4

IS1367(Part19):1997
IS0 3800 : 1993

Indian Standard
INDUSTRIAL FASTENERS -THREADED STEEL
FASTENERS -TEC’HNICAL SUPPLY CONDITIONS
PART 19 AXIAL LOAD FATIGUETESTING OF BOLTS, SCREWS AND STUDS

ICS 21.060.10; 19.060

0 BIS 1997

BUREAU OF INDIAN STANDARDS

MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG
NEW DELHI 110002

May 1997 Price Group 9

 IS1367(Part19):1997
IS0 3800 : 1993

Indian Standard
INDUSTRIAL FASTENERS -THREADED STEEL
FASTENERS -TECHNICAL SUPPLY CONDITIONS
PART 19 AXIAL LOAD FATIGUETESTING OF BOLTS, SCREWS AND STUDS

NATIONAL FOREWORD

This Indian Standard (Part 19) which is identical with IS0 3800 : 1993 ‘Threaded fasteners - Axial
load fatigue testing - Test methods and evaluation of results’, issued by the International Organi-
zation for Standardization (ISO), was adopted by the Bureau of Indian Standards on the recommen-
dation of Bolts, Nuts and Fasteners Accessories Sectional Committee and approval of the Light
Mechanical Engineering Division Council.

. The text of the International Standard has been approved as suitable for publication as an Indian
Standard without deviation. Certain terminology and conventions are not identical with those used
in Indian Standards. Attention is drawn to the following:

a) Wherever the words ‘International Standard’appear, referring to this standard, they should be
read as ‘Indian Standard’.

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

In this adopted standard, reference appears to certain International Standards for which Indian Stand-
ards also exist. The corresponding Indian Standards which are.to be substituted in their place are
listed below along with their degree of equivalence for the editions indicated:
.F

In terna tional Corresponding Degree of

Standard Indian Standard Equivalence

IS0 273 : 1979 IS 1821 : 1987 Dimensions for clearance Identical

holes for bolts and screws (third revision)

IS0 554 : 1976 IS 196 : 1966 Atmospheric conditions for Technically

testing (revised) equivalent

IS0 885 : 1976 IS 4172 : 1987 Dimensions for radii under Identical
the head of bolts and screws (first revision)

IS0 4032 : 1986 IS 1364 ( Part 3 ) : 1992 Hexagon head Identical

bolts, screws and nuts of product grades
A and B : Part 3 Hexagon nuts ( size
range Ml .6 to M64) (third revision)

IS0 4033 : 1979 IS/IS0 4033 : 1979 Hexagon nuts, Style Identical
2, Product grades A and B

IS0 8673 : 1988 IS 13722 : 1993 Hexagon nuts, Style 1, Identical

with metric fine pitch threads - Product
grades A and B

IS0 8674 : 1988 IS 13723 : 1994 Hexagon nuts Style 1, Identical

with metric fine pitch threads - Product
grades A and B
1
IS 1367 ( Part 19) : 1997
IS0 3800 : 1993

This standard ( Part 19 ) covers Technical supply conditions in respect of Axial Load Fatigue Testing
of Bolts, Screws and Studs. Other parts covering various aspects of the threaded steel fasteners and
their respective degree of equivalence with International Standards are as under:

IS No. Title Corresponding

IS0 Standard and
Degree of Equivalence

IS 1367 Technical supply conditions for threaded -

steel fasteners:

( Part 1 ) : 1980 Introduction and general information IS0 8992 : 1986

( second revision ) Not technically
equivalent

( Part 2 ) : 1979 Product grades and tolerances ( second Technically equivalent to

revision ) IS0 4759-l : 1978

( Part 3) : 1991 Mechanical properties and test methods Identical to IS0 898-l :
for bolts, screws and studs with full 1988
loadability ( third revision )

( Part 5) : 1980 Mechanical properties and test methods Technically

for set screws and similar threaded equivalent to
fasteners not under tensile stresses IS0 898-5 : 1980
( second revision)

( Part 6) : 1994 Mechanical propertiesand test methods Identical to

for nuts with specified proof loads ( third IS0 898-2 : 1992
revision )

( Part 7 ) : 1980 Mechanical properties and test methods Does npt exist
for nuts without specified proof loads
( second revision )

( Part 8 ) : 1980 Mechanical and performance properties Technically

for prevailing torque type steel hexagon equivalent to
nuts ( second revision ) IS0 2320 : 1983

( Part S/Set 1 ) : 1993 Surface discontinuities, Section 1 Bolts, Identical to

screws and studs for general applications IS0 6157-1 : 1988
( third revision )

( Part S/See 2 ) : 1993 Surface discontinuities, Section 2 Bolts, Identical to

screws and studs for special applications IS0 6175-3 : 1988
( third revision )

