A multi-segment cohesive zone model considering the effect of resin-rich zone and fiber bridging

Abstract

The application discloses a multi-section cohesive zone model analysis method considering the influence mechanism of a resin-rich zone and fiber bridging of a composite material, and belongs to the technical field of the cohesive zone model analysis method, and comprises the following steps: designing and preparing a multi-directional layer angle DCB sample to carry out a DCB experiment; calculating the I-type interlaminar fracture toughness-crack length data of the DCB sample with different interlaminar layer angles obtained in the experiment in S1, and drawing R curves; establishing a numerical analysis model of the DCB sample; analyzing the parameters of the four CZM units according to the J integral method combined with the data in the experiment to obtain the cohesive force model parameters of each unit; and simulating the delamination damage behavior of the composite laminate by using the multi-section cohesive zone model. The multi-section cohesive zone model analysis method considering the influence mechanism of the resin-rich zone and the fiber bridging of the composite material can obtain more accurate I-type delamination initial strain energy release rate, and can make the performance evaluation of the composite material more accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cohesive zone analysis method, and particularly relates to a multi-section cohesive zone analysis method considering the influence mechanism of a resin-rich zone and fiber bridging of a composite material. BACKGROUND

[0002] Carbon fiber reinforced resin matrix composite material is a kind of composite material with excellent performance, which has high specific strength, high specific modulus, high temperature resistance, corrosion resistance, high design freedom and other advantages, and is widely used in aerospace, automobile industry, shipbuilding and other fields. Since the interlaminar performance of the composite material laminated plate is much lower than its in-plane performance, delamination damage is one of the most common and most dangerous failure modes of the composite material laminated plate structure.

[0003] In the composite material, the main use of fracture energy is to describe and analyze the delamination damage. The interlaminar fracture toughness is an index for measuring the interlaminar fracture resistance of the material, and is a key parameter for evaluating the integrity and durability of the composite material. The double cantilever beam test is a composite material I-type fracture toughness test method specified in the ASTM D5528-13 standard, which embeds a non-adhesive insert (such as a polytetrafluoroethylene film) in the middle of the sample as a pre-delamination. When the polytetrafluoroethylene film is embedded as a pre-delamination, the resin in the pre-delamination area will flow along the smooth surface of the polytetrafluoroethylene film and accumulate in the artificial pre-crack tip to form a resin-rich zone. The existence of the resin-rich zone will have a significant impact on the load-displacement response of the DCB sample, and will cause errors in the calculation of the I-type interlaminar initial fracture toughness.

[0004] In order to avoid the influence of the resin-rich zone, there are two main processing methods: (1) regarding the "steep drop" in the load-displacement curve as experimental error, and directly ignoring its influence; (2) using the pre-cracking sample test suggested in the ASTM D5528-13 standard to reduce the influence of the resin-rich zone, that is, first stretching a crack length of 2-3 mm, and then starting to record data. However, the standard is only for unidirectional composite material laminated plates, and the length of the resin-rich zone corresponding to different layer angles is different. Using this "uniform" pre-opening length method, there is still a large deviation. If the pre-opening length is too short, the influence of the resin-rich zone cannot be completely eliminated; if the opening displacement is too large, the fiber bridging effect occurs between the layers, and the generation of the fiber bridging effect may cause the measured and calculated initial fracture energy to be too high. SUMMARY

[0005] The application aims to provide a multi-section cohesive zone model analysis method considering the influence mechanism of the resin-rich area and fiber bridging of a composite material, solve the problem that the resin-rich area formed by laying a polytetrafluoroethylene film during the preparation of a DCB sample can cause inaccurate calculation of the mode I fracture energy, and cause the evaluation of the integrity and durability of the composite material to be affected to a certain extent.

[0006] To achieve the above-mentioned purpose, the application provides a multi-section cohesive zone model analysis method considering the influence mechanism of the resin-rich area and fiber bridging of a composite material, comprising the following steps:

[0007] S1, designing and preparing a multi-directional layer angle DCB sample, and carrying out a DCB experiment;

[0008] S2, calculating the mode I interlaminar fracture toughness-crack length data of the DCB sample with different interlaminar layer angles obtained in S1, and drawing an R curve;

[0009] S3, establishing a numerical analysis model of the DCB sample, modeling the composite laminate plate by using a solid element, and modeling the interlaminar interface by arranging four cohesive zone model units at the same horizontal position;

[0010] S4, analyzing the parameters of the four CZM units according to the J integral method combined with the data in the experiment to obtain the cohesive zone model parameters of each unit;

[0011] S5, simulating the delamination damage behavior of the composite laminate plate by using the sectional cohesive zone model based on the above-mentioned cohesive zone model parameters.

[0012] Preferably, the DCB sample in S1 is designed as [0 11 / θ / / 0 12 ], wherein θ=0°, 45° and 90°, the symbol / / represents the position of the pre-crack introduced in the preparation, a 13 μm thick and 50 mm long polytetrafluoroethylene film is artificially laid in the middle of the 12th layer and the 13th layer of the sample as a pre-crack, the unidirectional plate is cut into a length of 180 mm, a width of 25 mm, a thickness of 4.8 mm, and a pre-crack length a0=30 mm.

[0013] Preferably, the mode I delamination experiment in S1 is carried out on a universal testing machine by using a double cantilever beam sample, the universal testing machine records the displacement-load data of the quasi-static delamination expansion in real time, and the corresponding crack propagation length is recorded by a digital camera system.

[0014] Preferably, the strain energy release rate in S2 is calculated by the modified beam theory method, and the formula is as follows:

[0015]

[0016] Where P is the load, D is the applied displacement, b is the specimen width, a is the delamination length, and Δ is the crack tip delamination length correction factor. Its characteristic value is obtained by plotting the cube root of compliance C against the delamination length a using the least squares method. Compliance C is the ratio of applied displacement to applied load, D / P.

