Method for estimating fatigue layering expansion rate of composite material by considering fiber bridging mechanism

Abstract

The invention discloses a composite material fatigue layering expansion rate estimation method considering a fiber bridging mechanism, and belongs to the technical field of composite material fatigue layering prediction. The method aims at the problem that prediction of the fatigue layering expansion rate of the composite material cannot be separated from fatigue test data support. Comprising the steps that a fiber bridging mechanism is considered, a fiber bridging factor is set, and a nonlinear continuous curve related to fracture toughness and layering length is obtained based on a static test; obtaining a tangential traction force and a normal traction force by combining the tangential displacement and the normal displacement; combining the surface internal stress resultant force, the surface internal bending moment and the surface internal shear stress resultant force of the upper sub-beam and the lower sub-beam to obtain the total strain energy of the composite laminated plate; a control equation set is obtained by establishing a laminated plate balance equation; solving to obtain an upper sub-beam fatigue load theoretical value, an upper sub-beam displacement theoretical value and a layering length theoretical value; and calculating a fatigue layering expansion rate, and fitting to obtain a fitting curve for estimating the expansion rate. The method is used for estimating the fatigue layering expansion rate.

Description

Technical Field

[0001] The present invention relates to an estimation method for the fatigue delamination growth rate of composite materials considering the fiber bridging mechanism, and belongs to the technical field of composite material fatigue delamination prediction. Background Art

[0002] Advanced composite materials are widely used in the aerospace field due to their advantages of high specific strength, high specific stiffness and low density. However, composites lack constraints in the thickness direction, and their interlaminar properties restrict the performance, which is the weak link in laminated plates, making composites extremely prone to delamination damage. Among various failure modes, fatigue delamination failure caused by cyclic loading is particularly common, and the delamination process is often accompanied by fiber bridging phenomena. This behavior can significantly increase the delamination growth resistance as the delamination expands, affecting the fatigue delamination growth rate, which also makes the mechanism of composite material fatigue delamination under cyclic loading more complex and the prediction of composite material fatigue delamination behavior more difficult.

[0003] Currently, fatigue delamination growth is mainly studied through experimental tests and finite element methods. However, due to the complexity of the fiber bridging mechanism, it is still challenging to study it using theoretical analysis methods. Although semi-empirical models have been proposed, such as using the Paris law or normalization methods to relate cyclic loading parameters to delamination growth rate, existing models still require fatigue test data to calibrate or calibrate model parameters, and there are obvious limitations. Experimental tests are both time-consuming and expensive, and are often difficult to implement for large structures. Therefore, there is an urgent need for an estimation method for the fatigue delamination growth rate of composite materials that does not rely on fatigue test data calibration and can consider the fiber bridging mechanism. Summary of the Invention

[0004] Aiming at the problem that the prediction of the existing composite material fatigue delamination growth rate cannot be separated from the support of fatigue test data, the present invention provides an estimation method for the fatigue delamination growth rate of composite materials considering the fiber bridging mechanism.

[0005] An estimation method for the fatigue delamination growth rate of composite materials considering the fiber bridging mechanism of the present invention includes:

[0006] Dividing the composite material laminated plate into an upper sub-beam and a lower sub-beam by the delamination interface, establishing displacement field models for the upper sub-beam and the lower sub-beam, and obtaining mid-plane displacement expressions in the length direction and the thickness direction; based on the mid-plane displacement, obtaining tangential displacement and normal displacement expressions of the delamination interface, as well as strain expressions of the upper sub-beam and the lower sub-beam; and obtaining expressions of in-plane stress resultant forces, in-plane bending moments and in-plane shear stress resultant forces of the upper sub-beam and the lower sub-beam from the strain expressions of the upper sub-beam and the lower sub-beam;

[0007] Considering the fiber bridging mechanism, set the fiber bridging factor, and obtain the non-linear continuous curve related to the fracture toughness and delamination length of the composite laminate based on the static test; combine the tangential displacement and the normal displacement to obtain the tangential traction force and the normal traction force between the delamination interfaces; then combine the in-plane stress resultant force, the in-plane bending moment, and the in-plane shear stress resultant force of the upper sub-beam and the lower sub-beam to obtain the total strain energy of the composite laminate;

[0008] Based on the total strain energy of the composite laminate and the potential energy of the fatigue load applied to the composite laminate, establish the laminate equilibrium equation; based on the laminate equilibrium equation, obtain the control equation set;

[0009] Solve the control equation set to obtain the theoretical value of the fatigue load of the upper sub-beam, the theoretical value of the displacement of the upper sub-beam, and the theoretical value of the delamination length under the fatigue load of the laminate;

[0010] Calculate the cyclic energy release rate according to the theoretical value of the fatigue load of the upper sub-beam, the theoretical value of the displacement of the upper sub-beam, and the theoretical value of the delamination length, and then obtain the fatigue delamination propagation rate of the composite laminate;

[0011] Perform data fitting on the fatigue delamination propagation rate of the composite laminate to obtain the fitting curve of the fatigue delamination propagation rate of the composite laminate;

[0012] In practical applications, measure the actual displacement value of the upper sub-beam and the actual fatigue load value of the upper sub-beam, calculate the actual cyclic energy release rate, and combine the fitting curve to determine the current fatigue delamination propagation rate of the composite laminate.

