FR3136857A1 - METHOD FOR MEASURING THE AXIAL RIGIDITY MODULE OF A SPECIMEN MADE OF CERAMIC MATRIX COMPOSITE MATERIAL - Google Patents

Abstract

The invention relates to a method (101) for measuring an axial rigidity modulus (E11) of a specimen, called a test specimen, resulting from machining along a plane (P) of a plate of composite material with ceramic matrix. The method (101) comprises measuring (103) a resonance frequency (f1e) of the test specimen and determining (105) the axial stiffness modulus (E11) from the resonance frequency (f1e). of the test specimen, a coefficient (K1e) obtained from a numerical simulation of the vibration behavior of a reference specimen and a density (d) of the test specimen. Figure for abstract: Figure 1

Description

METHOD FOR MEASURING THE AXIAL RIGIDITY MODULE OF A SPECIMEN MADE OF CERAMIC MATRIX COMPOSITE MATERIAL

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 axial modulus of rigidity of a specimen made of ceramic matrix composite material.

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 axial modulus of rigidity of a specimen before mechanically stressing it with the aim in particular of being able to determine other properties that can only be obtained by knowing this beforehand. module and/or for the purpose of defining the test conditions that will be applied to it.

To determine the axial modulus of rigidity of a specimen, it is known to carry out an interrupted test in the linear domain of the material. The method consists of carrying out a tensile test on the specimen, sufficiently instrumented to measure stress and deformation, but interrupting it before reaching its damage threshold. The stress-strain curve obtained then makes it possible to measure the rigidity modulus. The specimen having been stressed in the linear domain, it retains its initial mechanical properties and the test can be considered non-destructive. However, this method is long and requires complex implementation associated with carrying out a mechanical test (in particular due to the creation of test requests, test planning, management of the machine park, operation tests, report writing, etc.).

It is also known to estimate the mechanical behavior of a test piece based on results from so-called “neighboring” test pieces (coming from the same plate, presenting an iso-material health, presenting an iso-density, etc. ). However, the mechanical behavior of specimens from a CMC plate can be significantly different from one specimen to another, even when they come from the same plate or from the same manufacturing batch.

The present invention offers a solution to these drawbacks.

Thus, an objective of the invention is to measure a parameter 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 an axial modulus of rigidity of a 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 a resonance frequency of the test specimen; And,

b) determining the axial modulus of rigidity of the test specimen, from the resonance frequency of the test specimen, a coefficient obtained from a numerical simulation of the vibration behavior of a virtual specimen , called the reference specimen, and a density of the test specimen.

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

According to another method of implementing the process, the test specimen is a dumbbell specimen whose thickness is between 2 and 10 millimeters. The thickness may in particular be between 2 and 4 millimeters or between 6 and 7 millimeters.

According to another mode of implementation of the method, the measured resonance frequency is a resonance frequency of a bending mode in the machining plane in free-free conditions, preferably a first bending mode in the plane. Furthermore, the frequency of this first mode of bending in the plane is independent of the thickness of the specimen. Thus, the identification of the axial modulus of rigidity from this frequency does not depend on an additional measurement of the thickness which is a significant source of uncertainty given the fogging of the plates.

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 a resonance frequency of the reference specimen, of preferably carried out by the finite element method.

According to another mode of implementation of the method, the resonance frequency of the reference specimen is determined from predetermined parameters of said reference specimen including a thickness, a density and a reference 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 (in the machining plane) are preferably identical to the shape and dimensions of the test specimen.

According to another mode of implementation of the method, the coefficient K _1e , 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 coefficient as well as to the axial rigidity modulus, to the density and to a first resonance frequency of the reference specimen.

According to another method of implementing the method, the axial rigidity modulus of the test specimen is determined according to the formula:

where E ₁₁ , K _1e, f _1e and d correspond respectively to said axial rigidity modulus as well as to the coefficient obtained from the numerical simulation of the vibration behavior of the reference specimen, to the measured resonance frequency and to the density of the test specimen.

According to another method of implementing the process, the density of the test specimen has been determined beforehand by a hydro-type measurement or comes from a characterization file for the ceramic matrix composite material.

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 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 reference specimen as used in the method according to the invention.

