GOST 25.502-79

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  ГОСТ 25.502-79

GOST 25.502−79 Calculations and strength tests in mechanical engineering. Methods of mechanical testing of metals. Test methods for fatigue (with Change No. 1)

GOST 25.502−79

Group B09

INTERSTATE STANDARD

Calculations and strength tests in mechanical engineering

METHODS OF MECHANICAL TESTING OF METALS

Test methods for fatigue

Strength analysis and testing in machine building. Methods of metals mechanical testing. Methods of fatigue testing

ISS 77.040.10
OKP 00 2500

Date of introduction 1981−01−01

Resolution of the USSR State Committee on standards of November 30, 1979 N 4146 date of introduction is established 01.01.81

Limitation of actions taken by Protocol No. 2−92 of the Interstate Council for standardization, Metrology and certification (ICS 2−93)

INSTEAD 23026−78 GOST and GOST 2860−65 in clauses.6.1 and 6.2

EDITION with Change No. 1, approved in December 1985 (IUS 3 to 86).


This standard specifies methods of testing of samples of metals and alloys to fatigue:

tensile — compression, bending, shear and torsion;

for a symmetric and asymmetric cycles napryazhenii or deformation, changing a simple periodic law with constant parameters;

in the presence and absence of stress concentration;

at normal, low and high temperatures;

in the presence or absence of aggressive environment;

in many — and low-cycle elastic and elastic-plastic region.

Terms, definitions and symbols used in the standard — GOST 23207−78.

The standard was developed by taking into account the recommendation of ISO R 373 and recommendations of the CMEA PC 36−63.

The standard does not specify the test methods the samples used in testing of strength of high-stressed constructions.

Sections 2−4 of the standard applications can be used for testing fatigue of machine elements and structures.

1. SAMPLING METHODS

1.1. Testing metals for fatigue is carried out on smooth specimens of circular cross section types I (Fig.1, tab.1) and II (Fig.2, table 2) and rectangular section types III (Fig.3, tab.3) and IV (Fig.4, table.4).

Damn.1. The working part of the sample of type I

The working part of the sample of type I

Damn.1

Table 1

mm

5,0
7,5
10
12
15
20	90
25

Damn.2. The working part of the specimen type II

The working part of the specimen type II

Damn.2

Table 2

mm

5,0	25	5,0
7,5	37,5	7,0
10	50	10
12	60	12
15	75	15
20	100	20
25	125	25

Damn.3. The working part of the sample of type III

The working part of the sample of type III

Damn.3

Table 3

mm

The bending in the plane of size			The bending in the plane of size
Up to 3.0 incl.	10		3,0−20,0
SV. 3.0 to 10.0 incl.	15−30

Damn.4. The working part of the sample type IV

The working part of the sample type IV

Damn.4

Table 4

mm

Up to 3.0 incl.	10	5,65
SV. 3.0 to 10.0 incl.	1530

1.2. The sensitivity of the metal to stress concentration and the influence of the absolute sizes determine the samples of types:

V — with a V-shaped circular recess (Fig.5, tables.5−8);

Damn.5. The working part of the sample of type V

The working part of the sample of type V

Damn.5

Table 5

					degrees.
mm					Bending
10	5,0	2,5	2,5	Of 2.00	80	1,33	11,17
12	7,5	3,75	2,25	Of 1.09	70	1,68
15	7,5	3,75	3,75	Of 1.09	70	1,75
17	7,5	3,75	4,75	Of 1.09	70	1,75
20	10	5,0	5,0	0,78	65	2,20
24	12	6,0	6,0	0,61	60	2,63
10	5,0	2,5	2,5	Of 1.00	70	1,58	6,53
12	7,5	3,75	2,25	0,60	65	2,04
15	7,5	3,75	3,75	0,60	65	2,18
17	7,5	3,75	4,75	0,60	65	2,18
20	10	5,0	5,0	0,43	60	2,80
24	12	6,0	6,0	0,36	55	3,30
10	5,0	2,5	2,5	0,50	65	1,99	3,56
12	7,5	3,75	2,25	0,32	60	2,58
15	7,5	3,75	3,75	0,32	60	Of 2.83
17	7,5	3,75	4,75	0,32	60	Of 2.83
20	10	5,0	5,0	0,23	50	3,73
24	12	6,0	6,0	0,19	45	4,42

Table 6

					degrees.
mm					In tension-compression
10	5,0	2,5	2,5	Of 2.00	80	1,48	Of 15.67
15	7,5	3,75	3,75	1,33	70	1,95
20	10	5,0	5,00	Of 1.00	65	2,45
24	12	6,0	6,0	0,83	60	2,89
10	5,0	2,5	2,5	Of 1.00	70	1,87	7,87
15	7,5	3,75	3,75	0,87	65	2,60
20	10	5,0	5,0	0,50	60	3,35
24	12	6,0	6,0	0,42	55	3,99
10	5,0	2,5	2,5	0,50	65	2,45	3,92
15	7,5	3,75	3,75	0,33	60	3,58
20	10	5,0	5,0	0,25	50	4,65
24	12	6,0	6,0	0,21	45	5,55

