Method for determining the deformation field of at least one layer of paint applied to a substrate during the curing of the paint layer(s).

Abstract

- Method for determining the strain field of at least one paint layer applied to a substrate during the curing of the paint layer(s). - The determination method comprises a step (E1) of providing a sample (1), a step (E2) of 3D tomographic measurement of the sample (1), and a series of successive steps (S) repeated iteratively, including a step (E3) of dynamic mechanical analysis of the sample (1) subjected to at least one temperature cycle (C), a step (E4) of 3D tomographic measurement of the sample (1), and a step (E5) of determining the strain field of each paint layer (3) of the sample (1). Figure for the abstract: Fig. 1

Description

Title of the invention: Method for determining the deformation field of at least one layer of paint applied to a support during the curing of the paint layer(s). technical field

[0001] The present invention relates to a method for determining the deformation field of at least one layer of paint applied to a support during a crosslinking of the paint layer(s). State of the art

[0002] A fuselage or, more broadly, an aircraft structure (such as a wing, tail assembly, etc.) may comprise different structural layers. These structural layers may be metallic or, more recently, made of composite material, for example, carbon fiber-based.

[0003] Whether the fuselage is metallic or composite, it is painted to give a particular visual appearance, but also for reasons of protection against external aggressions.

[0004] Composite fuselages, and more broadly the main composite structures of aircraft, comprise a stack of layers of carbon fiber-based composite material. Once the composite fuselage or composite structure is manufactured, it must be painted to reflect the colors of the airline owning the aircraft and to protect it from external elements. This is achieved by applying various layers of material and paint to the topmost layer.

[0005] Generally, a first layer, corresponding to a lightning protection layer, can be applied to the last fold of the fuselage or structure. This lightning protection layer comprises a lightning-resistant copper foil embedded in a polymer film containing glass fibers to facilitate handling and application of the copper foil.

[0006] A base coat and an outer coat of primer can be applied to this lightning protection layer. These primer coats include ceramic pigments to obtain a white color onto which the airline logo can be applied.

[0007] On these primer layers, an intermediate coating can be applied which promotes stripping of the layers in the event that it is necessary to repaint the fuselage or the structure.

[0008] Finally, on the intermediate coating, a base coating can be applied followed by a transparent coating which brings shine to the fuselage or structure.

[0009] These different layers are applied to the last ply of the fuselage or structure after autoclave curing and prior application before polymerization of the lightning protection layer. It should be noted that the polymerization of the composite forming the fuselage or structure equipped with the lightning protection layer may exhibit residual stresses after curing due to an asymmetry introduced in the construction of the composite forming the fuselage or structure by the addition of the lightning protection layer and depending on the cooling cycle applied following curing.

[0010] The coatings are applied after curing by spraying at room temperature. It is therefore necessary to wait a certain amount of time, on the order of several hours, between the application of each coat to allow for drying by polymerization or cross-linking of each layer. Thus, the total cycle time for painting an aircraft is approximately three weeks.

[0011] Other embodiments are conceivable for applying the different layers such as layers applied by molding and compression.

[0012] The aircraft is then delivered to the airline that operates it. The aircraft is then subjected to temperature cycles generally ranging on average from -55°C in flight to 85°C on the ground. However, it has sometimes been observed that, when the aircraft is delivered to the airline, the polymerization or crosslinking of the different strains is not yet complete. Each layer continues its polymerization or crosslinking independently of the others. Their respective properties continue to evolve since the molecular chains are not fixed. The layers are therefore not in a thermostable configuration when the aircraft is delivered.

[0013] Consequently, during the aging of the layers, defects may appear on the fuselage or structural surface because they are more sensitive to thermal stresses, ultraviolet radiation, water, or oxidation, which accelerates the aging of the layers. Furthermore, the release of volatiles present in the layers during the crosslinking or polymerization process increases the internal stresses within the layers, which can cause cracking, blistering, etc., in the layers.

