Strength prediction method of resin matrix composite considering the influence of heating time

Abstract

The present invention discloses a method for predicting the strength of resin matrix composites considering the influence of heating time, comprising the following steps: 1) Establish a mesoscopic full-cell model of the resin matrix composite, and the size of the model in the thickness direction is the same as that of the test piece; 2) Endow the mesoscopic full-cell model with thermodynamic properties, set the heating time and heating temperature, and perform transient heat conduction calculation; 3) Obtain the temperature of each unit at this heating time, and obtain the mechanical properties at this temperature; 4) Endow the mechanical properties corresponding to the heating time into the mesoscopic full-cell model, apply periodic boundary conditions, and calculate the strength value of the resin matrix composite at this heating time; 5) Set the analysis step, perform the solution, add the corresponding damage judgment criterion according to the components, and obtain the strength value of the finite element model; 6) After the calculation of the current time analysis step is completed, perform the transient heat conduction calculation at the next moment, and repeat steps 2-5 until the calculation is completed. The present invention can be applied to the design and analysis of complex composite material structures in the aerospace field.

Description

Technical Field

[0001] The invention relates to the technical field of resin-based composite materials for aviation, and in particular to a strength prediction method for resin-based composite materials taking into account the influence of heating time. Background Art

[0002] Resin-based composite materials can have high strength and rigidity, can withstand large stress and strain, have good corrosion resistance, can be used in various environments, and therefore have a long service life. In addition, the processing technology of resin-based composite materials is relatively simple, and products of various shapes and sizes can be easily manufactured. Some traditional metal materials can be replaced, reducing product weight and reducing costs. Therefore, resin-based composite materials are widely used in aerospace, shipbuilding, wind power, automobiles and other fields due to their good performance.

[0003] When resin-based composite materials are used in aircraft engines and other parts, temperature has a great impact on the composite materials. The relevant technology focuses on the effect of temperature on the mechanical properties of materials, and there are few studies on the effect of heating time on the mechanical properties of resin-based composite materials. Summary of the invention

[0004] The present invention provides a strength prediction method for a resin-based composite material taking into account the influence of heating time, and determines appropriate heating and heat preservation time for mechanical tests of the composite material at different temperatures, so as to improve the accuracy and efficiency of the test.

[0005] An embodiment of the present invention provides a method for predicting the strength of a resin-based composite material taking into account the influence of heating time, comprising the following steps:

[0006] Step 1, establishing a microscopic whole-cell finite element model of resin-based composite materials;

[0007] Step 2, assign thermodynamic properties to the mesoscopic whole-cell finite element model, set a temperature load on the surface of one end of the mesoscopic whole-cell finite element model, set the time step and time increment, and perform transient heat conduction calculation;

[0008] Step 3, obtaining the temperature of each finite element unit at the current heating time, bringing the temperature value into the empirical fitting formula of the mechanical properties of the fiber bundle and the matrix under the temperature condition, and obtaining the material mechanical properties of each finite element unit at the current temperature;

[0009] Step 4: Assign the mechanical properties of the material at the current heating time to the mesoscopic whole-cell finite element model and apply periodic boundary conditions;

[0010] Step 5: Apply the corresponding damage judgment criteria according to the components of the resin-based composite material. When the damage criteria are triggered, bring the stiffness drop factor into the damage constitutive matrix of the component material for iterative calculation. Use the volume average method to obtain the average stress and average strain of the whole cell model, and draw the stress-strain curve. The peak value of the curve is the strength value of the microscopic finite element model at the current heating time.

[0011] Step 6: After the strength value calculation of the microscopic whole-cell finite element model of the current time analysis step is completed, the transient heat conduction calculation of the next moment is performed, and steps 2 to 5 are repeated until the calculation is completed to obtain the predicted result of the change in heating time on the strength value of the resin-based composite material.

