Thermal stress calculation method of carbon fiber composite material and metal mixed structure
By using a two-dimensional finite element model and an equivalent stiffness calculation method, the problem of predicting thermal stress in carbon fiber composite and metal hybrid structures under thermal load was solved, achieving efficient and accurate thermal stress calculation and supporting structural reliability assessment and lightweight design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-21
- Publication Date
- 2026-03-24
AI Technical Summary
Existing technologies struggle to quickly and accurately predict interfacial thermal stress in carbon fiber composite and metal hybrid structures under thermal loads, leading to stress concentration in the structures under temperature changes, which affects reliability and design optimization.
By employing a two-dimensional finite element model combined with an equivalent stiffness calculation method, and constructing a hybrid fastening structure model, using refined mesh generation and beam element simulation of fasteners, thermal expansion and strain differences are calculated to achieve efficient thermal stress prediction.
A fast and accurate method for calculating thermal stress is provided, which can effectively predict the thermal stress of carbon fiber composite and metal hybrid structures, improves calculation efficiency and reduces hardware resource requirements, and supports structural reliability assessment and lightweight design.
Smart Images
Figure CN121723743A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of thermodynamic analysis of composite materials, and specifically to a method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure. Background Technology
[0002] Carbon fiber composite and metal hybrid structures are increasingly used in complex load-bearing structures in aerospace, new energy equipment, and high-end manufacturing fields due to the lightweight and high-strength properties of the composite materials and the excellent toughness and process adaptability of the metal materials. For example, in the aerospace field, hybrid structures can be used to manufacture aircraft wings and fuselage frames, significantly reducing weight and improving fuel efficiency; in new energy equipment, key parts of wind turbine blades use such structures to ensure strength while adapting to complex environmental conditions. However, because carbon fiber composites have a very small coefficient of thermal expansion, while the coefficients of thermal expansion of metal materials are mostly positive, the difference in their coefficients of thermal expansion can be an order of magnitude. This significant difference in coefficients of thermal expansion makes the structure highly susceptible to interfacial thermal stress concentration under temperature changes or thermal loads. Over time, this stress concentration may lead to debonding, crack propagation, or even overall structural failure, seriously threatening structural reliability.
[0003] Traditional methods for calculating thermal stress mainly rely on finite element analysis or simplified engineering formulas. While these methods can simulate basic stress fields, they suffer from several key technical shortcomings in practical applications. From a theoretical model perspective, existing models provide a simplified description of the mechanical behavior of the interface layer. For example, they lack accurate characterization of complex phenomena such as bond failure and contact friction, and fail to reflect the impact of material property gradients and microstructural differences. In terms of numerical calculations, refined numerical simulations often require high-density mesh generation, which significantly increases computational complexity, leading to low computational efficiency and placing high demands on hardware resources, making it difficult to meet the needs of rapid iterative optimization in engineering design. Furthermore, actual service conditions typically include complex factors such as dynamic thermal loads and multi-field coupling, and traditional methods are insufficient in adapting to such conditions, resulting in significant deviations between calculated results and actual operating conditions. This severely restricts the optimized design and engineering application of hybrid fastening structures. Summary of the Invention
[0004] The purpose of this invention is to provide a method for calculating the thermal stress of carbon fiber composite materials and metal hybrid structures. This invention offers high calculation efficiency and accurate results.
[0005] The objective of this invention is achieved through the following technical solution: a method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure, comprising the following steps: Step 1. Obtain the mechanical property parameters of carbon fiber composite materials and metallic materials; Step 2. Construct a two-dimensional finite element model of the hybrid fastening structure of carbon fiber composite material and metal; Step 3. Calculate the equivalent stiffness of the hybrid fastening structure and assign material properties; Step 4. Construct unconnected carbon fiber composite plates and metal plates, and calculate the pure thermal expansion; Step 5. Subtract the calculated strain values of the composite material and metal plate in the non-connected structure from the calculated strain values of the carbon fiber composite material and the metal plate, respectively, to obtain the final predicted thermal strain.
