A method for testing interlaminar strain energy release rate of variable stiffness layup composites

Abstract

The application discloses a kind of variable stiffness layer composite interlaminar strain energy release rate test methods, first define fiber laying track formula, determine the functional relationship of variable stiffness layer angle with position;Sample is obtained by cutting from variable stiffness laminate, the range of variation of layer angle of target interface layer in sample is determined;Typical constant layer angle is selected for the range, the bending stiffness matrix is calculated, the dimensionless parameter for representing bending coupling effect and the dimensionless parameter for representing bending-torsion coupling effect are obtained, the maximum value is taken as evaluation value based on the worst principle, and double-parameter joint determination is carried out, if it does not satisfy the criterion, adjust the layer scheme and recalculate;The sample is prepared by using the layer scheme determined by the test, and the interlaminar strain energy release rate test is carried out.The application realizes the quantitative evaluation and screening of variable stiffness layer sample coupling effect through quantitative criterion, solves the technical problem that existing test method cannot be directly applied to variable stiffness layer composite material.

Description

Technical Field

[0001] This invention belongs to the field of advanced composite material testing and evaluation, specifically relating to a method for testing the interlaminar strain energy release rate of variable stiffness ply composite materials. Background Technology

[0002] Composite materials, due to their superior mechanical properties such as high specific strength and high specific modulus, have become key structural materials in the aerospace field. Traditional composite laminate designs typically employ a straight fiber layup method, where the fiber orientation of each layup remains constant throughout the laminate. While this design method is simple to manufacture, it does not fully utilize the significant anisotropy of composite materials, limiting further improvements in structural load-bearing efficiency. To overcome this limitation, the concept of variable stiffness structures with curved fiber layup has been proposed and has received widespread attention. With the rapid development of automated layup technology, variable stiffness laminates can now be fabricated at an acceptable cost by automatically laying multiple prepreg tapes along a preset curved path. Engineering applications are also transitioning from traditional constant stiffness laminates to variable stiffness composite laminates.

[0003] However, current research on variable stiffness composite materials mainly focuses on structural design aspects such as buckling performance analysis of laminates and fiber path optimization, while research on fundamental mechanical property evaluation, such as delamination damage and interlaminar fracture behavior, is severely lacking. It is well known that due to their layered structure, the interlaminar mechanical properties of composite laminates are a weak point, making them highly susceptible to delamination damage during actual service. The occurrence and propagation of delamination significantly reduce the overall load-bearing capacity and service stability of the structure. Therefore, accurately determining the interlaminar strain energy release rate of composite materials is a crucial prerequisite for evaluating their damage tolerance and conducting structural safety design, and it is also a key technology that must be mastered to achieve the engineering application of variable stiffness composite materials in critical fields such as aerospace.

[0004] Existing methods for testing the interlaminar strain energy release rate of composite materials, such as ASTM D5528 (Double Cantilever Beam DCB Test) and ASTM D7905 (End Notch Bending ENF Test), are primarily designed and validated for unidirectional laminates. Directly applying these methods to variable stiffness ply composites presents the following problems:

[0005] First, the fiber angle changes continuously along the spatial position, resulting in different internal ply conditions for samples cut from different positions of the same laminate. This lacks the basic premise of "samples in the same batch having the same ply" in constant stiffness testing, and the sampling principle is unclear.

[0006] Secondly, such asymmetric and non-equilibrium ply configurations can induce significant bending-bending coupling and bending-torsional coupling effects, leading to severe bending deformation at the delamination leading edge (e.g., Figure 2As shown), and make the strain energy release rate unevenly distributed along the width direction of the specimen (e.g. Figure 3 As shown in the figure, this directly violates the fundamental assumption of "two-dimensional plane strain state" in the testing theory;

[0007] Third, there are no criteria for quantitatively assessing whether the above coupling effects exceed the acceptable range of test error, and it is impossible to determine in advance whether a sample is suitable for obtaining effective data.

[0008] The three technical obstacles mentioned above are interconnected, resulting in a lack of guarantee for the accuracy, repeatability, and comparability of test results when the existing methods are applied to variable stiffness structures.

