Data-physical integration method for predicting fatigue layering energy of composite material laminated plate

Abstract

The invention discloses a data-physical integration method for predicting fatigue layering energy of a composite material laminated plate. The method comprises the following steps: acquiring basic data of fatigue layering damage of a composite material; calculating a flexibility method strain energy release rate; calculating the theoretical strain energy release rate of the beam; priori knowledge is summarized; on the basis of the principle of a physical knowledge neural network, fatigue layering physical knowledge and data, constructing and optimizing a data-physical integration model for predicting the fatigue layering energy of the composite material laminated plate to obtain a data-physical integration model for optimally predicting the fatigue layering energy of the composite material laminated plate; the optimal model can predict the fatigue layering energy of the composite material laminated plate under any fatigue layering damage basic data. According to the method, the fatigue layering energy of the composite laminated plate can be quickly and accurately predicted, and integration of physical knowledge restricts that a prediction result follows a physical rule and also reduces the degree of dependence of the method on the data volume.

Description

Technical Field

[0001] The present invention relates to the field of fatigue damage of composite materials, and more particularly to a data-physics integration method for predicting the fatigue delamination energy of composite laminates. Background Art

[0002] Composite materials are widely used in the aerospace field due to their excellent mechanical properties. The in-plane properties of composite laminates are excellent, but their interlaminar properties are weak, so they are prone to fatigue delamination damage. At present, there are two analysis perspectives for the fatigue delamination damage of composite laminates, one is the traditional stress-strain method, and the other is the energy method. Stress-strain information is easy to obtain, but it has limitations in complex problems; energy information is not easy to obtain directly, but compared with the traditional stress-strain method, it can more intuitively characterize the physical essence of fatigue damage, provide a unified description of crack initiation, propagation and final failure, and has stronger adaptability and universality for complex problems. Therefore, it is necessary to explore how to obtain energy information more accurately. In recent years, with the development of artificial intelligence technology, data-driven provides a new method for the research of fatigue delamination damage of composite materials. The pure data-driven method has the advantages of reliability, convenience and speed in obtaining fatigue delamination energy compared with the traditional empirical formula method and numerical simulation method, but this advantage is based on big data, and there will occasionally be phenomena that violate physical common sense in some problems. Nowadays, the data-physics integration method can improve this problem to a certain extent. Therefore, using the data-physics integration method to obtain the fatigue delamination energy of composite materials is a very promising idea, which will make a great contribution to the rapid and accurate analysis of fatigue delamination damage of composite laminates. Summary of the Invention

[0003] The purpose of the present invention is to provide a data-physics integration method for predicting the fatigue delamination energy of composite laminates, which helps to quickly and accurately analyze and predict the fatigue delamination propagation behavior of composite laminates.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] A data-physics integration method for predicting the fatigue delamination energy of composite laminates, characterized by comprising:

[0006] Obtaining the basic data of fatigue delamination damage of composite materials; the basic data of fatigue delamination damage includes fatigue load P, delamination opening displacement δ, crack length a, width b of the composite laminate and thickness h of the composite laminate;

[0007] Based on the modified compliance method in ASTM D5528-07 standard, calculating the compliance method strain energy release rate G according to the basic data of fatigue delamination damage MCC, the compliance method strain energy release rate G MCC Applied to the training stage of the data - physical integration method, its role is to act as a label in the training stage;

[0008] Based on the modified beam theory in ASTM D5528 - 07 standard, calculate the beam theory strain energy release rate G according to the basic data of fatigue delamination damage MBT , the beam theory strain energy release rate G MBT Applied to the training stage of the data - physical integration method, its role is to act as a physical constraint in the training stage;

[0009] Based on the analysis of the fatigue delamination damage process of composite materials, it is found that the prior knowledge that the strain energy release rate G decreases with the increase of the specific crack length a, that is, the first - order derivative of the strain energy release rate G with respect to the crack length a is less than 0;