[0006] In step 1 of the aforementioned method for calculating the thermal stress of carbon fiber composite materials and metal hybrid structures, the mechanical property parameters of the carbon fiber composite materials include: density, elastic modulus, Poisson's ratio, shear modulus, and coefficients of thermal expansion in the 0° and 90° directions.
[0007] In step 1 of the aforementioned method for calculating the thermal stress of carbon fiber composite materials and metal hybrid structures, the mechanical property parameters of the metal material include: density, elastic modulus, Poisson's ratio, and coefficient of thermal expansion. Step 2 of the aforementioned method for calculating the thermal stress of carbon fiber composite and metal hybrid structures includes the following steps: Step 2a. Simplify the connecting plate of the hybrid fastening structure into a shell element of equal thickness, select the neutral plane of the connecting plate as the reference plane of the shell element, and remove the corresponding geometric area according to the fastener diameter of the hybrid fastening structure to simulate the fastener hole. Step 2b. Divide the area around the fastener hole into a square region with the center of the hole as the midpoint. Use a fine mesh for the area around the hole edge and a coarse mesh for the area away from the hole edge. Use S4R to divide the mesh. Step 2c. Simplify the fastener into a beam element. Establish a node at the center of the fastener hole. The node and the connecting plate are on the same horizontal plane, serving as the endpoint of the beam element. Establish B3 to simulate the fastener by connecting the corresponding nodes on the composite plate and the metal plate. The beam element coordinate system is as follows: direction 1 is along the length of the test piece, direction 2 is along the width of the test piece, and direction 3 is along the thickness of the test piece. Use Coupling to establish motion coupling between all nodes at the edge of the hole and the endpoint of the beam element, constraining six degrees of freedom.
[0008] In step 3 of the aforementioned method for calculating the thermal stress of carbon fiber composite and metal hybrid structures, the equivalent stiffness relationship is as follows:
[0009] in, C This refers to the fastener flexibility coefficient. E beam The equivalent elastic modulus of the fastener beam element. S Let be the cross-sectional area of the fastener. I Let the moment of inertia of the cross section be...L Let the length be the beam element length. v For the material's Poisson's ratio, β This is a correction factor.
[0010] In the aforementioned method for calculating the thermal stress of carbon fiber composite and metal hybrid structures, when the cross-section is a solid circle: .
[0011] In the aforementioned method for calculating the thermal stress of carbon fiber composite and metal hybrid structures, when the cross-section is a circular tube: .
[0012] In the aforementioned method for calculating the thermal stress of carbon fiber composite and metal hybrid structures, the fastener compliance coefficient C is expressed as follows:
[0013] in, a Indicates the fastener material correction factor; b Indicates the fastener material correction factor; D Indicates the diameter of the fastener; E bolt Indicates the elastic modulus of the fastener material; E c This represents the equivalent modulus of elasticity of the composite material. E m Indicates the elastic modulus of a metal sheet; t c Indicates the thickness of the composite board; t m Indicates the thickness of the metal plate.
[0014] Beneficial effects: This invention is a thermal stress calculation method that can quickly predict the thermal stress of carbon fiber composite and metal hybrid structures, and can balance calculation accuracy and efficiency. It effectively solves the problem of predicting the interface stress of carbon fiber composite and metal hybrid structures under thermal load. It has high calculation efficiency and accurate results, and provides stronger technical support for structural reliability assessment and lightweight design. Attached Figure Description
[0015] Figure 1 A schematic diagram of a finite element model of a carbon fiber composite and metal hybrid structure; Figure 2 Schematic diagram of finite element models of unconnected carbon fiber composite plate and metal plate; Figure 3 Figure 1 shows the dimensions and strain gauge distribution of the carbon fiber composite and metal hybrid structure. Figure 4A flowchart illustrating a method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure provided by this invention. Detailed Implementation
[0016] The present invention will be described in detail below with reference to embodiments and accompanying drawings, so that those skilled in the art can more fully understand the inventive concept of the present invention. It should be understood that the scope of protection of the claims of the present invention is not limited to the following embodiments. For those skilled in the art, any equivalent alternative embodiments obtained without creative effort without departing from the core inventive concept of the present invention should be included within the scope of protection of the present invention.
