Page 404 - Mechanical Behavior of Materials

Problems and Questions 405

(a) For a safety factor of 2.8 against brittle fracture, what minimum fracture toughness
K Ic is required?
(b) For a safety factor of 2.0 against fully plastic yielding, what minimum yield strength
σ o is required?
(c) Given your results from (a) and (b), select an aluminum alloy from Table 8.1 that
meets both requirements.
8.14 A tension member has width b = 50 mm and thickness t = 5 mm. An axial force P is applied,
and the member may contain an edge crack as deep as a = 10 mm, as in Fig. 8.12(c).
(a) Estimate the force P at failure if the material is the ASTM A517-F steel of Table 8.1.
(b) Also estimate the force P at failure if the material is the AISI 4130 steel from Table 8.1.
(c) Which material would be the best choice if the member is to be used in an engineering
application? Why?
8.15 Bending members, as in Fig. 8.13(a), of depth b = 40 mm and thickness t = 10 mm are made
of 18-Ni maraging steel (vacuum melted). In service, the bending moment may be as high
as M = 5kN·m, and members with edge cracks larger than a = 1 mm are normally found in
inspection and scrapped.
(a) Estimate the moment M necessary to cause failure in this situation. What is the safety
factor?
(b) Assume that some of these members were accidentally not inspected and found their
way into actual service with cracks as large as a = 10 mm. Replacement is expensive.
Assume that you are the engineer who must make the decision on replacement. What
would you decide? Support your decision with additional calculations as needed.
8.16 A beam with a rectangular cross section has dimensions, as defined in Fig. 8.13(a), of b = 50
and t = 10 mm. The beam is made of 7475-T7351 aluminum and is subjected to a bending
moment of M = 1.0kN·m. A through-thickness edge crack of length as large as a = 4mm
may be present. Safety factors of 2.0 against yielding and 3.5 against brittle fracture are
needed.
(a) Are the safety factor requirements met?
(b) If not, what new beam depth b is needed, assuming that t and the other values given
remain unchanged?
8.17 For a round shaft with a circumferential crack, as in Fig. 8.14, derive equations for (a) the
fully plastic force P o , and (b) the fully plastic moment M o . Express these as functions of
crack length a, shaft radius b, and yield strength σ o .
8.18 A circular shaft of 50 mm diameter is subjected to bending and contains a circumferential
surface crack of depth a = 10 mm, as in Fig. 8.14. The shaft is made of the ASTM A517-F
steel of Table 8.1. Estimate the bending moment M that will cause the shaft to fail.
8.19 A thin-walled tube, as in Fig. P8.19, is loaded with an internal pressure p and has a
longitudinal through-wall crack of length 2a. Stress intensity factors f or this case from
Tada (2000) are
√ √
K = F(pr avg /t) πa, where F = F(λ), λ = a/ r avg t
√
F = 1 + 1.25λ 2 for λ ≤ 1, and F = 0.6 + 0.9λ for 1 ≤ λ ≤ 5