[0010] Based on the principle of physics - informed neural network, according to the fatigue load P, delamination opening displacement δ, crack length a, width b of composite laminate, thickness h of composite laminate, compliance method strain energy release rate G MCC , beam theory strain energy release rate G MBT And the prior knowledge, construct and optimize a data - physical integration model for predicting the fatigue delamination energy of composite laminates, so as to obtain an optimal data - physical integration model for predicting the fatigue delamination energy of composite laminates;

[0011] Using the optimal data - physical integration model for predicting the fatigue delamination energy of composite laminates can predict the fatigue delamination energy of composite laminates according to any basic data of fatigue delamination damage.

[0012] Furthermore, the optimal data - physical integration method for predicting the fatigue delamination energy of composite laminates specifically includes:

[0013] Optimize the data - physical integration model for predicting the fatigue delamination energy of composite laminates with the goal of minimizing the physics - informed loss function to obtain the optimal data - physical integration model for predicting the fatigue delamination energy of composite laminates; the physics - informed loss function is the sum of the prediction error function, the theoretical model constraint function with weight parameters, and the prior knowledge constraint function with weight parameters; the value of the prediction error function is determined by the compliance method strain energy release rate G MCC And the predicted strain energy release rate G obtained from the data - physical integration model for predicting the fatigue delamination energy of composite laminates pre Determined; the value of the theoretical model constraint function is determined by the beam theory strain energy release rate G MBT And the predicted strain energy release rate G obtained from the data - physical integration model for predicting the fatigue delamination energy of composite laminates preDetermined; the prior knowledge constraint function value is the predicted value G of the strain energy release rate obtained from the data-physics integration model for predicting the fatigue delamination energy of the composite laminate pre Determined by the Max function composed of the first-order derivative of the crack length a and 0.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] 1. The present invention is an integrated method of data and physical knowledge, which not only reduces the dependence of the method itself on the amount of data, but also restricts the prediction results to follow physical laws.

[0016] 2. The data-physical integration method for predicting the fatigue delamination energy of composite laminates proposed by the present invention can realize the prediction of different fatigue delamination energies. When the minimum fatigue load and the minimum delamination opening displacement are provided in the basic data, the minimum strain energy release rate can be predicted; when the maximum fatigue load and the maximum delamination opening displacement are provided in the basic data, the maximum strain energy release rate can be predicted.

[0017] 3. The data-physical integration method for predicting the fatigue delamination energy of composite laminates proposed by the present invention can control the predicted value of the fatigue delamination energy of the composite laminate within the error band of 1 standard deviation, and has high prediction accuracy. Description of the Drawings

[0018] Figure 1 It is the overall framework diagram of the data-physical integration method for predicting the fatigue delamination energy of composite laminates;

[0019] Figure 2 It is the result diagram of predicting the minimum strain energy release rate by the method of the present invention;

[0020] Figure 3 It is the result diagram of predicting the maximum strain energy release rate by the method of the present invention. Detailed Embodiments

[0021] The following further describes the present invention with reference to the drawings:

[0022] As Figure 1 shown, the embodiment of the present invention provides a data-physical integration method for predicting the fatigue delamination energy of composite laminates, including:

[0023] Step 1: Obtain the basic data of composite material fatigue delamination damage. The fatigue delamination damage basic data includes fatigue load P, delamination opening displacement δ, crack length a, composite laminate width b, and composite laminate thickness h.

[0024] Step 2: Based on the modified compliance method in ASTM D5528-07 standard, calculate the compliance method strain energy release rate G according to the basic fatigue delamination damage data MCC , the compliance method strain energy release rate G MCC is applied to the training stage of the data-physics integration method, and its role is to act as a label in the training stage. The expression of the modified compliance method is:

[0025]

[0026] In the formula, G MCC is the compliance method strain energy release rate, P is the fatigue load, C is the compliance, A 1 is the fitted slope constant value, b is the width of the composite laminate, and h is the thickness of the composite laminate.

