METHOD FOR MEASURING THE AXIAL STIFFNESS MODULUS OF A CERAMIC MATRIX COMPOSITE SPECIMEN
The method measures resonance frequency and uses a numerical simulation to calculate the axial stiffness modulus of CMC specimens, addressing time and uncertainty issues in existing methods, offering a fast, cost-effective, and non-destructive solution.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- SAFRAN CERAMICS SA
- Filing Date
- 2022-06-16
- Publication Date
- 2026-06-19
AI Technical Summary
Existing methods for determining the axial stiffness modulus of ceramic matrix composite (CMC) specimens are time-consuming, require complex setups, and suffer from measurement uncertainties due to variations in mechanical behavior among specimens from the same batch.
A method involving the measurement of resonance frequency using laser vibrometry and a numerical simulation of a virtual reference specimen to calculate the axial stiffness modulus, eliminating the need for destructive testing and thickness measurement.
This approach reduces measurement time, uncertainty, and cost while providing reliable and non-destructive determination of the axial stiffness modulus applicable to various specimen geometries.
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Abstract
Description
Title of the invention: METHOD FOR MEASURING THE AXIAL STIFFNESS MODULUS OF A CERAMIC MATRIX COMPOSITE TEST SPECIMEN technical field
[0001] The invention relates to the field of measuring the parameters of a test specimen intended for use in characterizing the thermomechanical properties of a ceramic matrix composite plate. It relates in particular to a method for measuring the axial stiffness modulus of a ceramic matrix composite test specimen. Previous technique
[0002] To characterize the thermomechanical properties of ceramic matrix composite (CMC) plates, which are used in particular for manufacturing 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 are made.
[0003] In this context, it may be necessary and / or useful to know the axial stiffness modulus of a specimen before mechanically stressing it, in particular in order to be able to determine other properties that can only be obtained by knowing this modulus beforehand and / or in order to define the test conditions that will be applied to it.
[0004] To determine the axial stiffness modulus of a specimen, it is known to perform an interrupted test in the linear range of the material. The method consists of performing a tensile test on the specimen, which is sufficiently instrumented to measure stress and strain, but interrupting the test before reaching its damage threshold. The resulting stress-strain curve then allows the stiffness modulus to be measured. Since the specimen has been subjected to stress in the linear range, it retains its initial mechanical properties, and the test can be considered non-destructive. However, this method is time-consuming and requires complex setup associated with performing a mechanical test (due in particular to the creation of test requests, test planning, machine fleet management, test analysis, report writing, etc.).
[0005] It is also known to estimate the mechanical behavior of a test specimen based on results from so-called "neighboring" specimens (from the same plate, having the same material properties, having the same density, etc.). However, the 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 plates from the same production batch. Summary of the invention
[0006] The present invention proposes a solution to these drawbacks.
[0007] Thus, an objective of the invention is to measure a parameter of a test specimen in a non-destructive manner, faster than the prior art, inexpensive, and reducing measurement uncertainties compared to known techniques.
[0008] To this end, the invention, according to a first aspect, relates to a method for measuring the axial stiffness modulus of a test specimen, referred to as a test specimen, made of a ceramic matrix composite material, said method comprising:
[0009] a) the measurement of a resonance frequency of the test specimen; and,
[0010] b) the determination of the axial stiffness modulus of the test specimen, by calculation using the resonance frequency of the test specimen, a coefficient obtained from a numerical simulation of the vibrational behavior of a virtual specimen, called the reference specimen, and a density of the test specimen.
[0011] According to one embodiment of the method, the resonance frequency of the test specimen is measured in step a) by laser vibrometry.
[0012] According to another embodiment of the method, the test specimen is a dumbbell-shaped specimen with a thickness of between 2 and 10 millimeters. The thickness may in particular be between 2 and 4 millimeters or between 6 and 7 millimeters.
[0013] According to another embodiment of the method, the test specimen is produced by machining a ceramic matrix composite plate along a plane, and the measured resonance frequency is the resonance frequency of a bending mode in said machining plane under free-free conditions, preferably a first bending mode in the plane. Furthermore, the frequency of this first bending mode in the plane is independent of the specimen thickness. Thus, the identification of the axial stiffness modulus from this frequency does not depend on an additional measurement of the thickness, which is a significant source of uncertainty given the deformation of the plates.
