Issue 48
A.C. de Oliveria Miranda et alii, Frattura ed Integrità Strutturale, 48 (2019) 611-629; DOI: 10.3221/IGF-ESIS.48.59
1.08 0.4 / , a t 2
a c
, q c a a F c t
(25)
( , )
2 c a a t
/ , 2
1.08 0.4 /
a c
1.08 0.15 / , a t 2
a c
, q a a a F c t
(26)
( , )
2 c a a t
/ , 2
1.08 0.15 /
a c
For the 1D crack growth regime, Tada [6] listed the SIF of a single edge-cracked plate as
3
2 c w
c
w c
c
2
0.752 2.02 0.37 1 sin
c
K
sec
tan
(27)
,1 I D
c
w
w
w
2
2
where c and w are the through-crack and plate widths. This expression is precise within 0.5% for any a/c ratio, since it models the significant bending moment caused by the presence of the single edge crack, which exists even under pure uniaxial tension. Analogously to the surface crack modeling, a modification for Eq. (23) is proposed based on a comparison with Eq. (27)
2 c w a t
, q w F c w a t ( ,
)
sec
(28)
3
c a w t
c a w t
c a w t
w t c a
2
0.752 2.02
0.37 1 sin
tan
2
2
The transition from 2D to 1D crack growth is then modeled considering a t in Eqs. (21-22), (24-26), and (28). Like for the surface cracks, the ratio c/t is replaced by a function r’(c/t, a’/t) that guarantees continuity between Eqs. (21) and (27). For corner quarter-elliptical cracks, the value of in Eq. (3) is 1.73, and thus the function r’ is defined by 2.3 1.3 ' 1.73 1.73 a t r c t (29) The 2D/1D transition from part-through corner to through single-edge cracks ( t < a’ < 2.3 t ) is then modeled under uniaxial tension by , , ( ) 1 I q w q q c K c c F M Q r F (30) , , ( ) I q w q q a K a t F M Q F (31)
Where
3
2 c w
c
w c
2
, q w F c w
0.752 2.02 0.37 1 sin c w
sec
tan
(32)
c
w
w
2
2
15
2 2.5 0.14 0.22 1 1.06 0.3 1 14.8 1 1 , r' 1 1.08 ' 0.03 0.125 , r' 1 r r r r r r
(33)
M r
q
618
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