Damage analysis of carbon fabric-reinforced composites under dynamic bending

2 1CESAT, Islamabad, Pakistan,

2Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Leicestershire, LE11 3TU, UK

*Corresponding author: uhimayat@gmail.com

Abstract— Fabric-reinforced polymer composites used in various applications can be subjected to dynamic loading such as impacts causing bending deformations. Under such loading scenarios, composite structures demonstrate multiple modes of damage and fracture if compared with more traditional, macroscopically homogeneous, structural materials such as metals and alloys. Among damage and fracture modes are fibre breaking, transverse matrix cracking, debonding between fibres and matrix and delamination. Damage evolution affects both their in-service properties and performance that can deteriorate with time. These failure modes need adequate means of analysis and investigation, the major approaches being experimental characterization and numerical simulations.

This study deals with analysis of damage in carbon fabric-reinforced polymers (CFRP) under dynamic bending. The properties of, and damage evolution in, the composite laminates were analysed using a combination of mechanical testing and microstructural damage analysis using optical microscopy. Experimental tests are carried out to characterize the behavior of CFRP composites under large-deflection dynamic bending in Izod type impact tests using Resil Impactor. A series of impact tests is carried out at various energy levels to obtain the force-time diagrams and absorbed energy profiles for laminates. Three-dimensional finite element (FE) models are implemented in the commercial code Abaqus/Explicit to study the deformation behavior and damage in composites for cases of dynamic bending. In these models, multiple layers of bilinear cohesive-zone elements are placed at the damage locations identified in microscopic study. Initiation and progression of inter-ply delamination at the impact and bending locations is studied numerically by employing cohesive-zone elements between each ply of the composite. Stress-based criteria are used for damage initiation, and fracture-mechanics techniques to capture its progression in composite laminates. The developed numerical models are capable to simulate these damage mechanisms as well as their subsequent interaction observed in tests and microscopy. Simulations results showed a good agreement when compared to experimentally obtained transient response of the woven laminates.

I. INTRODUCTION

Fibre-reinforced composites such as carbon fabric-reinforced polymers (CFRPs) are widely used in aerospace, automotive and construction structures due to their high specific strength and stiffness. Fabric-reinforced composite laminates offer a number of attractive mechanical properties compared to their unidirectional-

tape counterparts such as good resistance to fracture and transverse rupture due to weaving resistance and high impact strength [1]. These properties have attracted the sports industry to incorporate woven CFRP laminates in the design of sports products that could be subjected to large-deflection bending and multiple impacts in service conditions. Such types of quasi-static and dynamic loads generate high local stresses and strains leading to complex damage modes due to heterogeneity and anisotropy of composite laminates. Composite structures suffer more damage as a result of impact than similar metallic structures. The damage mechanisms typically caused by out-of-plane impact loads in laminates are matrix cracking, fibre breakage and delamination at interfaces within the composite structure [2]. Impact damage and, in particular, delamination occurring at low-velocity impact cause a significant decrease in the material’s in-plane compressive strength and stiffness. Such internal damage mechanisms that often cannot be detected by visual inspection degrade the load-carrying capacity of the structures. Therefore, it is important to study the damage suffered by the composites under impact loading conditions.

The low-velocity impact response of fabric-reinforced composites has been extensively treated in the literature employing experimental studies, analytical formulations and numerical simulations. Abrate [3] analysed dynamics of impacts using an analytical approach based on energy-balance and spring-mass models. Naik et al. [4] studied the behaviour of woven-fabric composite plates under transverse low-velocity impact with an analytical model based on a modified Hertz law and a 3D numerical model. Johnson et al. [5] presented a material failure model for composites with fabric reinforcement under impact loading, which included both intra-ply damage and plasticity based on continuum damage mechanics approach, and inter-ply delamination. Iannucci and Willows [6] presented an energy-based damage mechanics model and interface modelling technique for woven carbon composites under high-strain dynamic loading employing an explicit FE code. Reyes and Sharma [7] studied experimentally and numerically a low-velocity impact damage behaviour of woven GFRP laminates under various levels of impact energies. However, majority of these studies are dedicated to the impact behaviour of composites tested with instrumented drop-weight impact towers, which usually caused localised damage such as penetration and perforation in impacted laminates. A large-deflection dynamic bending behaviour of laminated composites caused by a pendulum-type impactor is rarely investigated. In this connection, the

Proceedings of 2014 11th International Bhurban Conference on Applied Sciences & Technology (IBCAST)Islamabad, Pakistan, 14th – 18th January, 2014 5

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authors studied earlier large-deflection behaviour of woven laminates under quasi-static bending and tensile loads [8-10]. Investigation of large-deflection impact bending-behaviour of CFRP composites has received little attention to date. In this regard few studies can be found (e.g. Silberschmidt et al. [11] and Casas-Rodriguez et al.[12,13]) where an instrumented impactor was used to study damage in adhesively bonded CFRP joints under repeated impacts; the loading mode was tensile there. Damage initiation and growth under large-deflection dynamic bending was also investigated experimentally and numerically in [14-16].