[0014] It can therefore be important to understand the phenomena involved during the crosslinking or polymerization of the layers, and in particular to detect how the layers evolve during their crosslinking or polymerization. Understanding these phenomena makes it possible to seek improvements in the application process of the layers and / or in the chemical formulation of the layers. Description of the invention

[0015] The present invention aims to provide a method for understanding the phenomena involved during the crosslinking or polymerization of layers and in particular to detect how the layers evolve during their crosslinking or polymerization.

[0016] For this purpose, it relates to a method of determining a deformation field of at least one layer of paint applied to a support during a crosslinking of the layer or layers of paint.

[0017] According to the invention, the determination process comprises the following steps: - a step of making available a sample comprising the support and the layer or layers of paint applied to the support; - a first step of three-dimensional tomographic measurement of the sample to obtain a first three-dimensional image of the sample; - a set of successive steps repeated iteratively until the difference between a loss modulus for a current iteration and a loss modulus obtained for a previous iteration is less than or equal to a predetermined threshold: • a step of dynamic mechanical analysis of the sample subjected to at least one temperature cycle evolving between a predetermined minimum temperature and a predetermined maximum temperature, to obtain a loss modulus of the sample, • a second three-dimensional tomographic measurement step of the sample to obtain a second three-dimensional image of the sample, • a step of determining a deformation field of each paint layer of the sample from the first image and the second image, the first image of the current iteration corresponding to the second image of the previous iteration.

[0018] Thus, by determining the loss modulus, the evolution of the crosslinking of the paint layer(s) can be monitored while simultaneously observing the deformations of the paint layer(s) using tomographic measurements. The number of tests is therefore limited to what is necessary.

[0019] Furthermore, the step of determining a deformation field includes: - a first sub-step of determining a displacement field between the first image and the second image by a volumetric image correlation, - a second sub-step of determining a deformation field of the paint layer(s) from the displacement field.

[0020] Advantageously, the first substep of determination includes calculating the argument of the minimum of a residual correlation field from the following relation: = +u(x)) -f(x) ]2dx' in which: ROI corresponds to a region of interest in which a displacement field analysis is performed, x corresponds to the coordinates of any voxel in the region of interest, / (x) corresponds to a grey level volume in the region of interest of the reference image, g(x) corresponds to a grey level volume in the region of interest of the deformed image, it (X) corresponds to the displacement field to be determined, corresponds to the residual correlation field.

[0021] Furthermore, the second sub-step of determination includes the calculation of the derivative of the displacement field to obtain the deformation field.

[0022] Furthermore, the first tomographic measurement step and the second tomographic measurement step are implemented by an X-ray microtomography measurement device.

[0023] In addition, the dynamic mechanical analysis step includes the implementation of mechanical boundary conditions on the sample at a predetermined frequency while the sample is subjected to at least one temperature cycle.

[0024] For example, the mechanical boundary conditions on the sample correspond to a bending at three points of the sample at a frequency of 1 Hz.

[0025] Furthermore, the temperature cycle corresponds to: - a gradual temperature increase from ambient temperature to the predetermined maximum temperature, then - a first plateau at the predetermined maximum temperature for a predetermined duration, then - a gradual temperature change from the predetermined maximum temperature to the predetermined minimum temperature, then - a second stage at the predetermined minimum temperature for a predetermined duration until the end of the temperature cycle.

[0026] Furthermore, the method includes a step of analyzing an evolution of the deformation field of the paint layer(s) from the deformation field(s) determined for each iteration of implementation of the set of successive steps, the analysis step being implemented after the last iteration of the set of successive steps S. Brief description of the figures

[0027] The accompanying figures will clearly illustrate how the invention can be implemented. In these figures, identical reference numerals designate similar elements.

[0028] Fig. 1 schematically represents the determination process.

[0029] Fig. 2 represents a cross-section of an example sample.

[0030] Figure [Fig. 3] represents a time evolution curve of temperature during a temperature cycle.

[0031] Fig. 4 represents a time evolution curve of the loss modulus.