[0017] Example 1. A method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure, the specific steps of which are as follows: Step 1: Obtain the mechanical property parameters of carbon fiber composite materials and metals. The parameters of carbon fiber composite materials include density, elastic modulus, Poisson's ratio, shear modulus, and coefficient of thermal expansion at 0° (along the fiber direction) and 90° (perpendicular to the fiber direction). The parameters of metal materials include density, elastic modulus, Poisson's ratio, and coefficient of thermal expansion.
[0018] Step 2: Construct a two-dimensional finite element model of the carbon fiber composite material and metal hybrid fastening structure: Step 2a: Simplify the connecting plate into a shell element of equal thickness, select the neutral plane of the connecting plate as the reference plane of the shell element, and remove the corresponding geometric area according to the fastener diameter to simulate the fastener hole. Step 2b: Divide the area around the fastener hole into square regions with the center of the hole as the midpoint to facilitate regular mesh division. Use a fine mesh for the area around the hole and a coarse mesh for the area away from the hole. Use S4R (4-node shell element) to divide the mesh. Step 2c: Simplify the fastener into a beam element. Create a node at the center of the fastener hole, with the node and the connecting plate on the same horizontal plane, serving as the endpoint of the beam element. Create B3 (2-node linear beam element) simulations of the fastener using the corresponding nodes connecting the composite plate and the metal plate. The beam element coordinate system is defined with direction 1 along the length of the specimen, direction 2 along the width of the specimen, and direction 3 along the thickness of the specimen. Use coupling to kinematically couple all nodes at the hole edge to the beam element endpoints, constraining six degrees of freedom.
[0019] Step 3: Calculate the equivalent stiffness of the fastener and assign material properties: Step 3a: Assign cross-sectional properties to the metal plate mesh and composite plate mesh according to their actual thickness and layup, and assign cross-sectional properties to the fasteners according to their actual diameter; Step 3b: Assign mechanical properties and coefficient of thermal expansion to the metal plate and the composite plate respectively. The coefficient of thermal expansion of the composite plate is assigned in three directions: direction 1 is along the fiber direction, and directions 2 and 3 are perpendicular to the fiber direction. Step 3c: The elastic modulus of the beam element simulating the fastener cannot be the elastic modulus of the fastener material; instead, modulus correction is required. The equivalent modulus relationship is as follows:
[0020] in, C Indicates the fastener compliance factor. E beam This represents the equivalent elastic modulus of the fastener beam element. S This represents the cross-sectional area of the fastener. I Represents the moment of inertia of the cross section. L Indicates the length of the beam element. v Indicates the Poisson's ratio of the material. β The value represents the correction factor, which is related to the cross-sectional shape. The relationship is shown in Table 1.
[0021] Table 1 Correction factor
[0022] The formula for the fastener compliance coefficient C is:
[0023] in, a This indicates the fastener material correction factor: 1.67 for steel bolts, 4 for titanium bolts, and 5 for aluminum rivets. b This represents the fastener material correction factor: 0.86 for steel bolts, 0.82 for titanium bolts, and 0.8 for aluminum rivets. D Indicates the fastener diameter, in mm; E bolt This represents the elastic modulus of the fastener material, expressed in MPa. E c This represents the equivalent elastic modulus of the composite board, in MPa. E m This represents the elastic modulus of a metal plate, expressed in MPa. t c Indicates the thickness of the composite board, in mm; t m Indicates the thickness of the metal plate, in mm.
[0024] Step 4: Using the same modeling method, establish a non-connected structural finite element model. Remove the constraints on beam elements and plates, delete beam elements and nodes, and constrain all degrees of freedom of any node on both the composite plate and the metal plate to limit rigid body displacement. Obtain the theoretical calculated values of thermal expansion of the composite plate and the metal plate under temperature load. Apply a temperature load to the test specimen, define the initial temperature and the termination temperature, submit the calculation, and obtain the pure thermal expansion strain.
