X-ray fluorescence spectrometry for characterizing the microstructure of a metallic alloy and detecting chemical segregations

Abstract

X-ray fluorescence spectrometry for characterizing the microstructure of a metallic alloy and detecting chemical segregations. One aspect of the invention relates to a method for determining at least one microstructural property of a metallic alloy on the surface of a part made from said metallic alloy.

Description

Title of the invention: X-ray fluorescence spectrometry for the characterization of the microstructure of a metal alloy and the detection of chemical segregations TECHNICAL FIELD OF THE INVENTION

[0001] The technical field of the invention is that of non-destructive testing for evaluating the properties of a metal alloy material.

[0002] The present invention relates to a method for determining at least one microstructural property of a material of a surface of a part. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] In aeronautics, as in other industrial fields, a large quantity of parts are manufactured in metal alloys, for example in nickel-based superalloy typically used for the low-pressure turbine disks of the LEAP turbojet (in English "Leading Edge Aviation Propulsion"). These alloys are composed, in particular, of a matrix of a material, having a certain concentration in each chemical element which constitutes it. This matrix comprises single crystals of the gamma phase, also called "grains". The material also comprises hardening precipitates, characterized by concentrations of chemical elements different from that of the matrix. These precipitates can take various shapes such as elongated or spherical and are small in size compared to that of the matrix.

[0004] Verification of the integrity and conformity of the microstructure of these alloys is essential in order to avoid premature failure of the part during its service life. In particular, the inspection of these parts makes it possible to detect and characterize abnormal chemical segregations in the metal alloys, such as a local overconcentration of a hardening chemical element, called "freckle" in English, or a local underconcentration of a hardening chemical element, called "white spot" in English (PD Généreux and CA Borg, Characterization of Freckles in a High Strength Wrought Nickel Superalloy, Superalloys, pp. 19-27, 2000). This verification can take place during the manufacture of the part, for example on a billet before forging, in pre-machining before heat treatment or at the end of the production line following the pre-machining carried out after heat treatment, or even during a maintenance operation.

[0005] The most widespread technique for detecting these anomalies is macrographic analysis, however it does not allow to achieve a sufficient degree of precision to precisely determine the properties of the material. On the contrary, the inspection techniques conventionally used in the laboratory based on the use of micro Electron microscopy (M.-A. Charpagne, Evolutions de microstructure au cours du forgeage de l'alloy René 65, thesis, Université Paris Sciences et Lettres, 2016), in particular electron backscattered diffraction (EBSD), in a scanning electron microscope (SEM), allows high quality inspection to be achieved. This technique produces a high-resolution map of crystal orientations on the surface of the sample being inspected.

[0006] EBSD is often coupled with energy dispersive spectroscopy (EDS). The latter consists of measuring the energy spectrum of the X-rays emitted by the sample, after interaction with the incident electrons, to carry out a chemical analysis, based on knowledge of the electronic transitions characteristic of each chemical element.

[0007] It is also known to use the technique of transmission electron microscopy (TEM), which requires the removal of a thin layer of the sample, typically by ion abrasion.

[0008] These techniques allow for the production of high spatial resolution images (typically a few tens of nanometers for EBSD) but have the disadvantage of only allowing the inspection of small samples that must be taken from the part to be inspected in a vacuum environment. It is therefore difficult to envisage this type of technique in a production or maintenance context.

[0009] X-ray fluorescence is also used to analyze the chemical composition of a sample (C. Vanhoof et al., Atomic spectrometry update - a review of advances in X-ray fluorescence spectrometry and its special applications, J. Anal. At. Spectrom., vol. 35, p. 1704, 2020) and to map the surface of a sample with a spatial resolution of up to a few tens of micrometers. This technique is, however, limited by the size of the X-ray beam incident on the sample, not giving access to smaller quantities, such as the size of grains and hardening precipitates in a metal alloy.

[0010] There is therefore a need for a non-destructive testing method applicable in an industrial production and / or maintenance context and which makes it possible to detect and characterize chemical segregation phenomena in metal alloys and superalloys. Summary of the invention

[0011] The invention provides a solution to the problems mentioned above, by allowing the analysis of X-ray fluorescence spectra measured by scanning a beam of rays X on the surface of a sample in order to obtain characteristics of the microstructure of the metal alloy that composes it, as well as to detect and characterize chemical segregations on this surface.

[0012] A first aspect of the invention relates to a method for determining at least one microstructural property of a metal alloy on the surface of a part manufactured from said metal alloy, the method comprising: • Obtaining a set of spectra acquired using an X-ray fluorescence spectrometry device, each spectrum in the set of spectra being associated with a sub-region of the surface of the part, the sub-regions being contiguous on the surface of the part and forming a continuous region, the continuous region being associated with the set of spectra; • Determine a plurality of photon numbers for a chemical element of the metal alloy from the set of spectra; • Construct, for the set of spectra, a histogram of photon numbers from the number of photons determined for each spectrum of said set of spectra for said chemical element; • Constructing a reference histogram by means of an iterative search mechanism as a function of a distance of the reference histogram with the histogram of the number of photons, said reference histogram being associated with at least one reference microstructural property, and said reference histogram being constructed from a random distribution of a plurality of theoretical numbers of photons randomly corrected according to a statistical law; • Determine, for the continuous region, the microstructural property of the metal alloy, the microstructural property being equal to the reference microstructural property.

