System and method for fatigue strength assessment of honeycomb structures

Abstract

Systems and methods for predicting expected mechanical characteristics (e.g., fatigue strength) of a component or portion thereof having a honeycomb structure are provided. In some embodiments, a method for predicting fatigue strength includes receiving, by a control circuit, image data of a sample to reconstruct a 3D model of the sample. The sample includes at least one cell of a honeycomb structure. The method further includes determining a local stress of the sample via finite element analysis of the three-dimensional model. The control circuit may then determine a fatigue strength of the sample based on the local stress to generate a distribution function of the fatigue strength of the at least one cell of the honeycomb structure. The control circuitry then applies the extremum statistics to the distribution function to predict an expected fatigue strength for a number of cells in the cellular structure.

Description

Technical Field

[0001] These teachings relate generally to honeycomb structures, and more particularly to the evaluation of fatigue strength of components having honeycomb structures. Background Art

[0002] Additive manufacturing and other manufacturing technologies offer the ability to produce components with complex structures, such as structures with three-dimensional honeycomb structures. Such honeycomb structures include a three-dimensional arrangement of repeating units to create a continuum. Components including honeycomb structures may be subject to different stresses and loads during use. Therefore, evaluating the mechanical properties of components with honeycomb structures, such as fatigue strength, may help understand their structural integrity and mechanical behavior. BRIEF DESCRIPTION OF THE DRAWINGS

[0003] Various needs are met, at least in part, by providing a system and method for fatigue strength assessment of a component as described in the following detailed description, particularly when studied in conjunction with the accompanying drawings. A full and enabling disclosure of various aspects of the present description, including the best mode thereof, is set forth in the specification with reference to the accompanying drawings, wherein:

[0004] Figure 1A Includes a graphic description of typical methods used to assess the fatigue strength of components;

[0005] Figure 1B includes a graphical depiction of a method for evaluating fatigue strength of a component according to various embodiments of these teachings;

[0006] Figure 2 A schematic diagram of a system for evaluating fatigue strength of a component including various embodiments according to these teachings;

[0007] Figure 3 A flow chart including a method for evaluating fatigue strength according to various embodiments of these teachings;

[0008] Figure 4 including flowcharts of methods according to various embodiments of these teachings;

[0009] Figure 5 Various embodiments according to these teachings may be Figure 4 Exemplary samples used in the method;

[0010] Figure 6 A flow chart including a method for generating a probability distribution function for a given volume of a honeycomb structure according to various embodiments of these teachings;

[0011] Figure 7 Fatigue limits (σ) for single cells, 8-cell volumes, and exemplary fatigue specimens according to various embodiments of these teachings are included.lim ) probability plot.

[0012] Figure 8 includes a graphical overview of the application of the methods described herein, showing fatigue strength as a function of number of cells according to various embodiments of these teachings; and

[0013] Fig.9A Included is an exemplary graph of fatigue strength according to various embodiments of these teachings.

[0014] Fig. 9B Included is an exemplary graph of fatigue stress according to various embodiments of these teachings.

[0015] The elements shown in the figures are shown for simplicity and clarity and are not necessarily drawn to scale. For example, the size and / or relative positioning of certain elements in the figures may be exaggerated relative to other elements to help improve the understanding of the various embodiments of the present teaching. In addition, common but easily understood elements that are useful or necessary in commercially feasible embodiments are generally not depicted to facilitate less obstructed observation of these various embodiments of the present teaching. Certain actions and / or steps may be described or depicted in a specific order of occurrence, and those skilled in the art will understand that such specificity about the order is not actually required. DETAILED DESCRIPTION

[0016] Various aspects of the present disclosure may be used to predict fatigue strength of a component or portion thereof having a honeycomb structure. The systems and methods described herein provide a robust and computationally feasible method for evaluation of additively manufactured metamaterials having a honeycomb structure. The systems and methods for determining fatigue strength apply homogenization, finite element analysis with periodic boundary conditions, and statistical tools to reduce the computational effort involved in evaluating honeycomb structures and capture the effects of real cell geometry in order to evaluate predicted stress states and strengths of real or as-manufactured components.

[0017] Because honeycomb structures may include a large number of repeating cells, the evaluation of mechanical properties (e.g., fatigue strength) of components that include honeycomb structures employs a large number of nodes in finite element analysis (FEA) simulations. Therefore, finite element analysis (FEA) simulations performed on analytical cell geometries of such honeycomb structures may require a large computational workload and a large amount of computing power and / or time to analyze the full-scale component. In addition, the additive manufacturing processes used to manufacture honeycomb structures may introduce inaccuracies and / or anomalies that make it challenging to predict the fatigue strength of the as-manufactured parts. Differences between the analytical model of the component and the real-world component may result in differences between the modeled stresses and the stresses observed in the real world due to the effects of the manufacturing process. These are significant challenges in the context of evaluating the fatigue strength of components having honeycomb structures with repeating cells.

[0018] As used herein, fatigue strength refers to fatigue strength along any portion of the SN diagram. The SN diagram defines the number of cycles to failure, Ncycles, when a material is repeatedly cycled within a given stress range S. Therefore, fatigue strength includes a finite life region (e.g., a region with low cycle fatigue and high cycle fatigue) and an infinite life region (e.g., a region where an infinite number of cycles can be applied without causing failure if the stress level is below a certain level) on the SN diagram. Therefore, the fatigue strength referred to herein may be the fatigue limit of a material, but is not limited thereto. For example, Fig.9A and 9B An exemplary SN diagram is depicted in FIG.

[0019] In general, various aspects of the present disclosure can be used to predict the fatigue strength of a component having a honeycomb structure. Honeycomb structures may include, but are not limited to, for example, lattice structures or triple periodic minimal surface (TPMS) honeycomb structures. Such components may be manufactured, for example, via an additive manufacturing process. The systems and methods described herein use a combination of homogenization and statistical tools to represent the variability of fatigue strength of a given volume consisting of a finite number of units. The methods described herein use CT scans (e.g., x-ray micro-computed tomography (μCT) scans) of a subset of units in a given volume of a component to reduce the computational workload involved in previous methods. Previous methods involving analysis of full-size components also have limitations (e.g., small voxel sizes from μCT scans), which limit the accuracy of such methods. Instead of evaluating a CT scan of the entire volume of a component, the fatigue strength of a subset of units can be evaluated and the results can be applied to a given volume via homogenization. The statistical tools used are based on extreme value statistics, which infer the fatigue strength of the entire volume of a component or any number of highly stressed units based on CT scans of a subset of units in the volume and finite element analysis of 3D image data obtained from the CT scans. These methods also apply periodic boundary conditions to further reduce the computational effort and avoid edge effects.

[0020] The methods for evaluating fatigue strength provided herein can provide robust predictions of fatigue strength of metamaterials with honeycomb structures at an early design stage without the need for complex and expensive testing campaigns. Since these methods utilize CT scanning and finite element analysis of a subset of cells, these methods can eliminate or reduce the need for extensive material testing. Therefore, the methods for evaluating fatigue strength of components described herein can reduce component development costs, shorten development lead times, and increase the confidence in design results.

[0021] The methods described herein can also be used to compare parts manufactured using different manufacturing conditions (e.g., different machines, parameters, pretreatment, post-treatment, etc.). For example, the manufacturing parameters can be adjusted to obtain a sample. The unit can then be scanned using μCT, the geometry of the unit reconstructed, and finite element analysis performed on the reconstructed unit to evaluate the fatigue strength of the sample. The fatigue strength of the component can then be evaluated based on the fatigue strength of the sample. When the manufacturing process is an additive manufacturing process, a large number of inputs or parameters can be adjusted and can affect the final component strength. Testing any possible changes in such inputs or parameters may be impossible, or may be costly and time-consuming. Assessing component strength via the methods described herein can help to assess the expected fatigue strength of the component in a cheaper and more time-saving manner.

[0022] The methods herein can be applied to components having a honeycomb structure (e.g., a lattice structure), or other structures having a repeating unit structure. Some examples of such components include, but are not limited to, components having a helical, diamond, or trident-shaped unit cell.

[0023] Figure 1A A graphical description of a typical method for evaluating fatigue strength of an additively manufactured part having a honeycomb structure is provided. The x-axis on the graphical description represents model size, ranging from cell-level models to part-level models. A cell-level model captures a single unit cell within the honeycomb structure of a part. A specimen-level model captures several cells in a part. A feature-level model captures a portion of a part. A part-level model captures all or a large portion of a part. The y-axis represents model accuracy.

