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AD-769 763

HARDNESS, STRENGTH AND ELONGATION CORRELATIONS FOR SOME TITANIUM-BASE ALLOYS

W. A. Houston, et al

Westinghouse Electric Corporation

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HARDNESS. STREMGTH AND ELONGATION CORRELATIONS FOR SOME TITANIUM-ItASE ALLOYS 4. DESCRIPTIVE NOTt» (Trpm at npcn mnd Inclutlve d*f)

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Previously published results on aluminum-base alloys and steels showed that accurate prediction of yield stress and ultimate tensile stress was possible from hardness data. The present study was undertaken to see if the relationships were also obeyed by titanium-base alloys. The intention was to permit exploitation of the economic advantages which would result from a saving in machining cost and in testing time, if the Judicious use of hardness testing were to provide data approximately equivalent to that obtained by tensile testing.

Rockwell hardness and tensile data obtained in an earlier study on three titanium base alloys (Ti-13V-llCr-3Al, Ti-5Al-2.5Sn and Ti-6Al-UV) have been augmented with Meyer, Vickers and Knoop hardness measurements. The tensile data have been analyzed to give the work hardening coefficient n and this has been correlated with (a) the ratios of both yield stress Oy and ultimate tensile stress o to Vickers hardness Hv; (b) the Meyer hardness coefficient m; and (c) uniform elongation. The correlations involving (a) and (b) above did not follow the expected behavior.

An attempt was also made to estimate points along the tensile curve from Meyer hardness data. The agreement was only moderately good for the Ti-13V-llCr-3Al alloy, and was poor for the other two alloys. After further analysis of the data, the breakdown of the correlation was attributed to a differnt deformation mechanism, presumably micro-twinning, occurring during hardness testing from that prevailing during tensile testing. This effect also explains, for the materials in the present study, the breakdown of both (i) the relationship between m and n, and (ii) the /j,

Xhifibi i of both (i) the relationship between m and n, ^jg^vg^^ess^nardnes^jg^j^^^^^^^IBIBI—^ t DD ,'r.,1473 UHcyflaiziBn — ..

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Titanium-base alloys

Hardness measurements

Hardness-strength correlations

Rockwell hardness

Vickers hardness

Brinell hardness

Meyer hardness

Knoop hardness

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HARDNESS, STRENGTH, AND ELONGATION CORRELATIONS FOR SOME TITANIUM-BASE ALLOYS

DJ.ABSON

W.A.HOUSTON

T.E.JONES

F.J.GURNEY

D D C

U| m i9 m

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it

FOREWORD

This report was prepared by the Westinghouse Electric Corporation, Astro- nuclear Laboratory, Pittsburgh, Pennsylvania, under U.S.A.F. Contract F33615-71- C-II63. The contract was initiated under Project No. 7351 "Metallic Materials", Task No. 735108, "Processing of Metals", and was administered under the direct- ion of the Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio with Mr. A. M. Adair and Mr. V. DePierre (AFML/LLM) as Air Force Project Engineers,

This report discusses research conducted from 1 November 1971 to 15 March 1972. It was submitted by the authors on 26 February 1973.

This Technical Report has been reviewed and is approved.

I. Perlmutter vJfF

Chief, Metals and Processing Branch Metals and Ceramics Division Air Force Materials Laboratory

ii

ABSTRACT

Previously published results on aluminum-base alloys and steels showed that accurate prediction of yield stress and ultimate tensile stress was possible from hardness data. The present study was undertaken to see if the relationships were also obeyed by titanium-base alloys. The intention was to permit exploitation of the economic advantages which would result from a saving in machining cost and in testing time, if the Judicious use of hardness testing were to provide data approximately equivalent to that obtained by tensile testing.

Rockwell hardness and tensile data obtained in an earlier studv on three titanium base alloys (Ti-13V-llCr-3Al, Ti-5Al-2.5Sn and Ti-6Al-ltV) huve been augmented with Meyer, Vickers and Knoop hardness measurements. The tensile data have been analyzed to give the work hardening coefficient n and this has been correlated with (a) the ratios of both yield stress ay and ultimate tensile stress au to Vickers hardness Hv; (b) the Meyer hardness coefficient m; and (c) uniform elongation. The correlations involving (a) and (b) above did not follow the expected behavior.

An attempt was also made to estimate points along the tensile curve from Meyer hardness data. The agreement was only moderately good for the Ti-13V- llCr-3Al alloy, and was poor for the other two alloys. After further analysis of the data, the breakdown of the correlation was attributed to a different deformation mechanism, presumably micro-twinning, occurring during hardness testing from that prevailing during tensile testing. This effect also explains, for the materials in the present study, the breakdown of both (i) the relationship between m and n, and (ii) the relationships which involve stress/hardness ratios.

iii

mnvm

TABLE OF CONTENTS

V CONCLUSIONS

VI REFERENCES

11 APPENDICES

\

Preceding page _.<>..*

Section Page

I INTRODUCTION 1.1. Stress/Hardness Relations 1 1.2. Derivation of Stress-Strain Curves from Hardness Data 3 1.3. Estimation of Ductility from Hardness Data 3

II EXPERIMENTAL h

III RESULTS 3.1. Stress/Hardness Ratios and Work Hardening Rates 6 3.2. Comparison of Stress-Strain Curves with Hardness Data 7 3.3. Correlation of Uniform Elongation with m and n 7

IV DISCUSSION h.l. Estimation of Strength from Hardness Data 8 k.2. Variation of Strength and Hardness with Processing 9

Temperature k.3. Correlation of Uniform Elongation with Tensile and 9

Hardness Data k.h. Comparison with Previous Work 10

■

11

12

7.1. Relation between Uniform Elongation and n 27 7.2. Considöre's Construction 28 7.3. Computer Program and Output for Brinell Test Data 29 7.^. Computer Programs for Manipulation of Load-Elongation ^0

Data 7.5. Output from Programs of Appendix k. kk

ILLUSTRATIONS

Figure Page

1. Predicted relationships between the stress/Vickers hardness ratio, the work hardening coefficient, and the Meyer hardness coefficient according to Eqs. 1, 3, 5 and 6. 15

2. Indentations made with a 2 mm diameter ball in two of the alloys, showing the occurrence of artifacts similar in appearance to deformation twins. x300 l6 (a) Ti-13V-llCr-3Al (b) Ti-5Al-2,5Sn

3. Experimental stress/Vickers hardness ratios as a function of work hardening coefficient. The relationships predicted by Eqs. 1, 3 and 5 are shown. (For key to data symbols, see 18). 17

k. Experimental stress/Vickers hardness ratios as a function of Meyer hardness coefficient. The full lines indicate the relationships predicted by combining Eqs. 1 and 5, in turn, with Eq. 6. The filled symbols are for UTS/hardness and the open symbols are for yield stress/hardness. The key identifies the symbols used in Figs. 3 through 8. 18

5. Comparison of true stress-true plastic strain curves with converted Meyer hardness data plotted according to Eqs. 8 and 9 for a typical specimen of each alloy: (a) Ti-13V-llCr-3Al (3375) (b) Ti-5Al-2.5Sn (3239) (c) Ti-6Al-iiV (3Wl) 19

6. Uniform strain plotted against work hardening coefficient. Note that, while the full line refers to total strain, all the data points and the dashed lines refer to true plastic strain. (a) Uniform strain data derived directly from the chart record. 20 (b) Univorm strain derived by means of Considfere's construction. 21

7. Yield and ultimate tensile stresses and Rockwell "C" hardness as a function of billet preheat temperature, after Gurney and Male6. Vickers hardness, determined in the present study, is also incorporated. (a) Ti-13V-llCr-3Al 22 (b) Ti-5Al.-2.5Sn 23 (c) Ti-6Al-i+V 2k

8. Comparison of ultimate tensile stress/hardness correlations from the present work with those of Hickey9. The lines represent the relationship(s), and ± two standard deviations, given by Hickey. (a) UTS vs. Vickers hardness. 25 (b) UTS vs. Rockwell "C" hardness. 26

vi

Table

I

II

TABLES

Post-Extrusion Heat Treatments

Stress, Strain and Hardness Data

Page

13

S

vix

I INTRODUCTION

Indeutaticn hardness testing provides a simple techaiqae for following changes in strength resulting from Ketal processing. However, due to the com- plexity of the deformation around an indentation, no universal linear conversion exists relating a single hardness value to either yield strength or ultimate tensile strength. Tabor1 has derived a single conversion factor, but the flow stress estimate obtained is that appropriate to about 8% engineering strain; hence the conversion is of limited value. More complex formulae1»2, although somewhat unwieldy, have application where tensile data are required, but where tensile testing is impossible, impractical or undesirable. Typical applicat- ions for these formulae might include room temperature testing of hot-torsion tested rods in the laboratory or the non-destructive estimation of the strength of castings, since in these situations tensile testing would be impossible. A further use would be for laboratory tests where economy of time or material are required such as in screening tests in studies of the effects of process variables on mechanical properties. It was this latter application,with a view to achieving cost savings, which prompted the present investigation.

In a tensile test, not only is information obtained about strength, but also about elongation. While it appears that hardness testing cannot differ- entiate between brittle and ductile metals, it has been suggested that an in- dication of ductility can be obtained, in some cases, in the form of an estimate of uniform elongation3.^ . The present study was undertaken to check if expected strength/hardness/ductility relationships were obeyed for titanium base alloys. A beta alloy (Ti-13V-llCr-3Al), an alpha alloy (Ti-5Al-2.5Sn) and an alpha-beta alloy (Ti-6A1-Uv) were evaluated.

1.1. Stress/Hardness Relations

Tabor1 has shown that, for steel and a variety of other metals, the ratio of the UTS a to the Vickers hardness H is given by

u v * ^

a u

H 2.9 v

(1-n) ri2.5nl n (l) mn

where n is the work hardening coefficient. The latter quantity is obtained from the slope of a log-log plot of true stress a vs. true stroin e, as implied in the relation

a = Ke" (2)

where both K and n are constants. Tabor suggested that, while a numerical factor of 2.9 in. Eq. 1 was appropriate to steel, a value of 3.0 applied to copper. Cahoon et al. maincained that a numerical factor of 3.0 WP.'' appropriate to steel, brass and aluminum, i.e.,

H " 3.0 L 1-n J

It should be noted that Eqs. 1 and 3 relate hardness to ultimate tensile stress. However, a relationship between the yield stress o and Vickers hardness H has been given by Gaboon et al.2 y

v

JL = (0-1)" U) Hv 3.0

Taking logarithms gives

log (ov/H ) = - n - log 3.0 (5)

As this relationship has been applied successfully to a variety of materials, including aluminum alloys and some steels2, it may have universal application. If so, then different materials, each with a range of values of the work hardening coefficient n, should all give data lying on the same straight line, of slope - 1 and intercept - log 3.0 on the log (a /H ) axis, when plotted according to Eq.. 5- y V

Where stress-strain data are not available, the work hardening coefficient may usually be estimated from the equation

n = (m-2) (6)

where m is the Meyer hardness coefficient. Eq. 6 has been shown to be true theoretically, and its validity has been demonstrated for a variety of materials1, The quantity m is obtained a3 the slope of a log-log graph of load W vs. indentation diameter 6 for a spherical indenter. These quantities are related by the equation

W = K'fi (T)

where K' and m are constants.

The relationships given in Eqs. 1, 3 and 5 are depicted in Fig. 1 where the range of n values covers that from hardened (n <0.l) to fully annealed (n « 0.5) materials. The corresponding range of m values, according to Eq. 6, is alsc shown. Thus it should be possible, by suitable analysis of a series of hardness indentations, to estimate both yield stress and UTS.

MM

1.2. Derivation of Stress-Strain Curves from Hardness Data

According to equations given by Tabor1, points along a stress-strain curve may be estimated by evaluation of equivalent stress and strain for a series of indentations made at different loads with a spherical indenter. The relevant equations are

o = H /2.8 = (1+W/TTD2)/2.8 m

e = 0.26/D

where o and E are the stress and strain estimates for a Meyer hardness H ; 6 is the diameter of the indentation produced by a ball of diameter D under an applied load W. Application of these two equations will be discussed in more diet ail later.

1.3. Estimation of Ductility from Hardness Data

One further relationship is worthy of note, since it may provide a means of estimating uniform elongation from hardness measurements1*. For metals which obey Eq. 2, it has been shown that the true strain to the ultimate tensile load should be numerically equal to the work hardening coefficient5, I.e.

= n (10)*

Here c is the total (i.e. elastic plus plastic) strain occuring during stable flow, before the load instability of necking. Incorporation of Eq. 6 gives

e = (m - 2) (11)

which suggests that estimation of uniform elongation from hardness data is possible. The application of this equation will be considered in greater detail later. In an alternative method due to Boklen3, uniform elongation is correlated with the height of the material piled up around an indentation. However, this technique is not considered further In the present work.

The derivation of this relationship is given in Appendix 1. It is of interest to note that a similar equation involving the equivalent engineering strain e .has been given by Tabor1 viz. e = n/(l-n).

II EXPERIMENTAL

The alloys used in this study were the subject of an earlier investigation6. In that study, three titanium-base alloys were extruded at a rang^ of tempera- tures and either cooled in air or water quenched. The extruded material was then subjected to an aging creatment, Table I. A tensile specimen was machined from a piece of each bar and Rockwell hardness readings made on an adjacent piece. In the present study, additional hardness readings were obtained and the tensile load-elongation curves were subjected to further analysis.

