JPH08178816A - Method for predicting rapid cooling thermal shock fatigue life - Google Patents

Abstract

PURPOSE: To determine the strength, the probability of fracture, and the number of times of thermal shock being applied repetitively before fracture of a test piece with high accuracy by determining the relation between the stress enlarging coefficient of crack and a crack developing rate, together with a thermal conductivity, in a test environment just identical to that for thermal shock fatigue test for measuring the fatigue characteristics directly. CONSTITUTION: A test piece having an arbitrary shape is cracked previously and a stress enlarging coefficient K1 is calculated based on the shape of the crack and the test conditions where the crack begins to develop while assuming a thermal conductivity. The maximum value of the coefficient K1 thus determined is then compared with a critical value thus determining a thermal conductivity (h) satisfying the conditions of K1 . On the other hand, initial length of the previously formed crack is measured and thermal impact is applied repeatedly with a temperature difference lower than the critical temperature difference where the test piece is not fractured by applying the thermal impact once. The crack length is measured after N1 cycle and a crack developing rate V is determined. Thermal stress is then analyzed using the thermal conductivity thus determined and a multiple mode weibull distribution or the like is assumed based on the K1-V thus determining the relationship of the number of times of repetition SPT.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting the fatigue life of brittle materials represented by ceramics due to rapid thermal shock.

[0002]

2. Description of the Related Art Brittle materials typified by ceramics are
For various industrial machinery devices such as chemical plants and machine tools, various power engines such as gas turbines and turbochargers, and various structural parts used under high load or high temperature atmosphere, or both conditions When it is used as a material, it is necessary not only to evaluate the mechanical properties and guarantee the strength, but also to fully ascertain the properties against various types of fatigue and guarantee the life.

One of the fatigue characteristics is thermal shock fatigue when thermal shock due to rapid cooling is repeatedly applied. For example, after the test piece is heated to a predetermined temperature T ₁ ,
This is generated by quenching to a temperature T ₂ lower than the temperature T _{1. As} a specific quenching method, for example, a test piece heated to T ₁ by a heater or the like is used in water set to T ₂ or There is a liquid quenching method that is dropped in a solder bath.

As a method for evaluating the durability against fatigue due to the repeated thermal shock as described above, it is assumed that the fatigue characteristics are directly measured by performing a thermal shock fatigue test and that the fatigue follows the crack growth law. There is a method of obtaining from Weibull statistical theory.

The method of directly measuring from the thermal shock fatigue test is to repeat the test for each thermal shock condition while changing the thermal shock applied to the test piece, that is, the thermal stress, and to determine the strength S and the failure probability P of the test piece. , And the relationship SPT between the number of repetitions until failure or the load time T of stress effective for fatigue, that is, the thermal shock fatigue characteristics (hereinafter, the thermal shock fatigue characteristics are referred to as SPT).

On the other hand, in the method using the crack growth law, the relationship K _I -V between the stress intensity factor K _I and the crack growth rate V is obtained for the target material, and the distribution and time change of the acting stress are analyzed by numerical calculation or the like. However, the SPT is obtained using a theory based on Weibull statistics (J. Materi).
als Science 14, 573-82, 197.
9, and the Transactions of the Japan Society of Mechanical Engineers (A), Volume 58, No. 547,
1992-3).

[0007]

However, in the method of directly measuring the fatigue characteristics from the thermal shock fatigue test using the liquid quenching method, it is necessary to conduct an experiment for each test condition,
In addition, since the measurement results vary from test piece to test piece, a large number of test pieces are required to obtain reliable measured values.

On the other hand, in the method of obtaining SPT from the crack growth law, it is necessary to measure the heat transfer coefficient and K _I -V, but the required number of test pieces can be considerably reduced as compared with the thermal shock fatigue test, An important method for measuring K _I- V has not been established.

[0009] That is, the K _I -V is material but also changes by just not the water content or the like in the test atmosphere, the fatigue characteristics K in exactly under the same environment as the thermal shock test to directly measure the _I
Since it is not easy to obtain −V, values measured by different test environments and test methods such as dynamic fatigue tests and static fatigue tests are used, or literature values considered to be close to the test environments are used.

