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 metallic 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 to evaluate the properties of a metallic alloy material.

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

[0003] In aeronautics, as in other industrial sectors, a large number of parts are manufactured from metallic alloys, for example, nickel-based superalloys typically used for the low-pressure turbine disks of the LEAP (Leading Edge Aviation Propulsion) turbofan engine. These alloys are composed, in particular, of a matrix of a material having a certain concentration of each constituent chemical element. This matrix comprises single crystals of the gamma phase, also called "grains." The material also includes hardening precipitates, characterized by chemical element concentrations different from those of the matrix. These precipitates can take various shapes, such as elongated or spherical, and are small compared to the matrix.

[0004] Verifying the integrity and conformity of the microstructure of these alloys is essential to prevent premature failure of the part during its service life. In particular, inspecting these parts allows for the detection and characterization of abnormal chemical segregations in the metallic alloys, such as a local overconcentration of a hardening chemical element, known as "freckle," or a local underconcentration of a hardening chemical element, known as "white spot" (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 manufacturing process, for example, on a billet before forging, during pre-machining before heat treatment, or at the end of the production line following pre-machining 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 for a sufficient degree of precision to accurately determine the properties of the material. On the contrary, the inspection techniques classically used in the laboratory, based on the use of the mi Electron microscopy (M.-A. Charpagne, Microstructure Evolutions During the Forging of René 65 Alloy, PhD thesis, Université Paris Sciences et Lettres, 2016), particularly electron backscattered diffraction (EBSD) in a scanning electron microscope (SEM), allows for high-quality inspection. This technique produces a high-resolution map of crystal orientations on the surface of the inspected sample.

[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, in order to perform 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 (in English, "Transmission Electron Microscopy" or TEM), which requires the removal of a thin layer of the sample, typically by ion abrasion.

[0008] These techniques allow for the acquisition 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, which must be taken from the part and inspected in a vacuum environment. It is therefore difficult to consider 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. However, this technique is limited by the size of the X-ray beam incident on the sample, which does not allow access to smaller quantities, such as the size of grains and hardening precipitates in a metallic alloy.

[0010] There is therefore a need for a non-destructive testing method applicable in an industrial production and / or maintenance context which allows the detection and characterization of chemical segregation phenomena in metallic alloys and superalloys. Summary of the invention

[0011] The invention offers a solution to the problems mentioned above, by enabling 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 metallic 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 metallic alloy on the surface of a part manufactured from said metallic alloy, the method comprising: • Obtain 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 metallic 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; • Construct a reference histogram using an iterative search mechanism based on a distance of the reference histogram from the photon number histogram, 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 photon numbers randomly corrected according to a statistical law; • Determine, for the continuous region, the microstructural property of the metallic alloy, the microstructural property being equal to the reference microstructural property.

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

[0014] The term "X-ray fluorescence spectrometry device" means a measuring instrument capable of emitting an X-ray beam towards a sample and capturing the re-emitted rays after interaction with the metallic alloy. These captured rays These 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 the energy of photons, absorbed by the photoelectric effect and then converted into an electronic signal, using a sensor made of semiconductor material, such as Silicon (for example with a Silicon Drift Detector architecture) or germanium.

[0015] The term "iterative search mechanism" means a tool that allows for the iterative search for an optimal solution to a given problem, in this case, the search for an optimal reference histogram with respect to a condition set on the distance of the reference histogram with 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 metallic 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, based on a statistical study of the acquired spectra, makes it possible to achieve a characterization scale for the material much lower than the spatial resolution classically obtained by this measurement technique, which is determined by the size of the X-ray beam on the sample. For example, it is possible to characterize hardening precipitates with a radius of 2 pm using an X-ray beam of 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, in relation 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 related to the measuring device.

