GOST 28830-90

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  ГОСТ 28830-90

GOST 28830−90 (ISO 5187−85) Connections are brazed. Test methods tensile and long durability

GOST 28830−90
(ISO 5187−85)

Group B09

INTERSTATE STANDARD

CONNECTION BRAZED

Test methods tensile and long durability

Soldered and brazed joints.
Test methods for tension and long-term strength

ISS 25.160.50
AXTU 0072

Date of introduction 1992−01−01

INFORMATION DATA

1. DESIGNED AND MADE with the USSR State Committee on management of quality and standards

2. APPROVED AND put INTO EFFECT by Decision of the USSR State Committee on management of quality and standards from 28.12.90 N 3466

This standard developed by the direct application of international standard ISO 5187−85 with additional requirements that reflect the needs of the national economy

3. INSTEAD 23047−78 GOST, GOST 25200−82, GOST 26102−84

4. REFERENCE NORMATIVE AND TECHNICAL DOCUMENTS

5. REPRINTING. February 2005


This standard applies to solder joints of metals and alloys, and establishes methods of static tests tensile and creep strength at normal, high and low temperatures from minus 269 °C to 1200°C.

Additional requirements and recommendations are in italics.

0. INTRODUCTION

The solder connection formed from materials with different physical and chemical properties. It consists of soldered material and solder. On the contact surfaces during soldering diffusion processes occur with the formation of new alloys in the mix.

The position of the theory of elasticity applied to a homogeneous metallic bodies in the calculation of stresses caused by external forces transmitted evenly from an element of a surface or volume to the adjacent elements to explore the strength of these heterogeneous compounds, do not use. The strength of the brazed joint differs from the strength of the brazed materials, solders and depends on various factors. Tests of strength should be carried out, taking into account:

— chemical composition and strength of brazed material;

— the shape of the sample;

geometry and surface condition of the connection;

— flux;

— technology of low-temperature (soft) and high temperature (hard) soldering (heat source, soldering temperature, heating rate, etc.);

— the dwell time at the soldering temperature;

— the gap between the brazed parts.

— the number of samples for testing;

— used methods presentation of the results;

— the nature and size of defects on the fracture surface.

This standard specifies the following characteristics of brazed structures:

a) high temperature soldering:

— temporary resistance to tensile at low, high and room temperatures;

— the ultimate strength in shear at low, high and room temperatures;

— long-term strength at elevated temperature;

b) when low-temperature soldering:

— the ultimate strength in shear at low, high and room temperatures;

— long-term strength at low, room and high temperatures;

— temporary resistance to tensile at low, high and room temperatures.

Notes:

1. Low temperatures should be temperatures from minus 269 °C to plus 15 °C.

2. Room temperature should be the temperature of (20±5) °C.

3. High temperatures should be considered temperature (20±5) °C to (1200±50) °C.


To obtain reproducible and comparable results of tensile testing and slice the standard provides the test procedure and the samples of a particular type.

1. THE AREA OF DISTRIBUTION

This standard specifies the basis and testing methodology designed to determine the conventional mechanical characteristics of solder joints under high-temperature and low-temperature soldering, proposes a method of processing the obtained results.

The standard specifies requirements for static short-term and long-term tests of brazed joints made of brazed materials, solders and fluxes by high-temperature and low-temperature brazing of ferrous and nonferrous metals and alloys.

The standard should be applied in the control and research trials.

2. TEST METHODS

2.1. The types of samples

2.1.1. The standard strength for shearing

To determine the standard strength in shear using telescoping sample with a predetermined gap, and the solder connection subjected to a voltage cutoff if the sample applied tensile stress. Samples of types I and II are shown in hell.1 and 2.

Damn.1. Samples of the type I test cut

Samples of the type I test cut

Damn.1

Damn.2. Blanks of the type I test cut

Blanks of the type I test cut

Damn.2

The type of the selected sample point in the test Protocol (Appendix 1).

2.1.2. Standard tensile strength tensile

To determine the standard strength used end connection of two cylindrical samples with a predetermined clearance within tolerance. Dimensions of specimen for tensile test is shown in hell.3.

Damn.3. Samples of type II for tensile testing

Samples of type II for tensile testing

Damn.3

2.1.3. The samples, mounted ISO 5187, are basic, however they do not cover all types of brazed joints and types of loadings. In order to better determine the properties of the brazed joints allowed the use of additional types and sizes of samples.

