A method to produce a component made of composite material including its fatigue design

Abstract

Method to produce a component (1) made of composite material including one or more plies (2, 3) associated with each other. Said method involves a series of steps (4) for the fatigue design of said component (1), including : (A) a first step in which a discretized model (5) is generated, for instance through a finite element model of the component (1), in which at least a first ply (2) and if appropriate at least a second ply (3) are divided, respectively, into two or more first portions (6) and two or more second portions (7), (B) a second step in which it is defined the location of one or more first damage initiation sites (8) and one or more second damage initiation sites (9), respectively within each of the two or more first portions (6) and in each of the two or more second portions (7), (C) a third step, in which a fatigue strength parameter is assigned to each of the damage initiation sites, (D) a fourth step, in which a load history to be simulated on the component is established, based on specific loading conditions, the total number of cycles (NC) to be simulated is divided into discrete blocks of cycles, assigning a loading condition for each block of cycles.

Description

[0001] A METHOD TO PRODUCE A COMPONENT MADE OF COMPOSITE MATERIAL INCLUDING ITS FATIGUE DESIGN

[0002] ***

[0003] The present invention relates to a method to produce a component made of composite material, including the step of fatigue designing it.

[0004] In the present text, "component made of composite material" means an artifact including one or more plies, reinforced, for instance, with continuous, discontinuous, or particulate fibers, associated with each other according to a specific overlapping series such that the respective reinforcements are oriented in a specific way with respect to a reference direction; said ply overlapping series is referred to as a "laminate".

[0005] In the present text, "lay-up" means a set of information aimed at defining the configuration of a laminate; said information can include, for instance: the material of the matrix of each ply, the material of the reinforcement of each ply, the elastic properties of each ply, the orientation of the reinforcement of each ply with respect to a reference direction, the thickness of each ply, and the ply overlapping series.

[0006] By the method according to the present invention, various typologies of structural elements can be produced, such as for instance: wind turbine blades, bicycle frames, pressure vessels, vehicle or aircraft components, etc...

[0007] When subjected to time-varying loads, composite laminates are progressively damaged; the gradual evolution of the damage leads to a reduction in the stiffness of the laminate from the first load application cycles, while the final failure of the component (separation into two or more parts) can also occur after a very high number of load cycles (even millions). It should be noted that the main damage events in composite laminates can include matrix cracks, delaminations (detachment between adjacent plies), and reinforcement failure.

[0008] Currently, methods are known to produce a composite laminate through an initial fatigue design step based on a so-called "damage- tolerant" approach using so-called "damage evolution" models.

[0009] It should be noted that the fatigue design based on a damage- tolerant approach is carried out by allowing the presence of damage events, provided that these do not cause, for instance, a component stiffness reduction below a certain threshold or the ability of the component to withstand a predetermined operational load.

[0010] It should also be noted that damage evolution models are models that allow to predict both the stiffness variation over time and the fatigue life of a composite laminate.

[0011] In patent EP2803968B1, owned by Siemens, a method is described, for instance, to produce a structural element made of composite material, including its fatigue design, through which the fatigue life of a structure is predicted. The fatigue design includes several steps. In a first step, the structure is modelled by a series of calculation points. Subsequently, for each point, the stresses and deformations caused by the load cycles and the hysteresis branches that define them are determined. Then, an accumulated damage due to the load cycles is predicted and recorded. For the prediction, first, using a hysteresis operator, a variation in stress along a portion of a hysteresis branch is calculated as a function of a time-varying load and, second, using the variation in stress and the recorded accumulated damage, a damage variation is calculated. Then, a variation in properties, including the structure stiffness, is also calculated. Then, a further variation in stresses and deformations is calculated based on the variation of these properties, to determine a new adapted hysteresis branch. Then, a further variation in stress along a further portion of the adapted hysteresis branch is calculated as a function of a further time-varying load.

[0012] At the end of the process, if no fatigue failure occurs, the structure is manufactured with the material, properties, and dimensions as specified by the model; otherwise, the model is adapted, and the life performance prediction is repeated.