Table 7

					degrees.
mm					Torsional
10	5,0	2,5	2,5	Of 2.00	80	1,17	17,50
15	7,5	3,75	3,75	0,92	Seventy	1,45
20	10	5,0	5,0	0,62	65	1,71
24	12	6,0	6,0	0,50	60	Of 1.94
10	5,5	2,5	2,5	0,50	65	1.52 m	6,57
15	7,5	3,75	3,75	0,30	60	1,96
20	10	5,0	5,0	0,22	50	2,40
24	12	6,0	6,0	0,18	45	2,77

Table 8

					degrees.
mm					In tension-compression	Bending	Torsional
10	5,0	2,5	2,5	0,5 0,25	65 50	2,45 3,35	1,99 2,63	1.52 m 1,83
12	7,5	3,75	2,25	0,5 0,25	65 50	-	2,28 Of 2.83	-
15	7,5	3,75	3,75	0,5 0,26	60 45	2,93 Of 4.04	2,33 3,14	1,68 Of 2.08
17	7,5	3,75	4,75	0,5 0,25	60 45	-	2,33 3,14	-
20	10 1	5,0	5,0	0,5 0,27	50 40	3,35 4,65	2,63 3,56	1,83 2,30
30	15	7,5	7,5	0,5	45	4,05	3,14	Of 2.08

VI with symmetric side notches V-shaped profile (Fig.6, table.9);

Damn.6. The working part of the specimen type VI

The working part of the specimen type VI

Damn.6

Table 9

						degrees.
mm						In tension — compression	Bending
10	5,0	10	2,5	2,50	0,50 0,25	65 50	2,94 4,07	2,18 2,90
15	7,5	15	3,75	3,75	0,50 0,25	60 55	3,55 4,98	2,57 3,48
20	10	20	5,00	5,00	0,50 0,25	50 40	4,07 5,73	2,9 3,95

VII — with the Central transverse round hole (damn.7, table.10);

Damn.7. The working part of the sample of the type VII

The working part of the sample of the type VII

Damn.7

Table 10

mm			In tension-compression	Bending
Up to 3.0 incl.	10		2,73	Of 2.08
SV. 3.0 to 10.0	5		2,73	2,28

VIII — with a circular recess of the circular profile (Fig.8, table.11);

Damn.8. The working part of the samples of the type VIII

The working part of the samples of the type VIII

Damn.8

Table 11

mm					In tension-compression	Bending	Torsional
6,00	5,00		0,50	0,50	2,18	1,89	1,46
9,00	7,50		0,75	0,75	2,18	1,89	1,46
12,0	10,0		Of 1.00	Of 1.00	2,18	1,89	1,46
17,0	15,0		Of 1.00	Of 1.00	2,18	1,89	1,46

IX — with two symmetrically arranged holes (Fig.9, table.12);

Damn.9. The working part of the sample of the type IX

The working part of the sample of the type IX

Damn.9

Table 12

mm
40	10	To 10.0	3,0	2,44
1,5	3,15

X with symmetric side notches V-shaped profile (Fig.10, table.13).

Damn.10. The working part of the sample of type X

The working part of the sample of type X

Damn.10

Table 13

					degrees.
mm
40	10	To 10.0	0,5	10	40	5,73

Sample sizes are selected in such a way that the similarity parameter of the fatigue damage varied widely as possible the limits for a given range of diameters (perimeter of the working cross-section of the sample or part thereof adjacent to the zone of increased tension; - the relative gradient of the first principal stress).

At bending with rotation, torsion and tension-compression specimens of types I, II, V, VIII ;

when bending in one plane samples of types III, IV, VI, and tensile-compression samples of type VI ;

tensile-compression samples of types III, IV, VII, IX, X .

1.3. For tests on low-cycle fatigue use samples of types II and IV, if there is no danger of buckling.

Allowed to use samples of types I and III.

1.4. The working part of the samples should be made for accuracy not below 7-th qualitities 25347−82.

1.5. The roughness parameter of the surface of the working part of the samples should be 0.32 mm to 0.16 µm according to GOST 2789−73.

The surface must not have any traces of corrosion, scale, casting peels and tint etc. if it is not stipulated objectives of the study.

1.6. The distance between the grips of the test machine chosen so as to prevent buckling of the sample and the impact of efforts in the grips of the tension in its working parts.

1.7. The cutting blanks, labeling and preparation of samples should not significantly influence the fatigue properties of the source material. Heating of the sample in the manufacture should not cause structural changes and physical-chemical transformations in metal; allowances for processing, the mode settings and the processing sequence should minimize work hardening and to eliminate local overheating of the samples during grinding as well as cracks and other defects. Removing the last chip from the working part and of the heads of the samples is carried out with one sample set; the burrs on the lateral faces of the samples and the edges of the notches should be removed. The workpiece is cut in the field with a specific orientation in relation to the macrostructure and the stress condition of the products.

1.8. Within the intended series of tests, the technology of manufacturing the samples of the same metals must be the same.

1.9. Measurement of the dimensions of the working parts are made of samples before testing should not cause damage to its surface.

