNOWLEDGMENTS 24 REFERENCES 25

5 iv LST OF TABLES Table Page 2.1 Experimental Technique for Variou Strain Rate Regime for Compreion Teting Effect of Strain Rate and Temperature on the Stre 3 Required to Compre Steel 2.3 Value of cr for Steel uing the Equation 3 o cr = cr o *.m E Value of m for Steel uing the Equation 3 cr = cr o * E m Effect of Strain Rate and Temperature on the Stre Required to Compre Aluminum Value of cr for Aluminum uing the Equation 3 o cr = cr o *.m E Value of m for Aluminum uing the Equation 3 cr = cr o *.m E Reult of Compreion Tet on Commercially Pure Aluminum at Contant True Strain Rate Baed on Equation 6 BE cr = A * (1 - e ) + C * E Chemical Compoition of the Sheet Steel Ued. Claification of the MTS Compreometer Function Generator Ramp Time and the Correponding Strain Rate Teted Mechanical Propertie of 100XF Sheet Steel Longitudinal Compreion... 33

6 v LST OF TABLES (cont.) Table Page 3.5 Teted Mechanical Propertie of 100XF Sheet Steel Tranvere Compreion Teted Mechanical Propertie of 50XF Sheet Steel Longitudinal Compreion Teted Mechanical Propertie of 50XF Sheet Steel Tranvere Compreion Teted Mechanical Propertie of 35XF Sheet Steel Longitudinal Compreion~ Teted Mechanical Propertie of 35XF Sheet Steel Tranvere Compreion Average Teted Mechanical Propertie of 100XF Sheet Steel Longitudinal Compreion Average Teted Mechanical Propertie of 100XF Sheet Steel Tranvere Compreion Average Teted Mechanical Propertie of 50XF Sheet Steel Longitudinal Compreion Average Teted Mechanical Propertie of 50XF Sheet Steel Tranvere Compreion Average Teted Mechanical Propertie of 35XF Sheet Steel Longitudinal Compreion, Average Teted Mechanical Propertie of 35XF Sheet Steel Tranvere Compreion... 41

7 vi LST OF TABLES (cont.) Table Page 3.16 Ratio of Dynamic to Static Compreive Yield Stree for Three Sheet Steel Baed on Table 3.10 to Value of Strain Rate Senitivitie m for Three Sheet Steel Baed on the Change of the Yield Stree at Different Strain Rate... 43

8 vii LST OF FGURES Figure Page 2.1 Relationhip Between Flow Stre and Natural Strain for 4 Low-Carbon Steel a) 900 deg. C., b) 1000 deg. C., c) 1100 deg. C., and d) 1200 deg. C Relationhip Between Flow Stre and Natural Strain for Medium-Carbon Steel 4 a) 900 deg. C., b) 1000 deg. C., c) 1100 deg. C., and d) 1200 deg. C Relationhip Between Flow Stre and Natural Strain for High-Carbon Steel 4 a) 900 deg. C., b) 1000 deg. C., c) 1100 deg. C., and d) 1200 deg. C Effect of Strain Rate on the Stre Required to Compre 3 Aluminum to 40% Reduction at Variou Temperature 2.5 Stre-Strain Curve for Aluminum in Tenion an. 7 d Compre1.on Stre-Strain Curve for 6061-T6 Aluminum in Compreion at Several Strain Rate Nominal Dimenion of Compreion Coupon Ued for All Sheet Steel MTS 880 Material Tet Sytem Ued for Compreion Tet MTS Load Frame, MTS Controller, CAMAC Data Acquiition Sytem, and Data General Graphic Diplay Terminal Ued for Compreion Tet... 52

9 viii LST OF FGURES (Cont.) Figure Page 3.4 Compreion Subpre, Jig, Compreometer, and Tet Specimen Ued for Compreion Tet a Aembly of Compreion Subpre, Jig, and Compreometer (Front View) b Aembly of Compreion Subpre, Jig, and Compreometer (Back View). MTS 880 Tet Controller and Function Generator. Data Acquiition Sytem. Data General Graphic Diplay Terminal. Data General MV Mini Computer. BM PS/2 Model 30 Peronal Computer with BM Color Plotter Ued for Compreion Tet. Typical Function Generator Ramp Waveform. Stre-Strain Curve for 100XF-LC Steel Under Different Strain Rate Stre-Strain Curve for looxf-tc Steel Under Different Strain Rate Stre-Strain Curve for SOXF-LC Steel Under Different Strain Rate

10 ix LST OF FGURES (Cont.) Figure Page 3.15 Stre-Strain Curve for 50XF-TC Steel Under Different Strain Rate Stre-Strain Curve for 35XF-LC Steel Under Different Strain Rate Stre-Strain Curve for 35XF-TC Steel Under Different Strain Rate Stre-Strain Curve for Determination of Mechanical Propertie of 35XF-TC Compreive Yield Stre v Logarithmic Strain Rate Curve for 100XF-LC Steel Compreive Yield Stre v Logarithmic Strain Rate Curve for 100XF-TC Steel Compreive for 50XF-LC 3.22 Compreive for 50XF-TC 3.23 Compreive for 35XF-LC 3.24 Compreive for 35XF-TC Yield Stre v Logarithmic Strain Rate Curve Steel Yield Stre v Logarithmic Strain Rate Curve Steel Yield Stre v Logarithmic Strain Rate Curve Steel Yield Stre v Logarithmic Strain Rate Curve Steel Tenile Yield Stre v Logarithmic Strain Rate Curve for 100XF-LT, (Virgin Material)... 75

11 x LST OF FGURES (Cont.) Figure Page 4.2 Tenile Yield Stre v Logarithmic Strain Rate Curve for 100XF-TT, (Virgin Material)... ~ Tenile Yield Stre v Logarithmic Strain Rate Curve for 50XF-LT, (Virgin Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 50XF-LT, (2% Cold-Stretched, Non-Aged Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 50XF-LT, (8% Cold-Stretched, Non-Aged Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 50XF-LT, (2% Cold-Stretched, Aged Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 50XF-LT, (8% Cold-Stretched, Aged Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 50XF-LT, (Virgin Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 50XF-LT, (2% Cold-Stretched, Non-Aged Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 50XF-LT, (8% Cold-Stretched, Non-Aged Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 50XF-LT, (2% Cold-Stretched, Aged Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 50XF-LT, (8% Cold-Stretched, Aged Material)... 86