[0017] Preferably, the interlayer interface in S3 is divided into a resin-rich region and a fiber-bridging extension region based on the damage characteristics of different regions. The cohesive model units in the resin-rich region and the cohesive model units in the fiber-bridging extension region are coupled and superimposed through nodes. The cohesive model unit in the resin-rich region represents matrix fracture, and the cohesive model unit in the fiber-bridging extension region is obtained by coupling three cohesive model units Element E1, Element E2 and Element E3. Element E1 represents matrix fracture of the composite material without fiber bridging, Element E2 represents long fiber fracture damage related to fiber bridging, and Element E3 represents short fiber fracture damage related to fiber bridging.

[0018] Preferably, the parameters of the four cohesive model elements in S4 are strain energy release rates, wherein the cohesive model element in the resin-rich region is the DCB sample with a high initial interlaminar strain energy release rate G due to rapid crack propagation after fracture in the resin-rich region. I-MC .

[0019] Preferably, the cohesive model element within the fiber bridging extension region uses the first interlaminar fracture toughness value during the stable extension and delamination process as the initial interlaminar strain energy release rate G. INI Steady-state interlaminar strain energy release rate G during the delamination process of composite laminates PROP From the initial interlaminar strain energy release rate G INI Steady-state fiber bridging strain energy G with fiber bridging BR The composition is represented by the following equation:

[0020] G PROP =G INI +G BR .

[0021] Preferably, the cohesive model parameters of each group of elements are split according to the separation (δ) of the cohesive elements:

[0022] When the opening displacement δ = δ′ of the cohesive model element in the resin enrichment zone is , it means that the crack has just formed in the resin matrix; when the opening displacement δ = δ0, it means that the matrix is ​​completely cracked, where δ′ is the initial damage displacement of the resin enrichment zone.

[0023] When the opening displacement δ = δ1 of the cohesive model element in the fiber bridging propagation zone, it indicates that a crack has just formed in the fiber bridging propagation zone, where δ1 is the initial damage displacement of the fiber bridging. Based on the damage mechanism, the initial interlaminar strain energy release rate G... INI Expressed as:

[0024] G INI =G I ′ -MC +G I-FD +G I-FB ;

[0025] Where: G INI It mainly consists of three microscopic damage mechanisms, among which G I ′ -MC G represents the strain energy release rate during matrix fracture. I-FD G represents the strain energy release rate of matrix / fiber interface separation. I-FB The strain energy release rate represents the fiber bridging at the crack tip;

[0026] When the cohesive model element in the fiber bridging extension region opens... At that time, the steady-state fiber bridging strain energy of the fiber bridging unit from damage initiation to complete failure is G. BR ;

[0027] Among them G BR The strain energy release rate G during the failure process of long fiber unit Element E2 I-L The strain energy release rate G during the failure process of short fiber element E3 I-S It consists of two parts, and the expression is as follows:

[0028] G BR =G I-L +G I-S ;

[0029] The distribution law of fiber bridging is described using the J-integral method. The expression for the J-integral method is:

[0030]

[0031] Differentiating the above equations yields the expression for fiber bridging stress:

[0032]

[0033] In the formula: δ represents the opening displacement at the initial crack propagation position;

[0034] The strain energy release rate G is described by an exponential function. BR (δ):

[0035]

[0036] The corresponding bridging stress expression is:

[0037]

[0038] where G a , G b , δ a and δ b are different constant coefficients determined by fitting experimental data.

[0039] Preferably, the parameters of the four cohesive zone elements in S4 are determined as follows: the high initial interlaminar strain energy release rate G I-MC , the initial interlaminar strain energy release rate G INI , the steady interlaminar strain energy release rate G PROP , the steady bridging strain energy G PROP = G INI + G BR , and the R curve fitting function. BR

[0040] Preferably, the parameters of the cohesive zone element in the resin-rich zone in S4 are determined as follows:

[0041] the high initial interlaminar strain energy release rate G I-MC is obtained from the DCB experiment, σ0 is obtained from the tensile test of the matrix, and δ0 is then obtained by

[0042] The parameters of the cohesive zone element E1 are determined as follows:

[0043]

[0044] G' Ι-MC = G INI - G I-FB - G I-FD ;

[0045] G I-FD = G INI - G br (δ) - G' Ι-MC ;

[0046]

[0047] The parameters of the cohesive zone elements E2 and E3 are determined as follows:

[0048] The maximum bridging stress of the fiber bridging and the opening displacement at complete failure ​​

[0049] When , get

[0050] σ br = σ br-L + σ br-S ;

[0051]

[0052] Wherein: is the maximum interface strength, δ0 is the matrix fracture failure displacement of the resin-rich region, δ1 is the fiber bridging damage starting displacement, δ2 is the fiber bridging damage failure displacement, G IC is the interlaminar strain energy release rate, K E1 is the stiffness of Element E1 cohesive zone model unit, K E2 is the stiffness of Element E2 cohesive zone model unit, K E3 is the stiffness of Element E3 cohesive zone model unit, G I-L is the strain energy release rate of the long fiber unit Element E2 failure process, G I-S is the strain energy release rate of the short fiber unit Element E3 failure process, σ br-L is the maximum adhesion stress of the long fiber region CZM unit, σ br-S is the maximum adhesion stress of the short fiber region CZM unit.

[0053] Therefore, the application adopts the above-mentioned multi-section cohesive element analysis method considering the influence mechanism of the resin-rich region and the fiber bridging of the composite material, and has the following beneficial effects:

[0054] (1) The corresponding constitutive relation is used to simulate the crack propagation delamination behavior in different damage mechanism regions, the corresponding damage mechanism of different regions is intuitively represented, and good description of the contribution of the three mechanisms is realized.

