Study on interlaminar fracture toughness of unidirectional composites

Carbon fiber composite is widely used in the nuclear industry and other fields due to their lightweight and high strength. There are various forms of failure in composite, including resin cracking, fiber fracture, and resin fiber interface debonding. At the initial stage of damage, they all exhibit the form of microcracks. As cracks propagate and fuse, they ultimately lead to macroscopic fracture of composite components. For safety reasons, it is necessary to study the fracture toughness of composite. This article uses a combination of winding method and double cantilever beam method to study the interlayer fracture toughness characteristics of high-strength (or high modulus) fiber epoxy resin composite under type I load. Choose a more suitable propagation GIC as a measurement metric. The results indicate that under the same resin matrix, the interlayer fracture toughness of high-strength fiber composite is much higher than that of high modulus fibers, which is related to the high surface chemical activity of high-strength fiber monofilament. Finally, combined with finite element analysis, its application in laminated structures was briefly analyzed.


Introduction
Carbon fiber composite is being applied in more and more fields due to their advantages of light weight and high strength [1].Composites are usually made from fibers and resins through a certain molding process.Different fibers, resins, and even molding processes can form different interfaces and sandwich structures, thereby affecting the performance of the entire product.Different brands of fibers have different spinning processes and surface treatments.At the same time, there are many types of resins available [2][3].For example, epoxy resins have five types based on their molecular structure: glycidyl ether, glycidyl lipid, glycidyl amine, linear aliphatic group, and alicyclic group.In terms of molding technology, there are prepreg manufacturing technology, compression molding, fiber winding, high-pressure kettle molding, extrusion molding, resin transfer molding, three-dimensional textile, vacuum assisted, microwave assisted [4], and so on.During the forming process, defects such as inclusions, pores, delamination, and cracks may appear inside the material, leading to low performance stability.
Carbon fiber composite, as an anisotropic and heterogeneous material, have complex failure mechanisms, including fiber fracture, matrix cracking, fiber matrix interface debonding, and delamination failure [5][6].Among them, the probability of delamination failure is relatively high [7], which seriously reduces the structural strength, stiffness, and integrity of the material.
Cracks and similar defects are inevitable in any engineering material and structure.They are either inherent in the material itself or caused during processing, manufacturing, and construction use.The existence of these cracks and defects will greatly reduce the load-bearing capacity of the structure and develop to a certain extent, leading to complete failure of the structure.The dispersed micro defects and micro damages in the material gradually develop into microcracks, which continuously develop and connect into macroscopic cracks, and then evolve from macroscopic cracks to catastrophic unstable cracks.This evolutionary process is known as the fracture process of the material.Compared with metal materials, the damage modes of composite are more complex, and their damage mechanisms and fracture characteristics require more research.
The macroscopic study of material fracture is called fracture mechanics, initiated by Griffith and enriched by Irwin, Orowan [8] and others.At present, the research methods of fracture mechanics mainly include experiments, theoretical analysis, and numerical simulation.In recent decades, numerical simulation has undergone tremendous development, with various computational methods emerging.Rybicki and Kanninen [9] used the virtual crack closure technique to calculate the energy release rate under different modes, while Daux et al. [10] used the extended finite element method to solve the discontinuity problem.However, these models and methods also have some shortcomings, such as the inability of the strength theory prediction model to be used for failure under low stress, the inability of the fracture mechanics prediction model to directly apply to the analysis of layered damage at interfaces without initial cracks, and the possibility of step changes in interface stiffness when using the damage theory prediction model.
The concept of cohesive zone model was first proposed by Dugdale and Barenblatt [11][12].Due to its ability to simultaneously predict crack initiation and propagation, it has been widely applied in the study of delamination failure mechanisms in composite and has become one of the most popular theories in the field of composite [13].
The delamination modes of material cracks typically include Type I, Type II, and Type III, as well as mixtures of these three types [14].Type I is an open crack, Type II is an in-plane shear crack, and Type III is an out of plane shear crack.Type I crack is a very common form of crack that has been studied in the evaluation of many materials [15].This study investigates the failure mechanism of composite and the matching of fibers and resins by studying their ability to resist the propagation of Type 1 cracks.

