Method for measuring crystal misorientation of single crystal blades

Abstract

The present invention relates to a method for measuring the crystal orientation difference of a single-crystal blade (10), the blade (10) comprising a material formed of dendrites (30) having a trunk (32) and branches (34) extending in a principal direction (Z'), the method comprising: defining a reference coordinate system (XYZ) for the blade, the reference coordinate system including a radial direction (Z); mechanically and chemically treating the blade (10) in a base plane (P1) to acquire a first image (I1) by photomicrography; mechanically and chemically treating the blade (10) in a comparison plane (P2) offset radially from the base plane (P1) by a distance (D) to acquire a second image (I2) by photomicrography; and processing the first and second images (I1, I2) to compare the position of the trunk (32) of each dendrite (30) in the two images (I1, I2) and thereby derive the orientation of the principal direction (Z') of the dendrite (30) relative to the radial direction (Z).

Description

Technical Field

[0001] This disclosure relates to the field of single-crystal blades, and in particular to the three-dimensional optical measurement of their crystal orientation. More specifically, this disclosure relates to a method for measuring the crystal orientation difference of single-crystal blades. Background Technology

[0002] Rotary aero engines must meet stringent airworthiness, quality, and performance standards. Their performance is typically related to the temperature of the combustion gases circulating within the turbine, particularly within the turbine blades. These blades endure extremely high temperatures and rotate at very high speeds for extended periods. Considering these stresses, the blades primarily undergo creep.

[0003] To withstand these stresses, these blades are typically made of superalloys called “single-crystal” or “single-grain” superalloys, which by definition have the advantage of having no grain boundaries, thus improving their resistance.

[0004] The manufacture of single-crystal turbine blades relies on a casting method in which the selection of seed crystals and the control of the growth direction of dendrites generated during cooling determine the final grain orientation, starting from the molten alloy. Dendrites are dendritic crystals that appear during alloy solidification and have a three-dimensional structure, including a central axis or trunk in the main direction in which the dendrites form, and branches extending from the trunk in secondary directions transverse to the main direction.

[0005] These dendrites can be visualized using known metallographic methods, including blade slicing, polishing, and chemical or electrochemical etching. The dendrites thus highlighted in cross-section are cruciform, with the center indicating the location of the main trunk and the arms corresponding to the branches.

[0006] Furthermore, the blade's resistance to stress, particularly creep, is directly related to the dominant orientation of the crystal (called the principal dendrite orientation) relative to the radial direction (along which the centrifugal stress associated with turbine rotation is applied). In other words, blade strength depends on the orientation of the principal dendrite orientation relative to the ideal theoretical axis to which the blade is targeted (i.e., 0° relative to the radial direction). The angle between the principal dendrite orientation and the radial direction (ideal theoretical axis) should typically be less than 15°, representing a trade-off between production costs and the scrap rate due to poor crystal orientation.

[0007] Therefore, turbine blades are often the subject of investigation aimed at observing their crystal orientation and highlighting the variable (the difference between the main direction of dendrites and the radial direction of the blade) in order to identify the causes and patterns of damage to these blades, especially deformation, cracking and fracture.

[0008] Furthermore, the effectiveness and quality of these investigations are critical factors in ensuring the responsiveness necessary for any action aimed at improving flight safety. However, current investigation methods have several drawbacks. In fact, known X-ray crystallography methods (such as the Laue method) require specialized equipment not typically available in traditional metallographic laboratories, necessitating outsourcing of these investigations and resulting in delays and costs associated with performing preliminary measurements, which are incompatible with the required effectiveness and responsiveness.

[0009] Other methods, which are more readily available in terms of technical resources, do not provide satisfactory reliability and measurement quality. In fact, depending on the method used, reliably identifying the trunk or distinguishing the orientation difference of dendrites relative to the radial direction can be particularly difficult.