[0013] The term “microstructural property” means a property characterizing the micro structure of the metal alloy at the grain scale. For example, this property includes a characteristic dimension of hardening precipitates and a phase surface ratio. The characteristic dimension is, for example, a diameter, a width, a length of hardening precipitate, and / or a combination of these, for the metal alloy. The surface ratio indicates the ratio of the surface area of ​​the y phase, i.e., that of the precipitates, to the surface area of ​​the Ÿ phase, i.e., that of the alloy matrix. Other properties may be involved, depending on the alloy of the material as well as the form and / or nature of the hardening precipitates.

[0014] The term "X-ray fluorescence spectrometry device" means a measuring device capable of emitting a beam of X-rays towards a sample and of capturing the re-emitted rays after interaction with the metal alloy. These captured rays allow the formation of a "spectrum" indicating the proportion of photons detected as a function of their frequency. The device can be based on the direct conversion of photon energy, absorbed by the photoelectric effect and then converted into an electronic signal, using a sensor formed from a semiconductor material, such as Silicon (for example with a Silicon Drift Detector architecture) or germanium.

[0015] The term “iterative search mechanism” means a tool for iteratively searching for an optimal solution to a given problem, in this case searching for an optimal reference histogram with respect to a condition set on the distance of the reference histogram from the histogram of the number of photons.

[0016] Thanks to the invention, it is therefore possible to determine one or more microstructural properties of a metal alloy from which the part is manufactured. These properties are evaluated at the surface of the part by analyzing spectra acquired using an X-ray fluorescence spectrometry technique. This analysis being based on a statistical study of the acquired spectra, it is possible to achieve a scale of characterization of the material much lower than the spatial resolution conventionally obtained by this measurement technique, given by the size of the X-ray beam on the sample. For example, it is possible to characterize hardening precipitates of 2 pm radius with an X-ray beam of size 20 pm on the surface of the part.

[0017] Advantageously, the characterization of the alloy makes it possible to detect anomalies in the estimated microstructural property, compared to the nominal theoretical properties of the alloy, and therefore to detect defects in the material, such as abnormal segregations of one or more chemical elements (“freckle” and “white spot”).

[0018] Furthermore, the application of the statistical law makes it possible to take into account the experimental conditions and the measurement uncertainties linked to the measuring device.

[0019] Finally, the proposed method also has the advantage of being simple and quick to implement, without modification of the spectra acquisition process, since it only concerns the post-processing of the acquired spectra. This method can therefore be used independently of the measuring equipment and experimental conditions. This method is therefore compatible with a production and / or maintenance environment.

[0020] In addition to the characteristics which have just been mentioned, the method according to the first aspect of the invention may have one or more complementary characteristics among the following, considered individually or according to all technically possible combinations.

[0021] In one embodiment, the metal alloy comprises a matrix and hardening precipitates, and the reference histogram is a theoretical histogram for which a predefined condition relating to a distance of the theoretical histogram with the histogram of the number of photons is verified, the construction of the theoretical histogram being carried out at each iteration of the iterative search mechanism by: • Selection, within a range of values, of a theoretical value of the microstructural property; • Determination of a theoretical number of hardening precipitates in the metal alloy of the part, on a cell of the same dimensions as the continuous region, from the selected theoretical value; • Random distribution, according to a uniform law, of hardening precipitates on the cell, the number of hardening precipitates distributed being equal to the theoretical number of hardening precipitates; • Determination, for the chemical element, of the plurality of theoretical numbers of photons, each theoretical number N of photons being associated with a sub-cell of a plurality of sub-cells included in the cell, each sub-cell corresponding to one of the sub-regions of the continuous region, each theoretical number of photons being determined by N = a(Cy.Sy + Cy'Sy') with: • has a proportionality factor; • Cy the theoretical concentration of the chemical element in the matrix of the metal alloy, in the associated sub-cell; • Sy the surface of the matrix of the metal alloy in the sub-cell; • Cy' the theoretical concentration of the chemical element in the hardening precipitates of the matrix of the metal alloy, in the associated sub-cell; • Sy' the surface of the hardening precipitates in the sub-cell; • Random correction, according to the statistical law, of the theoretical numbers of photons from the plurality of theoretical numbers; • Construction of the theoretical histogram from the plurality of theoretical numbers of corrected photons.

[0022] The construction of the reference histogram is thus easy and quick to implement. The random distribution according to the uniform law is used to model the spatial distribution of the hardening precipitates in a rapid manner that is representative of the statistical properties of the material. The random distribution according to the statistical law, for example the Poisson law, is used to take into account the variability of the measurement of the photons emitted by a given spatial distribution of the hardening precipitates, thus improving the reliability of the characterization. The application of the proportionality factor ensures that the numbers theoretical calculated photon values ​​are representative of the experiment carried out. This proportionality factor ensures the adjustment between the theoretical model and the measurement carried out.

[0023] Furthermore, the application of the proportionality factor and the statistical law to determine the reference histogram makes it possible to improve the consideration of experimental conditions and measurement uncertainties linked to the measuring device, thus improving the robustness and reliability of the characterization obtained.

[0024] In one embodiment, the proportionality factor is equal to a ratio between an average number of photons and a theoretical concentration of the chemical element at the surface of the part, the average number of photons being determined from an average of the plurality of numbers of photons.

[0025] The theoretical number of photons is thus weighted to realign the simulation of the measurement with the hypothesis underlying the proposed approach, which is that there is a proportional relationship between photon counting and the concentration of chemical elements.

[0026] In one embodiment, each of the randomly distributed hardening precipitates has dimensions randomly determined according to a normal distribution.

[0027] This embodiment makes it possible to obtain a distribution of the hardening precipitates and their size which is more representative of physical reality.