[0009] In summary, the existing technology lacks a method for testing the interlaminar strain energy release rate of variable stiffness ply composites that can systematically solve the above-mentioned technical obstacles. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method for testing the interlaminar strain energy release rate of variable stiffness plywood composites. This method establishes a complete testing process, from fiber trajectory definition, cutting and sampling, ply determination, quantitative calculation and judgment of coupling effects, to delamination propagation testing and simulation verification. It uses quantitative criteria for coupling effect parameters as a key screening method, ensuring from the sampling source that the sample meets the plane strain assumption of the testing theory, thereby achieving accurate determination of the interlaminar strain energy release rate.

[0011] The technical solution of the present invention is as follows:

[0012] A method for testing the interlaminar strain energy release rate of variable stiffness ply composite materials includes the following steps:

[0013] Step 1: Define the fiber placement trajectory, determine the functional relationship between the angle of the variable stiffness ply and its position, and obtain the fiber placement trajectory formula containing the angle expression;

[0014] Step 2: Obtain a sample by cutting from the variable stiffness laminate. Determine the range of layup angle variation of the interfacial layer within the sample based on the cutting position and the angle expression in the fiber layup trajectory formula. ;

[0015] Step 3: Regarding the range of angle changes Several typical constant ply angles were selected, and the bending stiffness matrix D corresponding to each constant ply angle was calculated based on classical laminate theory. Dimensionless parameters characterizing the bending coupling effect were also obtained. and dimensionless parameters characterizing bending-torsional coupling effects Based on the worst-case scenario principle, the maximum value of each of the two parameters is taken as the evaluation value of the sample. and The determination is made if the evaluation value of the current plying scheme simultaneously meets the following conditions. and If both criteria are met, the current ply scheme is adopted and the process proceeds to step 4. If either criterion is not met, the ply scheme is adjusted and the process returns to this step for recalculation.

[0016] Step 4: Prepare a sample using the approved layup scheme and test the interlayer strain energy release rate.

[0017] In a further preferred embodiment, the fiber placement trajectory formula in step 1 is defined using the linear angle placement method, and its angle expression is:

[0018]

[0019] in The reference path for the filament is at any position Tangent at the point and The angle between the positive axis and the axis; The width of the laminate specimen; The reference path for the filament bundle is at the geometric center of the laminate. Tangent of the curve at the point The angle between the positive axis and the axis; Let be the angle between the tangent of the curve of the reference path of the filament bundle at the boundary and the positive x-axis. .

[0020] A further preferred embodiment is that the coefficients in the bending stiffness matrix D mentioned in step 3... The calculation formula is:

[0021]

[0022] in The first element in the bending stiffness matrix D of the laminate is... Line 1 Column elements, ; This represents the total number of layers in the laminate. For the first Off-axis equivalent stiffness coefficient of a single-layer slab; For the first The signed coordinate values ​​of the distance from the bottom surface of the single-layer plate to the mid-surface. For the first The signed coordinate values ​​of the distance from the upper surface of the single-layer board to the mid-surface, where the values ​​above the mid-surface are positive and the values ​​below the mid-surface are negative.

[0023] A further preferred option is the dimensionless parameter in step 3. and Calculated by the following formula:

[0024]

[0025] in These are the coefficients in the bending stiffness matrix that are related to bending in the x-direction. These are the coefficients in the bending stiffness matrix that are related to bending in the y-direction. These are the coefficients in the bending stiffness matrix that characterize the coupling effect between bending in the x-direction and bending in the y-direction; These are the coefficients in the bending stiffness matrix that characterize the coupling effect between bending and torsion.

[0026] A further preferred embodiment is the range of ply angle variation mentioned in step 2. Determine as follows:

[0027] Suppose the cut rectangular specimen is along the original laminate. The range occupied by the axial direction is ,in For the sample along The x-coordinate of the boundary line of the end face on the negative axis. For the sample along Given the x-coordinate of the boundary line of the end face on the positive axis; then: , .

[0028] In a further preferred embodiment, the typical constant ply angle selected in step 3 includes the range of angle variations. The lower limit, median, and upper limit values.

[0029] A further preferred embodiment is that the adjustment of the ply scheme in step 3 includes increasing the number of 0° ply layers.

[0030] In a further preferred embodiment, the interlaminar strain energy release rate test in step 4 is a double cantilever beam DCB test, an end-notch bending ENF test, or a hybrid mode bending MMB test.

[0031] In a further optimized approach, step 4 also includes a quantitative verification process, using parameters... To evaluate the validity of the test results, Defined by the following formula:

[0032]

[0033] in The coordinates of the delamination leading edge at the edge position in the width direction of the sample are located in the length direction of the sample. The coordinates of the leading edge of the delamination at the center position in the width direction of the sample are located in the length direction of the sample.

