Multi-section cohesion unit analysis method considering composite material resin enrichment area and fiber bridging influence mechanism

Abstract

The invention discloses a multi-section cohesion unit analysis method considering a composite material resin enrichment area and a fiber bridging influence mechanism, and belongs to the technical field of cohesion unit analysis methods.The multi-section cohesion unit analysis method comprises the steps that a multi-direction laying layer angle DCB sample is designed and prepared, and a DCB experiment is carried out; s2, calculating data obtained in the experiment in S1 to obtain I-type interlayer fracture toughness-crack length data of the DCB samples with different interlayer laying angles, and drawing an R curve; establishing a numerical analysis model of the DCB sample; analyzing the parameters of the four CZM units according to a J integral method in combination with data in an experiment to obtain cohesion model parameters of each unit; and a sectional cohesion model is adopted to simulate the layering damage behavior of the composite material laminated plate. By adopting the multi-section cohesion unit analysis method considering the resin enrichment area and the fiber bridging influence mechanism of the composite material, a more accurate I-type layering initial strain energy release rate can be obtained, and the performance evaluation of the composite material can be more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of cohesion unit analysis methods, and in particular to a multi-segment cohesion unit analysis method that takes into account the influence mechanism of composite material resin-enriched areas and fiber bridging. Background Art

[0002] Carbon fiber reinforced resin matrix composite material is a composite material with excellent performance, high specific strength, high specific modulus, high temperature resistance, corrosion resistance, high degree of design freedom, etc. It is widely used in aerospace, automotive industry, shipbuilding and other fields. Since the interlaminar performance of composite laminates is much lower than its in-plane performance, delamination damage is one of the most common and dangerous failure modes of composite laminate structures.

[0003] In composite materials, fracture energy is mainly used to describe and analyze the delamination damage. Interlaminar fracture toughness is an indicator of the fracture resistance of material layers and is a key parameter for evaluating the integrity and durability of composite materials. The double cantilever beam test is a test method for the mode I fracture toughness of composite laminates specified by the ASTM D5528-13 standard. A non-adhesive insert (such as polytetrafluoroethylene film) is embedded in the middle of the specimen as a prefabricated delamination. When the polytetrafluoroethylene film is embedded as a prefabricated delamination, the resin in the prefabricated delamination area will flow along the smooth surface of the polytetrafluoroethylene film and accumulate and enrich at the tip of the artificial prefabricated crack to form a resin-rich zone. The existence of the resin-rich zone will have a significant effect on the load-displacement response of the DCB specimen and will cause errors in the calculation of the mode I interlaminar initial fracture toughness.

[0004] In order to avoid the influence of the resin-rich zone, there are two main treatment methods: (1) treat the "steep drop" in the load-displacement curve as an experimental error and directly ignore its influence; (2) follow the ASTM D5528-13 standard recommendation and use pre-cracked specimens to conduct tests to reduce the influence of the resin-rich zone, that is, first stretch the crack length by 2-3mm, and then start recording data. However, this standard only applies to unidirectional composite laminates, and the resin-rich zone lengths corresponding to different layup angles are different. Using this "unified" 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, a fiber bridging effect will occur between the layers. The fiber bridging effect may cause the measurement and calculation of the initial fracture energy to be too high. Summary of the invention

[0005] The purpose of the present invention is to provide a multi-segment cohesive unit analysis method that takes into account the influence mechanism of the resin-rich area and fiber bridging of the composite material, so as to solve the problem that the resin-rich area formed by laying polytetrafluoroethylene film during the preparation of DCB samples will lead to inaccurate calculation of mode I fracture energy, resulting in a certain impact on the evaluation of the integrity and durability of the composite material.

[0006] To achieve the above object, the present invention provides a multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials, comprising the following steps:

[0007] S1. Design and prepare multi-directional ply angle DCB specimens and conduct DCB experiments;

[0008] S2, calculating the experimental data obtained in S1 to obtain the I-mode interlaminar fracture toughness-crack length data of DCB specimens with different interlaminar angles, and plotting them into an R curve;

[0009] S3. A numerical analysis model of the DCB specimen was established. The composite laminate was modeled using solid units, and the interlayer interface was modeled in the form of four cohesive force model units arranged at the same horizontal position;

[0010] S4. Analyze the parameters of the four CZM units based on the J-integral method and the experimental data to obtain the cohesion model parameters of each unit;

[0011] S5. The segmented cohesive force model obtained based on the above cohesive force model parameters is used to simulate the delamination damage behavior of the composite laminate.

[0012] Preferably, the DCB sample ply design in S1 is [0 11 / θ / / 0 12 ], where θ = 0°, 45° and 90°, the symbol / / indicates the location of the prefabricated crack introduced in the preparation, a 13 μm thick and 50 mm long polytetrafluoroethylene film is artificially laid between the 12th and 13th layers of the sample as a prefabricated crack, and the unidirectional plate is cut into: 180 mm long, 25 mm wide, and 4.8 mm thick, with a preset effective crack length a 0 =30mm.