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

[0020] In addition to the characteristics just mentioned, the method according to the first aspect of the invention may have one or more complementary characteristics from 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 regarding the distance between the theoretical histogram and the photon number histogram is met, 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 metallic 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 photon numbers, each theoretical photon number N being associated with a subcell of a plurality of subcells contained within the cell, each subcell corresponding to one of the subregions of the continuous region, each theoretical photon number 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 metallic alloy, in the associated sub-cell; • Sy the surface of the metal alloy matrix in the subcell; • Cy' the theoretical concentration of the chemical element in the hardening precipitates of the metal alloy matrix, in the associated sub-cell; • Sy' the surface of the hardening precipitates in the subcell; • Random correction, according to the statistical law, of the theoretical numbers of photons of the plurality of theoretical numbers; • Construction of the theoretical histogram from the plurality of corrected theoretical photon numbers.

[0022] The construction of the reference histogram is thus easy and quick to implement. The random distribution according to the uniform law serves 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 distribution, serves to account for the variability in the measurement of 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 The theoretical values ​​of calculated photons are representative of the experiment performed. This proportionality factor ensures the alignment 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 related 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 on the surface of the part, the average number of photons being determined from an average of the plurality of photon numbers.

[0025] The theoretical number of photons is thus weighted to recalibrate the simulation of the measurement with the assumption underlying the proposed approach, which is that there is a proportionality relationship between the counting of photons 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 law.

[0027] This embodiment makes it possible to obtain a distribution of hardening precipitates and their size that 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 theoretical plurality of photons: • Discretize the position of each hardening precipitate distributed as a function of a set of source positions during the same spectrum measurement and the number of subcells; • Determine, for each hardening precipitate distributed, a coverage 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 hardening precipitate surface area, 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 in the plurality of number of photons 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 whose the energy (in keV) is associated with a specific chemical element and whose peak height is representative of the concentration of that material in the measurement area.

[0032] The estimation of the number of photons is thus determined in a fast, easy to implement and reliable manner.

[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 from the photon number histogram and reliably estimate the alloy property. Alternatively, it is possible to systematically search for the reference histogram that minimizes the distance from the photon number histogram and reliably estimate the alloy property.

[0035] In one embodiment, the metallic 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 by means of the iterative search mechanism as a function of a combination of the distances respectively calculated with the photon number histogram for the first and second elements.

[0036] It is thus possible to determine the microstructural property of the alloy by taking into account simultaneously several or all of the chemical elements that make up this alloy, thereby 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 a normal L1, between the photon number histogram and the reference histogram.

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

[0039] In one embodiment, the X-ray fluorescence spectrometry device is an energy-dispersive fluorescence device or a wavelength-dispersive 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 surface of the part when a value of at least one determined microstructural property of the metal alloy is not in conformity with a nominal value.

[0042] The method thus makes it possible to detect a microstructure 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" refers to a nominal value. nominal value » 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 allows access to 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 metallic alloy on the surface of a part made from said metallic 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, lead 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, lead 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 by reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0049] The figures are presented for illustrative purposes only and are in no way limiting of the invention. • Fig. 1 is a synoptic 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 piece in Fig. 2. • Fig. 5 is a representation of a histogram of detected photon numbers. • Fig. 6 is a map of a microstructural property of the part in Fig. 2. • The [Fig.7] is a map of another microstructural property of the part of the [Fig.2]. • Figure 8 represents the evolution of the distance between an experimental histogram and a theoretical histogram, as a function of the estimation of the properties of the metallic alloy, according to an embodiment. • The [Fig.9] is a set of maps obtained according to an embodiment of the process according to the invention. DETAILED DESCRIPTION

[0050] Unless otherwise specified, the same element appearing on different figures has a unique 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 metallic alloy or superalloy in 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 with different chemical compositions: the alloy matrix and the hardening precipitates. The hardening precipitates are composed of the same chemical elements as the matrix, but in 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 anomalous segregations, i.e., hardening precipitates, of a metallic alloy for which the two-phase approximation is possible. However, this method is entirely applicable to any metallic 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 metallic alloy on the surface of a part manufactured from said metallic alloy. The sequence of steps of method 100 is illustrated in [Fig. 1].