[0034] The present invention also proposes a variable stiffness plywood composite material specimen for interlaminar strain energy release rate testing, wherein the specimen is prepared using a plywood scheme determined by any of the above methods.

[0035] Beneficial effects:

[0036] Compared with the prior art, the present invention has the following outstanding advantages:

[0037] (1) This invention establishes a complete test procedure for determining the interlaminar strain energy release rate of variable stiffness ply composite materials. The method fully covers the entire process of fiber path definition, cutting and sampling, ply determination, quantitative evaluation of coupling effect and test verification. It is logically rigorous and highly operable.

[0038] (2) By adopting a dimensionless parameter quantitative criterion, the influence of the complex mechanical phenomenon of coupling effect is transformed into an engineering index that can be calculated, judged and screened, providing a scientific basis for ensuring the accuracy and repeatability of interlayer testing of variable stiffness ply composite materials.

[0039] (3) This method can serve as a general test basis for various modes of layered extension tests such as DCB, ENF, and MMB, and provides an effective test basis for the standardized testing of interlaminar fracture toughness of variable stiffness composite materials and the determination of allowable material values.

[0040] (4) This method accurately determines the minimum critical ply adjustment scheme that meets the test accuracy requirements through quantitative criteria, avoiding reliance on overly conservative experience design (such as unlimited increase of the number of 0° ply layers), thus ensuring test accuracy while taking into account structural efficiency and cost control.

[0041] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0042] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0043] Figure 1 A schematic diagram of a reference path curve for linear angle paving;

[0044] Figure 2 For curved layered extension leading edge and Parameter definition diagram; In the diagram, 1 is the delamination leading edge position at the edge of the sample, and 2 is the delamination leading edge position at the center of the sample width direction;

[0045] Figure 3 This is a schematic diagram showing the asymmetric distribution of strain energy release rate along the width direction in a DCB specimen.

[0046] Figure 4 Schematic diagram of a cutting scheme for variable stiffness plywood composite laminates;

[0047] Figure 5 The graph shows the theoretical calculation results; where (a) represents the results for different n values. Theoretical calculation results, (b) show the results for different n values. Theoretical calculation results;

[0048] Figure 6 Comparison of DCB layer propagation simulation results under different layups; where (a) n=2, crack interface layer is -60° / / -60°; (b) n=2, crack interface layer is -75° / / -75°; (c) n=12, crack interface layer is -60° / / -60°; (d) n=12, crack interface layer is -75° / / -75°.

[0049] Figure 7 Comparison of ENF delamination propagation simulation results under different layups; where (a) n=2, crack interface layer is -60° / / -60°; (b) n=2, crack interface layer is -75° / / -75°; (c) n=12, crack interface layer is -60° / / -60°; (d) n=12, crack interface layer is -75° / / -75°.

[0050] Figure 8 Comparison of MMB layer propagation simulation results under different layups; where (a) n=2, crack interface layer is -60° / / -60°; (b) n=2, crack interface layer is -75° / / -75°; (c) n=12, crack interface layer is -60° / / -60°; (d) n=12, crack interface layer is -75° / / -75°. Detailed Implementation

[0051] The present invention will be further described in detail below with reference to an embodiment, but this should not be construed as limiting the scope of the invention to this. All technologies implemented based on the content of this invention fall within the scope of this invention.

[0052] This embodiment uses a variable stiffness plywood composite laminate as an example. The effective size of the variable stiffness plywood composite laminate is 400mm × 400mm, and the initial ply design is as follows: The mechanical properties of the unidirectional laminate are: longitudinal modulus lateral modulus Shear modulus is Poisson's ratio in the plane is The thickness of a single layer is 0.15 mm. In the preliminary layup design, n is the number of 0° layups to be determined, which is also the core variable to be optimized in this embodiment.

[0053] In the above ply symbols, This indicates that the fiber angle within the layup is from to (or to ) Changes continuously along spatial position; Indicates and The layer symbols change in opposite directions at angles. The symbol " / / " represents a prefabricated layered interface, for example... This indicates that the ply angles on both sides of the layer interface change in opposite directions, with one side changing from... Change to (or from) Change to ), from the other side Change to (or from) Change to ), to produce the desired interface layup configuration.

