Validating the Classical Failure Criteria for Applicability to the Notched Woven-Roving Composite Materials

Table 1

Classical failure criteria of the composite materials.

Number	Name and reference	Failure criterion
1	Hill criterion (Hill) [35]	𝜎1𝐹1^2−1𝐹^21+1𝐹^22𝜎1𝜎2+𝜎2𝐹2^2+𝜎6𝐹6^2=1
2	Tsai-Hill yield criteria (Azzi and Tsai) [26]	𝜎1𝐹1^2−𝜎1𝜎2𝐹^21+𝜎2𝐹2^2+𝜎6𝐹6^2=1
3	Norris interaction (Norris and McKinnon) [36]	𝜎1𝐹1^2+𝜎2𝐹2^2+𝜎6𝐹6^2=1
4	Norris distortional energy (Norris) [20]	𝜎1𝐹1^2−𝜎1𝜎2𝐹1𝐹2+𝜎2𝐹2^2+𝜎6𝐹6^2=1; 𝜎1𝐹1^2=1;   𝜎2𝐹2^2=1
5	Hoffman theory; (Hoffman) [21]	𝜎^21−𝜎1𝜎2𝐹1𝑡𝐹1𝑐+𝜎^22𝐹2𝑡𝐹2𝑐+𝐹1𝑐−𝐹1𝑡𝐹1𝑐𝐹1𝑡𝜎1+𝐹2𝑐−𝐹2𝑡𝐹2𝑐𝐹2𝑡𝜎2+𝜎6𝐹6^2=1
6	(Tsai and Wu) [22]	1𝐹1𝑡−1𝐹1𝑐𝜎1+1𝐹2𝑡−1𝐹2𝑐𝜎2+𝜎^21𝐹1𝑡𝐹1𝑐+𝜎^22𝐹2𝑡𝐹2𝑐+2𝐻12𝜎1𝜎2+𝜎6𝐹6^21=1,𝐹1𝑡𝐹1𝑐1𝐹2𝑡𝐹2𝑐−𝐻^212≥0forstability
7	Tsai and Hahn [23]	The same criterion as Tsai Wu but the value of 𝐻12 is; 𝐻12=−0.51𝐹1𝑡𝐹1𝑐⋅1𝐹2𝑡𝐹2𝑐
8	Cowin [24]	The same criterion as Tsai-Wu but the value of 𝐻12 is; 𝐻12=1𝐹1𝑡𝐹1𝑐1𝐹2𝑡𝐹2𝑐−12𝐹^26
9	Puppo and Evensen [25]	𝜎1𝐹1^2𝐹−𝛾^1𝐹2𝜎1𝜎2𝐹1𝐹2𝜎+𝛾^2𝐹2^2+𝜎6𝐹6^2=1, where 𝛾=3𝐹^26𝐹1𝐹2
10	Ashkenazi [37]	𝜎1𝐹1^2+𝜎2𝐹2^2+𝜎6𝐹6^2+2𝐹12𝜎1𝜎2=1; 𝐹12=124𝜎^2𝑋−1𝐹^21−1𝐹^22−1𝐹^26; 𝜎𝑥 is the global of 45° tenstion test