Experiment
At present, the main testing standards for type I interlayer fracture toughness are ASTM D5528-13, GB-T 28891-2012/ISO 15024:2001, and HB 7402-96.There are differences and connections among the three.After comparing the sample size, embedded film size, testing process, and GIC calculation, ASTM D5528-13 was selected [16].
The form of composite I-type interlaminar fracture toughness test specimen is a double cantilever beam specimen (DCB).DCB specimen is widely used to measure the interlaminar fracture toughness of composite material I-type delamination due to its simple shape, easy preparation and testing.
The preparation of DCB samples is divided into three steps.Firstly, the production of test panels.A flat plate is formed by wet winding of fibers on a metal flat plate mold.When winding to the middle layer, for example, in this article, the fiber layer has a total of 10 layers, so a 65mm wide plastic film is laid between the 5th and 6th layers (the plastic film in the middle is used to make prefabricated cracks).The second step is to complete the cutting of the test plate.After the test plate is cured and demolded, it is cut into corresponding sizes according to the requirements of the ASTM D5528-13.The third step is to use a strong adhesive to bond the test fixture at one end of the prefabricated crack of the sample.The high-strength fibers and high-modulus fibers were respectively winding with epoxy resin to obtain composites, which named as T samples and M samples.
For the data processing of the DCB test, the basic formula for calculating the I-type interlaminar fracture toughness is the corrected beam theory obtained by Williams [17] by adding a length, Δ, to the DCB specimen to represent the shear effect of the beam and the effect of the root rotation.
G I = 3Pδ 2b(a + |Δ|) Among them, P is the load, is the displacement, is the crack length, and b is the width of the sample, Δ is the crack length correction value, respectively.
At the same time, it is necessary to consider the large deformation effect and multiply it by the corresponding coefficient.

Result and Discussion
The load-displacement curve of the DCB test of the T specimen is shown in Fig. 1(a).The VIS point represents the starting point of delamination visually observed at the edge of the sample, and tools such as a magnifying glass can be used to detect the VIS point.In this experiment, the fracture toughness at the VIS point was selected as the initial GIC.With the gradual expansion of the crack, the fibers on both sides of the crack are pulled out or broken from the matrix, which makes the apparent fracture toughness value gradually increase.In the process of crack propagation, when the number of bridging fibers corresponding to a unit crack area is constant, a stable state of crack propagation is reached, and the corresponding fracture toughness value is the propagation GIC.
The load-displacement curve is linear in the initial stage of crack propagation, where the onset of the crack is at the end of the film in the middle of the specimen, and there is no effect of fiber bridging at this stage.During crack propagation, the curve enters the nonlinear region and gradually decreases after the load value passes the maximum value.When carefully observing the local part of the loaddisplacement curve, it can be seen that the curve is not perfectly smooth, and the load value fluctuates up and down as the displacement increases.These fluctuations are caused by the breakage of the old fibers and the load on the new fibers during the crack propagation process, this phenomenon is called "stick-slip" [18].Fig. 1-2 show the DCB tests of specimens formed by winding with different fibers and resins.Among them, in the displacement and load curve, most of the samples show a trend of increasing first and then gradually decreasing, while some samples show a trend of increasing after a sudden drop in the middle of the curve, but the final part of the curve basically tends to level.The second half of the curve has less undulation and is a "stick-slip" behavior.However, for the M specimen, the fluctuations are more obvious, and the load-displacement curve presents a more obvious jagged shape, which belongs to the more obvious "stick-slip" behavior.The above phenomena indicate that there may be periodic start-stop behavior of cracks, which may be related to the surface morphology of the fibers used in the M test plate.As shown in Fig. 3, the fibers used in the M specimen have many grooves on the surface due to the dry-spraying and wet-spinning process.Therefore, in the subsequent formation of the composite interface, there may be a certain mechanical locking effect.As a result, the above curve characteristics are caused in the DCB test.The linear fitting correlation coefficient of crack length correction, △, for different test plates is basically above 0.99.It can be seen that in this experiment, due to the influence of the crack tip, it is necessary to increase the crack length by about 0.015mm to correct it.The correction factor for large deformation, F, is generally above 0.9, indicating that deformation has a small impact on the test results.In the American standard, the testing rate is specified to be very low, so this process can be considered as a quasi-static process.
The initial GIC and propagation GIC of the different panels are shown in Fig. .3.It can be seen that the propagation GIC is generally much higher than the initial GIC because in the initial stage of the test, since the crack starts from the end of the insert, it is not affected by fiber bridging at this time.With the gradual expansion of the crack, the fibers on both sides of the crack are pulled out or broken from the matrix, which makes the fracture toughness value gradually increase.In Fig. 4, the coefficient of variation of the initial GIC is large, which is affected by the more complex structure at the end of the film and the degree of hysteresis observed by humans.The coefficient of variation of the propagation GIC is lower than that of the initial GIC.
The propagation GIC of T and M samples made of the same resin were 645.2 and 272.2 J/m2, respectively, and the value of M sample was 57.8% lower than that of T sample.It can be seen that from the perspective of I-type fracture toughness and compatibility with epoxy resin, high-strength fibers are better than high-modulus fibers.As shown in Fig. 5, this is because high-modulus fibers have undergone higher temperatures in the fiber production process to achieve a higher degree of graphitization in order to pursue higher modulus, with high carbon content and low active groups.Therefore, the interfacial bond with the resin is lower, and the fracture toughness is also lowered.