[0032] Fig. 5 represents on the left a dynamic mechanical analysis machine comprising a sample and on the right a sample subjected to a three-point stress in the dynamic mechanical analysis machine. Detailed description

[0033] The method for determining a deformation field (hereinafter referred to as the "determination method") is schematically represented in [Fig. 1].

[0034] The determination method corresponds to a method for determining the deformation field of at least one paint layer 3 applied to a support 2 during a crosslinking of the paint layer(s) 3. This determination method also allows observation of the evolution of the deformation field.

[0035] The determination method includes a step 11 of providing a sample 1 comprising the substrate 2 and the paint layer(s) 3 applied to the substrate 2. During this step 11 of providing the sample, a representative sample 1 of the paint layer(s) 3 and the substrate 2 of a structural part is manufactured. The structural part may be an aircraft fuselage, a boat hull, or any other structure comprising at least one paint layer applied to a substrate.

[0036] In one embodiment of sample 1, the support 2 corresponds to a composite support comprising three plies having carbon fibers substantially parallel to each other in order to hold a layer of glossy primer and / or a transparent layer.

[0037] Figure 2 shows an example of a sample 1. In this example, the sample 1 provided comprises several layers 3 applied to a support 2. The sample 1 in this example comprises a first layer 4, which is a lightning strike protection layer. This lightning strike protection layer may include a lightning-resistant copper foil embedded in a polymer film containing glass fibers to facilitate handling and application of the copper foil.

[0038] Sample 1, according to the example, comprises a second layer 5 which corresponds to a basic primer layer and a third layer 6, which corresponds to an external primer layer. The second layer 5 and the third layer 6 are applied over the first layer 4. They contain ceramic pigments to obtain a white color onto which the airline logo can be applied.

[0039] Sample 1 according to the example includes a fourth layer 7 applied over the third layer 6. The fourth layer 7 corresponds to an intermediate coating which facilitates stripping of the layers in the event that it is necessary to repaint the fuselage or the structure.

[0040] Finally, sample 1 according to the example comprises a fifth layer 8 and a sixth layer 9 applied over the fourth layer 7. The fifth layer 8 and the sixth layer 9 correspond to a base coat and a transparent coating, respectively. The fifth layer 8 and the sixth layer 9 impart gloss to the fuselage or structure.

[0041] The determination method further comprises a first three-dimensional tomographic measurement step E2 of the sample 1 to obtain a first three-dimensional image of the sample 1. The first three-dimensional image of the sample 1 obtained in the first tomographic measurement step E2 may correspond to a three-dimensional grayscale image. The difference between grayscale levels corresponds to the difference in atomic density of the materials and therefore to the different materials of the paint layers 3.

[0042] The first image obtained in the first step E2 of tomographic measurement can be stored in a memory.

[0043] The first tomographic measurement step E2 can be implemented using an X-ray microtomography measuring device. This measurement method is non-destructive. It allows the microstructure of a material to be digitized in grayscale voxels via a three-dimensional image. The first tomographic measurement step E2 provides the first three-dimensional image, which corresponds to a reference scan of sample 1. Thus, in this first step E2, the first image corresponds to a reference image in which crosslinking has just begun.

[0044] The X-ray microtomography measurement device can correspond to an X-ray synchrotron of the "European Synchrotron Radiation Facility" (ESRF) in Grenoble or to a conventional laboratory X-ray tomograph.

[0045] Furthermore, the determination process comprises a set of successive steps S. This set of successive steps S is repeated iteratively until a difference (in absolute value) between, on the one hand, a loss modulus of sample 1 for a current iteration and, on the other hand, a loss modulus of sample 1 obtained for a previous iteration is less than or equal to a predetermined threshold. The predetermined threshold is determined to indicate that the loss modulus is approaching a plateau. Indeed, the smaller the difference between the loss moduli of two successive iterations, the more the loss modulus is approaching a plateau. For example, the predetermined threshold could be approximately zero or a value close to zero, meaning that the loss modulus is no longer changing significantly.

[0046] Each iteration corresponds to at least one test performed on sample 1.