[0057] For this metallic alloy, it is particularly possible to characterize a characteristic dimension of hardening precipitates and a ratio of hardening precipitate surface areas in the alloy. In the case of y / y alloys, this is a hardening precipitate radius y' and a ratio of the hardening precipitate surface area y' to the surface area of ​​the matrix V, respectively. Matrix Y includes the hardening precipitates y' called secondary and tertiary inserted into matrix T, the latter being of characteristic nanometric dimension.

[0058] Other microstructural properties can 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, a shape ratio, etc.

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

[0060] A step to obtain 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 X-ray spectroscopy (EDS or EDXS) device which allows, by means of a spectrometric detector, the construction of a histogram representing the distribution of 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 in 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 in the set of spectra is therefore associated with a sub-region of the surface of the part. Each sub-region is preferably a square with sides of length between 0.1 mm and 5 mm, for example, 1 mm. Each sub-region can also be of a shape and dimensions corresponding to the size of the incident X-ray beam.

[0062] As illustrated in [Fig. 3], the subregions 21 are preferentially contiguous, meaning that each subregion 21 shares at least one boundary with another subregion 21. The subregions 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 number of subregions selected, respectively. The continuous region is therefore associated with the set of spectra.

[0063] An example of a spectrum 10, measured in air, is shown in [Fig. 2]. The x-axis represents the energy of the detected photons and the y-axis represents the number of counts detected on a 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, particularly for the following elements: titanium, chromium, iron, cobalt, nickel, tungsten, niobium and molybdenum.

[0064] A step 120 is then implemented to determine a plurality of photon counts from the set of spectra. This photon count is performed for the chemical element. In other words, for each of the spectra in the set of spectra, a number of photons captured by the device is calculated for the chemical element.

[0065] Each photon count is calculated based on one or more metrics characterizing the peak in the relevant spectrum corresponding to the chemical element. For example, the photon count corresponds to Faire under the peak, that is, 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 subregion is then implemented. The construction is performed for the entire set of spectra and for the chemical element. In other words, the histogram represents, for the chemical element, the distribution of the photon number values ​​calculated in the entire set of spectra.

[0067] A photon number map, representing the distribution of the number of photons detected per sub-region for the titanium element of the alloy considered, is shown in [Fig. 4]. It can be observed that the distribution of the values ​​of the number 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 shown in [Fig. 5].

[0068] In the embodiment presented, method 100 includes a step 140 for determining a proportionality factor. This determination is carried out using the determined photon counts. This proportionality factor indicates the proportion of the average number of photons detected, per chemical element, as a function of the theoretical concentration of that 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 photon counts of the plurality of photon counts determined in the preceding step 120, or of a part of this plurality of counts, 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 photon counts.The average can be a weighted average, for example to account for variability in the X-ray beam or accessibility constraints at the time of acquisition. This 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 using an iterative search mechanism, the implementation of which allows the comparison of the photon number histogram with the recursively estimated reference histogram.

[0071] The iterative search mechanism is a recursive mechanism that allows, through successive iterations, the search for a theoretical histogram until a predefined condition relating to a calculated distance from the photon number histogram is satisfied. When the predefined condition is satisfied, the theoretical histogram is called the "reference histogram".

[0072] The distance is, for example, a squared deviation, a Mahalanobis distance, a maximum likelihood or a normal L1, between the photon number histogram and the reference histogram.

[0073] The iterative search mechanism is configured to search among a predefined range of values ​​for 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 surface area ratio of hardening precipitates. An example of the variation of the distance, here the root mean square 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 surface area ratio of phases y' and V in the alloy.