[0014] According to another embodiment of the process, the numerical simulation of the vibratory behavior of the reference specimen, carried out prior to step b), includes the determination of a resonance frequency of the reference specimen, preferably carried out by the finite element method.
[0015] According to another embodiment 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 stiffness modulus axial reference.
[0016] According to another embodiment of the method, the thickness, density, and axial stiffness modulus of the reference specimen are equal to a theoretical thickness, a theoretical density, and a theoretical axial stiffness 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.
[0017] According to another embodiment of the process, the Kie coefficient, obtained from the numerical simulation of the vibrational behavior of the reference specimen, carried out prior to step b), is determined according to the formula:
[0018] IZ _ ^ll_ref Ie“ dœfX(fie_simu)2
[0019] where Kie, En_ref, dref and fie_simu correspond respectively to said coefficient as well as to the axial stiffness modulus, the density and a first resonance frequency of the reference specimen.
[0020] According to another embodiment of the method, the axial stiffness modulus of the test specimen is determined according to the formula:
[0021] En = KlexdxV
[0022] where En, Kiefie and d correspond respectively to the axial stiffness modulus and to the coefficient obtained from the numerical simulation of the vibrational behavior of the reference specimen, to the measured resonance frequency and to the density of the test specimen.
[0023] According to another embodiment of the process, the density of the test specimen was determined beforehand by a hydro-type measurement or is derived from a characterization file of the ceramic matrix composite material. Brief description of the drawings
[0024] The present invention will be better understood and other details, features and advantages of the present invention will become more apparent upon reading the description of a non-limiting example that follows, with reference to the accompanying drawings in which:
[0025] [Fig.1] is a step diagram of an implementation method of the measurement process according to the invention;
[0026] [Fig.2] is a schematic top-view representation of a test specimen such as that measured by the measurement method according to the invention;
[0027] [Fig. 3] is a schematic representation of the steps involved in measuring the resonance frequencies of a test specimen by laser vibrometry; and,
[0028] [Fig. 4] is an illustration of a sensitivity matrix of a numerical simulation of the vibrational behavior of a reference specimen as used in the method according to the invention. Description of the implementation methods
[0029] With reference to [Fig. 1], we will now describe an implementation method of a method 101 for measuring the axial stiffness modulus of a ceramic matrix composite specimen according to the invention.
[0030] The test specimen 201, referred to as the test specimen, whose axial stiffness modulus En is measured by the method, is a thermomechanical characterization specimen produced by machining a ceramic matrix composite material plate (hereafter referred to as the CMC plate). Furthermore, in the following, the axial stiffness modulus En designates the axial stiffness modulus of the test specimen 201 along the longitudinal axis X of said test specimen 201 as shown in [Fig. 2]. In other embodiments, the test specimen is not necessarily produced by machining, but may be produced by another manufacturing method, provided that its in-plane profile is known and constant throughout its thickness.
[0031] Figure 2 shows a non-limiting example of the geometry of the test specimen 201 in the machining plane (referred to as plane P hereafter), i.e., outside the thickness of the test specimen 201. In the example shown, this geometry is that of a so-called dumbbell specimen. However, those skilled in the art will appreciate that the invention applies to any type of test specimen geometry.
[0032] 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. 2]. For example, the various dimensions shown in [Fig. 2] are typically between 10 and 25 millimeters for a, between 100 and 200 millimeters for b, between 5 and 20 millimeters for c, between 20 and 50 millimeters for d, between 50 and 400 millimeters for e, and between 0 and 5 millimeters for f. Furthermore, the thickness of the specimen is typically between 2 and 4 millimeters or between 6 and 7 millimeters.
[0033] The method 101 is therefore a method for measuring the axial stiffness modulus, denoted En, of a test specimen 201, called a test specimen, obtained from machining along a plane P of a CMC plate.
[0034] Step 103 consists of measuring a resonant frequency fie of the test specimen 201. In the non-limiting example of implementation of the process described here, the fie frequency is the resonant frequency of a first bending mode in the machining plane P. Furthermore, it is a resonant frequency under free-free conditions. That is to say, a resonant frequency of the test specimen 201 when it is not held at any of its ends (i.e., is free at all its ends).
