X-ray fluorescence spectrometry for characterizing the microstructure of metal alloys and detecting chemical segregation

Abstract

One aspect of the invention relates to a method for determining at least one microstructural property of a metal alloy on a surface (20) of a part made of said metal alloy.

Description

Technical Field

[0001] The technical field of this invention is the field of non-destructive testing for evaluating the properties of metallic alloy materials.

[0002] This invention relates to a method for determining at least one microstructural property of a material on the surface of a part. Background Technology

[0003] In the aerospace industry, as in other industrial sectors, many parts are made of metallic alloys, such as the nickel-based superalloys commonly used in the low-pressure turbine disks of LEAP (Leading-Edge Aero-Propulsion) turbofan engines. These alloys are, in particular, composed of a material matrix containing a specific concentration of each chemical element that constitutes it. This matrix comprises gamma-phase single crystals, also known as "grains." The material also includes hardened precipitates, characterized by a difference in the concentration of chemical elements compared to the matrix. These precipitates can take various shapes, such as elongated or spherical, and are relatively small in size compared to the matrix.

[0004] Verifying the integrity and conformity of the microstructure of these alloys is crucial for preventing premature component failure during their service life. In particular, inspecting these components can detect and characterize anomalous chemical segregation in the metallic alloys, such as locally high concentrations of hardening chemicals known as "spots" or locally low concentrations of hardening chemicals known as "white spots." This verification can be performed during part manufacturing, such as on billets before forging, during pre-machining before heat treatment, at the end of the production line after pre-machining following heat treatment, or even during maintenance operations.

[0005] The most common technique for detecting these anomalies is macroscopic image analysis, but it cannot provide sufficient precision to accurately determine the properties of the material. In contrast, commonly used laboratory techniques based on electron microscopy (M.-A. Charpagne, Evolutions de microstructure au cours du forgeage de l'alliage René 65, Thesis Manuscript, University Paris Sciences et Lettres, 2016) – particularly electron backscatter diffraction (EBSD) in scanning electron microscopy (SEM) – can achieve high-quality detection. This technique generates high-resolution crystal orientation maps on the surface of the sample being examined.

[0006] EBSD is often combined with energy dispersive spectroscopy (EDS). The latter involves measuring the energy spectrum of X-rays emitted after a sample interacts with incident electrons, and performing chemical analysis based on an understanding of the characteristic electronic transitions of each chemical element.

[0007] Transmission electron microscopy (TEM) is also commonly used, which requires the removal of a thin layer from the sample, usually by ion etching.

[0008] These techniques are used to create high spatial resolution images (typically tens of nanometers for EBSD), but their drawback is that they can only detect small samples that must be removed from the part under inspection and placed in a vacuum environment. Therefore, it is difficult to consider using such techniques in production and maintenance.

[0009] X-ray fluorescence is also used to analyze the chemical composition of samples (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 create spectra of sample surfaces with spatial resolution down to tens of micrometers. However, this technique is limited by the size of the X-ray beam incident on the sample, preventing the acquisition of lower-dimensional quantities, such as the size of grains and hardened precipitates in metallic alloys.

[0010] Therefore, there is a need for a non-destructive testing method suitable for industrial production and / or maintenance environments, capable of detecting and characterizing chemical segregation phenomena in metallic alloys and high-temperature alloys. Summary of the Invention

[0011] This invention solves the problems discussed above by analyzing the X-ray fluorescence spectrum measured by scanning an X-ray beam through the sample surface to obtain the microstructural characteristics of the metal alloy constituting the sample, as well as detecting and characterizing chemical segregation on the surface.

[0012] A first aspect of the present invention relates to a method for determining at least one microstructural property of a metal alloy on the surface of a part made of said metal alloy, said method comprising:

[0013] A set of spectra acquired by an X-ray fluorescence spectrometer is obtained, wherein each spectrum in the set of spectra is associated with a sub-region on the surface of the part, the sub-region being continuous on the surface of the part and forming a continuous region, the continuous region being associated with the set of spectra;

[0014] The number of multiple photons of a chemical element in the metal alloy is determined from the set of spectra.

[0015] For the set of spectra, a photon number histogram is constructed based on the number of photons measured for each chemical element in the set of spectra;

[0016] A reference histogram is constructed based on the distance between the reference histogram and the photon number histogram through an iterative search mechanism. The reference histogram is associated with at least one reference microstructure property and is constructed from a random distribution of multiple randomly corrected theoretical photon numbers according to statistical laws.

[0017] The microstructure properties of the metal alloy are determined for the continuous region, and the microstructure properties are equal to the reference microstructure properties.

[0018] "Microstructure properties" refer to properties that characterize the microstructure of a metallic alloy at the grain scale. For example, these properties include the characteristic size and phase surface area ratio of hardened precipitates. The characteristic size is, for example, the diameter, width, length, and / or combinations thereof of the hardened precipitates in the metallic alloy. The surface area ratio represents the ratio of the surface area of ​​the γ' phase (i.e., the precipitate) to the surface area of ​​the γ phase (i.e., the alloy matrix). Other properties may also be relevant depending on the alloy material and the shape and / or properties of the hardened precipitates.