1.10. The working part of the sample is measured with an accuracy of at least 0,01 mm.

2. EQUIPMENT

2.1. Testing machines, fatigue should ensure the loading of samples on one or a few schemes shit. 11−16. Testing machines for fatigue, it is ensured that the static burst tests, must meet the requirements of GOST 1497−84.

Damn.11. Pure bending when rotating samples of types I, II, V, VIII

Pure bending when rotating samples of types I, II, V, VIII

Damn.11

Damn.12. Transverse bending during the rotation of the samples of types I, II, V, VIII console when loading

Transverse bending during the rotation of the samples of types I, II, V, VIII console when loading

Damn.12

Damn.13. Pure bending in plane samples of types I-VIII

Pure bending in plane samples of types I-VIII

Damn.13

Damn.14. Transverse bending in one plane samples of types I-VIII under cantilever loading

Transverse bending in one plane samples of types I-VIII under cantilever loading

Damn.14

Damn.15. Again-the variable tension-compression specimens of types I-X

Again-the variable tension-compression specimens of types I-X

Damn.15

Damn.16. Again-alternating torsion specimens of types I, II, V, VIII

Again-alternating torsion specimens of types I, II, V, VIII

Damn.16

2.2. The total error of the loading process of the test samples depends on the type of machine and frequency of loading and shall not exceed in the range of 0.2−1.0 for each range of loading in percent of the measured value:

±2% at 0.5 Hz;

±3% at 0.5 to 50 Hz;

±5% at 50 Hz.

When tested on hydraulicing and resonant machines without strain-gauge cylosporine in the range of 0−0,2 of each range load accuracy of load measurement shall not exceed ±5% of specified voltage.

2.3. Measurement error, maintaining and recording the strains in low-cycle tests shall not exceed ±3% of measured value in the range of 0.2−1.0 for each range of loading.

2.4. The absolute error of the measurement, the maintenance and registration of loads and deformations in the range of 0−0,2 of each range must not exceed the absolute error at the beginning of this range of loading.

2.5. Load (soft load) or strain (hard loading) must meet 0.2 and 0.8 of the applicable measurement range.

2.6. When tested in low-cycle tension or compression and tension-compression, the additional bending deformation of the sample from the eccentricity of loading should not exceed 5% of the deformation of stretch or compression.

2.7. In tests on low-cycle fatigue should be provided with a continuous measurement, and continuous or periodic check of process of deformation of the working part of the sample.

2.8. Allowed calibration of test equipment for the static modes (including the misalignment of loading) with an estimate of the dynamic component of the error, or estimated by indirect methods.

3. TESTING

3.1. After testing is allowed in soft and hard loading.

3.2. Within the scheduled of the test series, all specimens loaded in one way and tested on similar machines.

3.3. Testing of samples is carried out continuously until the formation of cracks of a given size, complete destruction or to the base number of cycles.

Permitted breaks in tests with consideration of test conditions and mandatory assessment of the impact of interruptions on test results.

(Changed edition, Rev. No. 1).

3.4. In the process of testing samples stability control asked loads (deformation).

3.5. Test series of similar specimens in an asymmetric cycles carried out:

or if the same for all samples, the average stress (strain) cycle.

or if the same for all the samples the coefficient of cycle asymmetry.

3.6. To build the distribution curve of the durability and estimation of the mean and standard deviation of the logarithm of durability at a given level of stress experience a series of at least 10 identical samples to the complete destruction or the formation of macro cracks detection.

3.7. Tests on high-cycle fatigue

3.7.1. The main failure criteria in determining endurance limits and fatigue curves are complete destruction or the emergence of macro cracks detection of a specified size.

3.7.2. To build the fatigue curve and determine the endurance limit corresponding to a probability of failure of 50% experiencing at least 15 identical samples.

In the voltage range of 0.95 and 1.05 from the fatigue limit, the corresponding probability of failure of 50% must be tested at least three samples, at least half of them should not be destroyed to the base test.

3.7.3. Base tests to define the limits of endurance, was adopted:

10·10cycles for metals and alloys having almost horizontal part in the curve of fatigue;

100·10cycles for light alloys and other metals and alloys, the ordinates of the curves of fatigue which throughout the length of the continuously decrease with increasing number of cycles.

For comparative tests the database to determine the limits of endurance, respectively, is assumed to be 3·10and 10·10cycles.

3.7.4. To create a family of fatigue curves on the parameter of failure probability, constructing a distribution curve of endurance limit, estimation of the mean and standard deviation of the endurance limit have a series of at least 10 identical samples at each of 4−6 voltage levels.

3.7.5. From 10 to 300 Hz the frequency of cycles is not regulated, if the test is performed under normal atmospheric conditions (according to GOST 15150−69) and if the temperature of the working part of the specimen during the testing not exceeding 50 °C.

For samples of fusible and other alloys that detects changes of the mechanical properties to a temperature of 50 °C, full temperature test set separately.

In all cases, the frequency of cycles used when reporting the results of the tests.

Comparative tests are recommended, the frequency of loading.

3.8. Tests on low cycle fatigue (durability up to 5·10cycles*).
________________
* Number of cycles 5·10is the conventional boundary low — and high-cycle fatigue. This value for plastic steels and alloys characterizes the average number of cycles to the transition zone from elastic to elastic-plastic cyclic deformation. For high-ductility alloys, the transition zone shifts towards larger longevity, to the fragile — to smaller.

