RU1833802C - Method for measuring parameters of slow growth of cracks on brittle materials - Google Patents

Abstract

The invention relates to tests of brittle materials, namely the determination of the parameters of slow crack growth when testing a prismatic sample for three-point bending, on the stretched side of which is applied by an indenter crack. In order to increase accuracy and shorten test time and reduce labor intensity, the propagation length of indentation cracks along the axis of the specimen is measured. By comparing the change in the size of the crack lengths, for which the stresses are different, the slow crack growth parameter N is determined from the equation containing the indicated parameter Ai, parameters AI, Aa, It, 12, where A1 aoi / ai, A2-ao2 / a2. Asi, aoa, ai, aa are the initial and final sizes of crack 1 and 2, h, h, respectively, the distance from the external support to crack 1 and 2. In testing one specimen, it is possible to obtain up to 100 definitions of the parameters of slow crack growth. Parameter A is determined by the formula containing o - stress on crack 1 ((Л const), Y - geometrical factor (V 1,265), t - load action time a. 2 ill .. 1 table with

Description

The invention relates to the study of the strength properties of materials and can be used to determine patterns of development of cracks under load in brittle materials. In order to study the laws of slow (subcritical) development of cracks in brittle materials (ceramics), as a rule, methods are used that are based on determining the change in the compliance of a sample with the development of a crack. By processing the load relaxation diagram, the dependence is built

v f (Ki), (1)

where v is the crack propagation rate;

To | is the stress intensity factor on the crack. ,

Dependence (1) is represented in the form

f s

V AK |

N

(2)

Yu

where A and N are the parameters of the slow growth of cracks in the material.

By processing the data of the crack growth rate depending on the stress intensity factor, the parameters of the slow crack growth are determined. Known methods are: double torsion, double cantilever beam, double cantilever beam with constant moment, bending specimen with a crack. These methods are exploring

the crack propagation is long (1 mm), while the real cracks in the bearing parts of brittle materials are 1-2 orders of magnitude smaller.

Determination of the parameters of slow crack growth is necessary for the conditions corresponding to the operating conditions of the material. For materials such as structural ceramics, the temperature is 1000-1600 ° C. Testing at such temperatures by the indicated methods is a rather complicated technical problem related to the heat resistance of loading elements.

Iveggen is a method for determining the parameters of the slow growth of cracks in a material by observing the development of a small crack (100. 200 200 μm) in a ceramic sample after the load is applied to the sample. A crack is obtained by pressing an indenter into the surface of the sample. Then the sample is loaded with a certain constant load. The crack is subjected to stresses for some time. The determination of the change in length under the influence of this load makes it possible to determine the crack velocity corresponding to the stress intensity on it.

Kl a- Y- Vi,

(3)

where Y is the geometric factor determined by the location and shape of the crack;

a is the size of the crack.

As can be seen from formulas (2) and (3), as the crack grows, the stress intensity on it changes, and therefore the crack propagation velocity, defined as the average over the specified time interval, will not be determined exactly. As you can imagine, the described method is rather laborious to determine the dependence (2) v f (Ki). Each exposure under load essentially gives only one point of the dependence of v f (Ki), and to obtain significant information over the entire range of critical growth of cracks, it is necessary to repeat the measurement cycle many times, the tests are long and laborious, especially under conditions of testing at high temperatures. The inaccuracies noted above in determining the crack growth rate corresponding to the stress intensity factor allow only estimates of the parameters of slow crack growth to be made.

The aim of the invention is to increase the accuracy and information in determining the parameters of the slow growth of cracks, by monitoring the development

cracks located at a certain distance relative to each other. The microscope determines the size of the cracks before and after the load test and

the slow crack growth parameters are determined by the formula below.

The goal is achieved by using several cracks in the specimen located on an extended surface

of the specimen in such a way that the stress state on all cracks under loading by three-point bending is different. Thus, in one test of one sample, the entire range of subcritical crack growth is examined. To determine the slow growth parameters of cracks A and N, ratios are used that take into account the functional dependence of the crack velocity on the stress intensity factor.

To obtain cracks, one of the faces of the sample is polished to Rz 0.040 ... 0.080 to provide good reflection for subsequent observation of the crack in

microscope. Cracks are obtained by indentation by the Vickers pyramid at a certain distance from each other to provide different stress intensities on the cracks under loading.

The resulting defects have the shape of a half-disk crack (figure 1), the geometric factor of which is Y 1,265.

Loading modes are possible: with a constant rate of change of voltage Q - const, with a constant voltage st const.

We write equation (2) in differential form.

A- (a-Y-va) N. (4)

Let us consider separately 2 cases: constant-voltage loading; loading at a constant rate of change of voltage.

cg const.

Section variables, integrate equation (4)

55. a0 ao.

(5)

For the case under consideration, when the cracks grow from a0 to a Y const. Solving equation (5), we obtain an expression that describes the change in crack length ai over time t under load oi

-Ј + 1

aoi 2

N,.

ai 2 +1

N + 1-M + 1.2 + 12 + L

where aoi, ai are the dimensions of the crack before and after the tests.

Equation (6) can be written for any other crack. Solving together the equations from (6) for two different cracks, for which ai we obtain an expression from which the parameter N is determined by a numerical solution:

A -fl-I.AnV-fllV

 - s w

M1

T - 1 - # -§

li is the distance from the support to the crack 1 (fit 2);

 - distance from the support to the crack 2 (Fig. 1).

