Method for forecasting extension length of interlayer fatigue crack of composite material by considering temperature effect

Abstract

The invention relates to a temperature effect-considered composite material interlayer fatigue crack propagation length forecasting method, which aims at the fatigue layering damage and destruction problems of a plain woven composite material in different temperature environments, adopts a finite element numerical simulation method, and combines a cohesion bilinear constitutive model and a Paris formula theory to forecast the fatigue crack propagation length of the plain woven composite material. The damage evolution law of the cohesion model under the fatigue load of the composite material is deduced, and a set of complete plain woven composite material interlayer fatigue damage evolution model considering the temperature effect is established. Unit verification, ideal experiment verification and real experiment verification are adopted, the extension length of the interlayer crack under different initial loads considering the temperature effect is forecasted, the simulation result and the experiment result are well matched, and it is shown that the method can accurately simulate the interlayer fatigue performance of the plain woven composite material, and the method has good application prospects. The method can effectively predict the interlayer fatigue crack propagation length of the composite material in different temperature environments, and provides important calculation parameters and theoretical basis for forecasting the fatigue life of the composite material.

Description

Technical Field

[0001] The present invention belongs to the field of composite material engineering technology applications, and particularly relates to a method for predicting the interlaminar fatigue crack propagation length of plain woven composite materials considering temperature effects. Background Technique

[0002] For composite laminates, during the manufacturing process, they usually go through processes such as winding, layup, weaving, and curing. Delamination damage is a common damage form. Under working conditions such as drilling, impact, fatigue, and shear, delamination damage will occur in composite material structures. First, cracking occurs, then crack propagation and delamination, and finally fracture may occur. The appearance and propagation of such interlaminar cracks are often not easily detected because they occur inside the structure (as shown in Figure 1 ), and can increase continuously at a relatively low stress level, resulting in a certain degree of reduction in the structural stiffness.

[0003] The interlaminar properties of composite materials under high-temperature environments and fatigue working conditions are significantly different from those under normal temperature and static conditions. On the one hand, in a high-temperature environment, for the resin that is the matrix of the composite material, within the range of relatively high temperatures but below the glass transition temperature, its mechanical properties will degrade. On the other hand, under fatigue working conditions, according to damage theory, as the number of fatigue cycles increases, although the static failure load is not reached, the small damages inside the resin and at the interface gradually accumulate, and then pores are formed, and finally failure leads to crack propagation. The speed of such interlaminar fatigue crack propagation is one of the aspects that are highly concerned in the industry, and macroscopically, it is reflected in the change of the interlaminar crack propagation length of the structure corresponding to different fatigue load cycle numbers N.

[0004] Determining the interlaminar fatigue crack propagation length of composite materials can effectively predict the fatigue failure strength and fatigue life of the structure, and provide a feasible theoretical basis for the design and safety assessment of composite material structures. The fatigue delamination growth initiation test method recommended in ASTM D6115 is used to determine the fatigue damage threshold G th , that is, it is considered that once the energy release rate G exceeds the fatigue damage threshold G th , cracks will appear in the component and start to continuously delaminate and expand. This test standard requires first determining the interlaminar fatigue crack propagation length of the composite material through experiments.

[0005] The interlaminar fatigue performance of plain woven composites is evaluated by experimental methods. In the fatigue crack propagation experiment, the measurement process of the interlaminar fatigue crack propagation length is cumbersome and the human error is large. Due to fiber bridging and the uncertainty of the manufacturing process, many materials or actual working conditions are different from those required in the experimental standards, resulting in large deviations in the experimental results. In addition, composites are expensive, the fatigue experiment period is long, and the experimental results are relatively discrete. To obtain accurate experimental data, a larger number of samples are needed. All these factors make the experimental method costly, with a long test period and uncertain results.

[0006] Using the finite element method (FEM) to simulate the interlaminar mechanical behavior of composites is an effective research method. Based on this, many numerical methods for simulating cracks have been derived, such as the extended finite element method (XFEM), the cohesive zone method (CZM), the virtual crack closure technique (VCCT), the phase field method (PFM), etc. Among them, the cohesive force model has good effects in predicting quasi-static delamination and crack propagation, so it has been widely used.