[0047] The set of successive steps S includes a step E3 of dynamic mechanical analysis of the sample 1, a second step E4 of tomographic measurement and a step E5 of determination of a deformation field of each layer of paint 3.

[0048] Step E3 of dynamic mechanical analysis (DMA) can be implemented using a dynamic mechanical analysis machine 10 (drawing (A) in Figure 5). Dynamic mechanical analysis is a technique for studying and characterizing the mechanical properties of viscoelastic materials, such as polymers, under dynamic (stress) and thermal loading. Dynamic mechanical analysis allows the determination of a complex modulus E* of the form: E* - E + iE”, where E' corresponds to the conservation modulus characteristic of the elastic response of the analyzed material and E" corresponds to the loss modulus characteristic of the viscous response of the analyzed material. The loss modulus is generally expressed in Pascals. The loss modulus can be determined by a processor from measurements obtained by the dynamic mechanical analysis machine 10.

[0049] The analysis machine can correspond to the DMA Q800 from TA Instruments or the DMA +1000 from Metravib.

[0050] In step E3 of the dynamic mechanical analysis, sample 1 is subjected to at least one temperature cycle C, evolving between a predetermined minimum temperature T- and a predetermined maximum temperature T+, to obtain the loss modulus of sample 1. Without limitation, the predetermined maximum temperature T+ may be within a range between 60°C and 70°C, and the predetermined minimum temperature may be within a range between -40°C and -30°C. The temperature cycles may be implemented at a predetermined frequency.

[0051] Figure 3 represents an example of a temperature cycle C. In this example, the temperature cycle C corresponds to: - a progressive temperature evolution from an ambient temperature Ta (in which sample 1 is initially located) to the predetermined maximum temperature T+, then - a first SI step at the predetermined maximum temperature T+ for a predetermined duration tl, then - a gradual temperature change from the predetermined maximum temperature T+ to the predetermined minimum temperature T-, then - a second stage S2 at the predetermined minimum temperature T- for a predetermined duration t2 until the end of the temperature cycle C.

[0052] The E3 step of dynamic mechanical analysis may include the implementation of mechanical boundary conditions on sample 1 at a predetermined frequency while sample 1 is subjected to at least one temperature cycle C.

[0053] The mechanical boundary conditions on sample 1 can correspond to a three-point bending PI, P2, P3 of sample 1 at a frequency of 1 Hz, as shown in drawing (B) of [Fig. 5]. The three-point bending corresponds to the application of a predetermined force Fl at point PI and the application of a force F2 at point P2 and a force F3 at point P3 on either side of point PL. The forces Fl, F2, and F3 are collinear. The force Fl has the opposite direction to the forces F2 and F3.

[0054] The sequence of successive steps S further includes a second three-dimensional tomographic measurement step E4 of sample 1 to obtain a second three-dimensional image of sample 1. The second tomographic measurement step E2 makes it possible to obtain the second three-dimensional image, which corresponds to a scan of sample 1 after the dynamic mechanical analysis step E3. The second image is therefore substantially different from the first image. The second image obtained in the second tomographic measurement step E4 can be stored in memory.

[0055] The second step E4 of tomographic measurement can also be implemented using an X-ray microtomography measurement device. The X-ray microtomography measurement device can also correspond to an X-ray synchrotron of the "European Synchrotron Radiation Facility" (ESRF) in Grenoble or to a conventional laboratory X-ray tomograph.

[0056] The set of successive steps S further includes a step E5 for determining a deformation field of each paint layer 3 of the sample 1 from the first and second images. The determination step E5 can be implemented by a processor.

[0057] The first image of the current iteration of implementation of the sequence of successive steps S corresponds to the second image of the previous iteration of implementation of the sequence of successive steps S.

[0058] The deformation field for each iteration can be stored in memory.

[0059] Step E5 for determining a deformation field may include a first substep E51 for determining a displacement field between the first and second images by volumetric image correlation. Step E5 may also include a second substep E52 for determining a deformation field of the paint layer(s) from the displacement field.