[0035] As illustrated in [Fig. 3], the resonance frequency of the test specimen 201 can be measured by laser vibrometry. In this case, the specimen is subjected to acoustic excitation 301 with a frequency sweep (for example, from 100 Hz to 20 kilohertz), and a laser vibrometer 303 simultaneously acquires, at different points on the surface of the specimen, an optical signal representative of the vibrations of said specimen. 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 specimen. This type of measurement has the advantage of exhibiting low uncertainty in repeatability and reproducibility.
[0036] Step 105 consists of determining the axial stiffness modulus En of the test specimen 201, from the resonance frequency fk of the test specimen 201, a coefficient Kie obtained from a numerical simulation of the vibratory behavior of a virtual specimen 113, called the reference specimen, carried out beforehand, and a density d of the test specimen 201.
[0037] In the non-limiting example described here, the numerical simulation of the vibrational behavior of the reference specimen 113 includes in particular the determination of a resonance frequency, denoted fie simu, of said reference specimen 113. The numerical simulation of the vibrational behavior can be carried out for example by the finite element method.
[0038] The word "virtual" here refers to the fact that this test tube does not necessarily have a physical existence but rather constitutes a set of parameters used as input data for the numerical simulation in order to then retrieve the information sought in the form of output data from said numerical simulation.
[0039] In particular, the frequency fie_simu of the reference specimen 113 is determined from predetermined parameters of the reference specimen 113 which include a thickness href, a density dref and an axial stiffness modulus En_ref of said reference specimen 113.
[0040] More specifically, in the non-limiting example described, the thickness href, the density dref and the axial stiffness modulus En_ref of the reference specimen 113 are substantially equal to a theoretical thickness h0, a theoretical density d0 and a theoretical axial stiffness modulus En of the test specimen 201. The word "theoretical" here refers to the expected average parameters, taken from a characterization file of the material in which the specimen is made (in this case, CMC).
[0041] In other words, the parameters of the reference specimen href, dref and En_ref, which are used for the numerical simulation of its vibrational behavior, are taken to be equal to theoretical parameters of the test specimen 201. So that the com vibratory behavior which is simulated can be assimilated (i.e. considered equivalent) to that of test specimen 201.
[0042] 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.
[0043] As mentioned above, the determination of the axial stiffness modulus En of the test specimen 201 is carried out from a coefficient Kie obtained from the numerical simulation described above.
[0044] The determination of this coefficient results from a sensitivity analysis of the parameters of the numerical simulation of the 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.
[0045] For this purpose, each parameter of the numerical simulation of the vibratory behavior of the simulated specimen is subjected to a variation (for example of 10% or 20%) in order to then observe the influence of this variation on the resonance frequencies obtained in the end.
[0046] Figure 4 shows an example of a sensitivity matrix 401 linking certain material parameters (various stiffness moduli including the axial stiffness modulus En, the thickness h, the density d, the shear moduli, etc.) with different resonance frequencies. The hatching patterns in each cell correspond respectively to an amplitude (positive, zero, or negative) of the sensitivity, specified in the right-hand part of the figure, of each resonance frequency for each property. It is thus possible to see that some amplitudes are zero (or almost zero), which illustrates the fact that certain resonance frequencies determined by the simulation are insensitive to variations in certain parameters.
[0047] In particular, this sensitivity matrix of [Fig.4] illustrates in particular the fact that the use of a frequency other than the frequency fk (i.e. the use of a frequency of a bending mode outside the machining plane) would necessarily imply, subsequently, the use of the thickness to determine the axial stiffness modulus of the specimen.
[0048] It is therefore this sensitivity analysis which makes it possible to establish a mathematical relationship between the axial stiffness modulus and the measured resonance frequency, independent of the thickness and other stiffness moduli of the material considered.
[0049] In particular, in the example described, thanks to the sensitivity analysis carried out beforehand, the Kie coefficient, obtained from the numerical simulation of the vibrational behavior of the reference specimen 113, is determined according to the formula:
[0050] [Math.l] jÇ EH_ref E x(t lejâmn / 2
[0051] where Kie, En_ref, dref and fie_simu correspond respectively to the coefficient obtained from the numerical simulation of the vibratory behavior of the reference specimen 113 as well as to the axial stiffness modulus, the density and the first resonance frequency of the reference specimen 113.
