Disclosure to Promote the Right To Information

Whereas the Parliament of India has set out to provide a practical regime of right to information for citizens to secure access to information under the control of public authorities, in order to promote transparency and accountability in the working of every public authority, and whereas the attached publication of the Bureau of Indian Standards is of particular interest to the public, particularly disadvantaged communities and those engaged in the pursuit of education and knowledge, the attached public safety standard is made available to promote the timely dissemination of this information in an accurate manner to the public.

! $ ' +-Satyanarayan Gangaram Pitroda

Invent a New India Using Knowledge

01 ' 5 Jawaharlal Nehru

Step Out From the Old to the New

1 +, 1 +Mazdoor Kisan Shakti Sangathan

The Right to Information, The Right to Live

! > 0 B BharthariNtiatakam

Knowledge is such a treasure which cannot be stolen

Invent a New India Using Knowledge

IS 1501 (2002): Method For Vickers Hardness Test forMetallic Materials [MTD 3: Mechanical Testing of Metals]

Is 1501:2002ISO 6507-1:1997

[Superseding IS 1501 (Pstt 1) :1984,IS 1501 (Part 2) :1984, IS 1501 (Part 3) :1987,

IS 10927 (Part 1) :1984, IS 10927 (Part 2) :1984and IS 10927 (Part 3) : 1991]

mw=m

( rfk?m37%7)Indian Standard

METHOD FOR VICKERS HARDNESS TESTFOR METALLIC MATERIALS

( Third Revision)

Ics 77.040.10

0 61s 2002

BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

October 2002 Price f% 600.00

L,

Mechanical Testing of Metals Sectional Committee, MTD 3

NATIONAL FOREWORD

This Indian Standard (Third Revision) which is identical with ISO 6507-1:1997 Metallic materials Vickers hardness test Part 1: Test method issued by the International Organization forStandardization (ISO) was adopted by the Bureau of Indian Standards on the recommendation of theMechanical Testing of Metals Sectional Committee and approval of the Metallurgical EngineeringDivision Council.

The earlier Indian Standard on Method for Vickers hardness test for metallic materials was coveredby the following parts:

IS 1501 (Part 1):1984 Method for Vickers hardness test for metallic materials : Part 1 HV 5 toHV 100 (second revision)

IS 1501 (Part 2):1984 Method for Vickers hardness test for metallic materials : Part 2 HV 0.2to less than HV 5 (second revision)

IS 1501 (Part 3):1987 Method for Vickers hardness test for metallic materials : Part 3 Less thanHV 0.2 (second revision)

This revision of the standard has been prepared by merging all the above three parts, and alsoincluding the provisions of the following Indian Standards:

IS I 0927(Part 1) :1984 Tables of Vickers hardness values for use in tests made on flat surface :Part 1 HV5to HV 100

IS I 0927(Part 2) : 1984 Tables of Vickers hardness values for use in tests made on flat surface:Part 2 HV 0.2 to less than HV 5

IS I 0927(Part 3) : 1991 Tabk?of Vickers hardness values for use in tests made on flat surface: Part 3 Less than HV 0.2

In this adopted standard, certain terminology and conventions are, however, not identical to thoseused in Indian Standards. Attention is especially drawn to the following:

a) Wherever the words International Standard appear referring to this standard, they shouldbe read as Indian Standard.

b) Comma (,) has been used as a decimal marker while in Indian Standards, the currentpractice is to use a point (.) as the decimal marker.

In this adopted standard, reference appears to the following International Standard for which IndianStandard also exists. The corresponding Indian Standard which is to be substituted in its place islisted below along with its degree of equivalence for the edition indicated:

/nternationa/ Corresponding Indian Standard Degree of EquivalenceStandard

ISO 6507-2: 1997 IS 1754 :2002 Method for verification of IdenticalVickers hardness testing machines (thirdrevision)

In reporting the results of a test or analysis made in accordance with this standard, if the final value,observed or calculated, is to be rounded off, it shall be done in accordance with IS 2:1960 Rules forrounding off numerical values (revised).

is 1501 :2002ISO 6507-1 :1997

Indian Standard

METHOD FOR VICKERS HARDNESS TESTFOR METALLIC MATERIALS

( Third Revision)

1 Scope

This part of ISO 6507 specifies the method of Vickers hardness test for the three different ranges oftest force for metallic materials (see table 1).

Table 1

Ranges of test force, F Hardness symbol Previous designationN (ISO 6507-1 :1982)

/= ~ 49,03 >HV5 Vickers hardness test

1,961 < F < 49,03 HV 0,2 to c HV 5 Low load Vickers hardness test

0,09807 = F < 1,961 HV 0,01 ,to < HV 0,2 Vickers microhardness test

The Vickers hardness testis specified in this part of ISO 6507 for lengths of indentation diagonalsbetween 0,020 mm and 1,400 mm.

The force values in this part of ISO 6507 were calculated from kilogram force values. They wereintroduced before the S1-system was adopted. It was decided to keep the values based on the oldunits for this edition, but for the next revision it will be necessary to consider the advantage ofintroducing rounded values of test force and the consequence on the hardness scales.

NOTE In general, decreasingthe test force increases the scatter of results of the measurements. This isparticularly true for low-force Vickers hardness tests and Vickers microhardness tests where the principallimitation will arise in the measurement of the diagonals of the indentation. For Vtckers microhardness, the

d accuracy of determl atlon of the mean diagonal length is unlikely to be better than & 0,001 mm (see annex E).

For specific materials and/or products, particular International Standards exist.

2 Normative reference

The following standard contains provisions which, through reference in this text, constituteprovisions of this-partof1S06507. At the time of publication, the edition indicated was valid. Allstandards are subject to revision, and parties to agreements based on this part of ISO 6507 areencouraged to investigate the possibility of applying the most recent edition of the standard indicatedbelow. Members of IEC and ISO maintain registers of currently valid International Standards.

-----

ISO 6507-2:1997, Metallic materials Vickers hardness test Part 2: Verification of testing machines.

1

IS 1501 :2002ISO 6507-1 :1997

3 Principle

A diamond indenter in the term of a right pyramid with a square base and with a specified anglebetween opposite faces at the vertex is forced into the surface of a test piece followed bymeasurement of the diagonal length of the indentation left in the surface after removal of the testforce, F(see figure 1).