Four types of hardness measurement were carried out, normally on transverse sections:

1) A range of loads was used for Brinell tests with a steel ball on a Vickers hardness testing machine. The data obtained were used (a) to estimate equivalent stress and strain, as outlined above, and (b) to fit to Meyer's Law, Eq. 7> in order to determine m. According to Tabor7, the minimum load required to give fully plastic deformation, so that Eq. 7 is obeyed, can be estimated from a knowledge of the elastic properties of the specimen and the ball Indenter, and the yield stress of the former. For the 1-mm ball ussd in the present study, these approximate lower limits were 21, 11 and 15 kg. for the Ti-13V-llCr-3Al, Ti-5Al-2.5Sn and Ti-6A1-^V alloys respectively. A load range from kO to 120 kg was therefore used; from this data, a series of values of both Meyer and Brinell* hardness was determined. Log-log plots were drawn up according to Eq. 7 and values of the slope m were determined. Additional readings were made with applied loads of 5, 10 and 20 kg. Data from the four lowest loads then gave appropriate equivalent strains, according to Eq. 9, for comparison of the actual flow stresses with those estimated from Eq. 8.

2) Additional Rockwell hardness readings were made using a i/l6 inch diameter ball indenter and standard loads of the F, B and G scales, i.e. 60, 100 and 150 kg. Supplementary weights were also used, and further non-standard hardness readings taken corresponding to 72.5, 85, 112.5 and 125 kg. loads. Attempts to obtain straight lines on log-log plots, in order to derive a para- meter analogous to the Meyer hardness coefficient, proved unsuccessful. Among the plots tried were log (load) vs. log (100-hardness) and log (100 kg + load) vs. log (100-hardness) . However, none of the graphs gave satisfactory straight lines.

3) Vickers hardness tests were performed using a 100 kg. load. Three indentations were made on each specimen.

h) In order to try to detect the presence of anisotropy of hardness, and therefore of strength, Knoop hardness tests were performed with the long dia- gonal lying both parallel and transverse to the axis of the extrusion. However, there were no significant or systematic differences in the hardness values obtained in the two directions.

Since tables were not available for a l-mm ball and loads of hO, 60, 60, 100 and 120 kg., hardness was evaluated by means of a simple computer program. This program and the data generated are given in Appendix 3.

mitmwmm.'e» <******

Tensile load and displacement data from the earlier studyJ were converted to true stress and true ..;train by reading the co-ordinates of a series of points, and processing the data by computer. Since the chart record showed machine crosshead displacement, only the plastic strain could be derived directly from the data.# An estimate of elastic strain was made using a value of Young's Modulus ■ l6.5 x 106 psi [l.lh x 105 Nm"2), and this was added to the plastic strain to obtain ''total corrected strain".# The logarithm of this quantity was used in the log (true stress) vs. log (true strain) plots to determine the work hardening coefficient, n.

The simple computer programs, and the data output, are given in Appendices k and 5.

Ill RESULTS

3.1. Stress/Hardness Ratios and Work Hardening Rates

Analysis of the experimental data showed that several of the relationships obeyed by other materials did not apply to the Ti-base alloys in the present study. Typical of the anomalous behavior is the lack of correlation between the Meyer hardness coefficient m and the work hardening coefficient n (Table II). Instead of fitting Eq. 6, the data for the beta-alloy show an approximately constant value of n over a range of m values, while the converse is true for the other two alloys. The discrepancy between the observed and the predicted behavior results from a difference in the deformation conditions in a tensile and a hardness test, and may be attributable to a difference in deformation mechanism, as suggested by Lenhart8 for Mg and some Mg-base alloys. In his study, Lenhart observed deformation twins on the faces of the hardness indentations. In the present work, twins were not observed. However, features resembling twins were seen on the faces of some indentations. They were attributed to defects on the surface of the ball indenter since they occurred in corresponding locations in all indentations. Fig. 2.

Values of yield and ultimate tensile stresses, hardness and ratios of stress to hardness are given in Table II. The correlation of the ratios a /H and a /H with the work hardening coefficient n also did not follow the expected trend of Fig. 1; the experimentt»,l c'ata, presented in Fig. 3, show considerable deviation from the predicted lines. For the beta alloy, the points all occur at similar values of n and show a wide spread of values of o /H and a /H .

*■ y v u v

While the spread of the data in Fig. 3 is considerable, deviations from the predicted straight line representing the yield stress/hardness ratio can be rationalized if the data are considered according the structure present during the extrusion pre-heat (see key). The deviations correspond to changes in slope of the predicted line, and would be represented mathematically by changes in Eqs. k and 5.

Replotting of the ratios against the Meyer hardness coefficient showed stronger trends. Fig. k*, although the data did not fit the relationships expected from Eqs. 1, 3 and 5. In view of the poor correlation observed, it is suggested that prediction of yield and ultimate tensile stress from hardness data alone may be possible only for the beta alloy, although a trend is also apparent for the alpha-beta alloy.

* It should be noted that, while a ball indenter is used to obtain data for the Meyer hardness coefficient m, the strength/hardness ratios correlated with m in Fig. k involve the use of Vickers hardness values obtained with a pyramid indenter. Brinell hardness is unsuitable for the evaluation of these ratios since it shows some dependence on the size of the indentation, and therefore on the imposed load. This dependence can, however, be used to advantage, as discussed in the next section.

3.2. Comparison of Stress-Strain Curves with Hardness Data

In hardness tests carried out using the ball indenter, a range of loads was used. Therefore, a range of equivalent strain and corresponding stress values could be derived, according to Eqs. 9 and 8 respectively. Agreement between these derived data and the values of true stress, read from stress vs. plastic strain curves, was poor. In every case the converted hardness iata fell below the tensile data, said this was more marked in the alpha and alpha-beta alloys than in the beta alloy. Typical data are shown in Fig. 5. Thus, Tabor's claim that hardness provides a reliable measure of the shape of that part of the stress/strain curve which lies within the first 25^ of strain9, is not applicable to the alloys used in the present study. In order to adjust the converted hardness data to be of similar magnitude to the tensile data, the divisors required would be 'V 1.3 for the alpha and alpha-beta alloys and ^ 2.U for the beta alloy, rather than the 2.8 of Eq. 8*.

3.3. Correlation of Uniform Elongation with m and n.

In order to check the validity of Eqs. 10 and 11, uniform elongation was determined from the chart record and converted to true (plastic) strain. Since the elongation to peak load could not be determined unequivocally, a range of strain was obtained from each chart, as shown in Table II and in Fig. 6a, where the data are plotted against the work hardening coefficient n. More precise determination of the strain to peak load was obtained by the use of Considere's construction which required plots of true stress vs. engineering strain (see Ref. 5)+. The corresponding true strain values are plotted in Fig. 6b. It should be noted that, while the data points refer to plastic strain, Eq. 10 refers to total strain. A correction was therefore made by determining the mean UTS from the data for each alloy and subtracting the corresponding estimated elastic strain to give the dashed lines in Fig. 6. It can be seen that the data fit the predicted relationship reasonably well so that, to a first approximation, Eq. 10 is obeyed. However, the corresponding expression which incorporates the Meyer hardness coefficient m (Eq. ll) did not fit the predicted expression as a consequence of the breakdown of the relationship between m and n (Eq. 6) discussed earlier. As the experimental data showed considerable scatter, no well-defined trends are apparent and no correlation of the two variables is possible. Hence prediction of uniform strait, by this method does not appear possible for the three materials studied.

* See Appendix 3 for a listing of these ratios, evaluated for each hardness indentation after applying Eqs. 8 and 9.

t See Appendix 2 for a derivation of the relevant equation.

\

IV DISCUSSION

k.l. Esbimahion of Strength from Hardness Data

As the data in Table 1.1 and in Pig. 5 show, estimates of stress and strain according to Eqs. 8 and 9 do not give a good approximation to the stress-strain curve obtained in a tensile test, particularly for the alpha and alpha-beta alloys. The origins of the discrepancy, and the consequences of it, merit a closer examination and th^s will now be presented.

It should be noted that Eqs. 8 and 9 were derived empirically by Tabor1, although they have been verified by comparison of hardness data with both com- pressive 1»8 and tensile8 curves. If the converted hardness data presented in Fig. 5 is re-plotted according to Eq. 2 (a = Ken), apparent values of the work hardening coefficient n can be derived. Such an analysis yielcs values of approximately unity for (b) and (c) and approximately one third for (a). Several points of interest arise from this observation.

i. These apparent values of n do not agree with those derived from the tensile data.

ii. Evan for an annealed material, n values greater than approximately 0.5 do not occiir. Thus, during hardness indenting,, two of the materials in the present study have apparent work hardening coefficients higher than that obtained, even in soft materials, during deformation by slip. This lends support to Lenhart's suggestion8, mentioned in section 3.1, that a different deformation mechanism is occurring in each type of test. The converted hardness data in Figs. 5b and 5c lie approximately on straight lines which, when extrapolated, pass through the origin. The data are somewhat similar to those of Mote and Dorn10

who determined that the high rate of work hardening was associated with the occurrence of twinning in magnesium single crystals and bi- crystals tested in tension. It should be noted, too, that in Fig. 5 the converted hardness values all lie below the tensile curves, and this is also consistent with the suggestion that twinning occurred during hardness indenting.

iii. As a consequence of ii above, Eqs. 8 and 9 may not be valid, and the apparent stress and strain derived by their use may not ha,ve any physical significance. If this is true, then the precise values of the apparent work hardening coefficient n are not valid, although it is considered likely that, at least qualitatively, their magnitude has some significance.

iv. Eq. 6 (n = m-2) is still not obeyed by the new data; while the n values obtained from the tensile curves are too low, the apparent values obtained from the converted hardness data are too high. In the light of iii above, this is not surprising.

v. If the n values corresponding to tensile and hardness testing are different, as suggested above, then this invalidates the derivation of Eqs. 1 and 3 (on Page 10" of Ref. l) and of Eq. k (Ref. 2), both for the alloys in the present study and for other materials which show different work hardening behavior in tension and in hardness tests. The reason for the deviation from the expected behavior in Fig. 3 is therefore apparent.

At the present time, no alternative general hardness/strength convertion relationship is available for the materials which show this anomalous behavior. Instead, specific equations or relationships may be derived for each alloy. Thus, use of the dashed lines in Fig. k would permit convertion of hardness data for the beta and possibly the alpha-beta alloy for the limited range of Meyer hardness coefficients covered in the present study. The alternative is to accept a single convertion factor or a linear equation as discussed in section k.k.

k,2. Variation of Strength and Hardness with Processing Temperature.

Since hardness is commonly used to monitor the influence of processing on mechanical properties, it is instructive to compare hardness values with both yield and ultimate tensile stresses for a range of processing conditions. In Fig. 7, strength and Rockwell hardness data from Gurney and Male6 are shown plotted against billet pre-heat temperature; Vickers hardness, determined in the present study, is also given. The changes in hardness do not follow the strength changes exactly but show a variation in the ratio of strength to hardness with specimen history. Thus it is clear that a single hardness determination does not necessarily give a reliable measure of strength.

In addition to the variation of the yield stress/hardness ratio with the work hardening coefficient n, a dependence of the data on the structure during processing, and therefore on the room temperature rnicrostructurc, is apparent for the Ti-5Al-2.5Sn alloy. Fig. 3. However, the present study provided insufficient data to determine exactly the extent of the deviation from the predicted relationship.

h.3. Uniform Elongation, Work Hardening Coefficient and Meyer Hardness Coefficient.

The experimental data in Figs. 6a and 6b show that Eq. 10, relating uniform strain eu and work hardening coefficient, is obeyed. The agreement is, however, only approximate and has been investigated only over a limited range of the work hardening coefficient n. It should be emphasized that the data were all obtained from tensile test curves, and therefore the results cannot be applied to a hardness study alone unless an estimate of n can be obtained from hardness data, i.e. unless Eq. 6 is obeyed. For the three titanium alloys in the present study, the relationship between work hardening coefficient n and Meyer hardness coefficient ro of Eq. 6 is not obeyed, as discussed above. Therefore EJq. 11, which depends on it, and which relates cu and m, is also not obeyed. The behavior of the present alloys is unusual since Eq. 6 has been

shown to be valid for a variety of materials1»2, including both 65S aluminum alloy and \0kQ steel in which a range of strengths was obtained either by cold working or by heat treating2.

k.k. Comparison with Previous Work.

In Figs. 8a and 8b, the present data are compared with the linear relationships given by Hickey for Ti-base alloys11. In each case, the new data show substantial agreement with the earlier result'-. Almost all the data points lie within the scatter band drawn at 1 twice the standard deviation quoted by Hickey. A plot of Vickers hardness vs. Rockwell "C" hardness (not Bhown) also gave similar agreement with the published work.

In the material used in the present study, in contrast to that investigated by Zarkades12, no anisotropy was detected by Knoop hardness measurements. This is not surprising since, with the exception of two extrusions which were carried out at l6250F, the grain structure appeared equiaxed6. Such a structure indicates that recrystallization occurred either during or immediately after extrusion, thereby eliminating an elongated hot work grain structure.

In showing deviation from Eq. 8, as discussed, earlier, the present results are somewhat similar to those of Lenhart8 on Mg and Mg-Al alloys. Instead, of a divisor of 2.8 in Eq. 8, Lenhart's data would require divisors of ^ 1.5 for Mg and ^ 2 for the alloys, in order to adjust the hardness data to have a similar magnitude to the tensile data. Since the divisors appropriate to the alloys in the present study are 'v 1.3 for the alpha and alpha-beta alloys and ^ 2.it for the beta alloy*, once again, the materials are weaKer during hardness testing than expected from the tensile test results. Lenhart also carried cut compression tests and attributed discrepancies between compressjon, hardness and tension test results to the occurrence of profuse twinning during compression or hardness testing which gave rise to a lower flow stress than that expected from the tensile data. Thus, the most reasonable explanation of the anomalous hardness/ Stress ratios found in the present study is Lenhart's suggestion of twinning during hardness testing. Since the "wins were not detected by optical observation, it is possible that microtwinning occurred. Investigation of this suggestion by thin foil electron microscopy is, however, outside the scope of the present study.