[0024] The accuracy below line "X" is what can be achieved via standard modeling to evaluate fatigue strength. Typical methods involving standard modeling can evaluate material stiffness and stress (as designed). However, standard modeling may not be able to evaluate the actual stress concentration factor (Kt), which quantifies the degree of stress concentration in a mechanical part. Standard modeling also cannot evaluate or predict structural failure (e.g., when a material is stressed to its strength limit, resulting in fracture or excessive deformation) or functional failure (e.g., the material cannot perform the intended function of the standard performance). The accuracy limit of standard modeling may be limited by, for example, the inability to capture anomalies or geometric differences between unit cells of the as-designed and as-manufactured honeycomb structure.

[0025] Still refer to Figure 1AA typical approach for evaluating the fatigue strength of a honeycomb structure may involve constructing a three-dimensional (3D) analytical model of a unit cell of a component to evaluate stiffness. The component is then stiffness homogenized, that is, the stiffness of the unit cell is applied to a larger volume of the component, for example, the portion of the component that includes the cell. Submodels may then be constructed for individual features of the component to evaluate the stresses applied to the features (as designed). The submodel may include detailed 3D meshes and nodes involved in order to model the honeycomb structure of the feature. Modeling the honeycomb structure of the entire component under typical approaches may be overly cumbersome because it involves an excessive amount of computational effort due to the number of nodes involved in describing the 3D shape of the honeycomb structure at the required level of accuracy. In addition, the 3D analytical model of the unit cell may not capture anomalies and geometric differences in real cells.

[0026] Figure 1B A graphical description of the method presented in this paper is provided for predicting the fatigue strength of additively manufactured parts with honeycomb structures. The x-axis and y-axis are related to the reference Figure 1A Same as described. The method provided herein uses imaging data of the real unit cell geometry of the honeycomb structure (e.g., including images of a sample of a manufactured unit cell or several units), such as data from a computed tomography (CT) scan. Therefore, an actual 3D image or model of the real unit cell of the honeycomb structure can be used to evaluate the stress concentration factor (Kt), for example via finite element analysis. The method provided herein can perform finite element calculations based on the structure of the real unit cell. Using finite element analysis, simulations can be performed on the real unit cell to derive real constants that define the behavior of the material. These constants may include elastic modulus (E), yield stress (σ y ), ultimate strength (σ max ), fault strain (ε f ), fatigue limit (σ lim ), stress concentration factor (Kt), Poisson's ratio (ν), shear modulus (G), yield locus, etc. The real constants can then be applied to the entire component via homogenization. Using statistical tools (such as the weakest link theory and extreme value statistics) and periodic boundary conditions, the fatigue strength of the component or other metamaterial can then be derived.

[0027] Using the method for predicting fatigue strength provided herein, the occurrence of failure or part failure area can be predicted. The part failure area can be, for example, an area in a component that is subjected to high stress and is therefore prone to failure. The part failure area can also be referred to as a critical area. In addition, the method provided herein can eliminate the need to build a 3D analysis model of the entire or complete component (which will involve a large number of nodes in the 3D grid) or a model of the specific features of the component.

[0028] The terms and expressions used herein have the ordinary technical meanings given to these terms and expressions by those skilled in the art as described above, unless otherwise specifically defined herein. Unless otherwise expressly stated, the word "or" used herein should be interpreted as having a disjunctive structure rather than a conjunctive structure. Unless otherwise specified herein, the terms "connect", "fix", "attach to", etc. refer to both direct connection, fixation or attachment and indirect connection, fixation or attachment through one or more intermediate components or features.

[0029] The singular forms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise.

[0030] As used herein throughout the specification and claims, approximate language is used to modify any quantitative representation that can be permitted to vary without resulting in a change in the basic function to which it is related. Thus, a value modified by one or more terms (e.g., "about," "approximately," and "substantially") is not limited to the precise value specified. In at least some cases, approximate language may correspond to the precision of an instrument used to measure the value, or the precision of a method or machine used to construct or manufacture a component and / or system. For example, approximate language may refer to within a 10% margin.

[0031] The above and other benefits may become more apparent after a thorough review and study of the following detailed description. Figure 2 , a system 100 compatible with many of these teachings will now be described.

[0032] System 100 can be used to predict fatigue strength of a manufactured component 102 (e.g., for a true cell geometry). Component 102 has a honeycomb structure with cells 104, which may also be referred to as unit cells. In some aspects, component 102 is an additively manufactured component. In some embodiments, component 102 is a heat exchanger or a portion thereof for a gas turbine engine. It is contemplated that the systems and methods described herein may be applied to other gas turbine engine components. However, it should be understood that the systems and methods may also be applied to other types of parts or components including honeycomb structures.

[0033] System 100 can analyze sample 103 representing component 102, and use such analysis results to infer fatigue strength of manufactured component 102 (e.g., its entirety). Sample 103 is a unit geometry of real printing or manufacturing. Sample 103 can include one or more units. Sample 103 also has a honeycomb structure. Sample 103 can represent component 102 because sample 103 has the same or similar unit size as component 102 and / or has the same or similar unit geometry as component. In some aspects, sample 103 can also represent component 102 because sample 103 is manufactured under the same manufacturing conditions using the same type of manufacturing device (e.g., 3D printing device), is placed in the same or similar position in the build platform during the manufacturing process, and / or is oriented in the same way as component 102 during the manufacturing process. Therefore, sample 103 includes several units that reflect the real unit geometry of component 102. As described in further detail below, the sample will be scanned and reconstructed into a 3D model of the real unit geometry.

[0034] The system 100 includes a manufacturing device 105 , an imaging device 106 , a display device 108 , a user input device 110 , a three-dimensional (3D) model 112 , a finite element analysis (FEA) module 114 , and one or more databases 119 .

[0035] The manufacturing device 105 may be any type of manufacturing device capable of building an object having a honeycomb structure. In some embodiments, the manufacturing device 105 is an additive manufacturing device such as a 3D printer, and may build an object via one or more of binder jetting, directed energy deposition, material extrusion, powder bed fusion, sheet lamination, VAT polymerization, and material jetting. The manufacturing device 105 may be configured to manufacture the sample 103, the component 102, or a portion thereof.

[0036] The imaging device 106 is configured to scan the sample 103 or a portion thereof to reconstruct a three-dimensional (3D) image of the target object, including the internal structure (e.g., a honeycomb structure) of the target object. It is also contemplated that the imaging device 106 can scan the component 102 or a portion thereof. In some methods, the imaging device 106 can scan a subset of the cells 104 within the honeycomb structure of the component 102 or sample 103. In some aspects, the imaging device 106 can acquire image data without destroying the sample 103. In this way, the imaging device 106 can be used to provide a 3D image of the true cell geometry in the honeycomb structure of the sample 103. In one example, the imaging device 106 can be a μCT device that uses an x-ray source to illuminate the sample 103 and acquires a series of two-dimensional (2D) images from different angles, which are used to reconstruct a high-resolution 3D image of the sample 103.

[0037] The imaging device 106 can be any suitable three-dimensional imaging device or scanner, including, for example, an in-situ tomography scanner such as an x-ray micro-computed tomography (μCT) scanner, a synchrotron tomography scanner, or other optical scanner. The imaging device 106 can image the sample 103 at sub-micron resolution to reconstruct the shape or geometry of the cells in the honeycomb structure. In some embodiments, the imaging device 106 can be incorporated into or otherwise associated with the manufacturing device 105 or a corresponding manufacturing process.

[0038] Display device 108 may be configured to present a 3D image of sample 103 generated by imaging device 106. Display device 108 may be associated with imaging device 106. Display device 108 may be of any suitable type, including but not limited to a cathode ray tube (CRT) device, a liquid crystal display (LCD) device, a light emitting diode (LED) device, etc. Display device 108 may also present additional information or attributes associated with sample 103 and / or identifiers in the image, such as a name, model, type, production date, etc. associated with sample 103.

[0039] The user input device 110 is configured to receive input from a user. The user's input may include, but is not limited to, device settings, user preferences, component information, etc. The user input device 110 may take any suitable form. For example, the user input device 110 may include, but is not limited to, a mouse, a touch screen, a keyboard, a touch pad, a numeric keypad, etc.