Parameter A can be determined from equation (6) by substituting N

AND

)

aN / z- rflV-t

c const

Similarly, we obtain a solution for the case of a test with a constant loading rate, substituting in equation (5) 0 f (t), i.e. t The solution of equation (5) will have the form

N + 1-N + 1

ai 2

aoi 2

N, N T + 1T + 1

 A-6N.YN.t (N + 1) -iq-irT,

where t is the time to failure of the sample.

Writing down the system of equations from (9) for two cracks for which s & L and solving it, we obtain

N

N

AJN / S-I) - / {1 {))

A2N / 2 - 1J -1 W W {Щ.

i is the distance from the support to the crack 1 (Figure 2);

2 - distance from the support to the crack 2

; (Figure 2).

5 Parameter A can be determined from equation (9) by substituting.

L- / 1 -A N / 2 1.,. (N + D (11) 10 аГ2-1 -УЧ +1) (Ј11) (}

fifteen

twenty

25

For determination, any pair of defects can be used for which the acting voltage is not the same. The number of possible combinations when the number of defects applied is n greater than 100, provided that the stress state is different for all defects and only a fraction (50%) of them are suitable for measurement. As can be seen, the information content of one test is very high. The dimensions of the cracks before and after the tests are determined using an optical microscope.

On some cracks located farther from the center of the specimen, due to the low stress, crack growth will not occur, i.e. the stress intensity factor was below the threshold

thirty

,

(12),

Considering the development on neighboring cracks located to the center of the sample, we determine the parameters of a slow growth of cracks in the near-threshold region, i.e. respectively v m / s. Thus, it is possible to estimate the threshold stress intensity factor Ккь.

40

The method is carried out as follows.

As an example, the slow growth parameters of cracks A and N were determined on ceramic from reactive silicon nitride at 1000 ° C. A sample of 7x7x70 mm3 on one side was polished to Rz 0.040-0.080. On this side, the Vickers indenter made 8 prints with a load on the indenter P 10 10 Rn kg, and semi-disk, median cracks with a size of 2a 380 ± 25 μm formed on the surface (see Fig. 1, table). Cracks relative to the center of the specimen (point of application of force in tests on

55

. three-point bend)

so that the distances from cracks 4 and 5 to the center of the sample are 1.5 and 0.5 mm, respectively. This arrangement makes it possible to compare any pair of defects, since for them the condition

a & (T, o const 6j; oj, (7 const

for any I and J.

The sample was tested for three-point bending under conditions of a constant rate of change of stress (No. 0.6 MPa s). The results of measurements and the results of calculations by formulas are given in the table. Not all defects were investigated for measurement, since the location, shape of the defects obtained, conditions at the crack tip did not always correspond to the calculated model.

This, substituted into equation (10), is taken from the table to determine the parameter N.

Parameter A of equation (2) is determined by the formula

A1-.). (N + 1)

) .. oops.;; || (N 1} For the given example, parameter A was calculated according to equation (11), where

A -51 ratio of initial aoi to final ai

the size ai of the selected crack; N is the parameter of slow growth of cracks, as determined earlier; t is the loading time at a constant rate of change of stress before failure; Y is the geometric factor of the shape of the crack (for defects obtained by indentation in this example, Y 1,265).

Using the proposed method for determining the parameters of slow crack growth provides the following advantages compared to existing methods: measuring parameters on cracks of small (50-500 microns) sizes corresponding to the sizes of real defects in ceramic parts; testing a single specimen allows 10-100 determination of slow crack growth parameters; the method makes it possible to determine parameters for crack growth rates in m / s, which is important for determining the resource of long-loaded ceramic parts; the shape of the sample and the loading scheme allows the study to be carried out without difficulty at high temperatures corresponding to the operating temperatures using universal testing tools.

To determine one pair of values (vi, KU) in dependence (2) with acceptable accuracy, it is necessary to observe the change

crack lengths of the order of 10 μm, which for crack growth rates of the order of m / s gives an exposure time of 1 hour under load. In order to obtain information on

the entire range of slow crack growth needs to be done at least THEN measurements. For each measurement, the installation, loading process must be interrupted, which is usually not easy to do during high temperature tests. In addition, it is very important information on the slow growth of cracks will correspond to one crack, and materials of this class, as a rule, are heterogeneous and for

Claims (1)

When designing reliable structures from these materials, it is necessary to be able to make conservative estimates of their characteristics. The proposed method makes it possible to study the parameters of the slow growth of cracks in the volume of a material that fully reflects the heterogeneity of the properties. The load test process in the example described above was no more than 10 minutes. In this case, the parameters of slow crack growth are obtained over the entire range of subcritical crack growth and reflecting the possible heterogeneity of the properties in the material. The claims A method for measuring the parameters of the slow growth of cracks in brittle materials, by which a crack is preliminarily initiated in a prismatic sample, the sample is loaded with a transverse device, determine the length of the crack after a certain time and calculate the parameters of the slow growth of cracks Au and N, distinguishing both so that, in order to increase accuracy, shorten the test time and to reduce labor intensity, at least one more crack is preliminarily initiated in the sample, loading is carried out with a constant rate of change of stress, the distance And, 1a from the first and second cracks to one of the supports is preliminarily determined, the length of both cracks is determined through a certain time t, and the quantities A and N are determined from the equations .frV AЈN / 2 -) -1 W and d 1-A (). 1 a 01 W r h) G C) l aoi l ao2 A1 -aT: A2 where aoi, ai and ao2. 32 - respectively, the initial and final dimensions of the cracks; a-stress on one of the cracks; Y is a geometric factor. M „