[0013] In EP2803968B1, finite element analyses are used to determine the stress state in a structure, for instance, a composite structure. A series of loads is applied to the structure, and at each iteration, a continuous damage parameter is calculated for each element, based on local stresses. Based on said damage parameter, the material stiffness is updated, and the occurrence of the final failure is assessed.

[0014] However, the method described in said Siemens patent has some limits.

[0015] Indeed, it predicts the stiffness of the laminate without considering the presence of single damage events, such as matrix cracks, delaminations, and reinforcement failure, but instead by linking it through an empirical relationship to a single continuous damage parameter (a continuum damage mechanics approach). An approach of this type first requires expensive experimental campaigns to obtain the relationship between said damage parameter and said elastic properties of the laminate, a relationship that can also vary depending on the laminate lay-up and the type of load it is subjected to. Furthermore, said approach, using a continuous relationship between the number of cycles and the laminate stiffness, assumes that the damage is uniformly distributed within a given physical domain (such as an element of a finite element analysis or a component). This does not allow for an accurate prediction of fatigue damage in a structural element, especially if its geometry is relatively irregular or if said element includes discontinuities, such as for instance holes or surface irregularities, which are critical in real-world applications, at which even very sharp high-stress gradients are present, causing a damage localization.

[0016] The main task of the present invention is to overcome the above- mentioned drawbacks and, in particular, to produce a component made of composite material from a fatigue life design that allows for more accurate damage prediction by predicting single damage events as well-defined entities in space and time (a "discrete damage mechanics" approach) and correlating the laminate stiffness to their presence. Said approach can provide accurate predictions even in the presence of even very sharp stress gradients. A further advantage is the ability to predict the behaviour of the component even when the laminate lay-up and loading condition vary, once some basic material properties are known.

[0017] In the scope of said task, an object of the present invention is to accelerate the design, and thus the production, of a composite component optimized to withstand time-varying loads, by providing an accurate prediction of the physical damage evolution, further allowing to reduce time and costs relevant to experimental material characterization and design validation tests.

[0018] One aspect of the present invention concerns a method to produce a composite component having the features of claim 1.

[0019] Other advantageous features of the present invention are reported in the dependent claims.

[0020] The features and advantages of the present invention will become more apparent from the following exemplary and non-limiting description referred to the attached schematic drawings to one embodiment of the invention, in which:

[0021] - Figure 1 schematically illustrates a regularly shaped component having two plies by way of example; - Figure 2 schematically illustrates a discretized model, for instance using the finite element method, generated from the component of Figure 1;

[0022] - Figure 3 schematically illustrates the discretized model of Figure 2, in which damage initiation sites are highlighted;

[0023] - Figure 4 schematically illustrates a block diagram of the method according to the invention;

[0024] - Figure 5 schematically illustrates step (A) indicated in the block diagram of Figure 4;

[0025] - Figure 6 schematically illustrates step (B) indicated in the block diagram of Figure 4;

[0026] - Figure 7 schematically illustrates step (C) indicated in the block diagram of Figure 4;

[0027] - Figure 8 schematically illustrates step (D) indicated in the block diagram of Figure 4;

[0028] - Figure 9 schematically illustrates sub-step (DI) indicated in the block diagram of Figure 8;

[0029] - Figure 10 schematically illustrates sub-step (D2) indicated in the block diagram of Figure 8;

[0030] - Figure 11 schematically illustrates sub-step (D3) indicated in the block diagram of Figure 8;

[0031] - Figure 12 schematically illustrates sub-step (D4) indicated in the block diagram of Figure 8.

[0032] The present invention relates to a method to produce a component 1 made of composite material including at least a first ply 2 and if appropriate at least a second ply 3 associated with each other.