[0028] In one embodiment, the set of spectra is obtained by discretizing a continuous spectrum acquired by the X-ray fluorescence spectrometry device, the X-ray fluorescence spectrometry device comprising a source, the method comprising, before determining the plurality of theoretical numbers of photons: • Discretize the position of each distributed hardening precipitate as a function of a set of source positions during the same spectrum measurement and the number of sub-cells; • Determine, for each distributed hardening precipitate, a recovery rate for each sub-cell of the plurality of sub-cells as a function of the discretization of the position of said hardening precipitate; and the surface area of ​​hardening precipitate, in the associated sub-cell, is calculated based on the coverage rate of each hardening precipitate.

[0029] The method is thus compatible with a spectrum acquired continuously by the acquisition device.

[0030] In one embodiment, each number of photons of the plurality of photon numbers is determined from an integral, in one of the spectra of the set of spectra, of the area under a peak associated with said chemical element.

[0031] The term “peak associated with a chemical element” means a peak in a spectrum of which the energy (in keV) is associated with a specific chemical element and the height of said peak is representative of the concentration of this material in the measurement area.

[0032] The estimation of the number of photons is thus determined quickly, easily and reliably.

[0033] In one embodiment, the iterative search mechanism is an inversion or optimization algorithm or a brute force algorithm.

[0034] It is thus possible to search for an optimal reference histogram according to an optimization criterion to minimize the distance with the photon number histogram and reliably estimate the property of the alloy. Alternatively, it is possible to systematically search for the reference histogram which minimizes the distance with the photon number histogram and reliably estimate the property of the alloy.

[0035] In one embodiment, the metal alloy of the surface of the part comprises at least a first chemical element and a second chemical element, and the reference histograms for the first and second chemical elements, respectively, are jointly determined using the iterative search mechanism based on a combination of the distances respectively calculated with the histogram of the number of photos for the first and second elements.

[0036] It is thus possible to determine the microstructural property of the alloy by taking into account concomitantly several or all of the chemical elements which compose this alloy, thus increasing the robustness and reliability of the characterization.

[0037] In one embodiment, the distance is a quadratic deviation, a Mahalanobis distance, a maximum likelihood or an L1 normal, between the histogram of the number of photons and the reference histogram.

[0038] Distance is thus a robust metric, quick to calculate with low computational cost.

[0039] In one embodiment, the X-ray fluorescence spectrometry device is an energy dispersive fluorescence device or a wavelength fluorescence device.

[0040] The method is therefore applicable to conventional X-ray fluorescence spectrometry techniques.

[0041] In one embodiment, the method comprises: • Detect a microstructural anomaly of the part surface when a value of at least one determined microstructural property of the metal alloy does not conform to a nominal value.

[0042] The method thus makes it possible to detect a microstructural anomaly, for example a segregation defect (such as a freckle or a white spot) by comparing the characterization obtained with a nominal value of the property. The term "value" means nominal” a value of said property when no anomaly is present.

[0043] In one embodiment, the method comprises: • Construct a map of at least one microstructural property of the part.

[0044] The method thus makes it possible to access an easily interpretable visual representation of the characterization.

[0045] A second aspect of the invention relates to a system for determining at least one microstructural property of a metal alloy on the surface of a part manufactured from said metal alloy, the system being configured to implement the method according to the first aspect.

[0046] A third aspect of the invention relates to a computer program product comprising instructions which, when the program is executed on a computer, cause the latter to implement the steps of the method according to the first aspect.

[0047] A fourth aspect of the invention relates to a computer-readable recording medium comprising instructions which, when executed by a computer, cause the computer to implement the steps of the method according to the first aspect.

[0048] The invention and its various applications will be better understood upon reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0049] The figures are presented for information purposes only and in no way limit the invention. • [Fig.l] is a block diagram illustrating the sequence of steps of a method according to the invention. • [Fig.2] is a representation of a spectrum of X-ray radiation captured by a spectrometry device. • [Fig.3] is a schematic representation of a surface of a manufactured part. • [Fig.4] is a representation of a map of the number of photons detected per sub-region on the surface of the part in [Fig.2]. • [Fig.5] is a representation of a histogram of numbers of detected photons. • [Fig.6] is a mapping of a microstructural property of the part in [Fig.2], • [Fig.7] is a mapping of another microstructural property of the part in [Fig.2]. • [Fig.8] is a representation of the evolution of a distance between an experimental histogram and a theoretical histogram, as a function of estimating the properties of the metal alloy, according to one embodiment. • [Fig.9] is a set of maps obtained according to an embodiment of the method according to the invention. DETAILED DESCRIPTION

[0050] Unless otherwise specified, the same element appearing in different figures has a single reference.

[0051] The present invention relates to a method for analyzing spectra measured by X-ray fluorescence spectrometry to characterize one or more microstructural properties of a metal alloy or superalloy of a manufactured part. The method also makes it possible to detect abnormal chemical segregations on the surface of the part.

[0052] The proposed analysis implements a statistical study of the chemical elements constituting the metallic alloy of the part via the construction of histograms of the number of photons detected, in the different spectra, for each element.

[0053] The method is based on the approximation that the metal alloy material comprises two phases of different chemical compositions: the alloy matrix and the hardening precipitates. The hardening precipitates are composed of the same chemical elements as the matrix, but with different concentrations. The role of these hardening precipitates is to consolidate the alloy matrix to improve its mechanical properties.

[0054] For these materials, the method then makes it possible to characterize the characteristic dimension of the smallest phase (the hardening precipitates) and to estimate the area ratio between the phase of the hardening precipitates and the phase of the matrix.