[0012] Optionally, in one embodiment of the present invention, the mesoscopic whole-cell finite element model of the resin-based composite material is a mesoscopic geometric model of the fiber bundle and the matrix established in the modeling software, and the size of the mesoscopic geometric model in the thickness direction is the same as the actual thickness size of the test piece.

[0013] Optionally, in one embodiment of the present invention, the calculation formula of the material mechanical properties of each finite element unit at the current temperature is:

[0014] E 11 =0.999(V f E f1 +V m E m )(1-0.00158sinh((T-23) / (71.389-23)))

[0015]

[0016]

[0017]

[0018] μ 12 =V f μ f12 +V m μ m

[0019] μ 21 =E 22 μ 12 / E 11

[0020] X T =0.736(V f X f1 +V m X m )(1-0.000846sinh((T-23) / (57.308-23)))

[0021] X C =0.5058(V f X f +(1-V f )X m )(1+0.1402·sinh[(TT 0 ) / (-100.9-T 0 )])

[0022]

[0023]

[0024] S 12 =107.483(1+0.9417V f )(1-0.627sinh((T-23) / (299.998-23)))

[0025] E m =E 0 (1-0.115sinh(T-23) / 78.906)

[0026] X m =X 0 (1-0.23sinh((T-23) / 98.423))

[0027] Among them, E 11 is the axial elastic modulus of the fiber bundle, V f is the volume fraction of the fiber single filament, E f1 is the axial elastic modulus of the fiber, V m is the matrix volume fraction, E m is the matrix elastic modulus, T is the temperature, E 22 is the transverse elastic modulus of the fiber bundle, E f2 is the transverse elastic modulus of the fiber monofilament, E 45 is the shear modulus, G 12 is the in-plane shear modulus of the fiber bundle, μ 21 is the out-of-plane Poisson's ratio of the fiber bundle, μ 12 is the Poisson's ratio in the fiber bundle plane, μ f12 is the Poisson's ratio of the fiber monofilament in the plane, μ m is the matrix Poisson's ratio, X T is the axial tensile strength of the fiber bundle, X f1 is the tensile strength of the fiber monofilament, X C is the transverse tensile strength of the fiber bundle, X f is the transverse tensile strength of the fiber monofilament, X m is the matrix tensile strength, Y Cis the transverse compressive strength of the fiber bundle, T 0 is room temperature, Y T is the transverse tensile strength of the fiber bundle, S 12 is the in-plane shear strength, E 0 is the room temperature elastic modulus of the matrix, X 0 is the room temperature tensile strength of the matrix.

[0028] Optionally, in one embodiment of the present invention, in step 4, the periodic boundary condition applied is:

[0029]

[0030]

[0031] Among them, j+ and j- represent opposite sides, represents the tensile / compressive deformation caused by the load in the three main directions. Corresponding to the shear deformation in the three main directions, is the average strain of the microscopic unit cell model, is the distance between corresponding points on the opposite boundary surface.

[0032] Optionally, in one embodiment of the present invention, the damage judgment criterion applied by the component materials is:

[0033] Longitudinal fiber bundle stretch injury:

[0034]

[0035] Compression injury of longitudinal fiber bundles:

[0036]

[0037] Transverse fiber bundle stretch injury:

[0038]

[0039] Transverse fiber bundle compression injury:

[0040]

[0041] For the matrix component unit, the Mises failure criterion is as follows:

[0042]

[0043] Among them, σ 11 is the principal stress in the X direction of the fiber bundle, τ 12 is the in-plane shear stress of the fiber bundle, τ 13 is the out-of-plane shear stress of the fiber bundle, S 21 is the out-of-plane shear strength of the fiber bundle, σ22 is the principal stress in the Y direction of the fiber bundle, τ 23 is the out-of-plane shear stress of the fiber bundle, σ 33 is the principal stress in the Z direction of the fiber bundle, S 23 is the out-of-plane shear strength of the fiber bundle, J 2 is the second deviatoric stress invariant of the resin matrix, is the tensile / compressive strength of the resin matrix.