( Part 10 ) : 1979 Surface discontinuities on nuts ( second Technically equivalent IO

revision ) IS0 6175-2 : 1995

( Part 11 ) : 1996 Electroplated coatings ( third revision ) Identical to

IS0 4042 : 1989

2
 IS1367(Part19):1997
IS0 3800 : 1993

IS No. Title Corresponding

IS0 Standard and
Degree of Equivalence

( Part 12 ) : 1981 Phosphate coatings on threaded fasteners Does not exist

( second revision )

( Part 13 ) : 1983 Hot-dip galvanized coatings on threaded Does not exist

fasteners ( second revision )

( Part 14 ) : 1984 Stainless steel threaded fasteners Technically equivalent to

( second revision ) IS0 3506 : 1979

( Part 16 ) : 1979 Designation system and symbols ( second Does not exist
revision )

( Part 17) : 1996 Inspection, sampling and acceptance Identical to

procedure ( third revision ) IS0 3269 : 1988

( Part 18) : 1996 Packaging ( second revision ) Does not exist

( Part 20) : 1996 Torsional test and minimum torques for Identical to
bolts and screws with nominal diameter IS0 898-7 : 1992
1mmto10mm

NOTE -Formulation of Part 4and Part 15 of this standard purported tb cover ‘Mechanical properties and test methods
for bolts, screws and studs with reduced loadability’ and ‘Requirements at subzero and elevated temperatures’respectively,
will await corresponding International agreement.

For the purpose of deciding whether a particular requirement of this standard is complied with, the
final value, observed or calculated, expressing the result of a test or analysis, shall be rounded off
in accordance with IS 2 : 1960 ‘Rules for rounding off numerical values ( revised )‘. The number of
significant places retained in the rounded off value should be the same as that of the specified value
in this standard.

3
As in the Original Standard, this Page is Intentionally Left Blank
 IS 1367 (Part 19) : 1997
IS0 3800 : 1993

Indian Standard
INDUSTRIAL FASTENERS -THREADED STEEL
FASTENERS -TECHNICAL SUPPLY CONDITIONS
PART 19 AXIAL LOAD FATIGUETESTING OF BOLTS, SCREWS AND STUDS

1 Scope based on this International Standard are encouraged

to investigate the possibility of applying the most re-
This International Standard specifies the conditions for cent -editions of the standards indicated below.
carrying out axial load fatigue tests on threaded Members of IEC and IS0 maintain registers of cur-
fasteners, as we\\ as recommendations for the evalu- rently valid International Standards.
ation of the results.
IS0 273:1979, Fasteners - Clearance holes for bolts
Unless otherwise agreed, the tests are of the fluctu- and screws.
ating tension type and are carried out at room tem-
perature, the loading applied being centric along the IS0 554: 1976, Standard atmospheres for conditioning
longitudinal axis of the fastener. The influence of the and/or testing - Specifications.
compliance of clamped parts on the strain of the
fastener is not taken into account. IS0 885:1976, General purpose bolts and screws -
Metric series - Radii under the head.
This method allows determination of the fatigue
strength of threaded fasteners. IS0 4032:1986, Hexagon nuts, sty/e 1 -. Product
grades A and B.
The test results can be influenced by the test condi-
tions. For this reason, minimum requirements are IS0 4033:1979, Hexagon nuts, style 2 - Product
specified to reduce this effect. In addition, calibration grades A and B.
and centring control methods for the testing appar-
atus are included. IS0 8673:1988, Hexagon nuts, sty/e 1, with metric
fine pitch thread - Product grades A and B.
2 Normative references
IS0 8674:1988, Hexagon nuts, style 2, with metric
The following standards contain provisions which, fine pitch thread - Product grades A and B.
through reference in this text, constitute provisions
of this International Standard. At the time of publi- 3 Symbols and their designations
cation, the editions indicated were valid. All standards
are subject to revision, and parties to agreements See table 1.

5
IS 1367 (Part 19) : 1997
IS0 3800 : 1993

Table 1 - Symbols and their designations

Symbol Designation Symbol Designation

Area at nominal minor diameter, A, = x&4 Constant stress ratio bm,n/umax

43 4
S Width across flats of hexagons
Stress area A, = 2 2
4+4 z
As
( 1 Standard deviation of the fatigue load
Area to be used in calculatrons of mean stress and s(FA)
stress amplitude. By agreement between the user Standard deviation of the fatigue strength
S(aA)
and supplier, A, may be used.
S( log N) Standard deviation of logarithm of the fatigue life
d Nominal size of the thread of the load verification
stud Coefficients of regression line for the inclined part
a, B
of S/N curve
dl Basic minor diameter of the thread
Stress amplitude
*a
d2
Basic pitch diameter of the thread
Stress amplitude at endurance fatigue limit
Nominal minor diameter of the thread, DA
cs
(5=d,-f u ax Axial tensile stress