[0025] Step 5: Considering geometric nonlinearity, after the calculation is complete, extract the strain results of the element at the location of interest (or the average strain of the surrounding elements, while paying attention to distinguishing the bottom and top surfaces of the shell element). Subtract the strain calculation values of the composite plate and the metal plate in the non-connected structure from the strain calculation values of the composite plate and the metal plate, respectively, to obtain the final predicted thermal strain.
[0026] Example 2. This example provides a method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure. See [link to example]. Figures 1-4 It includes five steps: Step 1: Obtain the mechanical property parameters and coefficients of thermal expansion of the carbon fiber composite material and the metal. The parameters of the carbon fiber composite material include density, elastic modulus, Poisson's ratio, shear modulus, and coefficients of thermal expansion at 0° (along the fiber direction) and 90° (perpendicular to the fiber direction). The parameters of the metal material include density, elastic modulus, Poisson's ratio, shear modulus, and coefficient of thermal expansion. In this example, the metal material is aluminum, and the carbon fiber composite material is a unidirectional tape. The mechanical property parameters and coefficients of thermal expansion of the materials are shown in Table 2. E 1 represents the elastic modulus along the fiber direction. E 2 and E 3 represents the elastic modulus perpendicular to the fiber direction. α 1 is the coefficient of thermal expansion along the fiber direction. α 2 and α 3 is the coefficient of thermal expansion perpendicular to the fiber direction.
[0027] Table 2 Mechanical properties and coefficients of thermal expansion of carbon fiber composites and aluminum in the finite element model.
[0028] Step 2: Construct a two-dimensional finite element model of the carbon fiber composite material and metal hybrid structure: Step 2a: Simplify the connecting plate into shell elements of uniform thickness, select the neutral plane of the connecting plate as the reference plane for the shell elements, and remove the corresponding geometric region according to the fastener diameter to simulate the fastener hole. In this embodiment, the models of the composite plate and the metal plate are as follows: Figure 1 As shown, the length and width are 242mm and 50mm respectively, and the thickness of each is 3mm. The ply count of the composite board is [45 / -45 / 0 / 90 / 45 / -45 / 0 / 45 / -45 / 90]. sEach layer is 0.15mm thick. The composite board and the metal plate are connected together by seven fasteners, each with a diameter of 6.35mm. Along the length direction, each fastener is spaced 31.8mm apart, and the distance between the plate edge and the nearest fastener is 25.6mm. Along the width direction, the fasteners are equidistant from both sides. Seven circles with a diameter of 6.35mm are drawn in the corresponding geometric area and then removed to simulate fastener holes.
[0029] Step 2b: Divide the area around the fastener hole into square regions with the hole center as the midpoint and a side length of 12mm. This facilitates regular mesh division. A fine mesh is used for the area around the hole edge, while a coarse mesh is used for the area further away from the hole edge. The mesh is generated using S4R (4-node shell element). In this embodiment, the area further away from the hole edge is a quadrilateral mesh with a length of 1.5mm, while the area around the hole edge is an irregular quadrilateral with a minimum length of 0.6mm. The total number of meshes is 11367.
[0030] Step 2c: Simplify the fastener into a beam element. Establish a node at the center of the fastener hole, on the same horizontal plane as the connecting plate, as the endpoint of the beam element. Then connect the corresponding nodes to establish B3 (2-node linear beam element) to simulate the fastener. The beam element coordinate system is: direction 1 along the length of the test piece, direction 2 along the width of the test piece, and direction 3 along the thickness of the test piece. Use coupling to establish motion coupling between the edge of the hole and the endpoint of the fastener, constraining six degrees of freedom. In this embodiment, the beam element length is half the sum of the thicknesses of the metal plate and the composite plate, which is 3 mm.
