FR3136858A1 - METHOD FOR MEASURING THE THICKNESS AND METHOD FOR MEASURING THE DENSITY OF A SPECIMEN MADE OF COMPOSITE MATERIAL WITH CERAMIC MATRIX - Google Patents

Abstract

The invention relates to a method (101) for measuring a thickness and a density of a test piece resulting from machining along a plane of a plate made of composite material with a ceramic matrix. The method comprises measuring (103) a dry mass of the test piece, measuring (105) resonance frequencies of the test piece, determining (107) a thickness of the test piece, from the frequencies resonance of the test piece and coefficients obtained from a digital simulation of the vibration behavior of a reference test piece, and the determination (109) of a density of the test piece, from the measured dry mass, of a surface of the specimen according to the machining plane, and of the determined thickness. Figure for abstract: Figure 1

Description

METHOD FOR MEASURING THE THICKNESS AND METHOD FOR MEASURING THE DENSITY OF A SPECIMEN MADE OF COMPOSITE MATERIAL WITH CERAMIC MATRIX

The invention relates to the field of measuring the parameters of a test piece intended to be used for characterizing the thermomechanical properties of a plate made of composite material with a ceramic matrix. It relates in particular to a method for measuring the thickness as well as a method for measuring the density of a specimen made of composite material with a ceramic matrix.

To characterize the thermomechanical properties of ceramic matrix composite (CMC) material plates, which are used in particular for the manufacture of aircraft parts, it is known to machine test specimens from these plates. The specimens thus obtained are then subjected to tests (stress, deformation, etc.) to obtain useful information on their thermomechanical properties and by extension on those of the plate from which they come.

In this context, it may be necessary and/or useful to know the thickness and density of a test piece before mechanically stressing it with the aim in particular of being able to determine other properties that can only be obtained by knowing beforehand. thickness and density.

On the one hand, the known techniques for measuring the thickness of such a test piece are based on the use of a caliper, a ball comparator or even stereovision. The ISO18754 standard describes, for example, techniques known to those skilled in the art for determining the density and apparent porosity of so-called technical ceramics.

On the other hand, the known techniques for measuring the density of such a test piece are based on a measurement, called hydro density measurement, of the dry mass, the submerged mass and the soaked mass of the test piece to be tested.

However, with regard to the measurement of the thickness, taking into account the fogging of the plates made of composite material with a ceramic matrix (that is to say the local variation in dimensions of the plate linked to the weaving of the fibers which it contains), so-called manual methods of thickness measurement (i.e. the use of a caliper or a ball comparator) are very sensitive to local variations in the parameters of the test piece and present uncertainties high repeatability and reproducibility. In addition, the use of stereovision is long, complex and expensive to implement.

Furthermore, regarding the measurement of density, the hydro density measurement is very long (around twelve hours) and also presents high repeatability and reproducibility uncertainties.

The present invention offers a solution to these drawbacks.

Thus, an objective of the invention is to measure parameters of a test piece in a non-destructive manner, faster than the state of the art, inexpensive, and reducing measurement uncertainties compared to known techniques.

To this end, the invention according to a first aspect relates to a method for measuring the thickness of a test specimen, called a test specimen, resulting from the machining along a plane of a plate of composite material with a ceramic matrix. , said method comprising:

a) measuring the resonance frequencies of the test specimen; And,

b) determining a thickness of the test specimen, from the resonance frequencies of the test specimen and coefficients obtained from a digital simulation of the vibration behavior of a virtual specimen, called a test specimen reference.

According to one mode of implementation of the method, the resonance frequencies of the test specimen are measured in step a) by laser vibrometry.

According to another mode of implementation of the method, the thickness to be measured of the test specimen is between 2 and 10 millimeters, preferably between 2 and 4 millimeters or between 6 and 7 millimeters, and the test specimen is a dumbbell test tube.

According to another mode of implementation of the method, two resonance frequencies of the test specimen are measured in step a), a first frequency being a resonance frequency of a bending mode in the machining plane , preferably a first mode of bending in the plane, and a second frequency being a resonance frequency of a mode of bending outside the machining plane, preferably a first mode of bending out of the plane, the two frequencies of resonance being resonance frequencies in free-free conditions.