[0075] The range of values ​​may be continuous or discontinuous and is, for example, defined based on known theoretical values ​​for the alloy in question. The range of values ​​is, for example, delimited by a maximum and a minimum value, each corresponding to a percentage of a theoretical or empirical nominal value, for example, determined by an EDS-EBSD technique, for 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 that minimizes 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 between the theoretical histogram and the photon number histogram. Alternatively, the iterative search mechanism is a Bayesian method. The iterative search mechanism thus serves to iteratively search for a theoretical histogram that satisfies the predefined condition. This predefined condition, for an optimization or inversion algorithm, is the minimization of the distance, that is, 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 their domain knowledge, the desired precision of the characterization, and / or the specific characteristics of the experimental conditions. Alternatively, or in conjunction with this, the condition may also relate to a maximum number of iterations, which is defined by the operator based on the desired computational cost of the search and their domain knowledge.

[0077] Alternatively, the search algorithm is a brute-force method that evaluates the distance for a set of theoretical histograms; the reference histogram being the theoretical histogram for which the distance is the smallest among all the calculated distances. 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 performed. The predefined condition is that the distance of the reference histogram is the smallest among all those calculated by the brute-force algorithm. In the given 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, is constructed from an estimate of the microstructural property. In the example given, this is the characteristic dimension of hardening precipitates and the surface area ratio 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, referred to as the "reference" property, which is the property of the metallic alloy that allows the reference histogram to be formed.

[0079] In particular, the reference microstructural property may include a reference characteristic dimension and a reference surface area ratio. For example, it may be a reference precipitate diameter y' and a phase surface area ratio y' and Y.

[0080] Each theoretical histogram, like the reference histogram, is preferred The system is constructed by generating a random distribution of a plurality of theoretical photon numbers. These photon numbers are weighted by a predetermined proportionality factor. These photon numbers are also corrected by applying a statistical distribution, for example, a Poisson distribution, to account for measurement uncertainties related to the sensor. In this embodiment, the statistical distribution is a Poisson distribution whose parameter is the theoretical number of photons to be corrected.

[0081] Other types of laws could be used, such as a normal law, particularly if the photonic component, i.e., Poisson noise, is small compared to the influence of the variability in element concentration between pixels on 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 implementing 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 includes a substep 151 for selecting, for the microstructural property, a theoretical value from among the range of values. Where appropriate, a theoretical value is selected from the range of values ​​relevant to each of the microstructural properties. For example, a value for a theoretical characteristic dimension of hardening precipitates is defined and selected from the first range of values, and a value for a theoretical surface area ratio of hardening precipitates is selected from the second range of values.

[0085] A substep 152 for determining a theoretical number of precipitates in the metal alloy is then implemented. This theoretical number of precipitates is determined by a numerical calculation tool which, based on the values ​​of the selected microstructural property, calculates 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 area ratio of hardening precipitates, and the value of the surface area of ​​hardening precipitates, for example, by applying a proportionality rule. The numerical 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 random distribution step 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, according to the alloy and independently of the element(s) considered. Other laws may alternatively be used instead of the uniform law.

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

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

[0090] A step 154 ​​for determining the plurality of theoretical photon numbers is then implemented for the chemical element, based on the distribution of hardening precipitates. To do this, the cell, corresponding in dimensions to the region, is divided into a plurality of subcells. Each subcell corresponds to a subregion of the region; that is, the subcell is the same size as the subregion to which it is associated. Thus, each theoretical photon number is associated with one of the subcells, which is contained within 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 subcell, of the chemical element in the matrix of the metallic alloy; • Sy is the surface area of ​​the matrix in the subcell; • Cy' is the theoretical concentration, in the subcell, of the chemical element in the hardening precipitates of the metal alloy matrix; • Sy' is the surface area of ​​the hardening precipitates in the subcell.

[0092] This is therefore an estimate of a count of detected photons for the subcell that 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 applying the Poisson distribution. The distribution of the number of photons in the different sub-cells is thus modified randomly according to the Poisson distribution, which has as its parameter the theoretical number of photons N of each sub- cell.