[0007] There are many constitutions of the cohesive force model, such as bilinear, trilinear, trapezoidal, polynomial, etc. The most common one is the bilinear constitution. In this invention, for the quasi-static interlaminar performance of plain woven composites, the bilinear cohesive force model is used for description. The cohesive force model is the relationship between the traction stress and the opening displacement. For three-dimensional cohesive force units, its constitutive model is described by Equation (1):

[0008]

[0009] In the formula, σ 33 is the normal traction stress, σ 13 and σ 23 are the tangential traction stresses in the 13 direction and the 23 direction respectively, D k is the stiffness damage variable, K is the tangent stiffness, δ 33 is the normal relative displacement, δ 13 and δ 23 are the tangential relative displacements in the 13 direction and the 23 direction respectively. In the process of interlaminar failure of composites, the main role is played by δ 33 , and the corresponding one is σ 33 .

[0010] Describing the bilinear constitution requires three parameters: the tangent stiffness K, the interface strength σ max and the fracture toughness GIC , as the opening displacement δ increases, the traction stress rises from 0 with a slope of K and reaches σ max after which the traction stress gradually decreases to 0. The one-dimensional cohesive bilinear constitutive model is as Figure 2 shown, where δ0 is the damage initiation displacement and δ f is the failure displacement, and both can be derived from K, σ max and G IC through simple geometric relationships.

[0011] Let D k be the stiffness damage variable, D e be the energy damage variable, and W d be the energy dissipation. When D k = 1 or D e = 1, the element is considered to have failed. The expressions for the two damage variables are shown in Eqs. (2) and (3);

[0012]

[0013] where δ0 is the damage initiation displacement, δ f is the failure displacement, and δ is the opening displacement.

[0014] Currently, the fatigue crack growth is mainly described based on the Paris formula in fracture mechanics, as shown in Eq. (4):

[0015]

[0016] where a is the crack length, N is the number of stress cycles, C and n are both material constants, and G is the energy release rate. da / dN represents the crack growth rate, which is the rate of change of the crack length a with respect to the number of stress cycles N under fatigue loading, reflecting the speed of crack growth, and f(G) is the fitting function of the energy release rate G.

[0017] For the simulation model under fatigue loading, due to the large number of experimental cycles, it is extremely difficult to simulate by analyzing the stiffness damage cycle by cycle. For fatigue experiments with a large number of cycles, it is relatively easy to numerically approximate using the Paris curve. The loading method adopts envelope loading, and the loading process is divided into two parts: the first part is quasi-static loading, and after loading to a certain value, a hold load is started, and the hold load process is used to equivalent the cyclic loading behavior.

[0018] In summary, since the appearance and propagation of interlaminar cracks often occur inside components, it is still very difficult to determine the length of interlaminar cracks through experimental methods. Moreover, experimental methods are costly and have a long testing cycle. Using the finite element numerical simulation method to evaluate the fatigue failure performance of composites has a broader development prospect than experimental research methods. Currently, most of the models for predicting the fatigue crack propagation of plain woven composites are described based on the Paris formula in fracture mechanics. However, for interlaminar cracks in composites, it is difficult to obtain the strain near the crack tip. Therefore, using the finite element simulation method to predict the interlaminar fatigue crack length and fatigue life of composites under different temperature environments is still in the stage of continuous exploration and improvement. Summary of the Invention

[0019] The purpose of the present invention is to solve the problem in the background technology that there is a lack of an effective method for predicting the propagation length of interlaminar fatigue cracks in composites, and to provide a method for predicting the propagation length of interlaminar fatigue cracks in composites considering the temperature effect.

[0020] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0021] A method for predicting the propagation length of interlaminar fatigue cracks in composites considering the temperature effect, the method is: for a composite laminate under the action of a fatigue load considering the temperature effect, adopt the finite element numerical simulation analysis method, combine the Paris curve with the cohesive zone model, and predict the propagation length of interlaminar fatigue cracks in composites.