[0040] In some embodiments, the display device 108 and the user input device 110 may be integrated into a single component, such as a touch screen device. In some embodiments, the display device 108 and / or the user input device 110 may be included in a computing device, such as a desktop computer, a laptop computer, a tablet computer, a mobile device, etc. One or both of the display device 108 and the user input device 110 may also be associated with the imaging device 106 and / or an electronic device integrated with or communicatively coupled to the imaging device 106.

[0041] The 3D model 112 is a 3D model of the sample 103, the component 102, or a portion thereof (including any cellular structures therein). The 3D model 112 is stored in one or more databases 119. However, it is contemplated that the 3D model 112 need not be stored in the database 119, and in other configurations, may be stored or housed in other components or portions of the system 100, such as in the FEA module 114 or the component analysis module 116, or may be received from a database or the like external to the system 100. The 3D model 112 may be, for example, a model of the sample 103 or component 102 as designed. The 3D model 112 depicts the geometry of the sample 103 or component 102. Equations, point clouds, or other suitable methods may be used to reconstruct the 3D model 112 using image data or scans of the sample 103 and / or component 102 obtained using the imaging device 106. The 3D model 112 may provide the true unit geometry of the sample 103 based on the image data acquired by the imaging device 106. Simulations may be performed on 3D model 112 to evaluate performance and optimize the design of component 102. 3D model 112 may be any suitable type of 3D model, such as a computer-aided design (CAD) and / or computer-aided engineering (CAE) model. In some approaches, 3D model 112 is an implicit model.

[0042] In some embodiments, data from 3D model 112 may be exported or otherwise transmitted for input into FEA module 114. For example, FEA module 114 may receive a finite element mesh of specimen 103 from the 3D model. Such a finite element mesh may include a plurality of nodes that help define the structure of specimen 103.

[0043] The FEA module 114 is configured to perform finite element analysis to perform structural analysis on the specimen 103, the component 102, or a portion thereof, such as performing structural analysis on a cell of the component 102 or a subset of cells 104. Although the FEA module 114 is shown as being distinct from the control unit 118, it is contemplated that in some configurations, the FEA module 114 may be integrated into the control unit 118. For example, the processor 120 may be configured to perform one or more functions of the FEA module 114. For example, the FEA module 114 may be configured to employ calculations based on mathematical representations, models, and simulations of the specimen 103, the component 102, or a portion thereof to analyze how the component 102 behaves under various physical conditions (e.g., when subjected to various stresses). In this manner, the FEA module 114 may be employed to determine the fatigue strength of the specimen 103, the component 102, or a portion thereof, whether as designed (e.g., based on model data from the 3D model 112) or as manufactured (e.g., based on image data acquired from the imaging device 106).

[0044] The FEA module 114 may also be configured to receive data indicating mechanical properties, geometry (e.g., data regarding the cellular structure of the component 102), and / or data regarding the type of the component 102 and / or the specimen 103. It is contemplated that the FEA module 114 may receive and utilize model data from the 3D model 112, image data from the imaging device 106, and / or data from one or more databases 119 as input data.

[0045] The FEA module 114 may be configured to generate fatigue strength or other mechanical properties of the sample 103. The FEA module 114 may perform finite element analysis using image data of the sample 103 acquired by the imaging device 106. The FEA module 114 may derive constants indicating mechanical properties (e.g., fatigue strength) of the sample 103. These constants may include, for example, constants indicating stiffness, such as Young's modulus, Poisson's ratio, and tangent modulus. These constants may also include, for example, constants indicating static stress, such as yield stress and ultimate tensile stress. The FEA module 114 may also perform finite element analysis using one or more periodic boundary conditions to simulate the entire component 102 (or a portion thereof) by modeling a finite representative volume element, in which case the finite representative volume element may be the sample 103 scanned by the imaging device 106.

[0046] In some embodiments, FEA module 114 may be configured to identify local stresses of sample 103 and / or its unit cells. FEA module 114 may also be configured to identify local stresses on component 102.

[0047] In some aspects, the FEA module 114 may homogenize for properties such as stiffness. In addition, the FEA module 114 may homogenize for strength. Once homogenized, the FEA module 114 may not include cells of a honeycomb structure, but rather represent a bulk material without cells. Homogenization may be performed in the FEA module 114 to model the component 102 based on the properties and / or constants (e.g., stiffness) of the sample 103. For example, the stiffness of the sample 103 may be used to determine the macrostructural properties of the component 102. Homogenization may produce a homogenized model of the component 102 without spatially dependent properties and / or constants. Therefore, the properties of the sample 103 (e.g., microstructure) may be applied to the entire volume (e.g., macrostructure) of the component 102 or any number of cells 104 in the volume of the component 102. In this way, the properties of the real cell geometry present in the sample 103 may be applied to the complete volume (or larger volume) of the component 102. The homogenized material may then be analyzed via the FEA module 114 (and / or a FEA solver, eg, the FEA module 114 may be an input to a FEA solver) to obtain a homogenized stress for the component 102 .

[0048] The component assessment module 116 may utilize statistical tools to represent the variability of the fatigue strength of the sample 103 (e.g., in a given volume of the component 102 composed of a subset of the cells 104 or a limited number of cells 104). Although the component assessment module 116 is shown as being distinct from the control unit 118, it is contemplated that in some configurations, the component assessment module 116 may be integrated into the control unit 118. For example, the processor 120 may be configured to perform one or more functions of the component assessment module 116. The component assessment module 116 may be configured to employ various statistical tools, such as weakest link scaling and extreme value statistics. The component assessment module 116 may apply a weakest link model to estimate the behavior of several cells based on the stress of the failure region of the sample 103. Using weakest link scaling, if the link or unit cell with the lowest strength fails, the entire component fails. Weakest link scaling may use finite element analysis to provide the worst-case static and / or fatigue strength of a honeycomb structure. In one example, the failure region in the sample 103 may be used to estimate the behavior of the component 102 (e.g., its entirety) by applying extreme value statistics. Extreme value statistics provide deviations from the median of a probability distribution. Component evaluation module 116 may apply extreme value statistics to obtain a description of the tail of a distribution describing the strength of a single cell or a subset of cells in a honeycomb structure. The distribution describing the strength of sample 103 may then be used to infer a probability distribution of component 102 (e.g., its entirety or several of its cells). Component evaluation module 116 may be configured to perform a reference Figure 7 One or more methods described.

[0049] The system 100 may also include one or more databases 119 containing various types of data useful for fatigue strength assessment. In some embodiments, the database 119 may include image data of the sample 103, such as image data acquired from the imaging device 106. The database 119 may also include data on or from the 3D model 112, such as data used to reconstruct the 3D geometry of the sample or component 102.

[0050] The control unit 118 may be used as a computing device to perform the functions and methods described herein. It is contemplated that the control unit 118 may include one or more of the 3D model 112, the FEA module 114, and / or the component evaluation module 116, or may otherwise communicate with these components of the system 100. The control unit 118 may include one or more processors 120, an input / output (I / O) device 122, a transceiver 124, and a memory device 126. The processor 120 may include any suitable processing device, such as a microprocessor, a microcontroller, an integrated circuit, a logic device, or other suitable processing device. The processor 120 may be used to perform or assist in performing the steps of the processes, methods, functions, and techniques described herein, and to control various communications, decisions, programs, content, lists, services, interfaces, logs, reports, and the like. In addition, one or more processors 120 may access a memory device 126, which may store instructions 130, codes, and the like that are implemented by the processor 120 to achieve the intended functions.

[0051] The memory device 126 generally includes one or more processor-readable and / or computer-readable media accessed by at least the processor 120, and may include volatile and / or non-volatile media, such as RAM, ROM, EEPROM, flash memory, and / or other memory technologies. In addition, the memory device 126 is shown as being internal to the control unit 118; however, the memory device 126 may be internal memory, external memory, or a combination of internal and external memory. Similarly, some or all of the memory devices 126 may be internal memory, external memory, or a combination of internal and external memory of the processor 120. The memory device 126 may be substantially any relevant memory, such as, but not limited to, a solid-state storage device or drive, a hard drive, one or more Universal Serial Bus (USB) sticks or drives, a flash secure digital (SD) card, other memory cards, and other such memories or a combination of two or more such memories, and some or all of the memories may be distributed in multiple locations on a computer network. The memory device 126 may store data 128, such as code, software, executable files, scripts, data, content, lists, programming, programs, log or historical data, engine information, component information, and the like. The various components of the system 100 may be coupled together via a bus or, in some configurations, the various components may actually be coupled directly to the control unit 118 and / or one or more other components.