* S See Appendix 3-

10

V CONCLUSIONS

From an analysis of tensile and hardness data for the three titanium-base alloys, Ti-13V-llCr-3Al, Ti-5Al-2.^Sn and Ti-6A1-Hv, the following conclusions can be drawn:

1) A unique correlation between both of the stress/hardness ratios a /H and au/Hv and the Meyer hardness coefficient m has been shown to exist for the Ti-13V-llCr-3Al alloy; the relationships are not those predicted by the theoretical formulation of Tabor or Cahoon, but do permit the estimations of av and au from hardness data for this alloy.

2) Uniform elongation in tension was found to be approximately equal to the work hardening coefficient n; however, it did not correlate well with m. The expected relationship between m and n, viz n=(m-2) was not obeyed by any of the alloys.

3) The breakdown of the m-n relationship is attributed to a difference in deformation mechanisms operating during tensile and hardness testing. While micro-twins probably formed during hardness indenting, they were not observed in the present study.

h) As a consequence of 3 above, relationships involving stress/hardness ratios did not hold for the alloys in the present study. Thus, the equation given by Tabor relating au/Hv and n is not followed by any of the alloys studied. Data for the Ti-5Al-2.5Sn and Ti-6A1-Uv alloys show considerable scatter around the öy/Hv vs. n relation proposed by Cahoon et al.; for the limited range of n values studied, the discrepancies between predicted and actual ay/Hv values are 5 to 10^ and the values appear to show some dependence on the nature of the raicrostruct- ure.

5) As a further consequence of 3 above, points along the stress-strain curve, estimated from a series of Meyer hardness readings determined at different loads, for true strains of about h% to 10^, showed moderately good agreement only for the Ti-13V-llCr-3Al alloy. The relevant equations were not followed by the other two alloys.

11

■■ I»l. ill IJ ^—. -- ■ ■ ■ ■ • • I 11 I

VT INFERENCES

1. D. Tabor, "The Hardness of Metals" Clarendon Press, Oxford, 1951.

2. J. P. Cahoon, W. H. Broughton and A. R. Kutzak, Met. Trans., 2, 1971, 1979 - 83.

3. R. Boklen, "A Simple Method for Obtaining the Ductility from a 100° Cone Indentation" in "The Science of Hardness Testing and its Research Applicat- ions", H. Conrad and J. A. V/estbrook, Eds., A.S.M., 1972.

k, D. J. Abson, Discussion to paper by M. C. Shaw, "The Fundamental Basis of the Hardness Test", Ibid..

5. G. E. Dieter, Jr., Mechanical Metallurgy, Mcüraw Hill, New York, 196l.

6. F. J. Gurney and A. T. Male, Air Force Materials Laboratory, Wright- Patterson Air Force Base, Dayton, Ohio, Technical Report No. AFML-TR-71-28, 1971.

7. D. Tabor, Ref. 1, p. 51 et seq..

8. R. E. Lenhart, Wright Air Development Center, Wright-Patterson Air Force Base, Dayton, Ohio, Technical Report No. WADC-TR-55-111*, 1955.

9. D. Tabor, J. Inst. Metals, 79, 1951, 1-18.

10. J. D. Mote and J. E. Dorn, Trans. AIME, 2l8, i960, 1+91-7.

11. C. F. Hickey, Watertown Arsenal, Watertown 72, Mass. Technical Report No. WAL-TR-U05.22/1, April 1961.

12. A. Zarkades, Army Materials Research Agency Technical Report, R AMRA-TR- 67-0k, 1967.

12

■■■■■■MiMMMMMMWI

TABLE I

Post-Extrusion Heat Treatments6

Alloy

Ti-5Al-2.5Sn

Ti-6A1-W

Ti-13V-llCr-3Al

Treatment

1 hr. at 1000oF, air cool.

k hrs. at 1000oF, air cool,

2k hrs. at 900oF, air cool.

13

M a' B c a

-H T1 4J ■H C»

P B L B +-1

(' tu

k n Ä.S

I c

V B

O 1A o o \£i yj J r- o o o o

O lAVi) o o CO CO CO <u 'O o o o o o

o d o o d i I I I I

LA ir\ o iA o

o o o o o

o o o o

aj c\j fy aj

o iA in iA iA tr\ o vo -^ ô -* m u-\ in o o o o o o o

o o o o o o o

h- c^ (^ u^ vi3 i" in t~- <o o*\o t— t~ w* o o o o o o o

o o o c d d o i i i i i r i

o o j in co o in ^r in _^ cu -^ OJ f\i o o o o o o o o o d o o o o

H iH r-l ,-H iH r-t r4

o in in o vo in j -^ o o o o

i/\ in in t^ Oico r- Ch o o o o o o o o

I I I I in H o o oo ^r oj fy o o o o

d d o d

n B w + tl •

{. 1{ i< 11)

I. 0) «i a; ü

a o

»: 4' Vi >: n ^ u ^ to O f? o & ts: U

CM Oj cvj ry cy Oj

0\CO CO ON O O O O O O

C\J OJ C\J OJ 04 C\J f\J

Q cy ^r ^ o ô f^ vo aj r- \D vo vo u~\ o o o o o o o

o o o o o o o

1 o~i C\J cv

CO CM (AJ OJ OJ

VO IA lA OJ \D CO u^ t~ o o o o

a

a i 8 o IA .H IA - J IA O f'O IA IA Ov CO ON J' ^D ON IA

H in C: -? rn cv O ON ON C?\ CO CO h- r-l a f) CO C*

S ^^ 1-1 g on m nn ro ro fO OJ fy CM OJ Oj Oj On O'M'O CM OJ

•ri O d d d o d o o o o o o O O O O O

10 t) ~- m

it c s i 1 in to VD O ^f o o h- VX) rn oj o IA r- f- ON Oj VD H

~> S 'S 0

•H

iH C7\ O O ON ON CO h-co t-- f-vo rH CO CD VD f- 03 5 | on nj m rn ro C\J OJ CM OJ CM CM v^J on CM oj CM a- ^J o o o o o O O o o o o o o o o o o 5 Cl ^-• f'j

CM » "i M a i"1 n tn 1 i. t" S -^ h- H h- OJ en r-1 CO Cd co on m ON lAVO MJ ON r- *J II u OD 0\ t-OO CO CTN «H rH r-t CM on OJ CM ^J ^J LA LA LA

CO M on m m on r* rn on m oi m on nn m nn on on m on o b • •H d s

a > ats: s « >- .H n ^ H

V u V o moo CO CO CO LA on IAOO on co co co on co

o O ON f- co ON rH O H r-1 OJ OJ -* -3- IfWO CJ

1 03

-3 ^r nn m m oj on oi m on on m ci no en m m

* •r^

CO

O

IACC' on

oi ox-^r Q

O rH fO -J rt? 1/-N H LA CO CO VO LA

tA H CM on ro rn on

vo m -^ t— ON E I (.0 CTvco r-oD .'O m on LA IA LA ^* .-J b M H r-t H iH /-* rH f-H rH i-H cH ^H rH H ■-H rH nl

* ii t) a ■H U3 O ON CO on H oj -^ t— oj r- LA M IA ON Ol H fl) *H a u ta OJ (f| o. _r H r~i ON r* r-i t-Ô ^t LA CM CM IA r-

■H -U M r-M3 lAVi) vo m oi rj on oj nj CM LA -^ ,* o") on ^ CO M n^ rH rH H r-t rH rH rH rH p-H rH H rH rH rH rH

iA a o o o o t^- U^ O iA LA IA VO t— ON O H OJ rH H rH CM CJ CM

SI iA CO OJ 'A o -H r- o t-- to vo (n on on cj on oj o-i 1 r^ on on on on on i

IA UN u'N o o o o oi OJ LM NX- o -^J G VO :- CO CO ON ON rH r) rH H rH rH rH OJ

i on on on on i

LA LA iA O O CM r- CM c o vo f-cO ON H rH rH H -H CM

!?X LA Ch

-d II t]

0 1 r 1 dJ 'H ^ •H > 0 5! r-t .-1 a V) W) 4J M 1 13 0 ■rl o •X 0 o ij ^J ■H tA CO h r-j to

* G 4 u ja •H ^«. OJ ■H W. 0 ■H

Ü) • (/) rH a u .L-: Ifl ^ u 10 rH H

|« onw^ tu CJ u ^ • CO to c. u 1 > u ;- H 0J H ■*-> C to V. IA fe^ .> c a» ■L^ ** h to u <V I * • a to ±1 fJ 1 cvj c! a» C H 1 ..-1 G ,,. *•

0 ■H M on > ^ CH M •H • U :i X MH 3 x 0 O EH H 1 — a* a) (1 H CM n- cd a; H^f d a» m

-p rf frj H a; OJ p J3

+>

n C) +» +J

w d

at •H e a» o ()

m

■fl

.Tl :« f 0

Xi ■ i Pi .,^ a :«

Rl at

d -1 rfl

a' H H Tl

r^

. £3 F!

S .'• ti « i-i v.

B n ti o N £ ^ ti ♦'

+-J ?J ffl a > >

III

m?

2.0 10

0.9

0.8

0.7

0.6

CO 20.5 a oc

CO (DC

0.3

CO CO

CO 0.2

0.1

MEYER HARDNESS 2.1 2.2 2.3

COEFFICIENT 2.4 2.5 2.6

T T T T T

UTS TABOR1

1

CO 2 CO ' UJ

oc I- 00

CO CO

CO

o

0.1 0.2 0.3 0.4 0.5 0.6

WORK HARDENING COEFFICIENT

7

8

9

10

Figure 1. Predicted relationships between the stress/Vickers hardness ratio, the work hardening coefficient, and the Meyer hardness coefficient according to Eqs. 1, 3, 5 and 6.

15

■'f

a •>-.'-■•■ ''; ' ,- V4'

''■''

Mi"

b

Figure ?. Indentations male with a Sfflnj diameter ball in two of the alloys, showing ehe occurrence of artefacts similar in appc-arance tu deformation twins, (a) rri-13V-llCr-3Al; (b) Ti-5Ai-2.bSn. ^00

:.'.

0.34 CO CO

gE 0.28 CO

G.26

QC 0.32 <

CO

^ 0.30 K o

CO CO

—

UTS CÄH00N et al2

i

A

\ UTS TÄB0R1 A

^^

A

" v. ~ >^^ ——

A

. ^>~J f Z

\ ♦ ♦ ■ A _

mm \ A

YIELD STRESS \ _ CAH00N et al2

a

> A A

.\ ■0

o \ a — ^

\ V

.

o

c 0

a \ .

o a >y 1 i 1 i X"

- 2.8

0 0.02 0.04 0.06 0.08 0.10


* n CO 6Ai CO

co

3 2 co

- 3.4 CO

o 3.6 ^

3.8

Figure 3. Experimental stress/Vickers hardness ratios as a function of work hardening coefficient. The relationships predicted by Eqs. 1, 3 and 5 are shown. (For key to data symbols, see pg. 18).

17

Ti-13YHCr-3AI

Ti-6AI-4V

Ti-5AI-2.5Sn

STRUCTURE BEFORE EXTRUSION

0 0 + 0

o O

o <> O

CO CO

CO

0.34 r

0.32 -' CO GC LXJ

o 0.30

CO CO LU 0.28 -

0.26

- 3.0 co CO CO

CO CO

CO

o

Figure k.

2.0 2.1 2.2 2.3 2.4

MEYER HARDNESS COEFFICIENT

Experimental stress/Vickers hardness ratios as a function of Meyer hardness coefficient. The full lines indicate the relationships predicted by combining Eqs. 1 and 5, in turn, with Eq. 6. The filled symbols are for UTS/hardness and the open symbols ai ^ for yield stress/hardness. The key identifies the symbols us 3d in Figs. 3 through 8.

18

jj "ü 1 -

200 L ^— ̂mmmm ^ ^

^i'000***'^ &*

150 \Y f

150 - .|

g 100 Ul b

^ - ^

CO ^ -J UJ 50 - <r 3 cc f I 1

150 -

o 100

C

o^ c ^ y

50 « o

1 1 1 1 1 1 I

. E

0.02 0.04 0.06 0.08 %M

PLASTIC STRAIN

1.2

1.0

i.o

0.8

0.6

0.4

1.2

1.0

0.8

0.6

0.4

0.12

Figure 5. Comparison of true stress-true plastic strain curves with converted Meyer hardness data plotted according to Eqs. 8 and 9 for a typical specimen of each alloy: (a) Ti-13V-llCr-3Al (3375) (b) Ti-5Al-2.5Sn (3239) (c) Ti-6A1-1+V (3^81)

19

0.10 -

0.08 ae <

fe0.06

0.0* -

0.02 -

1 A \ ̂ /

<j>

M\ 1» \V /

k u

Q 1 A

rl 'r f ! I

U |

P"

f rl 5 | -A-

v- 1 r*

/ \ 1 ^ 1 Qs p i

/ A 1

s i o !> | A 1

r / 6 6 6 1

\/\ i 1 1 t 1 1 1 1 1 J 0 0.02 0.04 0.06 0.08 0.10


Figure 6. Uniform strain plotted against work hardening coefficient. Note that, while the full line refers to total strain, all the data points and the dashed lines refer to true plastic strain. (a) Uniform strain data derived directly from the chart record.