12 xi LST OF FGURES (Cont.) Figure Page 4.13 Tenile Yield Stre v Logarithmic Strain Rate Curve for 50XF-TT, (Virgin Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 50XF-TT, (Virgin Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 35XF-LT, (Virgin Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 35XF-LT, (2% Cold-Stretched, Non-Aged Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 35XF-LT, (8% Cold-Stretched, Non-Aged Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 35XF-LT, (2% Cold-Stretched, Aged Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 3SXF-LT, (8% Cold-Stretched, Aged Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 35XF-LT, (Virgin Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 35XF-LT, (2% Cold-Stretched, Non-Aged Material)... 9S 4.22 Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 35XF-LT, (8% Cold-Stretched, Non-Aged Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 35XF-LT, (2% Cold-Stretched, Aged Material)... 97

13 xii LST OF FGURES (Cont.) Figure Page 4.24 Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 35XF-LT, (8% Cold-Stretched, Aged Material) Tenile Yield Stre v Logarithmic Strain Rate Curve for 35XF-TT, (Virgin Material) Tenile Ultimate Stre v Logarithmic Strain Rate Curve for 35XF-TT, (Virgin Material)

14 1. NTRODUCTON Since May 1988, the reearch project on automotive component ponored by American ron and Steel ntitute (AS) at Univerity of Miouri-Rolla (UMR) ha been concentrated on a tudy of the effect of train rate on mechanical propertie of heet teel and the tructural behavior and trength of cold-formed teel member ubject to impact load. The reult of the tenile dynamic mechanical propertie of three elected heet teel, in the virgin condition a well a for the teel ubjected to different amount of cold tretching, were etabiihed in 1988 and early Detail of the tenion coupon tet were preented in the Eleventh Progre Report 1 During the pat few month, the UMR tudy primarily involved the experimental determination of the dynamic mechanical propertie in compreion for the ame heet teel ued in the Eleventh Progre Report. The train rate ued for thee compreion coupon tet were imilar to thoe ued for the tenion tet. They ranged from to 1.0 in. / in. / ec. Detail of the compreion coupon tet are dicued herein. Thi phae of tudy began with a review of the available literature relating to the efffect of the train rate on the mechanical propertie of heet teel in compreion. The literature urvey i ummarized in Section. Section preent the detailed information obtained from 54 compreion tet. Thi ection alo dicue the train rate effect on the compreive mechanical propertie of the heet teel teted. n

15 2 addition to the compreion coupon tet, the tet data preented in the Eleventh Progre Report for tenion coupon tet have been reevaluated for the purpoe of predicting the tenile dynamic mechanical propertie under high train rate. The newly developed equation and the correponding graphical preentation are given in Section V. Finally, all the reearch finding are ummarized in Section V.

16 3. REVEW OF LTERATURE A. GENERAL An extenive review of literature on the effect of train rate on tenile mechanical propertie of teel wa preented in the Eleventh Progre Report 1. Thi chapter preent a urvey of available literature on the effect of train rate on the compreive mechanical propertie of teel and a1uminum. Becaue mechanical propertie uch a yield trength and tenile trength can vary with train rate, it i often neceary to determine thee propertie under the condition that cloely match the expected deformation rate in ervice 2. Strain rate (e )i the rate of change of train (E) with repect to time (t) E = de dt (2.1) where E can be either the engineering or the true train. For a contant train rate experiment, the train rate i imply the total train divided by the duration of the tet 2 : E = E t -1 The unit of train rate i the invere of time ec (2.2) When E in Eq 2.1 i the engineering train, then: where L o de/dt = (l/l )(dl/dt) = V/L o 0 (2.3) i the original length of the pecimen, and V i the velocity at which the pecimen i b~ing deformed. A contant crohead peed in a mechanical teting machine yield a contant engineering train rate defined by Eq 2.3.

17 4 B. DYNAMC TESTNG FOR VAROUS STRAN RATES Standard tet are uually performed at a train rate of around 10-3 in./in./ec. 2 Tet at higher train rate require pecial equipment and experimental technique. Thee tet fall into four regime roughly defined by the experimental technique that are ued to achieve the pecified train rate. Low Strain-Rate Regime. A typical mechanical tet i performed at -3 a train rate of around 10 in./in./ec., which yield a train of 0.5 in 500 econd. The equiment and technique generally can be extended to train rate a high a 0.1 in./in./ec. without difficulty. Medium Strain-Rate Regime. n thi regime, the experimental technique are imilar to thoe ued at low train-rate, but pecial equipment i required. Servo-hydraulic load frame equipped with high-capacity valve can be ued to generate train rate a high a 200 in./in./ec. Another experimental technique developed for compreion teting in thi train-rate regime i the cam platometer, decribed in Reference 2. When more qualitative medium train-rate tet reult are deired, the drop tet, which i alo decribed in Reference 2, may be appropriate. High Strain-Rate Regime. At train rate greater than 200 in./in./ec., the required crohead peed exceed that eaily achieved with crew-driven or ervo-hydraulic frame. To generate high train rate, experimental technique that make ue of projectile impact and wave propagation phenomena have been employed. Technique baed on the Hopkinon bar have been ued uccefully to perform dynamic compreion tet at train rate exceeding 10 4 in./in./ec. with a maximum train up to 0.3 in.jin. At thee high train rate, inertia force begin to