[0033] Advantageously, the first ply 2 and / or the second ply 3 are reinforced, for instance, with continuous, discontinuous, or particulate fibers appropriately oriented with respect to a reference direction 11. As indicated above, it should be noted that the method according to the invention can also be used to produce structural elements including a single ply or, alternatively, a plurality of plies. In the present text, the configuration of the laminate that constitutes the component 1 (also referred to as "lay-up") is defined, for instance, by the series of the one or more plies 2, 3 that make it up, the orientation of the reinforcement of each ply 2, 3 with respect to the reference direction 11, the thickness of each ply 2, 3, the matrix material, the reinforcement material (for instance continuous fibers) of each ply 2, 3, and the elastic properties of each ply.

[0034] The method according to the invention involves a series of steps 4 through which the fatigue design of the component 1 is carried out. Said series of steps 4 includes a first step A in which a discretized model 5 is generated, for instance, through a finite element model of the component 1, in which the first (or single) ply 2 and / or the second ply 3 are divided, respectively, into two or more first portions 6 and two or more second portions 7.

[0035] In advantageous embodiments of the method according to the finding, a virtual three-dimensional model of the component 1, not illustrated in the attached figures, can be generated using any three- dimensional model software (CAD) among those available on the market.

[0036] In said advantageous embodiments, through the virtual three- dimensional model, first information aimed at describing the overall geometry of the component 1 is provided to a finite element software (SW-FEM); then, through the finite element software SW-FEM, the virtual three-dimensional model can be discretized according to a finite element discretization, thus obtaining the discretized model 5. In other advantageous embodiments of the method according to the finding, finite element model can take place entirely within the finite element software SW-FEM. In advantageous embodiments, within the finite element software SW-FEM, second information relevant to the lay-up of the laminate

[0037] 1 can be assigned to the discretized model 5, as well as third information aimed at describing the elastic properties of the first ply

[0038] 2 and the second ply 3. The third information can include, for instance, the longitudinal elastic modulus, the transversal elastic modulus, the Poisson's coefficient, and the shear modulus, etc., for each of the plies 2 and 3.

[0039] Advantageously, the first information aimed at describing the overall geometry of the component 1, the fourth information aimed at describing the finite element discretization of the discretized model 5, i.e., its division into the two or more first portions 6 and the two or more second portions 7, the second information relevant to the lay-up of the laminate 1, and the third information aimed at describing the elastic properties of the first ply 2 and the second ply

[0040] 3 are stored in a first database DB1.

[0041] Said series of steps 4 further includes a second step B in which it is defined the location of one or more first damage initiation sites 8 and one or more second damage initiation sites 9, respectively within each of the two or more first portions 6 and each of the two or more second portions 7.

[0042] In advantageous embodiments, through an appropriate calculation tool SW-CAL, it is defined the location of the one or more first damage initiation sites 8 and the one or more second damage initiation sites 9 in each of the two or more first portions 6 and each of the two or more second portions 7, based on the fourth information aimed at describing the finite element discretization of the discretized model 5, stored in the first data collection DB1; by way of example, the location of the one or more first damage initiation sites 8 and the one or more second damage initiation sites 9 may be in the same position, respectively, as the barycenter of one or more first sub-divisions 61 and with the barycenter of one or more second sub-divisions 71; the geometry of which can be decided by the user.

[0043] The location of the one or more first damage initiation sites 8 and the location of the one or more second damage initiation sites 9 is advantageously stored in said first database DB1.

[0044] Said locations can be arbitrarily selected and can refer, for instance, to the initiation of matrix cracks, delaminations, or reinforcement failure. If appropriate, pre-existing damage events can also be inserted into the structure.

[0045] Said series of steps 4 further includes a third step C, in which a fatigue strength parameter is assigned to each of the first damage initiation sites 8 and the second damage initiation sites 9, for instance, based on fifth information aimed at describing the fatigue behaviour of a material. Said fifth information is stored in a second database DB2, interconnected with said first database DB1.

