Damage mechanisms of bismaleimide matrix composites under transverse loading via quasi-static indentation

With the application of carbon fiber reinforced plastics (CFRPs), the damage behaviors and mechanisms are desirable to understand. In this work, the Bismaleimide (BMI) matrix composites were employed to study the damage mechanism under transverse loading through quasi-static indentation, where optical microscopy, ultrasonic C-scan, and scanning electron microscope were subjected to examine the damaged regions. The results show that cracks first take place in a resin-rich interlaminar region before the loading reached to a threshold value. Then, the cracks would develop into intralaminar cracks in the fiber bundle region consisting of the shear and bending cracks. Subsequently, the cracks randomly extend to adjacent plies and result in delamination. Finally, the back surface of composites presents a remarkable ply splitting and fiber breakage under increasing loading. Furthermore, conical-shaped indentation patterns in cross-sectional and the undamaged zone under the indenter suggest the BMI matrix composites possess potential applications in engineering materials with a superior stress-releasing structure.


Introduction
Carbon fiber reinforced plastics (CFRPs) have attracted increasing research interest over the past decades because of their superior properties [1][2][3]. Compared with traditional materials, CFRPs present great advantages in terms of low density, cost-effectiveness, good chemical resistance, and high specific strength and stiffness, which endows CFRPs as an ideal candidate in various fields including civil and military applications, such as automobile, aviation, or aerospace [4][5][6]. However, there are extensive micro-damages in CFRP composite laminate under low energy impact loading (e.g., dropping tool and runway debris), which are barely visible impact damage, and the mechanical properties as well as durability of the composite laminates are eventually affected [7][8][9]. Therefore, the understandings of the damage resistance of CFRPs are of great importance, especially the resistance to damages originating under different loading/force circumstances [10].
As reported, serials classical models, including intralaminar crack (transverse matrix cracking and fiber/matrixdebonding), interlaminar fracture (delamination), ply shear-out, and fiber fracture, were adopted to describe the damage caused by static or low-velocity impact loading [11,12]. Among these damage models, only the fiber fracture model is typically determined by the fiber failure strain, other models exhibit a strong dependence on matrix properties and the fiber-matrix interfacial interaction [13][14][15]. Nevertheless, damages often arise from a combination of different failure modes in real cases, which makes the analysis of inter-laminar toughening mechanisms much more complicated. For example, Kuboki et al. [16] demonstrated that delamination was caused by shear cracks rather than bending cracks by identifying the damage evolvement of transversely loading cross-ply glass fiber-reinforced polymers (GFRP). While Liu et al. [17,18] reported that mode I (tension mode) delamination was formed by bending cracks, and mode II (pure in-plane shear mode), as well as mode III (combined in-plane and out-of-plane shear mode), delaminations were initiated by shear cracks [14]. Additionally, there are also developments in damage mode. For instance, Cantwell et al. [19] suggested pine tree and reversed pine tree damage patterns following studies on the impact-induced cracks of both thick and thin composites laminate. De Freitas et al. [8] investigated the impact behaviors of CFRP composed of two sequentially stacked different epoxy resin/carbon fiber composites. The impact resulted in vertical matrix cracks with a pine tree damage pattern within the bottom layer.
BMI, one of the high-performance thermoset resins, is a type of polyimide synthesized from the reaction of maleic anhydride and a diamine. BMI exhibits high-temperature stability, which fills the gap between epoxy and polyimide. In addition, compared to traditional epoxy systems, easy processing characteristics, and excellent chemical and corrosion resistance make BMI wildly employed as structural matrix resins in various applications, especially in aerospace [20,21]. However, the brittleness of the traditional BMI has extremely limited its application as high-performance engineering materials [22]. Therefore, a series of methods for BMI modification have been developed, such as molecular chain modification [23][24][25] and elastomeric filling [26,27]. For instance, chain-extended BMI was developed to decrease the crosslink density by larger amounts of units for improvement of toughness [23,24,28]. Cheng et al. [26] employed a thermoplastic PAEK as a toughener to increase the interlaminar fracture toughness of BMI matrix composites. To this end, the toughened BMI has been extensively utilized to fabricate engineering composites [22,29]. However, the damage evolution mechanism of the BMI matrix composite is essentially not clear.