[0052] Typically, the control unit 118 also includes one or more communication interfaces, ports, or transceivers 124, etc., which allow the control unit 118 to communicate with other devices and / or other such communications or a combination of two or more such communication methods via a communication bus, distributed computers, and / or communication networks (e.g., a local area network (LAN), the Internet, a wide area network (WAN), etc.). In addition, the transceiver 124 can be configured as a wired, wireless, optical, fiber optic cable, satellite, or other such communication configurations or a combination of two or more such communications.

[0053] I / O device 122 may be any relevant port or combination of ports, such as, but not limited to, a USB, Ethernet, or other such port. I / O device 122 may be configured to allow wired and / or wireless communication to connect to external components. For example, I / O device 122 may provide wired and / or wireless communication (e.g., Wi-Fi, Bluetooth, cellular, RF, and / or other such wireless communications), and in some cases may include any suitable wired and / or wireless interface devices, circuits, and / or connection devices, such as, but not limited to, one or more transmitters, receivers, transceivers, or a combination of two or more such devices.

[0054] The control unit 118 may receive data from various components of the system 100. In addition, the control unit 118 may transmit data to various components of the system 100. For example, the control unit 118 may receive model data (which may include one or more design parameters) from the 3D model 112, and may transmit the model data to the manufacturing device 105 so that the manufacturing device can manufacture the component 102 according to the model data. The control unit 118 may also receive input data from the user input device 110, and provide instructions to the imaging device 106 and / or the manufacturing device based on such input data. The control unit 118 may also receive image data from the imaging device 106 and / or from one or more databases 119. The control circuit may transmit the image data to the 3D model 112 and / or the FEA module 114.

[0055] like Figure 2 As shown, the various components of system 100 can communicate directly or indirectly, such as through one or more distributed communication networks, such as network 132. For example, network 132 can include a LAN, WAN, Internet, cellular, Wi-Fi, and other such communication networks or a combination of two or more such networks.

[0056] In certain embodiments, the system 100 may also include one or more testing devices 133 configured to test the manufactured samples 103 and / or components 102. The testing device 133 may be any device suitable for mechanical testing, such as compression, tension, bending, torsion or fatigue testing. The testing device 133 may include one or more fatigue testing machines, such as a wheel disc-hub fatigue testing machine, a dynamic fatigue testing machine, a rotary bending fatigue testing machine, a servo-hydraulic fatigue testing machine, a zipper reciprocating fatigue testing machine, a spring fatigue testing machine, an axial fatigue testing machine, a torsion fatigue testing machine, a radial fatigue testing machine, and a cyclic fatigue testing machine. The testing device 133 may also include one or more universal testing machines (UTMs) configured to determine the strength and deformation behavior of a material under compression (extrusion) or tensile loads. Such UTMS may also be configured to perform bending tests, for example, to evaluate material ductility, bending strength, fracture strength, and fracture resistance. The testing device 133 may also include one or more torsion testing machines configured to simulate the torsional motion of a material to determine the torque load of a sample made of different materials. The testing apparatus 133 may include a test stand for holding the sample and a load cell for converting the magnitude of the measured force into a quantifiable electrical signal. The test stand may be configured to hold the sample during testing and, in some methods, include a top clamp for engaging a top portion of the sample and a bottom clamp for engaging a bottom portion of the sample. It is contemplated that different test stand configurations may be employed depending on the size and shape of the sample. The force gauge may collect measurements during the test and may output peak and / or average force values, which may be converted into material properties.

[0057] The test device 133 may be controlled by a test control unit, which may communicate with, for example, the control unit 118. The test control unit may respond to command signals to operate the test device 133. In addition, data acquired or generated by the test device 133 may be transmitted to the database 119, the finite element analysis module 114, and / or the component analysis module 116.

[0058] In operation, the system 100 may be used to assess fatigue strength of an as-manufactured component 102. Rather than manufacturing, acquiring images, and analyzing the entire component 102, the system 100 may manufacture a sample 103 that is representative of the as-manufactured component 102. Based on the analysis of the sample 103 as described herein, the component 102 may be subsequently manufactured and properties (e.g., fatigue strength) of the as-manufactured component 102 may be predicted.

[0059] The imaging device 106 acquires one or more images of the sample 103. In some approaches, the imaging device 106 may acquire images of a subset of the units 104 in the sample 103. The FEA module 114 uses the images acquired by the imaging device 106 to determine fatigue strength of the sample 103 or one or several units in the sample 103. The component evaluation module 116 uses the fatigue strength to evaluate the fatigue strength of the manufactured component 102 on a macro scale.

[0060] In some approaches, the testing device 133 may also be used to detect anomalies in the manufactured component 102. Anomalies may include any features that exist in the component 102 but should not exist according to design intent. Anomalies may include, for example, defects, geometric inaccuracies, and process-related anomalies in the component 102, such as pores, cracks, lack of fusion, etc. For example, the testing device 133 may perform compression, tension, and / or fatigue testing on the manufactured component 102 to detect defects or determine the mechanical properties of the manufactured component 102, such as fatigue strength. The results of such tests may be used to perform fractographic analysis to determine the relationship between the microstructure of the component 102 and crack initiation and propagation. In this way, the root cause of a crack or fracture in the component 102 may be determined.

[0061] In other methods, the test device 133 can measure the strength of the manufactured component 102, such as the actual fatigue strength. Therefore, the test device 133 can be used to generate a design curve for the component 102. The design curve may include the material allowable values ​​of the mechanical properties of the component 102. For example, the design curve may include the maximum stress at which the material is expected to yield or fatigue failure as a function of the number of fatigue cycles. The measured strength can be compared with the predicted strength (such as the predicted fatigue strength generated by the FEA module 114). In this way, the error or uncertainty in the predicted fatigue strength is determined.

[0062] Go to Figure 3 , a flow chart of an exemplary method for evaluating fatigue strength of a component having a honeycomb structure is provided. In some embodiments, the system 100 or a portion thereof can be used to perform these methods.

[0063] In method 134, the analytical cell strength of the component can be evaluated. The analytical cell strength provides the strength of the unit cell in the honeycomb structure of the component as designed and is therefore a theoretical value. A 3D analytical model 136 of the component can be generated. The 3D analytical model 136 model can provide an analytical cell geometry 138 of the component as designed. A finite element analysis 140 can be performed on the analytical cell geometry to obtain an analytical cell strength 142.

[0064] In method 135, the true cell strength of the component can be evaluated. For example, the true cell strength can be determined by analyzing a sample representative of the component as manufactured. The true cell strength provides the strength of the unit cell in the honeycomb structure of the component as manufactured. A manufacturing process 144 (e.g., an additive manufacturing process) is used to produce the true cell geometry 146 present in the component as manufactured. Finite element analysis 148 can be performed on the true cell geometry 146 to obtain the true cell strength 150. Extreme value statistics 152 can then be used to predict the expected component strength 154 based on the true cell strength 150. One or more design criteria 156 for the component (or a component of the same type as the component as manufactured) can be derived from the expected component strength 154.

[0065] Analyzed cell strength 142 may be compared to true cell strength 150 to assess strength differences caused by manufacturing process 144. For example, there may be defects or anomalies associated with manufacturing process 144 that may cause true cell strength 150 to be lower than analyzed cell strength 142.

[0066] In addition, testing 158 may be performed on the real cell geometry 146 and / or the as-manufactured component. For example, testing 158 may be performed to evaluate the measured strength 162 of the as-manufactured component including the real cell geometry 146. The measured strength 162 may then be compared to the expected component strength 154. This comparison may be used to evaluate errors or uncertainties associated with the finite element analysis 148. Errors and uncertainties may also be caused by 3D imaging resolution, inaccuracies during testing, and / or analytical models for fatigue strength definitions. It is also contemplated that testing 158 may be performed for defect identification 160 and, therefore, may be used to identify one or more defects, such as cracks, in the real cell geometry 146 or the as-manufactured component.

[0067] refer to Figure 4 , provides an exemplary method for predicting the expected fatigue strength of a manufactured component having a honeycomb structure (also referred to herein as a target component). In a typical application setting, Figure 4 Many (but not necessarily all) of the steps shown in are performed by control circuitry (eg, control unit 118).

[0068] The method involves analyzing a sample representing a target component. It is contemplated that the control circuit can analyze one or more samples. Increasing the number of samples can improve the accuracy of predicting fatigue strength. The sample includes at least one cell of a manufactured honeycomb structure (e.g., a true cell geometry). In some methods, the sample can include a group of cells in a honeycomb structure of the component. In other methods, the sample can be a complete component. The sample can have cells of the same size, type, and / or geometry as the target component. In addition, the sample can be manufactured under conditions similar to the manufacturing conditions of the target component.