In the present work, a large-deflection bending behaviour of woven-fabric CFRP laminates subjected to impact loads is studied. Flexural impact tests were carried out using a pendulum type impact tester at various energy levels. The type and location of damage were investigated with optical microscopy. Three-dimensional finite-element models were developed in Abaqus/Explicit forboth damaged and fractured specimens. The obtained modelling results have good agreement with our experimental data.

II. 2. EXPERIMENTAL METHODS

A. Experimental testingFabric-reinforced CFRP specimens were prepared from

laminates of woven fabric made of carbon fibres reinforcing thermoplastic polyurethane (TPU) polymer matrix. The fabric was produced from 0°/90° prepregs in the form of four plies designated as [0°,90°]2s, where 0° and 90° represent yarns in the warp and weft directions, respectively. The woven laminate had a 2/2 twill weaving pattern with a fibre volume fraction of 45%; the fabric had the same number of yarns in the warp and weft directions. Un-notched rectangular specimens of 40 mm length, 25 mm width and 1.0 mm thickness (each laminate had four layers of 0.25 mm thickness) were prepared.

Dynamic impact tests were carried out on an instrumented pendulum-type CEAST Resil impactor according to ISO 180 standard. In the impact tests, the bottom of the specimen was fixed firmly in the machine vice as a cantilever beam as shown in Fig. 1. The upper 30 mm of the specimen was struck by the striking nose of the pendulum hammer with a controlled level of energy, resulting in dynamic large-deflection bending. The

Figure 1. Resil impact test set-up

distance between the fixed support and the line of contact of the hammer’s striking nose was kept at 22 mm according to the standard. In this work, a calibrated impact hammer with a mass of 0.6746 kg and 0.3268 m length was used. The hammer can generate an impact of maximum energy of 2 J at impact velocity of 3.46 m/s corresponding to the initial angle of 150° to the striking position. The magnitude of initial impact energy and velocity can be varied by changing the initial angle of the hammer. Impact tests were performed on CFRP specimens at energy levels of 0.1 J - 0.6 J to determine the fracture energy of the specimens. It was found that the specimen fractured at 0.6 J corresponding to the initial angle of 64°. A piezoelectric force transducer was fixed rigidly to the hammer striking nose to capture the impact force signal. After the pendulum hammer is released from the pre-defined initial angle, the impact with the specimen generates a change in electrical resistance of the piezoelectric sensor that is captured by the data -acquisition system – DAS 8000 – connected to the Resil impactor. The signal is registered with a pre-defined sampling frequency of 833 kHz, with up to 8000 data points recorded per impact test. In order to decrease the data noise a 1 kHz filter was used in our tests. Typical records of force vs. time for CFRP specimens at various energy levels are presented in Fig. 2. From these plots, it is clear that the slope and the peak load of the force-time curves increased with increase in the impact energy. At low energy levels, a linear increase of force with time is observed at the start of loading, representing a purely elastic undamaged response of the specimen. The loading and unloading portions of the force-time curves have a nearly symmetric parabolic shape up to 0.4 J (Fig. 2), indicating that very little damage has occurred. As the impact energy was increased to 0.5 J, fluctuations in the force-time response could be observed before the peak load and this response became unsymmetrical with regard to its peak. Such oscillations associated with load drops are caused by initiation of damage such as delamination at low incident energy with an associated reduction in the specimen’s stiffness [17]. As the impact energy was increased to 0.6 J, the fabric fracture occurred. The fabric rupture is represented by a quick drop in impact force implying a momentary loss of contact between the hammer and specimen due to tensile fracture of fibres at the impacted side of the specimen.