F

1u

/

a) Indenter(diamondpyramid)

;----

b) VlckersIdentatlon

Figure 1 Principle of the test

The Vickers hardness is proportional to the quotient obtained by dividing the test force by the slopingarea of the indentation which is assumed to be a right pyramid with a square base, and having at thevertex the same angle as the indenter.

Is 1501 :2002ISO 6507-1 : 1997

4 Symbols and designations

4.1 See table 2 and figure 1.

Table 2

Symbol Designation

a Angle between the opposite faces at the vertex of the pyramidal indenter(136)

F Test force, in newtons

d Arithmetic mean, in millimeters, of the two diagonals length d, and d,(see figure 1)

HV Vickers hardness = Constant xTest force

Surface area of indentation

1362Fsin

= 0,102 2 = 0,1891 f-d2 d2

NOTE Constant = ~ =i

= 0,1029 9,80665

4.2 The Vickers hardness is denoted by the symbol HV preceded by the hardness value followed by

a) a number representing the test force (see table 3);b) the duration of loading, in seconds, if different from the time specified in 7.4.

EXAMPLES

640 HV 30= Vickers hardness of 640 determined with a test force of 294,2 N applied for 10 s to 15s.

640 HV 30/20= Vickers hardness of 640 determined with a test force of 294,2 N applied for 20s.

5 Testing machine

5.1 Testing machine, capable of applying a predetermined force or forces within the required rangeof test forces, in accordance with ISO 6507-2,

5.2 Indenter, a diamond in the shape of a right pyramid with a square base, as specified in 1S0 6507-2.

5.3 Measuring device, as specified in ISO 6507-2.

NOTE A suggested procedure for monitoring the uncertainty of the hardnesstesting machine by the users isgiven in annex D.

i

3

Is 1501 :2002ISO 6507-1 :1997

6 Test piece

6.1 The test shall be carried out on a surface which is smooth and even, free from oxide scale,foreign matter and, in particular, completely free from lubricants, unless otherwise specified inproduct standards. The finish of the surface shall permit accurate determination of the diagonallength of the indentation.

6.2 Preparation shall be carried out in such a way that any alteration of the surface hardness, due toheat or cold-working, for example, is minimized.

uue to the small depth of Vickers microhardness indentations, it is essential that special precautionsare taken during preparation. It is recommended to use a polishing/electropolishing process which issuitable for the material parameters.

6.3 The thickness of the test piece or of the layer under test shall be at least 1,5 times the diagonallength of the indentation (see annex A).

No deformation shall be visible at the back of the test piece after the test.

6.4 For tests on curved surfaces, the corrections given in annex B, tables B.1 to B.6 shall be applied,~

,,,,

6.5 For test pieces of small cross-section or of irregular shape, it maybe necessary to provide some*

form of additional support.

7 Procedure

7.1 In general, the testis carried out at ambient temperature within the limits of 10 C to 35 C,Tests carried out under controlled conditions shall be made at a temperature of (23 * 5) C.

7.2 The following test forces (see table 3) shall be used.

I Hardness test)Hardness Nominalsymbol value of the

test force F

N

HV 5 49,03

HV 10 98,07

HV 20 196,1

HV 30 294,2

HV 50 490,3

HV 100 980,7

Table 3

Low-force hardness teat Microhardnees test)Hardness Nominal value Hardness Nominalsymbol of the test syrhbol value of the

force F test force F

N N

HV 0,2 I 1,961 I HV 0.01 ~ 0,09807

HV 0,3 I 2,942 I HVO.015 I 0.1471

HV 0,5 1. 4;903 HV 0;02 I 0,1961

HV 1 9,807 HV 0,025 0,2452

HV 2 19,61 HV 0,05 0,4903

HV 3 2~,42 HV 0,1 0,9807

1) Nominal test forces greater than 980,7 N maybe applied.2) The test.forces for the microhardness test are recommended.

4

Is 1501 :2002ISO 6507-1 :1997

7.3 The test piece shall be placed on a rigid support. The support surfaces shall be clean and freefrom foreign matter (scale, oil, dirt; etc.). It is important that the test piece lies firmly on the support sothat displacement cannot occur during the test.

7.4 Bring the indenter into contact with the test surface and apply the test force in a direction

\perpendicu ar to the surface, without shock or vibration, until the applied force attains the specifiedvalue. The t me from the initial application of the force until the full test force is reached shall not beless than 2s nor greater than 8s. For low-force hardness and microhardness tests, this time shall notexceed 10s. For low-force hardness and microhardness tests, the approach speed of the indentershall not exceed 0,2 mm/s.

The duration of the test force shall be 10s to 15s,

For particular materials, a longer time for maintaining the force is provided; this time shall be applieawith a tolerance of * 2s.

7.5 Throughout the test, the testing machine shall be protected from shock or vibration.

7.6 The distance between the centre of any indentation and the edge of the test piece shall be at least2,5 times the mean diagonal length of the indentation in the case of steel, copper and copper alloysand at least three times the mean diagonal length ofthe indentation in the case of light metals, leadand tin and their alloys.

The distance between the centres of two adjacent indentations shall be at least three times the meandiagonal length of the indentation in the case of steel, copper and copper alloys, and at least six timesthe mean diagonal Iangth in the case of light metals, lead and tin and their alloys. If two adjacentindentations differ in size, the spacing shall be based on the mean diagonal length of the largerindentation.

7.7 Measure the lengths of the two diagonals. The arithmetical mean of the two readings shall betaken for the calculation of the Vickers hardness.

For flat surfaces, the difference between the lengths of two indentation diagonals should not begreater than 5 Y.. If the difference is greater, this shall be stated in the test report.

8 Uncertainty of the results

The uncertainty of results is dependent on various parameters which may be separated into twocategories:

a) parameters depending on the Vickers hardness testing machine (including the uncertainty ofthe verification of the testing machine and of the calibration of the reference blocks);

b) parameters depending on the application of the test method (variation of the operatingconditions).

NOTE In the absence of sufficient data on those parameters it is not possible, af present, to fix values ofaccuracy, but the uncertainty may approach approximately * 10 % of the measured hardness values.

l

Is 1501 :2002ISO 6507-1 :1997

9 Test report

The test report shall include the following information:

a) reference to this part of ISO 6507;

b) all details necessary for identification of the test piece;

c) the result obtained;

d) all operations not specified by this part of ISO 6507, or regarded as optional;

e) details of any Occurrence which may have affected the results;

f) the temperature of the test; if it is outside the range specified in 7.1.