[0046] In advantageous embodiments, the fifth information can include the relationship between fatigue strength and the number of cycles for the initiation of damage events (S-N curve), the statistical distribution of fatigue strength, the initial dimensions of the damage events, the law of damage propagation (for instance a relationship between the propagation speed and the elastic energy release rate). Said series of steps 4 further includes a fourth step D, in which a load history to be simulated on the component is established, and the total number of cycles NC to be simulated is divided into discrete blocks of cycles, assigning a loading condition for each block of cycles. The fewer the cycles contained in each block, the more accurate the damage prediction, however implying longer analysis times.

[0047] For each block of cycles, a calculation is carried out, including the following steps: • (DI) calculate one or more load parameters for each element of the discretized model,

[0048] • subsequently, perform, in parallel to each other if appropriate, the steps of o (D2) for each damage initiation site, calculate a damage initiation parameter PID using a fatigue damage initiation model Ml, if said parameter for one or more of said initiation sites reaches a predetermined initiation value, place a damage event on said initiation site. Furthermore, if the dimensions of the placed damage event exceed the perimeter of the element where the damage initiation site is located, the excess part of the damage event is placed in the adjacent element;

[0049] • and o (D3) for each damage event initiated in any previous block of cycles, calculate a damage propagation controlling parameter PCPD using a fatigue damage propagation model M3, and subsequently update the dimensions of each damage event. If the dimensions of the damage event after its propagation exceed the perimeter of the element where the damage event end was before its propagation, the excess part is placed in the adjacent element,

[0050] • (D4) calculate updated elastic properties for each portion (6, 7) of each ply based on the damage events located therein, using an appropriate model M4.

[0051] Said step D is carried out in detail as follows. The calculation of one or more load parameter for each element in sub-step DI, is carried out through a finite element analysis operated on said discretized model 5, said finite element analysis being based on elastic properties calculated at the end of the previous block of cycles (or the initial properties when the calculation is carried out for the first block of cycles) of each said portion of said first ply 2 and said second ply 3, applying to said discretized model 5 the loading conditions relevant to the block of cycles being analyzed. The load parameters are stored in a third database DB3.

[0052] Preferably, sub-step D2 produces for each of said one or more first damage initiation sites 8 and for each of said one or more second damage initiation sites 9, based on said load parameters acting on the element in which said damage initiation sites are located, the calculation of said damage initiation parameter PID using an appropriate damage initiation model Ml for fatigue damage and a stress redistribution model in the presence of damage M2. The damage events to be considered for the stress redistribution and for the PID calculation, are those located within the element where the initiation site is located, and if appropriate, also in adjacent elements, up to a distance that can be set by the user, for instance, based on the laminate features. If for one or more of said first damage initiation sites 8, or for one or more of said second damage initiation sites 9, said initiation parameter reaches a determined initiation value, a damage event is placed at the initiation site, through information adapted to define the location of one or more parts of said damage event in one or more portions of the pertaining ply.

[0053] In conclusion, in said sub-step D2, all the damage events initiated within the block of cycles being analyzed are placed.

[0054] Said information is collected in a fourth database DB4.

[0055] Preferably, sub-step D3 produces for each of said damage events initiated in the previous blocks of cycles, the calculation of said damage propagation controlling parameter PCPD using a fatigue damage propagation model M3 and a stress redistribution model in the presence of damage M2. The damage events to be considered for the stress redistribution and for the PCPD calculation are those located within the element where the damage event end was before its propagation, and, if appropriate, also in adjacent elements, up to a distance that can be set by the user, for instance, based on the laminate features. Based on the propagation, the dimensions of each damage event initiated in the previous blocks of cycles are updated (for instance, in the case of a crack, the location of its apexes). Said information is collected in the fourth database DB4.

[0056] If the dimensions of the damage event after its propagation exceed the perimeter of the element where the damage event end was before its propagation, the excess part is placed in the adjacent element. For instance, a crack after propagation can have an apex with coordinates outside the perimeter of the element where it ended before its propagation. In this case, the excess distance beyond the perimeter is reported to the adjacent element.