Figure 2. Experimental response of CFRP laminates at various impact energies

Proceedings of 2014 11th International Bhurban Conference on Applied Sciences & Technology (IBCAST)Islamabad, Pakistan, 14th – 18th January, 2014

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B. Microscopic damage analysis Microscopic analysis of the composite specimens is a

suitable technique for evaluation of damage in woven-fabric laminates. In order to visualize the type and location of damage, microscopic analysis allows for the study of the comprehensive damage behaviour of the composite specimen. This technique was also employed in [15,18] for damage characterisation of woven CFRP laminates. In this work, OLYMPUS BX-60M microscope was used to capture the images of the through-thickness side edge of the un-fractured specimen to observe the barely visible damage on the specimen surface. Image-Pro Plus software was used for the analysis of the microscopic images that were captured.

Inter-ply damage developed in the large-deflection dynamic bending is presented in micrograph of Fig. 3. The main mode of damage is delamination along the specimen’s longitudinal axis that was expected due to high in-plane shear stresses. At this stage of loading, weft yarn cracking (intra-ply delamination) and transverse matrix cracking can also be observed in the micrograph shown in Fig. 4. Here, it can be observed that damage initiation occurred at the weft yarn edge (crimp location) and then propagated into the weft yarn as well as inter-ply transverse matrix cracking. Interaction of Intra-ply weft yarn cracking and inter-ply transverse matrix cracking also occurred (Fig. 4). Intra-ply delamination in the weft yarn can be clearly seen in the microscopic image of Fig.5. Some of these damage modes, e. g. delamination, willbe incorporated in our FE models.

Figure 3. Inter-ply delamination in CFRP laminate

III. NUMERICAL MODELLING

A. Finite-element model Two Finite-element models – Models A and B – were

developed in the ABAQUS/Explicit representing the impact tests on, respectively, damaged (0.5 J) and fractured (0.6 J) 40 mm long, 25 mm wide and 1 mm thick CFRP laminates. In the damaged specimen (Model A) tested at 0.5 J impact energy, cohesive-zone elements were introduced at the resin-rich interfaces between the laminate’s plies. Hence, Model A consisted of three longitudinal cohesive layers - one in front of the beam’s

neutral plane (NP), the second coinciding with it, and the third on the back of the NP to simulate multiple delamination scenarios. Model B of the fractured specimen at 0.6 J contained of the same three interface layers with one additional through-thickness transverse cohesive layer at the specimen fracture location to model both the inter-ply and intra-ply damage and theirsubsequent interaction. The cohesive layers in Models A and B are referred as: FCL - front cohesive layer in front of the NP; MCL - mid cohesive layer coinciding with the NP; BCL - back cohesive layer to the back of the NP; CCL - crack cohesive layer which is the through-thickness transverse layer. These cohesive layers were included in the model since the location of damage initiation is apriori known from our microscopy analysis. All composite plies were assigned elastic flexural properties listed in Table 1. The hammer was assigned steel properties with the Young’s modulus of 200 GPa, Poisson’s ration 0.3 and density 8100 kg/m3.

Figure 4. Intra-ply tow delamination in weft yarn and transverse matrix cracking in CFRP laminate

Figure 5. Intra-ply delamination in weft tow in CFRP laminate

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Figure 6. Impact-test FE model: (a) 3D geometry with boundary conditions; (b) hammer-specimen contact interaction; (c) mesh of specimen in Models A and B (specimen is shown larger)

The modelled geometry of Models A and B is shown in Fig. 6 along with mesh and boundary conditions. The hammer was discretised with 4-noded linear tetrahedron C3D4 elements, whereas the specimen was meshed with 8-noded linear brick C3D8R elements using a structured meshing technique. These reduced-integration elements are capable of controlling hourglass and eliminating shear locking in bending-dominated problems. Each ply of the laminate was modelled with a single element through its thickness. Elastic as well as damage properties of inter-ply cohesive layers presented in Table 1 can be found in the previous work of the authors [8]. The surface-to-surface kinematic contact algorithm with finite sliding available in ABAQUS/Explicit was used to simulate contact between the hammer’s striking nose and the laminate’s surface. The impactor’s striking surface and specimen’s surfaces referred as S1 and S2 in Fig.s 5b and 5c, respectively, were defined as master and slave surfaces, in all FE models. A node at the pivot point of the hammer along the axis of rotation was created and then tied with the hammer’s cylindrical pivot surface through tie constraints. All translations and rotations of the pivot node were constrained except rotation about z-axis to simulate the hammer’s centre of rotation as shown in Fig. 5a. In the FE models, the initial position of the hammer’s striking nose was just in contact with the specimen to avoid the computational cost of bringing the hammer from its inclined position in tests. Initial angular velocities of 5.33 rad/s and 5.81 rad/s were applied to the whole hammer, corresponding to the impact energies of 05 J and 0.6 J in Models A and B, respectively. All the degrees of freedom

of the specimen’s bottom were constrained to replicate its boundary conditions in the test fixture.

