6. Hashin Criteria:
           
In the Tsai-Wu theory, the determination of constants like etc. requires a combined state of stress. These tests are very complicated and expensive. Further, Tsai-Wu theory is mathematically a smooth failure criterion which holds true for fibrous composite as well as an hexagonal crystal with only difference in the values of coefficients. These two materials have same material symmetry. However, their modes of failure are totally different.
           
In case of composites, the modes of failure can be fibre rupture in tension or buckling in compression, matrix may fail in transverse tension or compression. The Tsai-Wu theory predicts the ultimate failure very closely with experimental results, but the distinction between various modes of failure is not possible.
           
In the following we will see the mode dependent criteria proposed by Hashin [1].

Tensile Fibre Mode:
            If

(6.65)

Compressive Fibre Mode:
            If

(6.66)

Tensile Matrix Mode:
            If

(6.67)

Matrix Compressive Mode:
            If

(6.68)

Interlaminar Tensile Failure:
            If

(6.69)

Interlaminar Compressive Failure:
            If

(6.70)