3.8.1. The main type of loading in the tests is a tensile-compression.

3.8.2. The upper frequency level of the test is limited to values that exclude self-heating of the sample above 50 °C for light alloys and above 100 °C for steels.

In all cases, the frequency of cycles used when reporting the results of the tests.

Comparative tests are recommended, the frequency of loading.

For registration of the diagrams of deformation allowed during the test, the transition to a lower frequency corresponding to the required resolution and accuracy of the devices measuring and recording cyclic stresses and strains.

3.8.3. When testing tensile-compression samples of types II and IV the measurement of deformations should be carried out in the longitudinal direction.

When testing samples of types I and III are allowed to measure the deformation in the transverse direction.

Note. For approximate recalculation of transverse strain to longitudinal use the formula

,

where is the elastic component of lateral deformation;

plastic component of lateral deformation.

3.9. Testing at elevated and reduced temperatures

3.9.1. Tests at low and high temperatures is carried out under the same types of deformation of the same specimen at normal temperature.

3.9.2. It is recommended that tests are carried out at temperatures (in °C) that are multiples of 50, if a test is not required interpass temperature.

3.9.3. The temperature of the test specimens is controlled according to the dynamic calibration of the temperature differential between the sample and furnace chamber. Temperature calibration is carried out taking into account the influence of the duration of the trial. When calibration of the thermocouple fixed to the sample.

3.9.4. Thermocouple being checked before testing and afterwards at GOST 8.338−2002. When tested on databases for more than 10cycles also produce intermediate calibration of thermocouples.

3.9.5. The unevenness of the temperature distribution along the length of the working part when testing smooth samples of types II and IV shall not exceed 1% for 10 mm of the specified test temperature. When testing smooth specimens of types I, III and specimens with stress concentrators by the unevenness of the temperature distribution is governed at a distance of ±5 mm from the minimum cross section of the sample. Deviation from set temperature shall not exceed 2%.

3.9.6. In the process of testing permissible deviations of the temperature on the working part of the sample in °C should not go beyond:

to	600	incl.	± 6;
St.	601	to	900	«	±8;
«	901	«	1200	«	± 12.

3.9.7. The loading of samples is carried out after the steady-state thermal regime of the system «sample oven» when the preset temperature of the sample.

3.9.8. Base tests are passed in accordance with clause 3.7.3 of this standard.

3.9.9. For comparability of the test results of this series of samples performed at the same frequency and the base, if the purpose of the tests is to study the influence of frequency of loading. The test reports indicate not only the number of passed cycles, but total test time of each sample.

3.10. Testing in a corrosive environment

3.10.1. Test in hostile environment is carried out at the same types of deformation and on the same samples, and in the absence of aggressive environment. Simultaneous testing of groups of samples with the registration of the time of the destruction of each.

3.10.2. The sample must continuously be in a gaseous or liquid corrosive environment.

3.10.3. When tested in a corrosive environment must be ensured the stability of the parameters of aggressive environment and its interaction with the sample surface. Requirements for frequency control, the composition of the corrosive environment are determined by the medium composition and objectives of the study.

3.10.4. For comparability of the test results of this series of samples performed at the same frequency and the base, if the purpose of the tests is to study the influence of frequency of loading.

3.9−3.9.9, 3.10−3.10.4. (Introduced later, Rev. N 1).

4. PROCESSING OF THE RESULTS

4.1. The results of tests for fatigue are conducted:

the construction of the fatigue curve and the determination of the fatigue limit, the corresponding probability of failure of 50%;

the diagram of limit stresses and maximum amplitudes;

build the fatigue curve in low cycle region;

the diagram of elastic-plastic deformation and determination of their parameters;

construction of fatigue curves on the parameter of failure probability;

determination of endurance limit for a given level of failure probability;

determine the mean value and standard deviation of the logarithm of durability at a given level of stress or deformation;

determine the mean value and standard deviation of the endurance limit.

These characteristics of fatigue resistance of metals is determined for different stages of development of macro cracks detection and (or) destruction.

4.2. Processing of results of tests on high-cycle fatigue

4.2.1. The original data and the results of each test sample is fixed in the test report (attachments 1 and 2), and the results of testing a series of identical samples in a consolidated test report (attachments 3 and 4).

4.2.2. Curves are built in semi-logarithmic coordinates (; or ; ) or double logarithmic coordinates (; or ;

).

4.2.3. Curves in an asymmetric cycles build for a series of identical specimens tested under identical secondary voltages or at the same skewness.

4.2.4. Curves of fatigue test results a limited amount of samples (section 3.7.2) build method of graphical interpolation of the experimental results or by the method of least squares.

4.2.5. To build the curves of the distribution of longevity and endurance limits, assessment of average values and standard deviations, as well as constructing a family of fatigue curves according to the parameter probability of breaking the test results are subjected to statistical analysis (appendices 5−7).

4.2.6. The diagram of limiting stresses and amplitudes of limit build with the family of fatigue curves, obtained by testing at least three or four episodes of the same samples at different for each series of medium voltage or asymmetry of the stress cycle.