[0052] Furthermore, those skilled in the art will appreciate that the sensitivity analysis described above, which led to the determination of the previous formula, means that the use, by the numerical simulation, of different values of En_refet dref leads to obtaining a similarly different value fiE, but that, in this case, the coefficient Kie finally obtained remains unchanged.
[0053] Finally, the axial stiffness modulus En of the test specimen 201 is determined from the resonance frequency fie of the test specimen 201, the coefficient Kie obtained from the numerical simulation of the vibrational behavior of the reference specimen 113 and a density d of the test specimen 201, according to the formula:
[0054] [Math.2] Eh = d xf!e2
[0055] where En, Kiefie and d correspond respectively to the axial stiffness modulus and the coefficient, the resonance frequency measured in step a) and the density of the test specimen 201.
[0056] Furthermore, the density d of the test specimen 201 used in this calculation may have been determined beforehand by a hydrometric measurement. That is to say, a measurement involving the measurement of the dry mass, the soaked mass and the immersed mass in order to determine the density.
[0057] The density value can also be obtained from a characterization file of the ceramic matrix composite material.
[0058] In conclusion, the method according to the invention makes it possible to reduce the time required to control the test specimens, to make the data obtained more reliable and to reduce the uncertainties in the measurements of the axial stiffness modulus.
[0059] Furthermore, this method is non-destructive and applicable to all kinds of specimen geometries.
[0060] Finally, it is not necessary to measure the thickness of the specimen, which is a large source of uncertainty, to determine the axial stiffness modulus.
Claims
Demands
1. Method (101) for measuring an axial stiffness modulus (En) of a test specimen (201), referred to as the test specimen, made of ceramic matrix composite material, said method (101) comprising: a) the measurement (103) of a resonance frequency (fie) of the test specimen (201); and, b) the determination (105) of the axial stiffness modulus (En) of the test specimen (201), by a calculation using the resonance frequency (fie) of the test specimen (201), a coefficient (Kie) obtained from a numerical simulation of the vibrational behavior of a virtual specimen (113), referred to as the reference specimen, and a density (d) of the test specimen (201).
2. A method according to claim 1, wherein the resonance frequency (fle) of the test specimen (201) is measured in step a) by laser vibrometry.
3. A method according to claim 1 or claim 2, wherein the test specimen (201) is a dumbbell specimen having a thickness of between 2 and 10 millimeters, preferably between 2 and 4 millimeters or between 6 and 7 millimeters.
4. A method according to any one of claims 1 to 3, wherein the test specimen is obtained by machining along a plane (P) of a ceramic matrix composite material plate and the measured resonance frequency (fle) is a resonance frequency of a bending mode in said machining plane (P) under free-free conditions, preferably a first bending mode in the plane.
5. A method according to any one of claims 1 to 4, wherein the numerical simulation of the vibrational behavior of the reference sample (113), carried out prior to step b), includes the determination of a resonance frequency (fie_Simu) of the reference specimen (113), preferably carried out by the finite element method.
6. Method according to claim 5, wherein the resonance frequency (fie simu) of the reference specimen (113) is determined from predetermined parameters of said reference specimen (113) comprising a thickness (href), a density (dref) and a reference axial stiffness modulus (En_ref).
7. A method according to claim 6, wherein the thickness (href), density (dref) and axial stiffness modulus (En_ref) of the reference specimen (113) are equal to a theoretical thickness (h0), a theoretical density (do) and a theoretical axial stiffness modulus (En_0) of the test specimen (201).
8. A method according to claim 6 or claim 7, wherein the coefficient Kie, obtained from the numerical simulation of the vibratory behavior of the reference specimen (113), carried out prior to step b), is determined according to the formula: _ h; j where Kie, En_ref, dref and fie_simu correspond respectively to said coefficient as well as to the axial stiffness modulus, the density and a first resonance frequency of the reference specimen (113).
9. A method according to claim 8, wherein the axial stiffness modulus (En) of the test specimen (201) is determined according to the formula: Ej । = Klex dxf ie2 where En, Kiefie and d correspond respectively to said axial stiffness modulus as well as to the coefficient obtained from the numerical simulation of the vibrational behavior of the reference specimen, to the measured resonance frequency and to the density of the test specimen (201).
10. A method according to any one of the preceding claims, wherein the density (d) of the test specimen (201) has been determined beforehand by a hydro-type measurement or is derived from a characterization file of the ceramic matrix composite material.