Future path prediction

Abstract

Erdogan and Sih [I] were the first to investigate the angle at which the crack shown in Fig. 1 would propagate under uniform tension. Recently, Sih [2,3] has proposed a new concept for fracture path prediction. For elastic materials the new criterion is expressed in terms of the strain energy density factor, S. The application of the S-factor to fracture prediction is based on two hypotheses. i) Crack initiation occurs when the strain energy density factor reaches a critical value. 2) The initial crack growth takes place in the direction along which the strain energy density factor possesses a stationary value.Since strain energy is considered the prediction is a function of Poisson's ratio and will also differ for plane stress and plane strain conditions. Finnie and Weiss [4] performed two experiments with beryllium sheet in order to compare the new Sih theory with the original Erdogan and Sih approach. Beryllium was used for these tests as its Poisson's ratio in the plane of the sheet is almost zero and the experiments were simplified by making 8 = 45 deg. They state that their experimental results strongly support the original Erdogan and Sih analysis rather than Sih's new theory.Sih [S] in his discussion of paper [4] points out that any fracture criterion which excludes thickness deformation will be in error in predicting the fracture behaviour of metal specimens. Furthermore P~94A which is less sensitive to change in plate thickness is a more suitable material for testing two-dimensional theories of crack propagation.The present authors have carried out a finite element analysis of the specimen shown in Fig. i. To date the finite element analysis has been limited to the study of a square plate, with an inclined crack, subjected to uniaxial tension [6]. This work is being extended to include biaxial states of stress. The finite element analysis is a two-dimensional analysis. P~4Awas used for the experimental work (~ = 0.3) and good agreement was obtained between the numerical and experimental results. The results also compare favourably with the results of Sih.The t e c h n i q u e used f o r t h e a n a l y s i s i s b a s e d on e n e r g y c o n s i d e ra t i o n .T h i s approach does n o t r e q u i r e e x t r e m e l y small c r a c k t i p e l ements as e n e r g y r a t h e r than s t r e s s i n t e n s i t y n e a r t h e c r a c k t i p i s c o n s i d e r e d .The c o n f i g u r a t i o n o f c r a c k t i p e l e m e n t s used in t h e s t u d y i s shown in F i g . 2. P o i n t B moves on an a r c around t h e i n i t i a l c r a c k Int J'oua~ of Fracture i0 (1974)

The crack with a kinked tip

“…Recent papers [1][2][3][4] prompt us to report some related independent work in progress here and to which we referred at a recent meeting [5]. Let a semi-infinite crack have at its tip a kink of unit length making an angle ~ with the main crack ( Figure i).…”

Maximum-energy-release-rate criterion applied to a tension-compression specimen with crack

“…Wu (5) Finite-element calculation [14] The accuracy of a finite-element calculation when applied to a singular problem of this nature is doubtful. Wu (5) Finite-element calculation [14] The accuracy of a finite-element calculation when applied to a singular problem of this nature is doubtful.…”