[0027] Step 3: Based on the modified beam theory in ASTM D5528-07 standard, calculate the beam theory strain energy release rate G according to the basic fatigue delamination damage data MBT , the beam theory strain energy release rate G MBT is applied to the training stage of the data-physics integration method, and its role is to act as a physical constraint in the training stage. The expression of the modified beam theory is:

[0028]

[0029] In the formula, G MBT is the beam theory strain energy release rate, P is the fatigue load, δ is the delamination opening displacement, b is the width of the composite laminate, a is the crack length, and Δ is the fitted intercept constant value.

[0030] Step 4: Based on the analysis of the fatigue delamination damage process of the composite material, it is found that the strain energy release rate G decreases with the increase of the specific crack length a, that is, the first-order derivative of the strain energy release rate G with respect to the crack length a is less than 0. The mathematical expression of the prior knowledge is:

[0031]

[0032] Step 5: Based on the principle of the physics-informed neural network, construct and optimize a data-physics integration model for predicting the fatigue delamination energy of the composite laminate according to the fatigue load P, delamination opening displacement δ, crack length a, width b of the composite laminate, thickness h of the composite laminate, compliance method strain energy release rate G MCC , beam theory strain energy release rate G MBT and prior knowledge, so as to obtain an optimal data-physics integration model for predicting the fatigue delamination energy of the composite laminate.

[0033] Step 6: By using the data - physical integration model for optimally predicting the fatigue delamination energy of composite laminates, the fatigue delamination energy of composite laminates can be predicted based on any fatigue delamination damage basic data.

[0034] In practical applications, the data - physical integration model for optimally predicting the fatigue delamination energy of composite laminates specifically includes:

[0035] The data - physical integration model for predicting the fatigue delamination energy of composite laminates is optimized with the goal of minimizing the physical knowledge loss function to obtain the data - physical integration model for optimally predicting the fatigue delamination energy of composite laminates. The physical knowledge loss function is the sum of a prediction error function, a theoretical model constraint function with weight parameters, and a prior knowledge constraint function with weight parameters. The expression of the physical knowledge loss function is:

[0036] Loss=L data +αL theory +βL priori

[0037] The value of the prediction error function is determined by the strain energy release rate G MCC obtained by the compliance method and the predicted value G pre of the strain energy release rate obtained by the data - physical integration model for predicting the fatigue delamination energy of composite laminates. The expression of the prediction error function is:

[0038]

[0039] The value of the theoretical model constraint function is determined by the strain energy release rate G MBT obtained by the beam theory and the predicted value G pre of the strain energy release rate obtained by the data - physical integration model for predicting the fatigue delamination energy of composite laminates. The expression of the theoretical model constraint function is:

[0040]

[0041] The value of the prior knowledge constraint function is determined by the Max function composed of the first - order derivative of the predicted value G pre of the strain energy release rate obtained by the data - physical integration model for predicting the fatigue delamination energy of composite laminates with respect to the crack length a and 0. The expression of the prior knowledge constraint function is:

[0042]

[0043] More specifically, the data - physics integration method for predicting the fatigue delamination energy of composite laminates uses a neural network model. The neural network includes an input layer, a hidden layer, and an output layer. The input layer is used to input the basic data of fatigue delamination damage of the composite material; the hidden layer is used to calculate the non - linear mapping relationship between the basic data of fatigue delamination damage and the fatigue delamination energy, and then the network parameters are iteratively optimized through a physical knowledge loss function and a backpropagation algorithm; the output layer is used to output the predicted value of the fatigue delamination energy.

[0044] During the training process, calculate the physical knowledge loss function, and determine whether the value of the loss function reaches a preset error threshold or whether the number of iterations reaches a preset maximum number of iterations. If the value of the loss function is lower than the preset error threshold or the number of iterations reaches the preset maximum number of iterations, stop the training; otherwise, continue to optimize the weight parameters and bias parameters of the neural network using the backpropagation algorithm until the requirements are met. The data - physics integration model for predicting the fatigue delamination energy of the composite laminate obtained at this time is the optimal data - physics integration model for predicting the fatigue delamination energy of the composite laminate.

