Issue 33

Y. Wang et alii, Frattura ed Integrità Strutturale, 33 (2015) 345-356; DOI: 10.3221/IGF-ESIS.33.38 350   x xy xz n xy y yz xz yz z (t ) (t ) (t ) (t ) (t ) (t ) (t ) (t ) (t ) x x y z y z n t n n n n n                                    (16) E VALUATION OF STRAIN AND STRESS COMPONENTS RELATIVE TO THE CRITICAL PLANE onsider the body subjected to a complex system of time variable forces shown in Fig. 3. The applied load history is defined in the time interval [0, T ] and it is assumed to result in a VA multiaxial strain state at point O . By using the  -MVM, the orientation of the potential critical plane can be determined through that direction which experiences the maximum variance of the resolved shear strain. After determining the direction of maximum variance (MV), the shear strain resolved along this direction, MV ( ) t  , the shear stress resolved along the maximum variance direction, MV ( ) t  , and the stress normal to the plane experiencing the maximum variance of the resolved shear strain, n ( ) t  , can be evaluated, at any instant, t , of the load history, through Eq. (14) to (16). Attention can initially be focused on stress component, n ( ) t  , which is defined in the time interval [0, T ]. The mean value of this stress component is equal to T n, m n 0 1 σ σ ( ) T t dt   (17) The equivalent amplitude of n ( ) t  is suggested here as being calculated as follows:   n,a n σ 2 Var[σ ] t   (18) where Var[ n ( ) t  ] is the variance of stress component n ( ) t  , i.e. T 2 n n n,m 0 1 Var[σ ( )] [σ ( ) σ ] T t t dt    (19) Consider now the shear stress, MV ( ) t  , resolved along direction MV. Owing to the fact that also MV ( ) t  is a monodimensional stress quantity defined in the time interval [0, T ], its mean value and its equivalent amplitude can directly be determined by following a strategy similar to the one adopted above to calculate n,m  and n,a  . In particular, m  is equal to T m MV 0 1 τ τ ( ) T t dt   (20) whereas the equivalent amplitude of the shear stress resolved along direction MV takes on the following value:   a MV τ 2 Var[τ ] t   (21) where T 2 MV MV m 0 1 Var[τ ( )] [τ ( ) τ ] T t t dt    (22) Then a stress ratio  ρ , which will be used to adapt the Manson-Coffin curve to the degree of multi-axiality and non- proportionality of the stress/strain state at the assumed crack initiation site can be defined as follows: n, m n, a a σ σ ρ τ   (23) C