[0013] Preferably, in S1, a double cantilever beam specimen is used to perform a type I delamination experiment on a universal testing machine, and the universal testing machine records the displacement-load data of the quasi-static delamination extension in real time and records the corresponding crack extension length through a digital camera system.

[0014] Preferably, in S2, the strain energy release rate is calculated by a 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 △ is the crack tip delamination length correction factor. Its characteristic value is obtained by plotting the cube root of the flexibility C against the delamination length a using the least squares method. The flexibility C is the ratio of the applied displacement to the applied load, D / P.

[0017] Preferably, the interlayer interface in S3 is divided into a resin-enriched area and a fiber bridging extension area based on the damage characteristics of different areas. The cohesive model unit in the resin-enriched area and the cohesive model unit in the fiber bridging extension area are coupled and superimposed through nodes. The cohesive model unit in the resin-enriched area represents matrix fracture, and the cohesive model unit in the fiber bridging extension area is obtained by coupling three cohesive model units Element E1, Element E2 and Element E3, wherein Element E1 represents matrix fracture of the composite material in the absence of fiber bridging, Element E2 represents long fiber fracture damage associated with fiber bridging, and Element E3 represents short fiber fracture damage associated with fiber bridging.

[0018] Preferably, the parameters of the four cohesion model units in S4 are strain energy release rates, wherein the cohesion model unit in the resin-rich region is the DCB sample due to the rapid expansion of cracks after the resin-rich region breaks and produces a high initial interlaminar strain energy release rate G I-MC .

[0019] Preferably, the cohesive force model unit in the fiber bridge extension zone is to use the first interlaminar fracture toughness value in the stable extension delamination process as the initial interlaminar strain energy release rate G INI , the steady-state interlaminar strain energy release rate G during the delamination process of composite laminates PROP The initial interlaminar strain energy release rate G INI Steady-state fiber bridging strain energy G BR Composition, expressed by the following equation:

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

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

[0022] When the opening displacement of the cohesive model unit in the resin-rich region is δ = δ′, it means that the crack has just formed in the resin matrix; when the opening displacement is δ = δ 0 When , it represents complete cracking of the matrix, where δ′ is the initial damage displacement of the resin-rich region;

[0023] When the opening displacement of the cohesive model element in the fiber bridge extension area δ = δ 1When δ 1 is the initial damage displacement of the fiber bridge, and the initial interlaminar strain energy release rate G is calculated according to the damage mechanism. 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 represents the strain energy release rate of matrix fracture, G I-FD represents the strain energy release rate of matrix / fiber interface separation, G I-FB represents the strain energy release rate of fiber bridging at the crack tip;

[0026] When the fiber bridges the expansion zone, the opening displacement of the cohesive model element When the fiber bridge unit is damaged from the beginning to the complete failure, the steady-state fiber bridge strain energy is G BR ;

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

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

[0029] The J-integral method is used to describe the distribution law of fiber bridging. The expression of the J-integral method is:

[0030]

[0031] The fiber bridging stress expression is obtained by derivation of the above equation:

[0032]

[0033] Where: δ represents the opening displacement of the initial crack extension position;

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

[0035]

[0036] The corresponding fiber bridging stress expression is:

[0037]

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

[0039] Preferably, the parameters of the four cohesion model units in S4 are determined as follows: the high initial interlaminar strain energy release rate G measured by the DCB experiment I-MC , initial interlaminar strain energy release rate G INI , steady-state interlaminar strain energy release rate G PROP , the R curve and G calculated PROP =G INI +G BR The steady-state fiber bridging strain energy G is obtained BR and R curve fitting function.

[0040] Preferably, the parameters of the cohesion model unit in the resin-rich region in S4 are determined as follows:

[0041] High initial interlaminar strain energy release rate G I-MC Obtained from DCB experiment, σ 0 Obtained by tensile testing of the matrix, and then by Get δ 0 ;

[0042] The parameters of the Element E1 cohesion model unit 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 cohesion model units of Element E2 and Element E3 are determined as follows:

[0048] The maximum bridging stress of fiber bridges is obtained by J-integral method and the opening displacement at complete failure

[0049] when When

[0050] σ br =σ br-L +σ br-S ;

[0051]

[0052] in: is the maximum interface strength, δ 0 is the matrix fracture failure displacement in the resin-rich area, δ 1 is the initial displacement of fiber bridging damage, δ 2 is the fiber bridging damage failure displacement, G IC is the interlaminar strain energy release rate, K E1 is the stiffness of the Element E1 cohesive model unit, K E2 is the stiffness of the Element E2 cohesive model unit, K E3 is the stiffness of the Element E3 cohesive model unit, G I-L is the strain energy release rate of the long fiber unit Element E2 during failure, G I-S is the strain energy release rate of the short fiber unit Element E3 during failure, σ br-L is the maximum adhesion stress of CZM unit in the long fiber zone, σ br-S is the maximum adhesion stress of the CZM unit in the short fiber zone.