[0069] In some aspects, the sample can include about 2 to about 30 cells. In some aspects, the sample of true cell geometry can be about 2 cells x 2 cells x 2 cells, and in other aspects can be about 4 cells x 4 cells x 6 cells.

[0070] exist Figure 4 In the embodiment of the present invention, blocks 170 to 174 show the analysis of a cell (or a group of cells) in a honeycomb structure via a sample of the honeycomb structure to obtain the fatigue strength of the honeycomb structure as a function of the number of cells in the honeycomb structure. Blocks 175 to 177 show a component level analysis that uses homogenization of the component to obtain the spatial distribution of stresses experienced by the component.

[0071] At block 170, the control circuit receives image data of one or more samples to reconstruct multiple 3D models of the sample. In some methods, the control circuit reconstructs a 3D model of each unit in the sample. However, it is conceivable that in other methods, the control circuit can reconstruct 3D models of several (less than all) units in the sample. For example, the control circuit can reconstruct a 3D model of a group of units in the sample. Therefore, the 3D model can be a model of one or more units. The multiple 3D models are further analyzed at blocks 172 to 174 to create a fatigue strength distribution of the sample, which will be described in further detail below. It is also conceivable that in other embodiments, the 3D model can be analyzed to create a distribution of constants or characteristics indicating fatigue strength (e.g., fatigue stress concentration factor (Kf)). In some aspects, the control circuit can instruct one or more imaging devices to acquire an image of the sample. Then, the control circuit can receive image data from the imaging device and use the image data to reconstruct multiple 3D models of the sample. For example, the control circuit can communicate with an imaging device such as a μCT scanner, and can instruct the scanner to acquire one or more images, and then receive the images from the scanner to reconstruct the 3D model.

[0072] The image data may include, for example, one or more images of the manufactured honeycomb structure. It is also contemplated that the control circuit may directly or indirectly receive a 3D model of one or more samples, for example from a database. The control circuit may receive the image data directly or indirectly from an imaging device such as a μCT scanner. In some methods, the control circuit may receive the image data or 3D model from a database containing such data. In some methods, at block 170, the imaging device may scan or acquire an image of one or more samples to obtain image data of the manufactured honeycomb structure. The image data may then be transmitted from the imaging device to the control circuit. In some aspects, the sample may include about 2 to about 30 cells. In some aspects, the sample of the real cell geometry may be about 2 cells x 2 cells x 2 cells, while in other aspects, it may be about 4 cells x 4 cells x 6 cells. In other aspects, the sample may include a single cell (e.g., a single unit cell). It should be understood that multiple samples may be scanned and analyzed as described in blocks 172 to 174 to create a distribution indicating their mechanical properties or constants (e.g., stress concentration factor (Kf), fatigue limit (σ lim )), which will be described in further detail below.

[0073] Briefly go to Figure 5 In one non-limiting example, the control circuitry may analyze about 1 to M single cell models 182 of the honeycomb structure of the sample. The single cell model 182 is a 3D model of a single cell of the sample and reflects the real or manufactured cell geometry. The control circuitry may scan the sample using a μCT scanner and reconstruct the single cell model 182 using the scanned image data. In one example, where M=100, the sample includes 100 cells, and the control circuitry reconstructs a 3D model for each of the 100 cells. The cells of the sample and the cells of the target component may be of the same type (e.g., TPMS).

[0074] Still refer to Figure 5 In another non-limiting example, the control circuit may analyze approximately one (1) to N 8-cell volume models 184 of the cells of the honeycomb structure of the sample. The 8-cell volume model 184 includes a group of 8 cells of the honeycomb structure of the sample. The 8-cell volume model 184 is a 3D model of the volume of 8 cells as manufactured, and therefore can capture the true cell geometry of the sample. The control circuit can scan the sample using a μCT scanner and reconstruct the 8-cell volume model 184 using the scanned image data. In one example, where N=4, 4 8-cell volumes (e.g., 4 different 2-cell x 2-cell x 2-cell cell groups) are modeled to generate 4 8-cell volume models 184. The cells in the cell groups and the cells of the target component can be of the same type (e.g., TPMS).

[0075] Back to Figure 4 , at block 172, the control circuit determines a local stress for each of the plurality of 3D models reconstructed at block 170 for a given applied homogenous stress. The control circuit determines the local stress of the 3D model via finite element analysis with periodic boundary conditions. It is contemplated that the control circuit may determine any combination of stress tensors for the sample model nodes (e.g., true cell geometry). For example, the control circuit may analyze any function of the tensors for a single node or its surrounding nodes. In some embodiments, the control circuit may also determine the strain of the sample. The control circuit may also determine one or more constants of the sample, such as material-related parameters, such as El-Haddad's dimensional parameters.

[0076] In some methods, the control circuit may include a FEA module or communicate with the FEA module. The FEA module may determine the homogenized stress, strain, or other constants applied to the 3D model. The control circuit may use the FEA module to perform simulations to simulate the stress on the 3D model. The FEA module may be used to simulate tests on a 3D model of a sample (e.g., to a real cell geometry) to derive constants that define the behavior of the honeycomb structure when subjected to stress. The FEA module uses periodic boundary conditions to evaluate the strength of a larger volume component manufactured based on a real cell geometry modeled in 3D.

[0077] In some methods, the control circuit determines the fatigue strength of a fault region of the 3D model (e.g., a fault region in a cell or a fault region of a group of cells modeled via the 3D model). For example, the fatigue limit (σ lim ) may be determined as the applied stress which results in a maximum local stress equal to the fatigue strength of the constituent materials.

[0078] At block 173, the control circuit determines the fatigue strength of each of the plurality of 3D models for a given applied homogenous stress. Using the fatigue strengths for the various applied homogenous stresses, the control circuit generates a probability distribution function for a given 3D volume of cells present in the 3D model. For example, if the 3D model includes a single cell, the control circuit generates a probability distribution function that provides a probability that a single cell of the sample has a particular fatigue strength. In another example, if the 3D model includes eight (8) cells, the control circuit generates a probability distribution function that provides a probability that an 8-cell volume of the sample has a particular fatigue strength. Figure 7 An exemplary probability distribution function of fatigue strength is depicted in FIG. 2 (see line 202 for a single unit probability distribution function and line 206 for an 8-unit probability distribution function).

[0079] The control circuit uses the fatigue strength determined for each 3D model at block 173 to generate a probability distribution function, for example, for a single unit. Specifically, the control circuit generates a fatigue strength distribution for the 3D model and obtains the best fit of the distribution to create a probability distribution function. Again referring to Figure 7 , the control circuit may use the fatigue strength determined via FEA simulations of multiple single unit models to generate a fatigue strength distribution such as that shown by line 200 .

[0080] At block 174, the control circuit predicts the expected fatigue strength of a volume including a number of cells (e.g., a number of cells in a target component) by applying extreme value statistics to the probability distribution function generated at block 173. The control circuit can use extreme value statistics to infer the fatigue strength of any number of cells (e.g., a target number of cells) in a manufactured component based on the probability distribution function of the fatigue strength of the 3D model. Therefore, using extreme value statistics, the fatigue strength of a honeycomb structure as a function of the number of cells (Ncells) in the honeycomb structure can be determined. Figure 8 An exemplary graph is provided that may be generated using extreme value statistics by the method described at block 174. Specifically, Figure 8 Line 234 in provides the fatigue limit of the component as a function of the number of cells (Ncells).

[0081] Figure 7 An exemplary application of extreme value statistics to probability distribution functions is shown. Figure 7 , extreme value statistics are applied to a single cell probability distribution function (line 202) to derive a probability distribution function for a target component comprising 360 cells (line 210). Thus, the probability distribution function of the 3D model (e.g., which may include a single cell or a group of cells, such as an 8-cell volume) is used to extrapolate fatigue strength to a larger volume of honeycomb structure (e.g., to more cells or a complete component).

[0082] By some methods, the following formula may be used to infer the fatigue strength of an as-manufactured component based on the fatigue strength of a specimen determined from a 3D model of the specimen, where the 3D model may have 1 or more elements:

[0083] F T =F N (T / N)

[0084] in

[0085] T is the target number of units to be analyzed as required by the manufactured parts;

[0086] F T is the cumulative distribution function of the fatigue strength of T units in the manufactured component;

[0087] N is the number of elements in the 3D model, where N may be 1 or greater; and

[0088] F N is the cumulative distribution function of the fatigue strength of N units.