[0055] (2) The influence of the resin-rich region on the I-type delamination of the composite laminated plate is analyzed, the influence of the resin-rich region on the I-type delamination propagation behavior under static load can be predicted, a more accurate initial strain energy release rate of the I-type delamination is further obtained, and the performance evaluation of the composite material is more accurate.

[0056] The technical solutions of the application will be further described in detail below with the help of the drawings and examples. DETAILED DESCRIPTION

[0057] Figure 1 is the DCB sample and DCB experiment schematic diagram of the application;

[0058] Figure 2 is a schematic diagram of a DCB specimen partition of the present application;

[0059] Figure 3 is a schematic diagram of a partitioned CZM model of the present application;

[0060] Figure 4 is a schematic diagram of a partitioned CZM constitutive model of the present application;

[0061] Figure 5 is a macroscopic fracture diagram of a DCB specimen with different interlaminar ply angles of the present application;

[0062] Figure 6 is a load-displacement curve of a DCB specimen with different interlaminar ply angles of the present application;

[0063] Figure 7 is an R curve of a DCB specimen with different interlaminar ply angles of the present application;

[0064] Figure 8 is a simulation result of a DCB specimen with different interlaminar ply angles of the present application;

[0065] Figure 9 is a direct neglect method comparative analysis of a 0 / / 45 specimen of the present application;

[0066] Figure 10 is a pre-pull-apart method comparative analysis of a 0 / / 90 specimen of the present application;

[0067] Figure 11 is a micro-morphology diagram of a DCB specimen with different interlaminar ply angles of the present application. DETAILED DESCRIPTION

[0068] The technical solutions of the present application are further described below through the drawings and examples.

[0069] Unless otherwise defined, the technical terms or scientific terms used in the present application shall have the usual meanings understood by those with ordinary skills in the art to which the present application belongs.

[0070] Example One

[0071] The present application provides a multi-segment cohesive element analysis method considering the influence mechanism of composite material resin-rich zone and fiber bridging, comprising the following steps:

[0072] S1, a multi-directional ply angle DCB specimen is designed and prepared, and a DCB experiment is carried out, the DCB specimen is designed as [0 11 / θ / / 0 12where θ = 0°, 45° and 90°, the symbol / / indicates the position where a pre-crack is introduced in the preparation, a 13 μm thick polytetrafluoroethylene film is manually laid in the middle of the 12th layer / / 13th layer of the sample as a pre-crack, the unidirectional plate is cut into: 180 mm long, 25 mm wide, 4.8 mm thick, the pre-crack effective crack length a0= 30 mm, as shown in Figure 1 、 Figure 2 wherein Figure 1 (a) in the figure is a DCB experimental equipment device, Figure 1 (b) in the figure is a DCB sample size schematic diagram, Figure 1 (c) in the figure is a side view of the DCB sample after processing.

[0073] The I-type delamination experiment is carried out on a universal testing machine using a double cantilever beam sample, the universal testing machine records the displacement-load data of the quasi-static delamination expansion in real time and records the corresponding crack propagation length through a digital camera system.

[0074] S2, the strain energy release rate is calculated by the modified beam theory method, the formula is as follows:

[0075]

[0076] Where P is the load, D is the applied displacement, b is the width of the sample, a is the delamination length, and Δ is the crack tip delamination length correction coefficient, the characteristic value is obtained by least square method graph of the cube root of the compliance C to the delamination length a, and the compliance C is the ratio of the applied displacement and the applied load D / P. The data obtained by experiment is applied to the above formula, and the calculated data is plotted into the I-type interlaminar fracture toughness-crack length curve of the DCB sample with different interlaminar ply angles, that is, the R curve.

[0077] S3, a numerical analysis model of the DCB sample is established, the composite laminated plate is modeled by using solid elements, and the mechanical property parameters of the composite laminated plate material are shown in Table 1. The interlaminar interface is modeled by arranging four cohesive force model units at the same horizontal position, the interlaminar interface is divided into resin enrichment area and fiber bridging expansion area based on the damage characteristics of different areas, the cohesive force model units in the resin enrichment area and the cohesive force model units in the fiber bridging expansion area are coupled and superposed through nodes, the cohesive force model units in the resin enrichment area represent matrix fracture, and the cohesive force model units in the fiber bridging expansion area are coupled by three cohesive force model units Element E1, Element E2 and Element E3, wherein Element E1 represents matrix fracture of the composite material without fiber bridging, Element E2 represents long fiber fracture damage related to fiber bridging, and Element E3 represents short fiber fracture damage related to fiber bridging.

[0078] Table 1 Mechanical properties of composite laminates

[0079] Module Value E 11 / GPa 117 E 22 / GPa 7.47 E 33 / GPa 7.47 G 12 / GPa 4.07 G 13 / GPa 4.07 G 23 / GPa 2.31 12 ]]> ​ 0.33 13 ]]> ​ 0.33 23 ]]> ​ 0.3

[0080] Notes: E - Elastic modulus; G - Shear modulus; v - Poisson ratio; 1 - Direction of fiber; 2 - Direction of matrix; 3 - Thickness direction of layer.

[0081] S4, The parameters of the four CZM units are analyzed according to the J-integral method combined with the data in the experiment to obtain the cohesive model parameters of each unit, and the parameters of the four cohesive model units are strain energy release rates, wherein the cohesive model unit in the resin-rich zone is the DCB sample due to the fracture of the resin-rich zone, and the high initial interlaminar strain energy release rate G I-MC .