[0044] Optionally, in one embodiment of the present invention, in step 5, the volume averaging method is:

[0045]

[0046]

[0047] in, and is the average stress and average strain, V is the total volume of the unit cell model, v i is the volume of the i-th unit, and N is the total number of finite element units.

[0048] The resin-based composite material strength prediction method considering the influence of heating time in the embodiment of the present invention determines the appropriate heating and insulation time for mechanical tests of composite materials at different temperatures to improve the accuracy and efficiency of the tests, and can be applied to complex composite material structure design and analysis problems in the aerospace field.

[0049] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0051] Figure 1 A flowchart of a method for predicting the strength of a resin-based composite material taking into account the influence of heating time according to an embodiment of the present invention;

[0052] Figure 2 The implementation process of the method for predicting the strength of a resin-based composite material taking into account the influence of heating time according to an embodiment of the present invention;

[0053] Figure 3 A full-cell model of a resin-based composite material according to an embodiment of the present invention;

[0054] Figure 4 It is the temperature distribution cloud diagram of the composite material when the heating time is 2 minutes;

[0055] Figure 5 Schematic diagram of applying periodic boundary conditions to the whole cell;

[0056] Figure 6 is the strength value of the resin-based composite material at room temperature;

[0057] Figure 7 is the change of strength of resin-based composite material with heating time. DETAILED DESCRIPTION

[0058] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0059] like Figure 1 and Figure 2 As shown, the strength prediction method of the resin-based composite material considering the influence of heating time includes the following steps:

[0060] Step 1: Establish a microscopic whole-cell finite element model of resin-based composite materials.

[0061] In an embodiment of the present invention, the microscopic whole-cell finite element model of the resin-based composite material is a microscopic geometric model of the fiber bundle and the matrix established in the modeling software, such as Figure 3 The size of the micro-geometry model in the thickness direction is the same as the actual thickness of the test piece, and the mesh units are divided using finite element software.

[0062] Step 2: Assign thermodynamic properties to the mesoscopic whole-cell finite element model, set a temperature load on the surface of one end of the mesoscopic whole-cell finite element model, set the time step and time increment, and perform transient heat conduction calculation.

[0063] In the embodiment of the present invention, the thermal conductivity, specific heat and density of the component materials are assigned to the microscopic whole cell finite element model. A temperature load is set on the surface of one end of the model, and it is considered that the heat between the heat source and the material is transferred by heat conduction. The analysis step and time increment are set to perform transient heat conduction calculation.

[0064] The thermodynamic properties of the component materials are assigned to the microscopic whole-cell finite element model. The thermodynamic properties of the fiber single filament and the matrix are shown in the following table. The thermodynamic properties of the fiber bundle are obtained by the weighted average method:

[0065] Table 1 Thermodynamic properties of fiber monofilament and matrix

[0066]

[0067] Set the temperature load to 223℃, the total heating time to 30min, the time increment to 1min, and perform transient heat conduction calculation. Figure 4 This is the temperature distribution cloud diagram when the heating time is 2 minutes.

[0068] Step 3: Obtain the temperature of each finite element unit at the current heating time, and bring the temperature value into the empirical fitting formula of the mechanical properties of the fiber bundle and the matrix under the temperature condition to obtain the material mechanical properties of each finite element unit at the current temperature.

[0069] Read each analysis step, obtain the temperature value of each unit, and store it in the array. Substitute the temperature value into the empirical fitting formula of the mechanical properties of the fiber bundle and the matrix under temperature conditions to obtain the mechanical properties of the component materials at this temperature. The empirical fitting formula of the mechanical properties of the fiber bundle and the matrix under temperature conditions is obtained by fitting the experimental data.

[0070] Read the calculation results of this analysis step and obtain the temperature value of each unit through the finite element software command Store it in an array Among them, E i The unit number.