4.3. Processing of test results on low cycle fatigue

4.3.1. Processing of the results produced, as indicated in paragraph 4.2.4.

4.3.2. The source data and test results of each sample record in the test report, and test results of a series of identical samples in a consolidated test report (Annex 8 and 9).

4.3.3. The results of tests of specimens under severe loading build curves in double logarithmic coordinates (Fig.17):

the amplitude of the total strain  — number of cycles to formation of cracks or to failure ;

the amplitude of plastic deformation - number of cycles corresponding to the number of cycles to formation of cracks or to failure .

Notes:

1. The amplitude of plastic deformation is defined as half the width of the elastoplastic hysteresis loop , or as the difference between the specified amplitude of the total strain amplitude and elastic strain determined from the measured load corresponding to her stress and the elastic modulus of the material.

2. The plastic strain amplitude at number of cycles corresponding to the number of cycles until a crack or to failure determine by interpolation of the amplitudes with the pre-selected numbers of cycles, close to the expected.

Damn.17. Curves of fatigue under severe loading

Curves of fatigue under severe loading

Damn.17

4.3.4. The results of tests under mild loading build:

curve in semi-logarithmic or double logarithmic coordinates: the amplitude of the stress  — number of cycles to formation of cracks or to destruction (hell.18);

the amplitude of the plastic deformation (half the width of the hysteresis loop) of the number of half-cycles of loading for the parameter of amplitude of the voltage at the selected ratios of voltages (Fig.19).

Damn.18. The fatigue curve under soft loading

The fatigue curve under soft loading

Damn.18

Damn.19. The amplitude of the plastic deformation of the number of half-cycles of loading

The amplitude of the plastic deformation of the number of half-cycles of loading

Damn.19

and — for cyclic softening of the material: b — for cyclically stabilized material; in for cyclically hardenable material

ANNEX 1 (recommended). Test report sample

ANNEX 1
Recommended

PROTOCOL
the sample (Annex to the summary Protocol N ________)

Assigned test
Sample: cipher				, the transverse dimensions
Machine: type		N
Voltage cycle:
maximum			average					, amplitude
Load (the number of divisions on the scale of loads):
maximum			average					, amplitude
The readings, registered axialent loads or runout of the sample:
device N 1	the device N 2						the device N 3
Meter readings (date and time):
at the beginning of the test
at the end of the test
The number of passed cycles
Loading frequency
The failure criterion

Counter (time)		The number of cycles (time) travelled by the sample for a change	Signature and date		Note
in the beginning of the shift	at the end of shift	passed change	to have accepted the change

Tests conducted

signature

Head of laboratory

signature

APPENDIX 2 (recommended). Test report sample

ANNEX 2
Recommended

PROTOCOL N ________
the sample (Annex to the summary Protocol N _____)

The purpose of the test

Sample: cipher

, the transverse dimensions

Machine: type

N

Deformation cycle:

maximum

average

, amplitude

The number of divisions on the indicator strain: the maximum

,

secondary

, amplitude

The readings, registered axialent load:

device N 1

the device N 2

the device N 3

Meter readings (date and time):

at the beginning of the test

at the end of the test

The number of passed cycles

Loading frequency

The failure criterion

Counter (time)		The number of cycles (time) travelled by the sample for a change	Signature and date		Note
in the beginning of the shift	at the end of shift	passed change	to have accepted the change

Tests conducted

signature

Head of laboratory

signature

APPENDIX 3 (recommended). SUMMARY REPORT

APPENDIX 3
Recommended

SUMMARY REPORT N _______

The purpose of the tests
Material:
brand and condition
the direction of the fibers
stock type (in complex form attached to the plan of cutting out of samples)
Test conditions:
the type of loading
database testing
loading frequency
The failure criterion
Samples:
Type of samples and the nominal dimensions of the cross section
Surface condition
Testing machine:
type	N
Date of testing:
early testing of the first sample									the end of the test
the last sample

Cipher sample	The lateral dimensions of the sample	Voltage cycle			The great — duced the number of cycles	Note on the destruction of the sample (Yes, no)	Note
secondary	amplitude	maximum

Responsible for testing in this series of samples

signature

Head of laboratory

signature

APPENDIX 4 (recommended). SUMMARY REPORT

ANNEX 4
Recommended

SUMMARY REPORT N ________

The purpose of the tests
Material:
brand and condition
the direction of the fibers
stock type (in complex form attached to the plan of cutting out of samples)
Test conditions:
the deformations
database testing
loading frequency
Failure criteria
Samples:
type of samples and the nominal cross-sectional dimensions of
surface condition
Testing machine:
type	N
Date of testing:
early testing of the first sample										the end of the test the last sample

Cipher sample	The lateral dimensions of the sample	Deformation cycle			Passed the number of cycles	Note on the destruction of the sample (Yes, no)	Note
average	amplitude	maximum

Responsible for testing in this series of samples

signature

Head of laboratory

signature

APPENDIX 5 (recommended). THE CURVE OF THE DISTRIBUTION OF LONGEVITY AND THE AVERAGE AND STANDARD DEVIATION OF THE LOGARITHM OF DURABILITY

ANNEX 5
Recommended

THE CURVE OF THE DISTRIBUTION OF LONGEVITY AND THE AVERAGE AND STANDARD DEVIATION OF THE LOGARITHM OF DURABILITY

Test results a series of samples at a constant voltage level in a variation range in ascending order of longevity

.

