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ASA TECHNICALMEMORANDUM

NASA TM -73815

LTN

CO

CYCLIC STRESS-STRAIN CURVE DETERMINATION FOR

D6AC STEEL BY THREE METHODS

by Alfred J. NachtigallLewis Research CenterCleveland, Ohio 44135

NOV 1977

M

LM194266E

https://ntrs.nasa.gov/search.jsp?R=19780005240 2018-08-28T13:02:51+00:00Z

1 Report No 2 Government Accession No

NASA TM-738154 Title and Subtitle

CYCLIC STRESS-STRAIN CURVE DETERMINATION FORD6AC STEEL BY THREE METHODS

7 Authorlsl

Alfred J. Nachtigall

9 Performing Organization Name and Address

National Aeronautics and Space AdministrationLewis Research CenterCleveland, Ohio 44135

12 Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, D.C. 20546

15 Supplementary Notes

3 Recipient's Catalog No

5 Report D a t e . iAif 'tQTfNOV \3( '

6 Performing Organization Code

8 Performing Organization Report No

E-940210 Work Unit No

11 Contract or Grant No

13 Type of Report and Period Covered

Technical Memorandum14 Sponsoring Agency Code

16 Abstract

The room temperature cyclic stress- strain curve was determined for D6AC low alloy steelby three different methods. The method that involves the use of a single specimen monotomctension test after cyclic straining provided the best agreement with the accepted basic methodwhich requires a number of companion specimen tests. The single specimen test is also thesimplest to conduct.

17 Key Words (Suggested by Author(s)) 18 Distribution

Stress-strain curve; Strain cycling; UnclassIncremental step test; Monotonic tension test; STAR CCompanion specimen test; D6AC steel; Cyclicstress- strain curve

19 Security Qassif (of this report) 20 Security Classif (of this page)

Unclassified Unclassified

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ified - unlimitedategory 26

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* For sale by the National Technical Information Service Springfield Virginia 22161

CYCLIC STRESS-STRAIN CURVE DETERMINATION

FOR D6AC STEEL BY THREE METHODS

by Alfred J. Nachtigall

Lewis Research Center

SUMMARY

The room temperature cyclic stress-strain curve was determinedfor D6AC low alloy steel by three different methods. The first method,the accepted basic method of strain cycling several companion specimens,each at a different completely reversed strain range, is used as the basisof comparison for the other two. The other two methods are the singlespecimen incremental step test ard the morotonic tension test made after

g cyclic straining. The cyclic stress-strain curves generated by the threeoj methods are compared and mathematical expressions describing theseiW curves are determined. Inasmuch as the curve obtained from the monotonic

tension test after cyclic straining lies nearest to the data obtained with thecompanion specimen tests (accepted basic method) and requires the leastamount of programming equipment, the monotonic tension test after cyclicstraining is considered to be the simplest for this material.

INTRODUCTION

Designers and engineers have become increasingly aware of thevalue of the cyclic stress-strain curve in analyzing low-cycle fatigueproblems. The cyclic and monotonic stress-strain curves may differconsiderably because of the hardening or softening of the material causedby cyclic plastic straining. Testing procedures for generating the roomtemperature cyclic-stress-strain curve for a material are discussed inreference 1. Three of these, the companion specimen tests (the acceptedbasic method), the single specimen incremental step test, and the monotonictension test following strain cycling, (procedures discussed in ref: 1)were used in the low cycle fatigue program at the NASA-Lewis Research

Center to determine the cyclic stress-strain curve for the cyclic strainsoftening low alloy steel, D6AC (AMS 6431). The cyclic-stress-straincurves generated by the three testing procedures are compared andmathematical expressions describing these curves were determined.

This work was conducted using the customary U.S. system of units.Conversion to the International System of Units (SI) was made for reportingpurposes only.