[0082] The cohesive model unit in the fiber bridging expansion zone is the first interlaminar fracture toughness value in the stable expansion delamination process as the initial interlaminar strain energy release rate G INI , and the steady-state interlaminar strain energy release rate G PROP of the delamination process of the composite laminates is composed of the initial interlaminar strain energy release rate G INI and the steady-state fiber bridging strain energy G BR of the fiber bridging, and is represented by the following equation:

[0083] G PROP = G INI + G BR .

[0084] The cohesive model parameters of each group of units are split according to the separation (δ) of the cohesive element:

[0085] When the opening displacement δ of the cohesive model unit in the resin-rich zone is δ', it represents that the crack is just formed in the resin matrix; when the opening displacement δ is δ0, it represents that the matrix is completely cracked, wherein δ' is the initial damage displacement of the resin-rich zone;

[0086] When the opening displacement δ of the cohesive model unit in the fiber bridging expansion zone is δ1, it represents that the crack is just formed in the fiber bridging expansion zone, wherein δ1 is the initial damage displacement of the fiber bridging, and the initial interlaminar strain energy release rate G INI is expressed as:

[0087] G INI = G I ' -MC + G I-FD+G I-FB ;

[0088] where G INI is the strain energy release rate of matrix cracking, G I is the strain energy release rate of fiber / matrix interfacial debonding, and G -MC is the strain energy release rate of fiber bridging at the crack tip. I-FD ; I-FB

[0089] When the opening displacement of the fiber bridging extended cohesive zone , the steady-state fiber bridging strain energy of the fiber bridging element from damage initiation to complete failure is G BR .

[0090] where G BR is composed of two parts, the strain energy release rate G I-L of the long fiber element Element E2 failure process and the strain energy release rate G I-S of the short fiber element Element E3 failure process, and the expressions are as follows:

[0091] G BR = G I-L + G I-S .

[0092] The distribution of fiber bridging is described by the J-integral method, and the expression of the J-integral method is as follows:

[0093]

[0094] The fiber bridging stress expression is obtained by differentiating the above equation:

[0095]

[0096] where δ represents the opening displacement at the position of initial crack propagation.

[0097] The strain energy release rate G BR (δ) is described by an exponential function:

[0098]

[0099] The corresponding fiber bridging stress expression is:

[0100]

[0101] where G a , G b , δ a , and δ b ​are different constants determined by fitting the experimental data.

[0102] The parameters of the four cohesive zone elements are determined as follows: the high initial interlaminar strain energy release rate G I-MC , the initial interlaminar strain energy release rate G INI , the steady interlaminar strain energy release rate G PROP , the steady fiber bridging strain energy G PROP = G INI + G BR , and the R curve fitting function are obtained from the calculated R curve and G BR .

[0103] The parameters of the cohesive zone element in the resin rich zone are determined as follows:

[0104] The high initial interlaminar strain energy release rate G I-MC is obtained from the DCB experiment, σ0 is obtained from the tensile test of the matrix, and then δ0 is obtained by .

[0105] The parameters of the cohesive zone element E1 are determined as follows:

[0106]

[0107] G' Ι-MC = G INI -G I-FB -G I-FD .

[0108] G I-FD = G INI -G br (δ)-G' Ι-MC .

[0109]

[0110] The parameters of the cohesive zone elements E2 and E3 are determined as follows:

[0111] The maximum bridging stress of the fiber bridging and the opening displacement at complete failure are obtained by the J-integral method.

[0112] When , we get

[0113] σ br = σ br-L + σ br-S .

[0114]

[0115]

[0116] wherein: is the maximum interfacial strength, δ0 is the matrix failure displacement of the resin rich zone, δ1 is the onset of fiber bridging damage displacement, δ2 is the fiber bridging damage failure displacement, G IC is the interlaminar strain energy release rate, K E1 is the stiffness of Element E1 cohesive model element, K E2 is the stiffness of Element E2 cohesive model element, K E3 is the stiffness of Element E3 cohesive model element, G I-L is the strain energy release rate of the long fiber element Element E2 failure process, G I-S is the strain energy release rate of the short fiber element Element E3 failure process, σ br-L is the maximum cohesive stress of the long fiber zone CZM element, σ br-S is the maximum cohesive stress of the short fiber zone CZM element.

[0117] S5, using the segmented cohesive model based on the above-mentioned cohesive model parameters to simulate the delamination damage behavior of the composite laminated plate, and using the finite element software ABAQUS to simulate the I-type delamination propagation process of the composite laminated plate.

[0118] Example Two

[0119] The application provides a multi-segmented cohesive element analysis method considering the resin-rich zone and fiber bridging influence mechanism of a composite material, comprising the following steps:

[0120] Step one, preparing a composite double cantilever beam specimen with different interlaminar layups, and carrying out DCB test; the DCB specimen uses T700 grade unidirectional carbon fiber / epoxy resin prepreg, is prepared by manual laying, and is prepared by a hot press molding process, as shown in Figure 1 .

[0121] A 20mm hinge is bonded at the front end of the DCB specimen, both sides are sprayed with thin white paint to improve the visibility of the delamination surface, and a scale paper tape is pasted to help monitor the crack propagation length.

[0122] The DCB specimen is designed as: [0 11 / θ / / 0 12 / / , where 0 = 0°, 45° and 90°, and the symbol / / indicates the location where a pre-existing crack was introduced during fabrication. In the 12th layer / / 13th layer of sample, a 13 pm thick polytetrafluoroethylene film with a length of 50 mm was manually laid as a pre-existing crack between the 12th layer and the 13th layer. The unidirectional plate was cut into a length of 180 mm, a width of 25 mm, and a thickness of 4.8 mm. The pre-existing crack length was 50 mm.

[0123] a0= 30 mm.