For tensile tests it is possible to apply samples of types II and III, the cut — types I, IV and V, for long-term strength of types I-V.

The shape and dimensions of specimens shall be as specified in the hell.9−13 and table 5−7 of Annex 2.

When the material thickness is less than 3 mm using samples of type IV, with more than 3 mm are type V.

The shape and size of the heads flat and cylindrical specimens, as well as the size of the transition parts from the heads of the sample to its working parts are optional and are determined by the method of fastening in the grips of the testing machine. Options heads given on features.14−16 and table 8 of Annex 2.

When testing samples of types III and IV (without heads) with a thickness of less than 3 mm allowed the use of reinforcing plates in the gripper parts of the samples.

Samples to be tested in heat-treated should be subjected to heat treatment after brazing to the final processing of samples.

2.1.4. Requirements blanks

Samples for testing are produced from welded for this purpose blanks.

It is recommended to take the length of the workpiece, ensuring the clipping of at least three samples of types II, III and IV.

Blanks for the samples are cut by mechanical means. It is permitted to use other cutting methods, this should be provided allowance for removal of HAZ or peening.

When soldering of workpieces grade brazed material, surface preparation, solder, or flux environment, the gap between the brazed workpieces, the method and mode of soldering needs to be the same as in the developed technological process.

The width of the overlap is selected so that when the test sample destruction occurred at the brazed joint.

The width of the gap during soldering is recommended to ensure by means of appropriate devices. Allowed security clearance using shims. Strip recommended manufacturing of brazed material. Plot of the solder joint with pads should be removed in the process of making samples.

2.2. The choice of the brazed metal and clearance

When testing the tensile strength of solder joint should be lower than (or equal to) the yield strength of the brazed material. Material samples and the gap in the solder connection should correspond to real operating conditions.

Brazed metal and the gap in the solder connection is indicated in the test report (see Annex 1).

2.3. Surface preparation

Surface before soldering needs to be cleaned of dust, oxides, grease, oil, paint, etc. depending on the properties of the brazed material establish methods of cleaning and washing.

Surface samples of solder must have a roughness parameter of 1.6−3.2 µm for samples of copper and its alloys and 1,6−6,3 m — sample of non-alloy steel.

If the test is performed on samples of special purpose, the surface of the samples must comply with the requirements.

The test lead method of cleaning and purifying the substance and the surface condition at the joints.

2.4. The use of solders and fluxes for soldering

The component parts of the samples (types I and II) collected in a vertical position, and the solders and fluxes of the corresponding shapes (wire, powder, etc.) have on the one hand compounds in sufficient quantity to fill the joint after soldering.

If necessary, use flux, the solder and brazed metal. The flux used according to the manufacturer’s instructions. Characteristics of the flux should be given in the test report.

Samples must be made ways much closer to concrete technological processes of manufacture of brazed structures. In the case of research testing methods for the manufacture of brazed samples should be established by agreement with the customer.

2.5. The conditions of heating

To hold the samples (types I and II) in a vertical position according to the devil.1−3, in order to avoid load on the connection during the cooling process using support device. The support device should not interfere with the contraction and expansion of the sample.

Ration samples of types III-V may be performed in any position.

The conditions of heating should correspond to the chosen method of manufacture of the samples.

In the case of heating by oxygen-acetylene flame is allowed use of fixtures, given on features.4. The device consists of plate-base 1, which set the sample support 2, clamping device 3, the pendulum support 4 is shown schematically for burner 5. Can be used other mounting hardware depending on the method of heating.

Damn.4. The device length soldering samples

The device length soldering samples

Damn.4

The entire Assembly is heated to soldering temperature by means of the selected heating method (torch, furnace, induction, etc.). If the node is not heated uniformly along the entire length (for example by heating with a torch or by induction), it is necessary to ensure uniform heating temperature at a distance of 10 mm on each side.

Note. If the sample is heated by torch or by induction, the heating cycle must be such that the soldering temperature was achieved at 40−60 C; aging at this temperature is 5 C. In special cases, the samples shall be kept at the soldering temperature of 10−30 C. Working modes should be recorded in the test report. If the samples are made to obtain specific information, then the heating operation is set when the preliminary control trials.