[0054] The method for testing the interlaminar strain energy release rate of variable stiffness ply composite materials proposed in this embodiment includes the following steps:

[0055] Step 1: Define the fiber placement trajectory, determine the functional relationship between the angle of the variable stiffness ply and the position, and obtain the fiber placement trajectory formula containing the angle expression.

[0056] This step is fundamental to the entire testing process. By mathematically describing the fiber placement trajectory of the target variable stiffness laminate, the fiber orientation at any location on the laminate can be clearly defined.

[0057] In this embodiment, a linear angle placement method is used to define the fiber bundle reference path: a rectangular coordinate system is established with the center of the laminate as the origin. The axis runs along the length of the laminate, which is the direction in which the ply angle changes with spatial position, and is also the loading direction for subsequent interlaminar strain energy release rate testing. The axis runs along the width of the laminate. The axis is along the thickness direction of the laminate; definition Axis and fiber direction in The included angle in the plane is called the ply angle. The tangent of the curve at the center and boundary of the laminate is defined as... The included angles in the positive direction of the axis are respectively and The curve passes through the origin and is symmetrical about the origin. The fiber layup trajectory is fully described by the following two interrelated formulas (e.g., ...). Figure 1 (as shown)

[0058] The angular expression for the fiber layup trajectory is:

[0059]

[0060] in The tangent to the reference path of the filament at any position and The angle between the positive axis and the axis; The width of the laminate specimen; The reference path for the filament bundle is at the geometric center of the laminate. Tangent of the curve at the point The angle along the positive direction of the axis. ; For the reference path of the filament at the boundary Tangent of the curve at the point The angle along the positive direction of the axis. .

[0061] The corresponding fiber laying path coordinate expression is:

[0062]

[0063] In the subsequent steps of this method, angle expressions are mainly used. Determine the range of ply angles.

[0064] In this embodiment, , , The angular expression for the fiber layup trajectory is:

[0065]

[0066] in The unit is mm.

[0067] Step 2: Obtain test specimens by cutting from variable stiffness laminates. Determine the range of layup angle variation of the target interface layer within the specimen based on the cutting position and the angle expression in the fiber layup trajectory formula determined in Step 1.

[0068] Unlike constant-stiffness laminates where samples can be taken arbitrarily, this invention requires that the exact position of the sample within the original variable-stiffness laminate be recorded when cutting the specimen (e.g., ...). Figure 4 (As shown). Specifically, suppose the cut rectangular sample is along the original laminate. The range occupied by the axial direction is ,in For the sample along The x-coordinate of the boundary line of the end face on the negative axis. For the sample along The x-coordinate of the boundary line of the end face on one side of the positive axis; based on the angle expression in step 1. Any position inside the sample ply angle at the point All fall within the interval Inside, of which:

[0069]

[0070]

[0071] Because in the expression for the angle of the fiber laying trajectory defined in step 1, Follow Since it changes monotonically, the above extreme values ​​are determined as follows:

[0072] If the sample contains the centerline of the laminate ,Right now Then the maximum and minimum values ​​of the angle are at The angle is obtained at one end, and the other extreme value is obtained at the two ends of the sample boundary; if the sample is completely located on one side of the center line of the laminate, the angle obtains the minimum and maximum values ​​at the two ends of the sample boundary line respectively.

[0073] The range of ply angle variations within the sample was calculated using the above method. This interval is the input for the discretization calculation in step 3.

[0074] In this embodiment, reference Figure 4 The cutting scheme, from a piece of size Different positions of the variable stiffness laminate were cut for use The test specimens. To comprehensively characterize the interlaminar fracture behavior of variable stiffness plies in different angle ranges, this embodiment selects two extreme cutting locations: the central region and the edge region, representing the low-angle region (close to) within the variable stiffness ply angle range. ) and high-angle area (close to) ).

[0075] For test specimen A, which is cut at the center position, the specimen is positioned in the central region of the laminate, so that the specimen is along... The axial direction is about the geometric center of the laminate. Symmetrical distribution. The sample is distributed along the original laminate. The range occupied by the axial direction is ,along The range occupied by the axial direction is The specimen has a total length of 30 mm and a width of 25 mm. The specimen includes the geometric center of the laminate. Therefore, the minimum value of the fiber angle inside the sample is... Obtained from: The maximum value is obtained at both ends of the sample. Therefore, the range of variation of the variable stiffness ply angle inside specimen A is: The change in angle is Therefore, the specific layup pattern of test specimen A can be expressed as: To facilitate the rounding calculation of the discretized angles in subsequent step 3, the above angle range can be rounded to the nearest integer. .