[0057] Preferably, sub-step D4 performs the calculation of first elastic properties and second updated elastic properties (or at the end of the block of cycles being analyzed), respectively, of each said portion of said first ply 2 and, if appropriate, said second ply 3, based on the mentioned model M4 for calculating apparent elastic properties based on the damage events located therein.

[0058] In practice, the elastic properties of each ply portion are updated based on the current damage. For this purpose, said model M4 for calculating the apparent elastic properties of a ply in a laminate is provided as an input. The elastic properties of the damaged plies of each element are updated in the finite element software based on the new values calculated.

[0059] Step D provides that sub-steps D1-D4 are repeated until an unacceptability condition is reached or the user-specified number of cycles NC is reached. Furthermore, in step D, external models Ml- M4 are used as inputs to the method, which are themselves known. For instance, said model Ml for the initiation of matrix cracks and for the initiation of delaminations is respectively described in the articles Carraro PA, Quaresimin M, A damage-based model for crack initiation in unidirectional composites under multiaxial cyclic loading, Composites Science and Technology 2014; 99: 154-163 and Maragoni L, Carraro PA, Quaresimin M, A novel method to include crack-induced delamination in a fatigue damage predictive procedure for composite laminates, Composites Science and Technology 2023; 238: 110011; for instance, said models M2 and M4 are described in the articles Carraro PA, Quaresimin M, A stiffness degradation model for cracked multidirectional laminates with cracks in multiple layers, International Journal of Solids and Structures 2015; 58:34-51 and Carraro PA, Maragoni L, Quaresimin M, Stiffness degradation of symmetric laminates with off-axis cracks and delamination: an analytical model, International Journal of Solids and Structures 2021; 213:50-62; said model M3 can be represented, for instance, by the relationship between the damage event propagation speed and the elastic energy release rate.

[0060] Finally, step E provides that said component 1 is produced when a specific number of load cycles is reached without the occurrence of a specific unacceptability condition.

[0061] For the purposes of the present invention, unacceptability condition can mean, for instance, the reinforcement failure in any element of the component, or the component stiffness reduction below a specific value, or initiation of a specific number of damage events (even just one).

[0062] During the first calculation cycle, said initial elastic properties are the properties of the plies in the absence of damage, or with any preexisting damages already placed. During the cycles following said first calculation cycle, said initial elastic properties are equal to the updated elastic properties calculated during sub-step (D4) of the previous cycle.

[0063] Thus, it has been found that the method according to the present invention solves the task and the objects cited above.

[0064] Indeed, the present method tracks over time the location and dimensions of the single damage events, allowing their interaction between one element and another (both in terms of initiation of damage events and in terms of propagation).

[0065] This enables a more accurate damage prediction and allows to better treat regions where high-stress gradients are present, which are critical in real-world applications (consider, for instance, holes).

[0066] Said regions are characterized by an accentuated damage localization, which continuous damage methods cannot include.

[0067] Compared to discrete damage methods available for complex structures, the present method allows numerical stress calculation tools to interact with also analytical models (M1-M4) for predicting discrete damage events. The method manages stress analysis of the structure (which remains in the numerical model) and damage evolution (whose information is contained in appropriate databases) in separate environments. Said environments, however, remain closely interconnected, as the models M1-M4 use the results of the numerical analysis and provide it with the updated local elastic properties based on the present damage. This separate management allows a significant reduction in calculation times compared to the currently available discrete damage prediction methods for complex structures.