[0010] Therefore, it is necessary to overcome at least some of the aforementioned drawbacks and provide a reliable, efficient, and technically available method for measuring the crystal orientation of single-crystal blades to meet the efficiency and responsiveness requirements of these surveys. Summary of the Invention

[0011] This disclosure relates to a method for measuring the crystal orientation difference of a single-crystal blade. The blade extends radially between a blade root and a blade tip, and includes material formed of dendrites having a main trunk extending in a principal direction between the blade root and the blade tip, and branches extending transversely to the principal direction. The method includes: - Define the reference coordinate system for the blade, which includes the radial direction of the blade; - The blade is mechanically and chemically treated in a base plane perpendicular to the radial direction to acquire a first image in that base plane by photomicrography; - Mechanical and chemical treatments are performed on the blade in a comparison plane that is perpendicular to the radial direction and radially offset by a predetermined distance relative to the base plane, so as to acquire a second image in the comparison plane by photomicrography; - Process the first and second images to compare the position of the main trunk of each dendrite in the two images, and thereby deduce the orientation of the main direction of the dendrite relative to the radial direction of the blade.

[0012] It should be understood that the reference coordinate system of the blade is a Cartesian coordinate system, which includes the blade's nominal radial direction and a plane perpendicular to the radial direction, with the base plane parallel to this plane perpendicular to the radial direction.

[0013] In this method, mechanical and chemical treatment of the blade on two planes allows for the acquisition of microscopic images on these two planes (i.e., the base plane and the comparison plane). Therefore, the position of the trunk of each dendrite in these two images can be compared, and thus, given a predetermined distance between the two planes, the offset of the trunk of each dendrite between the two planes can be measured.

[0014] By processing the first and second images to compare the position of the main trunk, the main growth axis of the single-crystal dendrite can be derived, and thus the crystal orientation of the blade, or more precisely, the orientation difference of the crystal relative to the radial direction, can be derived.

[0015] The advantage of this method is that it reliably and accurately measures the principal crystal orientation of the blades using sample preparation methods readily available in conventional metallographic laboratories, without requiring specialized equipment that could incur significant costs and delays, which are incompatible with the efficiency and responsiveness requirements of these surveys.

[0016] In some embodiments, the method includes: creating a radial reference notch in the base plane prior to mechanically and chemically treating the blade, wherein the base plane and the comparison plane are arranged to intersect the reference notch.

[0017] It should be understood that the radial reference notch extends primarily in the radial direction and is perpendicular to the plane of the reference coordinate system that is perpendicular to the radial direction. The presence of the notch is advantageous because it provides a reference point, facilitating the superposition of the first and second images during processing, thereby improving the accuracy of the processing and the results obtained.

[0018] In some embodiments, the first image and the second image each include at least a portion of a reference cutout, and processing the first image and the second image includes superimposing the first image and the second image by superimposing the portion of the reference cutout.

[0019] It should be understood that the first and second images each include the same portion of the reference cut, which improves the accuracy of the overlay and the results obtained during image processing.

[0020] In some embodiments, the base plane is defined by the radial end of the blade root.

[0021] This improves the speed and efficiency of the method because the basal plane already exists, requiring minimal machining beyond polishing before chemical treatment. Furthermore, defining the basal plane at the blade root, rather than at other locations on the blade, and thus defining the comparison plane, facilitates the investigation of crystal orientation, as the amount of material is greater at the blade root.

[0022] In some embodiments, the predetermined distance between the base plane and the comparison plane is between 0.15 mm and 0.35 mm.

[0023] This distance allows for reliable estimation of the main growth axis of the dendrites and thus the crystallographic orientation, while limiting the amount of material removed by machining to prepare a comparative plane, thereby improving the efficiency of the method.

[0024] In some embodiments, the method includes: measuring the radial positioning of a base plane relative to a reference plane of the blade, and measuring the radial positioning of a comparison plane relative to the reference plane.

[0025] The radial positioning of the measurement base plane and the comparison plane relative to the same reference plane along the radial direction allows for precise determination of the predetermined distance between the two planes and their relative positions. This further improves the accuracy of crystal orientation measurements.

[0026] In some embodiments, the reference plane is defined by the radial end of the blade tip.

[0027] The plane defined by the radial end of the blade tip is easy to identify and accurately locate, which simplifies the implementation of the method and further improves its efficiency.

[0028] In some embodiments, mechanical treatment includes machining and / or polishing the surface of the blade in a base plane and a comparison plane, and chemical treatment includes applying acid to the machined and polished surface of the blade.