Herein, a toughening polymer with the RTMable BMI resin was employed to fabricate the CFRPs composites by the Resin transfer molding (RTM) method, and a series of characterization techniques, such as the optical microscopy, ultrasonic C-scan, and scanning electron microscope (SEM), were utilized to monitor the microstructure of damaged regions under quasi-static indentation. Based on the discussion of the process of quasi-static indentation testing and the related microstructures, the damage evolvement of BMI matrix composite under transverse loading can be divided into three stages. First, cracks took place in a resin-rich interlaminar region and then developed into the fiber bundle intralaminar region. Subsequently, the cracks randomly extended to adjacent plies and resulted in delamination. Finally, the back surface of composites presented remarkable ply splitting and fiber breakage under increasing loading.  [29,30].
The toughing polymer was an amorphous high-performance engineering thermoplastic polyethersulfone (PES) (VW-10200RFP, Solvay Specialty Polymers). The toughening polymer applied on ES TM fabric has an areal density of 35 g/m 2 .

Fabrication of laminates
The CFRP composites were fabricated by the RTM method with a quasi-isotropic stacking sequence [+45/0/−45/90] 4s . The thickness and fiber volume of the obtained CFRP composites were controlled at 5.3 mm and 55 ± 2 vol%, respectively.
The proposed temperature and time are programmed as in Figure 1. First, the ES TM fabrics were placed in an RTM mold. Then, the BMI-6421 was filled in the RTM mold to impregnate the porous ES TM fabrics at 115°C under a pressure of 0.2 MPa. The mold temperature was raised at a rate of 3°C/min to the three-step curing temperatures (150, 160, and 180°C), followed by a post-curing step (200°C, 8 h). Finally, the mold was cooled down to 60°C to take out the composite sample.

Quasi-static indentation experiment
The CFRPs composites were cut into 150 × 100 mm 2 specimens for Quasi-Static indentation. All the quasi-static indentation tests were performed by an Instron 4400R testing machine (Instron, USA) at a constant indenter nose and support fixture displacement rate of 0.5 mm/min (ASTM D7136).
As reported [31], quasi-static indentation testing was used to measure the BMI matrix composite's impact resistance at low velocity. And the quasi-static indentation testing was correlated successfully with the low-velocity impact of BMI matrix composites in terms of delamination parameters. Hence, it is convinced that the principles of damage development suggested here can also applied to the BMI matrix composite during low-velocity impact.

Microstructure characterization
According to the Quasi-static indentation, loading levels with significance were selected for later studies: (a) 5.5 kN, the load-increasing process before damages occurred, (b) 6.2 kN, a sudden drop of loading accompanied with sharp noise, (c) 8.2 kN, the propagation of delamination, (d) 13.3 kN, the initial breaks of fiber, (e) 14.4 kN, the maximum loading, and (f) 9.3 kN, a plateau region for penetration failure, respectively.
The ultrasonic C-scan system (SDI-5420 Delta X, Structural Diagnostics Inc., CA) was used to identify the areas of damage for all specimens. Specimen-sustained quasi-Static indentation experiments with different loading levels were collected and sectioned into slices in the 0-direction close to the contact point of the indentation.
The sliced specimens were first mounted in epoxy resin and then grounded by sandpaper with increasing mesh numbers. Subsequently, the cross-section was polished with the diamond polishing agent for microstructure characterization.
A fluorescent penetrant dye (Rhodamine B, by Tianjin BASF Chemical Co., Ltd.) was added to the mounting resin to enhance the contrast between the cracks and the surrounding matrix. An optical microscope (Leica DM750 fluorescence microscope, Leica microsystems co., Ltd) [32] was adopted to characterize the cracking patterns under polarized light. In this study, the Rhodamine-B-stained epoxy and BMI presented different colors, i.e., red and blue-green, respectively, under ultraviolet light.