NOTES

1 A strict comparison of hardnessvalues is only possible at identical test forces.

2 There is no general process of accurately converting Vickers hardness into other scales of hardness or intotensile strength. Such conversions therefore should be avoided, unless a reliable basis for conversion can beobtained by comparison tests.

3 It should be noted that for anisotropic materials, for example those which have been heavily cold-worked,there will be a difference between the Iengthsof the two diagonals of the indentation. Where possible, the indentation should be made so that the diagonals are inclined at approximately 45 to the direction ofcold-working. The specification for the product may indicate limits for the differences between the lengths of.thetwo diagonals.

4 There is evidence that some materials may be sensitive to the rate of straining which causes small changes inthe value of the yield stress. The corresponding effect on the termination of the formation of an indentation canmake alterations in the hardness value.

6

Is 1501 :2002ISO 6507-1 :1997

Annex A(normative)

Minimum thickness of the test piece in relation to the test force end to the hardness

%L~ %L * *5L 5L * %L$L %L *000> +@ m.. +-!J -d-*\\\\ +~.J& ~

53000

2000

1000

500

250

100

50

25

10a1,01 0,025 0,05 0,1 0,25 0,5 1 2,5 5 10

Thickness, mm

Figure A.1 Minimum thickness of the test piece in relation to the test force and to the hardness

(HV 0~ to HV 100)

7

Is 1501 :2002ISO 6507-1 :1997

The nomogram shown in figure A.2 has been designed for the minimum thickness of a test piece,assuming that the minimum thickness has to be 1,5 times the diagonal length of the indentation. Therequired thickness is given by the point of intersection of the minimum thickness scale and a line(shown dotted in the example in figure A.2) joining the test force (right-hand scale) with the hardness[left-hand scale).

4) s)

0,01 0,098 O?

31

+

0,022}

0,1961

0,005 148 22273,6 147 22173,3 147 22C73,0 146 21s72,7 145 21872,4 145 21772,1 144 21671,9 144 21671,6 143 21571,3 143 21471,0 142 21370,7 141 21270,5 141 21170,2 140 21169,9 140 21C69,7 139 20S69,4 139 20E69,1 138 20768,8 138 20768,6 137 20668,3 137 2(-J568,1 136 20467,8 136 20367,5 135 20367,3 135 20267,0 134 20166,8 134 20066,5 133 20066,3 133 19966,0 132 19e65,8 132 19765,5 131 19765,3 131 19665,0 130 19564,8 130 19464,6 129 19464,3 129 q9364,1 128 19263,8 128 191

HV 50 HV 100377 754375 751374 748372 745371 742369 739368 736366 733365 730364 727362 724361 721359 719358 716

354 707352 705351 702350 699348 697347 694346 691344 688343 686342 683340 681339 678338 675336 673335 670334 668333 665331 663330 660329 658328 655326 653325 650324 648323 646322 643320 641319 638

,-----

-J

72

~v~~y!.1

I74

,.

Is 1501 :2002ISO 6507-1 :1997

Table C.3 Range W 5 to HV 100 @onfhwed)

Mean Teat force, Fdiagonal Nof inden-

taticfn 49,03 I 98,07 I 196,1 I 294,2 I 490,3 I 980,7d Vickera hardneas

mm l-w 5 HV 10 \ HV 20 HV 30 HV 50 HV 1000,628 23,5 47,0 94,0 141 235 4700,629 23,4 46,9 93,7 141 234 4690,630 23,4 46,7 93,4 140 234 4670,631 ~3,3 46,6 93,1 140 233 4660,632 23,2 46,4 92,8 139 232 4640,633 23,1 46,3 92,5 139 231 4630,634 23,1 46,1 92,3 138 231 4610,635 23,0 46,0 92,0 138 230 4600,636 22,9 45,8 91,7 138 229 4580,637 22,8 45,7 91,4 137 228 4570,638 22,8 65,6 91,1 137 228 4560,639 22,7 45,4 90,8 136 227 4540,640 22,6 45,3 90,5 136 226 4530,641 22,6 45,1 90,3 135 226. 4510,642 22,5 45,0 90,0 135 225 4500,643 22,4 44,9 89,7 135 224 4490,644 22,4 44,7 89,4 134 224 4470,645 22,3 44,6 89,1 134 223 4460,646 22,2 44,4 88,9 133 222 4440,647 22,1 44,3 88,6 133 221 4430,648 22,1 4$2 88,3 132 221 4420,649 22,0 44,0 88,0 132 220 4400,650 21,9 43,9 87,8 132 219 439

t~

0,651 21,9 43,8 87,5 131 219 4380,652 21,8 43,6 87,2 131 218 4360,653 21,7 43,5 87,0 130 217 4350,654 21,7 43,4 86,7 130 217 4340,655 21,6 43,2 88,4 130 216 4320,656 21,5 43,1 86,2 129 215 4310,657 21,.5 43,0 85,9 129 215 4300,658 21,4 42,8 85,6 128 214 4280,659 21,3 42,7 85,4 128 213 4270,660 21,3 42,6 85,1 128 213 4260,661 21,2 42,4 84,9 127 212 4240,662 21,2 42,3 84,6 127 212 4230,663 21,1 42,2 84,4 127 211 4220,664 21,0 42,1 84,1 126 210 4210,665 21,0 41,9 83,9 126 210 4190,666 20,9 41,8 83,6 125 209 4180,667 20,8 41,7 83,4 125 208 4170,668 20,8 41,6 83,1 125 208 4160,669 20,7 41,4 82,9 124 207 4140,670 20,7 41,3 82,6 124 207 4130,671 20,6 41,2 82,4 124 206 412

,.,,

,!.,

Is 1501 :2002 :4ISO 6507-1 :1997 4

~,,,~,* %,

Table C.3 Range HV 5 to HV

I Mean I Test 1diagonal Iof inden- !I

I tation I 49,03 98,07 196,1II d I Vlckers

mm ~ HV5 HV 10 HV 200,672 I 20,5 41,1 82,1

~ ;