[0055] In the following, the implementation of the method is illustrated for the characterization and detection of abnormal segregations, i.e. hardening precipitates, of a metal alloy for which the approximation of two phases is possible. However, this method is entirely applicable to any metal alloy or superalloy compatible with this approximation.

[0056] Thus, a first aspect of the invention relates to a method for determining at least one microstructural property of a metal alloy on the surface of a part manufactured from said metal alloy. The sequence of steps of the method 100 is illustrated in [Fig.l].

[0057] For this metal alloy, it is in particular possible to characterize a characteristic dimension of hardening precipitates and a ratio of surfaces of hardening precipitates in the alloy. In the case of y / y alloys, this is a radius of hardening precipitate y' and a ratio of the surface of hardening precipitates y' relative to the surface of the matrix V, respectively. The matrix Y includes the so-called secondary and tertiary hardening precipitates y' inserted into the matrix T, the latter being of characteristic nanometric dimension.

[0058] Other microstructural properties may be characterized, such as the dispersion of the size of the precipitates, the dispersion being for example equal to a standard deviation of the dimensions of the precipitates; or such as geometric properties of the precipitates, for example a sphericity, a distance or area ratio, an aspect ratio, etc.

[0059] In another embodiment, the present method could be applied to an Inconel 718 alloy to characterize the properties of the hardening precipitates Ô in the Y matrix of this alloy.

[0060] A step for obtaining 110 a set of spectra is implemented. These spectra are or have been acquired by means of an X-ray fluorescence spectrometry device. In this embodiment, and by way of illustration, this device is an energy-dispersive fluorescence device (in English, Energy-Dispersive X-ray Spectroscopy, EDS or EDXS) which makes it possible, by means of a spectrometric detector, to construct a histogram representing the distribution of the X-rays as a function of the energy of the captured photons.

[0061] The surface of the part to be characterized is artificially divided into portions called “sub-regions”. Thus, each spectrum of the set of spectra is acquired by the device so as to correspond to a given sub-region of the surface of the part to be characterized. Each spectrum of the set of spectra is therefore associated with a sub-region of the surface of the part. Each sub-region is preferably a square whose side has a length of between 0.1 mm and 5 mm, for example 1 mm. Each sub-region may also be of a shape and dimensions corresponding to the size of the incident X-ray beam.

[0062] As illustrated in [Fig.3], the sub-regions 21 are preferably contiguous, that is to say that each sub-region 21 has at least one border in common with another sub-region 21. The sub-regions 21 thus form a continuous region 22 on the surface 20 of the part. The continuous region can be of any shape and any dimensions, which depend on the distribution and the number of sub-regions selected, respectively. The continuous region is therefore associated with the set of spectra.

[0063] An example of spectrum 10, measured in air, is shown in [Fig.2]. The abscissa axis corresponds to the energy of the detected photons and the ordinate axis to the number of counts detected in logarithmic scale. The equipment used is a Bruker™ M4 Tomado® equipped with a Rhodium tube and two 30 mm2 XFlash® detectors. The spectrum includes several peaks, each identified with a specific chemical element, in particular for the following elements: titanium, chromium, iron, cobalt, nickel, tungsten, niobium and molybdenum.

[0064] A step 120 of determining a plurality of numbers of photons from the set of spectra is then implemented. This counting of numbers of photons is implemented for the chemical element. In other words, for each of the spectra of the set of spectra, a number of photons captured by the device is calculated for the chemical element.

[0065] Each number of photons is calculated as a function of one or more metrics characterizing the peak, in the relevant spectrum, corresponding to the chemical element. For example, the number of photons corresponds to the Do under the peak, that is to say to the value of the integral of the area under said peak.

[0066] A step 130 of constructing a histogram of the number of photons detected in each sub-region is then implemented. The construction is carried out for the set of spectra and for the chemical element. In other words, the histogram represents, for the chemical element, the distribution of the values ​​of the numbers of photons calculated in the set of spectra.

[0067] A map of the photon numbers, representing the distribution of the numbers of photons detected per sub-region, for the titanium element of the alloy considered, is proposed in [Fig.4]. It can be observed that the distribution of the values ​​of the numbers of photons detected for titanium, and per spectrum, is notably different between the first region 31 and the second region 32. In the latter, a significant increase in the number of photons detected for this element is noted. Furthermore, an example of a histogram 40 constructed for the first region 31, for the titanium element, is represented in [Fig.5].

[0068] In the embodiment presented, the method 100 comprises a step 140 of determining a proportionality factor which is then implemented. The determination is carried out from the determined numbers of photons. This proportionality factor indicates the pro rata of the average number of photons detected, per chemical element, as a function of the theoretical concentration of this element in the metal alloy at the surface of the part 20. The proportionality factor a is therefore given by a — 4L A is the average value of the numbers of photons of the plurality of numbers of photons determined in the previous step 120, or of a part of this plurality of numbers, for the chemical element concerned, in this case the chemical element. TV is therefore the average number of photons calculated from the average of the plurality of numbers of photons.The average may be a weighted average, for example to account for variability in the X-ray beam or accessibility constraints at the time of acquisition. C is the average concentration of the chemical element. concerned in the alloy. This concentration is equal to the theoretical concentration of this element in the alloy.

[0069] Alternatively, the proportionality factor is calculated by averaging the photon numbers of several sets of spectra, each set of spectra being associated with a different region.