An SEM (Hitachi S-3000N) was used to characterize the morphology of fracture induced by indentation tests. Cross-sectional samples were cut and polished from the indentation-tested specimens. The fractured surface and cross-section were thoroughly etched with methylene chloride to increase the contrast.

Damage process investigation via indentation tests
Damage analysis was performed by a continuous indentation test, as shown in Figure 2, the data points (a-f, 5.5, 6.2, 8.2, 13.3, 14.4, and 9.3 kN, respectively), corresponding to (a) load-increasing process before damages occurred, (b) a sudden loading drop accompanied by a sharp noise, (c) the propagation of delamination, (d) the initial breaks of fiber, (e) the maximum loading, and (f) a plateau region corresponding to penetration failure, respectively. The indentation test was paused at each selected loading level, where specimens were removed for visual and ultrasonic C-scan examinations. As shown in Figure 3, the optical photographs of the front surface (contact with the indenter) and the back surface, as well as the ultrasonic C-scan images of the specimens under different loading levels, are presented. During the quasi-static indentation test, the indentation becomes more pronounced (in depth and size) with increasing loading. First, there is a significant loading decrease around 6.2 kN (point b) in Figure 2, where a small indentation on the top surface and short fiber splitting on the back represent the onset of delamination. As the loading increase to 8.12 kN (point c), a tear emerges on the top surface which is perpendicular to graphite fibers. In addition, there are more tears occur on the back surface, which ultimately leads to ply splitting with continuously increased loading. Furthermore, combined with the C-scan images under different loading, where the shape of the delamination area would turn from generally circular to diamond with increased loading. The evolution in damage area size monitored via ultrasonic C-scan further evidence the damage behavior observed from optical photography observations. Figure 4a shows the optical micrograph of the crosssection for Point a (in Figure 2), where the black shading and blue-green areas stand for the fibers and matrix, respectively, while the red region close to edge of the image is attributed to the mounting epoxy resin. It is found that fiber stacks in the 90°direction formed a horizontally positioned elliptical-like shaped area. The micrograph exhibits no epoxy resin (red) within the BMI matrix (blue-green), indicating no damage until the corresponding loading level. A complete wet out of fabric architecture by resin infusion and impregnation occurs. In addition, the BMI matrix composite was fabricated by the RTM process during which resin was injected into ordered dry fabric layers in close contact with varying degrees in a mold. The neighboring layers were nesting or mechanically interlocked at different locations owing to the compact structure. Consequently, composite structure within the specimen may vary due to differences in the orientations of local fabrics, and the sizes of resin-rich zones differ not only between layers but also different regions within the same layer [33]. Figure 4b is the micrograph of the cross-section at point b (in Figure 2) corresponding to the onset of delamination. Here, the red area is clearly observed inside the BMI matrix, which is the representation of the cracks. The damage is identified as a small indentation, matrix cracks, and delamination damage. The failure mode is close to the pattern suggested by Freitas et al. [8], where a pine-tree-patterned damage with the bottom layer forms cracks due to the bending of the vertical matrix.
This conical shape of the damaged area in the direction of thickness increases from the impact surface to the backside with the formation of multiple parallel cracks. Transverse shear cracks, owing to shear failure, appear initially in the −45°layer in the top half of the sample and in the +45°layer in the bottom half and then propagated through the 90°layer from the top down. Coincident with this shear crack extension into the 90°layer, longitudinal cracks, that is delamination, grew mostly in the 45°layer and lastly arrested at the 0°layer interfaces. These transverse shear cracks inclined about ±45°from the vertical position, and connected with the longitudinal cracks (delamination). It is worth noting that many matrix cracks existed in the termination spacing of a crack with the indication of the large deformation of the matrix resin ahead of the crack tip. Additionally, an approximately undamaged zone with a cone shape is visible inside the conical shape under the indentation point as well. Previous works also have reported this phenomenon [34][35][36][37], which is caused by the low-stress field surrounding the area where the matrix does not reach the delamination required failure point. However, the matrix cracks would generate when the laminate suffered tensile-bending stress, especially below the undamaged zone.