20

0 0.02 0.04 0.06 0.08 0.10 WORK HARDENING COEFFICIENT

Figure 6. Uniform strain plotted against work hardening coefficient. Note that, while the full line refers to total strain, all the data points and the dashed lines refer to true plastic strain, (b) Uniform strain derived by means of Ccnsidlre's construction.

21

SSBMHVH .3. lUMMOJI

CM «-I

«I sin i SS3S1S 013IA

CO

CM CM

CM I—

to

:UIUI/B)|

SSiMOMYH SlIBMOIA

Figvire 7- Yield and ultimate tensile stresses and Rockwell "C" hardness as a function of billet preheat temperature, after Gurney and Male6. Vickers hardness, determined in the present study, is also incorporated, (a) Ti-13V-llCr-3Al

22

SSSNOHVH .3. THMMOJI

l

•

/

1

0 (

i

CO

1 1

0 c -

// V 7 p

N

1/ / /■ if ^

1 1 1

1 ■ i 1

CM CM

CM

CO

«M

m sin 9 SSJHiS 013IA

ZUIUI/3)|

SSiNQHVH Sd3)i3IA

Figure 7. Yield and ultimate tensile stresses and Rockwell "C" hardness as a function of billet preheat temperature, after Gurney and Male6. Vickers hardness, determined in the present study, is also incorporated, (b) Ti-5Al-2.?Sn

23

ssiKosvH .3. mmm rsi

CM CM

CM

CO

m sin i SSU1S 013IA

CO

2UIUJ/B)|

SSBNQdVH

CM

S83M3IA

figure 7' Yield and ultimate tensile stresses and Rockwell "C" hardness as a function of billet preheat temperature, after Gumey and Male . Vickers hardness, determined in the present study, is also incorporated, (c) Ti-bAl-'+V

21*

z.uiN6oi 2

E E

c*»

CO

to O

» CO

CJ

CM CO

CO

CM CM *-4

!S)| SS3U1S 31ISN31 BiVIAIIiin

Figioi'e 8. Comparison of ultimata tensile stress/hardness correlations from the present work with those of Hickey9. The lines represent the relationship^), and 1 two standard deviations, given by Hickey. (a) UTS vs. Vickers hardness.

2S

2.uiN6oi 2

CO CO

CO

o

CO

5:

CO

o CO C»J

!S)i ssaais aiisNBi nvwinn Figure 8. Comparison of ultiüiate tensile stress/hardness correlations from the

present work with those of Kickey9. The lines represent the relationship(s), and t two standard deviations, given by Hickey. (b) UTS vs. Rockwell "C" hardness.

26

VII APPENDICES

7.1. Relation Betveen Uniform Elongation and n (See Ref. 3)

For those materials which obey Eq. 2 relating true stress and true strain

(a = KEn)

da „, n-1 n „ •r- " nKe = — a de E

(Al.l)

by differentiation. Also, by definition.

e • In (l+e) (Al.2)

where e = engineering strain. Therefore

de ■ de (1^)

(Al.3)

By combining Eqs. Al.l and Al.3

da de

n a e (l+e)

(Al.10

Comparison of Eq. Al.*! with Eq. A2.1+ of appendix 2, appropriate to peak load, gives

e

or u

e = n u

(Al.5)

27

where t is the total (i.e. elastic plus plastic) true strain at peak load. u

1.2. ConsidSre's Construction (See Ref. 5)

True stress a, load L, initial area A and engineering strain e are related by the equation

0=1 (l + e ) (A2.1) A o

Partial differentiation of this equation yields

12.- (H-e) SL + I|L_ (A2.2) 3e " A 3e A o o

At peak load, 3L/3e is zero so the Eq. A2.2 becomes

P- v n . = LU (A2.3) de peak load -r— o

where the suffix u indicates peak load. By the incorporation of Eq. A2.1,

— = 0u (A2 It) de peak load ; r W.*) e 1 + e u

The implication of Eq. A2.U is that a tangent to a curve of true stress vs. engineering strain, drawn from a point of strain -1, touches the curve at a point corresponding to peak load. This device is known as Considere's construction.

28

*»>mma :«Mi *i.Wvvm**f-*. Mfl iWI

7.3. Computer Program and Output for Brinell Test Data

C c c c c c c c c c

BRINELL HAROMESS

C C

C

C

20

21

THIS PROGRAM COMPUTES BRINELL AND MEYER HARDNESS VALUES AND RATIOS OF HARDNESS TO FLOW STRESS. IT USES A SERIES OF INDENTATI3N DIAMETERS AND FLOW STRESS VALUES AND GEN- ERATES DATA FOR INDENTER LOADS OF 5,10,20 AND kO KG.

♦

DIMENSION ANOIli ,W(*») DATA W/5.,10.,20.,^0./ FACTOR-l.<»2/2.S PI=3.m6 J=0 READ(5,1) L READS NUMBER OF DATA SETS REA0(5,2) 0 READS DIAMETER OF INDENTING BALL DSQRDsD*»2 DO 10 N=1,L READ(5,3) AND READS EXTRUSION NUMBER JsJ*l IF(J.EQ.2) GO TO 20 WRITE(6,4> AND GO TO 21 WRITE(6,5) AND J=J-2 WRITE(6,6) O WRITE(6,7) WRITE(6,8) WRITE(6,9) TOTALBsQ.O TOTALM'O.O 1 = 0 DO 10 M«l,^ " ' REA0(5,11) DELTA,SIGMAP READS INDENTATION DIAMETER AND FLOW STRESS AT EQUIVALENT PLASTIC STRAIN SQRsDELTA»»2 BRINELL = 2.0*WH)/(PI»D*(D-SQRT(DSQRD-SaR))) COMPUTES BRINELL HARDNESS VICOE" " ' ' AMEYERs<».0*W(M)/(PI»SQR) COMPUTES MEYER HARDNESS VALUE SIGESTB«BRINELL*FACTOR SIGESTMsAMEYER'FACTOR COMPUTE HARONESS/2.8 VALUES AND CONVERT TO KSI

29

^

IF(SIGMAP.EQ.O) GO TO 25 RATIOBaBRINElL/SIGMAP RATIOM=AMEYf.R/3IGMAP CALCULATE RATIOS OF HARDNESS TO FLOW STRESS RATIOXBsl.i»2»RATI0B RATI0XMsl.<»2»RftTI0M TOTALB=TOTALB*?ATIOB TOTALM«TOTALM+RATIOM DETERMINE RUNNING TOTALS OF VALUES OF «RATIOS* AND 'RATIOM* WRITE(6,12) W(H),DELTA,SIGMAP,BRINELL,RATI08,RATI0XB, fANEYER,RATIOH^ATIOXH,SIGESTB,SIGESTH IF(H-<») 10,30,30

25 WRITE(6,1J) W(i),DELTA,SRINELL,AMEYER,SIGESTB,SIGESTH 1 = 1*1 IF(N.LT.<») GO TO 10 RMEANM=TOTALM/<M-I) RMEANBsTOTALB/(M-I) GO TO 35

3ü RNEANBaTOTALB/M RNEANMsTOTALM/M DETERMINE MEAN VALUES OF «RATIOS« AND RATION«

35 XaMEAN=l.'»2»RMEANB XNMEAN=1.«»2»RMEANH WRITE(6,l<fr) RMEANe,XBMEAN,RMEANM,XMMEAN

10 CONTINUE 1 FORMAT (12) 2 FORMAT (1X,F3.1) 3 FORMAT (A10) k FORMAT (1H1///^,T12,»EXTRUSION NUMBER»,A10) 5 FORMAT (////,T12,»EXTRUSION NUMBER»,A10) 6 FORMAT (T12,»(3RINELL AND MEYER HARDNESS DATA, »,-Wl, ♦9H MM BALL)/)

7 FORMAT (T12,»LOAD»,T17,»INDENT.»,T25,»FLOW»,T31,»BRINELL», ♦ T'»0,»HB/SIG.»,T<»8,»HB/SIG.»,T58, »MEYER», Tb5,»HM/SIG.»,T 73, ♦•HM/SIG.»,T82,»HB/2.8»,T9 0,»HM/2.8»)

8 FORMAT (T18,»0IAM.»,T2'»,»STRESS»,T3i,»HARDNESS»,Ti»l,»MIXED», ♦ T<»8,»DIMEN-»,T57,»HARDNESS»,T66,»MIXED»,T73,»DIMEN-»)

9 FORMAT (T13,»K3»,T19,»MM»,T27,»KSI»,T'»1,»UNITS»,T*»8,»SIONLESS», fT66,»UNITS»,T73,»SI0NLESS»,T83,»<SI»,T91,»KSI»/)

11 FORMAT (1X,F5.3,1X,F5.1) 12 FORMAT (11X,F*».0,1X,F5.3,2X,F5.1,3X,F5.1,'»X,2(F5.3,3X) ,1X,

♦F5.1,3X,2(F5.3,3X),1X,2(F5.1,3X)) 13 FORMAT (11X,F1».0,1X,F5.3,2X,5H - ,3X,F5.1,'»X,2 (5H - ,3X),

♦1X,F5.1,3X,2(5H - ,3X),1X,2(F5.1,3X)) ik FORMAT (/T12,»*EAN VALUES»,18X,2(F5.3,3X,)9X,2(F5.3,3X))

STOP END

30

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on ^ «D in a) m in IM in cs • • • • • • • • • •

fv M K <r n; ifl M M TJ in oc ,r V 1^ Jf lf> «0 00 S, V) in K K <r i V * *** * Z V z ***i 14 *4

eo vo ni n> <r « K in N ro • • • • • • • • • •

(M 1-4 «o oo (r <r M M e ro in er V (0 ^ Ifi N. K S. V in N N. « n kf T4 ,4 *4 «H te * r4* r4 ■* X

V)

z

• to • (A O 1 M 2

UI fvj N «0 0D »4 19 1 Ul O CM T4 «D e -1 «0 oc J- «0 0^ M 2 -J (T O <T> 0" K

W UJ z <H CSJ in in fO (/) Ul Z CM «c m K in v r o • • • • • v r o • • • • • r M M M CM CO M CM X M M M CM CM CM CM I o Ul X Olfl

O O (/) M O ^ (T 4- O Of/) W CM * (T O M Ul K (VI T4 (T o «o M UIH ^H w M a> T^ ' V) X M in »OK or 10 M X W «o c «o cr on KM Z • • • • • KM Z • • • • • z r 3 <H H H .* ^-t r T 3 T^ TH TH Ti y>

z z ui en w w

CtUJ «0 H cr c £^ K 4 er in in 2 • • • • • • ■ • >- D o if\ tr «> V c «c in TH «c UJ or ff* r4 IT «O UJ a: <r 4 in öD r «r cvi ro »c rc T «t CM fO K) W

^ X 4m. X -i -i -1 tn -1 M «X • t/i < • CO ec O 1 Ul o to CJ *o OP CD IS 1 UJ

M 2 J 00 «C ^0 -H in

WZ -i in «o o K 4- N K 4" O n, r (/) UJ 2 ■H «M U> •<■ tn X 10 U) 2 CM in in K U\ r v r O • • • • • r V Z O • ■ • • m

on M M (Vi (VJ (VJ M CM CC M M CM (M CM <M CM e X o (^ o X c m •

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H MUJ 1- T4 (T U> «t in » M UJ »> O T4 IT a K ■I wx M in in K K i0 < VJ X M »0 « K CT N- H V M 2 • • • • • K X M 2 • • • • • « eo r 15 H iH r-t *-• r-t <r CC Z 3 «H T4 «■< i-t <rt a X o X

w </> 00 w V) _JV5 w -J tn Ui -JUJ O (r JT • UJ -1 UJ H <M 4- rc 2 UJZ • • • • 2 UJ z • • • • Q TO (T rH fO 4- o Z O N CM in ro K M Of «c ^t in in or M a 0" 4 4 N

in« a «i C\J M »O ^ tn « a «x CM M M 1*7 N X r x o i ff X fO w »o Q: w H f> or en H

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Cü M V\ <H T4 0> V V) ITN K 0^ O m * H X

V) • v>

O t UI cr ro vc IA »H H Z -i r« ^«O O a W UJ z e ro «o a u> X z o • ■ • • • Z M M ▼4 H <H (VJ M I D W

O Q (0 <0 If) J' CM N. M UJ K T4 fM r» <-( UN • V> X M K (T *< J- e N M Z • • • • • Z Z 3 ** w* M z

Ifl v>

a UJ u\ n o «o lüg • • • •

O J- *0 *> UK T< J- «0 fSJ z< T4 «H r4 (M ^* z

■J -1 Vi «t • C/) CD U I UJ ^ ro N «0 UN

M r -J O «0 O «5 J- r W UJ 2 e (M «0 «o 4 z N Z O • • • • •

CD M M «4 ^ «4 «^ *-» o z a to

•-• • OOP) K ^ CM <0 «e

r M UI »- o a ro CM M >* M K M K <r <-i ro o »- V H Z • • • • • * CD Z 3 •^ -« »H O Z

Vt (0 V) -J M u -1 UJ 0> «4 J- vH z UJ z • • • • o z o «o «4 cr in a M or O J- |V ^

ID «t a < «-««-• <H (M ro i CD z tu K» 0^ MM

UJ Z M W O ^( U> 0> or >- O bt ^ • • • • U) UJ -j a J sO 00 ■* m z U. h" in u> to «o z V) «H <H «-t «H z> o • z z H • CO

•a z z O N. O <M UJ z UJ < z * (TN N =) O -J O H Z CM CM ro * -J M -» z o • • • • < (^ Ui M > 3 Z Of M a • • • • z K DT « o U> e e e < x m o ^ <rt CM .» UJ UJ w «1 z