[0029] When the base plane is taken at the radial end of the blade root, only the radial end face of the blade root needs to be polished. To define the comparison plane, more extensive machining is required, in which a greater amount of material is removed over a predetermined distance.

[0030] In some embodiments, processing the first and second images includes analyzing them, which includes drawing the positions of the dendrite trunks in the first and second images.

[0031] Processing the first and second images involves analyzing them to locate the trunk in each image, either manually or using numerical methods. It should thus be understood that the trunk's location can be determined by a point corresponding to the center of the cross-shaped structure formed by the dendrites in the plane, and that analyzing each of the first and second images reveals a point cloud showing the location of the trunk for each dendrite.

[0032] In some embodiments, the method includes: after analyzing a first image and a second image, performing mathematical and / or statistical and / or triangulation on the processed images to determine the average principal direction of the dendrites, and measuring the principal angle between the average principal direction and the radial direction.

[0033] By overlaying the analyzed first and second images, particularly by overlapping reference cut sections, the positional variation of the trunks from one image to another can be visualized. This variation of each trunk can then be used as input data, which can be averaged (e.g., through statistical processing) to determine the average principal growth axis of the dendrites, and thus the average principal direction of the dendrites. Based on the latter, for example through trigonometric calculations, the principal angle between the average principal direction and the radial direction can be determined. Therefore, the principal angle of the crystal orientation difference can be accurately determined using simple and readily available processing tools.

[0034] In some embodiments, the method includes: for each dendrite, measuring the secondary angle between the branches of the dendrite on a first image and a second image.

[0035] Secondary angle measurements can be performed after image acquisition or during image analysis. Measuring secondary angles in addition to principal angles allows for a more accurate assessment of crystallographic orientation differences.

[0036] In some embodiments, the method includes: determining the Euler angles of the blade defined by the principal and secondary angles of the dendrites.

[0037] Knowing the Euler angles and thus the Euler coordinate system allows for precise knowledge of the crystal orientation of the blade relative to its reference coordinate system.

[0038] In some embodiments, the single-crystal blade is a turbine blade.

[0039] Brief description of the attached figures

[0040] The invention and its advantages will be better understood after reading the following detailed description of various embodiments of the invention (given by way of non-limiting examples). This description refers to the accompanying drawings, in which: [ Figure 1 ] Figure 1 A perspective view of a single-crystal turbine blade is shown; [ Figure 2 ] Figure 2 The diagram schematically shows a) a side view of the dendrite, and b) in... Figure 1 c) Image obtained by photomicrography in plane P of the leaf; d) 3D model of dendrites. [ Figure 3 ] Figure 3 The diagram schematically illustrates a) a 3D model of dendrites oriented with respect to the radial direction of the blade, and b) a 2D view of the model in a cutting plane perpendicular to the radial direction. [ Figure 4 ] Figure 4 A perspective view of a single-crystal turbine blade is shown in different steps of the crystal orientation difference measurement method according to the present invention; [ Figure 5 ] Figure 5 The illustration schematically shows the first image acquired by photomicrography in the first plane P1 of the blade; [ Figure 6 ] Figure 6 The illustration schematically shows a second image acquired by photomicrography in the second plane P2 of the blade; [ Figure 7 ] Figure 7 The analysis of the first and second images and the plotting of the main trunk positions in each image are illustrated schematically. [ Figure 8 ] Figure 8 The superposition of the first and second images and the variation in the position of the main stem are illustrated in a simplified form. [ Figure 9 ] Figure 9 Different steps of the method for measuring the crystal orientation difference of a single crystal blade according to the present invention are illustrated schematically. Detailed Implementation

[0041] Figure 1 The diagram shows a moving blade 10 of a high-pressure turbine, such as a metal moving blade. The turbine blade is formed of a single-crystal material. Of course, the invention can also be applied to other moving or stationary turbine blades of turbines made of single-crystal materials.

[0042] Blade 10 extends in the coordinate system XYZ, where Z is the principal radial direction of the blade along its extension, and the radial plane XY is perpendicular to the radial direction Z. Blade 10 conventionally includes an aerodynamic surface 12 (or airfoil) that extends radially between platform 14 and blade tip 16. It should be noted that, although Figure 1 The blade 10 shown has a bathtub-shaped recess at the blade tip, but the blade 10 may also have a blade head with a root, without departing from the scope of the invention.