18 5 affect the validity of tet. Higher train rate and larger train are poible with the rod impact (Taylor) tet. n thi experiment, the complicated tre wave propagation phenomena trongly influence the meaurement and hould be accounted for numerically. Very high Strain-Rate Regime. Very high train rate are alo poible. They are generally found only in hock front produced by very high vilocity impact or in the detonation of exploive 2 The train rate regime are ummarized in Table 2.1. For more detail.concerning the experimental technique mentioned above ee Reference 2. C. EFFECT OF STRAN RATE ON COMPRESSVE MECHANCAL PROPERTES t ha become known that the mechanical propertie of the vat majority of engineering material are uceptible to the rate of application of the load either in tenion or compreion ince the beginning of thi century. For mot material, the proportional limit, yield trength, and tenile trength tend to increae at a higher train rate. The following ection dicu the effect of train rate on compreive mechanical propertie of teel and aluminum. a. Steel. n 1955, Alder and Phillip3 tudied the combined effect of tratn rate and temperature on compreive mechanical propertie of teel, copper, and aluminum. The tre-train curve were determined for thee three material at contant true train rate in the range from 1 to 40 in./in./ec. The maximum compreive train wa 50% for temperature ranging from to 1200 C. The tet were conducted uing the cam 8 platometer compreion machine which wa deigned by Orwan and Lo in Table 2.2 preent their experimental reult for teel at variou train, train rate, and temperature. t can be oberved from thi table

19 6 that the increae in train rate or decreae in temperature reulted in the increae of the tre at any given compreion train. The effect of train rate on the tre for a given train could be expreed by a reaonable expreion a follow: where.m cr = cr E o (2.4) cr E m = true tre = true train rate = train rate enitivity exponent cr o = the tre at unit train rate The value of cr and m obtained from Alder and Phillip ' work are given o in Table 2.3 and 2.4, repectively. t can be een that m tend to increae while cr decreae and/or the temperature increae. o 4 n 1957, Cook ued the cam platometer machine to determine the compreive yield trength for twelve different type of teel at 900, 1000, 1100, and 1200 deg. C combined with contant train rate of 1.5, 8, 40, and 100 in./in./ec. The experimental reult obtained from thi invetigation for low, medium and high carbon teel are given in Fig. 2.1 through 2.3, repectively. Thee curve illutrate the relationhip between yield trength and natural train for three teel teted at different temperature and train rate. t i oberved from the reult of Cook, and Alder and Phillip that the yield trength of teel increae a the train rate increae and/or the temperature decreaed. However, a noticeable feature of many of the curve of thi invetigation i the drop in yield trength at high train which i contributed, a Cook concluded, to the predominance of thermal oftening of the teel

20 7 over train hardening a the compreion proceed. Comparion of the three curve hown in Fig. 2.1 to 2.3 for the three carbon teel alo reveal that the tendency for the tre to drop increae with the teel carbon content. By uing the Split Hopkinon method, Davie and HunterS invetigated in 1963 the dynamic compreion mechanical behavior of ome metal ineluding teel. The compreive loading cycle wa of 30 micro-econd duration which generated train rate in the range of to in./in./ec. The reult obtained from thi invetigation indicated that the ratio of the dynamic to tatic yield trength of the mild ~eel ued i 2.6. b. Aluminum. Structural aluminum were found to be le train rate enitive than teel in both compreion and tenion. Alder and Phillip3 alo performed compreion tet on aluminum to tudy the combined effect of train rate and temperature uing the cam platometer compreion teting machine. The compreion tet on aluminum were conducted under the train rate range of 1 to 40 in./in./ec. combined with o 0 temperature ranging from -190 C to 550 C. Figure 2.4 how typical tre veru logarithmic train rate curve at variou temperature. t i oberved from thi figure that the tre at a given train increae a the train rate increae and/or the temperature decreae. Table 2.5 preent the experimental reult for aluminum. The value of a and m according to Equation 2.4 are given in Table 2.6 and 2.7, reo pectively. No drop in tre wa oberved at high train a in the cae of teel.

21 8 6 Commercially pure aluminum pecimen were teted by Hockett in 1959 at room temperature uing the cam pltometer compreion teting machine at three train rate of 0.23, 0.455, and 1.46 in./in./ec. From the meaurement of load and time throughout each tet, true tre veru true train curve were plotted. Thee curve fit an equation of the form: BE cr = A (1 - e ) + C E (2.5) where cr i the true tre, E i the true train, A, B, and Care parameter determined from the tet, and e i the bae of natural logarithm. The parameter A and C were found to be dependent upon temperature and train rate, increaing with decreaing temperature and with large increae in train rate. The parameter B wa found to be eentially independent of temperature, but a large increae of train rate produce an increae in B. Table 2.8 preent the value of the parameter A, B and C a a reult of the compreion tet conducted on commercially pure aluminum at contant true train rate along with the tatitical parameter which were obtained from fitting the experimental data to Equation 2.5. Tet in compreion and tenion for a large number of metal under 7 high train rate were performed by Lindholm and Yeakley in Figure 2.5 how tre-train curve for aluminum in both tenion and compreion at variou train rate. The lower train rate tet were performed on a tandard ntron teting machine and the ret of the tet were performed uing the Split Hopkinon Preure Bar. For the comparion between the tenion and compreion data, all value of tre, train, and train rate are true value. t ha been oberved from the reult of many tet that for very low train rate, the tre level in tenion

22 9 and compreion agree well, although the increae in flow tre with increaing train rate differ in detail. Figure 2.6 how a number of compreion tre-train data for 6061-T6 aluminum alloy, for which the wide variation in train rate appear to have negligible effect on the tre level. Thi i found to be true for other high-trength aluminum alloy according to Lindholm and Yeakley. A a reult, the equivalence of the data obtained from the Split Hopkinon Preure Bar with that obtained at low train rate from an ntron machine indicate that wave propagation and inertia force are not contributing any ignificant error to the meaurement in the dynamic tet.