[0019] An "X-ray fluorescence spectroscopy device" is a device capable of emitting an X-ray beam at a sample and capturing the re-emitted X-rays after interaction with a metallic alloy. These captured X-rays can form a "spectrum" indicating the proportion of photons detected as a function of frequency. The device can be based on the direct conversion of photon energy, absorbed through the photoelectric effect, and then converted into an electronic signal, using a sensor made of semiconductor materials such as silicon (e.g., employing a silicon drift detector (SDD) structure) or germanium.

[0020] "Iterative search mechanism" refers to a tool that can iteratively search for the optimal solution to a given problem. In this case, it is searching for the optimal reference histogram under the condition of imposing a condition on the distance between the reference histogram and the photon number histogram.

[0021] With the aid of this invention, one or more microstructural properties of the metallic alloys used to manufacture parts can be determined. These properties are evaluated by analyzing spectra acquired using X-ray fluorescence spectroscopy on the surface of the part. Because this analysis is based on a statistical study of the acquired spectra, a material characterization scale with a spatial resolution (given by the size of the X-ray beam on the sample) far lower than that conventionally achieved by this measurement technique can be achieved. For example, a 20 µm X-ray beam on the surface of the part can be used to characterize hardened precipitates with a radius of 2 µm.

[0022] Advantageously, characterization of alloys can detect anomalies in microstructural properties estimated relative to the alloy's nominal theoretical properties, thereby detecting material defects such as anomalous segregation of one or more chemical elements ("spots" and "white spots").

[0023] Furthermore, the application of statistical principles allows for the consideration of experimental conditions and measurement uncertainties related to the equipment.

[0024] Finally, the provided method also has the advantages of simplicity and rapid implementation, as it involves only post-processing of the acquired spectra, thus requiring no modification to the spectral acquisition method. Therefore, this method can be used independently of the measurement equipment and experimental conditions. Consequently, this method is suitable for production and / or maintenance environments.

[0025] In addition to the features just discussed, the method according to the first aspect of the invention may have one or more additional features, which may be considered individually or in any technically possible combination.

[0026] In one embodiment, the metal alloy comprises a matrix and hardened precipitates, and the reference histogram is a theoretical histogram that satisfies a predetermined condition regarding the distance between the theoretical histogram and the photon number histogram, the theoretical histogram being constructed in each iteration of the iterative search mechanism in the following manner:

[0027] - Select the theoretical value of the microstructure property from a range of values;

[0028] -Based on the selected theoretical value, determine the theoretical amount of hardened precipitates in the metal alloy of the part on a cell with the same size as the continuous region;

[0029] -Based on a uniform distribution, hardened precipitates are randomly distributed on the unit, and the number of distributed hardened precipitates is equal to the theoretical number of hardened precipitates;

[0030] - A plurality of theoretical photon numbers are determined for the chemical element, each theoretical photon number N being associated with one of a plurality of sub-units contained in the unit, each sub-unit corresponding to a sub-region of the contiguous region, and each theoretical photon number being determined in the following manner: ,in:

[0031] -a is the scaling factor;

[0032] -Cγ is the theoretical concentration of the chemical element in the relevant subunit in the metal alloy matrix;

[0033] -Sγ is the surface area of ​​the metal alloy matrix in the subunit;

[0034] -Cγ' is the theoretical concentration of the chemical element in the relevant subunit in the hardened precipitate of the metal alloy matrix;

[0035] -Sγ' is the surface area of ​​the hardened precipitate in the subunit;

[0036] - Based on the statistical distribution, the theoretical photon number from the plurality of theoretical photon numbers is randomly corrected;

[0037] - Construct the theoretical histogram based on the corrected theoretical photon numbers.

[0038] Therefore, constructing a reference histogram is rapid and easy to implement. A random distribution based on the uniformity law is used to simulate the spatial distribution of hardened precipitates in a fast and representative manner of the material's statistical properties. A random distribution based on statistical laws (e.g., Poisson's law) is used to account for the variability in photon measurements emitted by hardened precipitates with a given spatial distribution, thereby improving the reliability of the characterization. The application of a scaling factor ensures that the calculated theoretical photon number is representative of the experiment performed. This scaling factor ensures a reconciliation between the theoretical model and the measurements.

[0039] Furthermore, applying scaling factors and statistical rules to determine the reference histogram allows for better consideration of device-related experimental conditions and measurement uncertainties, thereby improving the robustness and reliability of the obtained characterization.

[0040] In one embodiment, the scaling factor is equal to the ratio of the average number of photons to the theoretical concentration of the chemical element on the surface of the part, wherein the average number of photons is determined based on the average of the plurality of photon numbers.

[0041] Therefore, the theoretical photon count is weighted to reset the measurement simulation under the basic assumptions of the provided scheme, which is that there is a proportional relationship between the photon count and the concentration of chemical elements.

[0042] In one embodiment, each randomly distributed hardened precipitate has a size randomly determined according to the normal law.

[0043] This embodiment achieves a distribution and size of hardened precipitates that are more representative of physical reality.