2.6. The number of samples

2.6.1. Five samples for strength tests at room and low temperatures.

2.6.2. Five to ten samples to construct the curve or creep during high-temperature tests.

2.6.3. In conducting research trials, the number of samples is determined by the following procedure:

a) in most cases, experimental data on mechanical properties of brazed joints have a normal or close to it distribution;

b) based on the normal distribution to obtain reliable data with a given accuracy the number of samples is determined as follows:

— set the value of the relative error of the average values of determined characteristics and one-sided confidence probability . Value choose from a range of 0,90; 0,95; 0,99. For General engineering purposes confidence probability most often taken equal to 0.95;

— specify the expected coefficient of variation ;

for given values of , and at the table.1 determine the number of samples .


Table 1

The number of tests in the normal distribution law

The number of samples specify the aggregation of the results of the tests;

C) in justified cases, it is possible to use other distribution laws.

Table 2

The number of tests logarithmically normal law of distribution

Table 3

The number of tests tensile Weibull

2.7. Sample processing and requirements for samples

2.7.1. After soldering samples for tensile testing and cut is treated according to the devil.1−3, without breaking strength properties of soldered joints.

2.7.2. For samples to be tested in heat-treated should be subjected to heat treatment of the workpiece after soldering to the final processing of samples.

2.7.3. Edit and straightening brazed blanks are not allowed.

2.7.4. Samples from the brazed workpieces must be manufactured on machine tools or with anode-mechanical cutting. Samples of sheet materials is allowed to cut vulcanite disks. Burrs on the edges of the samples should be removed easy zapilovku with a radius of curvature not less than 1 mm.

2.7.5. Before the test measured error of less than 0.1 mm:

— the cross section of the cylindrical specimen at the location of the solder joint;

— the length and width of the solder joint flat samples;

— the width of the overlap.

According to the obtained results calculate the area of the solder joint, rounding value to 0.5 mm.

When calculating area of solder joint cross-section of the throat not taken into account.

2.7.6. Each sample should be marked where indicated on the devil.9, 11, 13, 14, 15.

2.7.7. The samples with soldered seam or working part warpage, mechanical damage, undercuts facing surface contaminants, pores, Naropa and nespa, delamination, voids, and cracks, to testing not permitted.

In the control tests the type and number of defects, samples shall not exceed the admissible values established for the solder products.

2.7.8. The allowable deviation from a given reference lengths of the samples of the leg length of the working part of the specimen on which the elongation is measured, should not exceed ±1%.

2.7.9. The runout of the cylindrical sample at check in centers must not exceed 0,02 mm.

2.7.10. The permissible deviation of cross sectional area shall not exceed ±0,5%.

2.7.11. Accuracy requirements for the measurement of samples before testing should correspond to GOST 9651, if not imposed more stringent requirements.

2.7.12. Flatness tolerance of the sample type IV must not exceed 2% of the thickness of the sample.

2.7.13. In the manufacture of samples of types I, IV and V should provide the radius of the fillets is not more than 0.3 mm. allowed machining of the throat.

2.8. The test slice tensile and long durability

2.8.1. The tests are carried out in devices specially treated to reduce bending stresses in the samples. Test cut samples given on features.1 and 2, carried out in the devices shown in hell.5 and 6.

Damn.5. Device for testing of samples of type I at slice

Device for testing of samples of type I at slice

Damn.5

Damn.6. Device for testing of samples of type II tensile

Device for testing of samples of type II tensile

Damn.6

The strength of the solder joint, expressed in megapascals, determined by dividing the efforts of the fracture, expressed in Newtons, of the surface area of the solder joint expressed in square millimeters. The results of a study of the destruction must be stated in the test report.

For comparative characteristics of the tested solders at short-term tests on shear and tensile at low and high temperatures and room temperature requires the loading of samples on testing machine to carry with adjustable speed in micrometers per second, or variable effort in Newtons per second.

Samples for testing the shear or tension during heating should be subjected to a load in the machine for tensile tests, which includes an oven. Sample temperature must be stabilized for 1 h before application of the load, and adjusting the oven temperature should be less than ±1%.

Test specimens for long-term strength test in discontinuous machines, in which the test temperature should be stable within 2 h before application of the load, the furnace temperature must be adjustable less than ±1%.

If the creep test is carried out at room temperature, then the machine choose without a furnace.

Fracture surface of the destroyed samples examined for the presence of defects, and the results of studies written in the magazine tests.

