HW Solution for Lecture9 - people.engr.ncsu.edu · HW solution for Lecture9 20. € K IC =Yδ f πa...
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Transcript of HW Solution for Lecture9 - people.engr.ncsu.edu · HW solution for Lecture9 20. € K IC =Yδ f πa...
HW solution for Lecture9 20.
€
KIC =Yδ f πac
ac =1π
KIC
Yσ f
⎡
⎣ ⎢
⎤
⎦ ⎥
2
=1π
22.0ksi inπ 82.0ksi( )
⎡
⎣ ⎢
⎤
⎦ ⎥
2
= 0.0073in
For an internal through crack, the critical crack length = 2aC =0.015 in
21.
€
KIC =Yδ f πac
ac =1π
KIC
Yσ f
⎡
⎣ ⎢
⎤
⎦ ⎥
2
=1π
25.5MPa mπ 400.0Mpa( )
⎡
⎣ ⎢
⎤
⎦ ⎥
2
= 4.12X10−4m = 0.412mm
For an internal through crack, the critical crack length = 2aC =0.824 mm
22. The crack length aC = 0.13in/2 = 0.065 in
€
σ f =KIc
Y πa=
23.0ksi in(1) π (0.065in)
= 50.9ksi
23. From Table 7.1, for 7075-T651, KIC = 24.2 MPam
1/2 and σYS = 495 MPa (a) σf =3σYS/4 = 371.25 MPa, assuming Y=1
€
ac =1π
KIC
Yσ f
⎡
⎣ ⎢
⎤
⎦ ⎥
2
=1π
24.2MPa m(1) 371.25Mpa( )⎡
⎣ ⎢
⎤
⎦ ⎥
2
=1.35X10−3m =1.35mm
For an internal through crack, the critical crack length= 2aC =2.7mm
(b) σf =σYS/2 = 247.5 MPa, assuming Y=1
€
ac =1π
KIC
Yσ f
⎡
⎣ ⎢
⎤
⎦ ⎥
2
=1π
24.2MPa m(1) 247.5Mpa( )⎡
⎣ ⎢
⎤
⎦ ⎥
2
= 3.04X10−3m = 3.04mm
For an internal through crack, the critical crack length= 2aC =6.08mm 24. The crack length aC = 1.90mm/2 = 0.95 mm. And from Table 7.1
€
KIC = 55.0MPa m
σ f =KIc
Y πa=55.0MPa mπ 9.5 •10−4m
= 568.0MPa
26.
€
KIC =Yδ f πac
ac =1π
KIC
Yσ f
⎡
⎣ ⎢
⎤
⎦ ⎥
2
=1π
23.5MPa m(1) 300.0Mpa( )⎡
⎣ ⎢
⎤
⎦ ⎥
2
=1.95X10−3m =1.95mm
For an internal through crack, the critical crack length = 2aC =3.90 mm
27.
28.