Such series for samples of aluminum alloy V95 brands tested in cantilever bending with rotation to the complete destruction of six voltage levels as an example, are given in table.1.

Distribution curves of longevity () is built on probability paper corresponding to a lognormal or other distribution. The abscissa shows the delay values of durability of the samples , and the y — axis values of the probability of destruction of samples (accumulated frequency), calculated according to the formula

,

where - the number of the pattern in the variation range;

 — the number of samples tested.

If the voltage level is destroyed not all samples of the series, building only the lower part of the distribution curve to the base durability.

Drawing on a lognormal probability paper, given a family of curves of the distribution based on the data table.1.

Table 1

Variational series of the number of cycles to failure of samples of alloy grade V95

	· 10	· 10	· 10	· 10	· 10	·10
when , kgf/mm(MPa)
33,0 (330)	Of 28.5 (285)	25,4 (254)	22,8 (228)	21,0 (210)	19,0 (190)
1	2,18	0,701	1,63	3,44	0,982	4,63
2	2,29	0,740	2,07	4,58	Of 1.97	6,90
3	2,58	0,809	2,15	4,61	2,20	9,57
4	2,80	0,910	2,27	Of 5.06	2,35	10,0*
5	Of 2.81	1,03	2,30	6,21	3,19	10,0*
6	Of 2.91	Of 1.09	2.54 mm	8,40	3,66	10,0*
Seven	2,97	1,17	2,56	Of 8.98	4,76	10,0*
8	3,05	1,18	2,62	9,47	4,98	10,0*
9	3,05	1,35	2,64	10,4	5,40	10,0*
10	3,27	1,42	2,69	15,4	6,53	10,0*
11	3,39	1,43	2,87	18,5	2,28	10,0*
12	3,48	1,54	3,02	18,8	9,04	10,0*
13	3,63	1,54	3,41	23,2	10,0	10,0*
14	3,82	1,57	3,72	23,7	10,0	10,0*
15	3,84	1,58	3,74	24,8	10,0	10,0*
16	4,10	1,80	4,25	27,7	10,90	10,0*
17	4,12	2,02	Of 5.23	33,0	10,0	10,0*
18	4,39	2,15	5,52	33,9	10,0	10,0*
19	5,21	2,22	Of 6.63	37,4	10,0	10,0*
20	5,72	2,35	7,06	Of 39.06	10,0	10,0*
21	-	-	Of 7.93	41,6	10,0	10,0*
22	-	-	8,00	47,6	10,0	10,0*
23	-	-	8,07	55,5	10,0	10,0*
24	-	-	8,64	55,5	10,0	10,0*
25	-	-	10,2	67,3	10,0	10,0*
26	-	-	10,3	-	-	-

______________
* Samples are not destroyed.

Distribution curves of the durability of the samples of alloy grade V95

1 — =

33 kgf/mm(330 MPa); 2 — = 28,5 kgf/mm(285 MPa);
3 — = 25.4 mm kgf/mm(254 MPa); a 4 = 22,8 kg/mm(228 MPa);
5 — = 21 kgf/mm(210 MPa); 6 — = 19 kg/mm(190 MPa)

The estimate of the average value and the standard deviation of the logarithm of durability is carried out for voltage levels, which destroyed all samples of the series. The sample mean value and sample standard deviation of the logarithm of the durability of the samples () are calculated by the formulas:

;

.

In table.2 to illustrate the calculation and for samples of the V95 alloy grade, tested at a voltage = 28,5 kgf/mm(285 MPa) (see table.1).

Table 2

	· 10
1	0,701	4,8457
2	0,704	4,8692
3	0,809	4,9079
4	0,910	4,9590
5	1,03	5,0128
6	Of 1.09	5,0374
7	1,17	5,0682
8	1,18	5,0719
9	1,42	5,1303
10	1,42	5,1523
11	1,43	5,1553
12	1,54	5,1875
13	1,54	5,1875
14	1,57	5,1959
15	1,58	5,1987
16	1,80	5,2553
17	2,02	5,3054
18	2,15	5,3224
19	2,22	5,3464
20	2,35	5,3711

= 102,59.

= 10524,75.

= 526,70.

= 5,13.

.*

_______________
* Formula conforms to the original. — Note the manufacturer’s database.

The volume of the sample series is calculated by the formula

or

,

where  — coefficient of variation values ;

and the ultimate relative error for confidence in the estimate of the average value and standard deviation values , respectively;

 — the probability of error of the first kind;

 — quantile of normalized normal distribution, the corresponding probability values (the most commonly used quantiles are given in table.3).

The error values selected in the range = 0,02−0,10 and = 0.1 to 0.5, the probability of error of the first kind take of 0.05−0.1.

Table 3

	0,05	0,06	0,07	0,08	0,09	0,10
	1,96	Of 1.88	1,81	1,75	1,70	1,64

APPENDIX 6 (recommended). THE CONSTRUCTION OF A SET OF FATIGUE CURVES ACCORDING TO THE PARAMETER PROBABILITY OF BREAKING THE

APPENDIX 6
Recommended

To build a family of curves of fatigue test is advantageously carried out at four to six stress levels.