According to another mode of implementation of the method, the digital simulation of the vibration behavior of the reference specimen, carried out prior to step b), comprises the determination of resonance frequencies of the reference specimen, corresponding to the first and second measured resonance frequencies of the test specimen, preferably carried out by the finite element method.

According to another mode of implementation of the method, the resonance frequencies of the reference specimen are determined from predetermined parameters of said reference specimen including a thickness, a density and an axial rigidity modulus.

According to another mode of implementation of the method, the thickness, the density and the axial rigidity modulus of the reference specimen are substantially equal to a theoretical thickness, a theoretical density and a theoretical axial rigidity modulus of the test specimen. Furthermore, the shape and dimensions of the reference specimen are preferably identical to the respective shape and dimensions of the test specimen.

According to another mode of implementation of the method, a first coefficient, obtained from the digital simulation of the vibration behavior of the reference specimen, carried out prior to step b), is determined according to the formula:

where K _1e , E _{11_ref} , d _ref and f _{1e_simu} correspond respectively to said first coefficient as well as to the axial rigidity modulus, to the density and to a first resonance frequency of the reference specimen,

and a second coefficient, obtained from the numerical simulation of the vibration behavior of the reference specimen, is determined according to the formula:

where K _1f, E _{11_ref} , d _ref , h _ref and f _{1f_simu} correspond respectively to said second coefficient as well as to the axial modulus of rigidity, to the density, to the thickness and to a second resonance frequency of the reference specimen .

According to another method of implementing the process, the thickness of the test specimen is determined according to the formula:

where h, K _1e, K _1f , f _1e and f _1f correspond respectively to said thickness as well as to the first coefficient, the second coefficient, the first and the second resonance frequency measured of the test specimen.

According to a second aspect, the subject of the invention is a method for measuring the density of a test specimen, called a test specimen, resulting from the machining along a plane of a plate of composite material with a ceramic matrix, the method including:

a) measuring a dry mass of the test specimen;

b) measuring a thickness of the test specimen in accordance with the method according to the first aspect; And,

c) determining the density of the test specimen, from the measured dry mass, a surface of the test specimen according to the machining plane, and the measured thickness.

According to one method of implementing the process, the density of the test specimen is determined according to the formula:

where d, m, S and h correspond respectively to said density as well as to the dry mass, to the surface in the machining plane and to the measured thickness of the test specimen.

The present invention will be better understood and other details, characteristics and advantages of the present invention will appear more clearly on reading the description of a non-limiting example which follows, with reference to the appended drawings in which:

there is a step diagram of a mode of implementation of the density measurement method according to the invention;

there is a photo and an image of the profile of the section of a test specimen such as that measured by the measurement method according to the invention;

there is a schematic representation seen from above of a test specimen such as that measured by the measurement method according to the invention;

there is a schematic representation of the steps for measuring the resonance frequencies of a test piece by laser vibrometry; And,

there is an illustration of a sensitivity matrix of a digital simulation of the vibration behavior of a test piece as used in the measurement method according to the invention.

In reference to the , we will now describe a mode of implementation of a method 101 for measuring the density of a specimen made of composite material with a ceramic matrix according to the invention. The method 101 described here includes the steps which form the method for measuring the thickness of a specimen made of ceramic matrix composite material according to the invention.

The specimen 201, also called a test specimen, whose thickness and density are measured using the process, is a thermomechanical characterization specimen resulting from the machining of a plate made of composite material with a ceramic matrix (called CMC plate in what follows). Furthermore, in other embodiments, the test piece is not necessarily the result of machining, but can be the result of another manufacturing method, provided that its geometry in the plane is constant and known on its entire thickness.

Test specimen 201 is described in more detail below with reference to and to the .

In addition, as said above, due in particular to local variations in the parameters of the CMC plate from which the specimen comes and the specificities of the machining making it possible to obtain the specimen (in particular the orientation of the plane of machining in the CMC plate), the thickness and density values which are measured using the process and which are discussed in the following are average values.

As an example, the shows (with a photo for the upper part of the figure and with an image of the profile for the lower part of the figure) the section of a test specimen 201. This figure illustrates in particular the local variation in the thickness of the test piece as well as the average thickness 203 that we seek to measure with the method. Furthermore, upon reading the following, those skilled in the art will appreciate that the invention applies regardless of the machining plane which is used in the CMC plate.

