First of all, I would like to thank IIT Hyderabad and the Department of Mechanical and Aerospace Engineering for continuously providing all the facilities required to carry out my research work without any hassle. The failure criteria of LaRC04 are based on a fracture mechanism that should determine the energy release rates (ERR) in mode I and mode II for CFRP panels.
Introduction and literature review
Introduction
Literature review
- Flexural study of composites
- Failures in composites
Failure analyzes through FEM can help to some extent to predict the behavior of components, but there is a need for failure criteria that provide accurate and meaningful failure predictions. 28] have proposed failure criteria based on physical models for each failure mode and nonlinear shear behavior of FRP composites.
Motivaion, Scope and objective of the study
Through cohesive zone modeling (CZM) between layers, the delamination can be introduced into the failure analysis.
Thesis layout
Introduction
Flexural properties CFRP composites
- Standard test methods
- Specimen fabrication
- Experimental setup
- Results and discussion
The load span is held half of the support span and placed symmetrically between support rollers. Vic-2D software (from Correlated Solutions, Inc.) is used for post-processing the images to obtain the maximum stress and the deflection of the specimen at the center of the support span.
Fracture toughness of CFRP composites
- Standard test methods
- Pure mode-I DCB test
- Pure mode-II ENF test
By Timoshenko beam theory, J-integral can be calculated without measuring the delamination length which is equal to the mode-I fracture toughness within the framework of linear elastic fracture mechanics (LEFM). The load-displacement curves for different samples are shown in Fig. 2.5a is plotted and mode-I fracture toughness is also plotted against displacement in Fig. The comparison of mode-I fracture toughness measured from MBT method and DIC is given in Table 2.2.
When delamination begins to propagate from a pre-implanted insert, the calculated fracture toughness value is referred to as non-pre-cracked fracture toughness. If delamination begins well before the insertion, it is called pre-cracked fracture toughness. Compliance with ENF is calculated in each case for different delamination lengths, i.e. from it the fracture toughness can be calculated according to Eq.
The mode II fracture toughness for PC and NPC is listed in Table 2.3. a= corresponding delamination length b = width of ENF sample. m= CC coefficient determined from fitting a curve of complianceCand demaination lengtha, C=A+ma3.
Closure
It is found that mode-II ERR in case of NPC test is found to be higher than that of PC test. Therefore, the value of mode-II ERR in PC test is used for further application, which is 1.22 kJ/m2. Second, DCB test is performed on the machine with 10kN load cell, and the maximum load taken by DCB sample is less than 100N.
Introduction
In general practice, quasi-isotropic laminates are used, the structure of which comes under load from all directions. Each layer of quasi-isotropic laminates has different mechanical and thermal properties in each direction because the properties of each layer are dependent on the fiber direction.
Specimen fabrication
A hole with a diameter of 5 mm was chosen to avoid the interaction of the hole with the edge (B/D > 3.5). Wooden plates are used on the side and bottom of the specimen to prevent damage to the specimen during processing. After fabrication, a speckle pattern is produced on the thickness side of the sample to study the delamination or edge interaction of the hole during the bending test, if any.
Experimental setup
Results and discussions
The unnotched specimen was first tested to know the full load bearing capacity of the specimen. The damage on different sides at ultimate failure for UD CFRP panels is shown in Fig. It turns out that the damage starts on the top layer of the panel, which is in a state of compressive stress.
The damage to the bottom layer observed is less different compared to the top layer. One of the reasons behind these events is the high tensile strength of the CFRP panel compared to the pressure one. In the case of quasi-isotropic panel, the edge interaction is not found on the thickness side.
On the compression side, the top layers were damaged and mostly in the transverse direction through holes except in the 2HD configuration.
Closure
Although the plies on the compression side were less damaged than those of UD CFRP sheets, delamination is significantly produced compared to UD sheets due to the different fiber orientation.
Progressive damage analysis of
CFRP laminates having single and multiple holes
Introduction
FEM modelling of four point bending
In the XY Z coordinate system, the length, width and thickness of the panel are oriented in the x, y and z directions respectively. The mesh pattern around the hole is kept finer to capture the high stress gradient near the hole. Since the deformation of rollers is not so important, they are kept as rigid bodies.
Additionally, the meshing near the contact was kept finer to obtain accurate solutions and avoid convergence issues.
Contact parameters
The equilibrium iterations continue until the final penetration falls below the required tolerance, increasing the contact tractions. Various contact parameters are required to define the contact pair, such as normal stiffness, tangential stiffness, penetration tolerance, friction coefficient, initial adjustment, pinball area, etc. A higher stiffness value leads to convergence problems and a lower stiffness value leads to more penetration and improper resolution.