In reference to the , we will now describe a mode of implementation of a method 101 for measuring an axial rigidity modulus of a specimen made of composite material with a ceramic matrix according to the invention.

The specimen 201, called the test specimen, whose axial rigidity modulus E ₁₁ is measured using the method, 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 what follows, the axial rigidity modulus E ₁₁ designates the axial rigidity modulus of the test specimen 201 along the longitudinal axis X of said test specimen 201 as it is visible at the . Furthermore, in other embodiments, the test specimen is not necessarily the result of machining, but can be the result of another manufacturing method provided that its profile in the plane is known and constant. over its entire thickness.

There shows a non-limiting example of 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, those skilled in the art will appreciate that the invention applies to any type of geometry of a test specimen.

In summary, in the example described, the test specimen 201 whose parameters are measured by the method has a dumbbell specimen geometry 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.

Method 101 is therefore a method of measuring the axial modulus of rigidity, denoted E ₁₁ , of a specimen 201, called a test specimen, resulting from machining along a plane P of a CMC plate.

Step 103 consists of measuring a resonance frequency f _1e of the test specimen 201. In the non-limiting example of implementing the method described here, the frequency f _1e is the resonance frequency d a first mode of bending in the machining plane P. Furthermore, it is a resonant frequency under free-free conditions. That is to say a resonance frequency of the test specimen 201 when it is not held by any of its ends (ie is free at all of its ends).

As illustrated by , the measurement of the resonance frequency of the test specimen 201 can be carried out by laser vibrometry. In this case, the test piece is subjected to acoustic excitation 301 with a frequency scan (for example ranging from 100 Hertz to 20 kilohertz) and a laser vibrometer 303 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 applying a Fourier transform, to extract the resonance frequencies of the different resonance modes of the measured test piece. This type of measurement has the advantage of having low repeatability and reproducibility uncertainty.

Step 105 consists of determining the axial rigidity modulus E ₁₁ of the test specimen 201, from the resonance frequency f _1e of the test specimen 201, of a coefficient K _1e obtained from d a digital simulation of the vibration behavior of a virtual test specimen 113, called a reference specimen, carried out beforehand, and of a density d of the test specimen 201.

In the non-limiting example described here, the digital simulation of the vibration behavior of the reference specimen 113 notably includes the determination of a resonance frequency, denoted f_{1e_simu}, of said reference specimen 113. 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 this 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 data output of said digital simulation.

In particular, the frequency f _{1e_simu} of the reference specimen 113 is determined from predetermined parameters of the reference specimen 113 which include a thickness h _ref , a density d _ref and an axial rigidity modulus E _{11_ref} of said specimen reference 113.

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. The word “theoretical” here designates the expected average parameters, resulting from a characterization file of the material in which the specimen is made (in l 'species, 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 its vibrational behavior are taken equal to theoretical parameters of the test specimen 201. 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 numerical 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 axial rigidity modulus E ₁₁ of the test specimen 201 is carried out from a coefficient K _1e resulting from the digital simulation described above.

The determination of this coefficient 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 numerical simulation on the resonance frequencies determined by the simulation.

For this, each parameter of the digital simulation of the vibration behavior of the test piece which is simulated is subjected to a variation (for example of 10% or 20%) to then observe the influence of this variation on the resonance frequencies obtained in fine .

There shows an example of a sensitivity matrix 401 linking certain parameters of the material (different rigidity moduli including the axial rigidity modulus E ₁₁ , the thickness h, the density d, the shear moduli, etc.) with different resonance frequencies. The types of hatching in each of the boxes correspond respectively to an amplitude (positive, zero or negative) of the sensitivity, explained in the right part of the figure, of each resonance frequency to each property. It is thus possible to see that certain amplitudes are zero (or almost zero), which illustrates the fact that certain resonance frequencies determined by the simulation are insensitive to the variation of certain parameters.

In particular, this sensitivity matrix of the illustrates in particular the fact that the use of a frequency other than the frequency f _1e (ie the use of a frequency of a bending mode outside the machining plane) would necessarily imply, subsequently, the fact to use the thickness to determine the axial modulus of rigidity of the specimen.