As the loading increased to point c (in Figure 2), more enhanced shear cracks near the edge of the undamaged zone under the indentation point are observed, as shown in Figure 4c, resulting in a change in the shape of the undamaged conical zone. Meanwhile, the delamination almost solely propagates within the 0°ply mostly on the bottom half of the sample with a large increase in the extent. The largest delamination occurs in the lowest 0°p ly. In addition, bending cracks were developed within a limit while no delamination in the central zone under the indentation point. Therefore, the delamination and shear cracks are the major failure mode at point c.
After continuously increasing the loading to point d (in Figure 2) where a slight decrease of the loading occurred, as shown in Figure 4d, there are remarkably increased damage areas containing shear cracks and delamination. The permanent indentation damage becomes more severe whereas the delamination on the 0°ply opens further. The undamaged zone under the indentation point still exists but with its size decreasing. Meanwhile, a new large delamination running through all the lowest 0°layer is formed in the bottom of the undamaged conical zone, which may be induced by the bending cracks. Due to tensile-bending stresses, a new fiber breakage was observed in the lowermost 45°ply of the specimen, which is consistent with the optical photography where a remarkable fiber splitting is observed. The delamination and shear cracks are suggested as dominant-failure modes of laminate.
The ply breakage occurred when the increase of loading to the maximum value (point e in Figure 2), where almost all 0°layers were under the indentation point at the bottom of the sample break (Figure 4e). Additionally, the serious shear cracks developed far from the central line of the indentation while tensile cracks developed close to it. And an almost undamaged zone below the indentation point still exists but is limited to the central zone in the top half of the specimen. In this zone, there are several small matrix cracks, with little signs of fiber breakage or delamination. As a result, delamination and fiber failure are the biggest failure modes.
After the maximum value of the loading, penetration failure occurred and the corresponding loading began to decrease slowly. Increasing the displacement of the indenter led to a larger and increased frequency of delamination along with an increase in depth of fiber failure beginning at the bottom half of the laminate. Figure 4f also shows that delamination cracks appear in a small localized cone under the indenter point, which is likely to be initialized from the concentration of stress as well as the contact indentation effect. Because of the complexity of the stress profile surrounding the contact indentation, the excessive matrix cracking would not follow the pattern and direction, which is different from the formation of the bending and shearing cracks. Ply splitting becomes more severe, which is in accordance with the result observed in optical photography. Figure 5 shows the fracture surface of the BMI matrix composite. The BMI matrix laminate presented more resin-rich zones in the intralaminar, inter-fiber-bundle regions, and the interlaminar regions, as indicated in Figure 4d. The nodular structure of BMI in the PES-rich matrix was observed at the fractured surface of the BMI matrix composite, where the BMI nodule exhibited a circular shape with a size of nearly 2 μm. Moreover, there was a large size difference in various nodular structures in the interlaminar regions, owing to the discontinuous distribution of the PES particle. Here, BMIs acted as the sites of high-stress concentration, which homogeneously form the crazes/micro-cracks around microscopic and submicroscopic. These crazes/micro-cracks were frequently difficult to coalesce into a true crack since they were stabilized by plastically deformed matrix resin.