[0044] In one embodiment, the set of spectra is obtained by discretizing a continuous spectrum acquired by the X-ray fluorescence spectrometry device, which includes a source, and the method includes, prior to determining the plurality of theoretical photon numbers:

[0045] - The location of the hardened precipitates in each distribution is discretized based on a set of source locations and the number of sub-units during the measurement of the same spectrum;

[0046] For each distribution of hardened precipitates, the coverage of each sub-unit of the plurality of units is determined based on the discretization of the hardened precipitate locations;

[0047] Furthermore, in the relevant sub-unit, the surface area of ​​the hardened precipitate is calculated based on the coverage of each hardened precipitate.

[0048] Therefore, this method is compatible with spectra acquired continuously by the acquisition device.

[0049] In one embodiment, each of the plurality of photon numbers is determined based on the area under the peak associated with the chemical element in one of the spectra in the set of spectra.

[0050] "A peak associated with a chemical element" refers to a peak in the spectrum whose energy (keV) is associated with a specific chemical element, and the height of the peak represents the concentration of the material in the measurement region.

[0051] Therefore, the photon number estimate is determined in a fast, easy-to-implement, and reliable manner.

[0052] In one embodiment, the iterative search mechanism is an inversion or optimization algorithm or a brute-force algorithm.

[0053] Therefore, an optimal reference histogram can be searched according to an optimization criterion to minimize the distance from the photon number histogram and reliably estimate the alloy's properties. Alternatively, a systematic search can be conducted to find the reference histogram that minimizes the distance from the photon number histogram and reliably estimate the alloy's properties.

[0054] In one embodiment, the metal alloy on the surface of the part includes at least a first chemical element and a second chemical element, and reference histograms for the first and second chemical elements are jointly determined by the iterative search mechanism based on a combination of distances calculated with the photon number histograms for the first and second elements, respectively.

[0055] Therefore, several or all of the chemical elements that make up the alloy can be considered at the same time to determine the microstructure properties of the alloy, thereby enhancing the robustness and reliability of the characterization.

[0056] In one embodiment, the distance is the squared difference between the photon number histogram and the reference histogram, the Mahalanobis distance, the maximum likelihood distance, or the L1 norm.

[0057] Therefore, this distance is a robust metric that is fast and computationally efficient.

[0058] In one embodiment, the X-ray fluorescence spectrometry device is an energy-dispersive fluorescence device or a wavelength-dispersive fluorescence device.

[0059] Therefore, this method is applicable to conventional X-ray fluorescence spectroscopy techniques.

[0060] In one embodiment, the method includes:

[0061] - When the measured value of at least one microstructural property of the metal alloy does not conform to the nominal value, an abnormal microstructural structure is detected on the surface of the part.

[0062] Therefore, this method can detect microstructural anomalies, such as segregation defects (like spots or white spots), by comparing the obtained characterization with the nominal value of the property. The "nominal value" refers to the value of the property when no anomaly is present.

[0063] In one embodiment, the method includes:

[0064] - Construct at least one microstructural property map of the part.

[0065] Therefore, this method provides an easily interpretable visual representation.

[0066] 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 made of the metal alloy, the system being configured to implement the method according to the first aspect.

[0067] A third aspect of the invention relates to a computer program product comprising instructions that, when the program is executed on a computer, cause the computer to perform the steps of the method described in the first aspect.

[0068] A fourth aspect of the invention relates to a computer-readable recording medium including instructions that, when executed by a computer, cause the computer to perform the steps of the method described in the first aspect.

[0069] A better understanding of the invention and its various applications will be gained by reading the following description and examining the accompanying drawings. Attached Figure Description

[0070] The accompanying drawings illustrate indicative, not limiting, embodiments of the invention.

[0071] Figure 1 This is a block diagram illustrating the sequence of method steps according to the present invention.

[0072] Figure 2 This is a representative diagram of the X-ray radiation spectrum captured by a spectroscopic device.

[0073] Figure 3 This is a schematic diagram of the surface of the manufactured part.

[0074] Figure 4 yes Figure 2 A representative image of the photon count spectrum detected in each sub-region on the surface of the part.

[0075] Figure 5 This is a representative histogram of the number of detected photons.

[0076] Figure 6 yes Figure 2 Microstructure property diagram of the component.

[0077] Figure 7 yes Figure 2 Another microstructural property map of the component.

[0078] Figure 8 This is a representative graph showing the change in distance between the experimental histogram and the theoretical histogram, based on an embodiment and estimation of the properties of the metal alloy.

[0079] Figure 9 This is a set of spectra obtained according to an embodiment of the method of the present invention. Detailed Implementation

[0080] Unless otherwise stated, the same elements appearing in different figures are identified by a single figure reference numeral.

[0081] This invention relates to a method for analyzing analytical spectra measured by X-ray fluorescence spectroscopy to characterize one or more microstructural properties of metallic alloys or high-temperature alloys in manufactured parts. The method can also detect anomalous chemical segregation on the surface of the parts.

[0082] The analysis provided is achieved by conducting a statistical study on the chemical elements of the metal alloys that make up the parts, and by constructing histograms of the number of photons detected in different spectra for each element.