[0053] Therefore, the present invention adopts the above-mentioned multi-segment cohesion unit analysis method considering the influence mechanism of the resin-rich region and fiber bridging of the composite material, which has the following beneficial effects:

[0054] (1) The corresponding constitutive relations are used in the regions with different damage mechanisms to simulate the crack propagation and delamination behavior, which intuitively represents the damage mechanisms corresponding to different regions and achieves a good description of the contributions of the three mechanisms.

[0055] (2) The effect of the resin-rich region on the type I delamination of composite laminates was analyzed. The effect of the resin-rich region on the propagation behavior of type I delamination under static load can be predicted, and a more accurate initial strain energy release rate of type I delamination can be further obtained, which can make the performance evaluation of composite materials more precise.

[0056] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of a DCB sample and a DCB experiment of the present invention;

[0058] Figure 2 It is a schematic diagram of the DCB sample partitioning of the present invention;

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

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

[0061] Figure 5 It is a macroscopic cross-sectional view of DCB samples with different inter-layer ply angles of the present invention;

[0062] Figure 6 is the load-displacement curve of the DCB specimens with different inter-ply angles of the present invention;

[0063] Figure 7 is the R curve of the DCB specimens with different inter-ply angles of the present invention;

[0064] Figure 8 It is the simulation result of DCB samples with different inter-layer ply angles of the present invention;

[0065] Fig. 9 It is a comparative analysis of the 0 / / 45 sample of the present invention by directly ignoring the method;

[0066] Fig.10 It is a comparative analysis of the 0 / / 90 sample pre-stretching method of the present invention;

[0067] Fig.11 It is the microscopic morphology of DCB samples with different interlayer ply angles of the present invention. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0069] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0070] Embodiment 1

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

[0072] S1. Design and prepare multi-directional ply angle DCB specimens and conduct DCB experiments. The DCB specimen ply design is [0 11 / θ / / 0 12], where θ = 0°, 45° and 90°, the symbol / / indicates the location of the prefabricated crack introduced in the preparation, a 13 μm thick and 50 mm long polytetrafluoroethylene film is artificially laid between the 12th and 13th layers of the sample as a prefabricated crack, and the unidirectional plate is cut into: 180 mm long, 25 mm wide, and 4.8 mm thick, with a preset effective crack length a 0 =30mm, such as Figure 1 , Figure 2 As shown, Figure 1 (a) is the DCB experimental equipment diagram. Figure 1 (b) is a schematic diagram of the DCB sample size. Figure 1 (c) Side view of the DCB sample after treatment.

[0073] Type I delamination experiments were carried out using double cantilever beam specimens on a universal testing machine, which recorded the displacement-load data of quasi-static delamination extension in real time and the corresponding crack extension length through a digital camera system.

[0074] S2. Calculate the strain energy release rate by using the modified beam theory method. The formula is as follows:

[0075]

[0076] Among them, P is the load, D is the applied displacement, b is the specimen width, a is the delamination length, △ is the crack tip delamination length correction factor, and its characteristic value is obtained by the least squares plot of the cube root of the flexibility C against the delamination length a. The flexibility C is the ratio of the applied displacement to the applied load D / P. The experimental data is applied to the above formula, and the calculated data is plotted into the I-mode interlaminar fracture toughness-crack length curve of the DCB specimens with different interlayer ply angles, that is, the R curve.

[0077] S3. A numerical analysis model of the DCB specimen was established. The composite laminate was modeled using solid elements. The mechanical properties of the composite laminate are shown in Table 1. The interlaminar interface was modeled by arranging four cohesive force model units at the same horizontal position. The interlaminar interface was divided into a resin-rich area and a fiber bridging extension area based on the damage characteristics of different regions. The cohesive force model unit in the resin-rich area and the cohesive force model unit in the fiber bridging extension area were coupled and superimposed through nodes. The cohesive force model unit in the resin-rich area represented matrix fracture. The cohesive force model unit in the fiber bridging extension area was obtained by coupling three cohesive force 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 associated with fiber bridging, and Element E3 represents short fiber fracture damage associated with fiber bridging.

[0078] Table 1 Mechanical properties parameters of composite laminate materials

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

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

[0081] S4. According to the J-integral method and the experimental data, the parameters of the four CZM units are analyzed to obtain the cohesive force model parameters of each unit. The parameters of the four cohesive force model units are strain energy release rates. The cohesive force model unit in the resin-rich area is the DCB specimen. The cracks in the resin-rich area expand rapidly after the fracture, resulting in a high initial interlaminar strain energy release rate G. I-MC .