[0013] According to the estimation method of the fatigue delamination propagation rate of the composite material considering the fiber bridging mechanism of the present invention, the expressions of the mid-plane displacements in the length direction and the thickness direction are:

[0014]

[0015] where u r is the displacement of the upper sub-beam and the lower sub-beam along the X-axis in the length direction, r = t, b, t represents the upper sub-beam, b represents the lower sub-beam; w r is the displacement of the upper sub-beam and the lower sub-beam along the Z-axis in the thickness direction; x is the X-axis coordinate, z r is the Z-axis coordinate of the upper sub-beam and the lower sub-beam, is the mid-plane displacement of the upper sub-beam and the lower sub-beam in the X-axis direction, is the mid-plane displacement of the upper sub-beam and the lower sub-beam in the Z-axis direction, is the rotation angle of the mid-plane of the upper sub-beam and the lower sub-beam relative to the normal direction.

[0016] According to the estimation method of the fatigue delamination propagation rate of the composite material considering the fiber bridging mechanism of the present invention, the expressions of the tangential displacement and the normal displacement of the delamination interface are:

[0017]

[0018] where Δu t represents the tangential displacement of the delamination interface, and Δu n represents the normal displacement of the delamination interface, and h b is the thickness of the lower sub - beam, and h t is the thickness of the upper sub - beam.

[0019] According to the method for estimating the fatigue delamination growth rate of a composite material considering the fiber bridging mechanism of the present invention, considering the geometric nonlinearity of the composite laminate, the strain expressions of the upper and lower sub - beams are:

[0020]

[0021] where is the normal strain of the upper and lower sub - beams, is the shear strain of the upper and lower sub - beams. In the variable subscript, x represents the derivative with respect to the corresponding variable;

[0022] Based on formula (3), the expressions for the in - plane stress resultant, in - plane moment, and in - plane shear stress resultant of the upper and lower sub - beams are obtained:

[0023]

[0024] where is the in - plane stress resultant of the upper and lower sub - beams, is the in - plane moment of the upper and lower sub - beams, is the in - plane shear stress resultant of the upper and lower sub - beams;

[0025] where B is the width of the composite laminate, is the normal stress in the X - axis direction, is the shear stress in the XZ plane, is the tensile stiffness of the upper and lower sub - beams, is the tensile - bending coupling stiffness of the upper and lower sub - beams, is the bending stiffness of the upper and lower sub - beams, is the shear stiffness of the upper and lower sub - beams.

[0026] According to the method for estimating the fatigue delamination growth rate of a composite material considering the fiber bridging mechanism of the present invention, the calculation method for the fracture toughness of the composite laminate is:

[0027]

[0028] where φ nis the fracture toughness of the composite laminate, P is the test value of the load applied to the upper sub-beam, W is the test value of the displacement of the upper sub-beam, a is the delamination length, η(a) is the set fiber bridging factor related to the delamination length, Δ is the delamination length correction value, and Δ is obtained by extrapolating the linear fitting equation of the cube root C 1 / 3 of the compliance C of the composite laminate with the delamination length a to C 1 / 3 = 0;

[0029] The fracture toughness φ of the composite laminate obtained from the static test is non-linearly fitted using a power function n to obtain a non-linear continuous curve related to the delamination length a:

[0030]

[0031] where q1, q2, and q3 are all fitting parameters.