[0083] This method is based on the approximation that metallic alloys consist of two phases with different chemical compositions: the alloy matrix and hardened precipitates. The hardened precipitates are composed of the same chemical elements as the matrix, but at different concentrations. The function of these hardened precipitates is to strengthen the alloy matrix to improve its mechanical properties.

[0084] For these materials, this method is therefore able to characterize the characteristic size of the minimum phase (hardening precipitates) and estimate the area ratio of the hardening precipitate phase to the matrix phase.

[0085] The following description uses the characterization and detection of anomalous segregation (i.e., hardened precipitates) in metallic alloys that can be approximated as two-phase as an example to illustrate the implementation of this method. However, this method is fully applicable to any metallic alloy or high-temperature alloy that is compatible with this approximation.

[0086] Therefore, a first aspect of the present invention relates to a method for determining at least one microstructural property of a metal alloy on the surface of a part made of the metal alloy. Figure 1 The sequence of steps of method 100 is shown.

[0087] For this type of metallic alloy, the characteristic size of the hardened precipitates and the ratio of their surface area to the total surface area in the alloy can be particularly characterized. For γ / γ' alloys, these are, respectively, the radius of the γ' hardened precipitates and the ratio of their surface area to the surface area of ​​the γ matrix. The γ matrix contains so-called secondary and tertiary γ' hardened precipitates intercalated within it, the latter possessing nanoscale characteristic sizes.

[0088] It can characterize other microstructural properties, such as the size dispersion of precipitates, for example, equal to the standard deviation of the precipitate size; or the geometric properties of precipitates, such as sphericity, distance or area ratio, aspect ratio, etc.

[0089] In another embodiment, the method of the present invention can be applied to Inconel 718 alloy to characterize the properties of δ-hardened precipitates in the γ matrix of the alloy.

[0090] The procedure involves acquiring a set of 110 spectra. These spectra have been acquired or are being acquired using an X-ray fluorescence spectrometry device. In this embodiment, for illustration, the device is an energy-dispersive X-ray spectrometer (EDS or EDXS), which, through a spectral detector, is capable of constructing a histogram representing the distribution of X-rays according to the energy of the captured photons.

[0091] The surface of the part to be characterized is artificially divided into portions called "sub-regions". Therefore, each spectrum in this set of spectra is acquired by the device to correspond to a given sub-region of the part surface to be characterized. Thus, each spectrum in this set of spectra is associated with a sub-region of the part surface. Each sub-region is preferably a square with a side length between 0.1 mm and 5 mm (e.g., 1 mm). Each sub-region may also have a shape and size corresponding to the size of the incident X-ray beam.

[0092] like Figure 3As shown, the sub-regions 21 are preferably continuous, meaning that each sub-region 21 shares at least one boundary with another sub-region 21. The sub-regions 21 thus form a continuous region 22 on the part surface 20. The continuous region can have any shape and any size, depending on the distribution and number of the selected sub-regions. Therefore, the continuous region is associated with a set of spectra.

[0093] Figure 2 An example of a spectrum 10 measured in air is provided. The horizontal axis corresponds to the energy of the detected photons, and the vertical axis corresponds to the number of counts detected on a logarithmic scale. The instrument used is a Bruker™ M4 Tornado® equipped with a rhodium tube and two 30 mm² XFlash® detectors. This spectrum contains multiple peaks, each corresponding to a specific chemical element, specifically the following elements: titanium, chromium, iron, cobalt, nickel, tungsten, niobium, and molybdenum.

[0094] The next step involves determining the number of more than 120 photons from this set of spectra. The photon count for this chemical element is determined. In other words, for each spectrum in this set, the computing device calculates the number of photons captured by that chemical element.

[0095] Each photon count is calculated based on one or more measures characterizing the peak in the relevant spectrum corresponding to that chemical element. For example, the photon count corresponds to the area under the peak, i.e., the integral value of that area under the peak.

[0096] Then, step 130 is performed to construct a histogram of the number of photons detected in each sub-region. This is done for the set of spectra and the chemical element. In other words, the histogram represents the distribution of the calculated photon values ​​for the chemical element in the set of spectra.

[0097] Figure 4 Photon number maps are provided, showing the photon number distribution detected by titanium in each sub-region of the alloy under discussion. It can be observed that there are significant differences in the photon number distribution detected by titanium, and for each spectrum, between the first region 31 and the second region 32. In the latter, a significant increase in the number of photons detected by this element is noted. Furthermore, Figure 5 This shows an example of a histogram 40 constructed for titanium in the first region 31.

[0098] In the described embodiment, a method 100 is implemented including the step of determining a scaling factor of 140. The determination is based on a determined number of photons. This scaling factor represents the ratio of the average number of photons detected for each chemical element based on the theoretical concentration of the element in the metal alloy on the surface of part 20. Therefore, the scaling factor a is determined by… Provided. It is the average of the number of photons (or a portion thereof) determined in step 120 above for the number of photons of the relevant chemical element (here, the chemical element). Therefore, it is an average photon count calculated based on the average of multiple photon counts. The average can be a weighted average, for example, to account for the variability or accessibility limitations of the X-ray beam at the time of acquisition. This is the average concentration of the chemical element in question within the alloy. This concentration is equal to the theoretical concentration of that element in the alloy.