B. Damage modelling Both the inter-ply and intra-ply damage in FE models

were simulated using cohesive-zone elements (CZEs). CZEs have the ability to capture the onset and propagation of delamination [19,8,20]. The cohesive behaviour assumes that failure of elements is characterised by progressive degradation of the material stiffness, which is driven by a damage process. Inter-ply damage modes in composite laminates initiate and propagate under the combined influence of normal and shear stresses. The nominal quadratic stress criterion was used for damage initiation. Damage propagation was based on the criterion proposed by Benzeggah and Kenane [21] :

(1)

where is the work by the interface tractions; is the fraction of cohesive energy dissipated by shear tractions; is the work done by the shear components of interface tractions; and are critical energy release rates in modes I and II, respectively, and η is the material mode-mixity parameter. The damage-initiation and fracture-toughness parameters presented in Table 1 were used in FE Model A. Apart from inter-ply damage modeling; CZEs were also used to model intra-ply damage mechanisms such as ply fracture in composite laminates. The initiation of intra-ply fabric damage was linked to the average ultimate flexural strength of 720 MPa in both warp and weft directions as observed in

Proceedings of 2014 11th International Bhurban Conference on Applied Sciences & Technology (IBCAST)Islamabad, Pakistan, 14th – 18th January, 2014

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TABLE I. MATERIAL PROPERTIES OF CFRP CONSIDERED IN FEMODEL

Elastic properties Inter-ply strength and toughnessE11 = E22 (GPa) E33 (GPa) G12 (GPa) G13 = G23 (GPa) ν12v13 = v23

44.78.04.4

3.00.050.3

σI0 (MPa) σII0 (MPa)GIc (J/m2) GIIc (J/m2)

1226

8001750

bending tests. Intra-ply fracture evolution was based on fabric fracture energy

y of 40 kJ/m2 in both warp and

weft directions as reported in [6] for a similar carbon fabric. Cohesive elements of size 0.3 mm x 0.3 mm with thickness of 10 μm were defined for computationally effective simulations of damage in our numerical models. Further details of the damage modeling approach can be seen in the author’s previous work [14,22].

IV. RESULTS AND DISCUSSION

A. Response of damaged specimens Results of experimental tests and numerical simulations

for the large-deflection dynamic bending behaviour of woven CFRP laminates are presented in this section. The load-time response calculated with numerical Model A of woven CFRP is compared with the respective experimental curve of damaged specimen in Fig. 7. The load drops in the experimental force-time history designated as Fdi-Exp in the figure represent the damage initiation such as delamination at low incident energy with an associated loss in the laminate stiffness. It can be observed that the global response and the impact durations are reasonably well predicted for the damaged specimen. However, the numerical damage thresholds Fdi-FE, at which a significant change in the laminate stiffness is detected, are clearly under-predicted. It is argued that the underestimation of damage thresholds and peak forces may be due to the meso-level consideration of the plies in FE formulations. Since in experiments, the woven laminates absorb more energy due to the resin-rich pockets and the interlacing of fibres (tows) in two mutually perpendicular directions, and, thus, offer more resistance to damage initiation, which are not taken into account in the FE models.

Figure 7. Experimental and numerical (Model A) force-time diagrams for CFRP laminates at impact energy of 0.5 J showing response of

damaged specimen

Figure 8. Delamination evolution in Model A at impact energy of 0.5 J at 3ms (a), and 6 ms (b)

Figure 8 shows the predicted delamination areas at three interfaces – FCL, MCL and BCL – in simulations with Model A at two different time intervals: at 3 ms (near Fdi-FE in Fig. 7) and at 6 ms (near peak load in Fig. 7). In this analysis, delamination initiated first at the area of hammer impact and then at the bending location of the cantilever CFRP specimen, i.e. the edge of the fixture. Due to sharp corners of the hammer’s striker, the ends of its trace were more damaged. Beyond the time corresponding to Fdi-FE, a large and quick increase in the delamination areas was observed simultaneously in all the layers. Apparently, the largest area of delamination occurred at the mid-plane interface layer MCL due to a high level of through-thickness shear stress at the mid-plane of the laminate. Therefore, a Mode-II type delamination initiated in the specimen’s mid-region where the shear stress reached the interface shear strength and grew more in MCL than FCL and BCL at the impact location. Similarly, in bending, the upper (front) and lower (back) plies experienced tension and compression, respectively. Thus, the maximum bending stresses were foremost responsible for damage formation at FCL and BCL of the specimen, especially at the bending location.

