Issue 33

J. Fan et alii, Frattura ed Integrità Strutturale, 33 (2015) 463-470; DOI: 10.3221/IGF-ESIS.33.51 469 2 2 2 ' 0 3/2 2 2 ' 0 2 0 2 ( , ) ( ) ( ) 1 ( ) 1 16 3 ( ) ( ) ( ) 1 1 3 8 3 3 u x a x x x f a f a a f a a a a H a G a G a G a x x H a a a a a H                                                                                             3/2 2 2 2 ' ( ) 1 ( ) ( ) 1 x x x f a f a a f a a a a                                                     (22) where f ′ ( a ), G ( a ) and G ′ ( a ) are, respectively, determined as:       ' 2 2 6 2 3 4 5 6 ' 6 2 3 4 5 6 2 3 1 ( ) 0.128 0.576 4.575 ( ) 0.5 0.0853 0.1399 0.5953 0.0789 0.1255 0.2907 ( ) 2 0.5 0.0853 0.1399 0.5953 0.0789 0.1255 0.2907 + 0.0853 0.2798 1.7858 0 f a p p b G a a b p p p p p p G a a b p p p p p p a p p p                       4 5 6 .3156 0.6274 1.7442 p p p            (23) Subsequently, substituting (22) into (20), the weight function h ( x , a ) for the center crack in a finite plate by the present method is obtained and written as: 2 2 2 ' 0 3/2 2 2 ' 2 ( , ) ( ) ( , ) 2 1 1 1 ( ) ( ) 3 ( ) ( ) ( ) 16 1 1 3 ( ) ( ) ( ) u x a f a a H x x x h x a a a a f a a f a a G a G a G a x x f a a a f a a f a a a                                                                                              3/2 2 2 2 ' ( ) 8 3 1 1 1 3 ( ) f a a x x x a a f a a                                                        (24) The weight function for a central through crack in an infinitely wide plate has been derived by Paris and Sih [4]:   , a x a x h x a a a x a x        (25) From Eq. (25), if x / a -value tends to be zero, the dimensionless weight function h ( x , a )√( πa ) tends to be a constant value of 2. This is the limiting condition for collinear cracks in an infinite plate and for center cracks in a finite plate. Based on Eq. (17b), (24) and (25), Fig.3(a) shows the variations of the weight function h ( x , a )√( πa ) for collinear cracks in an infinite plate and for center cracks in a finite plate at the center of the crack x / a =0. According to Eq. (1), (24) and (25), the SIFs for center cracks in mode I conditions are computed and presented in Fig.3(b). It is obviously found that the Eq. (25) used for crack problems will result in significant error for the calculations of weight functions and SIFs in finite plates since the correction function has not been considered. C ONCLUSIONS general approach has been presented to calculate the crack face displacement of collinear cracks in an infinite plate and of center cracks in a finite plate. The approximate and simple expression is able to be determined based on only one reference stress intensity factor and some criterions around the crack tip. The crack face A