How can I find GI and GII values from KI and KII found from a fracture test of a polymer composite? I am faced with two options that give different answers:
1 - As the fracture happens in the polymer not in the fibre, I can assume it as an isotropic problem and use the following relations:
G_I=K_I^2 (1-v^2)/E (1)
G_II=K_II^2 (1-v^2)/E (2)
Where E and v are stiffness and Poison's ratio of polymer.
2 - As the polymer composite is anisotropic material, I follow the method described by Sih et al (On cracks in rectilinearly anisotropic bodies. Sih, Paris, Irwin 1965 - equation 26), in which the relation between G and K in anisotropic materials is defined using transformed compliance tensor components of the composite (s^bar_ij).
I am not sure which formula can be used to find the G from K? I compared all of them and they are giving different results. I think the second method looks more reasonable. Any thoughts?
The equation you should use will depend on nature of problem as in case of plane strain and isotropic material you should use the first equation while in case of anisotropic material you can you use the second equation or many similar equations which uses fourth-order elasticity tensor. It is common in fracture mechanics that different models gives different result, you should go with one which you feel is appropriate and you must not choose an equation or model just because it is more complicated. And I believe that is you are dealing with isotropic material you should use the first equation.
And I guess "As the polymer composite is an isotropic material" is a typo. :)
Thanks Abhishek for reply and reminding me about typo. I corrected it. Regarding anisotropic material, do you know of other formula between K and G?
Thank you Vladimir. So if I am dealing with say LEFM and material is not isotropic, you recommend me to use the relations from Sih's paper?Do you know of any other relation between K and G for anisotropic material.
The material I am testing is glas fibre epoxy and I can get consistent values of KI and KII when I am using samples of thickness above 5mm. I know for neat polymer this value could be even higher.
The next question here is how thick is thick enough to assume the fracture as plane strain fracture?
I use the relation in Broek Elementary Engineering Fracture Mechanics, to find the ratio of plastic radius to the thickness and fnd if the material is in plane strain condition or not.
The relation reults in: Thk=2.5(K^2/sy.p^2) where sy.p. is the yield stress of the sample.
It is intersting that I get to consitent results for K values with smaller thicknesses compared to the theory. Thank you.
Principally, both methods give some approximate answer, but I would recommend the second one. It has been designed for anisotropic materials such as composites.
Thank you vlafimir. I am actually not familiar with G integral but as the plastic deformation in my polymer composites are not significant I don't use methods like J-integral.
Thank you Anousheh, I think the same way. As the materials I am studying are anisotropic I feel more confident to use anisotropic parametrs into consideration, however assuming isotropic relation simplifies the problem.
Use Stress intensity factor while analyzing Linear Elastic materials and J integral for Elasto-plastic analysis i.e non linear Elastic materials.
While using FEA softwares to overcome singularites near the crack tip, Crack Tip Opening Displacements and forces required to close them are estimated over the virtual crack extension and Strain Energy Release Rate G is calculated .
For Linear Elastic isotropic and orthotropic materials & and for the fracture Toughness Predictions at Bi-Material interfaces ENERGY RELEASE RATE(G) is used.
For Linear Elastic Materials J-Integral=ENERGY RELEASE RATE(G)
For Elasto Plastic Analysis Use J-Integral
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