MATERIALS, APPARATUS AND TEST PROCEDURES

Specimens

Heat treated stock of the low alloy steel, D6AC, was provided for theprogram by the Grumman Aerospace Corporation. The chemical compo-sition, heat treatment schedule, and mechanical properties are given intables I, n, and HI, respectively. The machined specimens had a0.635 cm (0.250 in.) minimum diameter hourglass test section withbutton head ends for attachment to the testing machine loading columns.Specimen details are shown in figure 1.

Apparatus and Test Procedure

The specimens were tested in a strain controlled closed-loop electro-hydraulically actuated fatigue testing machine. The details of this machineand its associated equipment are described in reference 2. The feedbacksignal in the closed loop came from the diametral extensometer thatsensed test section diametral displacement produced by cyclic axialloading. The cyclic loads were those required to produce the test sectiondiametral displacement programmed by a function generator. For thesetests the programmed signal was a triangular wave form. The cyclingfrequency for low strain range tests was as high as 1.0 Hz whereas forthe largest strain range test the frequency was as low as 0. 0833 Hz.

All tests were conducted in ambient air at room temperature.Companion specimen tests. - The accepted basic method for obtaining

the cyclic stress-strain curve for a material is by connecting the tips ofthe stable hysteresis loops from several companion specimens, each

at a different controlled strain range. Load and diametral displacement ofthe minimum test section diameter were recorded with strip charts movingat a specified rate as well as with an X-Y plotter. Stabilized values of thetensile and compressive stress and strain amplitude at the tips of the hys-teresis loop in the vicinity of the half life number of cycles were observedfor each test, A plot of the stress amplitude versus the corresponding com-pletely reversed strain amplitude for each specimen forms a representationof the cyclic stress-strain curve which is used as the basis of comparisonwith the other two methods.

Single specimen incremental step test. - This method was consideredbecause it requires that only one specimen need be tested. In accordancewith this testing procedure a single specimen was subjected to blocks ofgradually increasing and decreasing strain amplitudes as illustrated infigure 2, The programmed signal was obtained by slowly modulating theamplitude of the high frequency triangular waveform signal from a func-tion generator by passing the signal through a Research IncorporatedDatatrak before it was introduced into the servo controller. Blocks oflinearly increasing the decreasing amplitude of 6-minute duration wereobtained with the Datatrak programmer. Load and diametral displacementwere recorded on strip charts as well as with an X-Y plotter to producea series of superimposed hysteresis loops of increasing and decreasingsize. The locus of the loop tips trace out a cyclic strain curve such asshown in figure 3,

Monotonic tension test after strain cycling. - This method furthersimplified the procedure for determining the cyclic stress-strain curveby eliminating the need for the Datatrak to modulate the programmingsignal from a function generator. A single specimen was stabilized bystrain cycling,, A total of 335 cycles at an inelastic strain range of 0.0048was sufficient to achieve a stable hysteresis loop. The strain range wasgradually reduced to zero before the specimen was monotonically loadedin tension to failure. A plot of applied load vs. diametral displacementof the specimen test section was obtained during the monotonic tensiletest with the X-Y plotter, from which a stress-strain curve was constructed.

RESULTS AND DISCUSSION

The test results from each method were reduced to cyclic stressamplitude and cyclic strain amplitudes so that the cyclic stress-straincurves could be plotted and compared using the following equations.

(1)

where

Ae inelastic strain rangeAd inelastic diametrial displacementd initial diameter of test section

Aeel=|f (2)

where

Ae , elastic strain rangeAa stress rangeE elastic modulus

Aet = Aep + Aeel (3)

where

Ae. total strain range

For each of the companion specimen tests, the stabilized values ofthe tensile and compressive stress and inelastic strain amplitude at thetips of the hysteresis loop in the vicinity of the half life number of cycleswere plotted on a log-log grid.