[0082] The cohesive force model unit in the fiber bridge extension zone takes the first interlaminar fracture toughness value in the stable extension delamination process as the initial interlaminar strain energy release rate G INI , the steady-state interlaminar strain energy release rate G during the delamination process of composite laminates PROP The initial interlaminar strain energy release rate G INI Steady-state fiber bridging strain energy G BR Composition, expressed by the following equation:

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

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

[0085] When the opening displacement of the cohesive model unit in the resin-rich region is δ = δ′, it means that the crack has just formed in the resin matrix; when the opening displacement is δ = δ 0 When , it represents complete cracking of the matrix, where δ′ is the initial damage displacement of the resin-rich region;

[0086] When the opening displacement of the cohesive model element in the fiber bridge extension area δ = δ 1 When δ 1 is the initial damage displacement of the fiber bridge, and the initial interlaminar strain energy release rate G is calculated according to the damage mechanism. INI Expressed as:

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

[0088] Where: G INI It mainly consists of three microscopic damage mechanisms, among which G I ' -MC represents the strain energy release rate of matrix fracture, G I-FD represents the strain energy release rate of matrix / fiber interface separation, G I-FB represents the strain energy release rate of fiber bridging at the crack tip;

[0089] When the fiber bridges the expansion zone, the opening displacement of the cohesive model element When the fiber bridge unit is damaged from the beginning to the complete failure, the steady-state fiber bridge strain energy is G BR ;

[0090] Among them G BR is the strain energy release rate G of the long fiber unit Element E2 during failure. I-L and the strain energy release rate G of the short fiber unit Element E3 during failure I-S It consists of two parts, and the expression is as follows:

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

[0092] The J-integral method is used to describe the distribution law of fiber bridging. The expression of the J-integral method is:

[0093]

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

[0095]

[0096] Where: δ represents the opening displacement of the initial crack extension position;

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

[0098]

[0099] The corresponding fiber bridging stress expression is:

[0100]

[0101] Where G a , Gb ,δ a and δ b are different constant coefficients, which are determined by fitting the experimental data.

[0102] The parameters of the four cohesive force model elements are determined as follows: the initial interlaminar strain energy release rate G measured by DCB experiment I-MC , initial interlaminar strain energy release rate G INI , steady-state interlaminar strain energy release rate G PROP , the R curve and G calculated PROP =G INI +G BR The steady-state fiber bridging strain energy G is obtained BR and R curve fitting function.

[0103] The parameters of the cohesion model unit in the resin-rich region are determined as follows:

[0104] High initial interlaminar strain energy release rate G I-MC Obtained from DCB experiment, σ 0 Obtained by tensile testing of the matrix, and then by Get δ 0 ;

[0105] The parameters of the Element E1 cohesion model unit 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 cohesion model units of Element E2 and Element E3 are determined as follows:

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

[0112] when When

[0113] σ br=σ br-L +σ br-S ;

[0114]

[0115]

[0116] in: is the maximum interface strength, δ 0 is the matrix fracture failure displacement in the resin-rich area, δ 1 is the initial displacement of fiber bridging damage, δ 2 is the fiber bridging damage failure displacement, G IC is the interlaminar strain energy release rate, K E1 is the stiffness of the Element E1 cohesive model unit, K E2 is the stiffness of the Element E2 cohesive model unit, K E3 is the stiffness of the Element E3 cohesive model unit, G I-L is the strain energy release rate of the long fiber unit Element E2 during failure, G I-S is the strain energy release rate of the short fiber unit Element E3 during failure, σ br-L is the maximum adhesion stress of CZM unit in the long fiber zone, σ br-S is the maximum adhesion stress of the CZM unit in the short fiber zone.

[0117] S5. The segmented cohesive force model obtained based on the above cohesive force model parameters is used to simulate the delamination damage behavior of the composite laminate, and the finite element software ABAQUS is used to simulate the type I delamination expansion process of the composite laminate.

[0118] Embodiment 2

[0119] The present invention provides a multi-segment cohesive unit analysis method considering the influence mechanism of composite resin-rich regions and fiber bridging, comprising the following steps:

[0120] Step 1: Prepare composite double cantilever beam specimens with different interlayer layups and conduct DCB tests; DCB specimens are made of T700 grade unidirectional carbon fiber / epoxy resin prepreg, which are prepared by manual laying and autoclave molding process, such as Figure 1 shown.

[0121] A 20 mm hinge was bonded to the front end of the DCB specimen, a thin layer of white paint was sprayed on both sides to improve the visibility of the layer surface, and a scaled paper tape was pasted to help monitor the crack extension length.

[0122] The DCB sample ply design is: [0 11 / θ / / 0 12], where θ = 0°, 45° and 90°, and the symbol / / indicates the location of the prefabricated crack introduced during preparation. A 13μm thick and 50mm long polytetrafluoroethylene film is artificially laid between the 12th and 13th layers of the specimen as a prefabricated crack. The one-way plate is cut into 180mm long, 25mm wide and 4.8mm thick. Prefabricated effective crack length

[0123] a 0 =30mm.

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

[0125] Step 2: Calculate the curve of mode I interlaminar fracture energy versus delamination length for the ply specimens with different interlaminar lengths, and 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 specimen width, a is the delamination length, and △ is the crack tip delamination length correction factor. Its characteristic value is obtained by plotting the cube root of the flexibility C against the delamination length a using the least squares method. The flexibility C is the ratio of the applied displacement to the applied load, D / P.