[0089] The cumulative distribution function may refer to a real-valued random variable X or the distribution function of X evaluated at x, which provides the probability that X takes a value less than or equal to x.

[0090] Using extreme value statistics, such as applying the above formula, the control circuit can predict the expected fatigue strength of any volume including a number of cells. In one example, the control circuit predicts the expected fatigue strength of any number of cells in a honeycomb structure. Since the probability distribution function is generated based on a 3D model of the real cell geometry, the expected fatigue strength captures the effects present in the real cell geometry to improve the accuracy of the expected fatigue strength. Extreme value statistics can predict the expected fatigue strength of any number of cells having the same type of honeycomb structure as the sample (e.g., the real cell geometry captured in the 3D model).

[0091] At block 175, the control circuit identifies the properties of an equivalent homogenous material representing the cellular structure of the sample via homogenization. For example, the control circuit may identify an elastic tensor or any elastic property representing the cellular structure of the sample (and therefore also representing the cellular structure of the target component). For example, it may be desirable to simulate a component composed of a bulk material rather than a component composed of a honeycomb structure, which may be computationally intensive due to the large number of cells in the component. By obtaining the properties of an equivalent homogenous material representing the cellular structure of the sample (and the target component) as described at block 175, the target component may be modeled as a bulk material while still capturing the effects or properties of the cellular structure of the target component.

[0092] At block 176, the control circuit performs a component-level analysis of the stress of the target component. In the component-level analysis, the honeycomb structure of the target component is replaced by an equivalent homogeneous material determined at block 175. Specifically, the control circuit performs an FEA analysis of the component, for example, via an FEA module. In the component-level analysis, the control circuit generates a component model that is homogenized or composed of bulk materials. The control circuit homogenizes the component model (e.g., the FEA module of the component) to represent the target component as a bulk material rather than a honeycomb structure. The properties of the equivalent homogeneous material (representing the properties of the honeycomb structure) are applied to the bulk material in the FEA module. In this way, the bulk material of the modeled component is macroscopically equivalent to the honeycomb structure in the target component. The equivalent homogeneous material will exhibit macroscopic behavior equivalent to the microstructure (e.g., honeycomb structure) of the target component.

[0093] At block 177, the control circuit discretizes the modeled component into sub-volumes based on the spatial distribution of stress in the modeled component. The spatial distribution of stress provides stress on the modeled component as a function of position within the modeled component. For example, the control circuit can filter or apply a mask to the modeled component to select a specific stress value or range. In some methods, the control circuit can filter or mask the highest stress on the component to identify the failure area of ​​the modeled component. The control circuit can filter or apply a mask to the modeled component for a specific stress range to obtain a sub-volume of the modeled component having stress within the specific stress range.

[0094] For example, the control circuitry may filter or mask the modeled component for stresses in the range of 90-100 MPa.The control circuitry may then identify sub-volumes within the modeled component that are subject to stresses in the range of 90-100 MPa.

[0095] At block 178, the control circuit performs a fatigue strength assessment for each subvolume (or a number of subvolumes) of the modeled component. The control circuit performs the fatigue strength assessment by comparing the stress (from block 177) to the expected fatigue strength (from block 174) of the number of cells in the subvolume. The control circuit extrapolates the expected fatigue strength to a volume consisting of the number of cells present in the subvolume.

[0096] For example, if a subvolume of 8 cells of the modeled component is subjected to stresses in the range of 90-100 MPa, the control circuit determines the expected fatigue strength of the subvolume using a function (from block 174) that provides the expected fatigue strength as a function of the number of cells in the honeycomb structure. The control circuit then compares the expected fatigue strength of the subvolume with the stress on the subvolume determined by the spatial distribution of stresses in the modeled component (from block 177) to assess whether the component will exceed the fatigue strength. In this way, the control circuit can determine which subvolumes of the target component will fail first, which is indicative of the fatigue strength of the target component as a whole.

[0097] Based on the fatigue strength of the target component (or a portion or subvolume thereof), the control circuitry may generate one or more design parameters for the component as designed. The design parameters may be incorporated into the 3D analysis model to generate a blueprint or model of the component as designed. Such a blueprint or model in the 3D analysis model may be used to manufacture the component as designed. In one example, the design parameter may be a component geometry that maximizes or otherwise increases the fatigue strength of the component as designed. In some embodiments, the fatigue strength may be used to build margin into the design of the component.

[0098] The method may optionally include manufacturing or otherwise physically constructing the designed component according to the design parameters. In some methods, the control circuit may output design data indicating the design parameters. The control circuit may transmit the design data to a manufacturing device, such as a 3D printer. By one method, this may include 3D printing the designed component according to the design data derived in the method. It is also contemplated that the method may optionally include using the design parameters to physically construct the designed component.

[0099] In some methods, the control circuit can generate one or more manufacturing parameters or parameters for a manufacturing device (e.g., a 3D printer) based on the expected fatigue strength of the component (or a portion or subvolume thereof). The manufacturing device can then manufacture the designed component according to the one or more manufacturing parameters to build a physical component or part.

[0100] Go to Figure 6 , shows an exemplary flow chart illustrating the analysis of sample 190. The analysis provides information related to the above reference Figure 4 Further details of the analysis described in blocks 170 to 173 of FIG. Figure 6 One or more samples are shown analyzed. Sample 190 has a honeycomb structure and includes a plurality of cells.

[0101] An imaging device 192 (e.g., a μCT scanner) may acquire one or more images of the sample 190. The one or more images may be used to reconstruct a plurality of 3D models 194 of the sample 190. For example, the plurality of 3D models 194 may be 3D models of each cell in the sample 190. In another example, the plurality of 3D models 194 may be 3D models of the volumes of the cells in the sample 190. The 3D model may be a finite element model of the sample 190.

[0102] At block 196, the control circuit can then perform FEA analysis on multiple 3D models 194 using periodic boundary conditions. It is envisioned that the FEA module can use any other possible boundary conditions to simulate homogeneous materials. The inputs of the FEA module at block 196 are multiple 3D models 194, applied loads and boundary conditions. The applied stress is applied to the 3D model in a homogeneous manner, so it is a macroscopic applied stress. In other words, the load is applied to the entire surface and / or volume of the 3D model, rather than to its part. The output generated by the FEA module at block 196 is a local stress map in each of the multiple 3D models 194. The FEA module can simulate or apply various applied stresses to each (or some) of the multiple 3D models 194 to generate a local stress map.

[0103] At block 198, the control circuit can determine the homogenous fatigue strength of each (or some) of the plurality of 3D models 194 based on the local stress map generated at block 196. The maximum failure area in each 3D model reaches the fatigue strength of the 3D model. To obtain the homogenous fatigue strength, the control circuit amplifies the local stress. The analysis is linear, so if the applied double stress is doubled, the local stress is doubled. The control circuit then determines the failure area of ​​the 3D model that reaches the fatigue strength of the material of the sample 190 (for example, if the material of the sample 190 is an aluminum alloy, the fatigue strength of the aluminum alloy will determine the failure area). The fatigue strength of the failure area will give the homogenous fatigue strength.

[0104] The process described at blocks 196 and 198 can be applied to any possible homogenous stress state.

[0105] At block 199, the control circuit uses the results of the analysis of each of the plurality of 3D models 194 to generate a probability distribution function of the fatigue strength of the plurality of 3D models 194. Example results of such an analysis are shown in Figure 7 The center is presented at lines 200 and 202 .

[0106] The control circuitry may then use the probability distribution function to determine an expected fatigue strength of the component or a portion of a subvolume thereof. The control circuitry may generate one or more manufacturing parameters or parameters for a manufacturing device (e.g., a 3D printer) based on the expected fatigue strength of the component (or a portion or subvolume thereof). The manufacturing device may then manufacture the designed component according to the one or more manufacturing parameters to build a physical component or part.

[0107] Figure 7-8 An exemplary analysis of samples is provided to determine the expected fatigue strength of an as-fabricated component having a honeycomb structure. Figure 7-8 The analysis shown in was performed using Figure 5 The experiments were performed using the single unit model 182, 8-unit volume model 184 and experimental sample 186 shown in FIG.

[0108] Figure 7 The fatigue limits (σ) based on a single unit sample (eg, a single unit model 182), a volume sample (eg, an 8-unit volume model 184), and an experimental sample 186 are depicted. lim ). Fatigue limit (σ lim ) measures the limiting stress at which failure occurs in an infinite number of fatigue cycles.

