Hashin Criterion

The Hashin criterion identifies four different modes of failure for the composite material: tensile fiber failure, compressive fiber failure, tensile matrix failure, and compressive matrix failure.

= Value of σ₁₁ at longitudinal tensile failure

= Value of σ₁₁ at longitudinal compressive failure

= Value of σ₂₂ at transverse tensile failure

= Value of σ₂₂ at transverse compressive failure

= Absolute value of σ₁₂ at longitudinal shear failure

= Absolute value of σ₂₃ at transverse shear failure

If , the Tensile Fiber Failure Criterion is:

If , the Compressive Fiber Failure Criterion is:

If , the Tensile Matrix Failure Criterion is:

If , the Compressive Matrix Failure Criterion is:

Note, the Hashin equations include two user-specified parameters: and S₂₃.

• - User-specified coefficient that determines the contribution of the longitudinal shear stress to fiber tensile failure. Allowable range is 0.0 ≤ ≤ 1.0, and the default value is =0.
• S23 - Transverse shear strength of the composite material in the 23 plane.