SME
Materials Science & Material Properties · Problem type
Critical crack size
Use this for “A steel with KIc = 50 MPa√m carries 300 MPa. With Y = 1, how long a crack can it take before it breaks?”
Diagram
An edge crack ac deep (drawn larger; the plate is wide).
K
=
Yσ
√
πac
=
1
×
300
MPa
×
√
π × 0.008842 m
=
50
MPa√m,
and
the
crack
grows
once
K
reaches
KIc
=
50
MPa√m.
This is an example. Type your own values to start a new problem.
KIc (MPa√m)
=
Y
×
σ (MPa)
×
π
×
ac (mm)
Formulas
KIc
=
Y
×
σ
×
√(π
×
ac
1,000
)
50
=
1
×
300
×
√(π
×
8.8419
1,000
)
Assumptions
•
Linear elastic fracture: plane strain, with a small plastic zone at the crack tip.
•
a is an edge crack’s depth, or half the length of an interior crack.
•
Y depends on the crack and the part; Y = 1 is the wide-plate estimate.
•
The steps turn a from mm into m, as MPa√m needs.
Step-by-step
WE KNOW
KIc = 50 MPa√m, Y = 1, σ = 300 MPa
FIND
critical crack length (ac)
Step 1 · Find critical crack length (ac)
Use KIc = Y × σ × √(π × ac ÷ 1,000)
Divide KIc by Yσ, square it and divide by π for a in m; × 1000 gives mm.
ac
=
1,000
×
(KIc ÷ (
Y
×
σ
))²
π
ac
=
1,000
×
(50 ÷ (1 × 300))²
π
ac
=
1,000
×
0.16667
2
π
ac
=
1,000
×
0.027779
π
ac
=
27.779
π
ac = 8.8419 mm
Check
Put the numbers back in. Both sides should match.
50
=
1
×
300
×
√(π
×
8.8419
1,000
)
✓
Topic check
See what you know: 5 questions on this topic
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