Diameter at the point of tangency of the fillet Bending stress

4 Ob

4 Clearance hole diameter Mean stress

am

4 Shank diameter of the load verification stud Minimum stress

amin

D Nominal thread diameter of the threaded test

omax
Maximum stress
adaptor
Minimum stress at endurance fatigue limit
~Mltl
F Tensile load
Maximum stress at endurance fatigue limit
Tensile load at proof stress b,? Oklax
Fo.2
Fatigue strength at N cycles
Load amplitude aAN
Fa
Estimated value of finite life strength at
Difference of load amplitudes in the transition oAA
AFax, N=5x104
range
Estimated value of finite life strength at
Load amplitude at endurance fatigue limit OAE
FA N=l x106

Mean load Stress amplitude of the i* test in the finite life

Frn oa,i
range
H Height of the fundamental triangle of the thread
Stress amplitude of the jrh test by staircase method
oaj
N Number of stress cycles
Interval of stress amplitude of the test at the finite
The number of stress cycles in the case where the AaaI
NG life range (inclined part of S/N curve)
test has discontinued without failure
Difference in levels of stress amplitude in the tran-
AuaIl
P Failure probability sition range

Pf Failure probability in the finite life range

Failure probability in the transition range

NOTES
Pt
P Pitch of the thread 1 The symbol A is used in the case of estimated val-
ues. For example, the estimated value G, of the fatigue
Rm.mrn Minimum tensile strength
strength at the number of cycles N.

2 The symbol - is used in the case of ua or log N val-

ues which are derived from the regression line; e.g. og
or IogN.
4 Principle
Tests with constant mean stress 0, or constant
Test are made on threaded fasteners to determine
stress ratio R, = ~min/~max may be used. Constant
fatigue properties such as those shown by the
mean stress is used generally to determine infinite life
Wohler curve (S/N curve).
[see case (c) in figure 101.
Threaded fasteners to be tested are mounted in an
Constant stress ratio is generally for quality accept-
axial load fatigue testing machine and subjected to
ance testing [see case (a) in figure IO].
fluctuating tension type loading.
 IS 1367 (Part 19) : 1997
Is0 3800 : 1993

The test is continued until the test piece fails, or until total number of cycles per test. The testing machine
a predetermined number of stress cycles has been shall be calibrated periodically to ensure this accuracy.
exceeded. Generally the number of test cycles is de- The frequency range of testing shall be between
termined by the material or by the endurance fatigue 4,2 Hz and 250 Hz. The testing machine shall induce
strength of the test specimen. Unless otherwise a sinusoidal fluctuation in load in the test piece.
specified, the definition of failure is complete separ-
ation of the fastener into two parts. The testing machine shall have a device to prevent its
automatic restarting after stopping due to electrical
power service interruption.
5 Apparatus

5.1 Testing machine 5.2 Test fixtures

The testing machine shall be capable of maintaining The test fixtures shall be capable of transmitting an
automatically the loads to within + 2 % of the re- axial load to the test piece. Figures 1 and 2 give basic
quired values throughout the test and shall be requirements. Self-aligning devices are not rec-
equipped with a device for counting and recording the ommended, see 5.3.

Perpendicularity and concentricity tolerances tn

millimetres, surface roughness tn mlcrometres

tindo WS

dh is in accordance with IS0 273. fine series.

da is in accordance with IS0 885. finished products.

I) Surface may be case-hardened 0,25 mm to 0.5 mm deep: maximum hardness.

HRC 60: minimum hardness, 5 points HRC greater than that of the test part.

Figure 1 - Fixture without insert

 IS 1367 (Part 19) : 1997
IS0 3600 : 1993

Perpendicularity and concentricity tolerances in

millimetres, surface roughness in micrometres

.
indows

36 HRC to 40 HRC Counterbore (optional)

dh is in accordance with I50 273. fine series.

d, is in accordance with IS0 885, finished products.

I) The use of an insert shall not affect the rigidity of the test fixture.
2) Surface may be case-hardned 0.25 mm to 0.5 mm deep: maximum hardness,
HRC 60; minimum hardness, 5 points HRC greater than that of the test part.

Figure 2 - Fixture v&h insert

5.3 Test alignment any excentric loading may cause fatigue test results
to vary widely.
Periodically, the alignment of the test set-up shall be
verified. This shall be determined by using a load
5.4 Internally threaded component
verification stud (see figure31 with four strain gauges
located at 90” on a common centreline around the For fatigue testing of standard products, the appro-
axis. The length of the parallel part of the load veri- priate size and property class of nut in accordance
fication stud shall be four times its diameter. When with IS0 4032, IS0 4033, IS0 8673 or IS0 8674 or a
measured at 50 % of the load range used on the ma- threaded adapter shall be used.
chine, the difference between the maximum stress
bax + a,, and the nominal tensile stress u,, shall not If special bolt-nut combinations are tested, a precise
exceed 6 % of the nominal tensile stress (see description of the nut shall be given as specified in
figure 4). 8.2.

