Issue 33

M. Vormwald, Frattura ed Integrità Strutturale, 33 (2015) 253-261; DOI: 10.3221/IGF-ESIS.33.31 255 Challenge 2: Effective ranges From uniaxial loading it is known that cracks only grow when their crack flanks do not touch, see e.g. [20]. Little is known concerning crack closure under multiaxial loading. An example has been presented by Hoffmeyer [4]. A thin-walled tube from steel S460N was tested under stain control with a butterfly strain sequence, Fig. 2, two shear strain cycles,  , were applied during one normal strain cycle,  . Thirty-three surface replicas of a naturally initiated crack were taken during a butterfly cycle at the  -  combinations indicated by dots in Fig. 2. The snapshots are grouped together in an animation provided by a link. 0.0 30 25 20 15 5 10 1 0.2 0.4 -0.2 -0.4 0.00 0.25 0.50 -0.25 -0.50  in %  in % 300  m crack closed crack open 1  cy cle st 2  cy cle nd Figure 2 : Strain sequence, indicating (by dots) the  -  combinations of replicas, left, and inspection area of crack opening displacement evaluation, right, Hoffmeyer [4]. 0 1 2 3 4 30 25 20 15 10 5 1 1  cy cle 2  cy cle CMSD 2  in %  in % 0.0 0.2 0.4 -0.2 -0.4 5 6 CMOD in  m CMSD in  m 0 1 2 3 4 5 6 0.0 0.2 0.4 -0.2 -0.4 0.6 -0.6 10 1 20 30 st nd CMSD 1 crack closed crack closed Figure 3 : Crack mouth opening and sliding displacements, Hoffmeyer [4]. The crack mouth opening and sliding displacements, CMOD and CMSD, have been measured. In Fig. 3 the local crack flank displacements (taken in the middle of the section shown by a white square in Fig. 2 right) are plotted over the applied global strains. The crack flanks are in contact when the minimum normal strain is applied. The vertical line in Fig. 2 gives an estimate of the crack opening and closure strain. Crack flank sliding occurs while crack flanks are in contact, Fig. 3 right. However, sliding is reduced, CMSD 2 , compared to a shear cycle without any contact, CMSD 1 . Such observations of crack closure led to a phenomenological description of effective ranges in Eq. (1) to (3). For the mode I loading portion the crack opening and closure global strain ( ,op x  and ,cl x  are assumed to coincide) are modelled by first calculating an opening stress with ,op ,max 0 1 eqv,max max,eff ( / ) for 0 x x A A R R          0 max,eff F 0.535cos ( ) / (2 ) A    1 max,eff F 0.344( ) / (2 ) A    (4) 2 2 2 max,eff ,max 3( ) x xy xz        2 2 2 2 2 2 eqv,max ,max ,max ( ) ( ) ( ) 6( ) / 2 x y x z y z xy xz yz                   