[0128] Step 3, establish the numerical analysis model of DCB specimens, the composite laminate is modeled by solid units; the interlayer interface is modeled by arranging four cohesive force model units at the same horizontal position, where the damage characteristics of different regions are divided into resin-rich areas and fiber bridging extension areas. The cohesive force units in the resin-rich area and the fiber bridging extension areas are coupled and superimposed through nodes. The cohesive force unit in the resin-rich area represents matrix fracture. The cohesive force model unit in the fiber bridging extension area is obtained by coupling three cohesive force units (Element E1, Element E2, Element E3). Element E1 represents the matrix fracture of the composite material without fiber bridging and the matrix / fiber separation related to fiber bridging. Element E2 represents the long fiber fracture damage related to fiber bridging. Element E3 represents the short fiber fracture damage related to fiber bridging. The layout position and connection method of each cohesive force unit model are as follows: Figure 3 shown.

[0129] Step 4: Analyze the parameters of the four CZM units according to the J-integral method and the test data to obtain the CZM parameters of each unit;

[0130] Step 5: Use the segmented CZM model to simulate the delamination damage behavior of the composite material. Use the finite element software ABAQUS to simulate the type I delamination expansion process of the composite laminate. The three-dimensional finite element model is as follows: Figure 3 As shown. The implicit calculation method is adopted, the upper and lower plates use 8-node 3D solid elements (C3D8R), the CZM layer in the middle of the plate uses C0H3D8 elements, and the cohesive force unit is coupled and superimposed by the cohesive force unit in the resin-enriched area and the cohesive force unit in the fiber bridging extension area through nodes. Each layer is set as a unit in the thickness direction. In order to better simulate the stress and strain field when the crack tip extends, the mesh size of the crack tip extension area is 0.2mm, and the mesh size of the remaining areas is 0.5mm. Displacement loads in the y direction are applied to the upper and lower loading ends of the model, and constraints in the z direction are applied to the free end to keep the model constraints consistent with the experimental conditions.

[0131] Initial interface stiffness K of CZM element representing matrix cracking 1 , researchers usually set it to 10 12 Up to 10 15 N / m 3 , the present invention adopts 1x10 15 N / m 3 In order to avoid the convergence problem caused by stiffness degradation during the calculation process, the viscosity coefficient is introduced. The viscosity coefficient is 1x10 6 .

[0132] Figure 6The load-displacement curves of DCB specimens with different inter-ply angles are given. It can be found that the experimental results show that the load-displacement curves of specimens with the same inter-ply angles show similar change trends. Figure 6 (a) in the figure is the load-displacement curve of the 0 / / 0 specimen. The load-displacement curve of the 0 / / 0 specimen shows a linear relationship in the initial stage until the crack propagates and the load drops sharply. After the load drops sharply, it decreases slowly and smoothly. Figure 6 (b) is the load-displacement curve of the 0 / / 45 specimen. The load-displacement curve of the 0 / / 45 specimen shows a linear relationship in the initial stage until the crack expands and the load drops sharply. After the load drops sharply, the load rises to a certain level again and shows nonlinear characteristics, and then gradually decreases in an obvious fluctuating manner. Figure 6 (c) in the figure is the load-displacement curve of the 0 / / 90 specimen. The load-displacement curve of the 0 / / 90 specimen is consistent with that of the 0 / / 0 specimen and the 0 / / 45 specimen in the linear stage. When the crack propagates, the load drops sharply, and the load drop is extremely small. After the load drops sharply, the nonlinearity rises to a certain level and then gradually decreases in an obvious fluctuating manner.

[0133] Figure 7 The R curves of DCB specimens with different inter-ply angles are given. Figure 7 (a) is the R curve of the 0 / / 0 sample. Figure 7 (b) is the R curve of the 0 / / 45 sample. Figure 7 (c) is the R curve of the 0 / / 90 specimen. The test results show that the specimens with different interlayer angles have a relatively high initial interlayer strain energy release rate G due to the rapid crack expansion after the fracture of the resin-rich area. I-MC , which is called high initial fracture toughness value, high initial interlaminar strain energy release rate G I-MC Calculated by formula (1), the first interlaminar fracture toughness value in the stable extension delamination process is taken as the initial interlaminar strain energy release rate G INI During the rapid crack growth process, the interlaminar fracture toughness changes from high initial fracture toughness G I-MC Reduced to the initial interlaminar strain energy release rate G INI , and then the interlaminar fracture toughness increases with the crack extension, forming a typical R curve. High initial interlaminar strain energy release rate G of DCB specimens with different interlaminar plies I-MC and the initial interlaminar strain energy release rate G INI As shown in Table 2, it can be observed that the decrease in interlaminar fracture toughness is related to the interlaminar angle, among which the 0 / / 0 sample has the largest decrease in interlaminar fracture toughness, followed by the 0 / / 45 sample, and the 0 / / 90 sample has the smallest decrease. The decrease decreases with the increase of the interlaminar angle.