Self-aligning devices are not recommended. If they If threaded adapters according to figure5 are used,
are used, alignment shall be checked carefully since they shall be described in accordance with 8.2.

8
 IS 1367 ( Part 19) : 1997
IS0 3800 : 1993

Cylindricity, perpendicularity and concentricity

tolerances in millimetres. surface roughness in micrometres

I) The tolerance class of the screw thread shall be 4h.

2) d‘ = d

Figure 3 - Load verification stud

Parallel part of load

verification bar

_ 4F

Figure 4 - Stress distribution in the shank of the load verification stud

9
IS 1367 (Part 19) : 1997
IS0 3800 : 1993

61::. C-:CS,;:e::;eyjicularlty and concentricity tolerances

In m!hmetres

I) Thread tolerance 6H.

Figure 5 - Threaded test adaptsr

5.5 Test washers

A chamfered test washer may be used under the bolt The cctn,acity of the testing machine shall be selected
head to provide clearance for the head-to-shank !iilet, so tha? the maximum load on the test specimen is
or the fixtures may be chamfered. The maximum di- equal to or greater than 10 % of the maximum scale
ameter of the 45” included angle chamfer shall be capacity of the machine in the test configuration
equal to the diameter at the point of tangency of the selected. The bearing face of the nut or the face of
fillet (d,) with a + IT1 2 tolerance (see figure6). ‘The the threaded adapter shall be located at least four
faces of washers shall be parallel to within 0.01 mm. pitches from the unthreaded portion of the shank and
The hardness of the washer shall be the same as that the IX? threads shall be fully engaged; a bolt length
of the fixture. r,f at least 2P shall protrude beyond the test nut (see
+~gurc7f. fes? nuts shall be used once only.
Where a test washer is used, it shall be indicst~? i:.
the test report (see 8.3). Threaded test adapters may be used continually as
iong as they assemble freely on the externally
threaded par! each time and no damage has been
observed

II 0.01

r”
Figure 6 - Test washer (assembled) Figure 7 - Location of test nut

10
 IS 1367 (Part 19) : 1997
IS0 3890 : 1993

The specimen shall be assembled freely in the fixture Furthermore, this test shall be made by using either
without binding or forcing. No torsional stress shall the method to keep the mean stress ia,,) constant or
be induced in the assembly by torquing the nut; i.e. the method to keep the ratio (I?,) of the maximum
the load shall be induced in the assembly by the stress and the minimum stress constant (R, = l/IO is
testing machine. generally used).
,*
‘The threaded fastener and test nut shall be thoroughly
cleaned and then coated with SAE 20 oil or equivalent
7.1.1 Quality control test
prior to testing.
A statistically valid sample shall be taken for test pur-
The test frequency shall be selected so that the tem- poses as agreed between the user and supplier. The
perature of the test specimen does not rise more than sample should be increased by at least 10 % to allow
50 “C during the test period. The temperature should for unforeseen testing difficulties.
be measured at the first engaged thread.
7.1.2 Determination of position and slope of the
At frequent intervals throughout the test period, the finite life range (Design test)
load shall be monitored to ascertain that the load
conditions have not changed. The scatter in the number of stress cycles in the finite
life range can economically only be approximated us-
Results of fatigue tests are affected by atmospheric
inp rQ?istical calculation methods.
conditions. Therefore, if possible, atmospheric condi-
tions, particularly humidity, should be checked in ac- for assessment of the finite life range, the fatigue
cordance with IS0 554:1976, 2.1. tests shall be carried out on at least two stress levels,
which should be chosen so that numbers of stress
7 Evaluation of results cycles are obtained between lo4 and 5 x 105.