It is therefore this sensitivity analysis which makes it possible to establish a mathematical relationship between the axial rigidity modulus and the measured resonance frequency, independent of the thickness and other rigidity moduli of the material considered.

In particular, in the example described, thanks to the sensitivity analysis carried out beforehand, the 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 coefficient obtained from the numerical simulation of the vibration behavior of the reference specimen 113 as well as to the axial rigidity modulus, to the density and to the first frequency resonance of the reference specimen 113.

In addition, those skilled in the art will appreciate that the sensitivity analysis described above which led to the determination of the preceding formula results in the use, by numerical simulation, of different values of E _{11_ref} and d _ref leading to the obtaining a different value f _{1E_simu} but, in this case, the coefficient K _1e finally obtained remains unchanged.

Finally, the axial rigidity modulus E ₁₁ of the specimen 201 is determined from the resonance frequency f _1e of the test specimen 201, the coefficient K _1e obtained from the numerical simulation of the vibration behavior of the reference specimen 113 and a density d of test specimen 201, according to the formula:

where E ₁₁ , K _1e, f _1e and d correspond respectively to the axial rigidity modulus as well as the coefficient, the resonance frequency measured in step a) and the density of the test specimen 201.

In addition, the density d of the test specimen 201 used in this calculation may have been determined beforehand by a hydro-type measurement. That is to say a measurement involving the measurement of the dry mass, the soaked mass and the submerged mass to be able to determine the density.

The density value can also be taken from a characterization file for the ceramic matrix composite material.

In conclusion, the method according to the invention makes it possible to reduce the testing times of the test pieces, to make the data obtained more reliable and to reduce the uncertainties in measuring the axial rigidity modulus.

In addition, this process is non-destructive and applicable to all kinds of specimen geometries.

Finally, it is not necessary to measure the thickness of the specimen, which is a large source of uncertainty, to determine the axial modulus of rigidity.

Claims (10)

Method (101) for measuring an axial rigidity modulus (E ₁₁ ) of a specimen (201), called a test specimen, resulting from machining along a plane (P) of a plate of matrix composite material ceramic, said method (101) comprising:
a) measuring (103) a frequency (f _1e ) of resonance of the test specimen (201); And,
b) determining (105) the axial modulus of rigidity (E ₁₁ ) of the test specimen (201), from the frequency (f _1e ) of resonance of the test specimen (201), of a coefficient (K _1e ) obtained from a digital simulation of the vibration behavior of a virtual specimen (113), called the reference specimen, and a density (d) of the test specimen (201). Method according to claim 1, in which the resonance frequency (f _1e ) of the test specimen (201) is measured in step a) by laser vibrometry. A method according to claim 1 or claim 2, wherein the test specimen (201) is a dumbbell specimen whose thickness is between 2 and 10 millimeters, preferably between 2 and 4 millimeters or between 6 and 7 millimeters. Method according to one of claims 1 to 3, in which the measured resonance frequency (f _1e ) is a resonance frequency of a bending mode in the machining plane (P) in free-free conditions, preferably a first mode of bending in the plane. Method according to one of claims 1 to 4, in which the digital simulation of the vibration behavior of the reference sample (113), carried out prior to step b), comprises the determination of a frequency (f _{1e_simu} ) of resonance of the reference specimen (113), preferably carried out by the finite element method. Method according to claim 5, in which the frequency (f _{1e_simu} ) of resonance of the reference specimen (113) is determined from predetermined parameters of said reference specimen (113) comprising a thickness (h _ref ), a density (d _ref ) and a reference axial stiffness 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 the 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 coefficient as well as to the axial rigidity modulus, to the density and to a first resonance frequency of the reference specimen (113). Method according to claim 8, in which the axial rigidity modulus (E ₁₁ ) of the test specimen (201) is determined according to the formula:
where E ₁₁ , K _1e, f _1e and d correspond respectively to said axial rigidity modulus as well as to the coefficient obtained from the numerical simulation of the vibration behavior of the reference specimen, to the measured resonance frequency and to the density of the test specimen (201). Method according to one of the preceding claims, in which the density (d) of the test specimen (201) has been determined beforehand by a hydro-type measurement or comes from a characterization file for the matrix composite material ceramic.