[0124] The I-type delamination test was performed on a WANCE TSE254C universal testing machine using a double cantilever beam sample based on the ASTM D5528-13 standard. During the test, the quasi-static delamination propagation was recorded by the displacement-load data in real time by the testing machine and the corresponding crack propagation length was recorded by a digital camera system (Charge Coupled Device camera, CCD camera), and the crack propagation length recording accuracy was 0.05 mm. The loading mode was displacement control, and the quasi-static loading rate was set to 0.5 mm / min.

[0125] Step two, calculate the I-type interlaminar fracture energy curve of different interlaminar layer samples with delamination length, use the modified beam theory (MBT) provided by the DCB test standard ASTM D5528-13 to calculate the strain energy release rate (SERR), the formula is as follows:

[0126]

[0127] Where P is the load, D is the applied displacement, b is the width of the sample, a is the delamination length, and △ is the crack tip delamination length correction factor, and the characteristic value is obtained by the least square method graph of the cube root of the compliance C to the delamination length a, and the compliance C is the ratio of the applied displacement and the applied load D / P.

[0128] Step three, numerical analysis model of DCB sample is established, and the composite laminated plate is modeled by using solid element; the interlaminar interface is modeled by arranging four cohesive force model units at the same horizontal position, wherein based on the damage characteristics of different regions, it is divided into resin enrichment area and fiber bridging expansion area, the resin enrichment area cohesive force unit and the fiber bridging expansion area cohesive force unit are coupled and superposed through nodes, the resin enrichment area cohesive force unit represents matrix cracking, the fiber bridging expansion area cohesive force model unit is obtained by coupling three cohesive force units (Element E1, Element E2, Element E3), Element E1 represents matrix cracking and matrix / fiber separation related to fiber bridging in the case of no fiber bridging of the composite material, Element E2 represents long fiber fracture damage related to fiber bridging, and Element E3 represents short fiber fracture damage related to fiber bridging, the arrangement position and connection mode of each cohesive force unit model are as shown in Figure 3 .

[0129] Step four, the parameters of the four CZM units are analyzed according to the J integral method combined with test data, and the CZM parameters of each unit are obtained;

[0130] Step five, the delamination damage behavior of the composite material is simulated by using the sectional CZM model, the I-type delamination expansion process of the composite laminated plate is simulated by using the finite element software ABAQUS, and the three-dimensional finite element model is as shown in Figure 3 . The implicit calculation method is adopted, 8-node 3D solid elements (C3D8R) are used for the upper and lower plates, C0H3D8 elements are used for the CZM layer in the middle of the plate, the cohesive force units are coupled and superposed through nodes by the resin enrichment area cohesive force unit and the fiber bridging expansion area cohesive force unit, and each layer is set as one unit in the thickness direction. In order to better simulate the stress and strain field when the crack tip expands, the grid size of the crack tip expansion area is 0.2mm, and the grid size of the remaining area is 0.5mm. The displacement loading in the y direction is applied on the loading end of the model, and the constraint in the z direction is applied on the free end, so that the constraint conditions of the model are consistent with the experimental conditions.

[0131] The initial interface stiffness K1 of the CZM unit representing matrix cracking is usually set to 10 12 to 10 15 N / m 3 , and in the present application, 1x10 15 N / m 3 is adopted. In order to avoid the convergence problem caused by stiffness degradation in the calculation process, a viscous coefficient is introduced, and the viscous coefficient is 1x10 6 .

[0132] Figure 6The load-displacement curves of DCB specimens with different interlaminar ply angles are given, and it can be found that the experimental results show that the load-displacement curves of the specimens with the same interlaminar ply angle all show similar change trends. Figure 6 The (a) in FIG. 4 is a load-displacement curve diagram of the 0 / / 0 specimen, and the load-displacement curve of the 0 / / 0 specimen presents a linear relationship in the initial stage until the crack expands, the load sharply drops, and after the end of the load sharp drop, the load slowly and smoothly decreases. Figure 6 The (b) in FIG. 4 is a load-displacement curve diagram of the 0 / / 45 specimen, and the load-displacement curve of the 0 / / 45 specimen presents a linear relationship in the initial stage until the crack expands, the load sharply drops, and after the end of the load sharp drop, the load rises to a certain level again and presents a nonlinear characteristic, and then gradually decreases in an obvious fluctuation manner. Figure 6 The (c) in FIG. 4 is a load-displacement curve diagram of the 0 / / 90 specimen, and the load-displacement curve of the 0 / / 90 specimen is consistent with the 0 / / 0 specimen and the 0 / / 45 specimen in the linear stage, when the crack expands, the load sharply drops, and the load sharp drop is very small, after the end of the load sharp drop, the nonlinear rises to a certain level and then gradually decreases in an obvious fluctuation manner.

[0133] Figure 7 The R curves of DCB specimens with different interlaminar ply angles are given, Figure 7 The (a) in FIG. 5 is an R curve of the 0 / / 0 specimen, Figure 7 The (b) in FIG. 5 is an R curve of the 0 / / 45 specimen, Figure 7 The (c) in FIG. 5 is an R curve of the 0 / / 90 specimen. The experimental results show that the specimens with different interlaminar ply angles have a high initial interlaminar strain energy release rate G I-MC due to the rapid crack propagation after the fracture of the resin-rich zone, which is called a high initial fracture toughness value, and the high initial interlaminar strain energy release rate G I-MC The first interlaminar fracture toughness value in the stable delamination process is calculated by formula (1), and taken as the initial interlaminar strain energy release rate G INI . In the process of rapid crack propagation, the interlaminar fracture toughness decreases from the high initial fracture toughness G I-MC to the initial interlaminar strain energy release rate G INI , and then the interlaminar fracture toughness increases with the crack propagation, forming a typical R curve. The high initial interlaminar strain energy release rate G I-MC of the DCB specimens with different interlaminar plies INI As shown in Table 2, it can be observed that the interlaminar fracture toughness decrease amplitude is related to the interlaminar ply angle, wherein the interlaminar fracture toughness decrease amplitude of the 0 / / 0 specimen is the largest, the 0 / / 45 specimen is the second, and the 0 / / 90 specimen is the smallest, and the decrease amplitude decreases with the increase of the interlaminar ply angle.