2.8.2. In quality testing machines at short-term tensile tests and the cut should applied tensile and universal testing machine according to GOST 28840.

2.8.3. The choice of speed of movement of the active capture according to GOST 1497.

2.8.4. Samples of type I should be tested in the fixture shown in hell.5. The size of the fixtures should be recalculated in accordance with the dimensions of the samples (tensile strength of the materials of the fixture — not less than 700 MPa).

2.8.5. Cryostat (or the vessel with the cooling fluid) must provide cooling of samples and the ability to maintain a constant set temperature of the sample during the test.

Design and layout of the samples in the cryostat is shown in hell.19 and 20 of Annex 3.

2.8.6. For cooling the samples as coolers can be applied:

up to minus 70 °S — ethyl alcohol in a mixture with solid carbon dioxide;

— from -70 °C to minus 100 °C and ethyl alcohol with liquid nitrogen;

— from minus 100 °C to minus 196 °C liquid-vapor mixture of nitrogen;

— from minus 196 °C to minus 269 °C — vapor-liquid mixture helium.

As chillers can be applied and other liquids of organic and inorganic origin or a mixture of refrigerants that should not be toxic, corrosive, explosive. The oxygen content of the liquid nitrogen used for cooling the samples according to GOST 9293.

Use as a chiller liquid oxygen or liquid air is prohibited.

2.8.7. To measure the temperature of the cooling medium used is a liquid thermometer with a scale interval not more than 1 °C thermoelectric or resistance thermometer or thermoelectric converters with the secondary devices that meets the specified requirements in relation to the scale division value.

2.8.9*. Permissible deviation of the temperature of the cooling medium from the temperature tests:

±2 °C in the range from 0 to minus 100 °C;

±4 °C in the range from minus 100 °to minus 269 °C.
_______________
* Numbering corresponds to the original. — Note the CODE.

The level of liquid coolant in the cryostat is measured with a semiconductor resistance sensors, gauges and other devices. The error of determination of the level of liquid coolant — not more than 5 mm.

2.8.10. The temperature of the cooling medium in dehermetization cryostat maintained at the desired level by the addition of small portions of the chiller while stirring the mixture.

2.8.11. The holding time at the test samples in liquid nitrogen must comply with 5 min after the rapid boiling of the liquid, and in liquid helium and hydrogen — 5 min after fixing the required level of fill in the cryostat.

When tested in other refrigerants or mixed refrigerants exposure time of at least 10 min after reaching the test temperature. Allowed the supercooling of the samples during the exposure within the limits set by this standard.

2.8.12. The heating device must provide uniform heating of the working part of the specimen to a predetermined temperature and maintaining this temperature during the entire test time.

Deviation from the established set temperature shall not exceed:

±3 °C at the heating temperature to 600 °C;

±4 °C at the heating temperature from 600 °C to 900 °C;

±6 °C at the heating temperature from 900 °C to 1200 °C.

2.8.13. To protect the sample from oxidation during the period of heating is allowed to use in heating devices or other protective atmospheres or vacuum.

2.8.14. The temperature measurement error when using thermoelectric converters with secondary devices of accuracy class 0.5 shall not exceed ±1%.

2.8.15. To measure the temperature of the samples at the ends of their working parts should be mounted at least two thermoelectric converters.

Thermoelectric converters on samples of type I, should be fixed at a distance of not more than 5 mm from the surface of the nuts of tool (Fig.5) after mounting the sample in the test fixture.

2.8.16. Working ends of thermoelectric converters should be mounted on the sample zachekanka, contact welding or other methods that ensure reliable thermal contact with the sample surface. It is better to protect the working ends of thermoelectric converters from the influence of the heaters.

2.8.17. The duration of heating to the test temperature and soaking time at a given temperature should be given in the normative-technical documentation for the product. If such instructions are absent, then the duration of heating to the test temperature should be no more than 1 h, and exposure time of 20−30 min.

For samples of type I may increase the exposure time to 1 h.

2.8.18. Test considered invalid if one of the following conditions:

2.8.18.1. At break of the specimen in the grips of the testing machine.

2.8.18.2. When you break the lap of the sample against the base metal in the working parts or the area of the fillets.

When the gap of butt specimen for the base metal in the test section the test is deemed valid, the strength of the solder joints should be considered equal to the strength of the base metal.