Claims

CLAIMS1. A method to produce a component (1) made of composite material consisting of one or more plies (2, 3) associated with each other, characterized by the fact of involving a series of steps (4) for the fatigue design of said component (1), including:(A) a first step, in which a discretized model (5) is generated, for instance through a finite element model of the component (1), in which at least a first ply (2) and if appropriate at least a second ply (3) are divided, respectively, into two or more first portions (6) and two or more second portions (7),(B) a second step, in which it is defined the location of one or more first damage initiation sites (8) and one or more second damage initiation sites (9), respectively within each of the two or more first portions (6) and each of the two or more second portions (7),(C) a third step, in which a fatigue strength parameter is assigned to each damage initiation sites (8, 9),(D) a fourth step, in which a load history to be simulated on the component is established, based on specific loading conditions, and the total number of cycles (NC) to be simulated is divided into discrete blocks of cycles, assigning to each block of cycle a loading condition, performing for each block of cycles a calculation including the following sub-steps:• (DI) calculate one or more load parameter as resulting forces and moments for each element of the discretized model,• subsequently perform, in parallel to each other if appropriate, the steps of: o (D2) for each damage initiation site, calculate a damage initiation parameter PID using a fatigue damage initiation model (Ml), if said parameter reaches a predetermined initiation value for one or more initiationsites, place a damage event on said damage initiation site, if the dimensions of the placed damage event exceed the perimeter of the element where the damage initiation site is located, the excess part of the damage event is placed in the adjacent element.• and o (D3) for each damage event initiated in any previous block of cycles, calculate a damage propagation controlling parameter (PCPD) using a fatigue damage propagation model (M3), and subsequently update the dimensions of the damage event, if the dimensions of the damage event after its propagation exceed the perimeter of the element where the damage event end was before its propagation, the excess part is placed in the adjacent element,• (D4) calculate the updated elastic properties of each portion (6, 7) of each ply based on the damage events located therein, using an appropriate model (M4),(E) produce said component (1) when a specific number of cycles (NC) is reached without the occurrence of a specific unacceptability condition.

2. A method according to claim 1, wherein the calculation of one or more load parameter for each element in sub-step (DI) is carried out through an analyses, for instance using the finite element method, that uses the elastic properties calculated at the end of the previous block of cycles (or the initial properties when the calculation is carried out for the first block of cycles) for each said portion of said ply, applying to said discretized model (5) the loading conditions relevant to the block of cycles being analyzed.

3. A method according to claim 1, wherein said first step (A) and said sub-step (DI) are carried out using a first finite elementsoftware, and said second and third steps (B), (C) and said sub-steps (D2), (D3), (D4) are carried out using a calculation tool that is distinct from the structure solution step performed using said first finite element software.

4. A method according to one or more previous claims, wherein the calculation of said damage initiation parameter (PID) in sub-step (D2) is carried out using an appropriate fatigue damage initiation model (Ml) and a stress redistribution model in the presence of damage events (M2); the damage events to be considered for the stress redistribution and for the PID calculation are those located within the element in which the damage initiation site is located and, if appropriate, in adjacent elements, up to a distance that can be set by the user, for instance, based on the laminate features.

5. A method according to one or more previous claims, wherein the calculation of said damage propagation controlling parameter (PCPD) in sub-step (D3) is carried out using a fatigue damage propagation model (M3) and a stress redistribution model in the presence of damage events (M2); the damage events to be considered for the stress redistribution and for the PCPD calculation are those located within the element where the damage event end was before its propagation, and, if appropriate, in adjacent elements, up to a distance that can be set by the user, for instance, based on the laminate features.

6. A method according to one or more previous claims, wherein said unacceptability condition consists in the occurrence, before a specific number of cycles, of events such as, for instance, reinforcement failure in any element of the component, component stiffness reduction below a specific value, initiation of a specific number of damage events.

7. A method according to claim 1, wherein in said first step (A) information concerning the discretized model (5) are given withinthe finite element software SW-FEM, such as for instance first information relevant to the overall laminate geometry, second information relevant to the lay-up of the component (1), third information aimed at describing the initial elastic properties of the first ply (2) and if appropriate the second ply (3), including, for instance, the longitudinal elastic moduli, the Poisson's coefficients, and the tangential elastic moduli.

8. A method according to claim 1, wherein in said second step (B) the location of one or more first damage initiation sites (8) and the location of one or more second damage initiation sites (9) may be in the same position as the barycenter of one or more first sub-divisions (61) and if appropriate with the barycenter of one or more second sub-divisions (71), the geometry of which can be decided by the user.

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