0:678 ~ 20,2 40,3 80,70,679 20,1 40,2 80,40,680 20,1 40,1 80,20,681 20,0 40,0 80,00,682 19,9 39,9. 79,70,683 19,9 39,8 79,50,684 19,8 39,6 79,30,685 19,8 39,5 79,00,686 19,7 39,4 78,80,687 19,6 39,3 78,60,688 19,6 39,2 78,30,689 19,5 39,1 78,10,690 19,5 39,0 77,90,691 19,4 38,8 77,70,692 19,4 38,7 77,40,693 19,3 38,6 77,20,694 19,3 38,5 77,00,695 19,2 38,4 76,80,696 19,1 38,3 76,60,697 19,1 38,2 76,30,698 19,0 38,1 76,10,699 19,0 38,0 75,90,700 18,9 37,8 75,70,701 18,9 37,7 75,50,702 18,8 37,6 75,20,703 18,8 37,5 75,00,704 18,7 37,4 7fi,80,705 18,7 37,3 74,60,706 18,6 37,2 74,40,707 18,5 37,1 74,20,708 18,5 37,0 74,00,709 18,4 36,9 73,80,710 18,4 36,8 73,60,711 18,3 36,7 73,40,7121 18,3 I 36,6 73,10,7131 18,2 36,5 72,90,714 18,2 36,4 72,70,715 18,1 36,3 72,5

(continued

I, F

294,2InessHV 30

123123122122122121121121120120120119119119118118118117117117116116116115115115114114114113113113112112112111111111110110110109109109

490,3 I 980,7 I

HV 50205205204203203202202201 , >88,988,888,788,688,488,388,288,188,087,887,787,687,587,487,287,1

1 87,086,986,886,693

IS 1501 :2002ISO 6507-1 :1997

Table C.3 Range HV 5 to HV 100 (continued)

Mean Test force, Fdiagonal Nof inden-

tation 49,03 1 98,07 196,1 294,2 490,3 980,7d

mm HV 51,464 . . .1,465 . . .1,466 . . .1,467 .. . .1,468 . . .1,469 . . .

l-+-k+1,472 . . .1,473 . . .1,474 . . .1,475 . . .1,476 . . .1,477 . . .1,478 . . .1,479 . . .

HI=1,484 . . .1,485 . . .1,486 . . .1,487 . . .1,488 . . .1,489 . . .

r 1,49T1,490 . . .1,491 . . .1,492 . . .13 . . .1,494 . . .1,497 . . .1,498 ...1,499 . . .1,500 . . .1,501 . . .1,502 . . .1,503 . . .1,504 . . .1,505 . . .1,506 . . .1,507 . . .

Vickers hardnesaHV 10 HV20 HV 30 HV 50 HV 100

8,65 17,3 26,0 43,3 86,58,64 17,3 25,9 43,2 86,48,63 17,3 25,9 43,1 86,38,62 17,2 25,9 43,1 86,28,61 17,2 25,8 43,0 86,18,59 17,2 25,8 43,0 f35,98,58 17,2 25,7 42,9 85,88,57 17,1 25,7 42,8 85,78,56 17,1 25,7 42,8 85,68,55 17,1 25,6 42,7 ,85,58,54 17,1 25,6 42,7 85,48,52 17,0 25,6 42,6 85,28,51 17,0 25,5 42,6 85,18,50 17,0 25,5 42,5 85,08,49 17,0 25,5 42,4 84,98,48 17,0 25,4 42,4 84,88,47 16,9 25,4 42,3 84,78,46 16,9 25,4 42,3 84,68,44 16,9 25,3 42,2 84,48,43 16,9 25,3 42,2 84,28,42 16,8 25,3 42,1 84,28,41 16,8 25,2 42,0 84,18,40 16,8 25,2 42,0 84,C8,39 16,8 25,2 41,9 83,~8,38 16,7 25,1 41,9 83,t8,36 16,7 25,1 41,8 83,t8,35 16,7 25,1 41,8 83,5

8,34 16,7 25,0 41,7 83,48,33 16,7 25,0 41,7 83,38,32 16,6 25,0 41,6 83,28,31 16,6 24,9 41,5 83,18,30 16,6 24,9 41,5 83,68,29 16,6 24,9 41,4 82,98,28 16,5 24,8 41,4 82,~8,26 16,5 24,8 41,3 82,68,25 16,5 24,8 41,3 82,58,24 16,5 24,7 41,2 82,48,23 16,5 24,7 41,2 82,28,22 16,4 24,7 41,1 82,28,21 16,4 24,6 41,0 82,18,20 16,4 24,6 41,0 82,C8,19 16,4 24,6 40,9 81,$8,18 16,4 24,5 40,9 81,f8,17 16,3 24,5 40,8 81,1

----

l

94

Is 1501 :2002ISO 6507-1 :1997

Table Ci3 Range HV 5 to HV 100 (continued)

.

.

Mean Test force, Fdiagonal Nof inden-

tation 49,03 W,07 186,1 I 294,2 490,3 I 980,7

+

dmm HV 5

1,508 . . .1,509 . . .

1;512 . . .1,513 . . .I,5T4 .:.1,515 . . .1,516 . . .1,517 . . .1,518 . . .1,519 . . .1,520 . . .1,521 . . .1,522 . . .1,523 ,..1,524 . . .1,525 . . .1,526 . . .1,527 . . .1,528 . . .1,529 . . .1,530 . . .1,531 . . .1,532 . . .1,533 . . .1,534 . . .1,535 . . .1,536 . . .1,537 . . .1,538 . . .1,539 . . .1,540 ...1,541 . . .1,542 . ..1,543 . . .1,544 . . .1,545 . . .1,546 . . .1,547 . . .1.,548 . . .1,549 . . . .1,550 . . .1,551 . . .

Vickera herdneaaHV 10 HV 20 HV 30 HV 50 HV 100

8,16 16,3 24,5 40,8 81,68,14 16,3 24,4 40,7 81,48,13 16,3, 24,4 40,7 81,38,12 16,2 24,4 40,6 81,28,11 16,2 24,3 40,6 81,18,10 16,2 24,3 40,5 81,08,09 16,2 24,3 40,4 80,98,08 16,2 24,2 40,4 80,88,07 16,1 24,2 40,3 80,78,06 16,1 24,2 40,3 80,68,05 16,1 24,1 40,2 80,58,04 16,1 24,1 40,2 80,48,03 16,1 24,1 40,1 80,38,02 16,0 24,0 40,1 80,28,01 16,0 24,0 40,0 80,18,00 16,0 24,0 40,0 80,07,98 16,0 24,0 39,9 79,87,97 15,9 23,9 39,9 79,77,96 15,9 23,9 39,8 79,67,95 15,9 23,9 39,8 79,57,94 15,9 23,8 39,7 79,47,93 15,9 23,8 39,7 79,37,92 15,8 23,8 39,6 79,27,91 15,8 23,7 39,6 79,17,90 15,8 23,7 39,5 79,07,89 15,8 23,7 39,5 78,97,88 15,8 23,6 39,4 78,87,87 15,7 23,6 39,3 78,77,86 15,7 23,6 39,3 78,67,85 15,7 .23,5 39,2 78,57,84 15,7 23,5 ,39,2 78,47,83 15,7 23,5 39,1 78,37,82 15,6 23,5 39,1 78,27,81 15,6 23,4 39,0 78,17,80 15,6 23,4 39,0 78,07,79 15,6 23,4 38,9 77,97,78 15,6 23,3 38,9 77,87,77 15,5 23,3 38,8 77,77,76 15,5 23,3 38,8 77,67,75 i5,5 23,2 38,7 77,57,74 15,5 23,2 38,7 77,47,73 15,5 23,2 38,6 77,37,72 15,4 23,2 38,6 77,27,71 15,4 23,1 38,5 77,1

95

,,

.

