Evaluation of Energy Release Rate for Mode I Crack propagation in GFRP structures

Unstable propagation of a crack results in fracture due to applied stress. Fracture mechanics provides a methodology for prediction, prevention, and control of fracture in materials, components and structures subjected to static, dynamic, and sustained loads. De-lamination is considered to be the most occurring failure mode in composites, a partition of the layers that are stacked together to form laminates. Delaminations appear at stress free edges due to the difference in properties of the individual layers, at ply drops where thickness should be reduced, and at regions subjected to out-of-plane loading like bending of curved beams. An experimental analysis was performed for analyzing the energy release rate for mode I crack propagation of the DCB specimen for different volume fractions. Double Cantilever Beam Specimen was analyzed for mode I crack propagation subjected tensile load and Energy Release Rate was evaluated for different crack lengths using ANSYS 15. Virtual Crack Closure method was used to find the Energy Release Rate by considering the displacements (V) at the flagged nodes near the crack tip and then was compared with the analytical results. Virtual Crack Closure method showed very good agreement with the experimental results. Convergence was achieved through refinement and results were extracted for variation of SIF along the crack front. It was observed from the results that the ERR increased at a very slow rate in the beginning of the crack growth (a/w = 0.2 to a/w = 0.4). As a/w reached 0.5 there was a steep increase in the Energy Release Rate. This was purely because of the plastic zone at the crack tip getting increased. This in turn increases the resistance offered by the crack to the propagation.


II. EXPERIMENTAL ANALYSIS OF DCB SPECIMEN
The DCB specimen shown as for as ASTM standards. It consists of a rectangular, unidirectional, standardized thickness, laminated composite specimen contain a non-adhesive include at the mid-plane which serves as a delamination maker. Forces are applied to the specimen through an DCB fixture under displacement controlled loading. A record of the apply force opposed to center roller displacement is obtained using an x-y recorder or equivalent real-time plotting device. It can be obtained and stored digitally. The mode I inter-laminar fracture toughness, G IC , is obtained by using the compliance calibration (CC) method.

Fig.3 Experimental Testing
III. VIRTUAL CRACK CLOSURE TECHNIQUE Numerical analysis of energy release rate in Double Cantilever Beam specimen made of Glass-Epoxy composite was done using Virtual Crack Closure Technique to study the behavior of G with respect to change in volume of fiber and matrix content in the composite having unidirectional fiber orientation.  [1] Work W required to close the crack is evaluated by considering the stress field at the crack tip for a crack of length a and displacements in the configuration with the crack front appropriately extended from a to a+Δa ( Figure 4). The expression of the work W evaluated according to Virtual Crack Closure Technique is given by Eq. (1). ---------(1) shows the work done to close the crack [2] and the stress displacement distribution to the crack displacement shown above.  Figure 1 respectively giving the crack tip status, before and after the crack propagation. The evaluation of the Strain Energy Release Rate can be simplified by adopting an alternative approach: the one step Virtual Crack Closure Technique (VCCT). In VCCT it is assumed that an infinitesimal crack extension has minimal effects on the crack front hence both stress and displacement can be evaluated within the same configuration by considering only one analysis. By adopting this technique, the expression of the work W required to close the crack becomes as in Eq. (2).
shows the modified work done to close the crack considering both stress field and the displacement [2]

IV. NUMERICAL EVALUATION OF ENERGY RELEASE RATE
Double Cantilever Beam specimen (DCB) was simulated for mode I crack propagation using ANSYS V15 and Energy Release Rate was evaluated along the crack front and for different crack lengths. Dimensions of the DCB specimen were taken as per ASTM standards shown in Figure 6. Analytical solution for the DCB specimen was calculated for mode I crack propagation for different crack lengths from equation (7)  Where W is the work done on the crack faces. From equation (4), it can be seen that for homogenous crack problem mode I can be directly calculated using the square root of the mode I energy release rate. The properties of the Glass/Epoxy material are calculated using rules of mixtures. Preconditioned Conjugate Gradient (PCG) solver was used for the analysis of SIF. This solver starts with element matrix formulation. Instead of factoring the global matrix, PCG solvers assemble the full global stiffness matrix and calculate the DOF solution by iterating to convergence.

V. RESULTS AND DISCUSSIONS
The load versus deflection curve is obtained in the digital recorder of the universal testing machine.. The results obtained are compared with each other to find the fiber volume fraction at which possesses high inter-laminar fracture toughness. As the glass fiber reinforced polymer is a brittle material the load V/S curve drop vertically after the peak load.
A. Experimental results for different volume fraction of fiber Energy Release Rate was evaluated for opening mode of crack using Finite element method and Virtual Crack Closure method along the crack front and for different crack lengths. The Energy Release rate was calculated for volume fractions 0.4, 0.5 and 0.6. For 40% fiber volume fraction of the GFRP composite, Longitudinal young's modulus, E1=36.2GPa. The load vs. displacement arc recorded for the period of fracture toughness test for 0.4 Fibre Volume Fraction shown in the figure below    B. Numerical results in ANSYS software for different volume fraction of fiber Numerical method is carried out in ANSYS software using Virtual Crack Closure Technique (VCCT). In VCCT the strain energy release rate of each crack front node is can be obtained directly. From the literature survey it is found that the best numerical technique that can be used for fracture analysis is VCCT.  Figure 4 shows the stress condition and plastic zone size at the crack tip. G evaluation for fiber volume fraction 0.4, 0.5 and 0.6 is considered for the study in variation of SERR of the composite de-lamination using Virtual Crack Closure Technique. Variation of SERR along the crack front has been observed for details on effective magnitude of SERR along the crack front.  Figure 8 shows the variation of energy release rate for different volume fractions. As the fibre content increases the energy release rate is also increasing which clearly specifies that the as the brittleness of the glass epoxy composite increases the resistance to the crack propagation also decreases.
Hence it clearly indicates that fibre volume fraction 0.4 yields high resistance to crack propagation due to high ductility at the crack tip.
VI. CONCLUSIONS An extensive analysis for Mode I has been performed in order to study the pattern of Energy Release Rate variation with respect to change in fiber volume through numerical methodology. The study was performed for 00 orientation of glass fiber having 9 elastic constants. It is observed that the strain energy released increases as the composition of the glass fiber increases and corresponding stress increases. Lower composition of glass fiber in the GFRP composite laminate is desirable for resistance of crack propagation. The results obtained so far are quite satisfactory. VCCT gave more accurate results as a result mesh convergence.