[0070] A step 150 of constructing a reference histogram is then implemented. This reference histogram is a histogram of theoretical numbers of photons detected for the element. The determination of this reference histogram is carried out by means of an iterative search mechanism, the implementation of which allows the comparison of the histogram of the number of photons with the recursively estimated reference histogram.

[0071] The iterative search mechanism is a recursive mechanism which allows, by successive iterations, to search for a theoretical histogram until a predefined condition relating to a distance calculated with the histogram of photon numbers is satisfied. When the predefined condition is satisfied, the theoretical histogram is called “reference histogram”.

[0072] The distance is, for example, a quadratic deviation, a Mahalanobis distance, a maximum likelihood or a normal Ll, between the histogram of the number of photons and the reference histogram.

[0073] The iterative search mechanism is configured to search among a predefined range of values ​​of the microstructural property to be characterized. At least one range of values ​​is therefore defined for the microstructural property. When two or more structural properties are to be characterized, at least one range of values ​​is defined for each microstructural property.

[0074] In this case, the search mechanism scans a first predefined range of values ​​for the characteristic dimension of hardening precipitates and a second predefined range of values ​​for the ratio of surfaces of hardening precipitates. An example of variation of the distance, here the quadratic deviation is illustrated in Figure 8, as a function of variations in the radius r? of hardening precipitates y' and as a function of variations in the ratio of surfaces of the phases y' and V in the alloy.

[0075] The range of values ​​may be a continuous or discontinuous range and is, for example, defined according to known theoretical values ​​for the alloy considered. The range of values ​​is, for example, delimited by a maximum value and a minimum value, each corresponding to a percentage of a theoretical or empirical nominal value, for example by means of an EDS-EBSD technique, of the corresponding property. The nominal value then corresponds to the microstructural property of the material without defects. This range of values ​​is defined independently of the number of chemical elements considered.

[0076] The iterative search mechanism is, for example, an optimization algorithm minimizing an objective function, such as a local optimization algorithm like gradient descent, or a global optimization algorithm like a genetic algorithm. In this case, the objective function is the distance of the theoretical histogram from the histogram of photon numbers. Alternatively, the iterative search mechanism is a Bayesian method. The iterative search mechanism is therefore used to iteratively search for a theoretical histogram that satisfies the predefined condition. This predefined condition is, for an optimization or inversion algorithm, the minimization of the distance, i.e. to iterate the search until the distance is less than or equal to an optimality threshold.This optimality threshold is defined by an operator, based on his business knowledge, the desired precision of the characterization and / or based on the specificities of the experimental conditions. Alternatively or jointly, the condition can also relate to a maximum number of iterations, which is defined by the operator based on the desired computational cost of the search and business knowledge.

[0077] Alternatively, the search algorithm is a brute force method that evaluates the distance for a set of theoretical histograms; the reference histogram then being the theoretical histogram for which the distance is the smallest, among all the distances calculated. This algorithm is therefore configured to traverse the range(s) of values ​​with a predefined, constant or adaptive iteration step, until all possible iterations have been carried out. The predefined condition is that the distance of the reference histogram is the one that is the smallest among all those calculated by the brute force algorithm. In the proposed example, the brute force algorithm traverses the first and second ranges of values.

[0078] Regardless of the nature of the search mechanism, the reference histogram, as well as each theoretical histogram, are constructed from an estimate of the microstructural property. In the proposed example, this is the characteristic dimension of hardening precipitates and the ratio of surfaces of hardening precipitates. Each theoretical histogram constructed during the search is therefore associated with this estimated microstructural property. Similarly, the reference histogram is associated with an estimated microstructural property, called “reference”, which is therefore the property of the metal alloy that makes it possible to form the reference histogram.

[0079] In particular, the reference microstructural property may comprise a reference characteristic dimension and a reference surface ratio. For example, this is a reference precipitate diameter y' and a surface ratio of the phases y' and Y.

[0080] Each theoretical histogram, like the reference histogram, is preferred entially constructed by producing a random distribution of a plurality of theoretical numbers of photons. These numbers of photons are weighted by the previously determined proportionality factor. These numbers of photons are also corrected by applying a statistical law, for example a Poisson law in order to take into account measurement uncertainties related to the sensor. In this embodiment, the statistical law is a Poisson law which has as parameter the theoretical number of photons to be corrected.

[0081] Other types of laws could be used, such as a normal law, especially if the photonic component, i.e. the Poisson noise, is small compared to the influence of the variability of the concentration of elements between pixels in the standard deviation of the histogram values. In this case the photonic component could be neglected when constructing the reference histogram.

[0082] An example of implementation of the construction of a theoretical histogram is proposed below. When several regions are to be characterized, the following steps are implemented for each region considered. This implementation can be done concurrently or sequentially.

[0083] At each iteration of the search mechanism, the microstructural property is estimated to form a theoretical histogram.

[0084] Step 150 of constructing the reference histogram then comprises a sub-step 151 of selecting, for the microstructural property, a theoretical value from the range of values. Where appropriate, a theoretical value is selected from the range of values ​​relating to each of the microstructural properties. For example, a value of a theoretical characteristic dimension of hardening precipitates in the first range of values, and a value of a theoretical surface ratio of hardening precipitates in the second range of values ​​are defined and selected.

[0085] A sub-step 152 of determining a theoretical number of precipitates, in the metal alloy, is then implemented. This theoretical number of precipitates is determined by a digital calculation tool which, from the values ​​of the selected microstructural property, determines this theoretical number. In particular, for the present example, this theoretical number is determined from the value of the theoretical characteristic dimension of hardening precipitates, the value of the theoretical surface ratio of hardening precipitates and the value of the surface area of ​​hardening precipitates, for example by applying a proportionality rule. The digital simulation tool is therefore configured to calculate the theoretical number of hardening precipitates by providing it with the value of the microstructural property as input.