[0032] According to the method for estimating the fatigue delamination growth rate of a composite material considering the fiber bridging mechanism of the present invention, the expressions for the tangential traction force and the normal traction force between the delamination interfaces are:

[0033]

[0034] where T t is the tangential traction force, T n is the normal traction force, δ0 is the characteristic length of the cohesive zone, and D is the damage variable;

[0035]

[0036] where k is the correction coefficient, is the cyclic damage increment, is the monotonic damage increment, and t is the time;

[0037]

[0038] where is the cumulative displacement increment in one load cycle period, δ ∑ is the total displacement required to cause failure of the cohesive zone, is the total cohesive tension at the delamination crack interface, σ f is the cohesive fatigue limit, σ max is the normal cohesive strength after the number of load cycles N, σ max,0 is the interfacial cohesive strength when no damage occurs, H is the Heaviside function, is the cumulative displacement in one load cycle period, δ f is the separation displacement corresponding to the cohesive fatigue limit;

[0039]

[0040] wherein the cohesive fatigue limit σ f is determined using the conditional yield stress: Define the normal traction T n - the normal displacement Δu of the crack interface n a parallel line in the elastic response stage of the curve, and shift the parallel line by a specified plastic deformation amount d; the cohesive fatigue limit σ f through the shifted parallel line and the normal traction T n - the normal displacement Δu of the crack interface n the dimensionless parameter δ at the intersection point of the curve f / δ0 and σ f / σ max,0 are jointly determined.

[0041] According to the method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism of the present invention, the calculation method for the total strain energy of the composite laminate is as follows:

[0042]

[0043] where U is the total strain energy of the composite laminate, V t is the volume of the upper sub-beam, V b is the volume of the lower sub-beam, and A is the interlaminar area of the delamination interface;

[0044] The potential energy of the fatigue load applied to the composite laminate is expressed as V:

[0045]

[0046] where L is the length of the composite laminate, P t is the theoretical value of the fatigue load of the upper sub-beam, W t is the theoretical value of the displacement of the upper sub-beam, δ D is the Dirac function, x e is the X-axis coordinate of the fatigue load application position;

[0047]

[0048] The beneficial effects of the present invention: The present invention breaks through the limitation in the prior art that fatigue test data is required to calibrate or calibrate model parameters, applies the theoretical analysis method to consider the influence of the fiber bridging mechanism on the fatigue delamination propagation rate of the composite material, and obtains the fatigue delamination propagation resistance curve through simple static tests without relying on fatigue test data for calibration, realizing the estimation of the fatigue delamination propagation rate of the composite laminate.

[0049] The method of the present invention does not need to rely on fatigue data to calibrate model parameters. Only by using the strain energy release rate obtained from quasi-static tests can the effective prediction of the fatigue delamination propagation rate be achieved. It provides an efficient and convenient analysis tool for the evaluation of the fatigue delamination propagation behavior of composite materials, significantly improving the calculation efficiency of fatigue damage tolerance analysis while greatly enhancing its engineering applicability.

[0050] The method of the present invention takes into account the influence of the fiber bridging mechanism on the fatigue delamination propagation of composite materials. By performing non-linear fitting on the fracture toughness obtained from static tests, a non-linear continuous function related to the delamination length is obtained for the fracture toughness. Then, a theoretical analysis method combined with software programming is used to obtain the fatigue delamination propagation rate of composite materials under the fiber bridging effect. This method provides a powerful analysis method for predicting the fatigue delamination propagation behavior of composite materials affected by complex fiber bridging mechanisms. Brief Description of the Drawings

[0051] Figure 1 is a schematic diagram of the model of a composite laminate, where x t is the X-axis coordinate of the upper sub-beam, and x b is the X-axis coordinate of the lower sub-beam; L c is the pre-delamination length;

[0052] Figure 2 is a schematic diagram of the cohesive force model between the upper sub-beam and the lower sub-beam;

[0053] Figure 3 is a schematic diagram of the method for determining the delamination length correction value Δ in the method of the present invention;

[0054] Figure 4 is a schematic diagram of a non-linear continuous curve of the fracture toughness related to the delamination length;

[0055] Figure 5 is a schematic diagram of the method for determining the cohesive fatigue limit of the cohesive force model using the conditional yield stress;

[0056] Figure 6 is a schematic diagram of the constitutive relationship of the cohesive force model;

[0057] Figure 7 is a schematic diagram of the function obtained by fitting the delamination length and compliance data using a power function; in the figure, C = i*a^j represents the form of the fitting equation used; i and j are parameters to be determined by fitting, and the i and j in the table in the figure are the determined parameter values by fitting;

[0058] Figure 8 is a schematic diagram of the function obtained by fitting the number of cycles and the theoretical value of the delamination length using a power function; in the figure, a = I*N^J; I and J are parameters to be determined by fitting, and the parameter values are determined by fitting;

[0059] Figure 9 It is a comparison diagram of the fatigue delamination propagation rate curves of composite laminates obtained by theoretical calculation and experimental testing. Specific implementation manners

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0061] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0062] The present invention will be further described below in conjunction with the accompanying drawings, but it is not a limitation of the present invention.