2.8.18.3. Defects of solder joint in fracture of the specimen (foreign inclusions, pores, Naropa, naspi) in research trials.

2.8.18.4. In case of failure during the period of heating or cooling at least one thermoelectric Converter or thermometer.

2.8.18.5. Upon violation of a temperature mode test (disable, drop voltage, etc.).

2.8.19. In such cases the test should be repeated. The number of new samples tested must match the number of invalid tests if a test is repeated on samples taken from the same batch, or twice the number of samples taken from another batch manufactured on the same process technology.

3. PROCESSING OF THE RESULTS

3.1. The results of tensile testing and slice at room temperature

Use statistical processing of the results of tensile testing and slice at room temperature by calculating the average values of tensile strength and standard deviations of the tensile strength from test results.

The average tensile strength and standard deviation of tensile strength is determined as follows:

The results lead to specific brazed material, therefore, fixed the minimum allowable value of the average ().

The real processing of the results can be justified as follows:

— the relationship between the changes caused by the method of testing and the changes brought on by brazed material is unknown;

to fix «minimal tolerances» required a number of preliminary tests for all types of existing brazed material;

— the number of tests necessary for the evaluation of «minimum tolerance», usually more than the number necessary for the evaluation of average values. Taking into account the results of the tests establish a rule of acceptance brazed material, if it is characterized by the minimum acceptable average value .

Therefore:

— the probability of acceptance of the brazed material in which the average strength less than must be equal to the relatively small value of the risk of the consumer;

— the probability of acceptance of the brazed material in which the average strength of more than must be equal to a relatively large value of 1, where the risk of the manufacturer.

These conditions must be observed regardless of the standard deviations characterizing the behavior of the brazed material during testing.

Each brazed material is considered as satisfying this value , if the average of the measurement results , the number of tests corresponds to the condition

. (3)

If you specify the risk of 0.10 for 10%, using various existing tables of sample values, it is possible to for 5, of 0.68.

Under these conditions, to runs ratio

. (4)

The calculation and based on the normal distribution. Variable undefined

(5)

corresponds to the Central student distribution (if a  — minimum acceptable average value) or the non-Central student distribution 1,2816(when 10%), and values and define two options:

(6) for the Central distribution;

(7) for non-Central distribution.

Some value provided the risk is justified for the established modes of testing, since it requires a small number of trials, which is important from an economic point of view

.

3.2. Short-term durability during high-temperature tests of specimens cut

These tests allow us to construct a curve of destructive stresses in the coordinates: the strength megapascal is the temperature in degrees Celsius.

On the heck.7 shows an example of the curves obtained by the values of three temperature tests.

Damn.7. Typical curves of tensile strength at high temperature test cutoff

Typical curves of tensile strength at high temperature test cutoff

1 — a sample made of low-temperature soldering;

2 — a sample made brazing

Damn.7

3.3. Testing for long-term strength of the samples cut

The purpose of the tests at one or more temperatures of constructing one or more curves in the coordinates: the breaking stress in megapascal — the time to failure in hours.

Voltage should be chosen so as to obtain the time of the destruction is between 0.1 and 10h. For special occasions you can examine voltage, ensure the time of the destruction of 10or 10hours In hell.8 shows an example of presentation of results.

Damn.8. Typical curves of tensile test shear long-term strength

Typical curves of tensile test shear long-term strength

1 — the samples made of low-temperature soldering at 20 and 200 °C;
2 — the samples made of high-temperature soldering at 500 °C

Damn.8

3.4. Statistical processing of results of testing of samples of all types may be performed by another method to ensure accuracy and comparability of results.

One of the correct methods of processing the results is the method given in Annex 4.

3.5. Not allowed to compare the test results of samples of different types.

3.6. Ultimate resistance in tension (), MPa (kgf/mm), calculated according to the formula

, (8)

where — the maximum breaking load, N (kgf);

— the area of the solder joint, mm.

3.7. The ultimate strength in shear , MPa (kgf/mm), calculated according to the formula

. (9)

3.8. Long-term strength to denote and , where , is the voltage that causes the destruction for a specified time at a fixed temperature .

APPENDIX 1. The test of brazed tensile specimens with short and long term tests

ANNEX 1

PROTOCOL N
tests of brazed tensile specimens with a short
and long-term tests

Table 4

The results of tensile tests conducted on the short and long term tests

In the field «note» specify the defects found in the soldered seam and the heat affected zone after the destruction of the sample.