[0071] Read the data in the array and bring the temperature value of the unit into the fitting formula of the mechanical properties of the fiber bundle and the matrix under the temperature environment, as shown in the following table, to obtain the mechanical properties of each unit at its temperature.

[0072] Table 2 Mechanical properties of fiber bundles and matrix under temperature conditions

[0073]

[0074]

[0075] Among them, E 11 is the axial elastic modulus of the fiber bundle, V f is the volume fraction of the fiber single filament, E f1 is the axial elastic modulus of the fiber, V m is the matrix volume fraction, E m is the matrix elastic modulus, T is the temperature, E 22 is the transverse elastic modulus of the fiber bundle, E f2 is the transverse elastic modulus of the fiber monofilament, E 45 is the shear modulus, G 12 is the in-plane shear modulus of the fiber bundle, μ 21 is the out-of-plane Poisson's ratio of the fiber bundle, μ 12 is the Poisson's ratio in the fiber bundle plane, μ f12 is the Poisson's ratio of the fiber monofilament in the plane, μ m is the matrix Poisson's ratio, X Tis the axial tensile strength of the fiber bundle, X f1 is the tensile strength of the fiber monofilament, X C is the transverse tensile strength of the fiber bundle, X f is the transverse tensile strength of the fiber monofilament, X m is the matrix tensile strength, Y C is the transverse compressive strength of the fiber bundle, T 0 is room temperature, Y T is the transverse tensile strength of the fiber bundle, S 12 is the in-plane shear strength, E 0 is the room temperature elastic modulus of the matrix, X 0 is the room temperature tensile strength of the matrix.

[0076] Step 4: Assign the mechanical properties of the material at the current heating time to the microscopic whole-cell finite element model and apply periodic boundary conditions.

[0077] Apply periodic boundary conditions to the microscopic whole cell finite element model. The whole cell model only has two pairs of periodic parallel surfaces in the X-axis and Z-axis directions. In the thickness direction (Y-axis), the whole cell model is not periodic. The nodes on the parallel boundary surfaces of the whole cell finite element model are divided into three categories: face nodes, edge nodes and corner nodes, and the corresponding node sets are established. Figure 5 The schematic diagram of applying periodic boundary conditions to the whole cell is shown in the figure. The nodes are specifically divided into: (a) 3 pairs of face nodes: face ABFE and face DCGH, face BCGF and face ADHE; (b) edge nodes: AB and CD, AD and BC, EF and HG, EH and FG, AE FBHD; (c) corner nodes: A, B, C, D, E, F, G, H. The following constraint equations are applied to each node relationship:

[0078]

[0079]

[0080] Among them, j+ and j- represent opposite sides, represents the tensile / compressive deformation caused by the load in the three main directions. Corresponding to the shear deformation in the three main directions, is the average strain of the microscopic unit cell model, is the distance between corresponding points on the opposite boundary surface.

[0081] Step 5. Apply corresponding damage judgment criteria according to the components of the resin-based composite material. When the damage criterion is triggered, the stiffness drop factor is brought into the damage constitutive matrix of the component material for iterative calculation. The volume averaging method is used to obtain the average stress and average strain of the whole cell model, and the stress-strain curve is drawn. The peak value of the curve is the strength value of the microscopic finite element model at the current heating time.

[0082] Different damage judgments are used for different components. When the component material is damaged, the stiffness drop factor is brought into the component material constitutive matrix for iterative calculation. The strain and stress of the whole cell model are calculated using the volume average method, and the stress / strain curve is drawn, as shown in the attached figure. Figure 6 The peak value in the stress-strain curve corresponds to the strength value of the resin-based composite material.