Finite Element Analysis
In this paper, the finite element analysis is used to establish the DCB test finite element model of the Itype interlaminar fracture toughness of carbon fiber reinforced epoxy resin unidirectional laminates based on the cohesive zone model.
The layer information is [0] 10, and it is symmetrically distributed with the crack surface as the center.The material parameters and cohesive zone model of each layer are shown in Table 1.Fig. 6 shows the stress contours of the DCB finite element simulation.As shown in Fig. 6-7, the stress at the crack tip of the DCB specimen is the largest, and the stress near the inner side of the crack first decreases and then increases from the inside to the outside, and the middle layer is the smallest.
When the unidirectional layup angle is increased, the stress state of the material changes.The stress of the DCB specimen at 21° is less than that of 0°.According to the analysis, as shown in Fig. 8, the critical load value of the 0 ° unidirectional layered DCB specimen of the composite material is around 75N.And the critical load values of DCB samples with 0°, 21°, and 30° unidirectional laminates gradually decrease, which is consistent with the above results.

Conclusion
In DCB tests, as the crack gradually expands, the fibers on both sides of the crack are pulled out or broken from the matrix, which gradually increases the apparent fracture toughness value.Once the number of bridging fibers corresponding to the unit crack area is fixed during the crack propagation process, it enters a stable state of crack propagation.The data shows that the coefficient of variation of the propagation GIC is smaller than the initial one.Therefore, the propagation GIC of interlayer fracture toughness is more suitable as an indicator to characterize the fracture level of materials.The propagation GIC of T and M samples made of the same resin were 645.2 and 272.2 J/m2, respectively.
The results indicate that under the same resin matrix, the interlayer fracture toughness of high-strength fiber composite is much higher than that of high modulus fibers, which is related to the high surface chemical activity of high-strength fiber monofilament, indicating that the resin has better compatibility with high-strength fibers.This article uses the cohesive zone model to simulate fracture behavior.
After establishing the basic model, it helps to analyze the stress-strain changes of the layered structure under fracture behavior more visually and quantitatively.At the same time, the testing of fracture behavior under different layer designs can be achieved by modifying corresponding parameters, which not only solves the difficult situation of preparing certain samples, but also predicts whether the new layer design meets the usage requirements.The fracture behavior of unidirectional laminated structures with different angles was analyzed using this model.From Fig. 7, it can be seen that the stress state of the DCB sample with a total of 10 layers is symmetrical in the middle layer.In the distribution of 5 layers on one side, the stress values first decrease and then increase in the direction from the inside to the outside.In addition, when the ply angle changes, the crack will expand asymmetrically and reduce the toughness level of the material.

Figure 1 .
Figure 1.Test curve of T sample, a) load displacement curve b) curve of parameter △ c) trend of large deformation effect coefficient d)delamination Resistance Curve.

Figure 3 .
Figure 3. Initial GIC and propagation GIC of different samples.

Figure 4 .
Figure 4. Variation coefficients of initial GIC and propagation GIC for different samples.

Figure 5 .
Figure 5. Scanning electron microscopy photos and carbon content of fibers corresponding to samples T and M.

Figure 2 .
Figure 2. Test curve of M sample, a) load displacement curve b) curve of parameter △ c) trend of large deformation effect coefficient d)delamination Resistance Curve.

Figure 7 .
Figure 7.The stress of each layer of the I-type crack propagation of the DCB specimen (ply1-5 from the inner layer to the outer layer).

Figure 8 .
Figure 8. Critical load diagram of DCB specimens with different layup angles.

10th
Global Conference on Polymer and Composite Materials (PCM 2023) Journal of Physics: Conference Series 2652 (2023) 012007

Table 1 .
Material parameters used for finite element analysis