23 10. EXPERMENTAL PROGRAM A. MATERALS Three Type of heet teel (3SXF, SOXF, and 100XF) were elected to tudy the effect of train rate on the compreive mechanical propertie. Thee teel were ued previouly in the Eleventh Progre Report to tudy the effect of train rate on the tenile mechanical propertie. The chemical compoition for thee three material are lited in Table 3.1. B. COMPRESSON TESTS All thee three heet teel lited in Table 3.1 were uniaxially teted in compreion in the longitudinal (parallel to the direction of rolling) and tranvere (perpendicular to the direction of rolling) direction under three different train rate of ,10,and 1. 0 in./in./ec. Three identical tet were conducted for each cae. 1. ASTM Specification. The compreion tet followed the procedure outlined in the ASTM Specification lited below: E9-70 Standard Method of Compreion Teting of Metallic Material at Room Temperature E83-67 Standard Method of Verification and Claification of Extenometer Elll-82 Standard Tet Method for Young' Modulu, Tangent Modulu and Chord Modulu 2. Specimen. The compreion pecimen teted in the longitudinal and tranvere direction were prepared by the Machine Shop of the Department of Civil Engineering at the Univerity of Miouri-Rolla. The

24 11 tet pecimen were cut from the quarter point of the teel heet. The ketch in Figure 3.1 how the compreion pecimen dimenion for the three material (35XF, 50XF, and 100XF). The pecimen dimenion were elected to fit a Montgomery-Templin compreion tet fixture. The notche along one edge were for the intallation of the knife edge of the compreometer. Special care wa taken to enure that the end of the pecimen were parallel and thu the ame length wa ued for both longitudinal ide of the pecimen. A total of 54 coupon were teted in thi phae of tudy. They are ummarized in the following Table: Direction of Type of Number of Coupon Teting Material Ued Longitudinal Compreion ( LC ) 100XF-LC 50XF-LC 35XF-LC Tranvere Compreion ( TC ) 100XF-TC 50XF-TC 35XF-TC Equipment. All compreion tet were performed in the ame 110 kip 880 Material Tet Sytem (Figure 3.2) a previouly ued for the tenion tet. New MTS Compreion Platen were intalled for conducting the compreion tet. An aembly of the equipment ued for the com-

25 12 preion tet i hown in Figure 3.3. The load wa applied to the compreion pecimen by mean of a pecially made ubpre (Figure 3.4(A)). The ubpre bae and ram are contructed of a hardened teel in order to minimize their deformation when applying the load. The compreion pecimen wa held in a Montgomery-Templin compreion tet fixture (Figure 3.4(B)) which contain a erie of roller that may be tightened againt the pecimen to prevent buckling. An MTS compreometer (Figure 3.4(C)) with a 1-in. gage length wa ued to meaure train from zero to 2 percent in.jin. A pecial fixture wa deigned to fit the MTS compreometer in the compreion jig. The claification of thi compreometer according to ASTM Deignation E83 wa found to be dependent on the compreometer range ued in the tet. Table 3.2 contain the claification of four compreometer range according to the MTS tranducer calibration data. The aembly of pecimen, tet fixture and ubpre are hown in Figure 3.5a and 3.5b. Other equipment ued for the tet include the MTS controller (Figure 3.6), the data acquiition ytem (Figure 3.7), Data General graphic diplay terminal (Figure 3.8), Data General MV mini computer to tore and manipulate the data (Figure 3.9), and BM PSj2 Model 30 peronal computer with BM color plotter (Figure 3.10). The load wa meaured by an MTS Sytem Model load cell and aociated conditioning, which wa calibrated prior to teting according to the procedure of the National Bureau of Standard. The function of thi equipment i identical to that for tenion tet. For detail concerning the function of the MTS machine and the data acquiition ytem, See Section.B of the Eleventh Progre Report.

26 13 4. Procedure. Prior to teting, the dimenion of the compreive pecimen were meaured to the nearet in. The pecimen wa then placed in the Montgomery-Templin compreion tet fixture and the lateral roller upport of the fixture were thightened firmly againt the both ide of the pecimen. Special care wa taken to enure that the pecimen wa aligned vertically in the tet fixture. Next, the MTS compreometer wa attached to one ide of the tet fixture uch that the knife edge of the compreometer moothly inerted into the notche of the compreion pecimen. Then, with the pecimen, tet fixture, and compreometer attached together a a unit, the entire unit wa placed in the compreion ubpre. A mall tub i provided on each ide of the bottom urface of the tet fixture. Thee tub fit into indention on the bae of the ubpre in order to enure proper alignment of the ubpre ram with the pecimen' longitudinal axi. Next tep wa to place the ubpre, with the tet fixture, compreometer, and pecimen attached, between the compreion platen of the MTS loading frame uch that the longitudinal axi of the ubpre lined up with the center of the platen. The function generator wa then programmed to produce the deired ramp. Figure 3.11 how a typical function generator ramp waveform. Table 3.3 how the function generator ramp time and the correponding train-rate value. For all the tet, the train mode wa elected to maintain a contant train rate and Range 4 wa choen for the three MTS mode (i.e., Load, Strain, and Stroke). During the tet, the tretrain curve were plotted imultaneouly on the Data General graphic terminal. The tre-train data were recorded and tored by a computer for plotting and determination of the mechanical propertie at a later

27 14 time. Buckling of the unupported length at each end of the pecimen limited the obtainable range of the tre-train curve to approximately 1.8 percent. C. RESULTS 1. Ste-Strain Curve. The tre-train curve were plotted by uing the Data General graphic oftware nemed Trendview with the tre-train data recalled from the computer torage. Figure 3.12 through 3.17 preent the compreive tre-train curve for the following 6 different cae, which were tudied under three different train rate (0.0001, 0.01, and 1.0 in./in./ec.). Direction of Type of Figure Teting Material Number Longitudinal Compreion 100XF-LC 3.12 ( LC ) 50XF-LC XF-LC 3.16 Tranvere Compreion 100XF-TC 3.13 ( TC ) 50XF-TC XF-TC 3.17 For the purpoe of comparion, each figure include three tre-train curve repreenting the tet data obtained from the ame material for three different train rate. 2. Mechanical Propertie. The procedure ued for determining the mechanical propertie of heet teel are dicued in the ubequent ection (Section.C.2.a and.c.2.b). The mechanical propertie o determined are the proportional limit F,and the yield point F. pr y Thee teted mechanical propertie are preented in Table 3.4 through 3.9 for each individual tet. Table 3.10 through 3.15 preent the av-