[0083] The damage judgment criteria based on the component materials are:

[0084] Longitudinal fiber bundle stretch injury:

[0085]

[0086] Compression injury of longitudinal fiber bundles:

[0087]

[0088] Transverse fiber bundle stretch injury:

[0089]

[0090] Transverse fiber bundle compression injury:

[0091]

[0092] For the matrix component unit, the Mises failure criterion is as follows:

[0093]

[0094] Among them, σ 11 is the principal stress in the X direction of the fiber bundle, τ 12 is the in-plane shear stress of the fiber bundle, τ 13 is the out-of-plane shear stress of the fiber bundle, S 21 is the out-of-plane shear strength of the fiber bundle, σ 22 is the principal stress in the Y direction of the fiber bundle, τ 23 is the out-of-plane shear stress of the fiber bundle, σ 33 is the principal stress in the Z direction of the fiber bundle, S 23 is the out-of-plane shear strength of the fiber bundle, J 2 is the second deviatoric stress invariant of the resin matrix, is the tensile / compressive strength of the resin matrix.

[0095] Optionally, in one embodiment of the present invention, when the component material damage judgment criterion polynomial is ≥ 1, the component material is damaged. At this time, the stiffness sudden drop factor is brought into the component material constitutive matrix. The stiffness sudden drop factor is specifically:

[0096]

[0097] Optionally, in one embodiment of the present invention, after the load step calculation is completed, the method for calculating the average stress and the average strain is:

[0098]

[0099]

[0100] in, and is the average stress and average strain, V is the total volume of the unit cell model, v i is the volume of the i-th unit, and N is the total number of finite element units.

[0101] Optionally, in one embodiment of the present invention, a relationship graph of average stress and average strain curve is plotted, and the peak value in the graph is the strength value of the composite material at this heating time.

[0102] Optionally, in one embodiment of the present invention, a relationship diagram between the strength value and the heating time is plotted to obtain a curve diagram showing the relationship between the strength value of the composite material and the heating time.

[0103] Step 6: After the strength value calculation of the microscopic whole-cell finite element model of the current time analysis step is completed, the transient heat conduction calculation of the next moment is performed, and steps 2 to 5 are repeated until the calculation is completed to obtain the predicted result of the change in heating time on the strength value of the resin-based composite material.

[0104] After the calculation is completed, the material strength value versus heating time curve is obtained, as shown in the attached figure. Figure 7 shown.

[0105] The resin-based composite material strength prediction method considering the influence of heating time proposed in an embodiment of the present invention determines the appropriate heating and insulation time for mechanical tests of composite materials at different temperatures to improve the accuracy and efficiency of the tests. The method can be applied to the design and analysis of complex composite material structures in the aerospace field.

[0106] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0107] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0108] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present invention belong.

Claims

1. A method for predicting the strength of a resin-based composite material taking into account the influence of heating time, characterized in that: The following steps are involved: Step 1, establishing a mesoscopic whole-cell finite element model of a resin-based composite material; the mesoscopic whole-cell finite element model of the resin-based composite material is a mesoscopic geometric model of a fiber bundle and a matrix established in a modeling software, and the size of the mesoscopic geometric model in the thickness direction is the same as the actual thickness size of the test piece; Step 2, assign thermodynamic properties to the mesoscopic whole-cell finite element model, set a temperature load on the surface of one end of the mesoscopic whole-cell finite element model, set the time step and time increment, and perform transient heat conduction calculation; Step 3, obtaining the temperature of each finite element unit at the current heating time, bringing the temperature value into the empirical fitting formula of the mechanical properties of the fiber bundle and the matrix under the temperature condition, and obtaining the material mechanical properties of each finite element unit at the current temperature; Step 4: Assign the mechanical properties of the material at the current heating time to the mesoscopic whole-cell finite element model and apply periodic boundary conditions; Step 5: Apply the corresponding damage judgment criteria according to the components of the resin-based composite material. When the damage criteria are triggered, bring the stiffness drop factor into the damage constitutive matrix of the component material for iterative calculation. Use the volume average method to obtain the average stress and average strain of the whole cell model, and draw the stress-strain curve. The peak value of the curve is the strength value of the microscopic finite element model at the current heating time. Step 6: After the strength value calculation of the microscopic whole-cell finite element model of the current time analysis step is completed, the transient heat conduction calculation of the next moment is performed, and steps 2 to 5 are repeated until the calculation is completed to obtain the predicted result of the change in heating time on the strength value of the resin-based composite material.

