Issue 48

A.C. de Oliveria Miranda et alii, Frattura ed Integrità Strutturale, 48 (2019) 611-629; DOI: 10.3221/IGF-ESIS.48.59 615     , , ( ) I s w s s c K c c F M Q a c F        (4)   , , ( ) I s w s s a K a a F M Q F       (5) where Q is the crack shape parameter, F s,w is the specimen width effect, M s is the back face magnification factor, and F s,c and F s,a are respectively the front surface effects on the width and depth directions, given by     , , sec 2 s w F c w a t c w a t        (6) 2 24 4 2 4.5 2 2 0.89 1 1.13 0.09 0.54 0.5 14 1 , 0.2 0.65 , 0.04 0.2 0.11 , s a a a a a c c a c t a c c t a a M c t c c c a a a c a a a t t                                                                                              (7)        2 , 2 1.1 0.35 , , 1.1 0.35 , s c a t a c F a c a t c a a t a c         (8) , 1.0 s a F  (9) For the 1D crack growth regimen, Tada [7] lists the SIF of a center-cracked plate as       2 4 ,1 sec 2 1 0.025 0.06 I D K c c w c w c w             (10) where 2 c and 2 w are the through-crack and plate widths. The last polynomial term in Eq. (10) improves its precision from 2.6% to better than 0.2%. Therefore, comparing Eqs. (4) and (10), and noting that the only term in Eq. (4) that depends on c/w is F s,w , a modification for Eq. (6) is proposed       2 4 , ( , ) sec 2 1 0.025 0.06 s w F c w a t c w a t c w a t c w a t                           (11) Eqn. (11) improves Newman-Raju’s SIF solution to better model the plate width effect. The transition from a part-through 2D surface crack to a 1D through center crack is then modeled under uniaxial tension using Eqs. (4-5), (7-8), and (11), considering also F s,a  1.1 to account for the back face becoming a free surface at a  t , resulting in     , , ( ) I s w s s c K c c F M Q t c F             (12)   , , ( ) I s w s s c K a t F M Q F            (13) where the prime (’) symbol denotes the expressions for the 2D/1D transition from part-through 2D to through 1D cracks (for t  a’  2.3  t ), and thus         2 4 , ( ) sec 2 1 0.025 0.06 s w c F c w c w c w c w w           (14)