If the penetration is found to be higher than the given tolerance value, the solution is considered non-converged and iterations continue to drop the penetration value below the mentioned tolerance value. In the contact analysis, initial penetration is excluded and any initial hole is closed. The high value includes more contact elements, but the computer process will be marginally slowed down.
Introduction to PDM
PDM involving Hashin’s and Ye’s delamination criterion
- Introduction
- Results and discussions
The load-displacement curves predicted by the PDM simulations for the composite panels for the 1H, 2HL, 2HD and 2HT configurations are compared with the corresponding experimental behavior as shown in Figs. 4.5 - 4.8 show detailed illustrations of damage propagation predicted for damage progression in UD CF panels for configurations 1H, 2HL, 2HD and 2HT respectively at different load levels. Although Ye's delamination criteria are applied, no significant delamination is detected in the case of UD CFRP panels.
The quasi CFRP panels with lay-up sequence S are analyzed under bending loading with different single and multi-hole configurations. Ultimate load and corresponding displacement are tabulated in Table 4.4 Underprediction of the ultimate load and corresponding displacement is also found here in the case of quasi CFRP panels. The damage propagation with increasing bending load for CFRP panels with different hole configurations is shown in Fig.
In all cases, damage initiates in the outermost layer with fiber orientation 45◦ to the compression side. It starts transversely near the holes in the form of compression failure of the matrix. Burst in the case of quasi-CFRP panels is severe, but Ye's failure criteria are unable to accurately detect this failure.
![Figure 4.3: Flowchart of PDM [2]](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10486340.0/38.892.163.749.116.847/figure-4-3-flowchart-of-pdm-2.webp)
Delamination modelling and growth through CZM
- Introduction
- Calibration of CZM properties
After determining the initial stiffness, the separation can be calculated if the interfacial strength of the composite is known. Therefore, the separation at the end of delamination can also be calculated from the fracture toughness and interfacial strength. To obtain the correct prediction of delamination, there must be a sufficient number of elements in the cohesive zone.
It is suggested that the length of the CZM element in the direction of delamination propagation is 0.634 mm. The span length is kept at 100 mm and the load is applied 50 mm away from one of the support nodes. It is found that the form of the traction separation law does not affect the macromechanical behavior (load-displacement profile) unless and as long as the area under the curve, i.e.
It can be overcome by introducing the artificial damping in CZM modeling to stabilize the delamination propagation [43].
LaRC04 criteria
- Introduction
- Effect of thickness and fiber orientation on the strength of the ply
- Mohr-Coulomb criteria
- Fiber kinking
- List of failure criteria
The first is fiber twisting and the second is subsequent fiber failure due to matrix failure under shear stress. In the compressive failure of the matrix, the effect of friction is taken into account by the Mohr-Coulomb theory of failure. It is observed that the strength of the insert increases when it is confined by inserts with different fiber orientation.
Therefore, the fracture angle should ideally be 45◦ along the maximum shear stress plane, but the experimental results indicate that the fracture angle for most composite material is 53±2◦ due to the friction effect. Fiber buckling is the localized failure of the matrix due to shear along a belt and subsequent fiber breakage near the edges of the belt. In the buckling plane, the buckling angle ϕ at which the corner fibers are misaligned must be determined to transform the stresses to this angle in the buckling plane.
Matrix tensile failure due to matrix cracking is developed on the basis of fracture mechanics and Eshelby's inclusion problem.
Results and discussions
In the same way, the experimental results in this study can be provided with the appropriate values of the correction factors. It should also be noted that nonlinear shear behavior is not included in the PDM algorithm with LaRC04. It can be incorporated into PDM with appropriate experimental characterization of the nonlinear shear parameters.
Closure
Conclusion and recommendation for future work
Conclusions
Recommendations for future work
Embedded FBGs and 3-D DIC for stress analysis of a structural specimen subjected to bending. Composite structures. A comparison of progressive failure criteria in predicting dynamic flexural failure of laminated composite beams. Analysis of crack formation and crack growth in concrete using fracture mechanics and finite elements.
Numerical simulations of rapid crack growth in brittle solids. Journal of the Mechanics and Physics of Solids. Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites, ASTM International, West Conshocken, PA. Standard Test Method for Determining Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composite, ASTM International, West Conshohocken, PA.
Investigation of Experimental Characterization of Carbon Fiber Reinforced Polymer Panel Using Digital Image Correlation: A Sensitivity Analysis.
![Figure 1.1: Schematic of usage of composite in various parts of commercial aircrafts [1]](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10486340.0/13.892.140.783.107.448/figure-schematic-usage-composite-various-parts-commercial-aircrafts.webp)