The curved, inelastic strain portion of the locus of the tips of thehysteresis loops generated by the single specimen incremental step testshown in figure 3 was analyzed by selecting 32 stations equally spacedon the strain axis (16 on the tension side, 16 on the compression side)along the curve. Stress amplitudes were determined from measure-ments of vertical distances from the zero load line to the stations. In-

elastic strain amplitudes were determined from measurements of hor-izontal distances from the straight line extension of the elastic modulusline to the stations. The stress amplitude and inelastic strain amplitudefor each station were plotted on a log-log grid. The monotonic tensilestress-strain curve for cyclically strained material was also plotted inthe above manner.

Individual best-fit-by-eye straight lines were drawn through theplotted points for the tension side and for the compression side of thecycles, and equations representing these lines were obtained. Theequations for the tension and compression lines passing through theplotted data for the individual companion specimen tests are given inSI units and are:

t 0.113

a* = 2689 —2 tension (4)2

c °'119

ac = 2992 —H compression (5)2

For comparison the equations for the lines passing through the singlespecimen incremental test data are:

t 0.108

or1 = 2835 —B tension (6)

0.122ncr= 3149 —E compression (7)

2

and for the line passing through the plotted points for the monotonic ten-sion test after cyclic straining, the equation is:

a* = 3172 (e )°' 131 tension (i)

The data that was plotted and used to obtain the above equations are listedin table IV.

Cyclic stress and strain amplitudes for each of the methods werealso plotted on rectangular coordinates as shown in figure 4. Differencesin the cyclic stress-strain curves for the three test methods are relativelysmall. The single specimen incremental step test had the highest stressesfor a given inelastic strain amplitude. The stress-strain curve generatedby the monotonic tensile test after strain cycling lies nearest to the datafrom the five companion specimen tests. Since this method required theleast amount of programming equipment, it is also the simplest.

CONCLUDING REMARKS

Room temperature cyclic stress-strain curves are determined forD6AC low allow steel by three different methods. The accepted basicmethod of conducting strain cycling tests to failure with several companionspecimens, each at a different completely reversed strain range is usedas the basis of comparison for the other two. The other two methods arethe single specimen incremental step test and the single specimen mono-tonic tension test after cyclic straining.

The cyclic stress-strain curves generated by the three methods arecompared and mathematical expressions describing these curves aredetermined Inasmuch as the curves obtained from the monotonic tensiontest after cyclic straining lies nearest to the data obtained with the com-panion specimen tests (accepted basic method) and requires the least amountof programming equipment, the monotonic tension test after cyclic strainingis considered to be the simplest method for determining the cyclic stress-strain curve for D6AC low alloy steel. Further tests with other alloyswould have to be made to confirm whether this conclusion holds true forthe other materials as well.

7

REFERENCES

1. Landgraf, R. W.; Morrow, JoDean; and Endo, T.: Determination of theCyclic Stress-Strain Curve. ASTM Journal of Materials, vol. 4, no. 1,Mar. 1969, pp. 176-188.

2. Hirschberg, M. H.: A Low Cycle Fatigue Testing Facility. Manual onLow Cycle Fatigue Testing, Test. Mater., Spec. Tech. Publ. 465,1969, pp. 67-86.

TABLE IV - SUMMARY OF DATA FROM METHODS USED TO

MAKE CYCLIC STRESS-STRAIN PLOTS

(a) Companion specimen tests

(b) Single specimen Incremental step test

Specno

51

52

53

54

62

Loadingmode

TensionCompression

TensionCompression

Tension

Compression

TensionCompression

TensionCompression

Stressamplitude

ksi

230 4

248 8

151 5160 0

203 6216 2

176 7178 4

117 7110 1

MN/m2

15881715

10451103

14031491

12181230

812759

Longitudinalcyclic

inelasticStrain

amplitude

0 00950091

00020002

00290027

00070008

************

Longitudinalcyclictotalstrain

amplitude

0 01740176

00540057

00990100

00670069

00430040

Negligible

Stationno

123456789

1011121314151617181920212223242526272829303132

Loadingmode

Tension

Compression

Stressamplitude

ksl

163 1185 8198 5208 5213 9217 5224 7230 2233 8235 7238 3240 2242 9244 7246 5247 4156 8180 4195 7208 4217 5223 8230 2235 7239 3242 9245 6249 3251 9253 8255 6258 3