[0045] In this embodiment, the optimal data - physics integration model for predicting the fatigue delamination energy of the composite laminate is used to predict the minimum and maximum strain energy release rates of other composite laminates. The prediction results are as Figure 2 and Figure 3 shown. The predicted values of the fatigue delamination energy of the composite laminate at different crack propagation lengths a - a 0 can be within the error band of 1 standard deviation, verifying the effectiveness and reliability of the data - physics integration method for predicting the fatigue delamination energy of the composite laminate proposed in the present invention.

[0046] This embodiment is only an illustration of the concept and implementation of the present invention, not a limitation thereof. Under the concept of the present invention, technical solutions without substantial transformation are still within the protection scope.

Claims

1. A data-physics integrated method for predicting fatigue delamination energy of composite laminates, characterized in that: include: Obtain basic data on fatigue delamination damage of composite materials; The fatigue delamination damage basic data include fatigue load P, delamination opening displacement δ, crack length a, composite laminate width b and composite laminate thickness h; Based on the modified flexibility method in ASTM D5528-07 standard, the flexibility method strain energy release rate G is calculated according to the fatigue delamination damage basic data. MCC , the compliance method strain energy release rate G MCC Applied to the training phase of the data-physics integration method, its role is to serve as the label of the training phase; Based on the modified beam theory in ASTM D5528-07 standard, the beam theoretical strain energy release rate G is calculated according to the fatigue delamination damage basic data. MBT , the theoretical strain energy release rate of the beam G MBT Applied to the training phase of the data-physics integration method, its role is to act as a physical constraint in the training phase; Based on the analysis of the fatigue delamination damage process of composite materials, it is found that the strain energy release rate G decreases with the increase of the specific crack length a, that is, the first-order derivative of the strain energy release rate G with respect to the crack length a is less than 0; Based on the principle of physical knowledge neural network, according to the fatigue load P, layer opening displacement δ, crack length a, composite laminate width b, composite laminate thickness h, flexibility method strain energy release rate G MCC , beam theoretical strain energy release rate G MBT and prior knowledge to construct and optimize a data-physics integrated model for predicting fatigue delamination energy of composite laminates, thereby obtaining an optimal data-physics integrated model for predicting fatigue delamination energy of composite laminates; The data-physics integrated model for optimally predicting fatigue delamination energy of composite laminates can be used to predict fatigue delamination energy of composite laminates based on any fatigue delamination damage basic data.

2. A data-physics integrated method for predicting fatigue delamination energy of composite laminates according to claim 1, characterized in that: The data-physics integrated model for optimally predicting fatigue delamination energy of composite laminates specifically includes: The data-physics integrated model for predicting fatigue delamination energy of composite laminates is optimized with the goal of minimizing the physical knowledge loss function to obtain the optimal data-physics integrated model for predicting fatigue delamination energy of composite laminates; the physical knowledge loss function is the sum of the prediction error function, the theoretical model constraint function with weight parameters and the prior knowledge constraint function with weight parameters; the prediction error function value is the result of the flexibility method strain energy release rate G MCC and the strain energy release rate prediction value G obtained by the data-physics integrated model for predicting fatigue delamination energy of composite laminates pre Determined; the theoretical model constraint function value is determined by the beam theoretical strain energy release rate G MBT and the strain energy release rate prediction value G obtained by the data-physics integrated model for predicting fatigue delamination energy of composite laminates pre Determined; the prior knowledge constraint function value is the strain energy release rate prediction value G obtained by the data-physics integrated model for predicting fatigue delamination energy of composite laminates pre It is determined by the Max function consisting of the first-order derivative of the crack length a and 0.

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