JP3220342B2 - Prediction method of quenching thermal shock fatigue life - Google Patents

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 such as ceramics due to rapid thermal shock.

[0002]

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

[0003] One of the fatigue characteristics, has thermal shock fatigue when repeatedly acts thermal shock by rapid cooling, the thermal shock, for example, after heating the specimen to the predetermined temperature T _1,
This one which generated rapidly cooled to a lower temperature T ₂ 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, Ya set underwater T ₂ There is a liquid quenching method of dropping into a solder bath or the like.

[0004] Further, as a method of evaluating the durability against fatigue caused by repeated thermal shocks as described above, a method of directly measuring the fatigue properties by performing a thermal shock fatigue test and a method of assuming that the fatigue obeys the crack growth rule. There is a method of obtaining from Weibull statistical theory.

A method of directly measuring 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, to obtain the strength S and the probability of failure of the test piece P. And the relation SPT between the number of repetitions until fracture or the load time T of stress effective for fatigue, that is, the thermal shock fatigue property (hereinafter, the thermal shock fatigue property is referred to as SPT).

[0006] On the other hand, the method using the crack growth law obtains the relationship K _I -V between the stress intensity factor K _I and the crack growth speed V for the target material, and analyzes the distribution of the acting stress and the time change by numerical calculation or the like. Then, the SPT is obtained using a theory based on Weibull statistics (J. Materi).
als Science 14, 573-82, 197
9, and Transactions of the Japan Society of Mechanical Engineers (A), Vol. 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 perform an experiment for each test condition.
In addition, since the measurement results vary from one test piece to another, there is a problem that a large number of test pieces are required to obtain reliable measured values.

On the other hand, the method of obtaining the SPT from the crack growth rule requires measurement of the heat transfer coefficient and K _I -V. Although the number of required test pieces can be considerably reduced as compared with the thermal shock fatigue test, An important method of 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 find -V, values measured under different test environments and test methods, such as dynamic fatigue tests and static fatigue tests, are used, or literature values that are considered to be close to the test environment are used.

Further, the heat transfer coefficient required for performing the thermal stress analysis also varies depending on the type of the cooling medium, test conditions, and the like, but cannot be easily measured, and particularly, the handling as the cooling medium is easy. In the case where fresh water is used, the test piece has a high temperature, so that boiling occurs during cooling, and the heat transfer coefficient greatly varies depending on the test conditions and test methods.

Accordingly, the actual heat transfer coefficient since it is possible to directly measure is difficult, the heat transfer rate as well K _I -V, different test conditions from the thermal shock test to measure the fatigue properties directly,
The values measured by the test methods are corrected and used, or literature values are referenced.

As a result, the calculated SPT is K _I −
There is a problem that an error due to a difference between V and the heat transfer coefficient from the actual one is included, and may not coincide with the SPT obtained directly from the thermal shock fatigue test.

[0013]

SUMMARY OF THE INVENTION The present invention has been made in order to solve the above-mentioned problems, and has as its object to achieve high precision without requiring a large number of test pieces under the exact same environment as a thermal shock test for directly measuring fatigue characteristics. The present invention provides a method for determining the SPT.

[0014]

SUMMARY OF THE INVENTION The present inventor has, K _I thermal shock fatigue test exactly the same test environment for measuring fatigue properties directly
The present inventors have found that by determining -V and the heat transfer coefficient, it is possible to accurately determine the SPT from a small number of test pieces, and have reached the present invention.

That is, a crack is previously formed in a test piece to be subjected to a thermal shock fatigue test, and mechanical properties such as Poisson's ratio, Young's modulus and fracture toughness of the test piece, and thermal expansion coefficient, thermal conductivity and the like are determined. The thermal properties, as well as the shape of the formed crack are determined, and if 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 equation, the only unknown quantity is the heat transfer coefficient,
The required heat transfer coefficient can be obtained, and the heat transfer coefficient is a value under the conditions of the thermal shock test.

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

A thermal stress analysis is performed using the heat transfer coefficient obtained in this manner, and the strength (S), the probability of failure (P), the number of repetitions up to the failure or the number of repetitions up to the failure or fatigue is determined from the Weibull statistics and the K _I -V. The purpose of the present invention is to estimate the relationship between the stress application time (T) and the SPT and estimate the quenching thermal shock fatigue life of a brittle material represented by ceramics.

[0018]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below in detail. In the method for predicting the quenching 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.

Specifically, cracks are formed in advance in a test piece of an arbitrary shape. For example, as shown in FIG. 2, an indenter for measuring Vickers hardness is used around a cylindrical test piece 1. A plurality of cracks 2 may be formed.

Next, the shape of the crack and the test conditions under which the crack starts to propagate, 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 was measured, and the shape of the test piece was measured. Assuming the heat transfer coefficient from the test piece radius D, Poisson's ratio ν, Young's modulus Ε, thermal conductivity λ, thermal expansion coefficient α, fracture toughness value K _IC, etc., the stress intensity factor K _I It can be calculated by calculation or 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 this is repeated to obtain K _Imax = K _{I in} FIG.
The heat transfer coefficient h that satisfies the condition is obtained.