MN/m2

11251281136914381475150015491587161216251643165616751687170017061081124413491437

150015431587162516501675169317191737175017621781

Longitudinalinelastic

strainamplitude

0 00020005001000160022002800340041004800540061006700740081008800950001000500090014002000260032003800450051005800650071007800850091

Longitudinaltotalstrain

amplitude

0 00580068007800870095010201110120012801340142014901570165017201790055006700760085009401020111011801270133014201510157016501720179

(c) Monotonic tension test after strain cycling

Stationno

123456789

10

Stress amplitude

ksi

80 5151 0191 2209 3221 4230 7238 3242 7246 8251 6

MN/m2

555104113181443152615911643167417021735

Longitudinalinelastic

strain

0000300110025003800520067008100950111

Longitudinaltotal

straw

0 0028005500760101011401300148016401800197

TABLE I. - CHEMICAL COMPOSITION OF D6AC STEEL

Weight percent

Carbon

0.47

Manganese

0.75

Silicon

0.20

Vanadium

0. 12

Nickel

0.55

Chromium

1.1

Molybdenum

1.0

Iron

Balance

Supplied by Grumman Aerospace Corporation.

TABLE E. - HEAT TREATMENT OF D6AC STEEL

1. Austenitize at 927 ±14° C, heat 125 minutes in air or 30 minutesin salt bath and hold an additional 60 minutes.

2. Transfer piece to a furnace set at 518 ±6° C and allow to cool tothis temperature within 2 hours.

3. Quench piece in agitated oil bath at 60° C to 121° C until equalized.

4. Air cool to below 60° C.

5. Temper immediately to 552° C and air cool.

6. Retemper a second time.

TABLE m. - MECHANICAL PROPERTIES OF D6AC

Ultimate tensilestrength

MN/m2

1629

ksi

236.2

Yieldstrength

MN/m2

1472.

ksi

213.5

Elonga-tion

percent

11.2

Reduc-tion ofarea,

percent

36.9

Elasticmodulus

MN/m2

202X103

ksi

29.3X103

Fracturestrength

MN/m2

2116

ksi

306.9

Elastic modulus line ->12000

8000

4000

-4000

-8000

-12000

-Locusofhysteresisloop tips

-50-.040

I I

-.020 -010 0 010 020

Test section diametral displacement, mm

-I I I I-.0016 -.0012 - 0008 -.0004 0 .0004 .0008

Test section diametral displacement, m..0012 0016

Figure 3 - Cyclic load versus diametral displacement curve traced by hysteresis loop tips in singlespecimen incremental step test of DMC steel showing two sample stations on inelastic portionfor which cyclic stresses and inelastic strains were calculated.

E2

2000

1500

1000

500

0

500

1000

1500

2000

300,—

200

100

100

200

300

Single specimen incremental steptest

Monotonic tension test after straincycling

O Companion specimen tests

1-"020 - 016 -.012 -.008 -.004 0 004 .008 .012 .016

longitudinal total strain

Figure 4 - Comparison of cyclic stress-strain curves for D6AC steel obtained by three different test methods

020

0.84cm(0 33 in . )

1.91 cm (0.75,in )

8. 26 cm (3. Sin.)H~7-0.10cm (0.04 in.

r-K ^ 'J_ •* — i -

. n~^LJ ,J 'i cm (0. 250 in ) -/ ;8cm (1 5 in. ) rad-1'

Irad4 — I

_J];^ 1.270 cm 10 500 in )

1.267 cm (0499m I

Figure 1 - Test specimen geometry and dimensions.

6min

Time

Figure 2. - Programming blocks of linearly increasing-decreasingcommand signal for incremental step test

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