39

c

7.1*. Computer Programs for- Maulp.jlat.lun of Load-Elongation Data

♦♦♦♦»♦♦»♦♦»♦♦♦♦••♦♦♦♦••»♦•♦♦•♦•*••••*•♦♦♦»♦♦••♦•♦•♦♦♦•♦•♦•♦♦'

C ♦ C ♦ STRESS-STRAIN 3 (PLASTIC STRAIN» C * C • 1HIS PROGRAM CALCULATES ENGINEERING STRAIN, TRUE STRAIN, C • TRUE STKESS, LOGIO(TRU£ STRAIN), AND l.OG10{TRUE STRESS) C ♦ FROM CHART ELONGATION (IN INCHES) AND FROM LOAD VALUES C •

DIMENSION ANO(3) CHTFACT=2.86

C THIS FACTOR IS USED TO CONVERT CHART DISPLACEMENT, IN INCHES, C TO Y. ENGINEERING STRAIN FOR A UNIFORM SECTION LENGTH OF C 1.75 INCHES

REAO(5,ll)I C READS NUMBER Or DATA SETS

DO 2Ü M=1,I READ(5,8)AN0

C READS EXTRUSION NUMBER READ(5,1)L

C READS NUMBER OF CHART POINTS READ(5,3) AL0OELI.Q

C READS COORDINATES OF A POINT ON THE ELASTIC PART OF THE CHART READ(5i2) 0

C READS SPECIMEN DIAMETER WRITE(6,9)AN0 MRITE(6,12) WRITE(6,5) WRITE(6,6) WRITE(6,7) A = 3.1<»16»0»»2/!*. RATlO=DELL0/AL0 DO 20 N-1,L READ(5,3)AL,DELTAL

C READS COORDINATES OF A POINT ON THE CHART (LOAD IN LBS AND C DISPLACEMENT IN INCHES OF CHART)

ENG=(DELTAL-AL»RATIO)»CHTFACT C CALCULATES ENGINEERING STRAIN FROM TOTAL CHART INCHES BY FIRST C SUBTRACTING AN EXTRAPOLATION OF THE INITIAL LOADING CURVE

STRN=0.01»ENG TERMA=1,*STRN EPSILON*ALOG(TiRMA) SIGMA=0.001»AL»TERMA/A TERMB=ALOG10(EPSILON) TERMC=ALOG10(SIGMA) WRITE (6,<♦) AL,DELTAL,ENG,TERMA,SIGMA,EPSILON,TERMC,1ERMB

20 CONTINUE 1 FORMAT(I3)

1*0

.,^-»■.1 - — Ml. , , — ..—I

2 F0RMATUX,F5.3) 3 FORMAt<lX,F5.0,rx«F<»."2) k FORMAT(llX,F6.0«lX«F<».24lXfF6.2«lX,F6.3«lX,F6.1«lX«F6.3«2X« ♦F6.3«2X,F6.3)

5 FORMAT (T12,»LOAD»♦Tldt»CHART»,T26,"ENG.»,133»♦!+£♦,T39,»TRUE»♦ ♦ T<»6,»TRUE»<T53,»LOG10»,T61,»LÖG10»)

6 FORHATIT18,»EL3NG.»,125,»STRAIN»,T3ä,»STRESS»,ff5,»STRAIN», «•T53,*STRESS»,T61, »STRAIN»)

7 FORHAT(T12,»LBS.»,T19,»INS.»,T27,»7.»,T39,»KSI»/) 3 FORHAT(A10,A10,A10) 9 F0RMAT(1H1,//////T12,»EXTRUSION NUHBER»,3A10)

11 FORHATCI2) 12 FORMAT(T12,»( »LASTIC STRAIN >»/)

CONTINUE STOP END

Ul

\

c • ♦ C • STRESS-STRAIN 2 (CORRECTED TOTAL STRAIN) * C ♦ • C * THIS PROGRAM CALCULATES ENGINEERING STRAIN« TRUE STRAIN, » C * TRUE STRESS, LOGKMTRUE STRAIN), AND LOGiO(TRUE STRESS) • C * FROH CHART ELONGATION (IN INCHES)' AND FROH LOAD VALUES * C ♦ • C ******** ***************************************** ************

DIMENSION ANO<3) CHTFACT»2.86

C THIS FACTOR IS USED TO CONVERT CHART DISPLACEHENT, IN INCHES, C TO */. ENGINEERING STRAIN FOR A UNIFORM SECTION LENGTH OF C 1.75 INCHES

REA0(5,11)I C READS NUHBER OF DATA SETS

DO 20 H=l,I READ(5,8)AN0

C READS EXTRUSION NUHBER READ(5,1)L

C READS NUMBER 0- CHART POINTS REA0(5,3) AL0,3ELL0

C READS COORDINATES OF A POINT ON THE ELASTIC PART OF THE CHART READ(5,2) 0

C READS SPECIMEN DIAMETER HRITE(6,g)AN0 WRITE(6,12) WRITE(6,5) WRITE(6,6) WRITE(6,7) RATIO=OELL0/AL0 " A=3.1'»16»D*»2/l». E=16.5 E6 AEINV-1./(A«E) DO 20 N=1,L READ(5,3)AL,0ELTAL

C READS COORDINATES OF A POINT DN THE CHART (LOAD IN XB3 AND C DISPLACEMENT IN INCHES OF CHART)

ENGs(DELTAL-AL»RATIO)»CHTFACT+AL»AEINV»100. C CALCULATES ENGINEERING STRAIN FRON TOTAL CHART INCHES BY FIRST C SUBTRACTING AN EXTRAPOLATION OF THE INITIAL LOADING CURVE. C ELASTIC STRAIN IS ESTIHATED FOR E ■ 16,500 KSI AND IS ADDED TO C THE PLASTIC STRAIN DETERHINEÜ FROH THE GHAUT. THE STRAIN TS— C THEN AN ESTIHATE OF 'TOTAL CORRECTED STRAIN'

STRN«0.01*CNG TERMAsl.^STRN EPSILON«ALOG(TERMA) SIGMA-0.001*AL»TERMA/A

U2

TERNB«AL0610 lE'SILON) TERHCsALOGlO(SIGNA) WRITE (6«<♦) AL,OiLTAL»ENG,TERHA,SIGMA,EPSILON,TERMCTERMB

20 CONTINUE 1 FORMAT(I3) 2 F0RMATI1X,F5.3» 3 FORMAT(1X,F5.0,1X,F<*.2) I» FORMAT(liX,F6.0,lX,F«».2,iX,F6.2,lX,F6.3,lX,F6.1,lX,F6.3,2X, ♦F6.3,2X«F6.3)

5 F0RHAT(T12,»LOAD»,T18,»GHART»»T26,»ENG.♦,T33,n*E»,T39,»TRUE», ♦ T«»6,»TRUE»,T53,»LOG10»,T61,»LOG10»)

6 FORNAT«T18,»EL0NG.»fT25,»STRAIN»,T38,»STRESS»,T<»5,»STRAIN», ♦T53,»STRESS»,T61,»STRAIN»)

7 FORNAT(Tl2,»LBS.»,Ti9,»INS.»,T27,»y.»,T39,»KSI»/) 8 FORNAT(A10,A10,A10) 9 F0RNAT(1H1,//////T12,»EXTRUSION NUMBER»,3A10)

11 FORNAT(I2) 12 FORMAT(T12,»< :ORRECTED TOTAL STRAIN )♦/)

STOP END

1*3

\

■ .

Ill: Output From Programs of Appendix h

EXTRUSION NU'IBER 33/5 ( PLASTIC SWAIN )

LCAH 3HART tNGi Ut TRJE JRUZ LOG 10 -OG10 £LilNG. STRATI STRESS STRAIM STRESS STRAIN

LDS. INS. V. KSI

ItflOO. 2.51 .12 1.001 i7«t.ei .001 2.2i»3 -2.938 t7200. ?.71 .52 1.005 179.7 .005 2.255 -2.286 17ttQ0. 2.91 1.01 1.010 182.7 .010 2.262 -1.999 17S00. 3.12 1.52 1.015 135.7 .015 2.269 -1.820 17750. 3.31 2.00 1.020 188.2 .020 2.275 -1.702 17800. 3. b 1 2.^b 1. 0 2ö 189.7 .0 25 2.278 -1.599 1790G. 3.71 3.0=) 1.031 191.9 ,030 2.283 -1.517 1 ft 0 0 G . 3.91 3.62 1.035 193.9 .036 2.2d? -mso 16100. I*.12 (♦.17 1.0 HZ 195.0 .Otfl 2.292 •1.388 1^200. (». U 1+.S7 i.0^7 198. ü .OWä 2.297 -1.3U0 18300. U.51 5.20 1.052 200.1 .051 2.301 -1.295 Ift300. ^.71 5.7^ 1.058 201.2 .056 2.301+ -1.251 1P 3 0 0 . H.91 6.35 1.0o3 202.3 .062 2.306 -1.211 Ie300. 5,12 •i.95 1.0b9 2 01. «♦ .067 2.308 -i.173 lf.200. 5.31 7.5 3 1.075 2 0 i . '4 .073 2.308 -1.139 i«ion. i.51 «.15 1.0^1 203.5 .078 2.303 -1.106 17750. 5.71 8.«7 1.089 200.9 .095 2.303 •1.071 16500. 6.02 10.28 1.103 199.1 .098 2.277 -1.009

kk

EXTRUSION NUMBER 3103 ( PLASTIC STRAIN )

LOAD CHART cNG. 1+E TRUE TRUE L0G10 .0510 ELONG. STRAIM STRESS STRAIN STRESS STRAIN

LBS. INS. '/. KSI

1^550. 2.81 .13 1.001 166.5 .001 2.221 -2.880 16900. 3.01 .5ft 1.005 170.7 .005 2.232 -2.271 17200. 3.20 .91+ 1.009 17<*.«» .004 2.242 -2.030 msrj. 3.^1 1.'42 i.01<* 177.9 .014 2.250 -1.851 17652. ^.61 1.89 1.019 160.7 .019 2.257 •1.727 17775. 3.81 2.<tl 1.021» 182.9 .02^ 2.262 -1.624 17900. '».01 2.92 1.0 29 185.1 .029 2.267 -l.S^l 18000. «♦.21 3.«*£f 1.03^ 187.1 .034 2.272 -1.470 18100. if .<♦! 3.97 l.Oi+O 189.1 .039 2.277 -l.«flO 18150. h.bi <*.52 1.0^5 190.5 .0i*(* 2.280 -1.355 18175. «♦.81 5.03 1.051 191.9 .050 2.283 -1.305 18200. 5.01 5.6^ 1. 056 193.1 .055 2.286 -1.261 18250. 5.21 6.18 1.062 194.7 .060 2.289 -1.222 18250. 5.<»1 6.76 1.063 195.7 .06'? 2.292 -1.185 18200. 5.bl 7.35 1.07^ 196.3 .071 2.293 -1.149 18100. 5.81 7.97 1.030 196.3 .077 2.293 -1,115 18000. 6.01 8.59 1.086 196.1. .082 2.293 -1.084 16500. 6.52 10.77 1.108 183.5 .10? 2.26^ -.990

»»5

1 EXTRUSION NUMBtR 3272 f ( DLASTIC STRAIN )

| LOAD 3HART ENG. IfE TR'JE TRUE LOG10 .OG10 ELONG. STRAIM STRESS STRAIN STRESS STRAIN

1 LBS. INS. 7. <SI

17500. 3.57 .<t0 1.00<» 173.5 .00(* 2.239 -2.398 | 17550. 3.77 .89 1.009 175.9 .009 ?.2«t5 -2.053

17780, 3.97 1.39 LOU 178.1 .ou 2.251 -1.861 | 179 00. ^.17 1.89 1.019 180.2 .019 2.255 -1.727

18000. u.37 2.*1 1.021* 182.1 .024 2.260 -1.623 18100. '♦.57 2.92 1.0 29 m.o .029 2.255 -1.540 18150. (♦.77 3.*»7 1.035 185.5 .03(» 2.268 -1.467 16160. «♦.97 <*.Q2 l.Q<*0 185.8 .039 2.271 -1.404 18200. 5.17 H.58 1.0^6 183.0 .045 2.274 -1.349 18200. p. 37 5.15 1.052 189.1 .050 2.277 -1.299 18180. 5.57 5.7<« 1.057 189.9 .056 2.279 -1.253 18150. 5.77 6.33 1.063 190.7 .061 2.280 -1.212 18100. 5.97 b.93 1.069 191.2 .067 2.281 -1.174 U500. 7.01 10.71» 1.107 181.5 .102 2.259 -.991

1*6

■HM

EXTRUSION NUMBtR 33d5 ( PLASTIC STRAIN )