[0099] Alternatively, the scaling factor can be calculated by averaging the number of photons from multiple sets of spectra (each set of spectra is associated with a different region).

[0100] The next step is to construct a 150-reference histogram. This reference histogram is a histogram of the theoretical number of photons detected for the element. The determination of this reference histogram is performed through an iterative search mechanism, which involves comparing the photon number histogram with the recursively estimated reference histogram.

[0101] The iterative search mechanism is a recursive mechanism that searches the theoretical histogram through continuous iterations until a predetermined condition regarding the distance calculated from the photon number histogram is met. When the predetermined condition is met, the theoretical histogram is called the "reference histogram".

[0102] This distance can be, for example, the squared difference between the photon number histogram and the reference histogram, the Mahalanobis distance, the maximum likelihood, or the L1 norm.

[0103] The iterative search mechanism is configured to search within a predetermined range of values ​​for the microstructural property to be characterized. Therefore, at least one value range is defined for this microstructural property. When characterizing two or more structural properties, at least one value range is defined for each microstructural property.

[0104] Here, the search algorithm traverses a first predetermined range of characteristic dimensions of the hardened precipitates and a second predetermined range of surface area ratios of the hardened precipitates. Figure 8 The distance (here, the difference of squares ε²) is shown as a function of the radius of the γ' hardened precipitate. Examples of variations and how they change with the surface area ratio of γ' and γ phases in the alloy.

[0105] The range of values ​​can be continuous or discrete, and is defined, for example, based on known theoretical values ​​of the alloy under discussion. The range is defined, for example, by a maximum and a minimum value, each corresponding to a percentage of the theoretical or empirical nominal value of the corresponding property, obtained, for example, using EDS-EBSD technology. The nominal value corresponds to the microstructural properties of a defect-free material. This range of values ​​is defined independently of the number of chemical elements considered.

[0106] Iterative search mechanisms can be, for example, optimization algorithms that minimize an objective function, such as local optimization algorithms like gradient descent or global optimization algorithms like genetic algorithms. In this case, the objective function is the distance between the theoretical histogram and the photon number histogram. Alternatively, iterative search mechanisms can be Bayesian methods. These mechanisms are used to iteratively search for theoretical histograms that satisfy predetermined conditions. For optimization or inversion algorithms, this predetermined condition is minimizing the distance, i.e., iteratively searching until the distance is less than or equal to an optimal threshold. This optimal threshold is defined by the operator based on their domain expertise, desired representational accuracy, and / or specific experimental conditions. Alternatively, or in combination, this condition can also be about the maximum number of iterations, defined by the operator based on the required search computational cost and domain expertise.

[0107] Alternatively, the search algorithm is a brute-force method that evaluates the distances to a set of theoretical histograms; the reference histogram is the theoretical histogram with the smallest distance among all calculated distances. Therefore, the algorithm is configured to traverse the range of values ​​with a predefined, constant, or adaptive iteration step size until all possible iterations have been performed. A precondition is that the distance to the reference histogram is the smallest among all distances calculated by the brute-force algorithm. In the provided example, the brute-force algorithm traverses the first and second ranges of values.

[0108] Regardless of the nature of the search mechanism, both the reference histogram and each theoretical histogram are constructed based on estimates of microstructure properties. In the provided example, these are the characteristic dimensions of the hardened precipitates and the surface area ratio of the hardened precipitates. Therefore, each theoretical histogram constructed during the search is associated with that estimated microstructure property. Similarly, the reference histogram is associated with estimated microstructure properties (referred to as "reference" properties), which are therefore properties of the metallic alloys that enable the formation of the reference histogram.

[0109] In particular, reference microstructure properties can include reference feature size and reference surface area ratio. For example, this is the diameter of the γ' reference precipitate and the reference surface area ratio of the γ' and γ phases.

[0110] Each theoretical histogram is like a reference histogram. Figure 1 Preferably, this is constructed by generating a random distribution of multiple theoretical photon numbers. These photon numbers are weighted by a previously determined scaling factor. These photon numbers are also corrected by applying a statistical law (e.g., Poisson's law) to account for measurement uncertainties associated with the sensor. In this embodiment, the statistical law is Poisson's law, and the parameter is the theoretical photon number to be corrected.

[0111] Other types of rules can be used, particularly the normal rule, especially when the photon component (i.e., Poisson noise) has a small impact on the standard deviation of histogram values ​​relative to the inter-pixel element concentration variability. In this case, the photon component can be ignored when constructing the reference histogram.

[0112] Below is an example of how to construct a theoretical histogram. When characterizing multiple regions, the following steps are performed for each region under consideration. This implementation can be done simultaneously or sequentially.

[0113] In each iteration of the search mechanism, the microstructure properties are estimated to form a theoretical histogram.