[0086] The theoretical number of hardening precipitates is determined for a cell, that is to say for a numerical region which has the same dimensions as the region in which the characterization is carried out.

[0087] A step of random distribution 153 of the hardening precipitates in the cell is then implemented from this theoretical number of hardening precipitates. The number of these distributed hardening precipitates is equal to the theoretical number of hardening precipitates. This random distribution is, for example, implemented according to a uniform law. The parameters of the uniform law are defined, for example by the operator, as a function of the alloy and independently of the element(s) considered. Other laws can alternatively be used instead of the uniform law.

[0088] The size of each hardening precipitate is defined by the value selected from the relevant range of values, for example the value selected from the first range of values.

[0089] In certain embodiments, the dimension of each hardening precipitate is randomly defined, according to a normal law. The average value of this normal law is, for example, equal to the value selected in the range of values ​​relating to the dimension of the hardening precipitates, in this case the first range of values. The other parameters of this normal law are defined, for example by the operator, as a function of the alloy and independently of the chemical element(s) considered.

[0090] A step 154 ​​of determining the plurality of theoretical numbers of photons is then implemented, for the chemical element, from the distribution of the hardening precipitates. To do this, the cell, corresponding in dimensions to the region, is divided into a plurality of sub-cells. Each sub-cell corresponds to a sub-region of the region, that is to say that the sub-cell is of the same dimension as the sub-region with which it is associated. Thus, each theoretical number of photons is associated with one of the sub-cells, which is included in the cell.

[0091] Preferably, the theoretical number N of photons, for each sub-cell, is determined such that: N = a(Cy.Sy + Cy'Sy'\ where • a is the proportionality factor; • Cy is the theoretical concentration, in the sub-cell, of the chemical element in the matrix of the metal alloy; • Sy is the surface area of ​​the matrix in the sub-cell; • Cy' is the theoretical concentration, in the sub-cell, of the chemical element in the hardening precipitates of the matrix of the metal alloy; • Sy' is the surface area of ​​the hardening precipitates in the sub-cell.

[0092] This is therefore an estimate of a count of detected photons for the sub-cell which are intersected by one, several or none of the gains.

[0093] A correction step 155 of each theoretical number of photons is then implemented, by application of the Poisson law. The distribution of the number of photons in the different sub-cells is thus randomly modified according to the Poisson law which has as parameter the theoretical number of photons N of each sub- cell.

[0094] A step 156 of constructing the theoretical histogram is then implemented. The construction of the theoretical histogram is carried out from the plurality of theoretical numbers of photons after correction by the Poisson law. In a similar manner to the histogram of photon numbers, the theoretical histogram represents, for the chemical element, the distribution of the values ​​of the corrected theoretical numbers of photons determined for the relevant sub-cells.

[0095] Substeps 151 to 156 are implemented at each iteration of the iterative search mechanism.

[0096] A step 160 of determining the microstructural properties of the part is then implemented. This therefore involves producing an estimate of the microstructural property from the reference property, i.e. the one used to construct the reference histogram. In this case, the microstructural property to be characterized is equal to the reference property.

[0097] An optional step 170 of detecting a precipitate defect in the metal alloy, on the surface of the part, can be implemented. The detection is carried out by comparing the value of the microstructural property obtained with a nominal value. The nominal value can be a theoretical value or an empirical value. Preferably, a difference is calculated between the value of the microstructural property and the nominal value. When the difference is, in absolute value, greater than a predefined threshold, the value of the microstructural property is abnormal and there is a segregation defect.

[0098] Furthermore, the nature of the microstructural property makes it possible to define the nature of the detected segregation defect.

[0099] Other approaches than calculating the deviation between the two values ​​can be used to detect the precipitate defect, such as analyzing a distribution of deviations between the estimated and nominal values.

[0100] In one embodiment, the method is used to characterize the microstructural properties of two or more chemical elements of the alloy. In this case, a plurality of photon numbers is determined, in step 110, for each of the chemical elements in question. Therefore, a histogram is constructed for the set of spectra, in step 130, for each chemical element. In addition, a proportionality factor is determined for each of the chemical elements concerned, in step 140.

[0101] The step 150 of constructing the reference histogram is therefore implemented for each of the chemical elements considered. The sub-steps 151 to 153 are unchanged since they are not dependent on the number or the nature of the chemical elements for the characterization. In sub-step 154, the theoretical number N of photons is calculated for each chemical element in a part of the sub-cells or each sub-cell. The theoretical concentrations and the proportionality factor are determined independently for each chemical element in order to have a theoretical concentration and a proportionality factor per chemical element considered. In sub-step 155, a theoretical histogram is constructed for each of the elements considered. The theoretical histograms are generated, for the different chemical elements, independently of each other, for example with different statistical laws, such as different Poisson laws, one for each chemical element. The iterative search can be carried out jointly or sequentially for all the different chemical elements: the iterative search is then carried out independently for all these elements.The search can, alternatively, be implemented independently for each chemical element or dependently for two or more of these elements. When the search is done dependently, it is preferred that it also be jointly carried out for the different elements concerned. Thus, the microstructural property corresponds to the theoretical microstructural property associated with the reference histograms of the elements. In other words, the microstructural property is not dependent on a particular chemical element but is common to all these elements. The interest is then to minimize the uncertainty of characterization, compared to a characterization based on a single element.