APPENDIX 2 (recommended). THE SHAPE AND DIMENSIONS OF SAMPLES

ANNEX 2
Recommended

Damn.9. Type I

Damn.9

Table 5

Telescopic samples dimensions, mm

Damn.10. Type II

Damn.10

Table 6

The cylindrical samples dimensions, mm

Damn.11. Type III

 — the thickness of the solder joint

Damn.11

Damn.12. Type IV

Damn.12

Damn.13. Type V

Material thickness 3 mm; ;
;

Damn.13

Table 7

The dimensions of the flat specimen mm

_______________
* In brackets the size of samples for testing at low temperatures.

Damn.14−15. Embodiments of heads samples

Embodiments of heads samples

Damn.14

Damn.15

Table 8

Heads sizes of the samples, mm

Damn.16−17. The execution of the heads of specimens of type II used in test cryostat

The execution of the heads of specimens of type II used in test cryostat

Damn.16

When tested brazed joints, the strength of which is equal to or higher than the strength of brazed material, allowed the use of a cruciform (Fig.17). (Test data cruciform are estimates and cannot claim the accuracy of the actual values of the connection strength).

10; 15; 20 mm

Damn.17

Damn.18. The shape and dimensions of blanks cruciform

The shape and dimensions of blanks cruciform

Damn.18

APPENDIX 3 (recommended)

APPENDIX 3
Recommended

The scheme of placing the samples in sealed cryostat

Damn.19. The scheme of placing the samples in sealed cryostat

1 — tested sample; 2 — cryostat; 3 — trapping; 4 — level sensor cooler; 5 — sealing nut

Damn.19

Damn.20. The layout of the samples in the cryostat dehermetization

The layout of the samples in the cryostat dehermetization

1 — tested sample; 2 — upper link (extension bar); 3 — lower thrust; 4 — coolant;
5 — insulation; 6 — gasket (waxed graphite and asbestos); 7 — casing of the cryostat;
8 — nut-plug

Damn.20

APPENDIX 4 (recommended). THE PROCEDURE FOR STATISTICAL PROCESSING OF TEST RESULTS

ANNEX 4
Recommended

1. For statistical processing of test results are variation a number of characteristics or .

Ultimate resistance in tension (), MPa (kgf/mm), calculated according to the formula

, (10)

where  — the maximum breaking load, N (kgf);

 — the area of the solder joint, mm.

The ultimate strength in shear (), MPa (kgf/mm), calculated according to the formula

. (11)

Then spend the primary statistical processing of the obtained values of and . For test result take an arithmetic average of the obtained characteristics and that the standard deviation of the characteristics, confidence limits of random error characteristics.

Calculate the arithmetic mean value of the characteristics (and ) by the formulas:

, (12)

, (13)

where temporary resistance to tensile -th sample, MPa;

 — tensile strength shear on a sample, MPa;

 — the number of values of the characteristics or in the variational row;

1, 2, 3 …

.

2. The standard deviation of the characteristics determined by the formula:

; (14)

. (15)

3. To determine the distribution of test results to build a graph of distribution of experimental data in the coordinates of the probability — value characteristics.

Then compare it with the known laws of distribution are given in table.9.

Table 9

Next, check the agreement of the distribution of experimental data with the proposed theoretical distribution according to the criteria of consent.

4. The most commonly used distribution is normal.

Formulas for calculation of test results:

— when ravnodushnym dimensions

; (16)

; (17)

; (18)

; (19)

— with unequal dimensions

 — weighted average; (20)

weighted standard deviation, (21)

where is the number of test results;

the frequency of occurrence of random values in the interval;

 — the value of the variable value;

 — arithmetic mean value;

 — the number of intervals;

 — RMS value;

 — dispersion;

 — confidence limits of random error;

 — coefficient of student distributions, defined by table.10 and 11.

Table 10

The value of the coefficient t-test with one-sided confidence

 — the number of degrees of freedom,

Table 11

Value coefficients t-test for two-sided confidence

5. The definition of an unbiased estimator standard deviation

. (22)

Table 12

Coefficient values when

 — the number of degrees of freedom.


Confidence limits of random error with normal distribution is given by

; (23)

determination of confidence limits for standard deviation

; (24)

. (25)

The value is determined by the table.13.