[0022] Furthermore, the method is specifically as follows:

[0023] Use energy damage to describe the fatigue process. Since the relationship between D e and δ is linear, while the relationship between D k and δ is non-linear. In the finite element solution process, the fatigue delamination process is self-similar. The current time is denoted as t n , and the integral form of the cumulative energy damage within Δt time is:

[0024]

[0025] For the cumulative rate dD e / dt of the energy damage variable, the calculation process of this method is as follows:

[0026] Combine the Paris curve with the cohesive zone model to conduct a complete analysis of an element. When the element is completely damaged, it can be regarded that the interlaminar fatigue crack has propagated by one element length L e , therefore, the relationship between the propagation length L e of the interlaminar fatigue crack is as follows:

[0027]

[0028] wherein, t e is the time required for the complete failure of the unit, C and n are the fitting parameters of the Paris formula (both C and n are empirical parameters obtained by fitting), G max is the maximum energy release rate of the current unit, G ⅠC is the fracture toughness. Since the load in the fatigue stage is a constant load holding, the interlaminar fatigue crack propagation length in Equation (6) can be changed to:

[0029]

[0030] When considering the influence of the temperature effect, since the Paris formula changes with temperature based on the quasi-static results, the parameters C and n in the Paris formula (see Equation (4) for details) are also temperature-dependent, and thus a prediction method for the interlaminar fatigue crack propagation length of the composite material considering the temperature effect is obtained.

[0031] The beneficial effects of the present invention compared with the prior art are as follows: On the basis of not affecting the Paris form, based on the above background technology and development status, the Paris curve is combined with the cohesive bilinear constitutive model, and a complete fatigue damage evolution model considering the temperature effect is proposed for plain woven composites. This model can accurately predict the fatigue crack propagation length L of the cohesive unit when the composite laminate undergoes interlaminar fatigue fracture failure e . For a complete analysis of a cohesive unit, when the unit is completely damaged, it can be regarded as the interlaminar fatigue crack propagating by a unit length L e , therefore, the interlaminar fatigue crack propagation length L e has the following relationship:

[0032]

[0033] wherein, t e is the time required for the complete failure of the unit, C and n are the fitting parameters of the Paris formula (both C and n are empirical parameters obtained by fitting), G max is the maximum energy release rate of the current unit, G ⅠC is the fracture toughness.

[0034] This method can effectively predict the interlaminar fatigue crack propagation length of the composite material in different temperature environments, and provide important calculation parameters and theoretical basis for the prediction of the fatigue life of the composite material. Description of the Drawings

[0035] Figure 1Diagrams of delamination phenomena found in different experiments, (a) drilling, (b) impact, (c) fatigue, (d) shear;

[0036] Figure 2 Schematic diagram of one-dimensional bilinear cohesive force model;

[0037] Figure 3 Schematic diagram of element verification model;

[0038] Figure 4 Diagram comparing the cohesive force UMAT for element quasi-static verification with the built-in material constitutive model of ABAQUS;

[0039] Figure 5 Schematic diagram of the coordinate system of two-dimensional simulation model;

[0040] Figure 6 Diagram of experimental verification load-displacement curve results, (a) 20°C, (b) 60°C, (c) 100°C;

[0041] Figure 7 Diagram comparing ideal experimental verification results with theoretical values. Specific implementation manner

[0042] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention, without departing from the spirit and scope of the technical solution of the present invention, shall be covered by the protection scope of the present invention.

[0043] Aiming at the fatigue delamination damage and failure problems of plain woven composites in different temperature environments, the present invention adopts the method of finite element numerical simulation, combines the cohesive force bilinear constitutive model and Paris formula theory, deduces the damage evolution law of the cohesive force model under the fatigue load of composites, and establishes a complete interlaminar fatigue damage evolution model of plain woven composites considering the temperature effect. By using element verification, ideal experimental verification and real experimental verification, the propagation length of interlaminar cracks under different initial loads considering the temperature effect is predicted. The simulation results are in good agreement with the experimental results, indicating that this method can accurately simulate the interlaminar fatigue performance of plain woven composites, effectively predict the propagation length of interlaminar fatigue cracks of composites in different temperature environments, and provide important calculation parameters and theoretical basis for the prediction of the fatigue life of composites. Specific implementation manner one:

[0045] A method for predicting the propagation length of interlaminar fatigue cracks of composites considering the temperature effect, the method is: for the composite laminate under the fatigue load considering the temperature effect, adopt the method of finite element numerical simulation analysis, combine the Paris curve with the cohesive force model, and predict the propagation length of interlaminar fatigue cracks of composites.