[0063] Combined with Figure 1 As shown, the present invention provides an estimation method for the fatigue delamination propagation rate of composites considering the fiber bridging mechanism, including:

[0064] The composite laminate is divided into an upper sub-beam and a lower sub-beam by the delamination interface, and a displacement field model of the upper sub-beam and the lower sub-beam is established to obtain the mid-plane displacement expressions in the length direction and the thickness direction; based on the mid-plane displacement, the tangential displacement and normal displacement expressions of the delamination interface are obtained, as well as the strain expressions of the upper sub-beam and the lower sub-beam; and the in-plane stress resultant, in-plane bending moment and in-plane shear stress resultant expressions of the upper sub-beam and the lower sub-beam are obtained from the strain expressions of the upper sub-beam and the lower sub-beam;

[0065] Considering the fiber bridging mechanism, a fiber bridging factor is set, and a non-linear continuous curve related to the fracture toughness and delamination length of the composite laminate is obtained based on the static test; the tangential traction and normal traction between the delamination interfaces are obtained by combining the tangential displacement and normal displacement; and then the total strain energy of the composite laminate is obtained by combining the in-plane stress resultant, in-plane bending moment and in-plane shear stress resultant of the upper sub-beam and the lower sub-beam;

[0066] Based on the total strain energy of the composite laminate and the potential energy of the fatigue load applied to the composite laminate, a laminate equilibrium equation is established; a control equation set is obtained based on the laminate equilibrium equation;

[0067] The control equation set is solved to obtain the theoretical values of the fatigue load of the upper sub-beam, the theoretical value of the displacement of the upper sub-beam and the theoretical value of the delamination length under the fatigue load of the laminate;

[0068] The cyclic energy release rate is calculated based on the theoretical values of the fatigue load, displacement, and delamination length of the upper sub-beam, and then the fatigue delamination growth rate of the composite laminate is obtained.

[0069] Data fitting is performed on the fatigue delamination growth rate of the composite laminate to obtain the fitting curve of the fatigue delamination growth rate of the composite laminate.

[0070] In practical applications, the actual displacement value and actual fatigue load value of the upper sub-beam are measured, the actual cyclic energy release rate is calculated, and the current fatigue delamination growth rate of the composite laminate is determined in combination with the fitting curve.

[0071] In this embodiment, a mechanical model of the composite laminate is first established to calculate the interlaminar delamination growth of the composite laminate under monotonic or fatigue loads. The composite laminate is divided into upper and lower sub-beams by the delamination interface, and the model in the local coordinate system is as Figure 1 shown. The length and width of the composite laminate are L and B respectively, and the thicknesses of the upper and lower sub-beams are h t 、h b respectively. The displacement field models of the upper and lower sub-beams are established using the Timoshenko beam theory.

[0072] Furthermore, the expressions of the mid-plane displacements in the length direction and thickness direction are:

[0073]

[0074] where u r is the displacement of the upper and lower sub-beams along the X-axis in the length direction, r = t, b, t represents the upper sub-beam, and b represents the lower sub-beam; w r is the displacement of the upper and lower sub-beams along the Z-axis in the thickness direction; x is the X-axis coordinate, z r is the Z-axis coordinate of the upper and lower sub-beams, is the mid-plane displacement of the upper and lower sub-beams in the X-axis direction, is the mid-plane displacement of the upper and lower sub-beams in the Z-axis direction, is the rotation angle of the mid-plane of the upper and lower sub-beams relative to the normal.

[0075] The cohesive model is used to represent the constitutive relationship between the upper and lower surfaces of the delamination interface of the composite laminate, as Figure 2 shown. The expressions of the tangential displacement and normal displacement of the delamination interface are defined as:

[0076]

[0077] where Δu t represents the tangential displacement of the delamination interface, Δu n represents the normal displacement of the delamination interface, hb is the thickness of the lower sub - beam, h t is the thickness of the upper sub - beam.

[0078] Considering the geometric non - linearity of the composite laminate, the strain expressions of the upper and lower sub - beams are:

[0079]

[0080] In the formula is the normal strain of the upper and lower sub - beams, is the shear strain of the upper and lower sub - beams. In the variable sub - script, x represents the derivative with respect to the corresponding variable;

[0081] Based on formula (3), the expressions of the in - plane stress resultant, in - plane moment and in - plane shear stress resultant of the upper and lower sub - beams are obtained:

[0082]

[0083] In the formula is the in - plane stress resultant of the upper and lower sub - beams, is the in - plane moment of the upper and lower sub - beams, is the in - plane shear stress resultant of the upper and lower sub - beams;

[0084] In the formula, B is the width of the composite laminate, is the normal stress in the X - axis direction, is the shear stress in the XZ plane, is the tensile stiffness of the upper and lower sub - beams, is the tensile - bending coupling stiffness of the upper and lower sub - beams, is the bending stiffness of the upper and lower sub - beams, is the shear stiffness of the upper and lower sub - beams.

