STRENGHT, LAMINA FAILURE CRITERIA Zdeněk Padovec

Symbols F (failure) isotropic material composite material indexes L (Longitudinal), T (Transversal), c (compression), t (tension) isotropic material tensile strength (compressive strength) Ft, (Fc), may or may not be equal (cast iron, concrete Fc Ft) shear strength S, 𝑆= 𝐹 3 von Mises, 𝑆= 𝐹 2 Tresca composite material FTt and FLT crucial tensile strength in longitudinal direction compressive strength in longitudinal direction tensile strength in transverse direction compressive strength in transverse direction in-plane shear strength

Strength criterions non-interactive criterions – no coupling between normal and shear stresses maximum stress criterion maximum strain criterion interactive criterions - coupling between normal and shear stresses Hill criterion Tsai – Hill criterion Hoffmann criterion Tsai – Wu criterion Puck criterion LaRC criterion …

Non-interactive criterions maximum stress criterion σmax failure occurs when at least one of the stresses in material coordinates exceeds the corresponding experimental value of strength

Non-interactive criterions maximum strain criterion εmax conditions Hooke´s Law limit values of strain components

Non-interactive criterions maximum strain criterion εmax with the use of Hooke´s Law for for for for

Interactive criterions Hill criterion stress components in main directions L, T, T´ parameters A – F are related to the strength of material assumption – SAME STRENGTH IN TENSION AND COMPRESSION – Fit= Fic based on von Mises criterion for isotropic materials Hill extends this criterion for orthotropic materials this can be rewritten

Interactive criterions Tsai - Hill criterion simplification FT= FT´ Hoffmann criterion generalized Hill´s criterion, DIFFERENT TENSILE AND COMPRESSIVE STRENGHT Fit≠ Fic

Interactive criterions Tsai - Wu criterion general theory of failure based on polynomial function can be written as plane stress case or

Interactive criterions Tsai - Wu criterion where based on biaxial test

Graphics solution of some criterions Maximum stress Maximum strain