Further, the heat transfer coefficient required for the thermal stress analysis also varies depending on the type of the cooling medium, the test conditions, etc., but it cannot be easily measured, and is particularly easy to handle as a cooling medium. When pure water is used, the test piece is at a high temperature, so that boiling occurs during cooling, and the heat transfer coefficient greatly varies depending on the test conditions and the test method.

Therefore, since it is difficult to directly measure the actual heat transfer coefficient, the heat transfer coefficient, like K _I -V, is different from the thermal shock test in which the fatigue characteristics are directly measured.
The values measured by the test method are corrected and used, or the literature values are referenced.

As a result of the above, the calculated SPT is K _I −
There is a problem that V and the heat transfer coefficient include an error due to the fact that they are different from the actual values, and may not match the SPT directly obtained from the thermal shock fatigue test.

[0013]

SUMMARY OF THE INVENTION The present invention has been made as a solution to the above-mentioned problems, and its purpose is to achieve high accuracy without requiring a large number of test pieces under the same environment as a thermal shock test for directly measuring fatigue characteristics. It is to provide a method for obtaining the SPT of

[0014]

DISCLOSURE OF THE INVENTION The inventor of the present invention has found that in the test environment exactly the same as the thermal shock fatigue test for directly measuring the fatigue characteristics, K _I
The inventors have found that by obtaining -V and heat transfer coefficient, SPT can be accurately obtained from a small number of test pieces, and the present invention has been completed.

That is, a crack is formed in advance on a test piece to be subjected to a thermal shock fatigue test, and mechanical properties such as Poisson's ratio, Young's modulus, fracture toughness value, thermal expansion coefficient, thermal conductivity, etc. of the test piece. If the thermal physical property value and the shape of the formed crack are obtained, and the K _I of the crack reaches K _IC and a critical test temperature difference at which the crack starts to grow is found, the crack starts to grow. From the conditional expression, the only unknown quantity is the heat transfer coefficient,
The required heat transfer coefficient can be obtained, and the heat transfer coefficient becomes a value under the thermal shock test conditions.

Further, the same test piece on which a plurality of cracks have been formed in advance is repeatedly subjected to thermal shock under the condition that the K _I of the crack is smaller than K _IC , and the progress behavior of the crack is observed to observe the actual thermal shock. Determine K _I- V under the fatigue test environment.

Thermal stress analysis is carried out using the heat transfer coefficient thus obtained, and it is effective for strength (S), failure probability (P), number of repetitions up to failure or fatigue from Weibull statistics and the above K _I -V. The relationship between the stress application time (T) and the SPT is obtained to predict the rapid thermal shock fatigue life of brittle materials typified by ceramics.

[0018]

The present invention will be described in detail below. In the method for predicting the rapid thermal shock fatigue life of the present invention, first, the heat transfer coefficient in the thermal shock fatigue test is determined based on the procedure shown in FIG.

Concretely, a crack is formed in advance on a test piece having an arbitrary shape. For example, as shown in FIG. 2, an indenter for measuring Vickers hardness is used around a cylindrical test piece 1, It is sufficient to form a plurality of cracks 2.

Next, the shape of the crack and the test conditions under which the crack starts to grow, for example, as shown in the procedure of FIG. 1, the temperature difference between the heating temperature of the test piece and the cooling medium is measured, and the shape of the test piece is measured. Assuming the heat transfer coefficient, the stress intensity factor K _I is calculated from the test piece radius D and various physical properties such as Poisson's ratio ν, Young's modulus Ε, thermal conductivity λ, thermal expansion coefficient α, and fracture toughness K _IC. It can be calculated or calculated by an approximate expression.

[0021] Thus the maximum value K _Imax obtained stress intensity factor in the comparison with the threshold value K _IC, if the critical value K _IC smaller again stress the heat transfer rate a little greater intensity factor K _I is obtained and repeated to obtain K _Imax = K _{I in} FIG.
The heat transfer coefficient h satisfying the condition of is obtained.

The heat transfer coefficient under an arbitrary temperature difference condition can be obtained by changing the size of cracks formed in the test piece beforehand.
You can ask.