A comparative assessment of fatigue strength values The number of tests (sampling size) per stress level
is only possible when the tests and ?he evaluation of depends, on the selected statistical evaluation method
results are carried out in a uniform manner. and the required prediction reliability for the probabili-
ties of failure pf; e.g. pr = IO %, 50 % or 90 %.
Fatigue strength values can be determined in the fi-
nite life range (failure of all test pieces before a pra- The minimum number of test pieces should not be
determined number of stress cycles is reached) and less than six.
in the transition range where, up to the predetermined
The scatter in the finite life range on one stress !evel
number of stress cycles (in general 5 x IO6 to 10’
can then be determined by taking as a basis, for ex-
stress cycles), failures as well as non-failures will oc-
ample, the normal Gaussian distribution in the
cur (see figure 10). As a function of the test objective,
Gaussian probability net and by using the estimator
the fatigue tests are carried out and evaluated ac-
cording to two methods: 3i- 1
” = 3n + 1
a) a minimum number of stress cycles is reached at
a predetermined stress amplitude in the finite life where
range and’transition range, respectively;
Pf is the assessed value for the probability of
the position and size of scatter of the finite life failure in the finite life range;
b)
range and transition range, respectively, are de-
i is the ordinal number of a test piece;
termined using statistical evaluation methods.
n is the number of test pieces tested.
7.1 Tests in the finite life range
The following example explains the procedure’
The test in the finite life range is the test for obtaining
n = 8 bolts are tested with the constant stress ampli-
the finite fatigue life data of threaded fasteners and is
tude ga = 150 N/mm2. The stress cycles reached until
generally applied for production control of products,
failure are, in chronologicat order:
quality assurance at delivery and the like. When the _’/’
product specification defines the stress and the num- N = (169, 178,271;‘;29,405, 115, 280, 305) x 103.
ber of stress cycles and the other conditions are not
specified, generally a minimum of six products should At first the numbers of stress cycles are arranged ac-
be tested. cording to size, and ordinals i are assigned to them.

11
IS 1367( Part 19):1997
ISO 3800:1993

The first test piece with the lowest number of stress 7.2.2 Determination of position and size of the
cycles receives the ordinal i = 1, the nth test piece transition range
(with the highest number of stress cycles) the ordinal
i=n=8. By analogy with the finite life range: the scatter in the
transition range can economically only be approxi-
This results in the order or evaluation system given in mated using statistical calculation methods.
table 2.
In practice, two statistical evaluation methods are
Now the numbers of stress cycles belonging to the basically preferred:
respective probabilities of failure pf are plotted in a
Gaussian probability net (figure81 and the individual a) stepwise changing of the stress amplitude after
results are replaced by a compensation line (re- each individual test (staircase method);
gressron line). The lrmrts N,o, Nsa and N,, can be read
using this compensation line. b) changing of the stress amplitude after having
tested several bolts at a constant stress level (e.g.
EXAMPLE boundary method, arc sine method).

N,,=110x103,Ns0=213x103andNs,=415x103 These evaluation methods are based on model func-

(i.e. 10 % of all test pieces are expected to fail within tions which approximately represent the distribution
110 x lo3 stress cycles, 50 % within 213 x lo3 of the population of the test lot.
stress cycles and 90 % within 415 x lo3 stress cy-
cles). Therefore the median CA50 (fatigue strength with
50 % probability of failure) and the limits of the tran-
sition range (e.g. bA1o, aAs are t0 be determined.
7.2 Tests in the transition range (infinite life
range) Experience has shown that about 15 to 20 test pieces
are necessary in order to be able to determine the
fatigue strength oA5(, within a tolerance of + 5 %.
7.2.1 Achieving a given number of stress cycles *
without failure For the determination of the limits of the transition
range, the number of test pieces is clearly hrgher (e.g.
For checking whether the requirement for a minimum about 20 to 30 test pieces for aAIr,).
number of stress cycles is satisfied, a minimum of six
test pieces shall be tested at the predetermined As to the reliability and accuracy of the values to be
stress amplitude, unless otherwise agreed between obtained, the arc sine, the staircase and boundary
the user and supplier. The sample should be in- methods, which in general are based on the normal
creased by at least 10 % to allow for unforeseen dif- Gaussian distribution, are approximately equally good
ficulties. under the same test conditions.

Table 2 - Order system for the statistical evaluation of 8 fatigue tests with a stress amplitude
of CT,= 150 N/mm2 in the finite life range
Ordinal i 1 2 3 4 5 6 7 8

Number of stress cycles

115 129 169 178 271 280 305 405
N x lo3 (in ascending order)

Probability of failure, p,, %

pf = 3i_,l)() 8 20 32 44 56 68 80 92
3n + 1

12
 IS 1367 ( Part 19) : 1997
IS0 3800 : 1993

1 2 3 4 5 6

99

98

95

40

30

20

10

1
200 300 400 500 x10'
Number of stress cycles to failure

(A$,, NSo, A$, = number of stress cycles with 10 %, 50 % or 90 % probability of failure respectively)

Figure 8 - Probability of failure pf and number of stress cycles in the finite life range, determined on the
basis of 8 fatigue tests with U, = 150 N/mm2