28 15 erage value of the mechanical propertie for each material teted in either longitudinal compreion (LC) or tranvere compreion (TC) under different train rate (0.0001, 0.01, or 1.0 in./in./ec.). a. Proportional Limit. F The proportional limit i uually depr fined a the point above which the tre-train curve become nonlinear. Since it i often difficult to pinpoint the exact location of the true proportional limit, tandard method are normally ued o that comparable value of proportional limit may be determined by different reearcher. One uch method that i commonly ued for aircraft tructure and alo for cold-formed tainle teel member i the 0.01 percent offet method. For thi method a traight line with a lope equal to the modulu of elaticity i drawn parallel to the tre-train curve and offet uch that it interect the train axi at 0.01 percent train. The interection of thi line with the tre-train curve i defined a the proportional limit. n thi tudy, the 0.01 percent offet method wa choen to obtain the value of the proportional limit for the teel teted in compreion under the train rate of and 0.01 in./in./ec. a demontrated graphically in Figure 3.18 for the 35XF-TC-4 curve and lited in table 3.4 through 3.9. Becaue of the waving effect of the impact load on the tre-train curve of the tet conducted at the high train rate of 1.0 in./in./ec., reliable value for the proportional limit were difficult to obtain. b. Yield Strength or Yield Point. F. The method commonly ued to y determine the yield point of heet teel depend on whether the tretrain curve i of the gradual or harp-yielding type. For the type of

29 16 heet teel teted in thi tudy in compreion, the tre-train curve of the 50XF heet teel are the harp-yielding type, while the tretrain curve of the 35XF and 100XF teel are the gradual-yielding type. The yield point of the harp-yielding teel wa determined a the tre where the tre-train curve become horizontal. Typical harpyielding tre-train curve are hown in Figure 3.14 for the SOXF teel in the longitudinal direction. For thi cae, the lower yield point i given in Table 3.6 and 3.7 for longitudinal and tranvere direction, repectively. For the gradual-yielding type tre-train curve a hown in Figure 3.18 for 35XF-TC-4 curve, the yield point of 35XF teel wa determined by the interection of the tre-train curve and the traight line drawn parallel to the elatic portion of the tre-train curve at an offet of in. lin. A Fortran 77 code wa written to determine the yield point preented in Table 3.4, 3.5, 3.8 and 3.9 for the gradual-yielding type curve uing the Leat Square Method. D. DSCUSSON The tet reult preented in Section.C are dicued in thi ection with an emphai on the effect of train rate on the mechanical propertie of the heet teel teted in both longitudinal compreion and tranvere compreion. 1. Mechanical Propertie. The tet reult indicate that all mechanical propertie are affected by the train rate. Table 3.16 compare the dynamic yield tre determined at the train rate of 1.0 1n. " 11"n. ec. and the tatic yield tre determined at the train rate

30 17 of in./in./ec. The effect of train rate on proportional limit and yield trength are dicued in the following ection. a. Yield Strength or Yield Point, F. n Table 3.16, the dynamic y yield trength, (F )d' and the tatic yield trength, (F ), are compared y y by uing a ratio of (Fy)d/(Fy). n the above expreion, (Fy)d i the yield trength determined for the train rate of 1.0 in./in./ec. while (Fy) i the yield trength determined for the train rate of in./in./ec. t can be een that for all cae, the yield trength of heet teel increae with the train rate. The percentage increae in yield trength for the three teel tudied in thi invetigation are: 7% for 100XF teel, 9% to 10% for SOXF teel, and 24% to 33% for 3SXF teel when the train rate increaed from to 1.0 in./in./ec. t i oberved from thi table that the increae in yield trength for the virgin material are independent of the tet direction (LC or TC) for 100XF and SOXF heet teel. However, for 3SXF teel the increae in yield tre in the tranvere direction i larger than that in the longitudinal direction. b. Proportional Limit F. Similar to the effect of train rate on pr yield trength, the proportional limit of heet teel increaed with the train rate. The percentage increae in proportional limit for the three material tudied in thi invetigation are: 9% to 24% for 100XF teel, 4% to 22% for SOXF teel, and 14% to 24% for 35XF teel when the train rate increaed from to 0.01 in./in./ec. t i noted from thee value that the amount of percentage increae in proportional limit are larger than the amount of percentage increae in yield tre when the train rate increaed from in./in./ec. to 1.0 in./in./ec.

31 18 2. Strain Rate Senitivity. n the literature review, Equation 2.4 give the relation between the tre and the train rate at a given train a follow: 0" = 0" o.m E (3.1) By applying Equation 3.1 to two different train rate and eliminating 0" we have o m = n( 0"2 / 0"1 ) / n( E' 2 / E 1 ) (3.2) for two given value of the flow tre of a material at two different train rate, the train rate enitivty exponent m may be calculated by uing Equation 3.2. Table 3.17 lit the value of the train-rate enitivitie, which were calculated on the bai of Equation 3.2. The value of m wa cal 1 culated for the yield trength correponding to the train rate of in./in./ec. and 0.01 in./in./ec., while the value of m wa 2 calculated for the yield trength correponding to the train rate of 0.01 in./in./ec. and 1.0 in./in./ec. From Table 3.17, it can be een that, in general, the value of m in compreion increae a the train rate increae. The train rate enitivity decreae progreively a the tatic yield trength level increae. 3. Prediction of Yield Strength in Compreion for High Strain Rate. Figure 3.19 through 3.24 copmare the average value of the compreive yield trength at different train rate for different cae. The data plotted in thee figure are in term of yield tre v. logarithmic train rate. For each cae, the following econd degree polynomial wa developed uing the Leat Square Method in the train-rate range of to 1.0 in./in./ec.

32 19 Y = A + B X + C X 2 (3.3) where Y = yield tre X = log(e ) A, B, and C = contant The polynomial parameter A, B, and C are given at the top of the curve for each cae in Figure 3.19 through The value of the compreive yield trength of the teel ued in thi invetigation at higher train rate (larger than 1.0 and up to 1000 in./in./ec.) could be extrapolated by uing the equation or the curve for each individual cae. Thi report included compreion tet for teel in the virgin condition only. The dicuion on the combined effect of cold-tretching and train rate on teel mechanical propertie are dicued in detail in the Eleventh Progre Report.