[0102] The implementation of the optional step 170 of detecting a segregation defect can therefore be implemented for each of the chemical elements concerned.

[0103] In one embodiment, the characterization is performed in several regions of the surface of the part. In other words, in step 110, several sets of spectra are obtained, each associated with a different continuous region of a plurality of regions. These regions may be disjoint or partially cover each other. A histogram 40 is constructed, in step 130, for each set of spectra.

[0104] The iterative search mechanism is then implemented independently for each of the plurality of regions to produce a characterization for the chemical element in each of the regions.

[0105] An optional step 180 of constructing a map of the microstructural property can thus be implemented. The map then represents the distribution of the microstructural property characterized in the different regions. The map can be in shades of color, for example, in shades of gray, each color then corresponding to a value of the microstructural property. Each region is therefore associated with a color relating to the value determined for the region in question.

[0106] Figures 6 and 7 show diagrams of the properties of the alloy. characterized metallic. Figure 6 corresponds to the mapping of the radius 7 t' of the hardening precipitates y'. Figure 7 corresponds to the mapping of the surface ratio of the phases Y and y'. In each of the figures, a set of regions 22' is observed for which the microstructural properties of the surface of the part are normal, that is to say, the absolute value of the deviation is lower than the predefined threshold. It is also possible to observe a region 22” of [Fig.6] and two regions 22” of [Fig.7] for which a segregation defect has been detected, the absolute value of the deviation being here higher than the predefined threshold.

[0107] In this embodiment, the proportionality factor may be determined, in step 140, independently for each region of the plurality of regions or be calculated over several or all of the regions. In this case, the average number N of detected photons is calculated independently for each set of spectra and / or over a portion of the sets of spectra associated with these regions.

[0108] In one embodiment, several chemical elements are considered and the analysis is carried out in a plurality of regions. A histogram is then constructed, in step 130, for each chemical element and for each set of spectra. A proportionality factor is calculated, in step 140, for each chemical element concerned and the iterative search mechanism is implemented, in step 150, for each region of the plurality of regions. The alloy is therefore characterized for each of these regions and for each element concerned. The step 170 of detecting segregation defects and the step 180 of constructing a mapping for each of these elements can also, one and / or the other, be implemented.

[0109] An example of maps, obtained by implementing step 180, for several chemical elements is provided in [Fig.9]. A concentration contrast can thus be observed between the healthy zone and the segregated zone for several chemical elements such as titanium (Ti), chromium (Cr) and iron (Fe).

[0110] In one embodiment, the X-ray fluorescence spectrometry device is configured to acquire spectra continuously. That is to say, the device acquires, in a single acquisition, the same spectrum for several consecutive sub-regions of the surface of the part, for example in the form of a unidirectional scan. Consequently, in step 110, the set of spectra is obtained by discretizing one or more continuous spectra acquired by the spectrometry device. The discretization is carried out taking into account the scanning duration and the number of sub-regions which correspond to the surface of the part scanned by the beam at the acquisition. Each sub-region can thus be associated with a spectrum which is a portion of the continuous spectrum, acquired during a duration equal to the time taken by the X-ray beam to travel through said sub-region.This travel time of the sub-region by the beam is equal to the total acquisition time of the continuous spectrum. divided by the number of subregions associated with this continuous spectrum.

[0111] Furthermore, in this embodiment, the sub-step 154 ​​of determining the plurality of theoretical numbers of photons comprises three sub-sub-steps.

[0112] In a sub-sub-step 154-1, the position of each distributed precipitate is discretized. That is to say that the surface of each hardening precipitate is divided into a plurality of sub-surfaces. These sub-surfaces may be of the same dimensions or of different dimensions. These sub-surfaces may also be of the same shape or of different shapes. This discretization is implemented as a function of a set of positions of the source during the same spectrum measurement. These positions are therefore those of the beam emitted by the source on the part during the acquisition time of a spectrum.

[0113] In a sub-sub-step 154-2, a coverage rate is determined for each of the distributed hardening precipitates and for each sub-cell of the plurality of sub-cells. This coverage rate is determined as a function of the discretization of the position of said hardening precipitate. This coverage rate indicates the proportion of the surface of the hardening precipitate included in the sub-cell concerned. The coverage rate can be determined analytically, by calculating the intersections between the surfaces of the sub-cells, preferably rectangular, with the discretization of said hardening precipitate.

[0114] Thus, in a sub-sub-step 154-3, the theoretical number of photons is determined in a manner analogous to the approach of the previous step 154 ​​by taking into account the calculated coverage rate. The coverage rate is taken into account in the calculation of the theoretical number of photons by determining the surface fraction of the chemical element, in the sub-cell concerned, as a function of the coverage rate of each hardening precipitate. The surface fraction is therefore weighted, for each hardening precipitate, by its coverage rate. The surface fraction is therefore equal to the sum of the surfaces of the hardening precipitates, each weighted by the coverage rate relating to said hardening precipitate.

[0115] In some embodiments, the theoretical histogram is constructed by other approaches that do not require calculating the proportionality factor to recalibrate the theoretical model and the experiment. For example, the recalibration can be implemented by directly using a theoretical model that takes into account non-linear effects of the measurement, such as stacking effects, attenuation by dedicated physical models, the probability of fluorescence X-ray emission from photoelectric absorption, etc.

[0116] A second aspect of the invention relates to a computer configured to implement the method according to the invention. The computer comprises, for example, a processor and a memory, for example a volatile memory or a non-volatile memory. volatile. The memory contains instructions that, when implemented by the processor, cause it to implement the steps of the method.