[0085] The double - cantilever beam tensile test of the composite laminate with pre - fabricated delamination cracks is carried out under quasi - static monotonic loading to obtain the load - displacement response data of the structure, and the modified beam theory is used to calculate the interface fracture toughness of the composite laminate.

[0086] The calculation method of the fracture toughness of the composite laminate is:

[0087]

[0088] In the formula, φ n is the fracture toughness of the composite laminate, P is the experimental value of the load applied to the upper sub - beam, W is the experimental value of the displacement of the upper sub - beam, a is the delamination length, η(a) is the set fiber bridging factor related to the delamination length, which is determined by the static test; Δ is the delamination length correction value, and Δ is obtained by taking the cube root C 1 / 3Extrapolate the linear fitting equation with the delamination length a to C 1 / 3 to obtain; as Figure 3 shown.

[0089] Due to the fiber bridging effect, the delamination growth resistance increases significantly with the crack growth. The interfacial fracture toughness of the composite laminate calculated by formula (5) is not a stable value, but a non-linear function that increases with the crack length.

[0090] Use a power function to perform non-linear fitting on the fracture toughness φ n of the composite laminate obtained from the static test, and obtain a non-linear continuous curve related to the delamination length a:

[0091]

[0092] where q1, q2 and q3 are all fitting parameters. The test data and the fitted curve are shown as Figure 4 shown.

[0093] The expressions for obtaining the tangential traction force and the normal traction force between the delamination interfaces are:

[0094]

[0095] where T t is the tangential traction force, T n is the normal traction force, δ0 is the characteristic length of the cohesive zone, D is the damage variable, indicating the degradation degree of the interface performance;

[0096] φ n is the interfacial fracture toughness in the normal direction, equal to the fracture toughness calculated in the static test;

[0097] Under fatigue load, the expression of the damage variable D is:

[0098]

[0099] where k is the correction coefficient, with a value of 0.01; is the cyclic damage increment, is the monotonic damage increment, t is the time;

[0100]

[0101] where is the cumulative displacement increment of one load cycle period, δ ∑ is the total displacement required to cause the failure of the cohesive zone, T is the total cohesive tension of the delamination crack interface, σ f is the cohesive fatigue limit, σ maxis the normal cohesive strength after the number of load cycles N, σ max,0 is the interfacial cohesive strength when no damage occurs, H is the Heaviside function, is the cumulative displacement in one load cycle period, δ f is the separation displacement corresponding to the cohesive fatigue limit;

[0102] σ max = σ max，0 (1 - D);

[0103]

[0104] The function value is 1 only when the value inside the parentheses is greater than or equal to 0, otherwise the function value is 0;

[0105] Adopt the conditional yield stress to define the cohesive fatigue limit σ f of the cohesive force model; The determination method of the conditional yield stress is the same as that of the cohesive fatigue limit σ f :

[0106] Define the normal traction force T n - The normal displacement Δu of the crack interface n Parallel line in the elastic response stage of the curve, shift the parallel line by the specified plastic deformation amount d; The cohesive fatigue limit σ f (conditional yield stress) is determined by the dimensionless parameters δ n / δ0 and σ n at the intersection point of the shifted parallel line and the curve of the normal traction force T f / δ0 and σ f / σ max,0 jointly. As Figure 5 shown, the total displacement of the cohesive zone failure δ Σ is defined as 10δ0, and this displacement point corresponds to the tension value degraded to 0.1% of the initial cohesive strength. The schematic diagram of the constitutive relationship of the finally determined cohesive force model is as Figure 6 shown. When , both monotonic damage and fatigue damage occur simultaneously in the cohesive zone, and the two damage increments coexist. The larger one is the final damage increment of the current cycle, and the unloading path linearly unloads from the current state point back to the traction zero point; when , the cohesive tension exceeds the cohesive fatigue limit but is less than the cohesive strength, and only fatigue damage occurs in the cohesive zone, and the unloading path linearly unloads from the current state point back to the traction zero point; when , the cohesive tension is in the elastic section and no damage occurs, and the unloading path returns to the origin along the elastic section.