On the other hand, K _I -V is obtained by measuring the initial length C ₀ of the preformed crack and then applying thermal shock repeatedly with a temperature difference smaller than the critical temperature difference that does not cause destruction by one thermal shock. The crack length C _i after _i cycles is measured, and the crack growth rate V at this time is determined by the following equation.

[0024]

[Equation 1]

At this time, the stress intensity factor K _I is the crack length C.
And the shape is taken into consideration, and calculation is performed using a numerical calculation or an approximate expression.

Thermal stress analysis is carried out using the heat transfer coefficient thus obtained, and by assuming a multimode Weibull distribution from K _I -V, the strength (S) and failure probability (P) and the number of repetitions until failure or The relationship with the stress addition time (T) effective for fatigue can be obtained.

The method for predicting the rapid thermal shock fatigue life of the present invention will be described in detail below based on specific examples.

First, as shown in FIG. 2, a cylindrical silicon nitride sintered body having a diameter of 8 mm, a length of 70 mm and a tip 10 mm forming a cone of 30 ° is used as a measurement test piece, and the Vickers hardness measurement is performed on the measurement test piece. Using an indenter, press-fit load is 10 kg
f, 20 kgf, 30 kgf, and 50 kgf were changed to four test pieces, and a crack was formed in a spiral shape at a distance of 2 mm from the tip 20 mm in the longitudinal direction at each test piece at eight locations with the same press-fitting load at substantially equal intervals, The length C of the crack was measured.

Next, a thermal shock is applied to the test piece. The relationship between the press-fitting load and the temperature difference at which the crack propagates is roughly grasped in advance by a preliminary test, and the temperature difference sufficiently smaller than the temperature difference at which the crack propagates. Are set respectively, and for example, for a test piece in which a crack is formed with a press-fit load of 10 kgf, the temperature difference ΔT
From 640 ° C. to 20 kgf, 30 kgf, 50
For the test pieces of kgf, ΔT was set to 460 ° C. and 400, respectively.
℃, from 350 ℃ to 20 ℃ every 20 ℃ in order to make quenching treatment, the thermal shock is given, the crack length is observed each time, the average temperature difference which the crack which is formed beforehand begins to spread Δ
The Tc was calculated.

[0030]

[Table 1]

The average temperature difference ΔTc at which cracks start to grow when an infinite cylinder is rapidly cooled with a constant heat transfer coefficient is represented by the following equation.

[0032]

[Equation 2]

Here, σ _max ^* is expressed by the following approximate expression.

[0034]

(Equation 3)

In the above equations 2 and 3, ν, Ε, α,
λ, K _IC , Y and D are Poisson's ratio, Young's modulus, thermal expansion coefficient, thermal conductivity, fracture toughness value, shape coefficient and test piece radius, respectively, which are known quantities.

Therefore, by substituting the experimental data of Table 1 into equations 2 and 3, the only unknown quantity is the heat transfer coefficient h. However,
Ε, α, λ, and K _IC were polynomial-approximated as a function of temperature, and Y was a function of C. The temperature dependence of ν can be ignored.

Relationship between the obtained temperature difference condition and the heat transfer coefficient ΔT
-H is shown in FIG. Using these results, it is possible to analyze the thermal stress at any temperature difference in the thermal shock fatigue test.

Next, an example of obtaining K _I -V will be shown. First, two test pieces in which a crack was previously formed with a Vickers hardness measuring indenter with a press-in load of 30 kgf and a press-in load of 20 k
One test piece having a crack formed with gf was prepared.

One of the test pieces having a press-fitting load of 30 kgf was subjected to a thermal shock of 230 times at a temperature difference of 430 ° C., another one was subjected to a thermal shock of 230 times at a temperature difference of 460 ° C., and a press-fitting load of 20 kgf. The test piece was subjected to thermal shock 190 times at a temperature difference of 430 ° C. and the crack length was measured.
It was found that cracks of 0 μm, 120 μm and 10 μm were grown.