[0114] Then, step 150 of constructing the reference histogram includes a sub-step of selecting theoretical values ​​151 for the microstructure properties from a range of values. If necessary, theoretical values ​​are selected from a range of values ​​associated with each microstructure property. For example, values ​​for the theoretical characteristic size of the hardened precipitate are defined and selected from a first range of values, and values ​​for the theoretical surface area ratio of the hardened precipitate are defined and selected from a second range of values.

[0115] The next step involves determining the theoretical number of precipitates in the 152 metallic alloy. This theoretical number of precipitates is determined by a numerical simulation tool based on the values ​​of selected microstructure properties. Specifically, for this example, the theoretical number is determined based on the theoretical characteristic size value of the hardened precipitates, the theoretical surface area ratio value of the hardened precipitates, and the surface area ratio value of the hardened precipitates (e.g., by applying a proportionality rule). Therefore, the numerical simulation tool is configured to calculate the theoretical number of hardened precipitates by inputting the values ​​of the microstructure properties into it.

[0116] The theoretical quantity of hardened precipitates is determined for a single unit (i.e., a numerical region of the same size as the region being characterized).

[0117] Then, based on the theoretical quantity of hardened precipitates, the step of randomly distributing 153 hardened precipitates within the cell is performed. The number of these hardened precipitate distributions is equal to the theoretical quantity of hardened precipitates. This random distribution is performed, for example, according to a uniformity rule. The parameters of the uniformity rule are defined by the operator, for example, based on the alloy and independently of the elements considered. Alternatively, other rules may be used instead of the uniformity rule.

[0118] The size of each hardened precipitate is defined by a value selected from a relevant range of values, such as a value selected from a first range of values.

[0119] In some embodiments, the size of each hardened precipitate is randomly defined according to a normal distribution. The average value of this normal distribution is, for example, equal to a value selected from a range of values ​​associated with the size of the hardened precipitate (here, a first range). Other parameters of this normal distribution are defined by the operator, for example, based on the alloy and independently of the chemical elements considered.

[0120] Then, based on the distribution of the hardened precipitate, the theoretical photon count for this chemical element was determined using a method involving the determination of more than 154 theoretical photon counts. For this purpose, the unit cell corresponding to the region was divided into multiple sub-units. Each sub-unit corresponds to a sub-region of that region; that is, the sub-unit and its associated sub-region are the same size. Therefore, each theoretical photon count is associated with one of the sub-units contained within that unit.

[0121] Preferably, the theoretical photon number N of each sub-unit is determined as follows: ,in,

[0122] a is the scaling factor;

[0123] Cγ is the theoretical concentration of this chemical element in the metallic alloy matrix of the subunit;

[0124] Sγ is the surface area of ​​the matrix in the subunit;

[0125] Cγ' is the theoretical concentration of the chemical element in the hardened precipitate of the metallic alloy matrix in the subunit;

[0126] Sγ' is the surface area of ​​the hardened precipitate in the subunit.

[0127] Therefore, this is an estimate of the number of photons detected in a subunit that intersects with one, multiple, or no grains.

[0128] Then, by applying Poisson's law, a step is performed to correct 155 of the theoretical photon number. Therefore, the photon number distribution on each sub-unit is randomly modified according to Poisson's law, which uses the theoretical photon number N of each sub-unit as its parameter.

[0129] Then, the step of constructing the 156 theoretical histogram is performed. The theoretical histogram is constructed based on multiple theoretical photon numbers corrected for Poisson's rule. Similar to the photon number histogram, the theoretical histogram represents the distribution of corrected theoretical photon values ​​for the relevant subunits of the chemical element.

[0130] Sub-steps 151 to 156 are implemented in each iteration of the iterative search mechanism.

[0131] The next step involves determining the microstructural properties of the 160 parts. This involves estimating the microstructural properties based on reference properties (i.e., the properties used to construct the reference histogram). Here, the microstructural properties to be characterized are equal to the reference properties.

[0132] An optional step can be implemented to detect precipitate defects in the surface metal alloy of a 170 part. The detection is performed by comparing the obtained microstructural property values ​​with nominal values. The nominal values ​​can be theoretical or empirical. Preferably, the difference between the microstructural property values ​​and the nominal values ​​is calculated. When the absolute difference exceeds a predefined threshold, the microstructural property value is abnormal and segregation defects are present.

[0133] Furthermore, the properties of the microstructure allow for the definition of the properties of the detected segregation defects.

[0134] Other methods besides calculating the difference between two values ​​can be used to detect precipitation defects, such as analyzing the distribution of the difference between the estimated value and the nominal value.

[0135] In one embodiment, the method is used to characterize the microstructural properties of two or more chemical elements in an alloy. In this case, in step 110, multiple photon numbers are determined for each chemical element in question. Therefore, in step 130, a set of histograms of spectra is constructed for each chemical element. Furthermore, in step 140, a scaling factor is determined for each chemical element of interest.