There illustrates the geometry of the test specimen 201 in the machining plane (denoted plane P in the following), that is to say outside the thickness of the test specimen 201. In the example shown, this geometry is that of a test piece called a dumbbell test piece. However, as with the machining plane, the invention applies to any type of geometry of a test specimen.

In summary, by way of non-limiting example, the test specimen 201 whose parameters are measured by the method has a geometry of a dumbbell specimen as illustrated in Fig. . For example, the different coasts represented in the are typically included, respectively, for a between 10 and 25 millimeters, for b between 100 and 200 millimeters, for c between 5 and 20 millimeters, for d between 20 and 50 millimeters, for e between 50 and 400 millimeters, and for f between 0 and 5 millimeters. In addition, the thickness of the test piece is typically between 2 and 4 millimeters or between 6 and 7 millimeters.

The method 101 is therefore a method of measuring a thickness, denoted h, and a density, denoted d, of a specimen 201, called a test specimen, resulting from machining along a plane P of a plate CMC.

Step 103 consists of measuring a dry mass, denoted m, of the test piece 201. This measurement can be carried out simply, for example, by means of a balance in an environment whose humidity level, c that is to say the proportion of water in the gaseous state in the environment in question, is known and less than a determined value. This type of measurement has the advantage of having low repeatability and reproducibility uncertainty.

Step 105 consists of measuring the resonance frequencies of the test piece 201. In the non-limiting example of implementing the method described here, two resonance frequencies, respectively denoted f _1e and f _1f, are measured. In particular, for the first frequency f _1e it is the resonance frequency of a first mode of bending in the machining plane P, also called first mode of bending in the plane, denoted 1E and illustrated as d example in the upper part of the , and for the second frequency f _1f of a resonance frequency of a first mode of bending outside the machining plane P, also called first mode of bending outside the plane, denoted 1F and also illustrated by way of example in the upper part of the . Furthermore, the two resonance frequencies f _1e and f _1f are resonance frequencies in free-free conditions. That is to say the resonance frequencies of the test specimen 201 when it is not held by any of its ends (ie is free at all of its ends).

The measurement of the resonance frequencies of the test specimen 201 can be carried out by laser vibrometry. In this case, the test piece is subjected to acoustic excitation 401 with a frequency scan (for example ranging from 100 Hertz to 20 kilohertz) and a laser vibrometer 403 simultaneously acquires d at different points on the surface of the test piece. an optical signal representative of the vibrations of said test piece. The amplitude of this signal is then processed digitally, for example by Fourier transform, to extract the resonance frequencies of the different resonance modes of the test piece. Here again, this type of measurement has the advantage of having low repeatability and reproducibility uncertainty.

Step 107 consists of determining the thickness h of the specimen 201, from the resonance frequencies f _1e and f _1f of the specimen 201 determined in step 105 and coefficients K _1e and K _1f obtained from a digital simulation of the vibration behavior of a virtual test piece 113, called a reference test piece, carried out beforehand.

In the non-limiting example described here, the digital simulation of the vibration behavior of the reference specimen 113 notably includes the determination of two resonance frequencies, denoted f _{1e_simu,} f _{1f_simu} which correspond to the resonance frequencies which are measured for l test specimen 201. The digital simulation of the vibration behavior can be carried out for example by the finite element method.

The word “virtual” here designates the fact that the test piece does not necessarily have a physical existence but rather constitutes a set of parameters used as input data for the digital simulation to then be able to recover the information sought in the form of output data from said digital simulation.

In particular, the frequencies f _{1e_simu} and f _{1f_simu} of the reference specimen 113 are determined from predetermined parameters of the reference specimen 113 which include a thickness h _ref , a density d _ref and an axial rigidity modulus of said reference test piece 113 noted E _{11_ref} . More precisely, the axial rigidity modulus E _{11_ref} which is in question here and in what follows is the axial rigidity modulus along the longitudinal axis .

More precisely, in the non-limiting example described, the thickness h _ref , the density d _ref and the axial rigidity modulus E _{11_ref} of the reference specimen 113 are substantially equal to a theoretical thickness h ₀ , a theoretical density d ₀ and a theoretical axial rigidity modulus E _{11_0} of the test specimen 201. By “theoretical” we mean here the expected average parameters, taken from a material characterization file (in this case, the CMC).