33 20 V. ADDTONAL EVALUATON FOR THE TENSLE TEST DATA PRESENTED N THE ELEVENTH PROGRESS REPORT n the Eleventh Progre Report, the tenile mechanical propertie (i.e., yield trength, ultimate trength, and elongation) of the three teel (3XF, OXF, and 100XF) teted under the train-rate rage of to 1.0 in./in./ec. were etablihed. Thee three heet teel were teted under the virgin condition and different amount of cold tretching. Half of coupon were teted to tudy the combined effect of train rate, cold tretching, and aging on the teel heet mechanical propertie. Figure 3.28 through 3.58 of the Eleventh Progre Report compare the average value of the yield and ultimate tenile trength at different train rate for different cae. The tet data were plotted in thee Figure uing emi-log cale and were connected by traight line. The horizontal cale were limited to the train rate range from to 1.0 in./in./ec. which wa ued for all tenile tet. For the purpoe of predicting the value of the yield and ultimate trength of the teel for higher train rate above 1.0 in./in./ec., a econd degree polynomial equation imilar to Equation 3.3 wa developed by uing the Leat Square Method. n thee equation, the ultimate and yield trength are a function of logarithmic train rate for teel in the virgin condition a well a for teel ubjected to different amount of cold tretching including aged and non-aged condition. Graphical preentation and the correponding equation are hown in Figure 4.1 through The horizontal axi in thee Figure repreent the logarithmic train rate range from to 1000 in./in./ec. The value

34 21 of the yield and ultimate trength at a train rate higher than 1.0 and up to 1000 in./in./ec. can be predicted by extrapolation from the curve or calculated from the equation by uing the deired train-rate value.

35 22 V. CONCLUSONS Thi tudy dealt with the effect of train rate on mechanical propertie of heet teel. During the period from May 1988 through December 1988, progre wa made on a tudy of the effect of train rate on tenile mechanical propertie of heet teel. The reult of thi invetigation were preented in the Eleventh Progre Report. Since the beginning of 1989 through July of the ame year, the work continued to include the tudy of mechanical propertie of heet teel in compreion. Thi work included a review of literature and teting of 54 compreion pecimen. The literature urvey i preented in Section. Section contain the detailed information on the experimental invetigation, which include material, tet pecimen, equipment, tet procedure, tet reult, and the dicuion of the tet data. Additional evaluation of the tet data included in the Eleventh Progre Report i preented in Section V of thi report for the purpoe of predicting the mechanical propertie of heet teel at train rate higher than that ued in the tenion tet. The following concluion may be drawn from the tudy of the effect of train rate on tenile and compreive mechanical propertie of teel: 1. Proportional limit, yield trength, and ultimate trength increae with increaing train rate. 2. Yield trength i more enitive to train rate than ultimate trength.

36 23 3. The train rate enitivity value i not a contant. n mot cae it increae with increaing train rate. 4. The mechanical propertie of heet teel having low yield trength are more enitive for train rate effect. 5. A econd degree polynomial i well fitted to the experimental data for each cae in both tenion and compreion and can provide a better prediction for yield and ultimate trength at high train rate above the train rate-range ued in the tet. The reult of thi tudy will be ued in the future reearch work which will include the tudy of the tructural trength of cold-formed teel tub column and beam ubjected to dynamit; load.

37 24 ACKNOWLEDGMENTS The reearch work reported herein wa conducted in the Department of Civil Engineering at the Univerity of Miouri-Rolla under the ponorhip of the American ron and Steel ntitute. The financial aitance granted by the ntitute and the technical guidance provided by member of the Tak Force on Automotive Structural Deign, the AS Automotive Application Committee Deign Pannel, and the AS taff are gratefully acknowledged. Thee member are: Mer. S. J. Errera (Chairman), J. Borchelt, R. Cary, F. L. Cheng, A. M. Davie, J. D. Grozier, C. Haddad, J. D. Harrington, A. L. Johnon, C. M. Kim, J. P. Leach, K. H. Lin, J. N. Macadam, H. Mahmood, D. Malen, J. McDermott~ P. R. Mould, J. G. Schroth, P. G. Schurter, T. N. Seel, F. V. Slocum, R. Stevenon, and M. T. Vecchio. An expreion of thank i alo due to Mr. D. L. Douty for hi help. All material ued in the experimental tudy were donated by nland Steel Company and LTV Steel Company. Appreciation i expreed to Mer. K. Haa, J. Bradhaw, F. Senter, and J. Tucker, taff of the Department of Civil Engineering, for their technical upport and to Mr. C. L. Pan for hi valuable aitance in the preparation and performance of the tet. The advice provided by Dr. J. E. Minor, Chairman of the UMR Department of Civil Engineering, i greatly appreciated.

38 25 REFERENCES 1. Kaar, M. and Yu, W.W., "Deign of Automotive Structural Component Uing High Strength Sheet Steel: The Effect of Strain Rate on Mechanical Propertie of Sheet Steel", Eleventh Progre Report, Civil Engineering Study 89-2, Univerity of Miouri- Rolla, January Follanbee, P.S., "High Strain Rate Compreion Teting", Metal Handbook, American Society for Metal, Ninth Edition, Volume 8, 1985, pp Alder, J.F., and Phillip, V.A., "The Effect of Strain Rate and Temperature on the Reitance of Aluminum, Copper, and Steel to Compreion," Journal of the ntitute of Metal, Vol 83, , pp Cook, P.M., "True Stre-Strain Curve for Steel in Compreion at High Temperature and Strain Rate, for Application to the Calculation of Load and Torque in Hot Rolling," Conference on The Propertie of Material at High Rate of Strain, ntitute of Mechanical Engineer, 1957, pp Davie, E.D.H., and Hunter, S.C., "The Dynamic Compreion Teting of Solid by the Method of the Split Hopkinon Preure Bar," J. Mech. Phy. Solid, Vol 11, 1963, pp Hockett, J.E., "Compreion Teting at Contant True Strain Rate," Proc. ASTM, Vol 59, 1959, pp Lindholm, U.S., and Yeakley, L.M., "High Strain-Rate Teting: Tenion and Compreion," Experimental Mechanic, Vol 8, 1968, pp Orwan, E., Britih ron and Steel Reearch Aociation Report No. MW/F/22/ Sorouhian, P., and Choi, K.B., "Steel Mechanical Propertie at Different Strain Rate," Journal of Structural Engineering, Proceeding of the American Society of Civil Engineer, Vol. 113, No.4, 1987, pp Norri, C.H., Hanen, R.J., Holley, M.J. Jr., Bigg, J.M., Namyet, S., and Minami, J. K., :S..;:t..:r..;:uo.=co..:to..:u::.,:r""a=..l=--_D=e.:::;..:i""'g""n::--...:f;.;o;.;r=---=D... y-"'n:.;::a""m::..;:i;.;c=--...l=o.:::;a..=d= McGraw-Hill Book Company, 1959.