[0076] For specimen B, which is cut at the edge, the specimen is positioned in the edge area of ​​the laminate, close to the laminate boundary. Placement. The sample is placed along the original laminate. The range occupied by the axial direction is ,along The range occupied by the axial direction is The total length of the specimen is 30 mm, and the width is 25 mm. The specimen is located entirely on the centerline of the laminate. On the right side, the fiber angles at the two ends of the sample are as follows: , Therefore, the range of variation of the variable stiffness ply angle inside specimen B is: The change in angle is Therefore, the specific layup pattern of test specimen B can be expressed as: Similarly, to facilitate the rounding calculation of the discretized angles in subsequent step 3, the above angle range can be rounded to the nearest integer. .

[0077] Test specimen A covered the low-angle region from the center of the laminate to near the center (approximately Test piece B covered the high-angle area from the center to the edge (approximately...). Both together cover the variable stiffness ply angle from arrive The high and low ends of the complete range of variation are representative.

[0078] Step 3: For the range of angle changes determined in Step 2 Several typical constant ply angles were selected, and the bending stiffness matrix corresponding to each constant ply angle was calculated based on classical laminate theory. Dimensionless parameters characterizing the bending coupling effect were also obtained. and dimensionless parameters characterizing bending-torsional coupling effects Based on the worst-case scenario principle, the maximum value of each parameter is taken as the evaluation value of the sample for judgment.

[0079] This step is the core innovation of this invention. Since classical laminate theory is applicable to constant-angle layups but cannot be directly applied to continuously varying-angle layups, this invention utilizes the characteristic of extremely small angle variation range within a single sample, as determined in step 2, and employs a discretization approximation method to solve this problem. The specific process is as follows:

[0080] Step 3.1: Select a typical constant ply angle:

[0081] Within the range of angle changes At least three typical constant ply angles are selected within this range; in this embodiment, the lower limit of this range is selected. Median and upper limit value (Round up).

[0082] In this embodiment, for the interface of test specimen A, three typical constant layup angles were selected: a lower limit of 60°, a median value of... upper limit For the interface of specimen B, three typical constant ply angles were selected: lower limit value. median upper limit .

[0083] Step 3.2: Calculate the bending stiffness matrix:

[0084] Using the classical laminate theory of composite materials, the bending stiffness matrix D of the specimen containing prefabricated layers at the target interface was calculated for each of the above constant angle layup. The classical laminate theory is based on the following basic assumptions: (1) Linear elasticity and small deformation assumption: each single layer material is in the linear elastic stage and satisfies the small deformation condition; (2) Straight normal assumption: the straight line segment perpendicular to the mid-surface before deformation is still straight and perpendicular to the mid-surface after deformation (i.e., the influence of transverse shear deformation is ignored); (3) Isonormal assumption: the length of the normal perpendicular to the mid-surface remains unchanged (i.e., transverse normal strain is ignored); (4) Plane stress state assumption: each single layer is in the plane stress state; (5) Full interlayer bonding assumption: there is no relative slippage and separation between adjacent single layers, and the interlayer displacement is continuous. Based on the above assumptions, the coefficients in the bending stiffness matrix D of the laminate are calculated. The calculation formula is:

[0085]

[0086] in The first element in the bending stiffness matrix D of the laminate is... Line 1 Column elements, ; This represents the total number of layers in the laminate. For the first Off-axis equivalent stiffness coefficient of a single-layer slab; For the first The signed coordinate values ​​of the distance from the bottom surface of the single-layer plate to the mid-surface. For the first The signed coordinate values ​​of the distance from the upper surface of a single-layer slab to the mid-surface, where values ​​above the mid-surface are positive and values ​​below the mid-surface are negative. Under this definition, the first... Layer thickness .

[0087] Step 3.3: Calculate the coupling effect parameters:

[0088] Based on the calculated bending stiffness matrix coefficients, two key dimensionless coupling effect parameters are calculated. and :

[0089]

[0090] in For the bending stiffness matrix and Coefficients related to directional bending; For the bending stiffness matrix and Coefficients related to directional bending; Characterized in the bending stiffness matrix Directional bending and The coefficient of the directional bending coupling effect; These are the coefficients in the bending stiffness matrix that characterize the coupling effect between bending and torsion.