In other words, the parameters of the reference specimen h _ref , d _ref and E _{11_ref} which are used for the numerical simulation of the vibration behavior of the reference specimen 113 are taken equal to theoretical parameters of the specimen test 201 (the therefore represents the two test pieces). As a reminder, the thickness h _ref used for the reference specimen corresponds to an average thickness. So that the vibration behavior which is simulated can be assimilated (ie considered equivalent) to that of the test specimen 201.

Furthermore, with regard to the dimensions of the reference specimen 113 which are taken into account for the digital simulation of its vibrational behavior, these are the dimensions in the machining plane P which is used to machine the CMC plate and thus generate the test specimen 201.

As said above, the determination of the thickness h of the test specimen 201 is carried out using coefficients K _1e and K _1f resulting from the digital simulation described above. In the non-limiting example described, there are two of these coefficients, however those skilled in the art will appreciate that their number can be greater in a different mode of implementation of the method.

In all cases, the determination of these coefficients results from a sensitivity analysis of the parameters of the digital simulation of vibration behavior. Such a sensitivity analysis consists of numerically studying the influence of each parameter of the digital simulation on the determined resonance frequencies.

For this, each parameter of the digital simulation of the vibratory behavior of the simulated specimen can be subjected to a variation (of 10% or 20% for example) to then observe the influence of this variation on the resonance frequencies ultimately obtained. .

There shows an example of a sensitivity matrix 501 linking certain parameters of the material (rigidity moduli, thickness, density, shear moduli, etc.) with different resonance frequencies. The types of hatching in each of the boxes correspond to an amplitude (positive, zero or negative) of the sensitivity of each resonance frequency to each property. It is thus possible to see that certain amplitudes are zero, which illustrates the fact that certain frequencies are insensitive to the variation of certain parameters.

Thus, the sensitivity analysis makes it possible in particular to establish a mathematical relationship between the “thickness” parameter and the measured frequencies, independent of the density and rigidities of the material considered.

Thanks to the sensitivity analysis carried out beforehand, in the example described, the first coefficient K _1e , obtained from the digital simulation of the vibration behavior of the reference specimen 113, is determined according to the formula:

where K _1e , E _{11_ref} , d _ref and f _{1e_simu} correspond respectively to the first coefficient as well as the axial rigidity modulus, the density and the first resonance frequency of the reference specimen 113,

In addition, the second coefficient K _1f , obtained from the digital simulation of the vibration behavior of the reference specimen 113, is determined according to the formula:

where K _1f, E _{11_ref} , d _ref , h _ref and f _{1f_simu} correspond respectively to the second coefficient as well as the axial modulus of rigidity, the density, the thickness and the second resonance frequency of the reference specimen 113.

Finally, it is therefore from the measured resonance frequencies and the coefficients obtained from the simulation that the thickness h of the test specimen 201 is determined according to the formula:

where h, K _1e, K _1f , f _1e and f _1f correspond respectively to the thickness as well as to the first coefficient, the second coefficient, the first and the second resonance frequency measured of the test specimen 201.

Step 109 consists of determining the density d of the test specimen 201, from the measured dry mass m, the surface S of the specimen according to the machining plane P (previously known), and of the thickness h determined during step 107.

More precisely, the density d of test specimen 201 is determined according to the formula:

where d, m, S and h correspond respectively to the density as well as to the dry mass, to the surface in the machining plane P and to the thickness of the test specimen 201, determined in step 107.

In conclusion, the method according to the invention makes it possible to reduce test specimen inspection times, make the data obtained more reliable and reduce measurement uncertainties on the thickness and density of the specimens. Furthermore, this process is applicable to all kinds of specimen geometries. Finally, a single reference numerical simulation is necessary and re-applicable when the same machining plan is used for several specimens to the extent that the determination of the thickness and density depends on parameters which do not change in this case.