Is 1501 :2002ISO 6507-1 :1997

Tabla C.3 Range HV 5 to HV 100 (continued)

Mean ~ Test force, F)I diagonal N

of inden-~ tation 49,03 98,07 196,1 294,2 490,3 980,7

d I Vlckers hardnessmm HV 5 HV 10 I-Iv 20 HV 30 HV 50

1,552 . . . 7,70 15,4 23,1 38,5,1,553 . . . 7,69 15,4 23,1 38,41,554 . . . 7,68 15,4 23,0 38,41,555 . . . 7,67 15,3 . 23,0 38,31,556 . . . 7,66 15,3 23,0 38,31,557 .

II7,65 15,3 22,9 38,2

1,558 . . 7,64 15,3 22,9 38,21,5591 . . . 7,63 15*3 22,9 38,11,560 . . . 7,62 15,2 ] 22,9 38,11,561 . . . 7,61 15,2 I 22,8 38,01,562 . . . 7,60 15,2 22,8 38,01,563 . . . 7,59 15,2 22,8 38,01,564 . . . 7,58 15,2 22,7 37,91,565 . . . 7,57 15,1 22,7 37,91,566 . . . 7,56 15,1 22,7 37,81,567 . . . 7,55 15,1 22,7 37,81,568 . . . 7,54 15,1 22,6 37,71,569 . . . 7,53 15,1 22,6 37,71,570 . . . 7,521,571 . . . 7,511,572 . . .1,573 . . .1,574 . . .

-+4--=1,577 . . .1,578 . . .1,579 . . .

-+&-1,582 . . .1,583 . . .1,584 . . .

7,507,497,497,487,477,467,457,447,437,427,417,407,39

1,585 . . . 7,381,586 . . . 7,371,587 . . . 7,361,588 . . . 7,351,589 . . . 7,341,590 . . . 7,341,591 . . . 7,331,592 . . . 7,321,593 . . . 7,311,594 . . . 7,3a1,595 . . . 7,29

15,0 22,615,0 22,515,0 22,515,0 22,515,0 22,514,9 22,414,9 22,414,9 22,414,9 22,314,9 22,314,9 22,314,8 22,314,8 22,214,8 22,214,8 22,214,814,714,714,714,714,714,614,614,614,614,6

22,122,122,122,122,022,022,022,021,921,921,9

37,637,637,537,537,437,437,337,337,237,237,137,137,037,037,036,936,936,836,836,736,736,636,636,536,536,4

4HV 10077,076,976,876,776,676,576,476,376,276,176,075,975,875,775,675,575,475,3

.4

4 75,074,9 ,,----74,974,8 $; .74,774,6i

74,574,474,374,2 ,74,174,0

4 73,9 .73,873,773,6173,573,4

73,273,173,072,9

96

..

Is 1501 :2002ISO 6507-1 :1997

Table C.3 Range HV 5 to HV 100 (continued)

Mean Test force, Fdiagonal Nof inden-

tation 49,03 I 98,07 196,1 I 294,2 490,3 980,7d Vickers hardness

mm I-Iv 5 l-iv 10 HV 20 HV 30 HV50 1 Hv 100

1,596 .,. 7,28 14,6 21,8 36,4 72,81,597 . . . 7,27 14,5 21,8 36,4 72,71,598 . . . 7,26 14,5 21,8 36,3 72,61,599 . . . 7,25 14,5 21,8 36,3 72,51,600 . . . 7,24 14,5 21,7 36,2 72,41,601 . . . 7,24 14,5 21,7 36,2 72,41,602 . . . 7,23 14,4 21,7 36,1 72,31,603 . . . 7,22 14,4 21,7 36,1 72,21,604 . . . 7,21 14,4 21,6 36,0 72,11,605 . . . 7,20 14,4 21,6 36,0 72,01,606 . . . 7,19 14,4 21,6 35,9 71,91,607 . . . 7,18 14,4 21,5 35,9 71,81,608 . . . 7,17 14,3 21,5 35,9 71,71,609 . . . 7,16 14,3 21,5 35,8 71,61,610 . . . 7,15 14,3 21,5 35,8 71,51,611 ,.. 715 14,3 21,4 35,7 71,51,612 . . . 7,14 14,3 21,4 35,7 71,41,613 . . . 7,13 14,3 21,4 35,6 71,31,614 . . . 7,12 14,2 21,4 35,6 71,21,615 . . . 7,11 14,2 21,3 35,5 71,11,616 . . . 7,10 14,2 21,3 35,5 71,01,617 . . . 7,09 14,2 21,3 35,5 70,91,618 . . . 7,08 14,2 21,3 35,4 70,81,619 . . . 7,08 14,1 21,2 35,4 70,81,620 . . . 7,07 14,1 21,2 35,3 70,71,621 . . . 7,06 14,1 21,2 35,3 70,61,622 . . . 7,05 14,1 21,1 35,2 70,51,623 . . . 7,04 14,1 21,1 35,2 70,41,624 . . . 7,03 14,1 21,1 35,2 70,31,625 . . . 7,02 14,0 21,1 35,1 70,21,626 . . . 7,01 14,0 21,0 35,1 70,11,627 . . . 7,01 14,0 21,0 35,0 70,11,628 . . . 7,00 14,0 21,0 35,0 70,01,629 . . . 6,99 14,0 21,0 34,9 69,91,630 . . . 6,98 14,0 20,9 34,9 69,81,631 . . . 6,97 13,9 20,9 34,9 69,71,632 . . . 6,96 13,9 20,9 34,8 69,61,633 . . . 6,95 13,9 20,9 34,8 69,51,634 . . . 6,95 13,9 20,8 34,7 69,51,635 . . . 6,94 13,9 .20,8 34,7 69,41,636 . . . 6,93 13,9 20,8 34,6 - 69,31,637 . . . 6,92 13,8 20,8 34,6 69,21,638 . . . 6,91 13,8 20,7 34,6 69,11,639 . . . 6,90 13,8 20,7 34,5 69,0

97

!