[0091] The effect of bending coupling on the shape of the layered leading edge (causing the leading edge to bend) was quantitatively characterized. The smaller the value, the straighter the leading edge of the layer tends to be. The effect of bending-torsional coupling on the asymmetry of strain energy release rate distribution at the layered leading edge was quantitatively characterized. The smaller the value, the more symmetrical the distribution of strain energy release rate in the width direction.

[0092] Step 3.4: Conduct an assessment based on the worst-case scenario principle:

[0093] Based on the worst-case scenario principle, the multiple values ​​calculated for each sample at each discrete angle are... Values ​​and multiple The values ​​are taken, and the maximum value is taken as the final value of the sample. Evaluation value and Evaluation value :

[0094]

[0095]

[0096] in For the selected typical constant ply angle, This method of value selection can cover all coupling effects that may be caused by continuous changes in the internal stiffness ply angle in the most conservative way, ensuring that the specimens selected by the criteria have acceptable test accuracy at any position.

[0097] In this embodiment, the value of n is gradually increased. Calculate the cost of each scheme according to the formula above. and Based on the worst-case scenario principle, we take the discrete angles... The maximum value is taken as the value of the test piece. The evaluation value is taken from each discrete angle. The maximum value is taken as the value of the test piece. Evaluation value:

[0098]

[0099]

[0100] Calculations revealed that The maximum value appears interface, The maximum value appears interface. Figure 5 The two test specimens obtained from theoretical calculations are presented in graphical form. and The trend of n value variation. The evaluation values ​​of coupling parameters of the two test pieces under different n values ​​are shown in Table 1:

[0101] Table 1. Evaluation values ​​of coupling parameters for two test specimens under different n values ​​(retaining two decimal places).

[0102]

[0103] As can be seen from Table 1, the test specimen A... value( The interface is always larger than that of test piece B. value( Interface), is the control The key to the criterion; and the test piece B value( The interface is always greater than that of test piece A. value( Interface), is the control The key to the judgment.

[0104] Step 3.5: Perform a two-parameter joint determination:

[0105] Based on the above evaluation values, the following two-parameter joint determination is performed:

[0106] ,and .

[0107] The meanings and functions of the two criteria are as follows:

[0108] Criterion 1 ( This is the primary criterion, ensuring that the arcuate curvature of the leading edge in the width direction is within an acceptable range, and avoiding significant misalignment between the center and edge positions of the leading edge in the length direction of the specimen. The applicant's research found that when... When the curvature of the leading edge of the delamination increases sharply, the difference in the distribution of strain energy release rate in the width direction of the specimen exceeds the engineering acceptable test error range, which seriously impairs the effectiveness of the test.

[0109] Criterion 2 ( This is the parallel criterion, ensuring that the leading edge of the layer does not undergo significant left-right asymmetric distortion along the width direction, and guaranteeing the left-right symmetry of the strain energy release rate distribution along the width direction. Because even Very small, if If the strain is too large, the leading edge of the layer may still exhibit an "S"-shaped distortion, which would also compromise the test accuracy under the two-dimensional plane strain assumption.

[0110] If the evaluated sample layup scheme meets both of the above criteria, the scheme is deemed valid, and the process proceeds to step 4. If either criterion is not met, the scheme is deemed invalid, and the layup scheme needs to be adjusted, for example, by increasing the number of layers. The number of ply layers is increased to enhance bending stiffness and reduce coupling effects. The process then returns to step 3.1 to reselect typical angles, calculate the stiffness matrix, and coupler parameters until both criteria are simultaneously met. This iterative process embodies the screening logic of this invention: based on quantitative criteria, it successively approximates the ply design scheme that meets the test accuracy requirements. Furthermore, this scheme does not seek to increase the number of ply layers indefinitely. Increasing the number of plies (i.e., increasing the value of n) will reduce the coupling effect to zero. Instead, it provides quantitative criteria to accurately determine the minimum critical ply adjustment scheme that meets the test accuracy requirements while maintaining the characteristics of the variable stiffness ply structure and engineering weight constraints. This avoids relying on overly conservative empirical design and achieves a balance between test accuracy and structural efficiency.

[0111] In this embodiment, when At that time, test piece A If the value exceeds the threshold of 0.25, the criterion is not met. As n increases, all parameters monotonically decrease. When... At that time, test piece A ,satisfy The criteria, at the same time The value also dropped below 0.05. To further reduce... To obtain better test robustness, n=12 was ultimately chosen, at which point the two test pieces... and Both are at an excellent level and meet both criteria.