[0134] Table 2 Interlaminar fracture toughness values of DCB specimens

[0135]

[0136] The test results of the DCB specimens with different ply angles obtained by the analysis method are compared with the simulation results as shown in FIG. 6. Figure 8 Figure 8 (a) of FIG. 6 is a comparison diagram of the 0 / / 0 specimen and the numerical simulation load-displacement curve, Figure 8 (b) of FIG. 6 is a comparison diagram of the 0 / / 40 specimen and the numerical simulation load-displacement curve, Figure 8 (c) of FIG. 6 is a comparison diagram of the 0 / / 90 specimen and the numerical simulation load-displacement curve. The comparison results show that the load-displacement curve predicted by the cohesive zone model with the resin-rich zone is in good agreement with the load-displacement curve measured by the test. As can be seen from the figure, the load-displacement curve is divided into three stages: linear stage, nonlinear characteristic stage and load steep drop stage. In the linear stage, the load increases linearly with the increase of the applied displacement. It can be found that the greater the length of the resin-rich zone, the more energy accumulates in the resin-rich zone, and the greater the maximum linear growth of the load, resulting in different maximum loads of the specimen model with different interlaminar ply angles. In the load stage, with the further increase of the applied displacement, the resin-rich zone is broken and the load is steeply dropped. In the nonlinear characteristic stage of the load-displacement curve, the 0 / / 45 and 0 / / 90 specimens produce fiber bridging in the process of internal delamination propagation. The toughening mechanism related to fiber bridging causes the load to increase nonlinearly with the increase of the applied displacement to the ultimate load. After the ultimate load, with the increase of the applied displacement, the load gradually decreases. The 0 / / 0 specimen has almost no fiber bridging, and the load decreases slowly and smoothly with the increase of the applied displacement in the nonlinear characteristic stage of the load-displacement curve. The numerical simulation results show that adjusting the length of the resin-rich zone to be consistent with the actual length of the resin-rich zone of the corresponding interlaminar ply angle specimen can effectively simulate the influence of the resin-rich zone on the load-displacement curve, and further verify the influence of the resin-rich zone on the delamination damage behavior.

[0137] Figure 9 (a) of FIG. 8 is a comparison diagram of the 0 / / 45 specimen directly ignored and the experimental results load-displacement, and from Figure 9 (a) of FIG. 8, it can be observed that in the direct ignoring method, the resin fracture region of the load-displacement curve is corrected by adding the tangent method, and due to the difficulty in confirming the initial delamination damage position, the initial strain energy release rate of the I-type delamination is underestimated, which will have a certain influence on the selection and determination of the starting point. In the 0 / / 45 specimen, the load steep drop phenomenon is most intuitive. Therefore, the load-displacement curve of the 0 / / 45 specimen is selected to illustrate the influence brought by the direct ignoring method. Figure 9 ​(b) is the modified 0 / / 45 specimen direct neglecting method and the experimental results load-displacement comparison chart, from Figure 9 (b) in FIG. 6 can be seen that in the direct neglecting method, the resin fracture region in the load-displacement curve is corrected by introducing the tangent correction. However, due to the difficulty in determining the initial delamination damage position, this method may lead to underestimation of the initial strain energy release rate of I-type delamination.

[0138] Another method is pre-opening, and since the length of the resin-rich region of the 0 / / 90 specimen is extremely small, the impact is most intuitive, so we choose the 0 / / 90 specimen to illustrate. Figure 10 (a) in FIG. 7 is the pre-opening result of the 0 / / 90 specimen and the experimental results load-displacement comparison chart, Figure 10 (b) in FIG. 7 is the modified 0 / / 90 specimen pre-opening result and the experimental results load-displacement comparison chart, from Figure 10 It can be observed that when using the pre-opening processing method for testing, the initial strain energy of the specimen is higher than the actual value, which will produce a certain deviation to the results. Combined with the characteristics of fiber bridging crack propagation region delamination, it can be concluded that in the 0 / / 90 specimen, when the pre-opening distance is too large, the calculated value of the initial interlaminar fracture energy is high due to the fiber bridging effect.

[0139] Figure 11 The macroscopic and microscopic morphology of the cross section of the DCB specimen with different interlaminar ply angles is given, Figure 11 (a) in FIG. 8 is the microscopic morphology of the cross section of the 0 / / 0 specimen, Figure 11 (b) in FIG. 8 is the microscopic morphology of the cross section of the 0 / / 45 specimen, Figure 11(c) is the micro-morphology of 0 / / 90 specimen section, from the macro-morphology of specimen section, it is found that the resin-rich area of 0 / / 0 specimen is the largest, and there is about 5.4 mm resin-rich along the length direction; the resin-rich area of 0 / / 45 specimen is the second, and there is about 2.4 mm resin-rich along the length direction; the resin-rich area of 0 / / 90 specimen is the smallest, and there is only 50 μm resin-rich along the length direction. The resin-rich area shows a decrease with the increase of interlaminar ply angle. In the micro-morphology of section, it is observed that the section of 0 / / 0 specimen and 0 / / 45 specimen is covered by resin in the resin-rich area, and there is a large area of resin fracture; the section of 0 / / 90 specimen is covered by resin in the resin-rich area, and there is a small area of resin fracture. Therefore, the damage mode in the resin-rich area is matrix cracking. For 0 / / 0 specimen, there are a large number of resin matrix sections, a large number of "fiber grooves" along 0° direction formed by carbon fiber pull-out and a small number of broken fibers in the fiber bridging propagation area; for 0 / / 45 specimen, there are a large number of resin matrix sections, "fiber grooves" along 45° direction and broken fibers in the fiber bridging propagation area; for 0 / / 90 specimen, there are a large number of exposed fibers, "fiber grooves" along 90° direction and a large number of resin matrix sections in the fiber bridging propagation area. Therefore, the damage modes in the fiber bridging propagation area are mainly three, i.e. matrix cracking, matrix / fiber separation and fiber fracture.