[0031] Step 3: Calculate the equivalent stiffness of the fastener and assign material properties: Step 3a: Assign cross-sectional properties to the metal plate mesh and composite plate mesh according to their actual thickness and ply count, respectively; assign cross-sectional properties to the fasteners according to their actual diameter. In this embodiment, the metal plate is isotropic and has a thickness of 3 mm; the composite plate is anisotropic and its ply count is set to [45 / -45 / 0 / 90 / 45 / -45 / 0 / 45 / -45 / 90]. s Each layer is 0.15mm thick, and directions 1, 2, and 3 are set as the length, width, and thickness directions of the composite board, respectively. The diameter of the beam element is set to 6.35mm.
[0032] Step 3b: Assign mechanical properties and coefficients of thermal expansion to the composite board and the metal plate respectively. The coefficient of thermal expansion of the composite board is assigned in three directions: direction 1 is along the fiber direction, and directions 2 and 3 are perpendicular to the fiber direction. In this embodiment, the relevant parameters are input according to Table 2.
[0033] Step 3c: The elastic modulus of the beam element simulating the fastener cannot be the elastic modulus of the fastener material; instead, modulus correction is required. The equivalent modulus relationship is as follows:
[0034] in, C Indicates the fastener compliance factor. E beam This represents the equivalent elastic modulus of the fastener beam element. S This represents the cross-sectional area of the fastener. I Represents the moment of inertia of the cross section. L Indicates the length of the beam element. v Indicates the Poisson's ratio of the material. β This represents the correction factor, which is related to the cross-sectional shape. The relationship is shown in Table 3.
[0035] Table 3 Correction factor
[0036] The formula for the fastener compliance coefficient C is:
[0037] in, a This indicates the fastener material correction factor: 1.67 for steel bolts, 4 for titanium bolts, and 5 for aluminum rivets. b This represents the fastener material correction factor: 0.86 for steel bolts, 0.82 for titanium bolts, and 0.8 for aluminum rivets. D Indicates the fastener diameter, in mm; E bolt This represents the elastic modulus of the fastener material, expressed in MPa. E c This represents the equivalent elastic modulus of the composite board, in MPa. E m This represents the elastic modulus of a metal plate, expressed in MPa. t c Indicates the thickness of the composite board, in mm; t m Indicates the thickness of the metal plate, in mm.
[0038] In this embodiment, the fastener is made of titanium alloy with an elastic modulus of 110316 MPa, a Poisson's ratio of 0.31, and a coefficient of thermal expansion of 9.1 × 10⁻⁶. -6 / ℃. Therefore, the compliance factor, correction factor, and equivalent modulus of the fastener are:
[0039]
[0040]
[0041] Step 4: Using the same modeling method, establish a non-connected structural finite element model. Remove the constraints on beam elements and plates, delete beam elements and nodes, and constrain all degrees of freedom of any node on both the composite plate and the metal plate to limit rigid body displacement. Obtain the theoretically calculated values of thermal expansion of the composite plate and the metal plate under temperature load. Apply a temperature load to the test specimen, defining the initial temperature and the termination temperature. Submit the calculation and obtain the pure thermal expansion strain.
[0042] In this embodiment, other settings remain unchanged. The nodes and elements of the beam element are deleted. All degrees of freedom of one node are restricted on the metal plate and the composite plate respectively. A temperature load is applied to the entire model with an initial temperature of 20°C and a final temperature of 70°C. Then the calculation is submitted.
[0043] Step 5: Considering geometric nonlinearity, after the calculation is complete, extract the strain results of the element at the location of interest (or the average strain of the surrounding elements, while paying attention to distinguishing the bottom and top surfaces of the shell element). Subtract the strain calculation values of the metal plate and composite plate in the non-connected structure from the strain calculation values of the metal plate and composite plate respectively to obtain the final predicted thermal strain.