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

On the other hand, K _I -V is obtained by measuring the initial length C ₀ of a previously formed crack, and repeatedly applying a thermal shock at a temperature difference smaller than a critical temperature difference which does not cause a fracture by a single thermal shock. _i measured crack length C _i after the cycle, determining the growth rate V of the crack when the following equation.

[0024]

(Equation 1)

[0025] In this case, the stress intensity factor K _I is the crack length C
Calculation is performed using a numerical calculation or an approximate expression in consideration of the shape and the shape.

A thermal stress analysis is performed using the thus obtained heat transfer coefficient, and a multi-mode Weibull distribution or the like is assumed from K _I -V to obtain the strength (S), the probability of failure (P), and the number of repetitions until failure or The relationship with the time (T) of stress effective for fatigue is determined.

Hereinafter, the method for predicting the quenching thermal shock fatigue life of the present invention will be described in detail based on specific examples.

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

Next, a thermal shock is applied to the test piece. The relationship between the press-fit load and the temperature difference at which the crack grows is roughly grasped in advance by a preliminary test, and the temperature difference is sufficiently smaller than the temperature difference at which the crack grows. Is set, for example, a test piece having a crack formed under a press-fit load of 10 kgf has a temperature difference ΔT
From 640 ° C., 20 kgf, 30 kgf, 50 kgf
The ΔT was set to 460 ° C. and 400
Quenching at a set temperature gradually increased every 20 ° C. from 350 ° C. to 350 ° C. to apply a thermal shock. Each time, the crack length is observed, and the average temperature difference Δ at which the previously formed crack starts to propagate.
Tc was determined.

[0030]

[Table 1]

The average temperature difference ΔTc at which the crack starts to grow when the infinite cylinder is rapidly cooled with a constant heat transfer coefficient is expressed by the following equation.

[0032]

(Equation 2)

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

[0034]

(Equation 3)

In Equations 2 and 3, ν, Ε, α,
λ, K _IC , Y and D are Poisson's ratio, Young's modulus, coefficient of thermal expansion, thermal conductivity, fracture toughness, shape factor and specimen radius, respectively, which are known quantities.

Therefore, if the experimental data of Table 1 is substituted into Equations 2 and 3, the only unknown quantity is the heat transfer coefficient h. However,
Ε, α, λ, and K _IC are functions of temperature, and Y is a function of C, which is a polynomial approximation. Note that the temperature dependence of ν can be ignored.

Relation ΔT between the obtained temperature difference condition and the heat transfer coefficient
-H is shown in FIG. Using this result, it is possible to analyze the thermal stress at an arbitrary temperature difference in the thermal shock fatigue test.

Next, an example of obtaining K _I -V will be described. First, a Vickers hardness measurement indenter was press-fitted with a press-fit load of 30 kgf and two cracked test pieces were previously formed.
One test piece having a crack formed by gf was prepared.

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

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

From FIG. 4, since the experimental data is substantially linear on the log-log graph, the experimental data was fitted by the least squares method to obtain the following equation.

[0042]

(Equation 4)

However, A = 10 ^−4.69 and n = 19.43.

The SPT is obtained from the above results. The dual mode is used in the calculation, and the dual mode is set in consideration of the case where the breakdown occurs from a surface defect and the case where the breakdown occurs from an internal defect. However, the Weibull plot was the same on the surface and inside, and it was assumed that fatigue according to the crack growth rule occurred only on the surface. The SPT in this case is represented 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]

Where P is the probability of fracture, N is the number of repetitions, σ _max is the maximum applied 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 the thermal stress in the circumferential direction, σ _zz is the thermal stress in the axial direction, S is the surface area, V is the volume, H
Is a 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. Further, Y is assumed to be a semi-elliptical crack, and is set to 1.28.

The result of the SPT is shown by a solid line in FIG. The symbol is a result obtained from a thermal shock fatigue test of a 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 quenching thermal shock fatigue life of the present invention, a crack is formed in advance in a thermal shock fatigue test specimen, and the test environment is exactly the same as the thermal shock fatigue test in which the fatigue characteristics are directly measured. by obtaining the K _I -V and heat transfer coefficient can be determined accurately SPT from small specimens.

[Brief description of the drawings]

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

FIG. 2 is a view showing the 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.

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

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)

(57) [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 having a known shape in advance, and the stress intensity factor K _{I of the} crack is determined. the thermal shock repeatedly the test piece under the condition that less than fracture toughness addition, the relationship K _I -V of stress intensity factor K _I and crack propagation velocity V under thermal shock fatigue test environment from propagation behavior of the crack
Together seek, seeking heat transfer coefficient from the temperature difference of the critical stress intensity factor K _I of the crack starts cracks developed reaches the fracture toughness value, by thermal stress analysis of the heat transfer rate, 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 Forecasting method.