B. Response of fractured specimens Fabric fracture occurred as the impact energy was

increased to 0.6 J in experimental tests. The predicted evolution of impact force in Model B is compared with experimental one at this level of energy in Fig. 9. Here, too, delamination initiation is presented by the load drops designated as Fdi-Exp and Fdi-FE for the experiments and numerical results, respectively. The experimental curve shows more fluctuations due to significant damage after the damage threshold Fdi-Exp at higher impact energy, followed by the ultimate ply fracture at 4.8 ms. The final fabric failure is presented by a sudden drop in contact force implying that the impactor has lost its contact with the specimen due to ply’ fracture on the tension side of the specimen. However, the load didn't drop to zero, because

Proceedings of 2014 11th International Bhurban Conference on Applied Sciences & Technology (IBCAST)Islamabad, Pakistan, 14th – 18th January, 2014

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Figure 9. Experimental and numerical (Model B) force-time diagrams for CFRP laminates at impact energy of 0.6 J showing response of

fractured specimen

in dynamic bending the distal plies in compression were not fractured causing a residual load of about 22 N. The numerical analysis showed the ply fracture at a higher load of 83 N and somewhat earlier - at 4.38 ms, which might be due to the low ply fracture initiation strength defined in Model B. Still, the simulation gave a good prediction of the important features of the failure process.

The sequence of inter-ply delamination, intra-ply fabric breakage and interaction of these two modes in Model B is illustrated in the deformed contour plots of damage shown in Fig. 10. Here, the interface layers subjected to tensile stress in bending are delaminated before the fabric breakage initiates, as represented by the laminate mid-region in Fig. 10a. The first ply’s fracture occurred at 4.38 ms as shown in Fig. 9b followed by fracture of the second ply in Fig. 10c at 4.62 ms. The third and fourth plies remained intact because of compressive stresses on back side of the specimen in the bending. As the load is increased, the ply elements move relative to each other as in Mode-II fracture along the delaminated interface layers as shown in Fig. 10d. There may be fibre kinking due to buckling instability in the back plies under compression; however, this behaviour is not studied in these meso-scale

models. After the ply fracture, almost every interface was damaged.

V. CONCLUSIONS

The dynamic behaviour of woven CFRP laminates under large-deflection bending was studied using experimental tests, microscopy analysis of damage and numerical simulations. Impact tests were carried to characterise the material’s dynamic behaviour till its ultimate fracture. Experimental results highlighted the energy absorbing capabilities of the CFRP composites.Microscopy analysis was carried out to observe different damage modes in the impacted specimens. Matrix cracking, inter-ply and intra-ply delamination were the prominent modes of damage observed. This analysis formed a basis for damage modelling of the tested composite laminates.

Meso-scale 3D FE models of CFRP laminates were developed to simulate some modes of damage observed in woven composites such as delamination and ply fracture in microscopy analysis. Simulations were performed to study the onset, progression and interaction of inter-ply and intra-ply damage processes under mixed-mode dynamic bending by employing multiple layers of CZEs in the FE models. The laminate’s transverse bending fracture was also modelled with CZEs instead of the traditional continuum damage mechanics approach. The experimental results for contact-force histories were compared with respective numerical predictions for several impact energies, which gave a good agreement. The numerical models demonstrated their capability to reproduce the damage sequence and pattern observed experimentally in composite laminates, although micro-cracking (e.g. matrix cracks) was not accounted for by the meso-scale modelling approach. The FE models helped to gain better understanding of the complex damage phenomena that occurred at various stages of impact bending. Based on the results of simulations of damaged and fractured CFRP specimens, it can be concluded that the models represented reasonably well the onset and propagation of delamination, coupling between delamination and ply cracking and the final fracture of the specimen as a result of fabric fracture in impact bending.

Figure 10. Evolution of inter-ply and intra-ply damage interaction in bending area in Model B at impact energy of 0.6 J at 4.2 ms (a), 4.38 ms (b), 4.62 ms (c) and 6.0 ms (d) (side view; scaling factor 0.5)

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