Furthermore, although this is not the subject of the measurement method described here, those skilled in the art will appreciate that from the determination of the density d described here (which has the advantage of be simple and precise) and the first coefficient K _1e as explained above, it is also possible to determine the axial rigidity modulus E ₁₁ along its longitudinal axis X of the test specimen 201 using the formula:

Claims (11)

Method for measuring a thickness (h) of a test specimen (201), called a test specimen, resulting from machining along a plane (P) of a plate of composite material with a ceramic matrix, said method (101) including:
a) measuring (105) frequencies (f _1e , f _1f ) of resonance of the test specimen (201); And,
b) determining (107) a thickness (h) of the test specimen (201), from the frequencies (f _1e , f _1f ) of resonance of the test specimen (201) and coefficients ( K _1e , K _1f ) obtained from a digital simulation of the vibration behavior of a virtual test piece (113), called a reference test piece. Method according to claim 1, in which the resonance frequencies (f _1e , f _1f ) of the test specimen (201) are measured in step a) by laser vibrometry. Method according to claim 1 or claim 2, in which the thickness to be measured of the test specimen (201) is between 2 and 10 millimeters, preferably between 2 and 4 millimeters or between 6 and 7 millimeters, and The test specimen (201) is a dumbbell specimen. Method according to one of claims 1 to 3, in which two frequencies (f _1e , f _1f ) of resonance of the test specimen (201) are measured in step a), a first frequency (f _1e ) being a resonance frequency of a bending mode in the machining plane (P), preferably a first bending mode in the plane, and a second frequency (f _1f ) being a resonance frequency of a bending mode outside the machining plane (P), preferably a first mode of bending out of the plane, the two resonance frequencies (f _1e , f _1f ) being resonance frequencies in free-free conditions. Method according to one of claims 1 to 4, in which the digital simulation of the vibration behavior of the reference specimen (113), carried out prior to step b), comprises the determination of frequencies (f _{1e_simu,} f _{1f_simu} ) resonance of the reference specimen (113), corresponding to the first (f _1e ) and the second resonance frequency (f _1f ) measured of the test specimen, preferably carried out by the finite element method. Method according to claim 5, in which the frequencies (f _{1e_simu} , f _{1f_simu} ) of resonance of the reference specimen (113) are determined from predetermined parameters of said reference specimen (113) comprising a thickness (h _ref ) , a density (d _ref ) and an axial rigidity modulus (E _{11_ref} ). Method according to claim 6, in which the thickness (h _ref ), the density (d _ref ) and the axial rigidity modulus (E _{11_ref} ) of the reference specimen (113) are substantially equal to a theoretical thickness (h ₀ ), a theoretical density (d ₀ ) and a theoretical axial rigidity modulus (E _{11_0} ) of the test specimen (201). Method according to claim 6 or claim 7, in which a first coefficient (K _1e ), obtained from the digital simulation of the vibration behavior of the reference specimen (113), carried out prior to step b), is determined according to the formula:
where K _1e , E _{11_ref} , d _ref and f _{1e_simu} correspond respectively to said first coefficient as well as to the axial rigidity modulus, to the density and to a first resonance frequency of the reference specimen (113),
and a second coefficient, obtained from the digital simulation of the vibration behavior of the reference specimen (113), is determined according to the formula:
where K _1f, E _{11_ref} , d _ref , h _ref and f _{1f_simu} correspond respectively to said second coefficient as well as to the axial modulus of rigidity, to the density, to the thickness and to a second resonance frequency of the reference specimen (113). Method according to claim 8, in which the thickness (h) of the test specimen (201) is determined according to the formula:
where h, K _1e, K _1f , f _1e and f _1f correspond respectively to said thickness as well as to the first coefficient, the second coefficient, the first and the second resonance frequency measured of the test specimen (201) . Method (101) for measuring a density (d) of a test specimen (201), called a test specimen, resulting from machining along a plane of a plate made of composite material with a ceramic matrix, the method (101) including:
a) measuring (103) a dry mass (m) of the test specimen (201);
b) measuring (105, 107) a thickness (h) of the test specimen (201) in accordance with the method according to any one of the preceding claims; And,
c) determining (109) the density (d) of the test specimen (201), from the dry mass (m) measured, of a surface (S) of the test specimen (201) according to the machining plane (P), and the thickness (h) measured in step b). Method according to the preceding claim, in which the density (d) of the test specimen (201) is determined according to the formula:
where d, m, S and h correspond respectively to said density as well as to the dry mass, to the surface in the machining plane (P) and to the measured thickness of the test specimen (201).