Is 1501 :2002ISO 6507-1 :1997

Table C.3 Range HV 5 to W 100 @onfinued)

Mean Test force. Fdiagonal Nof inden-

tation 49,03 I 98,07 196,1 I 294,2 I 490,3 I 980,7d Vickere hardness

mm HV 5 I-Iv 10 HV 20 HV 30 HV 50 HV 1001,640 . . . 6,90 13,8 20,7 34,5 69,01,641 . . . 6,89 13,8 20,7 34,4 68,91,642 . . . 6,88 13,8 20,6 34,4 68,81,643 . . . 6,87 13,7 20,6 34,3 68,71,644 . . . 6,86 13,7 20,6 . 34,3 88,61,645 . . . 6,85 13;7 20,6 34,3 68,51,646 . . . 6,84 13,7 20,5 34,2 68,41,647 . . . 6,84 13,7 20,5 34,2 68,41,648 . . . 6,83 13,7 20,5 34,1 68,31,649 . . . 6,82 13,6 20,5 34,1 68,21,650 . . . 6,@l 13,6 20,4 34,1 68,11,651 . . . 6,80 13,6 20,4 34,0 68,01,652 . . . 6,80 13,6 20,4 34,0 88,01,653 . . . 6,79 13,6 20.4 33,9 67,91,654 . . . 6,78 13,6 20,3 33,9 67,81,655 . . . 6,77 13,5 20,3 33,8 67,71,656 . . . 6,76 13,5 20,3 33,8 67,61,657 . . . 6,75 13,5 20,3 33,8 67,51,658 . . . 6,75 13,5 20,2 33,7 67,51,659 . . . 6,74 13,5 20,2 33,7 67,41,660 . . . 6,73 13,5 20,2 33,6 67,31,661 . . . 6,72 13,4 20,2 33,6 67,21,662 . . . 6,71 13,4 20,1 33,6 67,11,663 . . . 6,71 13,4 20,1 33,5 67,11,664 . . . 6,74) 13,4 20,1 33,5 67,01,665 . . . 6,69 13,4 20,1 33,4 66,91,666 . . . 6,88 13,4 20,0 33,4 66,81,667 . . . 6,67 13,3 20,0 33,4 66,71,668 . . . 6,67 13,3 20,0 33,3 88,71,669 ... 6,66 13,3 20/0 33,3 66,61,670. . . . 6,65 13,3 19,9 33,2 86,51,671 . . . 6,64 13,3 19,9 33,2 66,41,672 . . . 6,63 13,3 19,9 33,2 66,31,673 . . . 6,63 13,2 19,9 33,1 66,31,674 . . . 6,62 13,2 19,9 33,1 66,21,675 . . . 6,61 13,2 19,8 33,0 86,11,676 . . . 6,60 13,2 19,8 33,0 86,01,677 . . . 6,59 13,2 19,8 33,0 65,91,678 . . . 6,59 13,2 19,8 32,9 65,91,679 . . . 6,58 13,2 19,7 32,9 65,81,680 . . . 6,57 13,1 19,7 32,8 65,71,681 . . . 6,56 13,1 19,7 32,8 65,61,682 . . . 6,56 13,1 19,7 32,8 65,61,683 . . . 6,55 13,1 19,6 32,7 65,5

.

.

98

mr.

A

Is 1501 :2002ISO 6507-1 :1997

Table C.3 Range HV 5 to HV 100 @ontinued)

Mean T@ force, Fdiagonal Nof inden-

tation 49,03 I 98,07 1, 196,1 I 294,2 I 490,3 I 980,7d Viera hardness

mm HV5 w 10 HV 20 HV 30 HV 50 HV 1001,684 .. . 6,54 13;1 19,6 32,7 65,41,685 . . . 6,53 13,1 19,6 32,7 65,31,686 . . . 6,52 13,0 19,6 32,6 65,21,887 . . . 6,52 13,0 19,5 32,6 65,21,688 . . . 6,51 13,0 19,5 32,5 65,11,689 . . . 6,50 13,0 19,5 32,5 65,01,890 . . . 6,49 13,0 19,5 32,5 64,91,691 . . . 6,49 13,0 19,5 32,4 64,91,692 . . . 6,48 13,0 19,4 32,4 64,81,693 . . . 6,47 12,9 19,4 32,3 64,71,694 . . . 6,46 12,9 19,4 32,3 64,61,695 . . . 6,45 12,9 19,4 32,3 64,51,696 . . . 6,45 12,9 19,3 32,2 64,51,697 . . . 6,44 12,9 19,3 32,2 64,41,698 ... 6,43 12,9 19,3 32,2 64,31,699 . . . 6,42 12,8 19,3 32,1 64,21,700 . . . 6,42 12,8 19,3 32,1 64,21,701 . . . 6,41 12,8 19,2 32,0 64,11,702 . . . 6,40 12,8 19,2 32,0 64,01,703 . . . 6,39 12,8 19,2 32,0 63,91,704 . . . 6,39 12,8 19,2 31,9 63,91,705 . . . 6,38 12,8 19,1 31,9 63,81,706 . . . 6,37 12,7 19,1 31,9 63,71,707 . . . 6,36 12,7 19,1 31,8 63,61,708 . . . 6,36 12,7 19,1 31,8 63,61,709 . . . 6,35 12,7 19,0 31,7 63,51,710 . . . 6,34 12,7 19,0 31,7 63,41,711 . . . 6,33 12,7 19,0 31,7 63,31,712 . . . 6,33 12,7 19,0 31,6 63,31,713 . . . 6,32 12,6 19,0 31,6 63,21;714 . . . 6,31 12,6 18,9 31,6 63,11,715 . . . 6,31 12,6 18,9 31,5 63,11,716 . . . 6,30 12,6 18,9 31,5 63,01,717 . . . 6,29 12,6 18,9 31,4 62,91,718 . . . 6,28 12,6 18,8 31,4 62,81,719 . . . 6,28 12,5 18,8 31,4 62,81,720 . . . 6,27 12,5 18,8 31,3 62,71,721 . . . 6,26 12,5 18,8 31,3 62,61,722 . . . 6,25 12,5 18,8 31,3 62,51,723 . . . 6,25 12,5 18,7 31,2 62,51,724 . . . 6,24 12,5 18,7 31,2 62,41,725 . . . 6,23 12,5 18,7 31,2 62,31,726 . . . 6,23 12,4 18,7 31,1 62,31,727 . . . 6,22 12,4 18,7 31,1 62,2

11i

..-.