13
IS 1367 ( Part 19) :1997
ISO 3600:1993

7.2.3 Procedures of staircase, boundary and arc cles NG,the load amplitude is subsequently increased
sine methods until the first test piece fails. In the example, this is
the load amplitude F,,= 4 000 N. Carry out several
7.2.3.1 Staircase method tests on the level on which there is now for the first
time an event (failure or non-failure) deviating from the
Test the first test piece at a stress level which shall previous tests. Thereby the number of test pieces
be as close as possible to the expected median of the depends on the required accuracy of the result. In this
transition range. If failure occurs, decrease stepwise example, the number of test pieces is eight. For the
the load for the next test pieces (the same step size) selection of the second load amplitude, it is advan-
until there is non-failure. After a non-failure, increase tageous to know the width of the transition range; this
the load stepwise until failure occurs. If non-failure is allows the second level to be chosen, in a math-
recorded for the first test piece, the procedure is re- ematically useful way, at its limit where the expected
versed. In practice, the procedure very quickly centres result becomes more exact.
on the median and, in the case of a large number of
test pieces and a favourable position of the starting The following applies to the determination of the
stress level, the frequencies of failure and non-failure second level:
are the same or nearly the same. The event occurring
less frequently as a whole is used for the calculation. Fa2 = Fal + AFaIl

The evaluation comprises the following steps: with

a) expected median AF,,= (1- +)BF,, for r < 0,5n

FA50 = Fao+ ua, or

hF,ll = - f BF,,for r 2 0,5n

(See explanations of symbols in table3.J
Quantity B takes account of the width of the transition
b) expected standard deviation
range. For B, a value between 0,15 and 0,2 is rec-
ommended.
S(FA)= 1,62AF,,CE-A2 +0,029
C2
On the second load amplitude, found in the example
in figure9, again eight test pieces are tested and the
where ‘5 - A2 shall be > 0,3 probabilities of failure, pt, are plotted in the Gaussian
C2 probability net according to the estimator:

(See explanations of symbols in table 3.) 3r - 1

Pl = -3nf 1

Table 3 shows an example of the evaluation of fatigue

tests by the staircase method. [figure 9, b)]

7.2.3.2 Boundary method where

r is the number of failures;

The procedure for the boundary method is explained
on the basis of figure9. As the position of the transi- n is the number of test pieces tested.
tion range is not known prior to the test and can in
general only be approximated, first test a test piece Using the normal Gaussian distribution, the two points
on a first load amplitude. In this case, this load ampli- determined can be connected to form a straight line
tude Fa= 2 500 N. If this first test piece shows no which then allows determination of the median FA,,
failure up to the predetermined number of stress cy- and of the limiting values, such as FAloand FAW,etc.

14
 IS 1367 ( Part 19) : 1997
IS0 3800 : 1993

Table 3 - Example of the evaluation of fatigue tests by the staircase method

Test piece Hexagon head bolt IS0 4014 - Ml0 x 80 - 8.8

Mean load F, : 0,6F,,2 (N)

1 2 3 4 5 6 7 8

FA (N) x Failure o Non-failure x 0 2 f zf zy

4 700 X 103000

4 300 X x 1 0 X 3 1 2 1 2 4

3 900 X X 0 0 X 0 x 4 3 1 3 3 3

3 500 0 0 0 0 3 0 3 0 0

Test piece No. 1 23456789 10 11 12 13 14 15

Sum of columns 3, 4. 6. 7, 8 8 7 - 7 5 7

C A E

FA5O = Fa, + %,I

s(F,t,)= 1,62hF,,,

Column 1: load amplitude

Column 2: indication of event (failure x, non-farlure o)
Column 3: number of failures per load amplitude
Column 4: number of non-failures per load amplitude
Column 5: ordinal z, starting with 0 at the lowest load amplitude

It is assigned to the event with the lower frequency in columns 3 and 4 respectively. In the example
in table3, it is column 4 with only 7 non-failures as compared to column 3 with 9 failures.
Column 6: frequency, repetition of values from column 3 or 4 with the lower sum (here column 4).
Column 7: product of columns 5 and 6 (zf)
Column 8: product of columns 5 and 7 Cz’fi
C, A, E: sum of columns 6, 7 and 8

Fao : lowest load amplitude in columns 3 or 4 with the lower number of events (here column 4,
Fao = 3 500 N)

FASO : median, load amplitude with 50 % probability of survival

+ 0.5 when column 6 = column 4
x:
- 0.5 when column 6 = column 3

step (here AF,,, = 400 N)

standard deviation

15
IS 1367 (Part 19) : 1997
IS0 3600 : 1993

4 500

z
I4 000

G
i 3500
3
c
“a
E
: 3 000
:

J
0

2 500
2 4 6 0 3 000 3 500 4 000
Number of test piece- Load amplitude * F,, N -

0 Fallure
o Non-failure

Figure g - Example of the execution and evaluation of fatigue tests according to the boundary method

7.2.3.3 Arc sine method 7.4 Combined test method

The procedure for the arc sine method is similar to

that for the boundary method. Carry out fatigue tests
on several equidistant alternating load levels with the
same number of test pieces per level. For each of
these levels, calculate the corres onding probabilities 7.4.1 Number of test specimens
of survival using the arcsin P p transformation, for
example,
r=arcsin Jm+arcsin Jm
At least 14 specimens are required for the test, that
Determine the transition range either graphically in a is 2 specimens for each of four stress amplitude lev-
corresponding probability net or mathematically by els (8 pieces in total) in order to determine the inclined
determining a regression line after the corresponding part of the S/N cutve, and 6 specimens in order to
transformation of the calculated values determine the horizontal part because the staircase
method requires a small number of specimens. Since
7.3 Development of complete Wiihler curve the test does not always proceed, in practice, as
(S/N curve) shown in figure 11 and there are some cases where
more than 14 specimens are required, reserve some
For the development of a complete Wtihler curve, the extra specimens.
results of the test according to 7.1.2 and 7.2.2 are
represented graphically in figure 10.

