Since toughness is the measure of a material to deform past its elastic stage while retaining its stiffness, will the toughness obtained from compression tests correspond linearly with toughness obtained from flexural tests?
If you use flexural mode for testing and determining toughness, you will most likely use a SENB (Single Edge Notched Beam Configuration). The size of the defect/crack is known (notch depth-usually 50% of total sample thickness) and the results for K1C will be more controlled and accurate. The crack will actually be subject to tensile opening during bending. In a simple compression test, the flaw size and distribution is unknown. The areas under the stress strain curve can be used on a comparative basis measure fracture energies. The results from the two techniques will not be comparable.
I agree with Dr Rajendra U. Vaidya. If you apply pure tension into a certain cross section of sample in bending and pure compression into sufficient size of sample without end effect etc., results gathered from the two methods can be related eachother with a satisfactory regression curve. Plain concrete works to compression rather than tension because compression rehabilitate crack development in concrete during the test up to a certain point. Concrete is too fragile to fracture in flexural test. thus, there are sensitive test procedures with regard to loading rate, satisfactory sample cross section etc.
I think that dépends on the nature of the material ''Elastic, hyperelastic, plastic ...etc'' you might find some corrélation or no.
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