[0107] Furthermore, the calculation method of the total strain energy of the composite laminate is as follows:

[0108]

[0109] Where U is the total strain energy of the composite laminate, V t is the volume of the upper sub-beam, V b is the volume of the lower sub-beam, and A is the interlaminar area of the delamination interface;

[0110] The potential energy of the fatigue load applied to the composite laminate is expressed as V:

[0111]

[0112] Where L is the length of the composite laminate, P t is the theoretical value of the fatigue load of the upper sub-beam, W t is the theoretical value of the displacement of the upper sub-beam, δ D is the Dirac function, x e is the X-axis coordinate of the fatigue load application position;

[0113]

[0114] The function value is 1 only when the value in the parentheses is 0, otherwise the function value is 0.

[0115] Based on the principle of minimum potential energy and the variational method, the equilibrium equation of the laminate is established:

[0116] δ(U - V) = 0(14),

[0117] Where δ is the variational symbol;

[0118] Based on the equilibrium equation of the laminate, the following control equation set is obtained:

[0119]

[0120] The above first-order ordinary differential equation set can be solved by programming with numerical calculation software to obtain the theoretical value P of the fatigue load of the upper sub-beam under the fatigue load of the laminate t and the theoretical value W of the displacement of the upper sub-beam t and the theoretical value of the delamination length;

[0121] The cyclic energy release rate calculated based on the theoretical value P of the fatigue load of the upper sub-beam t , the theoretical value W of the displacement of the upper sub-beam t and the theoretical value of the delamination length is expressed as ΔG:

[0122]

[0123] C = W t / P t ;

[0124] Where is the maximum theoretical value of the fatigue load of the upper sub-beam, is the minimum theoretical value of the applied load of the upper sub-beam, a t is the theoretical value of the delamination length; The functional relationship can be obtained by fitting the delamination length and flexibility data, and the differential operation is performed on the functional relationship.

[0125] For the theoretical value of the delamination length a t and the number of cycles N are fitted with a power function to obtain a functional relationship, and the differential operation is performed on the functional relationship to obtain the fatigue delamination growth rate da t / dN of the composite laminate.

[0126] Finally, the fatigue delamination growth rate da t / dN and the cyclic energy release rate ΔG are plotted in a double logarithmic coordinate system to obtain the fatigue delamination growth rate curve of the composite laminate; then the Paris law is used to fit the curve to obtain the fitted curve;

[0127] The method of using the Paris law to fit and determine da t / dN is:

[0128]

[0129] where F is a material-related constant and m is the exponential constant of the Paris law.

[0130] All the calculation processes of the fatigue crack growth rate described in this embodiment can be realized by software programming, that is, all the above calculation processes can be realized by software programming to obtain the fatigue crack growth rate of the composite laminate.

[0131] Example:

[0132] S1. Prepare a composite laminate structure with a prefabricated delamination crack. As Figure 1 shown, the total length L of the specimen is 140 mm, the width B is 20 mm, the total thickness is 3 mm, the upper and lower sub-beams are evenly divided into sub-beams of equal thickness by the prefabricated delamination crack, and the prefabricated crack length Lc is 20 mm. The basic mechanical properties of the composite material used are shown in Table 1. A tensile load is applied to the composite laminate structure with the prefabricated delamination crack at the position of x e = 5 mm, and the double-cantilever beam tensile test under monotonic load is carried out to obtain the load-displacement response data of the structure, and the interfacial fracture toughness of the composite laminate structure is calculated by formula (5).

[0133] Table 1 Basic mechanical properties of the composite laminate

[0134]

[0135] S2. Establish a mechanical model of the composite laminate structure based on the geometric parameters and material parameters of the structure in step S1, and input the basic mechanical properties of the composite laminate into formula (4).

[0136] S3. Calculate the interface fracture toughness of the composite laminate corresponding to different delamination lengths using formula (5), and perform a non-linear fitting on the fracture toughness data to obtain a non-linear continuous function φ related to the crack length, as shown in n (a), and substitute it into formula (6). (a), and substitute it into formula (6).

[0137] S4. Define the cohesive fatigue limit of the cohesive force model using the conditional yield stress. As shown in Figure 5 , draw a parallel line to the elastic response stage of the traction-displacement curve, offset by the specified plastic deformation amount d. The conditional yield stress value is jointly determined by two non-dimensional parameters (δ f / δ0 and σ f / σ max,0 ) at the intersection point of the offset line and the traction-displacement curve. f / δ0 and σ f / σ max,0 ) at the intersection point of the offset line and the traction-displacement curve.

[0138] S4. Solve the control equation group formulas (15)-(26) to obtain the interlaminar delamination length a, the number of cycles N, the theoretical value P of the load applied to the upper sub-beam, and the theoretical value w of the displacement of the upper sub-beam under the fatigue load of the composite laminate structure obtained by theoretical calculation. t and the theoretical value w of the displacement of the upper sub-beam t .

