Progressive Failure Analysis of Carbon Fiber Reinforced Polymer Composite with a Circular Notch by Varying Fiber Orientation

Progressive failure for Carbon Fiber Reinforced Polymer (CFRP) was computationally studied and analyzed using Hashin’s failure criteria. It was an interactive failure criterion having 4 separate modes of failure. 8 layers of plies were oriented at specific stacking sequences to create different laminates with dimensions being specified using the ASTM D5766 standard. A total of 7 types of laminate were modeled and simulated to predict the failure for each type under tensile loading. A circular notch was added in the center for the concentration of stress. The damage to the fiber and matrix propagated and failed the structure. Contour plot analyses showed failure progression of fibers and matrix around the circular notch. Results show that matrix failure most predominant and critical type of failure for most laminates. From the stress vs. strain curves, it was seen that the [0/90]4 cross-ply laminate showed the highest open-hole tensile strength.


Introduction
The increased usage of composite structures worldwide has made it critical that the failure of composites be fully analyzed.The complex and multimodal failure mechanism for composites requires intricate and thorough analysis from damage initiation to complete structural failure.Failure can be as simple as the breakage of multiple fibers to multiplex failures.The initiation is internal in most cases.When the damage to the constituents goes beyond a certain extent, the failure becomes easily observable from the degradation of performance quality.Initiation of failure doesn't mean the structure has undergone complete failure.Rather an ultimate loading is required for complete failure.However, initiation of failure means the fiber or matrix has started to fail.Which is permanent in nature.The maximum stresscarrying capacity accepted in this study is the first ply failure.However, the ultimate failure of a fiberreinforced composite is used to determine the factor of safety.It is tough to determine accurately.Open hole testing (OHT) method was used which tests the strength of composites with a hole.Real-life structures are made by connecting panels of composite.One of the methods of doing that is using fasteners.Therefore, the presence of holes is very common in composite structures.Stress concentration occurs near the hole.It reduces the maximum stress-carrying capacity.Simple tensile properties in the ideal case don't apply to practical problems that are faced in real-life usage.
In this study, one of the most popular and widely used composites, Carbon Fiber Reinforced Polymer (CFRP) was modeled and studied in tensile testing conditions.Similar studies have been carried out by researchers to accurately estimate the properties of CFRP.Carbon fiber itself has a very high reinforcing quality in terms of tensile strength.O'Higgins et al. [1] conducted CFRP and GFRP OHT with nondestructive techniques which enabled them to observe the progression of damage.Quasi-isotropic and cross-ply laminate were tested.Test results showed matrix crack growth near the notch which then progressed to delamination failure.The cross-ply configuration showed matrix cracks in plies where the fiber is perpendicular to the loading direction.Higher levels of damage occurring reduced the stress concentration and resulted in larger stress values and energy absorbed to failure.Isna et al. [2] tested non-OHT and OHT specimens made of unidirectional CFRP and Lycal resin.Results suggest that while there is a reduction of tensile strength of the OHT sample, a similar percentage of increase of elastic modulus was seen for the OHT specimens.Ueda et al. [3] tested quasi-isotropic CFRP with a hole.The hole machining method was studied between punching and drilling.No substantial difference was found.Bakhshan et al. [4] studied the progressive failure of a plate that was made of unidirectional laminate.Yamada-sun's failure criteria were modified using Camanho's degradation model.It was validated with experimental results.Experimental results showed more load-carrying capacity while the computational models showed slight conservative results.Wisnom and Hallett [5] studied the effects of delamination of IM7/8552 CFRP in OHT tensile test conditions using different ply thicknesses and total thickness while retaining the same width-to-diameter ratio.Surface cracks on the matrix propagating to create delamination failure were observed and in contrast to conventionally accepted findings, they observed the failure strength to increase with the increase of hole size in one of the test cases.However, the study was limited to quasi-isotropic laminates only.Irhirane et al. [6] studied different failure criteria and their applicability on laminated beams.Failure load, mode, etc. were studied for a total of six failure criteria.Which included both interactive and non-interactive criteria.Specimens had 24 to 32 plies.It was found for symmetrical cross-ply, a little deviation for failure load was found.Angle ply composites for their unique orientation provided similar results due to having the same rigidity along depth for all criteria.It was also found that Hashin's failure criteria show composite failures at the highest applied stress levels.While the smallest load failing was given by the Tsai Wu failure criterion.Previous researchers, either studied the effects of different failure criteria, specific composites, specific orientations, multiple loading conditions, etc.As such, in this study, seven different laminates were created by stacking at specific sequences.These laminates had a circular notch in the center.Then their response to tensile loading conditions and ultimately failure defined by Hashin's failure criterion was analyzed.