[0117] In one embodiment, the calculator is implemented in the X-ray fluorescence spectrometry device.

Claims

Claims

1. Method (100) for determining at least one microstructural property of a metal alloy on the surface (20) of a part manufactured from said metal alloy, the method (100) comprising: - Obtaining (110) a set of spectra (10) acquired by means of an X-ray fluorescence spectrometry device, each spectrum (10) of the set of spectra (10) being associated with a sub-region (21) of the surface (20) of the part, the sub-regions (21) being contiguous on the surface (20) of the part and forming a continuous region (22), the continuous region (22) being associated with the set of spectra (10); - Determining (120) a plurality of photon numbers for a chemical element of the metal alloy from the set of spectra (10); - Construct (130), for the set of spectra (10), a histogram (40) of photon numbers from the number of photons determined for each spectrum (10) of said set of spectra (10) for said chemical element; - Constructing (150) a reference histogram (40) by means of an iterative search mechanism as a function of a distance of the reference histogram (40) with the histogram (40) of the number of photons, said reference histogram (40) being associated with at least one reference microstructural property, and said reference histogram (40) being constructed from a random distribution of a plurality of theoretical numbers of photons randomly corrected according to a statistical law; - Determine (160), for the continuous region (22), the microstructural property of the metal alloy, the microstructural property being equal to the reference microstructural property.

2. Method (100) according to the preceding claim, wherein the metal alloy comprises a matrix and hardening precipitates, and wherein the reference histogram (40) is a theoretical histogram (40) for which a predefined condition relating to a distance of the theoretical histogram with the histogram (40) of the number of photons is verified, the construction of the theoretical histogram (40) being carried out at each iteration of the iterative search mechanism by: Selection (151), within a range of values, of a theoretical value of the microstructural property; Determination (152) of a theoretical number of hardening precipitates in the metal alloy of the part, on a cell of the same dimensions as the continuous region (22), from the selected theoretical value; Random distribution (153), according to a uniform law, of hardening precipitates on the cell, the number of hardening precipitates distributed being equal to the theoretical number of hardening precipitates; Determination (154), for the chemical element, of the plurality of theoretical numbers of photons, each theoretical number N of photons being associated with a sub-cell of a plurality of sub-cells included in the cell, each sub-cell corresponding to one of the sub-regions (21) of the continuous region (22), each theoretical number of photons being determined by N = aÇCySy 4- Cy'Sy') with: • a a proportionality factor; • Cy the theoretical concentration of the chemical element in the matrix of the metal alloy, in the associated sub-cell; • Sy the surface of the matrix of the metal alloy in the sub-cell; • Cy' the theoretical concentration of the chemical element in the hardening precipitates of the matrix of the metal alloy, in the associated sub-cell; • Sy' the surface of the hardening precipitates in the sub-cell; Random correction (155), according to the statistical law, of the theoretical numbers of photons from the plurality of theoretical numbers; Construction (156) of the theoretical histogram from the plurality of corrected theoretical numbers of photons.

3. The method (100) of claim 2, wherein the proportionality factor is equal to a ratio between an average number of photons and a theoretical concentration of the chemical element at the surface (20) of the part, the average number of photons being determined from an average of the plurality of numbers of photons.

4. Method (100) according to one of claims 2 and 3, in which each of the randomly distributed hardening precipitates has dimensions randomly determined according to a normal distribution.

5. Method (100) according to one of claims 2 to 4, wherein the set of spectra (10) is obtained by discretizing a continuous spectrum (10) acquired by the X-ray fluorescence spectrometry device, the X-ray fluorescence spectrometry device comprising a source, the method (100) comprising, before determining (154-3) the plurality of theoretical numbers of photons: - Discretizing (154-1) the position of each distributed hardening precipitate as a function of a set of positions of the source during a same spectrum measurement (10) and the number of sub-cells; - Determining (154-2), for each distributed hardening precipitate, a recovery rate for each sub-cell of the plurality of sub-cells as a function of the discretization of the position of said hardening precipitate;and wherein the surface area of hardening precipitate, in the associated sub-cell, is calculated as a function of the coverage rate of each hardening precipitate.;

6. Method (100) according to one of the preceding claims, in which each number of photons of the plurality of number of photons is determined from an integral, in one of the spectra (10) of the set of spectra (10), of the area under a peak associated with said chemical element.

7. Method (100) according to one of the preceding claims, wherein the iterative search mechanism is an inversion or optimization algorithm or a brute force algorithm.

8. Method (100) according to one of the preceding claims, in which the metal alloy of the surface (20) of the part comprises at least a first chemical element and a second chemical element, and in wherein the reference histograms (40) for the first and second chemical elements, respectively, are jointly determined by means of the iterative search mechanism based on a combination of the distances respectively calculated with the histogram (40) of the number of photons for the first and second elements.

9. Method (100) according to one of the preceding claims, in which the distance is a quadratic deviation, a Mahalanobis distance, a maximum likelihood or a normal L1, between the histogram (40) of the number of photons and the reference histogram (40).

10. A method (100) according to one of the preceding claims, wherein the X-ray fluorescence spectrometry device is an energy dispersive fluorescence device or a wavelength fluorescence device.

11. Method (100) according to one of the preceding claims comprising: - Detecting (170) a microstructural anomaly of the surface (20) of the part when a value of the at least one determined microstructural property of the metal alloy does not conform to a nominal value.

12. Method (100) according to one of the preceding claims comprising: - Constructing (180) a mapping of the at least one microstructural property of the part.

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