39 26 Table 2.1 Experimental Technique for Variou Strain Rate Regime for Compreion Teting 2 Strain Rate Regime Experimental Technique Wave Propagation Low train rate e ~0.1-1 Standard mechanical teting procedure Not ignificant Medium train rate : ~ e ~ Servo-hydraulic frame, cam plaometer, drop tet High train rate : 200 -l ~ e ~ Hopkinon preure bar Very hi~h train rate E' ~ Rod mpact (Taylor) tet Flyer plate impact nfluence load meaurement Affect uniform tre approximation Analyi required for interpretation of reult Critical

40 27 Table 2.2 Effect of Strain Rate and Temperature on the Stre Required to Compre Stee1 3 Speci- StraiD Average Stree (los lb./in. ) to OompreM: men Temp Dia., eo. Rate, llec_-l mm. 10% 20% 30% 40% 60% low ' WOO j g ' , ' '9 11' '

41 Table 2.3 Value of 00 for Steel uing the Equation = 00 * e m Value of a. tor a Compreion of: Temp., C. 10~~ 20~~ 300" 41)% 50% 1, : ; i ij Table 2.4 Value of m for Steel uing the Equation3 cr = cr * e m o Temp.~ 00. Value of ""'for a Compreion of: 10% 20% 30% 40% 50% :

42 Table 2.5 Effect of Strain Rate and Temperature on the Stre 29 Required to Compre Aluminum3 - Specimen ~..teh Dia., mm. Temp., C. Strain AVl)r&ge Stre (10 1 b./in. l ) to Compre : Hate, eec.-1 10% 20% 30% ~O% 60% ~ b ' b b ' ' a a low ' a 18 1' a ll, g ' a b '9 a 18 7' '9 a 18 12' S 23 0 b 12 12' a a 18 39' a ' ' ' a '5 2' ' '9 9' ' ' a '15t ' g O S.-g o 9-4 9'7 39' '8 9' a 18.ao "~-6. " " li O ls ", ' ~' '

43 Table Value of 0 0 for Aluminum uing the Equation 3 o = 0 o * e m Metal Temp., 00. Value of <1. for a Compreion of: 10~~ 2~'~ 30% 41)% 50%. Al ' : : 5 4 4: ') Table 2.7 Value of m for Aluminum uing the Equation 3 o = 0 o * e' m Hetal Temp., 00. Value of mfor a Compreion of: 10% 20% 30% 40% 50% A

44 31 Table 2.8 Reult of Compreion Tet on Commercially Pure Aluminum at Contant True Strain Rate6 Baed on Equation: a = A * (1 - e BE ) + C * E Stand- Stand- Variance o( Standard Firt Second ard Stand- Num- ~- Stu.in Rale, Third yo 2 Devialion Paramard Deper Puun- vialion Pafam- 5eC 1l. / 01 Fil, Sf cter. A vialion cter, B of B, cler. C viatiod Poinu. of A,.. 01 C,le S ard Oc- ber 0' X 10-1,, ' X ,

45 32 Table 3.1 Chemical Compoition of the Sheet Steel Ued AS Thick C Mn P S Si V CU Al Cb Zr Deigna. in. 035XF XF XF Table 3.2 Claification of the MTS Compreometer Range Maximum Strain Maximum Error ASTM Claification in /in. in./in. 100% Cla B-1 50 % Between Clae A and B-1 20 % Between Clae A and B-1 10 % Cla A

46 33 Table 3.3 Function Generator Ramp Time and the Correponding Strain Rate Ramp Time ec. Strain Rate in./in./ec Table 3.4 Teted Mechanical Propertie of 100XF Sheet Steel Longitudinal Compreion Tet Strain Rate F pr F Fpr/Fy No. in. lin. ec. (ki) (ks1) LC LC LC LC LC-S LC ***** **** LC ***** **** LC ***** **** LC ***** ****

47 34 Table 3.5 Teted Mechanical Propertie of 100XF Sheet Steel Tranvere Compreion Tet Strain Rate F pr F Fpr/F y No. in./in./ec. (ki) (ks1) TC TC-2 -Q.OOO TC TC TC TC TC ****** **** TC ****** **** TC ****** ****

48 35 Table 3.6 Teted Mechanical Propertie of 50XF Sheet Steel Longitudinal Compreion Tet Strain Rate F pr F y Fpr/F y No. in. / in. / ec. (ki) (ks1) LC LC LC LC LC LC LC ***** **** LC ***** **** LC ***** ****

49 36 Table 3.7 Teted Mechanical Propertie of 50XF Sheet Steel Tranvere Compreion Tet Strain Rate F pr F y Fpr/F y No. in./in./ec. (ki) (kl.) TC TC TC TC TC TC TC ***** **** TC ***** **** TC ***** ****

50 37 Table 3.8 Teted Mechanical Propertie of 35XF Sheet Steel Longitudinal Compreion Tet Strain Rate F pr F y Fpr/F y No. in. lin. ec. (ki) (ks1) LC LC LC LC LC LC LC ***** **** LC ***** **** LC ***** ****