Methodology
Hashin [7] introduced a three-dimensional failure criterion for unidirectional fiber composite materials.This is an interactive failure criterion that differentiates among various intralaminar failure modes.The criteria are expressed by 2 nd -order stress polynomials.These polynomials are specified in terms of isotropic constants of the applied average stress state in the transverse direction.The criteria involved four different failure modes with failure indices corresponding to the tensile and the compressive failure of fibers and matrix.The failure surface acquired by this criterion is piecewise and smooth.As such this failure criterion was chosen to be the failure model for this study.4 Whenever the value for each equation is more than 1, the respective laminate is considered to have failed.In this study, the first stress level at which failure first occurred is considered for stress values.Further, loading reflects the failure propagation using the abovementioned equations.

Geometry
A 3-dimensional deformable part was created, selecting shell type as the base feature using finite element software Abaqus/CAE.Each part is rectangular and has a dimension of 250 mm x 25 mm with the thickness of the plies and the number of stacks defining the thickness of the specimen (according to ASTM 3039).Thickness was set to be 2mm.Each stack size is 0.25 mm.A circular notch of 4.1667 mm radius is made at the center of the specimen for analysis purposes.The specimen width to the diameter of the hole ratio is defined by ASTM D5766 to be 6.

Stacking Sequence
The laminas were oriented in a specific sequence, which is reflected in Table 1.All the different laminate sequences were tested using same-sized test coupons.As in real life, geometry is defined beforehand.The material is custom-tailored for application.So, the stacking sequences show what type of laminate is created.In

Meshing
Mesh density is an important factor in the case of finite element analysis.Finer mesh quality increases the quality of the result obtained.Finding a mesh that is computationally efficient while ensuring solution convergence requires dexterity.Datum planes were created and partitions were made on the face of the structure, around the circular notch to create finer mesh around the stress concentration zone.0.25mm meshes were seeded in the region near the notch.While the rest of the body was meshed at 0.75mm.The geometrical model and mesh are seen in Fig. 2. Also, the endpoints were partitioned as they represent tabs used in the experiment.

Results and Discussions
The increasing stress occurring due to the loading condition on the model slowly results in the start of permanent damage to the composite after a certain threshold.This is called damage initiation.Damage then progresses as the fibers and matrix absorbs energy and starts to fail.When fiber and matrix fail, they can no longer carry the load.Their load is then distributed to the nearby region.The failure starts occurring at a micro level and as the damage progresses visible macroscopic failure can be seen.The crack starts to propagate from the initial damage.Usually following the first ply failure.Matrix tension failure is predominant in most cases.Failure occurs around the notch.As we can see increased stress near the hole.The pattern of failure is consistent with the failures observed by the authors previously discussed in the introduction section and also with ASTM standards [8].
(a) ( Hashin's failure criteria imply that when the value reaches 1, which is the red color in the contour plot the material has failed.From Fig. 3.We see fiber breakage along the perpendicular direction of the loading boundary condition applied.The breakage is concentrated near the notch region.Fiber failures are not predominant and only appear at later time steps.Considerable matrix failure has occurred by then.Some composites like the CFRP unidirectional composite showed matrix failure around the hole in the loading axis.Cross-ply composite fiber tension failures cause the composite shape to be kinked and distorted after significant displacement of the edges.Matrix compression failures moving upwards from the notch.For balanced quasi-isotropic CFRP, we see nearly no fiber tension failures rather mostly matrix tension failures occur.For different angle ply CFRP material, we see that multiple failures around the notch such as matrix tension, fiber tension, and matrix compression failures cause the shape to rapidly deform around the notch very quickly and create a 'x' shaped failure zone.For symmetric laminate, we see that

Conclusion
Computational study was validated with failure patterns observed by researchers in experiments.The effect of stacking sequences on tensile strength ranking was consistent with those carried out by Harris and Morris [9].OHT result offers an insight into how composite structures respond to tensile stress in real-life usage conditions.The failure pattern in the wake of initial failure is very intricate.Cracks propagation along the fiber direction are seen at a macroscopic level.Since, failure mechanics of composites are still explained by multiple failure theories, combining computational study parallel to experimental and non-destructive study is of paramount importance as it will create more safer and efficient structures for real-life applications.

Fig 1 ,
the ply stacking sequence for Balanced and Symmetric quasi-isotropic laminate is shown.The individual layers of fibers alongside their orientation while maintaining the homogenous thickness of the layers are shown.

Figure 2 .
Figure 2. (a) Geometry model of the CFRP, (b) Mesh near the notch of the model 3.4.Loading A displacement of 5mm was given on the top face of the geometry.It equals a strain of 2%.While the opposite face was made rigid.

Figure 5 .
Figure 5. Accumulated stress vs strain graph for the failure of all laminates Tensile matrix failure for  22 + 33 > 0 3 3.