[0043] The aerodynamic surface 12 has a leading edge 18, a trailing edge 20, a pressure side surface 22, and a suction side surface 24 (which is shielded). The leading edge 18 is arranged opposite to the hot airflow from the turbine combustion chamber, the trailing edge 20 is opposite to the leading edge 18, and the sides 22 and 24 connect the leading edge 18 to the trailing edge 20.

[0044] The blade 10 also includes a blade root 26, which is intended to be mounted in a recess of a moving turbine disk (not shown). Thus, the blade 10 extends radially between the radially inner end portion 28 of the blade root 26 and the blade head 16 at its radially outer end portion. Furthermore, the blade head 16 extends in a plane at the radially outer end portion of the blade 10, which is hereinafter referred to as the reference plane R, preferably parallel to the plane XY.

[0045] Single-crystal blades can be manufactured using known casting methods, in which a molten alloy (e.g., a nickel-based superalloy) is placed in a ceramic mold and then cooled by directional solidification, during which the cooling of the alloy is controlled to obtain a material with the desired quality and properties. Specifically, seed crystals are selected, and the crystal growth direction is controlled during cooling; this selection and control of the growth direction determines the final crystal orientation. The crystals forming the final single-crystal material are dendritic in shape and have a three-dimensional structure.

[0046] Figure 2 Dendrite 30 is schematically shown in image a). Dendrite 30 includes a central axis or trunk 32 defining a principal direction Z' or main direction of dendrite 30, which corresponds to the main growth axis of the dendrite. Dendrite 30 also includes arms or branches 34 extending from the trunk 32 in a direction transverse to the principal direction Z'.

[0047] Dendrites 30 of the material constituting blade 10 can be highlighted by known metallographic preparation methods, including cutting the part in a cutting plane, polishing the surface of the cut part, and chemically or electrochemically etching the surface with a suitable acid.

[0048] Figure 2 Image b) schematically illustrates the process of using photomicrography to examine a cross-sectional plane P along a direction perpendicular to the radial direction Z. Figure 1 An example of an image obtained from a cross-section made at the root 26 of the blade 10. The resulting 2D (two-dimensional) image I lies in a plane parallel to the XY plane and shows multiple dendrites 30 arranged in a cross shape in that plane. The center of the cross shows the position of the trunk 32 at plane P, and the arms of the cross show the positions of the branches 34.

[0049] Figure 2 Image c) is a 3D (three-dimensional) model of dendrite 30 in image a (e.g., image a). This model is in the shape of an extruded cross, allowing the definition of the intrinsic angles of dendrite 30, i.e., the Euler angles of dendrite 30. The center of the extruded cross in the model of dendrite 30 corresponds to the trunk 32, defining the principal direction Z' or the main direction. The arms of the cross extend from the trunk 32, corresponding to branches 34 that extend along secondary directions Y', Z' transverse to the principal direction Z'.

[0050] The orientation of the Euler coordinate system X'Y'Z' of dendrite 30 relative to the fundamental coordinate system (or the Cartesian coordinate system inherent to blade 10), i.e., the previously defined coordinate system XYZ, allows for the determination of the crystal orientation of blade 10. Specifically, the orientation of the principal direction Z' of dendrite 30 relative to the radial direction Z of blade 10 (which is the theoretically ideal direction of dendrite 30) defines the principal angle of the crystal orientation. Furthermore, the angle between the secondary directions X' and Y' defines the secondary angles of the crystal orientation.

[0051] Figure 2 Image c) shows the “ideal” case, where the principal direction Z’ is parallel to and coincides with the radial direction Z (therefore the principal angle is zero), and the secondary angle between the secondary directions X’ and Y’ is a right angle.

[0052] In practice, the casting manufacturing method involves unavoidable and inherent defects in the blades, which means that the principal direction Z' is not perfectly aligned with the radial direction Z. Figure 3 Image a) shows a model of dendrite 30, where the principal direction Z' is tilted and forms a principal angle θ with the radial direction Z. Due to this tilt, the branches 34 themselves are not perpendicular to each other. In fact, in the cross-section of the dendrite 30 model perpendicular to the radial direction Z (e.g. Figure 2 As shown in image b), the secondary directions X' and Y' form secondary angles β and β', where β' = 180° - β.