LOAD CHART ENG. !♦•£ TRUE ™UE LOG10 .OG10 ELONG. STRAIM STRESS STRAIN STRESS STRAIN

LBS. INS. */. KSI

1*550. 2.72 .15 1.002 166.5 .002 2.221 -2.800 1C900. 2.92 .57 1.006 170.9 .006 2.232 -2.2<*6 17150. 3.12 1.03 1.010 17<*.l .010 2.2i»l -1.991 17!»50. 3.32 l.Hb 1.015 177.9 .011» 2.250 -1.839 17&50. 3.5? 1.9«» 1.019 180.8 .019 2.257 -1.716 17750. 3.72 2.^7 1.025 182.7 .02<* 2.262 -1.613 17900. 3.92 2.97 1.030 185.2 .029 2.266 -1.53<» Ib050. '4.12 3.«»7 1.035 187.5 .03<t 2.273 -l.i»67 18125. «♦.32 <*.01 1.0<*0 189.tf .039 2.277 -l.<*05 1P200. f+.52 <*.55 1.0 <t5 191.2 .0(»<f 2.281 -1.352 18275. H.72 5.09 1.051 192.9 .050 2.285 -1.305 16300. ^♦.92 5.6<f 1.055 19«».2 .055 2.288 -1.260 18350. 5.12 6.19 1.062 195.8 .060 2.292 •1.221 1R350. 5.32 6.77 1.068 195.8 .065 2.29<t -1«18<» 18300. 5.52 7.36 1.07'* 197.<♦ .071 2.295 -1»1*»9 18250. 5.72 7.95 1.080 197.9 .077 2.297 -1.116 18075. 5.92 8.61 1.0 86 197.2 .083 2.295 -1.083 17700. 6.13 9.38 1.09t 19-*.5 .090 2.289 -1.0<*7

hi

EXTRUSION NUMPtR 33.31 ( PLASTIC STRAIN )

LCAD ^HART ENG. If E MUE TRJE LO&10 .OGin £LONG. STRAIM STRESS STRAIN STRESS STRAIN

LRS. INS. '/. <SI

15700. ?.l« .«♦1 1.00^ 165.7 .00'-» 2.219 -2.«»01 11900. ?. 37 .87 1.009 168.6 .0 01 2.227 -2.06k It250. 2.56 1,21 1.013 173.0 .013 2.238 -1.396 leuoo. 2.77 1.82 1.019 175.6 .013 2.24 k -1.7k3 11500. 2.97 2.36 1.02^ 177.6 .023 2.2k9 -1.632 if^no. 3.17 2.85 1.029 180.5 .023 2.257 -1.550 if «00. 3.37 3.39 1.034 182.5 .033 2.262 -l.k77 16900. 3.57 3.93 1.0 39 134.7 .039 2.266 -l.klk 17000. 3.77 i»»«»6 1.045 186.7 ,0k* 2.271 -1.360 17100. 3.97 5*00 i.asn 183.8 .0^9 2.276 -1.312 17150. ^.17 5.55 1.055 190.3 .03k 2.279 -1.268 17200. t».37 5.10 1.061 191.9 .059 2.233 -1.227 17200. «♦.57 6.63 1.067 192.9 .063 2.235 -1.190 17200. k,77 7.23 1.072 193.9 .070 2.288 -1.155 17200. «♦.97 7.82 1.073 195.0 .075 2.290 -1.123 lf.700. 5.0^ 8.32 1.083 190.? .080 2.279 -1.097

kQ

EXTRÜSION NUMBER IZkb ( PLASTIC STRAIN )

LOAD 3HART £NG. 1+E TRJ£ TRJE LOG10 .0510 iLONG. STRAIN STRESS STRAIN STRESS STRAIN

LBS. INS. '/. KSl

12700. 2.10= .09 1.001 130.5 .001 2.116 • •3.068 12700. 2.21 ,i*0 1,0 Qk 131.0 .004 2.117 • •2.399 12500. 2.<tl .93 1.009 132.8 .009 2.123 « •2.036 12870. 2.61 l.tf6 1.015 134.2 .013 2.128 • •1.837 12900. 2.fll 2.02 1.020 135.2 .020 2.131 • •1.698 12970. 3.01 2.56 1.0 26 135.7 .025 2.135 • •1.597 13000. 3.21 3.12 1.031 137.8 .031 2.139 • •1.512 13010. 3.<*1 3.69 1.037 139.6 .036 2.U2 • •1.441 13370. 3.61 «♦.23 1.0<*2 140.0 .041 2.146 • •1.383 13060. 3.81 <».80 1.048 140.9 .0t»7 2.149 • •1.329 13080. (f.01 5.37 1.054 141.6 .052 2.151 ■ •1.281 13080. **.21 5.94 1.059 142.<* .053 2.154 • •1.239 13075. (».m 6.52 1.065 143.1 .063 2.156 • •1.200 13050. (».61 7.10 1.071 143.S .069 2.157 • •1.164 13013. <*.81 7.69 1.077 14(*.0 .07«» 2.158 • •1.130 13000. 5.01 8.27 1.083 144.6 .079 2.160 • •1.100 12280. 5.91 11.18 1.112 140.3 .105 2.147 -.975 10300. 6.43 Ik.bk 1.146 123.7 .137 2.092 -.864

U9

\

rXTPÜSlDN NimtR 3'4 äl ( PLASTIC STRAIN »

LOAD CHART ENG. l*E T^UE TRUE LOCIO .OGIO ILONG. STRAIM STRiSS STRAIM STRESS STRAIN

LÖS. INS. X <3I

1^000. ?.16 .05 l.OQl i^s.g .001 2.158 -3.288 m200. 2.31 .39 l.OOJf l^o.5 .00'« 2.166 -2.i»05 1^700. 2.53 .80 1.004 152.3 .008 2.183 -2.097 l^BOO. 2.73 1.33 1.013 15*t.l .013 2.188 -1.878 1C900. 2.95 1.92 1.011 156.0 .019 2.193 -1.721 i^gto. 3.15 2.tf7 1.0 25 157.V .02^ 2.197 -1.513 1&000. 3.35 3.02 1.030 158.8 .030 2.201 -1.527 leooo. 3.51 3.^7 1.035 159.5 .03^ 2.203 -l.'»66 IflOO. 3.77 ■♦.17 i.Ok? 161,6 .fli+l 2.209 -1.388 11190. 3.97 «♦.71 1.0^7 163.'■» .0(*6 2.213 -1.337 IflOO. !t.l6 5.29 1.053 163.!♦ .052 2.213 -1.^88 15100. if.36 5.85 1.059 loi+.S .057 2.216 -l*Zkk 15100. t».58 6.t9 1. Oo5 165.2 .063 2.218 -1.201 15100. »♦.88 7.35 1.073 165.6 .071 2.222 -i.i^g UOOO. 5.37 8.79 1.0 88 157.7 .08^ 2.225 •1.07t» IWfiOO. 5.86 10.28 1.103 167.7 .098 2.225 -1.009 IUWOO. 6.17 11.35 1.113 16'«.8 .107 2.217 -.969 1^000. 6*i*0 12.18 1.122 161.1» .115 2.208 -.9«»0 13100. 6.75 13.-37 1. 1 SS 152,9 .127 2.18t» -.895

50

EXTRUSION NUMBER 31o9 ( PLASTIC STRAIN )

LOAD CHART ENG. 1*£ T^'JF TRUE LOG10 .OG10 ELONG. STRAIN STRESS STRAIM STRESS STRAIN

LBS. INS. */. KSI

1P70G. 2.10 .23 1.002 134.6 .002 2.129 -2.537 1?600. 2.23 .65 1.006 134.1 .006 2.127 -2.190 12610. 2.51 i.(*<* 1.014 135.3 .014 2.131 -1.843 12620. 2.91 2.59 1.0 26 136.9 .026 2.136 -1.593 12650. 3.20 3.^0 1.034 138.3 .033 2.141 •1.476 12700. 3.it0 3.95 1.039 139.6 .039 2.145 -1.412 12700. 3.61 ^.55 1.045 140.4 .044 2.147 -1.352 12700. 3.60 5.09 1.051 141.1 .050 2.150 -1.304 12700. (».00 5.66 1.057 141.9 .055 2.152 -1.259 12680. 4.20 6.25 1.06? 14?. 5 .061 2.154 -1.218 12650. i*.<*Q 6.S3 1.0 69 142.9 .066 2.155 -1.180 12590. <4.60 7.^3 i.07«f 143.0 .072 2.155 •1.145 i2*qo. t».81 8.0» 1.091 142.7 .078 2.155 -1.110 12300. 5.51 10.17 1.102 143.3 .097 2.156 -1.014 9700. 6.5U 1^.29 1.143 117.2 .134 2.069 -.874

51

.

fXTRUSION NUMBER 32 35 ( PL4STIC STRAIN )

LOAD ^HART LNG. UE TR'JE TRJE LOG10 .OG10 ü'LOMG. STRAIN STRESS STRAIN STRESS STRAIN

LBS. INS. */. KSI

1?300. 1.69 .01 1.000 127.0 .000 2.10«» -«♦.I'tb 13I+50. l,$k .07 1.0Ü1 13Ö.7 .001 2.136 •3.159 1U100. 2.25 .99 1.010 l^**^ .010 2.160 -2.006 1U300. 2.«*6 1.51 1.015 1U7.5 .015 2.169 -1.823 UUOO. 2.65 2.02 1.0 20 li»9.S .020 2.17«» -1,699 l^^^O. 2.R7 2.63 1.0 23 150.7 .025 2.178 -1.586 1^^50. 3.06 3.17 1.032 151.5 .031 2.1R0 -1.505 1*4^50. 3.?6 3.7W 1.037 152.3 .037 2.183 -1.U35 iui*5f\. 3.H6 «♦.32 1.0H3 153.2 .0«*2 2.1^5 -1.374 mso. 3,bb ^.89 1.0<»9 15i».0 .OkA 2.187 -1.321 1U500. ii.33 b.79 1.06 3 157.3 .065 2.197 -1.1S3 l^SOQ. 5.50 10.13 1.101 16?.2 .097 2.210 -1.015 1<*200. 5.76 10.99 1.110 160.1 .104 2.20i* -.982 1U000. 5.46 11.6<* 1.116 151.P .110 2.201 -.95 8 12750. 6.53 13.75 1.136 11*7.it .129 2.158 -.890 12700. ü.^sn 13.97 1.1**0 U»7.1 .131 2.168 -.863

52

EXTRUSION NUMBER 5?39 ( PLASTIC STRAIN )

LOAD CHART ENG. l*c. TRUE TRUE Lyr.io -OGlfl ZLONG. STRAIN STRESS STRAIN STRESS STRAIN

LPS. INS. y. <SI

11100. 1.9<* .35 1.003 123.«. .003 2.091 -2.«»57 iiaqo. 2.1^ .83 1.008 125.1 .003 2.101 -2.081 11390. ?.35 1.39 1.0 1<» 127.9 .01«» 2.107 -1.861 II^IO. 2.55 1.95 1.019 128.9 .019 2.110 •1.711» 11500. 2.7<* 2.^5 1.025 130.5 .02«» 2.116 -1.616 11550. 2.9«» 3.00 1.030 131.8 .030 2.120 -1.529 11500. Z,ik 3.55 1.035 133.1 .035 2.12«» -l.«»58 11610. 1,31* «♦.12 l.O^l 133.9 .0«»0 2.127 -1.39«» 11660. 3.5«* (».65 1.0<»7 135.«» .0<»5 2.132 -1.3«»2 11700. 3.73 5.19 1.052 135.«» .051 2.135 -1.296 11710. 3.9«» 5.78 1.058 137.2 .056 2.137 -1.250 11730. (».13 6.3? 1.063 138.2 .061 2.1«»0 -1.213 11730. k,Si* 6.92 1.069 135.0 .067 2.1'»3 -1.175 11730. k»5k 7.<*9 1.0 75 139.7 .072 2.1«»5 -i.m 11700. k*7f* d.08 1.081 mo.i .078 2.1«»6 -1.11Ü 11600. 5tU 9.27 1.093 l^O.«» .089 2.H»7 -1.052 1U00. 5.5«» 10.51 1.105 139.6 .100 2.1«»5 -1.000 11010. 5.9U 11.83 1.118 136.<» .112 2.135 -.951

88Ü0. 7.1<» 16.30 1.163 113.«» .151 2.055 -.821

33

■

EXTRUSION NUMBER 3?.kl ( PLASTIC STRAIN )

LOAD CHART ENG. UE TRJE TRUE LOG10 -0610 £LONG. STRAH STRESS STRAIN STRESS STRAIN

LBS. INS. */. <SI

12680. 2.09 .21 1.002 132.8 .002 2.123 -2.676 12800. 2.29 .73 1.007 13'+.8 .007 2.130 -2.139 12880. 2.51 1.32 1.013 136.(» .013 2.135 -1.882 12950. 2.70 1.83 1.018 137.9 .Old 2.139 -1.741 13000. 2.90 2.38 1.02t» 139.1 .02V 2.143 -1.628 13080. 3.10 2.92 1.0 29 1*0.7 .029 2.1*8 -1.541 13110. 3.29 3.^5 1.03I* lui.8 .03* 2.152 -1.470 13120. 3.«»9 (».02 1.0<»0 l't2.7 .039 2.15'» -1.405 13120. 3.69 i*.59 1.0 i+o 1*3.t» .0*5 2.157 -1.348 13100. 3.90 5.20 1.052 l^.l .051 2.159 -1.295 13080, ^♦.09 5.75 1.057 ik^.b .056 2.160 -1.253 13000. i».28 6.33 1.0o3 ikh,? .061 2.160 -1.212 12800. «♦.68 7.55 1.076 1<»3.9 .073 2.158 -1.137 11100. 5.95 11.97 1.120 129.9 .113 2.114 -.947

^

mm ■

EXTRUSION NUMBER 3243 ( PLASTIC STRAIN )