[0136] Therefore, step 150, constructing a reference histogram, is performed for each chemical element under consideration. Substeps 151 to 153 remain unchanged because they do not depend on the number or properties of the chemical elements used for characterization. In substep 154, the theoretical photon number N is calculated for each chemical element in a subset or each subunit. The theoretical concentration and scaling factor are determined independently for each chemical element to provide theoretical concentration and scaling factor for each chemical element under consideration. In substep 155, a theoretical histogram is constructed for each element under consideration. Theoretical histograms are generated independently for each chemical element, for example, using different statistical laws, such as different Poisson laws, one for each chemical element. Iterative searches can be performed jointly or sequentially for all the various chemical elements: then interrelated iterative searches are performed for all these elements. Alternatively, the search can be performed independently for each chemical element or in a correlated manner for two or more of them. When the search is performed in a correlated manner, it is preferably performed jointly for the different elements of interest. Thus, the microstructural properties correspond to the theoretical microstructural properties associated with the reference histograms of these elements. In other words, the microstructure properties do not depend on any particular chemical element, but are common to all these elements. Therefore, the goal is to minimize the uncertainty of characterization relative to characterization based on a single element.

[0137] Therefore, optional steps for detecting 170 segregation defects can be implemented for each chemical element of interest.

[0138] In one embodiment, characterization is performed in multiple regions on the surface of the part. In other words, in step 110, multiple sets of spectra are acquired, each set associated with a different consecutive region from the multiple regions. These regions may be non-intersecting or partially overlapping. In step 130, a histogram 40 is constructed for each set of spectra.

[0139] Then, an iterative search mechanism is implemented independently for each of the multiple regions to generate a characterization for the chemical element in each region.

[0140] Therefore, an optional step of constructing a 180 microstructure property map can be implemented. This map then represents the distribution of microstructure properties characterized across different regions. The map can be a color gradient, such as a gray gradient, with each color corresponding to a value for a microstructure property. Thus, each region is associated with a color associated with which a value is determined for that region.

[0141] Figure 6 and Figure 7 The properties of the characterized metallic alloys are depicted in a spectrum. Figure 6 The radius corresponding to the γ' hardened precipitate Atlas. Figure 7 The surface area ratio maps correspond to the γ and γ' phases. In each map, a set of regions 22' are observed whose part surface microstructure properties are normal, i.e., the absolute value of the difference is below a predefined threshold. Figure 6 A region 22'' and Figure 7 Segregation defects can also be observed in the two regions 22'', where the absolute value of the difference is greater than the predefined threshold.

[0142] In this embodiment, the scaling factor can be determined independently for each of the multiple regions in step 140, or the scaling factor can be calculated across multiple or all regions. In this case, the average number of detected photons is calculated independently for each set of spectra and / or across a subset of the spectral sets associated with these regions. .

[0143] In one embodiment, several chemical elements are considered, and analysis is performed across multiple regions. Then, in step 130, a histogram is constructed for each chemical element and each set of spectra. In step 140, a scaling factor is calculated for each chemical element of interest, and in step 150, an iterative search mechanism is implemented for each of the multiple regions. Thus, the alloy is characterized for each of these regions and for each element of interest. The steps of detecting 170° segregation defects and / or constructing 180° spectra for each of these elements can also be implemented.

[0144] Figure 9Examples of spectra obtained by implementing step 180 are provided. Thus, concentration comparisons between healthy and segregated regions can be observed for several chemical elements, such as titanium (Ti), chromium (Cr), and iron (Fe).

[0145] In one embodiment, the X-ray fluorescence spectrometry apparatus is configured to acquire spectra continuously. That is, the apparatus acquires the same spectrum for several consecutive sub-regions of the part surface in a single acquisition, for example, in a unidirectional scan. Therefore, in step 110, the set of spectra is obtained by discretizing one or more continuous spectra acquired by the spectrometry apparatus. Discretization takes into account the scan duration and the number of sub-regions of the part surface scanned by the beam during the acquisition. Thus, each sub-region can be associated with a spectrum that is part of the continuous spectrum, and the acquisition duration is equal to the time it takes for the X-ray beam to pass through the sub-region. The time it takes for the beam to pass through the sub-region is equal to the total acquisition duration of the continuous spectrum divided by the number of sub-regions associated with that continuous spectrum.

[0146] Furthermore, in this embodiment, step 154, which determines multiple theoretical photon numbers, includes three sub-steps.

[0147] In sub-step 154-1, the location of each distribution of precipitates is discretized. That is, the surface of each hardened precipitate is divided into multiple sub-surfaces. These sub-surfaces may have the same size or different sizes. These sub-surfaces may therefore have the same shape or different shapes. This discretization is performed based on a set of source locations during the measurement of the same spectrum. Therefore, these locations are the positions of the beams emitted by the sources towards the part during the spectral acquisition time.

[0148] In sub-step 154-2, a coverage ratio is determined for each distributed hardened precipitate and for each sub-unit among multiple sub-units. This coverage ratio is determined based on the discretization of the hardened precipitate locations. The coverage ratio indicates the proportion of the hardened precipitate surface area contained within the relevant sub-unit. The coverage ratio can be determined analytically by calculating the intersection between the sub-unit (preferably rectangular) surface and the discretization of the hardened precipitate.