[0053] The principal angle θ and the secondary angles β and β' constitute the Euler angles of dendrite 30, the values ​​of which allow the determination of the orientation of the Euler coordinate system X'Y'Z' relative to the inherent coordinate system XYZ of blade 10, and thus the crystal orientation of blade 10.

[0054] Sometimes it is necessary to know the crystal orientation as precisely as possible, especially the orientation difference of dendrite 30 relative to the ideal radial direction (the principal angle θ must be less than 15°), in order to identify the causes and modes of damage to these blades, including any deformation, cracking, and fracture they may have experienced. See below. Figures 4 to 9 The described process allows for the efficient conduct of such investigations using equipment readily available in conventional metallographic laboratories.

[0055] This example relates to a method for measuring as described above and in... Figure 1 The method for determining the crystal orientation difference of a single-crystal turbine blade is shown in the figure.

[0056] Initially (step S100), an inherent reference coordinate system is defined for the blade 10. In this example applied to the turbine blade 10, this reference coordinate system is the previously described Cartesian coordinate system XYZ, where Z is the radial direction of the blade 10.

[0057] Next, a reference cut E is made in the leaf root 26 (step S200). Figure 4Image a). Preferably, the notch E is made starting from the radially inner end portion 28 of the blade root 26, perpendicular to the plane formed by the radially inner end portion 28, i.e., perpendicular to the radial plane XY. Preferably, the size and measurement of the notch E are derived from empirical optimization of accuracy, material, and preparation time. In other words, the notch E constitutes a quick reference point for standby processing, and the size of the notch E is further precisely determined and known in order to improve the accuracy of superposition and the described subsequent processing.

[0058] Then, the base plane P1 is defined (step S300). Figure 4 Image b). In this example, the base plane P1 approximately corresponds to the plane formed by the radially inner end portion 28 of the blade root 26, on which the fabrication is performed. This fabrication includes polishing the radially inner end portion 28, followed by chemical etching to expose the dendrites 30.

[0059] Furthermore, the positioning dimensions of the base plane P1 are measured in this step. For this purpose, the distance between the prepared base plane P1 and the previously described reference plane R can be measured. Therefore, step S300, which defines the base plane P1, includes the preparation described above (step S310) and the measurement of the positioning dimensions (step S320).

[0060] Then, the first image I1 is acquired in the base plane P1 (step S400). Figure 5 The first image I1 was obtained in the base plane P1 by the previously described photomicrographic method and shows multiple dendrites 30. The acquisition of the first image I1 was performed on a portion of the base plane P1 that includes a reference notch E (e.g., the edge 29 of the notch in the base plane P1 and the end 291 of the edge 29).

[0061] Then, the comparison plane P2 is defined (step S500). Figure 4 Image c). Similar to the base plane P1, the definition of the comparison plane P2 includes preparation (step S510) and measurement of the positioning dimensions (step S520).

[0062] The comparison plane P2 is parallel to the base plane P1 and is obtained by machining a predetermined distance D from the base plane P1 (approximately corresponding to the radial inner end 28) along the radial direction Z. The distance D between the base plane P1 and the comparison plane P2 can be, for example, between 0.15 mm and 0.35 mm, and is less than the height of the reference notch E. After this machining, the resulting surface is polished and chemically etched to reveal the dendrites 30 in the plane P2. Therefore, step S510 of preparing the comparison plane P2 includes the above-described machining, polishing, and chemical etching.

[0063] The aforementioned distance D can be chosen arbitrarily and approximately, as long as it is within the range mentioned in the previous paragraph and remains less than the height of the cut E. In order to accurately know the positioning dimensions of the comparison plane P2 in the coordinate system XYZ, a positioning dimension measurement is performed (step S520), wherein the distance between the comparison plane P2 obtained after preparation and the reference plane R is measured.