LOAD CHART ENG. !<•£ TRUE TRUE LOG10 .0310 EL0N6. STRAIN STRESS STRAIN STRESS STRAIM

LBS. INS. X KSI

11800. 1.98 .09 1.001 127.8 .001 2.107 -3.025 12100. 2.10 .30 1.0 03 131.3 .003 2.118 -2.529 12250. 2.30 .80 1.008 133,6 .008 2.126 •2.100 12310. 2.50 1.3<» 1.013 135.0 .013 2.130 -1.875 12<*00. 2.70 1.87 1.019 136.7 .019 2.136 -1.732 12(»30. 2.90 2.M 1.02(f 137.8 .02e» 2.139 -1.520 12510. 3.10 2.96 1.030 139.<♦ .029 2.1M* -1.535 12550. 3.30 3.52 1.035 U0.5 .035 2.1<*8 -l.'»62 12600. 3.50 <».06 1.0<»1 i^i.g .0^0 2.152 •l.<*00 12600. 3.70 <*.&(» 1.0<»6 1«»2.7 .01*5 2.15«» -1.3«»«» 12S00. 3.90 5.21 1.052 t(»3*S .051 2.157 -1.29«» 12580. <*.20 6.08 1.061 1^.«» .059 2.160 -1.229 12500. <*.50 6.97 1.070 I'f'»^ .067 2.160 •1.171 12200. (f.90 8.26 1.083 l<f2.9 .079 2.155 -1.101 10900. 5.90 11.73 1.117 131.8 .111 2.120 -.955

55

CXTRUSrON NUMBER 3?3«» ( PLASTIC STRAIN )

L.CAD :HAPT ENG. !♦£ TRJE TRJE LOS10 -OG10 ELONG. STRAIM STRiSS STRAIN STRESS STRAIN

LFS. INS. */. <sr

i?oon. 2.00 .02 1.000 12it.O .0110 2.094 -3.641 12U0Q, 2.21 .43 1.004 128.7 .004 2.110 •2.364 12500. 2.<40 .93 1.0 09 130.1» .009 2.115 -2.0 34 1?580. 2.61 1.49 1.015 131.9 .0J5 2.120 -1.829 12600. 2.79 2.00 1.0 20 132.8 .020 2.123 -1.704 12620. 3.01 2.62 1.026 133.8 .025 2.127 -1.588 12580. 3.21 3.16 1.032 135.2 .031 2.131 -1.507 12690. 3.^0 3.70 1.037 13Ö.C .035 2.134 -1.440 12960. 3.61 4.17 1.042 139.5 .041 2.145 -1.389 12690. 3.80 4.84 1.048 137.5 .047 2.138 -1.325 126B0. d.OO 5.H2 1.054 139.1 .053 2.140 -1.278 12600. «♦.30 5.32 1.063 138.4 .051 2.141 •1.213 IP^OO. (*.80 7.84 1.073 138.2 .0 75 2.141 -1.122 12200. 5.01 8.54 1.085 136.8 .082 2.136 -1.087 10700. 6.00 12.08 1.121 123.9 .114 2.093 -.943

56

wmm

EXTRUSION NUMRER 31 Vf ( OLASTIC STRAIN )

LOAD "HART ENG. H-E TRJE TRUE LOG1D .OG10 SLONG. STRAIN STRESS STRAIN STRESS STRAIN

LPS. INS. X KSI

12i00. 1.75 .10 1.001 123.9 .001 2.110 -2.983 12700. 1.95 .6<» 1.005 130.5 .003 2.115 -2.197 12300. 2.15 1.17 1.012 132.3 .012 2.122 -1.93(» 12900. 2.35 1.70 1.017 13^-1 .017 2.127 -1.772 13000. 2.55 2.2'+ 1.022 135.8 .022 2.133 -1.655 13100. 2.75 2.77 1.026 137.5 .027 2.138 -1.561» 13200. 2.95 3.30 1.0 33 139.3 .032 2.U* -l,i*83 13200. 3.15 3.87 1.039 IHO.1 .033 2.146 -l.<*20 13200. 3.35 «♦.«♦S 1.0^ 1^0.9 .0>m 2.U9 -1.361 1320r. 3.55 5.02 1.050 im.o .DM 2.151 -1. 310 ISlfJ. 3.75 5.63 1.056 1^1.«♦ .055 2.150 -1.261 13100. 3.95 o.20 1.062 ik2,2 .060 2.153 •1.221 13000. '♦.IS b.81 1.063 1^1.9 .066 2.152 -1.181 12800. «♦.IS 7.^6 1.075 1«*0.5 .072 2.1^8 -1.1<»3 llbOQ. 5.36 10.87 1.109 131.1* .103 2.119 -.986

57

EXTRUSION MUMPER 317<» ( PLASTIC STRAIN )

LOAD CHART ENG. IfE TRJE TRJE L0310 .0510 ELONG. STRAIN STRESS STRAIN STRESS STRAIN

LRS. INS. */. <SI

1?700. ?.12 .25 1.003 130.1 .003 2.114 •2.600 1P700. 2.33 .85 1.009 130.9 .008 2.117 -2.071 12700. 2.^3 1.^2 I.OIV 131.3 .014 2.119 -1.849 12750. 2.13 .26 1.003 130.6 .003 2.116 -2.590 12750. 2.93 2 >5 1.025 133.6 .025 2.126 -1.600 12750. 3.13 3.12 1.031 134.3 .031 2.128 -1.513 12800. 3.33 3.67 1.0 37 135.6 .035 2.132 -1.444 12800. 3.53 «♦.2<* 1.0it2 135.3 .042 2.135 -1.382 12800. 3.73 «♦.81 l.O^B 137.1 .047 2.137 •1.328 12800. 3.93 5.38 1.05«» 137.8 .052 2.139 -1.280 12800. ^.13 5.95 1.060 138.5 .058 2.142 -1.238 12800. «♦.33 6.53 1.065 139.3 .063 2.144 •1.199 12800. <f.53 7.10 1.071 HfO.i .069 2.146 •1.164 12900. ^.73 7.67 1.077 140.8 .074 2.149 •1.131 12800. U.93 8.2«« 1.082 141.6 .079 2.151 •1.101 12800. 5.13 8.81 1.088 142.3 .084 2.153 •1.073 12500. 5.33 9.<t8 1.095 140.9 .091 2.149 -1.043 12(f00. S.53 10.1«» 1.101 139.6 .097 2.145 -1.015 10000. 6.92 15.22 1.152 117.7 .142 2.071 -.849

58

■MMMOWMnMna »■ill- HI ii ■ ■■ ■ —

EXTRUSION NUMBER 3i»75 ( -'LASTIC STRAIN )

LOAD CHART ENG. 1*E TRUE TRUE LOG10 -OG10 cLONG. STRAIN STRESS STRAIN STRESS STRAIN

LBS. INS. X <SI

UkOO. 2.31 .02 1.000 1«»3.1 .000 2.156 -3.766 U790. 2.51 ,kl 1.00^ 1W7.5 .00<» 2.169 -2.387 l&OOO. 2.73 .9«» 1.009 150.(♦ .009 2.177 -2.027 1P100. 2.99 1.6(4 1.016 152.5 .016 2.183 -1.788 15200. 3.21 2.23 1.022 ISh.k .022 2.189 -1.657 15220. 3.U1 2.79 1.023 15-5.1» .027 2.191 -1.561 15290. 3.61 3.33 1.033 157.0 .033 2.196 -l.^S 15300. 3.81 3.90 1.039 157.9 .033 2.198 •i,kl6 15320. (t.ll *,fk 1.0'♦7 IS^.U .0<»6 2.203 -1.33'» 15350. «f.31 5.30 1.053 160. S .052 2.206 -1.287 15360. (».52 5.90 1.059 161.5 .057 2.208 -1.2<»1 15350. (♦.70 5.^2 1.06'* 162.3 .062 2.210 -1.206 15350. ^^l 7.02 1.070 163.2 .063 2.213 •1.169 15350. 5.11 7.59 1.076 16<f.l .073 2.215 -1.136 15300. 5.30 8.16 1.082 ibk.k .078 2.216 -1.106 15300. 5.60 9.01 1.090 165.7 .086 2.219 •1.06(» 15200. 5.92 9.98 1.100 166.1 .095 2.220 -1.022 15000. b.Ok 10.(»1 l.lOi» 16'».5 .099 2.216 -l.OOi* l^OO. 6.68 13.09 1.131 161.8 .123 2.209 -.910 12000. 7.8t» 16.93 i..l69 139.«♦ .156 2. U<f -.806

59

I-XTRUSION NUM ■'--! n «♦1 ( CCRP •ICTEO T OVAL STRAIN )

LOAD CHAM .NG. 1+c TRUE TRUE I.OGIO LOG10 ELONG. cTf<AIM STRESS STRAIN STRESS STRAIN

LBS. INS. '/. KSI

125 00. 2.00 .83 1.008 131.7 .008 2.120 -2.084 12700. 2.10 1 .04 1.010 134.1 .010 2.128 -1.987 127S0. 2.20 1 .30 1.011 135.0 .013 2.130 -1.888 1?8C0. 2.30 1.57 l.Oln 135.9 .016 2.133 -1.803 12d50. 2.40 1.63 1.01S 136.6 .018 2.136 -1.740 12900. 2.^0 '.10 1.021 137.7 .021 2.139 -1.682 IP^^O. 2.B0 .'.37 1.0 24 13H.6 .023 2.142 -1.631 12975. 2.70 ?.64 1.0 25 139.2 .026 2.144 -1.583 12990. 2.80 2.9? 1.029 139.8 .029 2.145 -1.540 13010. 2.90 3.20 1.0 32 140.4 .0 32 2.147 -1.501 13025. 3.00 3.H6 1.033 140.9 .034 2.149 -1.466 13050. 3.10 3.7ft 1.038 141.5 .037 2.151 -1.433 13075. 3,20 ♦ .03 1.040 142.2 .040 2.153 -1.403 13100. 3.30 ■♦.31 1.043 142.8 .042 2.155 -1.375 13125. 3.40 4.59 1.046 143.5 .045 2.157 -1.343 13150. 3.50 4.86 1.049 144.1 .047 2.159 -1,323 13150. 3.60 5.15 1.051 144.5 .050 2,160 -1.299 13150. 3.70 ; .4^ 1.054 144,9 .053 2,161 -1.276 13150. 3.89 5.72 1.057 145.3 .056 2,162 -1.255 17125. 3.90 b.02 1.060 145.5 .053 2.163 -1.233 13100. H.00 o.31 1.063 lH5.b .061 2.163 -1,213 13075. «♦.10 6.61 1.066 145.7 .064 2.163 -1,194 13050. «♦.20 ( .90 1.069 145.8 ,067 2.164 -1,175 13025. 4.30 ^.20 1.07? 146.0 .070 2.164 -1,153 12975. «♦.«♦0 7.51 1.075 145.8 .072 2.164 -1,140 12925. «».50 7.81 1.0 78 145.7 .075 2.163 -1,124 12875. 4. to 4.12 1.0 81 145.5 .074 2.163 -1.103 12825. 4.70 a.42 1.084 145.4 .081 2.162 -1.092 12725. u.ao .s.75 1.087 144.7 .084 2.160 -1.076

60

EXT* USJOÜ MUMM R ..316.7 ( COROFCTED TOTftL STRAIN )

LOftO CHART

INS.

FNT,. STRAIN

y.

1 + E TRUE STRESS. KSI

TRUE STRAIN

LOGIO SLRESS.

LOG10 .STßMN _..

11900. 1?400.

1.55 1.65

.5<*

.66 1.005 1»M7.

122.3 127,5

,005 .007

2.087 2.106

-2.268 -2.179

12600. 12700.

1.75 • ftfl 1.009 i.ou

129.9 131.2 131.6 132.5 "l33.«^ 13«^.2

.009 • OIL. .01«t .017 .019 .022

2.m 2.118

-2.055 -1.946

12700. 12750. 12800. 12P50.

1.95 2.05 2.15 2.25

!.«♦? 1.69 1.96 2.23

l.Ol«^ 1.017 1.020 1,022

2.119 2.122 2.125 2.128

-1.850 -1.775 -1.711 -1.65&

12900. 12950.

2.35 ?.<*5

2.50 2.77

1.025 1.028

135,1 136.0

.025

.027 2.131 2.13«t

-1.607 -1.563

13000. 13050.

2.55 2.65 2.75 2.85

3.0^ '.31 3,60 3.88

1.030 1.033 1. Ö 36 1.039

136.9 137.8 138.1 138.5

.030

.033 .035 .038

2.136 2.139

-1.523 -l.«^7

13050. 13050.

2.U0 2.1«»2

-1.U52 -l.«+19

13100. 13150.

2.95 3.05

«».15 1,0«^2 1.0«^

139.«♦ 1«^0.3

.0«^1 , 0«^3

2.1»^«^ 2.1^7

-1.391 -1.36«»

13150. 13150.

3.15 3.25

«♦.71 «♦.99

1,0«^7 1.050

l«+0.7 1«^1.1

, 0«*6 .0«^9

2.1«^8 2.1^9

-1.337 -1.312

13150. 13150.

3.35 3.^5

5.28 5.57

1.05 3 1.056

1U1.5 i<»l.8

.051

.05«^ 2.151 2.152

-1.289 -1.966

13150. 13150.

3.55 3.65

5.85 6.U

1.059 1.061

1«^2.? 1«^2.6

.057 • 060 . 062 .065

2.153 2.15«^

-1.2«*5 -1.225

13150. 13150.

3.75 3.«5

6.«^2 6.71

1.06<+ 1.067

1«43.0 1«^3.«^

2.155 2.156

-1.206 -1.187

13150. 13100.

3.95 1».05 Jf.15 «♦.25

7.00 7.30

1.070 1.073

1«^3.8 l«+3.6

.068 ,070

2.158 2.157

-1.170 -1.152

13000. 12950.