[0140] In summary, the resin-rich area is formed at the end of pre-crack of DCB specimen due to resin-rich, and the resin-rich area shows a decrease with the increase of interlaminar ply angle. In the test process, with the increase of applied displacement, the energy is accumulated in the resin-rich area, when it reaches the critical value, the resin-rich area is fractured, and due to its strength being higher than the interlaminar strength of composite material, the crack is rapidly expanded in the interlaminar interface area, resulting in Figure 4 the load drop phenomenon of load-displacement curve in the transition zone of linear stage and nonlinear characteristic stage, and the decrease of interlaminar fracture toughness in the initial stage of R curve, Figure 5 (a) is the macro-morphology of 0 / / 0 specimen, Figure 5 (b) is the macro-morphology of 0 / / 45 specimen, Figure 5 (c) is the macro-morphology of 0 / / 90 specimen. It is further observed that the load drop of load-displacement curve and the decrease of interlaminar fracture toughness in the initial stage of G ΙC curve all show an increase with the increase of resin-rich area.

[0141] Aiming at the problem of the resin-rich area generated by laying polytetrafluoroethylene film as a prefabricated delamination during the preparation of the DCB sample affecting the delamination fracture behavior, the DCB test of multi-directional layup angle is designed, the "steep drop phenomenon" of the load-displacement curve is researched, the scanning electron microscope is used to characterize the micro-morphology of the DCB crack section, and the influence area of the resin-rich area is quantified. The DCB numerical model containing the resin-rich area and the fiber bridging expansion area is established, the influence law of the resin-rich area on the initial fracture toughness of the I-type delamination is explained and revealed through quantitative analysis, and the following conclusions are obtained:

[0142] The micro-morphology of the sample section is observed by the scanning electron microscope, and it is found that there is a significant resin-rich phenomenon at the prefabricated crack tip. The area of the resin-rich area is related to the interlaminar layup angle of the sample, the area of the resin-rich area of the 0 / / 0 sample is the largest, the area of the resin-rich area of the 0 / / 45 sample is the second, and the area of the resin-rich area of the 0 / / 90 sample is the smallest, and the area of the resin-rich area decreases with the increase of the interlaminar layup angle.

[0143] The load-displacement curve is observed, the load-displacement curve of the 0 / / 0 sample has the most significant load steep drop, but the load-displacement curve in the expansion stage presents the characteristics of smooth and smooth decline, because the resin-rich area is relatively long, and the fiber bridging effect of the 0 / / 0 sample is weak; the load-displacement curve of the 0 / / 45 sample also presents a significant steep drop phenomenon, but the load-displacement curve in the expansion stage is not smooth, the main reason is that the resin-rich area is relatively short, and the fiber bridging effect is more obvious than that of the 0 / / 0 sample, and the two are not perfect transition; the fiber bridging effect of the 0 / / 90 sample is the most obvious, but the length of the resin-rich area is the shortest, so the load-displacement curve presents a slight decrease and then a significant increase.

[0144] The DCB model established by the fiber bridging expansion area and the resin-rich area can not only predict the change law of the load-displacement curve of different layup angles, but also the predicted load and displacement values are basically consistent, which verifies the influence law of the resin-rich area on the initial fracture toughness of the I-type delamination.

[0145] Therefore, the multi-section cohesive element analysis method considering the resin-rich area and the fiber bridging influence mechanism of the composite material is adopted, the corresponding constitutive relation of different damage mechanisms is used to simulate the crack expansion delamination behavior in different damage mechanism areas, the damage mechanism of different areas is directly expressed, the contribution of the three mechanisms is well described, the influence law of the resin-rich area on the initial fracture toughness of the I-type delamination is analyzed, the influence of the resin-rich area on the I-type delamination expansion behavior under static load is simulated, and the evaluation of the integrity and durability of the composite material is more accurate.

[0146] It should be pointed out finally that the above examples are only used to illustrate the technical solutions of the present application but not to limit it, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can still be modified or replaced equivalently, and these modifications or equivalent replacements should not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment regions and fiber bridging in composite materials, characterized by: Includes the following steps: S1. Design and prepare multi-directional layup angle DCB specimens and conduct DCB experiments; S2. Calculate the interlaminar fracture toughness-crack length data of DCB specimens with different interlaminar layup angles using the experimental data obtained in S1, and plot the data as an R curve. S3. Establish a numerical analysis model for the DCB specimen. The composite laminate is modeled using solid elements, and the interlayer interface is modeled using four cohesive model elements arranged at the same horizontal position. The interlayer interface is divided into a resin-rich region and a fiber-bridging extension region based on the damage characteristics of different regions. The cohesive model units in the resin-rich region and the cohesive model units in the fiber-bridging extension region are coupled and superimposed through nodes. The cohesive model unit in the resin-rich region represents matrix fracture, and the cohesive model unit in the fiber-bridging extension region is obtained by coupling three cohesive model units Element E1, Element E2 and Element E3. Element E1 represents matrix fracture of the composite material without fiber bridging, Element E2 represents long fiber fracture damage related to fiber bridging, and Element E3 represents short fiber fracture damage related to fiber bridging. S4. Based on the J-integral method and the experimental data, the parameters of the four CZM elements are analyzed to obtain the cohesive force model parameters of each element. S5. The delamination damage behavior of composite laminates is simulated using a segmented cohesive model obtained based on the above cohesive model parameters.

2. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 1, characterized in that: The DCB sample layup design in S1 is [0 11 / θ / / 0 12 ], where θ = 0°, 45° and 90°, and the symbol / / indicates the location of the pre-crack introduced during preparation. A 13μm thick and 50mm long polytetrafluoroethylene film is artificially laid between the 12th and 13th layers of the sample as a pre-crack. The one-way plate is cut into the following dimensions: 180mm long, 25mm wide and 4.8mm thick. The effective pre-crack length a0 = 30mm.

3. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 2, characterized in that: In S1, a double cantilever beam specimen is used to conduct a type I delamination test on a universal testing machine. The universal testing machine records the displacement-load data of quasi-static delamination propagation in real time and records the corresponding crack propagation length through a digital camera system.

4. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 3, characterized in that: In S2, the strain energy release rate is calculated using the modified beam theory method, as shown in the following formula: Where P is the load, D is the applied displacement, b is the specimen width, a is the delamination length, and Δ is the crack tip delamination length correction factor. Its characteristic value is obtained by plotting the cube root of compliance C against the delamination length a using the least squares method. Compliance C is the ratio of applied displacement to applied load, D / P.

5. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 1, characterized in that: The parameters of the four cohesive model elements in S4 are strain energy release rates. Among them, the cohesive model element in the resin-rich region is the DCB sample with a high initial interlaminar strain energy release rate G due to the rapid crack propagation after fracture in the resin-rich region. I-MC .

6. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 5, characterized in that: The cohesive model element in the fiber-bridged extension region uses the first interlaminar fracture toughness value during the stable extension and delamination process as the initial interlaminar strain energy release rate G. INI Steady-state interlaminar strain energy release rate G during the delamination process of composite laminates PROP From the initial interlaminar strain energy release rate G INI Steady-state fiber bridging strain energy G with fiber bridging BR The composition is represented by the following equation: G PROP =G INI +G BR 。 7. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 6, characterized in that: The cohesive model parameters of each group of elements are separated based on the separation (δ) of the cohesive elements: When the opening displacement δ = δ′ of the cohesive model element in the resin enrichment zone is , it means that the crack has just formed in the resin matrix; when the opening displacement δ = δ0, it means that the matrix is ​​completely cracked, where δ′ is the initial damage displacement of the resin enrichment zone. When the opening displacement δ = δ1 of the cohesive model element in the fiber bridging propagation zone, it indicates that a crack has just formed in the fiber bridging propagation zone, where δ1 is the initial damage displacement of the fiber bridging. Based on the damage mechanism, the initial interlaminar strain energy release rate G... INI Expressed as: G INI =G′ I-MC +G I-FD +G I-FB ; Where: G INI It mainly consists of three microscopic damage mechanisms, among which G′ I-MC G represents the strain energy release rate during matrix fracture. I-FD G represents the strain energy release rate of matrix / fiber interface separation. I-FB The strain energy release rate represents the fiber bridging at the crack tip; When the cohesive model element in the fiber bridging extension region opens... At that time, the steady-state fiber bridging strain energy of the fiber bridging unit from damage initiation to complete failure is G. BR ; Among them G BR The strain energy release rate G during the failure process of long fiber unit Element E2 I-L The strain energy release rate G during the failure process of short fiber element E3 I-S It consists of two parts, and the expression is as follows: G BR =G I-L +G I-S ; The distribution law of fiber bridging is described using the J-integral method. The expression for the J-integral method is: Differentiating the above equations yields the expression for fiber bridging stress: In the formula: δ represents the opening displacement at the initial crack propagation position; The strain energy release rate G is described by an exponential function. BR (δ): The corresponding expression for fiber bridging stress is: In the formula G a G b δ a and δ b These are different constant coefficients, which are determined by fitting experimental data.

8. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 7, characterized in that: The parameters of the four cohesive model elements in S4 are determined as follows: the high initial interlaminar strain energy release rate G measured by DCB experiments. I-MC Initial interlaminar strain energy release rate G INI Steady-state interlayer strain energy release rate G PROP The calculated R curve and G PROP =G INI +G BR The steady-state fiber bridging strain energy G is obtained. BR And the R-curve fitting function.

9. The multi-segment cohesive element analysis method considering the influence mechanism of resin enrichment region and fiber bridging in composite materials according to claim 8, characterized in that: The parameters of the cohesive model element in the resin-rich region of S4 are determined as follows: High initial interlaminar strain energy release rate G I-MC The results were obtained from DCB experiments, and σ0 was obtained from matrix tensile testing, followed by... We obtain δ0; The parameters of the Element E1 cohesive model element are determined as follows: G' Ι-MC =G INI -G I-FB -G I-FD ; G I-FD =G INI -G br (d)-G' Ι-MC ; The parameters of the cohesive model elements Element E2 and Element E3 are determined as follows: The maximum bridging stress of the fiber bridging was obtained using the J-integral method. and opening displacement at complete failure when At that time, s br =s br-L +s br-S ; in: δ0 represents the maximum interfacial strength, δ1 represents the matrix fracture failure displacement in the resin-rich region, δ2 represents the fiber bridging damage initiation displacement, and G represents the fiber bridging damage failure displacement. IC K represents the interlaminar strain energy release rate. E1 K represents the stiffness of the cohesive model element of Element E1. E2 K represents the stiffness of the cohesive model element of Element E2. E3 G represents the stiffness of the Element E3 cohesive model element. I-L G represents the strain energy release rate during the failure process of the long fiber element E2. I-S σ represents the strain energy release rate during the failure process of the short fiber element ElementE3. br-L The maximum adhesion stress of the CZM unit in the long fiber region is σ. br-S This represents the maximum adhesion stress of the CZM unit in the short fiber region.

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