[0060] Digitizing sample 1 yields gray levels assigned to voxels. Thus, by comparing a reference volume f(x) of the first image with a reference volume g(x) using volumetric correlation, it is possible to determine a displacement field u(x) between the two volumes. The principle of volumetric image correlation relies on the assumption of gray level conservation. This volume displacement allows us to obtain a deformation field of the different paint layers 3 of sample 1.

[0061] Advantageously, the first substep E51 of determination may include calculating the argument of the minimum of a residual correlation field from the following relation: ^JroiUC +u(x)) -f(x) ]2dx' in which: ROI corresponds to a region of interest in which a displacement field analysis is performed, x corresponds to the coordinates of any voxel in the region of interest, f(x) corresponds to a gray level volume in the region of interest of the reference image, g(x) corresponds to a gray level volume in the region of interest of the deformed image, il(X) corresponds to the displacement field to be determined, and corresponds to the residual correlation field.

[0062] The second substep E52 of determination may include the calculation of the derivative of the displacement field to obtain the deformation field.

[0063] As previously stated, the set of successive steps S is repeated iteratively until the difference between, on the one hand, a loss modulus of sample 1 for a current iteration and, on the other hand, a loss modulus of sample 1 obtained for a previous iteration is less than or equal to a predetermined threshold. Indeed, the number of iterations is determined based on the loss modulus, which is representative of the overall viscosity of the paint layers 3 of sample 1, to which each paint layer 3 contributes. When a material reaches the end of curing, the loss modulus changes very little. It is therefore It is possible to monitor the evolution of the behavior of sample 1 only during the loss modulus evolution phase. Indeed, it is during this period that the phenomena generating the defect appear.

[0064] Figure 4 shows an example of a time-dependent loss modulus curve. During a time D between time i and time i+n, the loss modulus increases from E'^ to E"M, reaching a plateau where the loss modulus changes very little. Thus, by determining the difference between, on the one hand, a loss modulus of sample 1 for a current iteration and, on the other hand, a loss modulus of sample 1 obtained for a previous iteration, it is possible to limit the number of iterations based on the evolution of the loss modulus.

[0065] After the last iteration of the set of successive steps S, the determination process may include a step E6 of analysis of an evolution of the deformation field of the paint layer(s) 3 from the deformation field(s) determined in step E5 for each implementation iteration of the set of successive steps S. The analysis step E6 may be implemented by a processor or by an operator from the deformation field(s) which may be stored in memory.

[0066] The ability to limit the number of iterations using the loss module addresses an industrial constraint where the number of tests performed must remain relevant to the time and financial constraints of aircraft manufacturing. Thus, it is possible to perform a series of temperature cycles in the dynamic mechanical analysis machine 10 and construct the evolution of the loss module ([Fig. 4]). This allows us to determine the range within which the loss module's evolution phase lies and therefore to determine the strictly necessary number of temperature cycles. Tests performed according to this method provide information much more quickly than tests carried out under real-world conditions.

[0067] Thus, in just two or three iterations, it is possible to reconstruct the profile of the different paint layers 3 of the sample and to analyze which paint layer(s) 3 are responsible for the defect. Indeed, thanks to the images obtained, the deformation levels of the layers of the sample 1 can be detected, and it is possible to determine when a deformation becomes too great: in this case, the stress level generated by this deformation can lead to the formation of a crack. The analysis of the evolution of the deformation field can help to determine the paint layer(s) 3 responsible for the origin of a defect appearing through crosslinking. For example, a single paint layer can be the origin of a defect appearing on another paint layer. Thus, the analysis The evolution of the deformation field makes it possible to determine the paint layer that caused the defect.

[0068] Following this determination process, it is therefore possible to identify the paint layer(s) 3 responsible for the defect and thus to: - to work on the industrial coating deposition process in order to eliminate or limit deformations, through better consideration of the crosslinking of paint layers 3: recommendations for drying time, drying accelerator, and / Or - modify the chemical formulation of the paint layer(s) 3 so that it adopts a behavior during curing that does not generate excessive deformations, and / or - use 3 coats of paint whose curing is already advanced at the time of application, and / or - use a catalyst to accelerate crosslinking or an external means of acceleration such as UV radiation lamps.