7.6? 7.92

1.076 1.079

1U3.0 l«^?.8

.073

.076 2.155 2.155 2.151

-1.13«+ -1.118

12*00. «♦.35 8.25 1.083 1«^1.6 .079 -1.101

6l

-,

EXTPUSION NUMnF'? •!?1«» ( CORPECTFO TOTAL STRAIN )

LOAO

—----

12100. 121*00.

CHART ELONG.

INS,

2 .10 2.20

ENG. ST'ATN

'f.

',9U l.lfl

IfE

1,0 09 1.012

TRUE STRESS

KSI

128,3 129.7

TRUE STRAIN

.009

.012

LOG10 STRESS,

~2;i(iv 2.113

LORIO STRAIN

-2.030 -1.930

121*50. 12500,

2.30 2.1*0

1.1*5 1.71

1.011* 1.017 1.02 0 1.023 i.025 1.028

130.5 131.1* 132.3 132.9 133.5 131*.0 131*.5 135.0 135.5 136.1 136.8 1^7.1

.011*

.017 • 020 .022 . 025 .028 .030 .033 .0 36 .0 39 . (m .01*1* .01*7 .01*9 .052 .055 .058 .060

2.116 2.119 2.121 2.123

-1.81*3 -1.770

12550. 12575.

2.50 2.60

1.9^ 2.25

-1.708 -1.652

12600. 12615.

2.70 2.80

2.53 2.81

2.126 2.127 2.129 2.130 2.132 2.131* 2.136 2.137 2.138 2.11*0 2.11*1 2.11*2

-1.602 -1.557

12625. 1261*0. 12650. 12675. 12700. 12700,

9.90 3,00 3.10 3.20 3.30 3.1*0 3.50 3.60 3.70 3.80 3.90 i*.00

3.09 3.37 3.65 3.93 l*.2Ö i*.i*9

1.031 1.031* l.O^/ 1.039 1.01*2 1.045

-1.517 --l.J*79_. -1.1*1*5 -1.1*11* -1.385 -1.357

12700. 12700. 12700. 12700.

«♦.78 5.06 5.35 5.63 5.92 6.22

1,01*8 1.051 1,053 1.056 1.059 1.062

137.5 137.9 138.3 138.6 139.0

...155.1

-1.331 -1.306 -1.283 -1.261

12700. 12675.

2.1U3 2.11*3

-1.21*0 -1.220

12650. 12625. 12600, 12575.

<*.10 JL._2.P

I*.-«O i*.i*0 i*.50 i*.60

6.51 6.81 7.11 7.1*0 7,70 8,00

1.065 1.068 1,071 1.071* 1,0^7 1.080

139.2 139.1* 139,5 139.6 139.7 139.5

. 063

.066

. 069

.071

.071*

.077

2.11+1* 2.1i*i* 2.ii*i* 2.1i*5

-1.200 -1.181 -1.163 -1.1U6

12550. 12500.

2.1U5 2.11*5

-1.130 -1.113

121*50. 121*00. 1230 0. 12200. 1210 0. 120O0.

i*.70 i*.80 ü.^0 5.00 5.10 5.20

8.31 ?.62 8,91* P.27 0,60 9,93

1.083 1.086 1.089 1,0P3 1.096

.1.099..

139.1* 139.2 138.5 137.8 137.1 136.1

.080

.083

.086 .089 .092 •095

2.11*1* 2.1i*i* 2.11*1

. 2..139. 2.137

2.132

-1.098 -lt083 -1.Ö67 -1.052 -1.Ö38 -1.021*

ll^OO. 5.30 10.25 1.103 135.6 .098 -1.010

62

EXTPUSION NUMRER •5?^5 ( COPPECTFO TOTAL S TPAIN )

TRUE"" LOAP CHAPT TRUE LOGIO LOR10 ELONG,

IN«. STPATN

v. - - STRESS KSI

5TPATN STRESS _.5lRft™ LRS.

l?P0fl. 1.75 TB? 1,009 131.2 ."008 2.118 "■-'zTöTz 1^700. 1.A5 .97 1,010 136.4

' iTÖ. 8" .010 .011

2.115 2.149

-2.013 1^700. 1.Q5 1.11 i.oii ~-1.949 1"*«5Q. 2.05 l.-<7 1,014 U2.6 .014 2.154 -1.867 {«♦10 0. 2.15 1.57 1.016 145.5 .016 2.163 -1.807 I*t200. 2.25 1.81 1.018 146.9 .018 2.167 -1.742 1<»200. 2.35 2.11 1.021 147.1 .021 2.168 -1.680 lU^OO. 2.45

2.55 2.17 2.62

1.024 148.7 .023 2.172 -1.6M luuon. 1.026 150.1 .026 2.176 -1.587 ^♦'♦Si). 2.65 2.89 1.029 151.1 .028 2.179 -1.545 1U500. 2.75 i.i6 1.032 152.0 .'0 3i 2.182 -1.507 i^no. 2.«5 3.45 1.014 152.4 .014 2.1^3 -1.470 li»50(J. 2.95 3,71 1.017 152.8 .017 2.184 -1.436 1U55(]. 1.05

1.15 4.00 4,2Q

1.040 1.043

151.7 .019 2.187 -1.408 I'fBSO. '154.2" .042 2.188 -1,377 1«*550. 1.25 4.57 1.046 154,6

155,0 .045 .047

2.1«9 2.19Ö

-1,150 IWSSfJ. 1.15 4.86 1.049 -1,124 l^BSO. 3.45 5,15

5,41 It-QSl 1.054

155,4 155,9

.050

.053 2.192 2,103

-1,100 14550. 1.55 -1,277 14550. 1.65 5,72 1.057 156,1

156,7 ,056 7058

2.1Q4 2.195

-1,255 14550. 1.75 6,00 1.060 -1,214 14600. 1.85 6,27 1.063 157.6 ,061 2.1^8 -1,216 14600. 1.05 6,56 1.066 158.1 ,064 2.199 -1,197 14600. 4.05 6,84 1.068 158,5 ,066 2.200 -1.179 14600. 4,15 7,11 1.071 158.9 ,069 2.201 -1,162 14600. 14600.

4.25 4.15

7.42 7,70

1.074 1.077

159.3 159.8

,072 "",074

2.202 2.203

-1,145 -1,130

14600. 4.45 7,99 1.080 160.2 ,077 2.205 -1,114 1460 0. 4.55 8,27 1.0 81 160.6 ,080 2.206 -1,100 14600» 4.65 e.56 1.086 161.0 ,082 2.207 -1,085 14600. 4.75 8,85 1.088 161.5 .085 2.20« -1,072 14600, 4.85 9,11 UJlqi 161.9

162.1 .087 .090"

2,209 2,210

-1,059 14600, 4.Q5 9,a? i. o'cj 4 -1,046 14600. 5.05 9,70 1.097 162.7 .093 2.211 -1,031 14550. 5.15 10,01 1,100 162.6 .095 2.211 -1,021 14500. 5.25 10,11 1,101 162.5 .098 2,211 -1,008 14500. 5.15 10,60 1,106 162.9 .101 2.212 -,997 14500. 5.45

5,55 10,88 11,18

1,109 1,112

161.4 161.2

.101 2,211 -,986 14450. " .106 2,211 -,975 14400. 5.65 11,uq 1,115 161.1 .109 2.212 -,9^4 14100. 5.75 11,80 1,118 162.4 .112 2.211 -,952

63

?XTRUS ION NUMBER 31 ^..9 ( CO?R ECTLO TOTAL S TKfilN )

LOAD :Hft(?T ZNG. Ut TRUE Ti?UE LOilO LOG10 ilLONG. STRAIN STRESS STRAIN STRESS STRAIN

ins. INS. '/. <SI

i?7Pn. 2,00 .76 1,003 135,7 .008 2.131 -2.122 1?1U0. 2.10 .97 1.010 137.7 .010 2.139 -2.017 t?7G0. 2.20 1.33 1.013 136.1 .013 2.13»4 -1.879 i?e.f-o. 2.30 1.6^ 1.016 136.0 .016 2.133 -1.790 1?550. 2.^0 1.92 1.019 136.? .019 2.135 -1.720 I?f25. 2.^0 2.22 1.02? 136.5 .022 2.135 -1.659 1P6 25. 2. »■> 0 2.50 1.025 136.8 .025 2.136 -1.607 l?b?5. 2.70 2.79 1,028 137.2 .028 2.137 -1.560 l?o5n. 2.30 3.07 1.031 137.9 .030 2.139 -1.520 1P675. 2.(:)0 3.3^ 1.033 135.5 .033 2.1»4l -1.483 12675. 3.00 3.63 1.0 3c 138.9 .036 2.1'43 -1.44 8 1?700. 3.10 3.90 1.031 139.5 .038 2.145 -1.417 1?700. 3.20 »♦.19 1.0^2 139.9 .OUl 2.1*46 -1.387 1?703. 3.7 0 »♦.»♦'J 1.0^5 1^0.3 .0<4<4 2.1*47 -1.359 1P700. 3.^0 »♦.76 1.0^ 1*40.7 .0»47 2.148 -1.332 1P700. 3.tO 3.05 1.050 Ul.l .0t49 2.149 -1.308 iZTZb, 3.6 0 5.32 1.053 li*1.7 .052 2.151 -1.255 1?725. 3.70 5.61 1.0S6 1142.1 .055 2.153 -1.263 1?7?5. ■».80 5.90 1.0 59 1^2.5 .057 2.154 -1.242 12725. 3.90 6.18 1.062 1^2.9 .060 2.155 -1.222 12725. •4.00 6.»*7 1.065 1^3.3 .063 2.156 -1.203 12725. H.10 6.75 l.Ob'i 1<*3.6 .065 2.157 -1.185 12725. <f.20 7.0^ 1.070 1^•♦.G .063 2.158 -1.167 12700. ^.3 0 7.3»t 1.073 ll4»4.1 .071 2.159 -1.150 12b75. '».«fO 7.63 1.076 !£♦'♦. 3 .07'4 2.159 -1.133 12650. U.50 7.93 1.079 i^^.u .076 2.159 -1.117 12650. »♦.60 6.21 1.052 Ik*,* .079 2.161 -1.103 12600. «4.70 8.52 1.0B5 l»4!4.e .082 2.160 -1.087 12575. «♦. e o Ö.82 1.081 l^^ .08^4 2.160 -1.073 12525. »♦.90 9.12 1.091 1*4 »4.5 .087 2.160 -1.059 12i»50. 5.00 9.<»<» 1.09^ 1»4«4.1 .090 2.159 -1.045 12360. 5.10 9.76 1.09SJ 1«4J.3 .093 2.156 -1.031

61»

.

EXTRUSION MUMPER 3272 ( CORRECTtO TOTAL STRAIN )

LOAD CHART ENG. i+e TRUE TRUE LOG10 LOG 10 ELONG. STRAIN STRESS STRAIN STRESS STRAIN

LPS. INS. '/. KSI

If 3«0. 3.07 .5« 1.006 162.8 .006 2.212 -2.239 U590. 3.17 .76 1.008 165.1 .003 2.218 -2.121 If 780. 3.27 .95 1.010 167.3 .009 2.224 -2.024 Ifc^OO. 3.37 1.18 1.012 163.9 .012 2.228 -1.932 17030. 3.U7 1.40 1.014 170.6 .014 2.232 -1.858 17190. 3.57 1.60 1.016 172.5 .01S 2.237 -1.798 17300. 3.67 1.83 1.013 174.0 .013 2.241 -1.740 17«»00. 3.77 2.07 1.021 175.5 .020 2.244 -1.688 17500. 3.87 2.31 1.023 176.9 .023 2.248 -1.642 1759Q. 3.97 2.55 1.025 17'J.2 .025 2.251 -1.599 17650. 4.07 2.80 1.023 IM, 3 .028 2.253 -1.558 17733. 4.17 3.05 1.030 180.5 .030 2.256 -1.522 17800. k»27 3.30 1.033 131.7 .032 2.259 -1.489 17950. 4.37 3.56 1.036 182,6 .035 2.262 -1.456 17900. 4.47 3.32 1.033 133.6 .033 2.264 -1.426 17950. 4.57 4.08 1.041 134.6 .040 2.266 -1.398 18000. 4.67 4.34 1.043 185.5 .043 2.263 -1.371 18030. 4.77 4.61 1.046 135.3 .045 2.270 -1.3t«6 18100. 4.87 4.87 1.049 187.5 .048 2.273 -1.323 18130. 4.97 5.14 1.051 139.3 .050 2.275 -1.300 16150. 5.07 5.41 1.054 189.0 .053 2.276 -1.278 18200. 5.17 5.67 1.057 190.0 .055 2.279 -1.258 16230. 5.27 5.94 1.059 190.8 .058 2.231 -1.238 18250. 5.37 6.22 1.062 191.5 .060 2.282 -1.219 18250. 5.47 6.51 1.065 192.0 .063 2.293 -1.200 16250. 5.57 6.79 1.063 192.5 .066 2.285 -1.132 16250. 5.67 7.08 1.071 193.1 .068 2.286 -1.165 18250. 5.77 7.36 1.074 193.6 .071 2.287 -1.148 16250. 5.87 7.65 1.077 194.1 .074 2.286 -1.132 16230. 5.97 7.95 1.079 194.b .076 2.289 -1.117 18200. 6.07 8.25 1.032 194.6 .079 2.289 -1.101 18150. 6.17 6.56 1.086 19«».7 .082 2.289 -1.086 18100. 6.27 8.87 1.0 89 194.7 .085 2.289 -1.071 16000. 6.37 9.21 1.092 194.2 .088 2.238 -1.055 17900. 6.47 9.54 1.095 193.7 .091 2.287 -1.040

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ad-769 763 hardness, strength and elongation correlations … · 2018-11-09 · ad-769 763...

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