AD-769 763 HARDNESS, STRENGTH AND ELONGATION CORRELATIONS FOR SOME TITANIUM-BASE ALLOYS W. A. Houston, et al Westinghouse Electric Corporation Prepared for: Air Force Materials Laboratory June 1973 DISTRIBUTED BY: KTui National Teciinical Information Service U. S. DEPARTMENT OF COMMERCE 5285 Port Royal Road. Springfield Va. 22151
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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
Prepared for:
Air Force Materials Laboratory
June 1973
DISTRIBUTED BY:
KTui National Teciinical Information Service U. S. DEPARTMENT OF COMMERCE 5285 Port Royal Road. Springfield Va. 22151
UNCLASPTWn ■ I mi ■■?■■■■■& Mii*.jt'ii»i"ü1
DOCUMENT CONTROL DATA R&D (Stcutllr clmtiillcillon ol ml», body of mbMltmcl mnd Indrtlnf mnolmllon mum 6T tnltnd when jfcj onrmll trnpotl la clmttlllfdj
1 ORIGINATING * C T I vt T V fCorpof«(« ■ufhor)
Westinghouse Electric Corporation Astronuclear Laboratory Pittsburgh, Pennsylvania
2*. REPORT tKCURITV CLASSIFICATION
UNCLASSIFIED
J BCPORT TITLE
HARDNESS. STREMGTH AND ELONGATION CORRELATIONS FOR SOME TITANIUM-ItASE ALLOYS 4. DESCRIPTIVE NOTt» (Trpm at npcn mnd Inclutlve d*f)
Interim Technical Report 1 November 1971 to 15 March 1972 s AUTHOnitl (Flnt nmm, aitddlm Inlllml, Imtlnmm») " ""~
W. A. Houston T. E. Jones
D. J. Abson F. J. Gurney
»■ REPORT DATE
June 1973 M. CONTRACT Ol iRANTNO.
F33615-71-:-ll63 6. PROJECT NO
7351
««•735108
7«. TOTAL NO. OP PACES
65 76. NO. OP REFS
12 M. ORIGINATOR'S REPORT NUMBERISI
•d. OTHER REPORT NOISI (Any other numb*» thai may 6« •isffntrf (hi« fport)
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Approved for public release; distribution unlimited.
11 SUPPLEMENTARV NOTES 12. SPONSORING MILITARY ACTIVITY
Air Force Materials Laboratory Wright-Patterson Air Force Base, Ohio
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 approx- imately 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 augment- ed 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 — ..
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
Approved for public release; distribution unlimited
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 relation- ships 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 test- ing.
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 relation- ship 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 de- formation 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 vari- ables 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 fac- tor 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 hard- ness 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 hard- ening 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 accord- ing 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. indent- ation 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 correl- ated 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 dia- meter 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 direct- ly 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 deter- mine 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 be- havior 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 ex- pected 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 esti- mated 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 ob- tained 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 relat- ionship 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 hard- ness with specimen history. Thus it is clear that a single hardness determin- ation 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 uni- form 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 relation- ships 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 compress- ion tests and attributed discrepancies between compressjon, hardness and tension test results to the occurrence of profuse twinning during compression or hard- ness 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 obser- vation, 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 discrep- ancies 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 moder- ately 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 -^ ^o -* 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 ^o 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
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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
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•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-^O ^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 deform- ation 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
WORK HARDENING COEFFICIENT
* 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
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. (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 incorpor- ated, (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 incorpor- ated, (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 incorpor- ated, (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 relation- ship^), 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 relation- ship(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 con- struction.
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«
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 • • • • • • • • • •
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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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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
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'