The minimum level should be chosen so that to the basic number of cycles collapsed from about 5% to 15% of the samples, the subjects in this voltage level. The following (in ascending order) voltage level must give away 40% — 60% of the samples.

The maximum voltage level is selected based on the requirements on the length of the left branch of the fatigue curve (5·10cycles). The remaining levels are distributed evenly between the maximum and minimum voltage levels.

The results of the tests for each voltage level in a variation ranks on the basis of which to build a family of curves of the distribution of longevity in the coordinates (Appendix 7).

Specify values of failure probability and on the basis of the curves of distribution of durability of build the family of fatigue curves is equal to the probability.

The drawing shows the curves of fatigue specimens of alloy grade V95 for probability of failure = 0,5; 0,10; 0,01 constructed on the basis of graphs.

The minimum required number of samples for constructing a family of fatigue curves determined depending on confidence limit and relative error in the evaluation of the fatigue limit for a given probability based on the formula

,

where  — coefficient of variation of endurance limit;

 — quantile of the normalized normal distribution;

function depending on probability to determine the endurance limit. The values of this function found by the method of statistical modeling are given in the table.

	0,5	0,3	0,2	0,1	0,05	0,01
	2,5	2,7	3,5	4,5	6,0	8,5

Curves of fatigue specimens of alloy grade V95

1 —= 1%; 2 —= 10%; 3 —= 50%

APPENDIX 7 (recommended). BUILDING A DISTRIBUTION CURVE OF ENDURANCE LIMIT AND AN ESTIMATE OF ITS AVERAGE VALUE AND STANDARD DEVIATION

ANNEX 7
Recommended

BUILDING A DISTRIBUTION CURVE OF ENDURANCE LIMIT AND THE ESTIMATION OF ITS MEAN AND STANDARD DEVIATION

To build a distribution curve of endurance limit of the specimens tested in a six voltage levels.

The highest voltage level are chosen so that all samples are at the same voltage collapsed to the base number of cycles. The value of the maximum voltage accepted (1,3−1,5) of the value of endurance limit for a =0,5. The other five levels are distributed so that on average destroyed about 50%, two at 70% — 80% and at least 90% and two low — less than 10% and 20% — 30% respectively.

The value of the voltage in accordance with a given probability of destruction choose on the basis of analysis of available data for similar materials or pre-tests.

After the test results are in the form of variational series on the basis of which to build distribution curves of durability by the method described in Annex 5.

On the basis of the curves of distribution of durability of build the family of fatigue curves for a range of probabilities of failure (Annex 8). It is advisable to use the probability 0,01, 0,10, 0,30, 0,50, 0,70, 0,90 and 0.99.

On these curves of fatigue determine the corresponding values of the fatigue limit. The endurance limit for probability of failure =0.01 to find a method of graphical extrapolation of the fatigue curve corresponding to a base number of cycles.

The obtained values of the limits applied on the graph with coordinates: the probability of failure at a scale relevant to the normal distribution, — limit of endurance in kgf/mm(MPa). Using built point pursuing a line representing a graphical evaluation of the distribution function of the fatigue limit. Divide the range of variation of endurance limit for 8−12 intervals, determine average values of the fatigue limit and its standard deviation according to the formulas:

;

,

where is the mean value of the fatigue limit;

 — the standard deviation of the endurance limit;

 — the value of endurance limit in the middle of the interval;

 — the number of intervals;

 — the increment of the probability within one interval.

As an example, the results of tests on cantilever bending with the rotation of the 100 samples from aluminium alloy grade AB, are presented in table.1, build the distribution function of the fatigue limits for base 5·10cycles and determine the average value and the standard deviation.

Table 1

The values of durability of samples of alloy grade AB

Room p/p	· 10				·10	·10
when , kgf/mm(MPa)
11,0 (110)	11,5 (115)	12,0 (120)	12,5 (125)	13,5 (135)	The 16.5 (165)
1	3,02	Of 2.05	1,26	0,594	3,38	5,83
2	4,49	2,57	1,33	Of 1.00	3,75	11,0
3	4,77	3,81	2,12	1,12	Of 4.23	12,0
4	4,90	A 4.53	Of 2.74	1,54	6,75	12,9
5	5,00*	5,00*	3,01	1,73	8,01	18,1
6	3,69	2,20	8,17	21,8
7	5,00*	2,31	Of 9.26	22,3
8	2,67	10,3	26,5
9	5,00*	12,4	16,5
10	14,6	33,6
11	16,5	38,4
12	18,2	62,4
13	23,9	75,9
14	-	-	24,0	-
15	32,1
16	-	45,9
17	47,7
18	50,0*

_____________
* Samples are not destroyed.


On the basis of variational series (table.1) build distribution curves of longevity (Fig.1).