16
 IS 1367 (Part 19) :1997
ISO 3800:1993

,04
103

NG
Number of stress cycles, N

Figure 10 — Wohler curve (S/N curve) u, =f(N)

IS 1367 (Part 19) : 1997
IS0 3800 : 1993

160
r
l Failure
160 - o Non-failure at 5 x IO6

c(
g 140-
1
b”
$j 120 -
7
c Horizontal part, 6 pieces
E Staircase method
z 100 - L
c
L
Gi
80 -

60
F

40 t’ 1 1 1 llllll I 1 I Ill111 1 I I I11111

IO4 5x104 105 5 x 10s 106 5 x 106
Number of stress cycles, N

NOTE - The numbers in the figure show the order of test.

Figure 11 - Example of basic pattern of combined test method with 14 specimens

7.4.2 Test in the finite life range Test the first specimen at the stress amplitude level
u;(l) = uM - AQ.

Test one specimen at a time in the order

The test method for the finite life range (inclined part u,(2) = ~~(1) - Au,,, u,(3) = u,(2) - Au,,, .. ..
of the S/N curve) is as follows.
by lowering the stress amplitude levels by AcT,~each
Predict the finite life strength ~~ and uAa of the time until the first unbroken specimen is obtained’). In
specimen at N =-5 x lo4 and N = 1 x lo6 by referring this case, check the value of Au,~ as the test pro-
to existing data on materials of the same class, gresses, correct it and reset Au,, for subsequent lev-
specimens of the same shape and stress cycles of els, if necessary.‘)
the same type.
Test one specimen at each of the stress amplitude
Obtain Au,~ = (uAA- u&/3. (Round off the numerical levels at which no specimen has been broken, among
values.) Take this value of Au,~ as the initial set value the four higher levels adjacent to the level*’ at which
for intetvals of the test stress amplitude in the in- the unbroken specimen has been obtained, so that
clined part, and take uAA + kAaaI (k = f 1, f 2, . ...) as one broken specimen is obtained at each of those
the initial set value for the test stress amplitude level. four stress amplitude levels.

1) If the predictions for uAAand oAB are notably inadequate, some specimens will not be broken at o,(l). In that case, test one
specimen at a time in the order

44 = ~~(1) + *AUK,,,u,(3) = u,(2) + *Au,,, ...(

until the first broken specimen is obtained, by raising the stress amplitude level by *Aa,, each time instead of lowering it by
%P
2) When there are two or more stress amplitude levels at which no specimen has been broken (this is possible in the case
corresponding to footnote Y, the highest stress amplitude level among them shall be taken.

18
 IS 1367 (Part 19) : 1997
IS0 3600 : 1993

Carry out the test on the second specimen31 at the order from the lowest of the stress amplitude levels at each
higher levels of stress amplitude adjacent to the of which two specimens have been broken at the same
stress amplitude leve12’ at which no specimen has stress amplitude.

been broken, in ascending order, starting from the

lower of those stress amplitude levels, until eight
7.4.3 Method of testing fatigue strength at
broken specimens in total have been obtained.
NG=5x lo6
Arrange the obtained data of eight broken specimens
The method of testing fatigue strength, in which the
in a semi-logarithmic graph (aa, log N) and obtain S/N
test is cut off at the number of cycles (NG) of
curves.
5 x 106, is as follows,
Determine the inclined part and the standard deviation
Use the staircase method with a small number of
of the S/N curve for a 50 % failure probability by the
samples to estimate the fatigue strength at
following formula.
Nc=5x 16

Regression line for the inclined part of the S/N curve

Take as the test stress amplitude a,(l) applied to the
is given by: first specimen by the staircase method, the stress
amplitude level at which no specrmen was broken
IogN =G+ja,
(take the highest stress amplitude level when such
stress amplitude levels are two or more). However,
where one unbroken specimen has already been obtained at
the level 09, this shall be regarded as the test result
ii= IogN -k on the first specimen by the staircase method and the
test at Q, is not carried out again.
2 [u,(i) - TfJ [log N(i) - WN]
The successive difference hoarI, in levels of stress
$= i=l n
(see note 1) amplitude in Jhe staircase method shall be the esti-
2 [us(i) - ZJ2 mated value S(a,) of the standard deviation of the fa-
ix1 tigue strength with time (the numerical value shall be
rounded off properly).