[0112] Moreover, as mentioned earlier, this method does not seek to increase the size of an unlimited number of cells. Increasing the number of plies (i.e., increasing the value of n) will reduce the coupling effect to zero. The reasons are: (1) Increasing the value of n without limit will lead to a significant increase in the total thickness of the laminate and the structural weight, which violates the fundamental design principle of lightweight composite material structures; (2) Excessive ply ratio will severely dilute the fiber angle variation characteristics of variable stiffness ply, making the sample essentially similar to a conventional constant stiffness laminate, thus losing its representativeness as an evaluation of the fracture performance of "variable stiffness ply composite material"; (3) In DCB tests, excessively thick samples will deviate from the basic assumptions of linear elastic fracture mechanics due to excessive bending stiffness of the cantilever beam, resulting in the theoretical failure of the test results. Therefore, this method accurately determines the ply adjustment scheme that meets the test accuracy requirements through quantitative criteria, thereby avoiding reliance on overly conservative empirical design and achieving a balance between test accuracy and structural efficiency.

[0113] Step 4: Prepare a sample using the approved layup scheme and test the interlayer strain energy release rate.

[0114] In this embodiment, the final determined sample layup is as follows: DCB, ENF, and MMB samples were prepared using the approved layup scheme. The sample dimensions were... Pre-formed layers are introduced at one end of the sample.

[0115] Interlaminar strain energy release rate testing was performed using a double cantilever beam (DCB) test, an end-notched bending (ENF) test, or a mixed-mode bending (MMB) test. In this embodiment, the DCB test was performed according to ASTM D5528, the ENF test according to ASTM D7905, and the MMB test according to ASTM D6671. The specimens were tested under standard environmental conditions (temperature...). relative humidity After undergoing at least 48 hours of conditioning, testing was conducted. During the test, load-displacement curves and delamination lengths were recorded, and the interlaminar strain energy release rate was calculated according to the relevant standard formulas.

[0116] In addition, this step also includes a quantitative verification process, through parameters. To evaluate the validity of the test results, Defined as the difference between the delamination leading edge position at the edge of the specimen and the delamination leading edge position at the center of the specimen width along the specimen length direction:

[0117]

[0118] in The coordinates of the delamination leading edge at the edge of the sample (both ends in the width direction) in the length direction of the sample; The coordinates of the leading edge of the delamination at the center position in the width direction of the sample are located in the length direction of the sample. The smaller the value, the straighter the delamination front is, the more uniform the distribution of interlaminar strain energy release rate along the width direction, and the more accurate the test results. When The value is within an acceptable range (as in the DCB test in this embodiment). ENF test MMB Trial When the test result is confirmed to be valid, it can be confirmed that the test result is valid.

[0119] The results of this embodiment are shown in Tables 2 to 4. Figure 6 , Figure 7 , Figure 8 The simulation results of the layered extended leading edge morphology under three experimental modes, DCB, ENF and MMB, are presented and compared.

[0120] Table 2 Comparison of DCB layered expansion leading edge bending degree under different n values ​​(unit: mm)

[0121]

[0122] Table 3. Comparison of the degree of bending at the leading edge of ENF layered expansion under different n values ​​(unit: mm)

[0123]

[0124] Table 4. Comparison of the degree of bending at the leading edge of MMB layered expansion under different n values ​​(unit: mm)

[0125]

[0126] Tables 2 to 4 show that the two test specimens The values ​​all decrease synchronously as n increases. When n=12, in the DCB experiment... Not exceeding 0.6 mm, in ENF test Not exceeding 0.4 mm, in MMB test The thickness is less than 0.2 mm, and the leading edge of the layer has been basically restored to a straight shape, meeting the requirements for accurate testing.

[0127] For a direct comparison, Tables 5 to 7 show the degree of bending at the leading edge of DCB, ENF, and MMB under two typical layup schemes with n=2 and n=12, respectively.

[0128] Table 5 Comparison of DCB Layered Extension Leading Edge Bending Degree

[0129]

[0130] Table 6 Comparison of the degree of bending at the leading edge of ENF layered extension

[0131]

[0132] Table 7 Comparison of the degree of bending at the leading edge of the MMB layered extension

[0133]

[0134] It is clearly evident that the layup selected using the method of this invention exhibits a straight leading edge and a uniform strain energy release rate along the width direction, verifying the effectiveness of this method. The verification results demonstrate that the layup scheme selected using this method can effectively guarantee the accuracy of various static delamination propagation tests such as DCB, ENF, and MMB.