Process of damage development
Crazes/micro-cracks may initiate tears when stresses were well beyond the resin bulk shear yield strength. Then, the non-continuous cracks (intralaminar cracks) propagated along the surface of the individual bundles. These intralaminar cracks could release the residual stresses developed within individual fiber bundles owing to a combination of cure shrinkage and thermal expansion mismatch between the carbon fibers and the BMI resin, as well as the stress concentration due to the transverse load. The distinguishing feature of intralaminar cracks is that they propagate along the bundle and exist within a fiber bundle. There were three types of intralaminar cracks observed in the BMI matrix composite, as shown in Figure 6. Type I cracks, namely bending cracks, was perpendicular to the bundle axis owing to tensile/bending stress, and type II cracks, namely shear cracks, were inclined to the bundle axis due  to shear stress, whereas type III cracks run parallel to the bundle axis, often being formed at the interface between two bundles in close contact. Type III cracks were also seldom observed lonely, existing rather accompanied by Type II cracks. According to Karbhari and Rydin [33], Type II cracks were the result of the relative motion of adjacent reinforcing layers under transverse load.
The growth of intralaminar cracks could be associated with the deformation of the fiber bundle itself. As mentioned, the fiber bundle is compacted together tightly in RTMable composite, which can be regarded as a composite with a very high fiber volume fraction (about 80% [3]) [33]. However, the nominal fiber volume fraction in the BMI matrix composite is 57%. Under stress, the loading can transfer through the plastic deformation of the corresponding small volume of the matrix in a bundle as well as the elastic deformation of the individual fibrils. The intralaminar cracks developed when exceeding the failure strain. For the BMI matrix composites, the bending cracks occur on the bottom half of a conical damage zone while shear cracks mainly occur on the inside edge of one.
Delamination or interlaminar cracking is shown in the schematic (Figure 7) and appears as a result of crack propagation between layers of reinforcing fabric. Depending on the resin-rich regions between the fiber bundles, there are four modes of onset of delamination identified in Figure 7. Type a delamination appears to be initiated from an intralaminar crack and propagates along the interface, namely micro-delamination. The onset of Type b delamination is similar to the formation of Type a delamination but propagates on both sides of intralaminar cracks. In Type c delamination, the intralaminar crack initiates the microdelamination separately and eventually joins together. However, in Type d delamination, intralaminar cracks coalesce into a main crack in the bundle and then result in delamination. The degree of intra-or interlaminar crack is related to the stress concentration, which depends on the applied load and local fabric structure. The current study suggests that shear cracks are only responsible for the delamination at lower loading whereas bending cracks-resulted delamination happens in the lower half of the cross-section at higher loading. The shear cracks-resulted delamination could happen independently, with no relationship to the bending cracks-induced delamination, which is consistent with that of Kuboki et al. [35]. In addition, it should be clarified that delamination can appear to mainly grow along 90°ply at lower loading and then transfer to propagate  downward through 0°ply with increasing loading. The characteristic of craze, intralaminar cracks, as well as delamination cracks are shown schematically in Figure 8. The fiber breakage occurs on the reverse side of the laminate with a further increase in the loading up to the maximum value, which led to the ultimate failure of the composite.
It is worth noting that a conical undamaged zone in the thickness direction under the indentation point existed until the penetration failure occurred. The size of the undamaged zone decreased with the increasing loading. As expected, the BMI matrix composite shows phase separation and inversion microstructure, which can dissipate the impact energy effectively and then release the stress concentration, eventually leading to no delamination at lowstress field under the indenter.

Conclusions
In conclusion, the progression of damage in BMI matrix RTMable composites was studied by a combination of the quasi-static indentation test and microstructure characterization. The demonstration of C-scan and optical micrographs under different loading revealed the evolution of the damage. According to the damage behavior, the cracks propagated from the resin-rich interlaminar region to the fiber bundle intralaminar region and eventually resulted in delamination and further fiber breakage. Moreover, the detailed description of the damage process is demonstrated as follows: (1) First, cracks took place in a resin-rich interlaminar region and then developed into the fiber bundle intralaminar region. (2) Second, the cracks randomly extended to adjacent plies due to the shear and bending cracks and resulted in delamination. (3) Finally, the back surface of composites presented remarkable ply splitting and fiber breakage with increasing loading.
Furthermore, the BMI matrix composite exhibited an excellent energy absorption capability as the existence of a conical undamaged zone under the indentation point even when the penetration failure happened, which endows a potential application in engineering materials.