2. The method according to claim 1, characterized in that The calculation formula for the material mechanical properties of each finite element at the current temperature is: E 11 =0.999(V f E f1 +V m E m )(1-0.00158sinh((T-23) / (71.389-23))) m 12 =V f m f12 +V m m m μ 21 =E 22 μ 12 / E 11 X T =0.736(V f X f1 +V m X m )(1-0.000846sinh((T-23) / (57.308-23))) X C =0.5058(V f X f +(1-V f )X m )(1+0.1402·birth[(T-T0) / (-100.9-T0)]) S 12 =107.483(1+0.9417V f )(1-0.627sinh((T-23) / (299.998-23))) E m =E0(1-0.115sinh(T-23) / 78.906) X m =X0(1-0.23sinh((T-23) / 98.423)) Among them, E 11 is the axial elastic modulus of the fiber bundle, V f is the volume fraction of the fiber single filament, E f1 is the axial elastic modulus of the fiber, V m is the matrix volume fraction, E m is the matrix elastic modulus, T is the temperature, E 22 is the transverse elastic modulus of the fiber bundle, E f2 is the transverse elastic modulus of the fiber monofilament, E 45 is the shear modulus, G 12 is the in-plane shear modulus of the fiber bundle, μ 21 is the out-of-plane Poisson's ratio of the fiber bundle, μ 12 is the Poisson's ratio in the fiber bundle plane, μ f12 is the Poisson's ratio of the fiber monofilament in the plane, μ m is the matrix Poisson's ratio, X T is the axial tensile strength of the fiber bundle, X f1 is the tensile strength of the fiber monofilament, X C is the transverse tensile strength of the fiber bundle, X f is the transverse tensile strength of the fiber monofilament, X m is the tensile strength of the matrix, Y C is the transverse compressive strength of the fiber bundle, T0 is the room temperature, Y T is the transverse tensile strength of the fiber bundle, S 12 is the in-plane shear strength, E0 is the elastic modulus of the matrix at room temperature, and X0 is the tensile strength of the matrix at room temperature.

3. The method according to claim 2, characterized in that In step 4, the periodic boundary conditions applied are: Among them, j+ and j- represent opposite sides, represents the tensile / compressive deformation caused by the load in the three main directions. Corresponding to the shear deformation in the three main directions, is the average strain of the microscopic unit cell model, is the distance between corresponding points on the opposite boundary surface.

4. The method according to claim 3, characterized in that The damage judgment criteria based on the component materials are: Longitudinal fiber bundle stretch injury: Compression injury of longitudinal fiber bundles: Transverse fiber bundle stretch injury: Transverse fiber bundle compression injury: For the matrix component unit, the Mises failure criterion is as follows: Among them, σ 11 is the principal stress in the X direction of the fiber bundle, τ 12 is the in-plane shear stress of the fiber bundle, τ 13 is the out-of-plane shear stress of the fiber bundle, S 21 is the out-of-plane shear strength of the fiber bundle, σ 22 is the principal stress in the Y direction of the fiber bundle, τ 23 is the out-of-plane shear stress of the fiber bundle, σ 33 is the principal stress in the Z direction of the fiber bundle, S 23 is the out-of-plane shear strength of the fiber bundle, J2 is the second deviatoric stress invariant of the resin matrix, is the tensile / compressive strength of the resin matrix.

5. The method according to claim 1, characterized in that In step 5, the volume averaging method is: in, and is the average stress and average strain, V is the total volume of the unit cell model, v i is the volume of the i-th unit, and N is the total number of finite element units.

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