[0064] Knowing precisely the positioning dimensions of the base plane P1 obtained in step S320 and the comparison plane P2 obtained in step S520 allows for the accurate derivation of the distance D between the base plane P1 and the comparison plane P2. Knowing precisely the distance D, as well as the positions of planes P1 and P2 along the radial direction Z, allows for a more accurate evaluation of the principal angle θ, which will be described later.

[0065] The second image I2 is acquired based on the comparison plane P2 (step S600). Figure 6 The second image I2 was obtained in the same manner as the first image I1, that is, by means of photomicrography in the comparison plane P2, and shows the same multiple dendrites 30 as in the first image I1, but in the comparison plane P2.

[0066] Specifically, the acquisition of the second image I2 is performed on a portion of the comparison plane P2 that is similar to a portion of the base plane P1, on which the acquisition of the first image I1 is performed. This portion includes the same portion as the reference notch E, including edge 29 in the comparison plane P2 (i.e., the same edge as in the base plane P1 but offset by a distance D in the radial direction) and end 291 of the edge 29.

[0067] Then analyze the resulting images I1 and I2 (step S700). Figure 7 The analysis of these images specifically includes locating the trunk 32 on each image I1, I2, corresponding to the center of the cross-shaped structure where the dendrites 30 are visible (step S710). In this step, only the position of the center 32 in the XY plane is important. Therefore, Figure 7 The images I1 and I2 shown are in the form of point clouds, symbolizing the center of the cross in planes P1 and P2, respectively, which is the position of the trunk 32 of each dendrite 30.

[0068] Optionally, secondary orientations, particularly secondary angles β and β', can also be measured on each image I1 and I2 (step S720). More specifically, secondary angles β and β' can be measured on image I1 and then checked on image I2 to verify the measurement performed on image I1. In addition to the measurement of the principal angle θ described below, measuring secondary angles β and β' allows for a more accurate assessment of crystallographic orientation differences.

[0069] The above processing can be performed manually by manually measuring the position of each center 32 on images I1 and I2, as well as the secondary angles β and β', or digitally using appropriate digital tools to perform these measurements. It should also be noted that the order of steps S720 is not restrictive; the measurements of the secondary angles β and β' can be performed first on the first image I1, immediately following step S400 of acquiring the first image I1, and then on the second image I2, immediately following step S600 of acquiring the second image I2.

[0070] In step S710, the position of the trunk 32 is measured, allowing for a comparison of the position of the trunk 32 on the base plane P1 (first image I1) and the comparison plane P2 (second image I2) for each dendrite 30. For this purpose, the image processed in step S700 is then subjected to mathematical and / or statistical and / or triangulation processing (step S800).

[0071] During this step, the previously obtained first and second images I1, I2 are superimposed to visualize the positional evolution of the trunk 32 of each dendrite 30 between the base plane P1 and the comparison plane P2 (step S810). A reference notch E, created in step S200 and partially included in images I1 and I2, facilitates this superposition and improves its accuracy. The notch E serves as a reference point by superimposing the edges 29 and ends 291 of each image I1, I2.

[0072] The result of this superposition is illustrated in... Figure 8 middle, Figure 8 Only about ten pairs of points are shown, symbolizing the location of the trunk 32. Each pair of points (e.g., 32a, 32b, 32c) represents the same trunk 32, whose location is slightly offset between the first image I1 and the second image I2 (i.e., between the base plane P1 and the comparison plane P2). This slight offset between planes P1 and P2 is represented by the distance ε.

[0073] Knowing the distance ε (especially its amplitude) of each dendrite 30 visible in images I1 and I2 allows for statistical measurements of all dendrites 30. For example, the set of measured distances ε can be represented as a Gaussian curve, retaining only its peak value as the average offset of the trunk 32. Therefore, precise knowledge of the distance D and the average offset ε allows for the derivation of the principal orientation, and in particular the principal angle θ, through triangulation (step S820).

[0074] Finally, knowing the principal angle θ determined in step S820 and the secondary angles β and β' determined in step S720 allows the Euler angles of the dendrite 30 to be determined, thereby defining the crystal orientation of the blade 10 (step S900). However, it should be noted that this final step S900 (and step S720 for determining the secondary angles β and β') is optional, and the method may stop at step S820, which determines the principal angle θ. In fact, knowing the principal angle θ is crucial because it allows estimation of the crystal orientation difference relative to the radial direction Z, which alone may explain any damage to the blade 10. However, knowing the secondary angles β and β' allows for a more refined assessment of this orientation difference.