[0135] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for testing the interlaminar strain energy release rate of variable stiffness ply composite materials, characterized in that: Includes the following steps: Step 1: Define the fiber placement trajectory, determine the functional relationship between the angle of the variable stiffness ply and its position, and obtain the fiber placement trajectory formula containing the angle expression; Step 2: Obtain a sample by cutting from the variable stiffness laminate. Determine the range of layup angle variation of the interfacial layer within the sample based on the cutting position and the angle expression in the fiber layup trajectory formula. ; Step 3: Regarding the range of angle changes Several typical constant ply angles were selected, and the bending stiffness matrix D corresponding to each constant ply angle was calculated based on classical laminate theory. Dimensionless parameters characterizing the bending coupling effect were also obtained. and dimensionless parameters characterizing bending-torsional coupling effects Based on the worst-case scenario principle, the maximum value of each of the two parameters is taken as the evaluation value of the sample. and The determination is made if the evaluation value of the current plying scheme simultaneously meets the following conditions. and If both criteria are met, the current ply scheme is adopted and the process proceeds to step 4. If either criterion is not met, the ply scheme is adjusted and the process returns to this step for recalculation. Step 4: Prepare a sample using the approved layup scheme and test the interlayer strain energy release rate.

2. The method according to claim 1, characterized in that: The fiber placement trajectory formula in step 1 is defined using the linear angle placement method, and its angle expression is: in The reference path for the filament is at any position Tangent at the point and The angle between the positive axis and the axis; The width of the laminate specimen; The reference path for the filament bundle is at the geometric center of the laminate. Tangent of the curve at the point The angle between the positive axis and the axis; Let be the angle between the tangent of the curve of the reference path of the filament bundle at the boundary and the positive x-axis. .

3. The method according to claim 1, characterized in that: The coefficients in the bending stiffness matrix D mentioned in step 3 The calculation formula is: in The first element in the bending stiffness matrix D of the laminate is... Line 1 Column elements, ; This represents the total number of layers in the laminate. For the first Off-axis equivalent stiffness coefficient of a single-layer slab; For the first The signed coordinate values ​​of the distance from the bottom surface of the single-layer plate to the mid-surface. For the first The signed coordinate values ​​of the distance from the upper surface of the single-layer board to the mid-surface, where the values ​​above the mid-surface are positive and the values ​​below the mid-surface are negative.

4. The method according to claim 3, characterized in that: Dimensionless parameters in step 3 and Calculated by the following formula: in These are the coefficients in the bending stiffness matrix that are related to bending in the x-direction. These are the coefficients in the bending stiffness matrix that are related to bending in the y-direction. These are the coefficients in the bending stiffness matrix that characterize the coupling effect between bending in the x-direction and bending in the y-direction; These are the coefficients in the bending stiffness matrix that characterize the coupling effect between bending and torsion.

5. The method according to claim 1, characterized in that: The range of ply angle variation mentioned in step 2 Determine as follows: Suppose the cut rectangular specimen is along the original laminate. The range occupied by the axial direction is ,in For the sample along The x-coordinate of the boundary line of the end face on the negative axis. For the sample along The x-coordinate of the boundary line of the end face on one side in the positive direction of the axis; but: , .

6. The method according to claim 1, characterized in that: The typical constant ply angle selected in step 3 includes the range of angle variations. The lower limit, median, and upper limit values.

7. The method according to claim 1, characterized in that: The adjustment of the ply plot scheme described in step 3 includes increasing the number of 0° ply plots.

8. The method according to claim 1, characterized in that: The interlaminar strain energy release rate test mentioned in step 4 is a double cantilever beam DCB test, an end-notch bending ENF test, or a mixed-mode bending MMB test.

9. The method according to claim 1, characterized in that: Step 4 also includes a quantitative verification process, using parameters... To evaluate the validity of the test results, Defined by the following formula: in The coordinates of the delamination leading edge at the edge position in the width direction of the sample are located in the length direction of the sample. The coordinates of the leading edge of the delamination at the center position in the width direction of the sample are located in the length direction of the sample.

10. A variable stiffness plywood composite specimen for testing interlaminar strain energy release rate, characterized in that, The sample was prepared using a layup scheme determined by the method described in any one of claims 1 to 9.

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