51 38 Table 3.9 Teted Mechanical Propertie of 35XF Sheet Steel Tranvere Compreion Tet Strain Rate F pr F y Fpr/F y No. in./in./ec. (ki) (ks1) TC-l TC TC TC TC TC TC ***** **** TC ***** **** TC ***** ****

52 39 Table 3.10 Average Teted Mechanical Propertie of 100XF Sheet Steel Longitudinal Compreion Strain Rate F pr F y in./in /ec. (ki) (ks1) ***** **** Table 3.11 Average Teted Mechanical Propertie of 100XF Sheet Steel Tranvere Compreion Strain Rate F pr F y in. in. ec. (ki) (ks1) Fpr/F y ****** ****

53 40 Table 3.12 Average Teted Mechanical Propertie of 50XF Sheet Steel Longitudinal Compreion Strain Rate F pr F y in. / in. / ec. (ki) (k~) ***** **** Table 3.13 Average Teted Mechanical Propertie of 50XF Sheet Steel Tranvere Compreion Strain Rate F pr F y in. / in. / ec. (ki) (k~) ***** ****

54 41 Table 3.14 Average Teted Mechanical Propertie of 35XF Sheet Steel Longitudinal Compreion Strain Rate F pr F y in. in. ec. (ki) (kj.) ***** **** Table 3.15 Average Teted Mechanical Propertie of 35XF Sheet Steel Tranvere Compreion Strain Rate F pr F y in. lin. ec. (ki) (kj.) Fpr/Fy ***** ****

55 42 Table 3.16 Ratio of Dynamic to Static Compreive Yield Stree for-three Sheet Steel Baed on Table 3.10 to 3.15 Type of Sheet Steel 100XF-LC 100XF-TC 50XF-LC 50XF-TC 35XF-LC 35XF-TC Note dynamic yield tre for the train rate of 1.0 in./in./ec. tatic yield tre for the train rate of in./in./ec.

56 43 Table 3.17 Value of Strain Rate Senitivitie m for Three Sheet Steel Baed on the Change of the Yield Stree at Different Strain Rate Type of Sheet Steel m 1 m 2 100XF-LC XF-TC XF-LC XF-TC XF-LC XF-TC Note: m = 1 m = 2 train rate enitivity baed on the change of yield tre between train rate of in./in./ec. and 0.01 in./in./ec. train rate enitivity baed on the change of yield tre between train rate of 0.01 in./in./ec. and 1.0 in./in./ec.

57 44 ~ ,----,---,--...,---..-_ ~~=~ l..---""'- i / 14r ~---~ ~ /v ~.-!--+--~ ~ %'"" - L------, i" ~ _~~~L-"" ---t----t-+-_~~ ;;: 1----,..,., >= " 1/. 4' i!it 2 c Z 0, C >=,,, i!io c a ~, >= 4 i t. c ȧ, l Ī -... ~ W...»- :z0 Q.._L-.J : :: f ~' / --~- b d --l,--...,--r, l : 100: los. i, 100 ' 0-, Fig. 2.1 Relationhip Between Flow Stre and Natural Strain for Low-Carbon Steel4 a) 900 deg. C., b) 1000 deg. C., c) 1100 deg. C., and d) 1200 deg. C !. 'S- 0-7

58 45 18 l 100 ~16 6 '"... '"... ",14 Z 0 l Ī ~'2... c -... '" 910 >= 8,. i 14 ' 100 ~ 6 40 '"... "" 12 '"Z >- :1...!;; "" J ):,. 12' ~ z 0 7 ;...,;... '" t;; "", 0...!!:! >- "" ~._':-~---!---~--~--~:-----:----:.~,, 100 " ~ ~ "". :t: ~ ~, :0- ",' e4 S0, ~--- ".. ~ 100, ~----./ ' S./ io"""""" t Fig. 2.2 Relationhip Between Flow Stre and Natural Strain for Medium-Carbon Steel 4 a) 900 deg. C., b) 1000 deg. C., c) 1100 deg. C., and d) 1200 deg. C. 41

59 46 ~V ~ , V ~ ~14 7 >.. /..f.-- ::112 ~ e ọ... ~O..~ ~ V t a, f'1 loll' 14}-'--+--T----=b;:;;;o-if---j---r-...:;~ ~ ~ 00:12 L-...J::: ,,_~~=t===1====P-~~ ~ ~ 7 10 r--jt!.~---t-_=:t::::::::;:*::::::::t::::=-_r-l >.. a- e t--:;;;f~::f==_1r---t=:::::::lr ): '!-,-L f-, {..... i., ~,/ / / - 40 ~ ~ r--! 7 v---- -"-. /' C, loll' "... ~ ~ ~.,...,- 1'5 ",.. tl Fig. 2.3 Relationhip Between Flow Stre and Natural Strain for High-Carbon Steel 4 a) 900 deg. C., b) 1000 deg. C., c) 1100 deg. C., and d) 1200 deg. C '5

60 ȯ 10 STRAN RATE. SEC:"' Fig. 2.4 Effect of train rate on the Stre Required to Compre Aluminum to 40% Reduction at Variou Temperature3

61 48 20 ~ 16 '" ~ 12 L.. -Vl Aluminum Tenion '\ <. 4.0 x lo'~ ec"/ ) ~. 1.8 x lo o (ec- ' ) Compreion Strain ('ro) Z40 Fig. 2.5 Stre-Strain Curve for Aluminum in Tenion and Compreion]

62 49 80 i o 0 ; fo V AV V' O. 10 a 0 A O ~ 0 a! _.- 0 :>& \A 0! - :! : '-., 0 0- t- 2 X 10 ' ec-' a- E- 2 x 10 z ec-' i i 0 0- t - 2 X 10 ' ec-' 0- E- 780 ec-'! CJ A- E- 960 ec-' i re Strain t!!,." 0.12 ~. Fig. 2.6 Stre-Strain Curve for 6061-T6 Aluminum in Compreion at Several Strain Rate 7

63 " < -,.. ~ " 2.7" 1. 0" <- 0.8S" L.. L.. ~'Cl<NESS Fig. 3.1 Nominal Dimenion of Compreion Coupon Ued for All Sheet Steel