[0139] S5. Using the load and displacement data obtained in step S4, calculate the cyclic energy release rate ΔG of the structure under the fatigue load using formula (27). The in the formula is obtained by fitting the function relationship through the delamination length and compliance data and performing a differential operation, as shown in Figure 7 . Figure 7 ]>shown.

[0140] S6. Using the crack propagation length and number of cycles data obtained in step S4, fit the calculated data using a power function to obtain a function relationship. The crack propagation rate da t / dN can be obtained through a differential operation, as shown in Figure 8 . Figure 8 shown.

[0141] S7. Plot the theoretically calculated crack propagation rate da t / dN and the cyclic energy release rate ΔG in a double logarithmic coordinate system to obtain the fatigue delamination propagation rate curve of the composite laminate structure, as shown in Figure 9As shown in the figure. The Paris law is used to fit the fatigue delamination growth rate curves obtained from theoretical calculations and experimental tests, and the exponential constants of the Paris law are obtained, as shown in Table 2.

[0142] Table 2 Exponential constant m of the Paris law obtained from theoretical calculations and experimental tests

[0143]

[0144] Although the present invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed, as long as they do not depart from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein can be combined in a manner different from that described in the original claims. It should also be understood that the features described in connection with a single embodiment can be used in other described embodiments.

Claims

1. An estimation method for the fatigue delamination growth rate of a composite material considering the fiber bridging mechanism, characterized in that Including: Dividing the composite laminate into an upper sub - beam and a lower sub - beam by the delamination interface, establishing displacement field models for the upper and lower sub - beams, and obtaining the mid - surface displacement expressions in the length and thickness directions; based on the mid - surface displacements, obtaining the tangential and normal displacement expressions of the delamination interface, as well as the strain expressions of the upper and lower sub - beams; and obtaining the expressions of the in - plane stress resultant, in - plane bending moment, and in - plane shear stress resultant of the upper and lower sub - beams from the strain expressions of the upper and lower sub - beams; Considering the fiber bridging mechanism, setting the fiber bridging factor, and obtaining the non - linear continuous curve of the fracture toughness of the composite laminate related to the delamination length based on static tests; combining the tangential and normal displacements to obtain the tangential traction and normal traction between the delamination interfaces; and then combining the in - plane stress resultant, in - plane bending moment, and in - plane shear stress resultant of the upper and lower sub - beams to obtain the total strain energy of the composite laminate; Based on the total strain energy of the composite laminate and the potential energy of the fatigue load applied to the composite laminate, establishing the laminate equilibrium equation; Based on the laminate equilibrium equation, obtaining the control equation set; Solving the control equation set to obtain the theoretical values of the fatigue load of the upper sub - beam, the displacement of the upper sub - beam, and the delamination length under the fatigue load of the laminate; Calculating the cyclic energy release rate according to the theoretical values of the fatigue load of the upper sub - beam, the displacement of the upper sub - beam, and the delamination length, and then obtaining the fatigue delamination propagation rate of the composite laminate; Performing data fitting on the fatigue delamination propagation rate of the composite laminate to obtain the fitting curve of the fatigue delamination propagation rate of the composite laminate; In practical applications, measuring the actual displacement value of the upper sub - beam and the actual fatigue load value of the upper sub - beam, calculating the actual cyclic energy release rate, and combining with the fitting curve to determine the current fatigue delamination propagation rate of the composite laminate.

2. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 1, characterized in that The mid - surface displacement expressions in the length and thickness directions are: where u r is the displacement of the upper and lower sub - beams along the X - axis in the length direction, r = t, b, t represents the upper sub - beam, b represents the lower sub - beam; w r is the displacement of the upper and lower sub - beams along the Z - axis in the thickness direction; x is the X - axis coordinate, z r is the Z - axis coordinate of the upper and lower sub - beams, is the mid - surface displacement of the upper and lower sub - beams in the X - axis direction, is the mid - surface displacement of the upper and lower sub - beams in the Z - axis direction, is the rotation angle of the mid - surface of the upper and lower sub - beams relative to the normal direction.

3. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 2, characterized in that The tangential and normal displacement expressions of the delamination interface are: where Δu t represents the tangential displacement of the delamination interface, and Δu n represents the normal displacement of the delamination interface, h b is the thickness of the lower sub-beam, and h t is the thickness of the upper sub-beam.

4. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 3, characterized in that Considering the geometric non - linearity of the composite laminate, the strain expressions of the upper and lower sub - beams are: In the formula are the normal strains of the upper sub-beam and the lower sub-beam, are the shear strains of the upper sub-beam and the lower sub-beam. In the variable subscripts, x represents the derivative of the corresponding variable; Based on formula (3), the expressions of the in - plane stress resultant, in - plane bending moment, and in - plane shear stress resultant of the upper and lower sub - beams are obtained: In the formula is the in-plane stress resultant of the upper and lower sub-beams, is the in-plane bending moment of the upper and lower sub-beams, is the in-plane shear stress resultant of the upper and lower sub-beams; where B is the width of the composite laminate, is the normal stress in the X-axis direction, is the shear stress in the XZ plane, is the tensile stiffness of the upper and lower sub-beams, is the tensile-bending coupling stiffness of the upper and lower sub-beams, is the bending stiffness of the upper and lower sub-beams, is the shear stiffness of the upper and lower sub-beams.

5. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 4, characterized in that The calculation method of the fracture toughness of the composite laminate is: where φ n is the fracture toughness of the composite laminate, P is the test value of the load applied to the upper sub-beam, W is the test value of the displacement of the upper sub-beam, a is the delamination length, η(a) is the set fiber bridging factor related to the delamination length, Δ is the delamination length correction value, and Δ is obtained by extrapolating the linear fitting equation of the cube root C 1 / 3 of the compliance C of the composite laminate to C 1 / 3 = 0; The fracture toughness φ of the composite laminate obtained from the static test is nonlinearly fitted by a power function n to obtain a nonlinear continuous curve related to the delamination length a: Where q1, q2, and q3 are all fitting parameters.

6. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 5, characterized in that The expressions for obtaining the tangential traction and normal traction between the delamination interfaces are: where T t is the tangential traction force, T n is the normal traction force, δ0 is the characteristic length of the cohesive zone, and D is the damage variable; where k is the correction coefficient, is the cyclic damage increment, is the monotonic damage increment, and t is time; where is the cumulative displacement increment in a load cycle period, δ ∑ is the total displacement required to cause the cohesive zone to fail, is the total cohesive tension at the delamination crack interface, σ f is the cohesive fatigue limit, σ max is the normal cohesive strength after N load cycles, σ max,0 is the interfacial cohesive strength without damage, H is the Heaviside function, is the cumulative displacement in a load cycle period, δ f is the separation displacement corresponding to the cohesive fatigue limit; where the cohesive fatigue limit σ f is determined using the conditional yield stress: defining the normal traction T n - the normal displacement Δu of the crack interface n a parallel line in the elastic response stage of the curve, shifting the parallel line by a specified plastic deformation amount d; the cohesive fatigue limit σ f through the shifted parallel line and the normal traction T n - the normal displacement Δu of the crack interface n the dimensionless parameter δ at the intersection point of the curve f / δ0 and σ f / σ max,0 are jointly determined.

7. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 6, characterized in that The calculation method of the total strain energy of the composite laminate is as follows: where U is the total strain energy of the composite laminate, and V t is the volume of the upper sub-beam, and V b is the volume of the lower sub-beam, and A is the interfacial area of the delamination interface; The potential energy of the fatigue load applied to the composite laminate is expressed as V: where L is the length of the composite laminate, P t is the theoretical value of the fatigue load of the upper sub-beam, W t is the theoretical value of the displacement of the upper sub-beam, δ D is the Dirac function, x e is the X-axis coordinate of the fatigue load application position; 8. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 7, characterized in that Based on the principle of minimum potential energy and the variational method, establish the laminate equilibrium equation: δ(U - V) = 0 (14), where δ is the variational symbol; Based on the laminate equilibrium equation, the following control equation set is obtained:

9. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 8, characterized in that Solving the control equations to obtain the theoretical value \(P\) of the fatigue load of the upper sub-beam under the fatigue load of the laminated plate t and the theoretical value \(W\) of the displacement of the upper sub-beam t and the theoretical value of the delamination length; Express the cyclic energy release rate as ΔG: C = W t / P t ; In the formula is the maximum theoretical value of the fatigue load of the upper sub-beam, is the minimum theoretical value of the applied load of the upper sub-beam, a t is the theoretical value of the delamination length; The theoretical value a of the delamination length t and the number of cycles N are fitted by a power function to obtain a functional relationship, and the functional relationship is differentiated to obtain the fatigue delamination growth rate da t / dN.

10. The method for estimating the fatigue delamination propagation rate of a composite material considering the fiber bridging mechanism according to claim 9, characterized in that Plot the fatigue delamination growth rate da t / dN and the cyclic energy release rate ΔG in a double logarithmic coordinate system to obtain the fatigue delamination growth rate curve of the composite laminate; then use the Paris law to fit the curve to obtain the fitted curve; The method of determining da t / dN by fitting with Paris law is as follows: where F is a material-related constant and m is the exponential constant of the Paris law.

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