[0046] The fatigue process is described using energy damage because D e has a linear relationship with δ, while D k has a non-linear relationship with δ. During the finite element solution process, the fatigue delamination process is self-similar, and the current time is denoted as t n . The integral form of the cumulative energy damage within the time Δt is as follows:

[0047]

[0048] For the cumulative rate dD e / dt of the energy damage variable, the calculation process of this method is as follows:

[0049] The Paris curve is combined with the cohesive force model to conduct a complete analysis of an element. When the element is completely damaged, it can be regarded as the interlayer fatigue crack having propagated by an element length L e . Therefore, the relationship between the interlayer fatigue crack propagation length L e is as follows:

[0050]

[0051] where t e is the time required for the complete damage of the element, C and n are the fitting parameters of the Paris formula (both C and n are empirical parameters obtained through fitting), G max is the maximum energy release rate of the current element, and G ⅠC is the fracture toughness. Since the load during the fatigue stage is a constant load hold, the interlayer fatigue crack propagation length in Equation (6) can be changed to:

[0052]

[0053] When considering the influence of the temperature effect, since based on the quasi-static results, the Paris formula changes with temperature, the parameters C and n in the Paris formula (see Equation (4) for details) are also temperature-dependent, and thus a prediction method for the interlayer fatigue crack propagation length of the composite material considering the temperature effect is obtained.

[0054] Example 1:

[0055] Use this method to determine the interlayer fatigue crack propagation length L e and estimate the fatigue damage threshold G th .

[0056] When the energy release rate G exceeds the fatigue damage threshold G thWhen fatigue damage begins to accumulate. Calculate the element life from the perspective of cohesive elements. When the element enters the fatigue damage stage, assuming that the quasi-static loading displacement exceeds δ0 and has entered the weakening stage, when the quasi-static loading ends, the element begins to accumulate fatigue damage until failure, and the time required for this process is also t e , and this cumulative process can be expressed by Equation (8).

[0057]

[0058] In the formula, is the energy damage in the fatigue stage, is the energy damage at the beginning of the fatigue stage. Similarly, assuming that the energy release rate is constant in this stage, then there is:

[0059]

[0060] By combining the two equations, we get:

[0061]

[0062] Substitute the interlayer fatigue crack propagation length L determined by the present invention e into Equation (10), and calculate the increment of the fatigue damage variable at each increment step through the Paris formula. The current energy release rate is solved by an indirect method. Let the displacement at a certain moment be the failure displacement δ f and the corresponding traction stress be σ d , and the solution method of the energy release rate is shown in Equation (11):

[0063]

[0064] The fatigue damage threshold G th It is considered that the crack will not propagate below this energy release rate level. When this value is unknown, in the cohesive model, the fatigue damage threshold G th can be estimated by Equation (12):

[0065]

[0066] Example 2:

[0067] Use this method to determine the interlayer fatigue crack propagation length L e , and perform an element verification model.

[0068] The physical model uses two two-dimensional solid elements with a cohesive element inserted in the middle. The loading method uses fixed normal displacement, and a lateral displacement constraint is added to the upper solid element, as Figure 3As shown. In the quasi-static test, check whether the traction stress-opening displacement curve of the cohesive element is the same as the preset value, and at the same time compare the calculation results with the built-in cohesive constitutive model of ABAQUS. In the fatigue test, check whether the life of the cohesive element matches the theoretical value of the Paris formula. The parameters used are shown in Table 1. Figure 4 For the bilinear constitutive model of the element and its comparison with the built-in material properties of ABAQUS, it can be found that the two match well.

[0069] Table 1 Cohesive model parameters used for element verification

[0070] K (MPa / mm) <![CDATA[σ max (MPa)]]> <![CDATA[G IC (N / mm)]]> C n 959 17 0.467 0.00235 5.89081

[0071] Example 3:

[0072] Use this method to determine the interlayer fatigue crack propagation length L e , and verify the model with real experiments.