99

is 1501 :2002ISO 6507-1 :1997

Table C.3 Range HV 5 to HV 100 (continued)

Mean Test force, F! diagonal NI of inden-

tation 49,03 98,07 I 196,1 294,2 I 490,3 I 980,7I d I

k&-~ 1,733 . . .

1,734 . . .1

I 1,7391 . .1,740 . . .1,741 . . .1,742 . . .1,743 . . .1,744 . . .1,745 . . .1,746 . . .1,747 . . .1,748 . . .1,749 . . .1,750 . . .1,751 . . .1,752 . . .1,753 . . .1,754 . . .1,755 . . .1,756 . . .1,757 . . .1,758 . . .1,759 . . .1,760 . . .1,761 . . .1,762 . . .1,763 . . .1,764 . . .

t---+++1,767 . . .1,768 . . .1,769 .,.1,7701 . . .1,771] . . .

HV 10m

6,206,206,196,186,176,176,166,156,156,146,136,136,126,116,106,106,096,086,086,076,066,066,056,046,036,036,026,016,016,005,995,995,985,975,975,965,955,955,945,935,935,925,91

Vickers hardnessHV 20 HV 30 HV 50

12,4 18,6 31,112,4 18,6 31,012,4 18,6 31,012,4 18,6 30,912,4 18,5 30,9:12,3 18,5 30,912,3 18,5 30,812,3 18,5 30,812,3 18,5 30,812,3 18,4 30,712,3 18,4 30,712,3 18,4 30,712,2 ,X3,4 30,612,2 18,4 30,612,2 18,3 30,612,2 18,3 30,512,2 18,3 30,512,212,212,212,112,112,112,112,112,112;112,012,012,012,012,012,012,011,911,911,911,9.11,911,911,911,811,811,8

18,318,218,218,2i8r218,218,118,118,118,118,118,01$,018,018,018,017,917,917,917,917,917,817,817,817,817,817,7

30,4z

30,430,330,330,330,230,230,230,130,130,130,030,030,029,929,929,929,829,829,829,729,729,729,629,629,6

HV 10062,162,062,061,$61,~61,761,761,661,561,561,461,261,261,261,161,C61,C60,~

60,E60,C60,760,t60,(6or~

60,460,C60,C60,:60,160,160,C59,959,959,E59,759,759,t59,559,5

59,459,:59,:59,259,1

100 I

Is 1501 :20021s0 6507-1 :1997

Table C.3 Range HV 5 to HV 100 (continued)

Mean Test force, Fdiagonal Nof inden-

tation 49,03 I 98,07 198,1 I 294,2 I 49ti,3 I 980,7d

-+---

-1--1,777 . . .1,778 . . .1,779 . . .1,780 . . .1,781 . . .1,782 . . .1,783 . . .1,784 . . .

-+--1,787 . . .1,788 . . .1,789 . . .1,790 . . .1,791 . . .1,792 . . .1,793 . . .1,794 . . .1,795 . . .1,796 . . .1,797 . . .1,798 . . .1,799 . . .1,800 . . .1,801 . . .1,802 . . .1,803 . . .1,804 . . .1,805 . . .1,806 . . .1,807 . . .1,808 . . .1,809 . . .1,810 . . .1,811 . . .1,812 . . .1,813 . . .1,814 . . .1,815 . . .

Wckers hardnesew 10 HV 20 w 30 HV 50 HV 100

5,91 11,8 17,7 29,5 59,15,90 11,8 17,7 29,5 59,C5,89 11,8 17,7 29,5 58,~5,89 11,8 17,7 29,4 58,$5,88 11,8 17,6 29,4 58,E5,87 11,7 17,6 29,4 58,75,87 11,7 17,6 29,3 58,15,86 11,7 17,6 29,3 58,f5,85 11,7 17,6 29,3 58,!

.5,85 11,7 17,5 29,2 58,55,84 11,7 17,5 29,2 58,45,83 11,7 17,5 29,2 58,;5,83 11,7 17,5 29,1 58,25,82 11,6 1,7,5 29,1 58,25,81 11,6 17,4 29,1 58,15,81 11,6 17,4 29,0 58,15,80 11,6 17,4 29,0 58,05,79 11,6 17,4 29,0 57,95,79 11,6 17,4 28,9 57,s5,78 11,6 17,3 28,9 57,E5,77 11,5 17,3 28,9 57,75,77 11,5 17,3 28,8 57,75,76 11,5 17,3 28,8 57,65,76 11,5 17,3 28,8 57,e5,75 11,5 17,2 28,7 57,5

5,74 11,5 17,2 28,7 57,45,74 11,5 17,2 28,7 57,45,73 11,5 17,2 28,6 57,:5,72 11,4 17,2 28,6 57,25,72 11,4 17,2 28,6 57,25,71 11,4 17,1 28,6 57,15,70 11,4 17,1 28,5 57,C5,70 11,4 17,1 28,5 57,05,69 11,4 17,1 28,5 56,$5,69 11,4 17,1 28,4 56$5,68 11,4 17,0 28,4 56,[5,67 11,3 17,0 28,4 56,;5,67 11,3 17,0 28,3 56,:5,66 11,3 17,0 28,3 56,(5,65 11,3 17,0 28,3 56,!

5,65 11,3 16,9 28,2 56,!

5,64 11,3 16,9 28,2 56,,5,64 11,3 16,9 28,2 56,,5,63 11,3 16,9 28,1 56,:

-...-

101

Is 1501 :2002ISO 6507-1 :1997

,

11,21 16,9 I 28,1 I 56,2

Table C.3 Range W 5 to W 100 (continued)

Mean Test force, Fdiagonal Nof inden-

tation 49,03 1. 98,07 I 196,1 294,2 490,3. I 980,7

=m@+%flickershardneIHV20 I HV30 ] HV50 j HVIOO I+

1,817 . . .1,818 . . .1,819 . . .1,820 . . .1,821 . . .1,822 . . .1,823 . . .1,824 . . .1,825 .,.1,826 . . .1,827 . . .1,828 . . .1,829 . . .1,830 . . .1,831 . . .1,832 . . .1,833 . . .1,834 . . .1,835 . . .1,836 . . .1,837 . . .1,838 . . .1,839 . . .