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

[0135]

[0136] The comparison between the test results and simulation results of DCB samples with different ply angles obtained by this analysis method is shown in Figure 2. Figure 8 As shown, Figure 8 (a) is a comparison of the load-displacement curves of the 0 / / 0 specimen and the numerical simulation. Figure 8 (b) is a comparison of the load-displacement curves of the 0 / / 40 specimen and the numerical simulation. Figure 8 (c) in the figure is a comparison of the load-displacement curves of the 0 / / 90 specimen and the numerical simulation. The comparison results show that the load-displacement curve predicted by the cohesive force model containing the resin-rich region is in good agreement with the load-displacement curve measured by the experiment. As can be seen from the figure, the load-displacement curve is divided into three stages: the linear stage, the nonlinear characteristic stage, and the 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 longer the length of the resin-rich region, the more energy is accumulated in the resin-rich region, and the larger the maximum value of the linear increase of the load, resulting in different maximum loads of the specimen models with different inter-layer layup angles. In the load stage, as the applied displacement further increases, the resin-rich region breaks and the load drops sharply. In the nonlinear characteristic stage of the load-displacement curve, the 0 / / 45 and 0 / / 90 specimens produce fiber bridging during the internal delamination expansion process. The toughening mechanism related to the fiber bridging causes the load to increase nonlinearly with the increase of the applied displacement to the limit load. After the limit load, the load gradually decreases with the increase of the applied displacement. Since there is almost no fiber bridging in the 0 / / 0 specimen, the load decreases slowly and smoothly with the increase of applied displacement in the nonlinear characteristic stage of the load-displacement curve. The numerical simulation results show that the adjustment of the length of the resin-rich zone is consistent with the actual length of the resin-rich zone of the specimen with the corresponding interlayer layup angle, which can effectively simulate the influence of the resin-rich zone on the load-displacement curve at different interlayer layup angles, and further verify the influence of the resin-rich zone on the delamination damage behavior.

[0137] Fig. 9 (a) is the load-displacement comparison analysis diagram of the 0 / / 45 specimen directly neglected and the experimental results. Fig. 9 It can be observed from (a) that in the direct neglect method, by adding the tangent method to correct the resin fracture area of ​​the load-displacement curve, it is difficult to confirm the initial delamination damage position, which will lead to an underestimation of the initial strain energy release rate of type I delamination. This method will have a certain impact on the selection and determination of the starting point. In the 0 / / 45 specimen, the load drop phenomenon is most intuitive. Therefore, the load-displacement curve of the 0 / / 45 specimen was selected to illustrate the impact of the direct neglect method. Fig. 9(b) is the modified 0 / / 45 specimen directly neglected and the load-displacement comparison analysis diagram of the experimental results. Fig. 9 As can be seen from (b) in the direct neglect method, the resin fracture area in the load-displacement curve is corrected by introducing a tangent correction. However, due to the difficulty in determining the initial delamination damage location, this method may lead to an underestimation of the initial strain energy release rate of mode I delamination.

[0138] Another method is pre-opening. Since the length of the resin-enriched zone of the 0 / / 90 sample is extremely small, the impact it produces is the most intuitive, so we choose the 0 / / 90 sample for illustration. Fig.10 (a) is the load-displacement comparison analysis diagram of the 0 / / 90 specimen pre-opening result and the experimental result. Fig.10 (b) is the load-displacement comparison analysis diagram of the modified 0 / / 90 specimen pre-opening result and the experimental result. Fig.10 It can be observed that when the pre-opening treatment is used for testing, the initial strain energy of the specimen is higher than the actual value, which will cause a certain deviation in the results. Combined with the characteristics of the fiber bridging crack extension zone, 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 too high due to the fiber bridging effect.

[0139] Fig.11 The macroscopic and microscopic morphologies of the cross-section of DCB specimens with different inter-ply angles are given. Fig.11 (a) is the microscopic morphology of the cross section of the 0 / / 0 sample. Fig.11 (b) is the microscopic morphology of the 0 / / 45 sample cross section. Fig.11(c) in the figure is the microscopic morphology of the cross section of the 0 / / 90 sample. From the macroscopic cross-sectional image of the sample, it is found that the resin-enriched area of ​​the 0 / / 0 sample is the largest, with about 5.4 mm of resin enrichment along the length direction; the resin-enriched area of ​​the 0 / / 45 sample is the second largest, with about 2.4 mm of resin enrichment along the length direction; the resin-enriched area of ​​the 0 / / 90 sample is the smallest, with only 50 μm of resin enrichment along the length direction. The area of ​​the resin-enriched area decreases with the increase of the interlayer angle of the sample. In the cross-sectional microscopic morphology image, it is observed that in the resin-enriched area, the cross sections of the 0 / / 0 sample and the 0 / / 45 sample are covered with resin, and there is a large area of ​​resin fracture. The 0 / / 90 sample has a small area of ​​resin fracture due to the extremely small area of ​​the resin-enriched area. Therefore, the damage mode in the resin-enriched area is matrix cracking. For the 0 / / 0 specimen, there are a large number of resin matrix sections, a large number of "fiber grooves" formed by pulling out carbon fibers along the 0° direction, and a small number of broken fibers in the fiber bridging extension area; for the 0 / / 45 specimen, there are a large number of resin matrix sections, "fiber depressions" along the 45° direction, and broken fibers in the fiber bridging extension area; for the 0 / / 90 specimen, there are a large number of exposed fibers, "fiber grooves" along the 90° direction, and a large number of resin matrix sections in the fiber bridging extension area. Therefore, there are three main damage modes in the fiber bridging extension area, namely, matrix cracking, matrix / fiber separation, and fiber breakage.