Distribution curves of the durability of the samples of alloy grade AB

1 — = 16,5 kgf/mm(165 MPa); 2 — = 13,5 kgf/mm(135 MPa);
3 — = 12,5 kgf/mm(125 MPa); a 4 = 12,0 kgf/mm(120 MPa);
5 — = 11,5 kgf/mm(115 MPa); 6 — = 11,0 kgf/mm(110 MPa)

Damn.1

Producing horizontal sections of the curves of distribution of durability (Fig.1) for probability levels = 0,01, 0,10, 0,30, 0,50, 0,70, 0,90, 0,99 (or 1, 10, 30, 50, 70, 90, 99%), find the appropriate durability to the specified voltage on the basis of which to build curves in the parameter probability of breaking the (hell.2).

Curves for samples of alloy grade AB for various probabilities of destruction

1 — = 1%, 2 —= 10%, 3 —= 30%, 4 —= 50%,
5 — = 70%, 6 — = 90%, 7 — = 99%

Damn.2

From the graphs (Fig.2) remove values of fatigue limits for base 5·10cycles. The values of the endurance limits are given in table.2.

Table 2

The values of the limits of endurance of the samples of alloy grade AB (base of 5·10cycles)

The probability of failure , %	0,01	0,10	0,30	0,50	0,70	0,90	0,99
The limit of limited endurance , kgf/mm(MPa)	With 10.6 (106)	11,0 (110)	11,5 (115)	12,0 (120)	12,5 (125)	13,5 (135)	Of 14.5 (145)

The results are given in table.2, build a distribution curve of endurance (damn.3).

Distribution curve of the limit of the limited endurance of the samples of alloy grade AB (base of 5·10cycles)

Damn.3

To determine the average values of the fatigue limit and its standard deviation range of variation in the fatigue limit divided into 10 intervals of 0.5 kgf/mm(5 MPa). The calculation of the specified characteristics in accordance with the formulas presented in table.3.

Table 3

Calculation of average value and standard deviation of the limit of the limited endurance of the samples of alloy grade AB

Room p/p	The boundaries of the interval, kgf/mm	The middle of the interval () kgf/mm(MPa)	The value of probability at the boundaries of the interval
1	10,0−10,5 (100−105)	10,25 (102,5)	0−0,004	0,004	0,4410	-1,856	3,445
2	10,5−11,0 (105−110)	10,75 (107,5)	0,004−0,08	0,076	0,8170	-1,356	1,839
3	11,0−11,5 (110−115)	11,25 (112,5)	0,08−0,30	0,220	2,4750	-0,856	0,733
4	To 11.5−12.0 (115−120)	11,75 (117,5)	0,30−0,52	0,220	2,5850	-0,356	To 0.127
5	12,0−12,5 (120−125)	12,25 (122,5)	0,52−0,70	0,180	2,2050	0,144	0,021
6	12,5−13,0 (125−130)	12,75 (127,5)	0,70−0,82	0,120	At 1.5300	0,644	0,415
7	13,0−13,5 (130−135)	13,25 (132,5)	0,82−0,91	0,090	1,1925	1,144	1,309
8	13,5−14,0 (135−140)	13,75 (137,5)	0,91−0,963	0,053	0,7280	1,644	2,703
9	14,0−14,5 (140−145)	14,25 (142,5)	0,963−0,99	0,027	0,3847	2,144	4,597
10	14,5−15,0 (145−150)	14,75 (147,5)	0,99−1,00	0,010	0,1475	2,644	6,991

The necessary amount of fatigue tests to construct the distribution curve of endurance limit is determined by the formula of Annex 6.

= 12,106 kgf/mm(121,06 MPa); = 0,851;

Of 0.922 kg/mm(which 9.22 MPa)

ANNEX 8 (recommended). Test report sample

ANNEX 8
Recommended

PROTOCOL N ________

the sample (Annex to the summary Protocol N _______)

The purpose of the test
Sample: cipher				, the transverse dimensions
material		, heat treatment						,
hardness		microhardness
Machine: type			N
Voltage cycle:
maximum			minimum
secondary	, amplitude
Deformation cycle:
maximum			minimum
average	, amplitude
Meter readings (date and time):
at the beginning of the test
at the end of the test
Scale check: deformation (mm/%)											,
load (mm/MN)					,
The number of completed cycles before the formation of microcracks with a length of
The number of completed cycles to failure
Loading frequency

Testimony counter		The number of cycles (time) travelled by the sample for a change	Signature and date		Note
in the beginning of the shift	at the end of shift	passed change	to have accepted the change

Treatment of hysteresis loops

The number of cycles

The number of half-cycles

, %

, %

Note

Tests conducted

signature

Head of laboratory

signature

APPENDIX 9 (recommended). SUMMARY REPORT

ANNEX 9
Recommended

SUMMARY REPORT N_________

The purpose of the tests
Material:
brand and condition
the direction of the fibers
stock type (in complex form attached to the plan of cutting out of samples)
Mechanical characteristics
Test conditions:
type of loading
the type of loading
test temperature
loading frequency
Samples:
sample type and nominal cross-sectional dimensions of
surface condition
Testing machine:
type	N
Date of testing:
early testing of the first sample
the end of the test the last sample

Cipher sample

The number of cycles to failure

The number of cycles before formation of a macrocrack

, %

, %

kg/mm

Note

Responsible for testing in this series of samples

signature

Head of laboratory

signature