[0073] Real experiments are used to verify the load-displacement curve, stress distribution in the quasi-static experiment, and crack propagation length in the fatigue delamination propagation experiment. The real experimental model uses two-dimensional solid elements to establish the models of the beam and the loading block, and a fixed constraint is adopted between the beam and the loading block. For the material properties, a homogeneous material is selected, the elastic modulus is set to 270 GPa, and the Poisson's ratio is 0.3; for the cantilever beam part, considering that the plain woven composite material is a transversely isotropic material, the material constitutive is set as the engineering constants in ABAQUS.

[0074] After determining the mesh division of the experimental verification model, it is necessary to assign material properties to the finite element model. For the material properties of the cantilever beam, the simulation model uses a two-dimensional model, where the 1 direction represents the crack propagation direction, the 2 direction represents the out-of-plane direction, and the 3 direction represents the thickness direction, as Figure 5 shown. The finally determined interlayer parameters are shown in Table 2.

[0075] Table 2 Fatigue cohesive parameters under different temperature environments

[0076] T(℃) K (MPa / mm) <![CDATA[σ max (MPa)]]> <![CDATA[G IC (N / mm)]]> C n 20 1000 16.38 0.560 0.00235 5.12909 60 1000 14.00 0.566 0.015700 5.89081 100 1000 12.00 0.694 0.012600 4.63946

[0077] Compare the obtained load-displacement curve with the experimental results. The load-displacement curve is as Figure 6 shown. It can be seen from the figure that the slopes of the rising segments at the three temperatures are relatively consistent, and the critical load and critical displacement values are also relatively reasonable. After the initial fracture of the specimen, it enters the crack propagation stage, and the trend of the simulated load-displacement curve is the same as that in the real experiment.

[0078] Example 4:

[0079] Use this method to determine the interlayer fatigue crack propagation length L e, Ideal experiment verification model.

[0080] The ideal experiment verification model is used to analyze whether the crack growth rate conforms to the input Paris formula. The ideal experiment model uses moment loading to ensure that the energy release rate at the crack tip is constant, thereby ensuring uniform crack growth. The crack growth rate is obtained by calculating the time corresponding to a certain crack growth length. When dividing the mesh, considering the sensitivity of the fatigue cohesive method to the mesh size, the element sizes of the crack growth section beam and the cohesive zone are set to 0.1 mm, and the element size of the solid element of the remaining part of the beam is still 0.4 mm.

[0081] Since the working condition is a constant energy release rate and the crack grows uniformly, after the loading step is stable, the crack growth length and its corresponding cycle number are taken to calculate the crack growth rate, and the energy release rate is obtained from the state variables of the cohesive elements at the crack tip. The results are as Figure 7 shown.

Claims

1. A method for predicting the fatigue crack propagation length between layers of a composite material considering the temperature effect, characterized in that: The method is as follows: for a composite laminate under fatigue load considering temperature effect, a finite element numerical simulation analysis method is adopted, combining the Paris curve with the cohesive force model to predict the fatigue crack propagation length between composite material layers.

2. A method for predicting the interlaminar fatigue crack propagation length of a composite material considering temperature effect according to claim 1, characterized in that: Specifically, the method is as follows: Using energy damage to describe the fatigue process, in the finite element solution process, the fatigue delamination process is self-similar. Combining the Paris curve with the cohesive model, a complete analysis of a single element is carried out. When the element is completely damaged, it is considered that the interlaminar fatigue crack has extended by a single element length L e ; Therefore, the interlaminar fatigue crack propagation length L e has the following relationship: where t e is the time required for the complete failure of the unit, C and n are the fitting parameters of the Paris formula, G max is the maximum energy release rate of the current unit, G ⅠC is the fracture toughness; Since the load in the fatigue stage is constant force holding, the interlaminar fatigue crack propagation length in Equation (6) can be changed to: When considering the influence of temperature effect, based on the quasi-static results, the Paris formula changes with temperature, so the parameters C and n in the Paris formula are also related to temperature, thus obtaining a prediction method for the interlaminar fatigue crack propagation length of composite materials considering temperature effect.

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