[0149] Therefore, in sub-step 154-3, the theoretical photon number is determined in a manner similar to that of step 154 ​​described above, taking into account the calculated coverage. The surface integral of the chemical elements in the relevant sub-unit is determined based on the coverage of each hardened precipitate, and the coverage is considered when calculating the theoretical photon number. Therefore, for each hardened precipitate, the surface integral is weighted by its coverage. Thus, the surface integral is equal to the sum of the surface areas of each hardened precipitate, each weighted by its associated coverage.

[0150] In some embodiments, theoretical histograms are constructed using other methods that do not require calculating scaling factors to readjust theoretical models and experiments. For example, readjustment can be implemented by directly using theoretical models that take into account nonlinear effects of measurement, such as stacking effects, attenuation through dedicated physical models, X-ray fluorescence emission probability of photoelectric absorption, etc.

[0151] A second aspect of the invention relates to a calculator configured to implement the method according to the invention. The calculator includes, for example, a processor and memory, such as volatile or non-volatile memory. The memory includes instructions that, when executed by the processor, cause the calculator to perform the steps of the method.

[0152] In one embodiment, the calculator is integrated into an X-ray fluorescence spectroscopy device.

Claims

1. A method (100) for determining at least one microstructural property of a metal alloy on the surface (20) of a part made of a metal alloy, the method (100) comprising: - Acquire (110) a set of spectra (10) acquired by an X-ray fluorescence spectrometry device, wherein each spectrum (10) in the set of spectra (10) is associated with a sub-region (21) of the surface (20) of the part, the sub-region (21) being continuous 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 the number of multiple photons of a chemical element of the metal alloy (120) from the set of spectra (10); - For the set of spectra (10), a photon number histogram (40) is constructed (130) based on the number of photons determined for each of the chemical elements in the set of spectra (10); - By means of an iterative search mechanism, a reference histogram (40) is constructed based on the distance between the reference histogram (40) and the photon number histogram (40), the reference histogram (40) being associated with at least one reference microstructure property, and the reference histogram (40) being constructed from a random distribution of multiple randomly corrected theoretical photon numbers according to statistical laws; - Determine (160) the microstructure properties of the metal alloy for the continuous region (22), the microstructure properties being equal to the reference microstructure properties.

2. The method (100) according to claim 1, wherein the metal alloy comprises a matrix and hardened precipitates, and wherein the reference histogram (40) is a theoretical histogram (40) that satisfies a predetermined condition regarding the distance between the theoretical histogram and the photon number histogram (40), the theoretical histogram (40) being constructed in each iteration of the iterative search mechanism in the following manner: - Select the theoretical value of the microstructure property from a range of values ​​(151); -Based on the selected theoretical value, determine the theoretical amount of hardened precipitates in the metal alloy of the part (152) on a unit with the same size as the continuous region (22); - According to the uniform distribution, hardening precipitates are randomly distributed (153) on the unit, and the number of distributed hardening precipitates is equal to the theoretical number of hardening precipitates; - A plurality of theoretical photon numbers (154) are determined for the chemical element, each theoretical photon number N being associated with one of a plurality of sub-units contained in the unit, each sub-unit corresponding to a sub-region (21) of the continuous region (22), each theoretical photon number being determined in the following manner: ,in: -a is the scaling factor; -Cγ is the theoretical concentration of the chemical element in the relevant subunit in the metal alloy matrix; -Sγ is the surface area of ​​the metal alloy matrix in the subunit; -Cγ' is the theoretical concentration of the chemical element in the relevant subunit in the hardened precipitate of the metal alloy matrix; -Sγ' is the surface area of ​​the hardened precipitate in the subunit; - Based on the statistical distribution, the theoretical photon number of the plurality of theoretical numbers is randomly corrected (155); - Construct the theoretical histogram (156) based on the corrected theoretical photon numbers.

3. The method (100) according to claim 2, wherein the scaling factor is equal to the ratio of the average number of photons to the theoretical concentration of the chemical element on the surface (20) of the part, and the average number of photons is determined based on the average of the plurality of photon numbers.

4. The method (100) according to claim 2 or 3, wherein each randomly distributed hardened precipitate has a size randomly determined according to the normal law.

5. The 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: -The location of the hardened precipitate for each distribution is discretized (154-1) based on a set of source locations and the number of sub-units during the measurement of the same spectrum (10); - For each distribution of hardened precipitates, the coverage of each sub-unit of the plurality of sub-units is determined (154-2) based on the discretization of the hardened precipitate locations; -And in the relevant sub-unit, the surface area of ​​the hardened precipitate is calculated based on the coverage of each hardened precipitate.

6. The method (100) according to any one of the preceding claims, wherein each of the plurality of photon numbers is determined based on the area under the peak associated with the chemical element in one of the spectra (10) of the set of spectra (10).

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

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

9. The method (100) according to any one of the preceding claims, wherein the distance is the squared difference between the photon number histogram (40) and the reference histogram (40), the Mahalanobis distance, the maximum likelihood, or the L1 norm.

10. The 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. The method (100) according to any one of the preceding claims, comprising: - When the value of at least one microstructure property of the metal alloy is determined to be inconsistent with the nominal value, detect (170) the microstructure anomaly of the surface (20) of the part.

12. The method (100) according to any one of the preceding claims, comprising: - Construct at least one microstructure property map of the part described in (180).

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