[0069] This reduces manufacturing time by targeting the layer(s) requiring action. Furthermore, this process is easily applicable to new materials and allows for reliable results to be obtained from the very first aircraft.

Claims

Demands

1. A method for determining a deformation field of at least one paint layer (3) applied to a substrate (2) during curing of the paint layer(s) (3), characterized in that it comprises the following steps: - a step (El) of making available a sample (1) comprising the support (2) and the layer or layers of paint (3) applied to the support (2); - a first step (E2) of three-dimensional tomographic measurement of the sample (1) to obtain a first three-dimensional image of the sample (1); - a set of successive steps (S) repeated iteratively until the difference between a loss modulus for a current iteration and a loss modulus obtained for a previous iteration is less than or equal to a predetermined threshold: • a step (E3) of dynamic mechanical analysis of the sample (1) subjected to at least one temperature cycle (C) evolving between a predetermined minimum temperature (T-) and a predetermined maximum temperature (T+), to obtain a loss modulus of the sample (1), • a second step (E4) of three-dimensional tomographic measurement of the sample (1) to obtain a second three-dimensional image of the sample (1), • a step (E5) of determining a deformation field of each paint layer (3) of the sample (1) from the first image and the second image, the first image of the current iteration corresponding to the second image of the previous iteration.

2. Method according to claim 1, characterized in that step (E5) of determining a deformation field comprises: - a first sub-step (E51) of determining a displacement field between the first image and the second image by a volumetric image correlation, - a second sub-step (E52) of determining a deformation field of the paint layer(s) from the displacement field.

3. A method according to claim 2, characterized in that the first substep (E51) of determination comprises the calculation of the argument of the minimum of a residual correlation field from the following relation: ^Mroi^ +u(x) ) -f(x) ]2dr in which: ROI corresponds to a region of interest in which a displacement field analysis is performed, x corresponds to the coordinates of any voxel in the region of interest, f (x) corresponds to a gray level volume in the region of interest of the reference image, g(x) corresponds to a gray level volume in the region of interest of the deformed image, u ( x ) corresponds to the displacement field to be determined, corresponds to the residual correlation field.

4. A method according to any one of claims 2 and 3, characterized in that the second substep (E52) of determination includes the calculation of the derivative of the displacement field to obtain the strain field.

5. A method according to any one of claims 1 to 4, characterized in that the first tomographic measurement step (E2) and the second tomographic measurement step (E4) are implemented by an X-ray microtomography measurement device.

6. A method according to any one of claims 1 to 5, characterized in that the step (E3) of dynamic mechanical analysis comprises the implementation of mechanical boundary conditions on the sample (1) at a predetermined frequency while the sample (1) is subjected to at least one temperature cycle (C).

7. Method according to claim 6, characterized in that the mechanical boundary conditions on the sample (1) correspond to a bending at three points (PI, P2, P3) of the sample (1) at a frequency of 1 Hz.

8. A method according to any one of claims 1 to 6, characterized in that the temperature cycle (C) corresponds to: - a progressive temperature evolution from an ambient temperature (Ta) to the predetermined maximum temperature (T+), then - a first plateau (S1) at the predetermined maximum temperature (T+) for a predetermined duration (t1), then - a progressive temperature evolution from the predetermined maximum temperature (T+) to the predetermined minimum temperature (T-), then - a second plateau (S2) at the predetermined minimum temperature (T-) for a predetermined duration (t2) until the end of the temperature cycle (C).

9. A method according to any one of claims 1 to 8, characterized in that it comprises a step (E6) of analyzing an evolution of the deformation field of the paint layer(s) (3) from the deformation field(s) determined for each implementation iteration of the set of successive steps (S), the analysis step (E6) being implemented following the last iteration of the set of successive steps S.

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