[0075] Although the invention has been described with reference to specific embodiments, it will be apparent that modifications and changes can be made to these examples without departing from the overall scope of the invention as defined by the claims. In particular, individual features of the various embodiments shown / mentioned may be combined in other embodiments. Therefore, the specification and drawings should be regarded as illustrative rather than restrictive.

Claims

1. A method for measuring the crystal orientation difference of a single-crystal blade (10), the blade (10) extending radially between a blade root (26) and a blade head (16), and comprising a material formed of dendrites (30), the dendrites (30) having a main trunk (32) extending in a principal direction (Z') between the blade root (26) and the blade head (16) and branches (34) extending transversely to the principal direction (Z'), the method comprising: - Define the reference coordinate system (XYZ) of the blade, the reference coordinate system (XYZ) including the radial direction (Z) of the blade (10). - The blade (10) is mechanically and chemically treated in a base plane (P1) perpendicular to the radial direction (Z) to acquire a first image (I1) in the base plane (P1) by photomicrography. - The blade (10) is mechanically and chemically treated in a comparison plane (P2) that is perpendicular to the radial direction (Z) and radially offset by a predetermined distance (D) relative to the base plane (P1) to acquire a second image (I2) in the comparison plane (P2) by photomicrography. - Process the first image and the second image (I1, I2) to compare the position of the trunk (32) of each dendrite (30) in the two images (I1, I2) and thereby deduce the orientation of the main direction (Z') of the dendrite (30) relative to the radial direction (Z) of the blade (10).

2. The method as described in claim 1, characterized in that, include: Before mechanically and chemically treating the blade (10) in the base plane (P1), a radial reference notch (E) is made, and the base plane (P1) and the comparison plane (P2) are arranged to intersect the reference notch (E).

3. The method as described in claim 2, characterized in that, The first image and the second image (I1, I2) each include at least a portion (29) of the reference cutout (E), and processing the first image and the second image (I1, I2) includes superimposing the first image and the second image (I1, I2) by superimposing the portion (29) of the reference cutout (E).

4. The method according to any one of claims 1 to 3, characterized in that, The base plane (P1) is defined by the radial end (28) of the blade root (26).

5. The method according to any one of claims 1 to 4, characterized in that, The predetermined distance (D) between the base plane (P1) and the comparison plane (P2) is between 0.15 mm and 0.35 mm.

6. The method according to any one of claims 1 to 5, characterized in that, include: Measure the radial positioning of the base plane (P1) relative to the reference plane (R) of the blade (10), and measure the radial positioning of the comparison plane (P2) relative to the reference plane (R).

7. The method as described in claim 6, characterized in that, The reference plane (R) is defined by the radial end of the blade head (16).

8. The method according to any one of claims 1 to 7, characterized in that, The mechanical treatment includes machining and / or polishing the surface of the blade (10) in the base plane (P1) and the comparison plane (P2), and the chemical treatment includes applying acid to the machined and polished surface of the blade (10).

9. The method according to any one of claims 1 to 8, characterized in that, Processing the first and second images (I1, I2) includes analyzing them, the analysis including plotting the position of the trunk (32) of the dendrite (30) in the first image (I1) and in the second image (I2).

10. The method as described in claim 9, characterized in that, include: After analyzing the first image and the second image (I1, I2), mathematical and / or statistical and / or triangulation is performed on the processed images to determine the average principal direction (Z') of the dendrite (30) and to measure the principal angle (θ) between the average principal direction (Z') and the radial direction (Z).

11. The method according to any one of claims 1 to 10, characterized in that, include: For each dendrite (30), the sub-angles (β, β') between the branches (34) of the dendrite (30) are measured on the first image (I1) and the second image (I2).

12. The method as described in claims 10 and 11, characterized in that, include: Determine the Euler angle of the blade (10) defined by the principal angle (θ) and the secondary angles (β, β') of the dendrite (30).

13. The method according to any one of claims 1 to 12, characterized in that, The single-crystal blade (10) is a turbine blade.

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