[0109] Line 200 depicts the fatigue limit (σ lim). The simulation data in line 200 are derived from FEA simulations of single unit models (1...M). The circular data points of line 200 each represent simulation results from a different single unit model (e.g., results from each sample - single unit model 2, single unit model 3, etc. to single unit model M FEA simulation). Specifically, each circular data point represents the lowest fatigue limit (σ) in the single unit model determined via FEA simulation. lim ) value. For example, the lowest fatigue limit (σ lim ) is located in the failure region 182a. The failure region of each single unit model (1...M) is determined, and the fatigue limit of the failure region is used to construct the line 200. The minimum fatigue limit (σ lim ) value is the fatigue limit of the failure area in a single unit model (σ lim ). Each different single cell model is obtained by manufacturing and acquiring images of the single cell to construct a 3D model of the true cell geometry. The 3D model of the true cell geometry is then analyzed using FEA simulations to estimate the fatigue limit of the single cell of each sample or at least some of the samples. Thus, the simulation data in line 200 provides the fatigue limit (σ lim )’s unit-to-unit variability.

[0110] Line 202 provides the fatigue limit of a single element (σ lim ). Line 202 is fitted to the single unit simulation data of line 200. That is, line 202 is the best fit to the data in line 200.

[0111] Line 204 depicts the fatigue limit (σ lim ). The simulation data in line 200 are derived from FEA simulations of 8-element volume models (1...N). The square data points in line 204 each represent simulation results from a different 8-element volume model (e.g., results from FEA simulations of each sample—8-element model 2, 8-element model 3, etc. to 8-element model N). Specifically, each square data point represents the lowest fatigue limit (σ ) in the 8-element volume model determined via FEA simulation. lim ) value. Minimum fatigue limit (σ lim ) is the fatigue limit of the failure area in the 8-element volume model (σ lim For example, the minimum fatigue limit (σ lim) is located in the failure region 184a. The failure region of each 8-unit volume mode (1...N) will be determined and the fatigue limit of the failure region will be used to construct the line 204. Each different 8-unit volume model is obtained by manufacturing and acquiring images of the 8-unit volume to construct a 3D model of the real unit geometry. The 3D model of the real unit geometry is then analyzed using FEA simulation to estimate the fatigue limit (σ) of the 8-unit volume of each sample or at least some of the samples. lim ).

[0112] Line 206 provides the fatigue limit (σ lim ) is a statistical estimate of . Line 206 is obtained using the following formula: F8 = F1 8 , where F1 is the function represented by line 202. Thus, line 204 provides the fatigue limit (σ lim ), while line 206 provides the numerically obtained fatigue limit (σ lim ). Comparison of line 204 with line 206 shows that the predicted fatigue limit (σ lim ) and the fatigue limit (σ lim ) data, which captures the real cell geometry. Therefore, the extrapolation using extreme value statistics is validated by simulations with real cell geometries.

[0113] Line 208 depicts the fatigue limit (σ lim ) The data of line 208 is obtained by performing a fatigue test on the experimental sample 186. The fatigue test can be performed using any suitable fatigue testing device.

[0114] Line 210 provides the fatigue limit (σ) of the experimental sample 186 of 360 units based on extreme value statistics using the following formula: lim )’s estimated value: F 360 =F1 360 , where F1 is the function represented by line 202. Thus, line 208 provides the fatigue limit (σ lim ), while line 210 provides the fatigue limit (σ) obtained numerically using extreme value statistics. lim ) distribution. Comparison of line 208 with line 210 shows that the predicted fatigue limit (σ lim ) and the fatigue limit (σ lim ) data, which captures the true cell geometry. Therefore, the extrapolation performed using extreme value statistics is validated by the experimental data.

[0115] Figure 8 A graph depicting fatigue strength as a function of the number of cells in a component is shown. The graph shows the effect of actual cell geometry compared to analytical cell geometry (e.g., cell geometry as designed). Line 230 provides the fatigue strength of the bulk material, that is, without stress concentrations. Line 232 provides the fatigue strength of the cell as designed. Line 234 provides the fatigue strength of the cell as manufactured (e.g., as built). In addition, line 234 includes a confidence band showing a 95% confidence interval for the fatigue strength of the cell as manufactured. The fatigue strength values ​​of line 234 are determined using the method described herein.

[0116] The fatigue strength of the cell as manufactured (line 234) is lower than the fatigue strength of the cell as designed (line 232). As discussed above, this is due to the effects of the manufacturing process, such as the variations introduced via the manufacturing process. In addition, the fatigue strength of the cell as designed (line 232) is lower than the fatigue strength of the bulk material (line 230). This is due to the effect of the cell geometry on fatigue strength.

[0117] Fig.9A An exemplary SN diagram generated via the methods described herein is shown. The fatigue stress will depend on the material and geometry of the honeycomb structure. Using the homogenized FEA module, the number of cycles to failure (Ncycles) can be obtained based on the number of cells in the honeycomb structure (Ncells) and based on the homogenized stress (S) on the component subvolume. Therefore, the FEA module of the modeled component has been homogenized using an equivalent homogenous material representing the honeycomb structure. The FEA module can be used to generate fatigue strength values ​​for the modeled component, which is a function of the number of cycles to failure (Ncycles). The number of cycles to failure (Ncycles) can be generated as a function of the number of cells in the component (Ncells) and the applied stress (S) on the component:

[0118] Ncycles=f(Ncells,S)

[0119] The fatigue strength (which can be used to generate the SN curve) is a function of the number of cells (Ncells). Therefore, the SN curve will vary based on the number of cells (Ncells) in the component, where as the number of cells (Ncells) in the component increases, the stress in the SN will decrease. Therefore, a specific SN curve can be used to evaluate the fatigue strength of a target component based on the number of cells in the target component. Using Fig.9AThe SN curve of the component can be used to determine the number of failure cycles of the component based on the SN curve, knowing the homogeneous stress on the target component and the number of units in the target component. The component life corresponds to the number of failure cycles (Ncycles). Different areas of the component will have different homogeneous stresses and therefore different numbers of failure cycles (Ncycles). The failure area of ​​the component is the area with the fewest failure cycles because this is the area where the component fails first. In this way, determining the weakest link of the component can predict the failure of the entire component.

[0120] Fig. 9B A graph depicting fatigue stress as a function of the number of cells in a honeycomb structure. Fig. 9B The curve in Figure 2 shows the fatigue stress as Fig.9A The stresses of the honeycomb structure are shown as a function of the number of cells in the component in the various regions of the SN curve shown in FIG. For the limited life region, several cells of the honeycomb structure will withstand lower stresses in a large number of cycles (e.g., 300k cycles) and can withstand higher stresses in a smaller number of cycles (e.g., 30k cycles) before failure. For the infinite life region, several cells of the honeycomb structure will withstand even lower stresses in a very large number of cycles (e.g., infinite life).

[0121] Assumption Fig. 9B The curve shown in Figure 8 is generated in a manner similar to that described for line 234.

[0122] The systems and methods described herein can be used to analyze honeycomb structures or other lattice structures manufactured, for example, via additive manufacturing. Due to the large number of cells in a component having a honeycomb structure, existing analytical methods for determining the expected fatigue strength of a target component are computationally expensive in terms of computing power and time. By using finite element analysis with periodic boundary conditions and homogenization of the finite element analysis model, the methods described herein can reduce the computational workload involved in analytical methods for determining the expected fatigue strength of a target component. In addition, the systems and methods described herein allow the fatigue strength of the entire target component to be predicted or determined based on the analysis of the fatigue strength of a smaller number of cells (e.g., a single cell or a sub-volume of a cell) by using statistical tools that extrapolate the characteristics of a smaller number of cells to the entire target component.

[0123] Further aspects of the disclosure are provided by the subject matter of the following clauses:

[0124] A computer-implemented method comprises: receiving image data of a sample from an imaging device, the sample comprising a plurality of cells of a manufactured honeycomb structure; reconstructing a plurality of three-dimensional models of the sample using the image data, the plurality of three-dimensional models each comprising a given volume of the sample; determining a local stress of at least one of the plurality of three-dimensional models for a given applied stress via a finite element analysis with periodic boundary conditions; determining a fatigue strength of the at least one of the plurality of three-dimensional models based on the local stress to generate a probability distribution function for the given volume of the sample; predicting an expected fatigue strength of a volume comprising a plurality of cells of a honeycomb structure by applying extreme value statistics to the probability distribution function for the given volume of the sample; and causing a manufacturing device to form a part based on the expected fatigue strength.