Table 13

6. The dispersion obtained in unequal measurements (calculate  — intervals on the basis of their means), is overpriced. To clarify the applied dispersion correction Sheppard.

, (26)

where is the size of the interval.

7. Next, you should check the supplies of characteristics or the variation of a number to a normal distribution.

8. Determine the estimated coefficient of variation and compare it with the accepted value .

(27)

or . (28)

If the estimated coefficient of variation is more accepted, the extent of tests count for the found coefficient of variation.

9. In the case that the variation in the number of characteristics or , obeying the normal distribution law, one or more values to cause doubt of their belonging to a given row, then use the rules of evaluating the abnormality of test results for rejection stands out sharply (a drop down) values.

Note. If an abnormal value characterizing the lower bound properties of a brazed joint and is minimal, repeated, and fractographic analysis of the connection quality, then this result should not be deleted, and the tests shall be repeated on a doubled batch of samples.

10. In determining gross errors for other distributions use other criteria for rejection of outliers. The criterion used should be specified in the test report.

11. If you exclude one or more values of characteristics or the variation of the series should be recalculated arithmetic mean of the measurement results, standard deviation and confidence limits of random error for the values of the new row.

12. The values obtained are the final results of the tests and are issued in the form of a table.14 annexed to the test report.

Table 14

The results of the statistical analysis (Annex to the Protocol N)

EXAMPLES OF STATISTICAL PROCESSING OF TEST RESULTS

The number of samples required for the experiment, determined in accordance with Annex 2.

According to table.1 to 10%=0,1; 0.95 and 10%=0.1 in the case of the normal distribution 5.

Example 1

When processing test results of five brazed samples were obtained the following ordered series of values 18,7; 18,2; 17,4; 16,2; 16,0 kgf/mm.

The arithmetic mean value calculated from the formula (12)

kgf/mm.

To determine the standard deviation to find the value (see table.15).

Table 15

kgf/mm

________________
* Consistent with the original. — Note the CODE.


According to the formula (14) determine the standard deviation

kgf/mm.

Confidence limits of random error is calculated by the formula (19)

kgf/mm.

The value of the find tab.10 or 11. For when of 0.95.

Check coefficient of variation, which according to the formula (27) find the value , and the result is compared with the accepted ratio.

The resulting coefficient of variation is less than the specified, therefore, identified correctly.

To assess the accessories stand out sharply (a drop down) values of the variational row of a decision to exclude or abandonment kgf/mm, composed of a number determine the standard deviation without outliers

; (29)

kgf/mm.

Find the ratio of the difference between outliers and the arithmetic mean to standard deviation:

; (30)

.

The results are compared with that taken from the table.16 or 17 for a given number of samples and the accepted confidence probability .

Table 16

The limit value at 21

.

Note. Values marked with an asterisk belong to a new variational row with no abnormal («dropdown») values.

If , then suspected of abnormality, the result may be excluded, otherwise it belongs to the variational row and it do not exclude.

At 21 the value of the find tab.16.

Table 17

The limit value at 21

where .

From table 16 for 4 and find of 0.95 and 1.46, i.e.

.

The value obtained in the first test sample, is a gross error and belongs to the variational row.

Consequently, the value obtained by statistical processing of test results are final:

The 17.3 kgf/mm, 1,19 kg/mm; of 0.95 to 1.13 kgf/mm.

Example 2

When processing the results of testing five samples brazed received the following ordered series of values 18,7; 17,8; 17,1; 16,7; 16,2 kgf/mm.

The arithmetic mean value of 17.3 kgf/mm.

Table 18

According to the formula (14) determine the standard deviation

kgf/mm,

according to the formula (19) find

kgf/mm.

Determined by the formula (27) estimated coefficient of variation

.

the estimated less than specified, therefore, identified correctly.

The definition of abnormal (falls) results in the sample

kgf/mm,

kgf/mm,

why by the formula (14) count , and of 18.7 kgf/mmisn’t taken into account

kgf/mm.

According to the formula (30) we find

.

At tabulated value of 1.46

,

therefore, the value obtained by testing the first sample, is a gross error and can be eliminated from the variational series.

In this case, compute new values , and :

kgf/mm;

kgf/mm;

kgf/mm.

Record the final test result:

17 kgf/mm, or 0.68 kg/mm, of 0.95 to 0.72 kg/mm.