14 THE HILL-TSAI FAILURE CRITERION There are many failure criteria for orthotropic materials.The most commonly used for design calculations is the so-called "Hill-Tsai"criterion.'This criterion can be interpreted as analogous to the Von Mises criterion which is applicable to isotropic material in elastic deformation.We will review at the beginning the principal aspects of the Von Mises criterion. 14.1 ISOTROPIC MATERIAL:VON MISES CRITERION The material is elastic and isotropic.In Figure 14.1,one denotes by I,II,IlI the principal directions of the stress tensor E for a given point.The corresponding matrix is 0 0 0 Ou 0 0 0 GIL The general form of the deformation energy dw for an elementary volume dV surrounding the point considered can be written as: which can be reduced to 1 dWou=(+uen+mem)dv TSee failure of composite materials in Section 5.3.2. 2003 by CRC Press LLC14 THE HILL–TSAI FAILURE CRITERION There are many failure criteria for orthotropic materials. The most commonly used for design calculations is the so-called “Hill-Tsai” criterion. 1 This criterion can be interpreted as analogous to the Von Mises criterion which is applicable to isotropic material in elastic deformation. We will review at the beginning the principal aspects of the Von Mises criterion. 14.1 ISOTROPIC MATERIAL: VON MISES CRITERION The material is elastic and isotropic. In Figure 14.1, one denotes by I,II,III the principal directions of the stress tensor S for a given point. The corresponding matrix is The general form of the deformation energy dW for an elementary volume dV surrounding the point considered can be written as: which can be reduced to 1 See failure of composite materials in Section 5.3.2. sI 0 0 0 sII 0 0 0 sIII dWtotal 1 2 -- sij eij dV j Âi = Â dWtotal 1 2 -- sIeI + + sIIeII sIIIeIII = ( ) dV TX846_Frame_C14 Page 273 Monday, November 18, 2002 12:30 PM © 2003 by CRC Press LLC