-%&+-1,842 . . .1,843 . . .1,844 .,.1,845 . . .1,846 . . .1,847 . . .1,848 . . .1,849 . . .

-+3-++1,852 . . .1,853 . . .1,854 . . .1,855 . . .1,856 . . .1,857 . . .1,858 . . .1,859 . . .

-!5,625,6?5,605,605,595,59 ~5,585,575,575,565,565,555,545,545,535,535,525,515,515,505,505,495,485,485,475,475,465,455,455,445,445,435,425,425,415,415,405,405,395,385,385,375,37

11,211,211,211,211,211,211,211,111,111,111,111,111,111,111,111,011,011,011,011,011,011,011,011,010,910;910,910,910,910,910,910,910,810,810,810,810,810,810,810,810,816,710,7

16,9 28,1 56,216,8 28,1 56,116,8 28,0 56,016,8 28,0 56,016,8 28,0 55,916,8 I 27,9 I 55,9 I16,716,716,716,716,716,6-16,616,616,616,616,616,516,516,516,516,516,516,416,416,416,416,416,316,316,316,316,316,316,216,2 I16,216,216,216,216,116,116,1

27,9 55,827,9 55,727,8 55,727,8 55.627,8 55,627,7 55,527,7 55,427,7 55,427,7 55,3

G1-427,5 55,027,4 54,927,4 54,827,4 54,827,4 54,727,3 54,727,3 54,627,3 54,527,2 54,527,2 54,427,2 54,427,1 54,327,1 54,2

27,0 54,127,0 54,027,0 54,026,9 53,926,9 53,826,9 53,826,9 53,726,8 53,7

102

v,AJt!.,

...

/

l

.

,

Is 1501 :2002ISO 6507-1 :1997

Table C.3 Range HV 5 to HV 100 (continued)

Mean fest force, Fdiagonal Nof inden-

tation 49,03 I 98,07 I 196,1 I 294,2 I 490,3 I 980,7d Vickers hardness

mm HV 5 ~v 10 I Hv 20 HV 30 HV 50 HV 1001,860 . . . 5,36\ 10,7 16,1 26,8 53,61,861 . . . 5,35 10,7 16,1 26,8 53,51,862 . . . 5,35 10,7 16,0 26,7 53,51,863 . . . 5,34 10,7 16,0 26,7 53,41,864 . . . . 5,34 10,7 16,0 26,7 53,41,865 . . . 5,33 10,7 16,0 26,7 53,31,866 . . . 5,33 10,6 16,0 26,6 53,31,867 . . . 5,32 10,6 16,0 26,6 53,21,868 . . . 5,31 10,6 15,9 26,6 53,11,869 . . . 5,31 10,6 15,9 26,5 53,11,870 . . . 5,30 10,6 15,9 26,5 53,01,871 . . . 5,30 10,6 15,9 26,5 53,01,872 . . . 5,29 10,6 15,9 26,5 52,91,873 . . . 5,29 10,6 15,9 26,4 52,91,874 . . . 5,28 10,6 15,8 26,4 52,81,875 . . . 5,28 10,5 15,8 26,4 52,81,876 . . . 5,27 10,5 15,8 26,3 52,71,877 . . . 5,26 10,5 15,8 26,3 52,61,878 . . . 5,26 10,5 15,8 26,3 52,61,879 . . . 5,25 10,5 15,8 26,3 52.51,880 . . . 5,25 10,5 15,7 26,2 52,51,881 . . . 5,24 10,5 15,7 26,2 52,41,882 . . . 5,24 10,5 15,7 26,2 52,41,883 . . . 5,23 10,5 15,7 26,1 52,31,884 ,.. 5,22 10,4 15,7 26,1 52,21,885 . . . 5,22 10,4 15,7 26, 1 52,21,886 . . . 5,21 10,4 15,6 26, 1 52,11,887 . . . , 5,21 10,4 15,6 26,0 52,11,888 . . . 5,20 70,4 15,6 26,0 52,01>889 . . . 5,20 10,4 15,6 26,0 52,01,890 . . . 5,19 10,4 15,6 26,0 51,91,891 . . . 5,19 10,4 15,6 25,9 51,91,892 . . . 5,18 10,4 15,5 25,9 51,81,893 . . . 5,18 10,3 15,5 25,9 51,81,894 . . . 5,17 10,3 15,5 25,8 51,71,895 . . . 5,16 10,3 15,5 25,8 51,61,896 . . . 5,16 10,3 15,5 25,8 51,61,897 . . . 5,15 10,3 15,5 25,8 51,51,898 ,.. 5,15 10,3 15,4 25,7 51,51,899 . . . 5,14 10,3 15,4 25,7 51,41,900 . . . 5,14 10,3 15,4 25,7 51,41,901 . . . 5,13 10,3 15,4 25,7 51,31,902 . . . 5,13 10,3 15,4 25,6 51,31,903 . . . 5,12 10,2 15,4 25,6 51,2

103

,...

[s 1501 :2002ISO 6507-1 :1997

Table C.3 Range HV 5 to HV 100 (continued)

Mean Test forae, Fdiagonal Nof inden-

tation 49,03 98,07 ,1 196,1 I 294,2 I 490,3. I 980,7d

mm I HV 5 I HV 10Vickers hardness I

HV 20 HV 3015,315,315,315,315,315,315,215,215,215,215,215,215,215,115,115,115,1

HV 50 3HV 10051,251,151,051,050,950,950,850,810,2 25,625,525,525,525,525:425,425,41,9051,9061,9071,9081,9091,9101,9111,9121,9131,9141,9151,9161,9171,9181,919

--l--+ 10,210,210,210,210;210,210,210,110,110,110,1

. . .

. . .

. . .

5,1C5,0$5,0$

. . .

-1---5,07. . . 5,0;. . . 5,0t. . . ..5,0(. . . 5,0~ 25,425,325,325,325,325,225,225,225,2

50,750,750,650,650,550,550,450,450,350,350,250,150,150,050,049,949,949,849,8

10,1. . .

. . .

. . .

5,0!5,(3i5,t3L

10,1!0110,110,1

--+=-

5,(K5,0:5,0:5,05,0