[0094] A construction step 156 of the theoretical histogram is then implemented. The theoretical histogram is constructed from the plurality of theoretical photon numbers after correction by the Poisson distribution. Similar to the photon number histogram, the theoretical histogram represents, for the chemical element, the distribution of the values ​​of the corrected theoretical photon numbers determined for the relevant subcells.

[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 involves producing an estimate of the microstructural property based on the reference property, that is, 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 for detecting a precipitate defect in the metal alloy, on the surface of the part, can be implemented. Detection is performed by comparing the value of the microstructural property obtained with a nominal value. The nominal value can be a theoretical or empirical value. Preferably, a deviation is calculated between the value of the microstructural property and the nominal value. When the deviation 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 besides calculating the difference between the two values ​​can be used to detect the precipitate defect, such as analyzing a distribution of differences 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 in the alloy. In this case, a plurality of photon counts is determined, in step 110, for each of the chemical elements in question. Consequently, a histogram is constructed for the set of spectra, in step 130, for each chemical element. Furthermore, a proportionality factor is determined for each of the relevant chemical elements, in step 140.

[0101] The construction step 150 of the reference histogram is therefore implemented for each of the chemical elements considered. Substeps 151 to 153 are unchanged since they are not dependent on the number or nature of the chemical elements for characterization. In substep 154, the theoretical number N of The number of photons is calculated for each chemical element in a subset of subcells or for each subcell. Theoretical concentrations and proportionality factors are determined independently for each chemical element to obtain a theoretical concentration and proportionality factor for each element considered. In substep 155, a theoretical histogram is constructed for each of the elements considered. Theoretical histograms are generated independently for the different chemical elements, for example, using different statistical distributions, such as different Poisson distributions, one for each chemical element. The iterative search can be performed jointly or sequentially for all the different chemical elements; in the latter case, the iterative search is performed independently for all these elements.The search can alternatively be implemented independently for each chemical element or in a dependent manner for two or more of these elements. When the search is done in a dependent manner, it is preferable that it also be carried out jointly 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 advantage 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 part's surface. In other words, in step 110, several sets of spectra are obtained, each associated with a different continuous region from a plurality of regions. These regions may be disjoint or partially overlapping. 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 regions of the plurality of regions in order to produce a characterization for the chemical element in each of the regions.

[0105] An optional construction step 180 of a microstructural property map can thus be implemented. The map then represents the distribution of the characterized microstructural property 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 pertaining to the value determined for the region in question.

[0106] Figures 6 and 7 schematically represent maps of the alloy properties Characterized metallic structure. Figure 6 corresponds to the radius map 7t' of the hardening precipitates y'. Figure 7 corresponds to the surface area ratio map of phases Y and y'. In each figure, a set of regions 22' are observed for which the microstructural properties of the part surface are normal, i.e., whose absolute value of the deviation is less than the predefined threshold. A region 22" in [Fig. 6] and two regions 22" in [Fig. 7] can also be observed for which a segregation defect has been detected, the absolute value of the deviation being greater than the predefined threshold.

[0107] In this embodiment, the proportionality factor can 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 subset of the sets of spectra associated with these regions.

[0108] In one embodiment, several chemical elements are considered and the analysis is performed 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 relevant chemical element, and the iterative search mechanism is implemented, in step 150, for each region of the plurality of regions. The alloy is thus characterized for each of these regions and for each relevant element. The step 170 for detecting segregation defects and the step 180 for constructing a map for each of these elements can also, either or both, be implemented.

[0109] An example of maps, obtained by implementing step 180, for several chemical elements is shown in [Fig.9]. A contrast in concentration 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, the device acquires, in a single acquisition, the same spectrum for several consecutive subregions of the part's surface, 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 performed taking into account the scan time and the number of subregions corresponding to the part's surface scanned by the beam during acquisition. Thus, each subregion can be associated with a spectrum that is a portion of the continuous spectrum, acquired over a duration equal to the time taken by the X-ray beam to traverse said subregion.The time it takes for the beam to travel through the sub-region is equal to the total acquisition time of the continuous spectrum. divided by the number of sub-regions associated with this continuous spectrum.