Based on the above results, the average value of the crack growth rates calculated by the equation 1 and the Raju-Newman equation (J.
C. Newman, Jr. and I. S. Raju, N
ASA. Tech. Paper, 15, 78 (197)
9). FIG. 4 shows the relationship between the stress intensity factor K _I and the crack growth rate V, which are obtained by using However, the horizontal axis is standardized by the critical stress intensity factor K _IC .

From FIG. 4, since the experimental data is almost a straight line on the log-log graph, the experimental data was fitted by the least squares method, and the following equation was obtained.

[0042]

[Equation 4]

However, A = 10 ^−4.69 and n = 19.43.

The SPT is obtained from the above results, but a Weibull distribution with two parameters is used for the calculation, and a dual mode is set considering the case where the destruction occurs from the surface defect and the case where the destruction occurs from the internal defect. However, the Weibull plot was assumed to be the same on the surface and inside, and it was assumed that fatigue according to the crack growth law only occurred on the surface. The SPT in this case is expressed by the following equation.

[0045]

(Equation 5)

However,

[0047]

(Equation 6)

[0048]

(Equation 7)

[0049]

(Equation 8)

[0050]

[Equation 9]

[0051]

[Equation 10]

[0052]

[Equation 11]

P is the failure probability, N is the number of repetitions, σ _max is the maximum load stress, S _E is the effective surface area, V _E is the effective volume, m is the Weibull coefficient, n is the fatigue index, and σ ₀ is the scale. Parameter, σ _a is average strength, V _E4 is effective volume of 4-point bending strength test, Γ _{(1 + 1 / m)} is gamma function, _tw is effective load time of stress, Y is shape factor, and A is constant. , Σ _QQ is circumferential thermal stress, σ _zz is axial thermal stress, S is surface area, V is volume, H
Is the Heaviside step function.

The average value σ _a of the four-point bending strength of the silicon nitride sintered body to be measured was 796.0 MPa, and the Weibull coefficient m was 11.4. Furthermore, Y was set to 1.28 assuming a semi-elliptical crack.

The result of SPT is shown by the solid line in FIG. The symbol is the result obtained from the thermal shock fatigue test of the direct measurement method using 70 test pieces, and it can be seen that the two agree relatively well.

[0056]

According to the method for predicting the rapid thermal shock fatigue life of the present invention, a crack is formed in advance on a thermal shock fatigue test piece, and the fatigue test is conducted under the same test environment as that for directly measuring the fatigue characteristics. By obtaining K _I- V and heat transfer coefficient, SPT can be obtained accurately from a small number of test pieces.

[Brief description of drawings]

FIG. 1 is a diagram showing a procedure for obtaining a heat transfer coefficient according to the present invention.

FIG. 2 is a diagram showing a shape of a measurement test piece according to the present invention.

FIG. 3 is a diagram showing a relationship between a temperature difference ΔT and a heat transfer coefficient h according to the present invention.

FIG. 4 is a diagram showing a relationship between a stress intensity factor K _I and a crack growth rate V according to the present invention.

FIG. 5 is a comparison diagram of the results obtained from the thermal shock fatigue test of the SPT according to the present invention and the direct measurement method.

[Explanation of symbols]

 1 test piece 2 crack

Claims (1)

[Claims] 1. A test piece having a known Poisson's ratio, Young's modulus, fracture toughness value, thermal expansion coefficient, and thermal conductivity is formed with a plurality of cracks of known shapes, and the stress intensity factor K _{I of the} cracks is determined. A thermal shock is repeatedly applied to the test piece under the condition that the fracture toughness is smaller than the fracture toughness. From the crack growth behavior, the relationship between the stress intensity factor K _I and the crack growth rate V under the thermal shock fatigue test environment K _I −V
And the stress intensity factor K _I of the crack reaches the fracture toughness value and the heat transfer coefficient is calculated from the critical temperature difference at which the crack starts to develop, and thermal stress analysis is performed from the heat transfer coefficient to determine the Weibull statistics and the from K _I -V, strength (S) and fracture probability (P) and quenching thermal shock fatigue life and obtaining a relationship SPT and an additional time (T) of the effective stress on the number of repetitions or fatigue to failure Prediction method.