Issue 48

M. K. Hussain et alii, Frattura ed Integrità Strutturale, 48 (2019) 599-610; DOI: 10.3221/IGF-ESIS.48.58 [28] Hussain, M.K. and Murthy, K.S.R.K. (2019). Calculation of mixed mode (I/II) stress intensities at sharp V - notches using finite element notch opening and sliding displacements, Fatigue Fract. Eng. Mater. Struct. pp. 1–18. DOI: 10.1111/ffe.12977. [29] Hussain, M.K. and Murthy, K.S.R.K. (2018). A point substitution displacement technique for estimation of elastic notch stress intensities of sharp V-notched bodies, Theor. Appl. Fract. Mec., 97, pp. 87–97. DOI: 10.1016/j.tafmec.2018.07.010. [30] Henshel, R.D. and Shaw, K.G. (1976). Crack tip finite elements are unnecessary, Int. J. Numer. Meth. Eng., 9, pp. 495–507. DOI: 10.1002/nme.1620090302. [31] Barsoum, R.S. (1976). On the use of isoparametric finite elements in linear fracture mechanics, Int. J. Numer. Meth. Eng., 10, pp. 25–27. DOI: 10.1002/nme.1620100103. [32] ANSYS. Theory reference manual. Release 11. Swanson Analysis Systems, Inc., 2007. [33] Zhao, Z. and Hahn, H.G. (1992). Determining the SIF of a V-notch from the results of a mixed-mode crack, Eng. Fract. Mech., 43(4), pp. 511–518. DOI: 10.1016/0013-7944(92)90195-K. [34] Ayatollahi, M.R. and Nejati, M. (2011). Experimental evaluation of stress field around the sharp notches using photoelasticity, Mater. Des., 32, pp. 561–569. DOI: 10.1016/j.matdes.2010.08.024.

N OMENCLATURE

a

notch length

, A B

parameters related to finite element displacements

0 0 2 , , A B B

parameters related to rigid body motion

 n A n  n B n

  1, 2,3,...   1,3, 4,...

Williams coefficients for mode I Williams coefficients for mode II

Young’s modulus

E

, F F

modes I and II normalized notch stress intensity factors compressive point load on the sharp V-notched Brazilian disc

I

II

F G

shear modulus

semi-height of the notched plate

h

L

notch tip element length

N

, K K

modes I and II notch stress intensity factors radius of the sharp V-notched Brazilian disc

I

II

R 

residual

   , r

polar coordinate components

r r

optimum point optimum radius

opt

op

, u v

notch field displacement

w

plate width

 

parameter related to notch angle

notch inclination angle notch opening angle





Kolosov constant

modes I and II eigenvalues correspond to the singularity term modes I and II eigenvalues correspond to the n -th term

  1 1 , I II   , I II n n



Poisson’s ratio far field stress



  , u v

notch opening and sliding displacements

609