[0111] Moreover, in this embodiment, substep 154 ​​of determining the plurality of theoretical photon numbers comprises three sub-substeps.

[0112] In a sub-substep 154-1, the position of each distributed precipitate is discretized. That is, the surface of each hardening precipitate is divided into a plurality of sub-surfaces. These sub-surfaces may have the same dimensions or different dimensions. They may also have the same shape or different shapes. This discretization is implemented based on a set of source positions during a single spectral measurement. These positions are therefore those of the beam emitted by the source onto the part during the spectral acquisition time.

[0113] In a sub-substep 154-2, an overlap ratio is determined for each of the distributed hardening precipitates and for each sub-cell of the plurality of sub-cells. This overlap ratio is determined based on the discretization of the position of said hardening precipitate. This overlap ratio indicates the proportion of the hardening precipitate surface area contained within the relevant sub-cell. The overlap ratio 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-substep 154-3, the theoretical number of photons is determined in a manner analogous to the approach in the preceding step 154, 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 relevant sub-cell 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 thus equal to the sum of the surfaces of the hardening precipitates, each weighted by the coverage rate applicable 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 calibrate the theoretical model and the experiment. For example, calibration can be implemented by directly using a theoretical model that takes into account non-linear measurement effects, 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 memory, for example volatile memory or non-volatile memory. volatile. Memory contains instructions which, when implemented by the processor, lead the processor to carry out the steps of the method.

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

Claims

Demands

1. A method (100) for determining at least one microstructural property of a metallic alloy on the surface (20) of a part manufactured from said metallic alloy, the method (100) comprising: - Obtain (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 subregion (21) of the surface (20) of the part, the subregions (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); - Determine (120) a plurality of photon numbers for a chemical element of the metallic 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; - Construct (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 corrected randomly according to a statistical law; - Determine (160), for the continuous region (22), the microstructural property of the metallic 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 The correlation between the theoretical histogram and the photon number histogram (40) is verified, with 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 metallic 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 photon numbers, each theoretical photon number N being associated with a subcell of a plurality of subcells contained in the cell, each subcell corresponding to one of the subregions (21) of the continuous region (22), each theoretical photon number being determined by N = aCySy 4- Cy'Sy') with: • a a proportionality factor; • Cy the theoretical concentration of the chemical element in the matrix of the metallic alloy, in the associated sub-cell; • Sy the surface of the metal alloy matrix in the subcell; • Cy' the theoretical concentration of the chemical element in the hardening precipitates of the metal alloy matrix, in the associated sub-cell; • Sy' the surface of the hardening precipitates in the subcell; Random correction (155), according to the statistical law, of the theoretical numbers of photons of the plurality of theoretical numbers; Construction (156) of the theoretical histogram from the plurality of corrected theoretical numbers of photons.

3. Method (100) according to 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 on the surface (20) of the part, the average number of photons being determined from an average of the plurality of photon numbers.

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

5. Method (100) according to any 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 photon numbers: - Discretizing (154-1) the position of each distributed hardening precipitate as a function of a set of positions of the source during the same measurement of spectrum (10) and the number of subcells; - Determining (154-2), for each distributed hardening precipitate, an overlap rate for each subcell of the plurality of subcells as a function of the discretization of the position of said hardening precipitate;and in which the surface area of ​​the 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 any one of the preceding claims, wherein each number of photons in 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 any 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 any one of the preceding claims, wherein the metallic alloy of the surface (20) of the part comprises at least a first chemical element and a second chemical element, and in in which the reference histograms (40) for the first and second chemical elements, respectively, are jointly determined by means of the iterative search mechanism as a function of 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 any one of the preceding claims, wherein the distance is a quadratic deviation, a Mahalanobis distance, a maximum likelihood or a normal L1, between the photon number histogram (40) and the reference histogram (40).

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

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

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

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