[0140] In summary, the DCB specimen forms a resin-rich zone at the end of the prefabricated crack due to resin enrichment, and the area of ​​the resin-rich zone decreases with the increase of the interlayer angle of the specimen. During the test, as the applied displacement increases, the energy in the resin-rich zone continues to accumulate. When it reaches a critical value, the resin-rich zone breaks, and because its strength is higher than the interlayer interface strength of the composite material, the crack rapidly expands in the interlayer interface area, causing Figure 4 The load-displacement curve shows a steep drop in the transition zone between the linear stage and the nonlinear characteristic stage, and the interlaminar fracture toughness of the R curve decreases in the initial stage. Figure 5 (a) is the macroscopic cross-section of the 0 / / 0 sample. Figure 5 (b) is the macroscopic cross-section of the 0 / / 45 sample. Figure 5 (c) is a macroscopic cross-section of the 0 / / 90 specimen. Further observation revealed that the load-displacement curve had a steep drop in load and G ΙC In the initial stage of the curve, the decrease in interlaminar fracture toughness increases with the increase in the area of ​​the resin-rich zone.

[0141] In view of the problem that the resin-enriched area generated by laying polytetrafluoroethylene film as a prefabricated layer during the preparation of DCB samples affects the delamination fracture behavior, the present invention designs a multi-directional laying angle DCB test, studies the "steep drop phenomenon" of the load-displacement curve, uses a scanning electron microscope to characterize the microscopic morphology of the DCB crack section, and quantifies the resin-enriched influence area. A DCB numerical model containing a resin-enriched area and a fiber bridging extension area is established, and a quantitative analysis is carried out to explain and reveal the influence of the resin-enriched area on the initial fracture toughness of type I delamination, and the following conclusions are drawn:

[0142] The cross-sectional microstructure of the specimens was observed by scanning electron microscopy, and it was found that there was a significant resin enrichment phenomenon at the prefabricated crack tip. The area of ​​the resin enrichment zone is related to the interlayer ply angle of the specimen. The 0 / / 0 specimen has the largest resin enrichment zone area, followed by the 0 / / 45 specimen, and the 0 / / 90 specimen has the smallest resin enrichment zone area. The resin enrichment zone area decreases with the increase of the interlayer ply angle.

[0143] Observing the load-displacement curve, the load-displacement curve of the 0 / / 0 sample has the most significant load drop, but due to the longer resin-rich area and the weaker fiber bridging effect of the 0 / / 0 sample, the load-displacement curve in the expansion stage shows a smooth and smooth decline; the load-displacement curve of the 0 / / 45 sample also shows a significant steep drop, 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 significant than that of the 0 / / 0 sample, and the two have not completed a 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 presented is a slight decrease followed by a significant increase.

[0144] The established DCB model containing fiber bridging extension zone and resin-rich zone can not only predict the change law of load-displacement curves at different layup angles, but also the predicted load and displacement values ​​are generally consistent, verifying the influence of resin-rich zone on the initial fracture toughness of mode I delamination.

[0145] Therefore, the present invention adopts the above-mentioned multi-segment cohesive unit analysis method that considers the influence mechanism of resin-rich areas and fiber bridging of composite materials, and adopts corresponding constitutive relations in areas with different damage mechanisms to simulate the crack propagation delamination behavior, intuitively represents the damage mechanisms corresponding to different areas, and achieves a good description of the contributions of the three mechanisms. It analyzes the influence of resin-rich areas on the initial fracture toughness of type I delamination, and can simulate the influence of resin-rich areas on type I delamination extension behavior under static load, so that the evaluation of the integrity and durability of composite materials is more accurate.

[0146] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials, characterized by: The following steps are involved: S1. Design and prepare multi-directional ply angle DCB specimens and conduct DCB experiments; S2, calculating the experimental data obtained in S1 to obtain the I-mode interlaminar fracture toughness-crack length data of DCB specimens with different interlaminar angles, and plotting them into an R curve; S3. A numerical analysis model of the DCB specimen was established. The composite laminate was modeled using solid units, and the interlayer interface was modeled in the form of four cohesive force model units arranged at the same horizontal position; S4. Analyze the parameters of the four CZM units based on the J-integral method and the experimental data to obtain the cohesion model parameters of each unit; S5. The segmented cohesive force model obtained based on the above cohesive force model parameters is used to simulate the delamination damage behavior of the composite laminate.

2. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 1, characterized in that: The DCB sample ply design in S1 is [0 11 / θ / / 0 12 ], where θ = 0°, 45° and 90°, the symbol / / indicates the location of the prefabricated crack introduced in the preparation, a polytetrafluoroethylene film with a thickness of 13 μm and a length of 50 mm is artificially laid between the 12th layer / / 13th layer of the specimen as a preset crack, and the unidirectional plate is cut into: 180 mm long, 25 mm wide, and 4.8 mm thick, with a preset effective crack length a0 = 30 mm.

3. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 2, characterized in that: In S1, a type I delamination experiment was carried out using a double cantilever beam specimen on a universal testing machine. The universal testing machine recorded the displacement-load data of the quasi-static delamination extension in real time and recorded the corresponding crack extension length through a digital camera system.

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

5. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 4, characterized in that: The interlayer interface in S3 is divided into a resin-rich area and a fiber bridging extension area based on the damage characteristics of different regions. The cohesive model unit in the resin-rich area and the cohesive model unit in the fiber bridging extension area are coupled and superimposed through nodes. The cohesive model unit in the resin-rich area represents matrix fracture, and the cohesive model unit in the fiber bridging extension area is obtained by coupling three cohesive model units Element E1, Element E2 and Element E3, where Element E1 represents the matrix fracture of the composite material without fiber bridging, Element E2 represents the long fiber fracture damage related to fiber bridging, and Element E3 represents the short fiber fracture damage related to fiber bridging.

6. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 5, characterized in that: The parameters of the four cohesion model units in S4 are strain energy release rates. The cohesion model unit in the resin-rich region is the DCB specimen. The cracks in the resin-rich region rapidly expand after fracture, resulting in a high initial interlaminar strain energy release rate G. I-MC .

7. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 6, characterized in that: The cohesive force model unit in the fiber bridge extension zone takes the first interlaminar fracture toughness value in the stable extension delamination process as the initial interlaminar strain energy release rate G INI , the steady-state interlaminar strain energy release rate G during the delamination process of composite laminates PROP The initial interlaminar strain energy release rate G INI Steady-state fiber bridging strain energy G BR Composition, expressed by the following equation: G PROP =G INI +G BR 。 8. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 7, characterized in that: The cohesion model parameters of each group of units are split according to the separation (δ) of the cohesion unit: When the opening displacement of the cohesive model unit in the resin-rich area is δ = δ′, it means that the crack has just formed in the resin matrix; when the opening displacement is δ = δ0, it means that the matrix is ​​completely cracked, where δ′ is the initial damage displacement of the resin-rich area; When the opening displacement of the cohesive model unit in the fiber bridging extension zone is δ = δ1, it means that the crack has just formed in the fiber bridging extension zone, where δ1 is the initial damage displacement of the fiber bridging. According to 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 represents the strain energy release rate of matrix fracture, G I-FD represents the strain energy release rate of matrix / fiber interface separation, G I-FB represents the strain energy release rate of fiber bridging at the crack tip; When the fiber bridges the expansion zone, the opening displacement of the cohesive model element When the fiber bridge unit is damaged from the beginning to the complete failure, the steady-state fiber bridge strain energy is G BR ; Among them G BR is the strain energy release rate G of the long fiber unit Element E2 during failure. I-L and the strain energy release rate G of the short fiber unit Element E3 during failure I-S It consists of two parts, and the expression is as follows: G BR =G I-L +G I-S ; The J-integral method is used to describe the distribution law of fiber bridging. The expression of the J-integral method is: The fiber bridging stress expression is obtained by derivation of the above equation: Where: δ represents the opening displacement of the initial crack extension position; The strain energy release rate G is described by an exponential function. BR (δ): The corresponding fiber bridging stress expression is: Where G a , G b , δ a and δ b are different constant coefficients, which are determined by fitting the experimental data.

9. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 8, characterized in that: The parameters of the four cohesive force model elements in S4 are determined as follows: the initial interlaminar strain energy release rate G measured by DCB experiment I-MC , initial interlaminar strain energy release rate G INI , steady-state interlaminar strain energy release rate G PROP , the R curve and G calculated PROP =G INI +G BR The steady-state fiber bridging strain energy G is obtained BR and R curve fitting function.

10. The multi-segment cohesive unit analysis method considering the influence mechanism of resin-rich regions and fiber bridging of composite materials according to claim 9, characterized in that: The parameters of the cohesion model unit in the resin-rich region of S4 are determined as: High initial interlaminar strain energy release rate G I-MC obtained by DCB experiment, σ0 was obtained by matrix tensile test, and then by Get δ0; The parameters of the Element E1 cohesion model unit 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 cohesion model units of Element E2 and Element E3 are determined as follows: The maximum bridging stress of fiber bridges is obtained by J-integral method and the opening displacement at complete failure when When s br =s br-L +s br-S ; in: is the maximum strength of the interface, δ0 is the matrix fracture failure displacement of the resin-rich area, 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 the Element E1 cohesive model unit, K E2 is the stiffness of the Element E2 cohesive model unit, K E3 is the stiffness of the Element E3 cohesive model unit, G I-L is the strain energy release rate of the long fiber unit Element E2 during failure, G I-S is the strain energy release rate of the short fiber unit ElementE3 during failure, σ br-L is the maximum adhesion stress of CZM unit in the long fiber zone, σ br-S is the maximum adhesion stress of the CZM unit in the short fiber zone.

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