[0044] In this embodiment, all degrees of freedom of any node in the hybrid structural model composite plate (or metal plate) are restricted, and a temperature load with an initial temperature of 20°C and a final temperature of 70°C is applied to the entire model, considering geometric nonlinearity, before calculation. The region of interest is on the surface of the composite plate and the metal plate, with strain gauges 1-16 positioned as follows: Figure 3 As shown in the figure, the strain at corresponding locations in the hybrid structure and the non-connected structure were extracted respectively, and the result of the non-connected structure model was subtracted from the result of the hybrid structure model to obtain the final predicted thermal strain. The comparison with the experimental results is shown in the table below. As can be seen from Table 4, the predicted results are in good agreement with the experimental results.
[0045] Table 4 Comparison of Experimental Values and Predicted Values
[0046] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure, characterized in that, Includes the following steps: Step 1. Obtain the mechanical property parameters of carbon fiber composite materials and metallic materials; Step 2. Construct a two-dimensional finite element model of the hybrid fastening structure of carbon fiber composite material and metal; Step 3. Calculate the equivalent stiffness of the hybrid fastening structure and assign material properties; Step 4. Construct unconnected carbon fiber composite plates and metal plates, and calculate the pure thermal expansion; Step 5. Subtract the calculated strain values of the composite material and metal plate in the non-connected structure from the calculated strain values of the carbon fiber composite material and the metal plate, respectively, to obtain the final predicted thermal strain.
2. The method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure according to claim 1, characterized in that, In step 1, the mechanical property parameters of the carbon fiber composite material include: density, elastic modulus, Poisson's ratio, shear modulus, and coefficients of thermal expansion in the 0° and 90° directions.
3. The method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure according to claim 1, characterized in that, In step 1, the mechanical property parameters of the metallic material include: density, elastic modulus, Poisson's ratio, and coefficient of thermal expansion.
4. The method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure according to claim 1, characterized in that, Step 2 includes the following steps: Step 2a. Simplify the connecting plate of the hybrid fastening structure into a shell element of equal thickness, select the neutral plane of the connecting plate as the reference plane of the shell element, and remove the corresponding geometric area according to the fastener diameter of the hybrid fastening structure to simulate the fastener hole. Step 2b. Divide the area around the fastener hole into a square region with the center of the hole as the midpoint. Use a fine mesh for the area around the hole edge and a coarse mesh for the area away from the hole edge. Use S4R to divide the mesh. Step 2c. Simplify the fastener into a beam element. Establish a node at the center of the fastener hole. The node and the connecting plate are on the same horizontal plane, serving as the endpoint of the beam element. Establish B3 to simulate the fastener by connecting the corresponding nodes on the composite plate and the metal plate. The beam element coordinate system is as follows: direction 1 is along the length of the test piece, direction 2 is along the width of the test piece, and direction 3 is along the thickness of the test piece. Use Coupling to establish motion coupling between all nodes at the edge of the hole and the endpoint of the beam element, constraining six degrees of freedom.
5. The method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure according to claim 1, characterized in that, In step 3, the equivalent stiffness relationship is as follows: in, C This refers to the fastener flexibility coefficient. E beam The equivalent elastic modulus of the fastener beam element. S Let be the cross-sectional area of the fastener. I Let the moment of inertia of the cross section be... L Let the length be the beam element length. v For the material's Poisson's ratio, β This is a correction factor.
6. The method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure according to claim 5, characterized in that, When the cross-section is a solid circular cross-section: 。 7. The method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure according to claim 5, characterized in that, When the cross-section is a circular tube with a circular cross-section: 。 8. The method for calculating the thermal stress of a carbon fiber composite material and metal hybrid structure according to claim 5, characterized in that, The formula for the fastener compliance coefficient C is: in, a Indicates the fastener material correction factor; b Indicates the fastener material correction factor; D Indicates the diameter of the fastener; E bolt Indicates the elastic modulus of the fastener material; E c This represents the equivalent modulus of elasticity of the composite material. E m Indicates the elastic modulus of a metal sheet; t c Indicates the thickness of the composite board; t m Indicates the thickness of the metal plate.