log N = iglog N(i) (see note 1)

i=l

nu,(i) Carry out the test on the second specimen at the level
q=- 1
a c
i=l
(see note 1)

Estimated value of the standard deviation S( log N) Carry out the test on the third to sixth specimens at
of the logarithm of the fatigue life is given by: the levels

u,(j) = u,o’ - 1) & Aaau lj = 3, 4, 5, 6)

s^( IogN) = [ $T(log N(i) - [G + $,ii)])‘] “2
where the minus sign shall be taken when the
i=l
Q- l)‘h specimen is broken and the plus sign when
it is not broken.
(see note 1)
Obtain the test stress amplitude applied to the sev-
Estimated value of the standard deviation S(a,) of the
enth specimen from
fatigue strength is given by:
o,(7) = o,(6) _+ Aaan

where the minus sign shall be taken when the speci-

men is broken at a,(6) and the plus sign when it is
NOTE 3 In the tests carried out on the first to the nfh not broken. However, the test on the seventh speci-
specimen, use the data from eight broken specimens, in the men is not actually carried out.

3) If the second specimen is not broken at a certain stress amplitude level, add one more test at the required stress amplitude
level so that two broken specimens can be obtained each of the four higher levels of stress amplitude adjacent to that stress
amplitude level.

19
IS 1367 ( Part 19 ) : 1997
IS0 3600 : 1993

Estimate the fatigue strength CJ~ for the failure of the following (deviations from this International
probability p = 50 % at N = 5 x lo6 from the following Standard shall be pointed out clearly).
formula:
8.1 Definition of externally threaded fastener:

a) type and property class designation (if applicable);

b) thread size, pitch, length of fastener, thread toler-

7.4.4 Determination of Wiihler curve (S/N curve)
ance and profile;

The Wohler curve (S/N curve) (see figure 12) for the
c) manufacturing method of fastener and thread;
failure probability p = 10 % and 90 % can be obtained
by the following formula. dl actual mechanical properties (tensile strength and
oroof stress);
Inclined part:

e) surface coating and supplementary lubrication;

IogN =&;a,f 1,28;(logN)

f) nut or adapter location (distance from nut or

Horizontal part:
adapter face to thread runout);

6, = s,* +s^( IogN)

g) raw material.
II
B
8.2 Definition of internally threaded component:
The double signs of the formulae shall be minus for
p=lO%andplusforp=90%.
a) type and property class of nut or height of
threaded test adapter;
7.5 Development of a Haigh diagram
b) actual hardness;
To select a fastener correctly, a designer may need
additional information concerning the influence of c) raw material;
mean stress on the fatigue strength. The Haigh dia-
gram (figure 13) presents the required data in a d) surface coating and supplementary lubricant.
convienent form and shows the fatigue strength for
10 %, 50 % and 90 % probability of failure. Using 8.3 Application of test washer.
statistical methods as defined in 7.2 or 7.4, this chart
may be developed using a minimum number of parts,
8.4 Type and frequency of testing machine.
on each of the following mean stress levels:

a) high constant mean stress CT, = 0,7R,,m,,; 8.5 Stress area used in the calculation (A,, A, or
other).
b) medium constant mean stress 0, = 0,4R,,,,,;
8.6 Type of stress cycle (for example, mean stress
c) low mean stress 6, = 1,220~ (for R, = 0, I) and stress amplitude or R, and either Q,,, or crmax).

Other mean stresses may be used by agreement be-

tween the user and supplier. 8.7 Location of failure.

8 Test report 8.8 The applied statistical evaluation methods

In reporting fatigue data, the test conditions shall be 8.9 Atmospheric conditions (range of temperature
clearly defined and the test report shall include details and humidity during test).

20
 IS 1367 (Part 19) : 1997
IS0 3600 : 1993

180
f-

l Failure
1601
0 Non-failure

80
t

60
F

40 I I 1 lIIl,l I , I I II,,/ 1 , , II,,1

10' 5x10' 105 5x105 106 5x106
Number of stresscycles,N

Figure 12 - Example of Wiihler curve (S/N curve)

100

Examples for probability of failure

90
N
E
2 80

tp
$ 70

I I I I
Cb) U,= 0.7R m.min
(a)

0
0 100 200 300 400 500 600 700 800 900
Meanstress. q,,N/mm 2

Figure 13 - Haigh diagram

21
Bureau of Indian Standards

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development of the activities of standardization, marking and quality certification of goods and attending to
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of ‘BIS Handbook’ and ‘Standards : Monthly Additions’.

This Indian Standard has been developed from Dot : No. LM 14 ( 0045 ).

Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

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