[0125] The computer-implemented method according to any of the preceding clauses further includes: identifying properties of an equivalent homogeneous material representing the honeycomb structure; performing a stress analysis on a target component to generate a stress spatial distribution on the target component, wherein the honeycomb structure of the target component is replaced by the equivalent homogeneous material; discretizing the target component into a plurality of sub-volumes based on the stress spatial distribution; and performing fatigue assessment on at least some of the plurality of sub-volumes by comparing the stress on the sub-volume with the expected fatigue strength of the several units in the sub-volume.

[0126] The computer-implemented method according to any of the preceding clauses, further comprising: applying a weakest link analysis to the multiple sub-volumes, wherein the weakest link analysis comprises: determining a failure region in the target component based on the fatigue strength of the multiple sub-volumes and the stresses on the multiple sub-volumes; and determining the fatigue strength of the target component based on the failure region.

[0127] The computer-implemented method of any preceding clause, wherein the stress analysis of the target component is performed via a finite element analysis model of the target component that has been homogenized with the equivalent homogenous material.

[0128] The computer-implemented method of any preceding clause, wherein the property is an elastic property.

[0129] The computer-implemented method of any preceding clause, wherein the fatigue strength is an infinite life fatigue strength.

[0130] The computer-implemented method of any preceding clause, wherein the honeycomb structure is a lattice structure.

[0131] The computer-implemented method of any preceding clause, further comprising generating design parameters for a component including the honeycomb structure based on the expected fatigue strength, wherein the manufacturing device forms the part based on the design parameters.

[0132] The computer-implemented method of any preceding clause, further comprising: scanning a sample comprising a plurality of cells of a honeycomb structure using an imaging device to generate the image data, the imaging device being configured to acquire an image of the honeycomb structure.

[0133] The computer-implemented method of any preceding clause, wherein the sample is manufactured via an additive manufacturing device, and wherein the imaging device is an X-ray micro-computed tomography (μCT) scanner.

[0134] The computer-implemented method of any preceding clause, further comprising determining a number of cycles to failure of the target component based on the local stress and a target number of cells in the target component.

[0135] A computer-implemented method as in any preceding clause, wherein the image data is obtained from an X-ray micro-computed tomography scanner configured to scan the sample.

[0136] A computer-implemented method according to any of the preceding clauses, wherein the expected fatigue strength of the several cells in the honeycomb structure is predicted via the following formula: FT = FN(T / N), wherein T is the number of cells in the honeycomb structure, FT is the cumulative distribution function of the expected fatigue strength of the several cells, N is the number of cells in each sample, wherein N can be 1 or greater, and FN is the cumulative distribution function of the several cells in each sample.

[0137] A system for predicting fatigue strength, the system comprising: at least one imaging device; at least one processor, the at least one processor communicating with the at least one imaging device; and a memory device, the memory device storing instructions, the instructions, when executed by the at least one processor, causing the at least one processor to perform operations, the at least one processor being configured to: receive image data of a sample from the at least one imaging device, the sample comprising a plurality of cells of a honeycomb structure; reconstruct a plurality of three-dimensional models of the sample using the image data, the plurality of three-dimensional models each comprising a given volume of the sample; determine local stresses of at least one of the plurality of three-dimensional models for a given applied stress via finite element analysis with periodic boundary conditions; determine fatigue strength of the at least one of the plurality of three-dimensional models based on the local stresses to generate a probability distribution function for the given volume of the sample; and predict expected fatigue strength of a volume comprising a plurality of cells of a honeycomb structure by applying extreme value statistics to the probability distribution function for the given volume of the sample.

[0138] A system according to any of the preceding clauses, wherein the at least one processor is further configured to: identify properties of an equivalent homogeneous material representing the honeycomb structure; perform a stress analysis on a target component to generate a stress spatial distribution on the target component, wherein the structure of the target component is replaced by the equivalent homogeneous material; discretize the target component into a plurality of sub-volumes based on the stress spatial distribution; and perform fatigue assessment on at least some of the plurality of sub-volumes by comparing the stress on the sub-volume with the expected fatigue strength of the plurality of units in the sub-volume.

[0139] A system according to any preceding clause, wherein the at least one processor is further configured to: generate design parameters of a component including the honeycomb structure based on the expected fatigue strength; and manufacture the component as designed according to the design parameters via at least one manufacturing device in communication with the at least one processor.

[0140] A system according to any preceding clause, wherein the at least one processor is further configured to transmit at least one signal to a manufacturing device, wherein the at least one signal indicates instructions for manufacturing a component including the honeycomb structure, the instructions being based on the expected fatigue strength of the number of cells in the manufactured honeycomb structure.

[0141] A system according to any preceding clause, wherein the system further comprises at least one testing device configured to obtain a measured fatigue strength of the sample, and wherein the processor is further configured to compare the measured fatigue strength with the expected fatigue strength to determine an amount of error in the expected fatigue strength.

[0142] A computer-implemented method comprises: causing an imaging device to scan a sample including multiple cells of a honeycomb structure, the scanning generating image data of the sample; reconstructing multiple three-dimensional models of the sample, each of the multiple three-dimensional models including a given volume of the sample; determining the local stress of at least one of the multiple three-dimensional models for a given applied stress via a finite element analysis with periodic boundary conditions; determining the fatigue strength of the at least one of the multiple three-dimensional models based on the local stress to generate a probability distribution function of the given volume of the sample; and predicting the expected fatigue strength of a volume including several cells of the honeycomb structure by applying extreme value statistics to the probability distribution function of the given volume of the sample.

[0143] The computer-implemented method of any preceding clause, further comprising causing a manufacturing device to form a part based on the expected fatigue strength.

Claims

1. A computer-implemented method, characterized in that: include: receiving image data of a sample from an imaging device, the sample comprising a plurality of cells of a manufactured honeycomb structure; reconstructing a plurality of three-dimensional models of the sample using the image data, the plurality of three-dimensional models each including a given volume of the sample; determining a local stress of at least one of the plurality of three-dimensional models for a given applied stress via a finite element analysis with periodic boundary conditions; determining a fatigue strength of the at least one three-dimensional model of the plurality of three-dimensional models based on the local stress to generate a probability distribution function of the given volume of the sample; predicting the expected fatigue strength of a volume comprising a number of cells of a honeycomb structure by applying extreme value statistics to the probability distribution function for the given volume of the sample; and A manufacturing apparatus is caused to form a part based on the expected fatigue strength.

2. The computer-implemented method of claim 1, wherein: Further including: identifying properties of an equivalent homogeneous material representing the honeycomb structure; performing stress analysis on a target component to generate a stress spatial distribution on the target component, wherein the structure of the target component is replaced by the equivalent homogeneous material; discretizing the target component into a plurality of sub-volumes based on the stress spatial distribution; as well as Fatigue assessment is performed on at least some of the plurality of subvolumes by comparing stresses on the subvolumes to the expected fatigue strengths of the number of elements in the subvolumes.

3. The computer-implemented method of claim 2, wherein: Further including: applying a weakest link analysis to the plurality of sub-volumes, wherein the weakest link analysis comprises: determining a failure region in the target component based on the fatigue strengths of the plurality of sub-volumes and the stresses on the plurality of sub-volumes; and determining the fatigue strength of the target component based on the failure region.

4. The computer-implemented method of claim 2, wherein: The stress analysis of the target component is performed via a finite element analysis model of the target component that has been homogenized with the equivalent homogenous material.

5. The computer-implemented method of claim 2, wherein: The property in question is an elastic property.

6. The computer-implemented method of claim 1, wherein: The fatigue strength mentioned here is infinite life fatigue strength.

7. The computer-implemented method of claim 1, wherein: The honeycomb structure is a lattice structure.

8. The computer-implemented method of claim 1, wherein: Further including: Design parameters of a component including the honeycomb structure are generated based on the expected fatigue strength, wherein the manufacturing device forms the part based on the design parameters.

9. The computer-implemented method of claim 1, wherein: Further including: The image data is generated by scanning a sample including a plurality of cells of a honeycomb structure using an imaging device configured to acquire an image of the honeycomb structure.

10. The computer-implemented method of claim 1, wherein: Wherein the sample is manufactured via an additive manufacturing device, and wherein the imaging device is an X-ray micro-computed tomography (μCT) scanner.

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