Page 403 - Mechanical Behavior of Materials

404 Chapter 8 Fracture of Cracked Members

dimensions are width b = 35 and t = 5 mm, and the crack may be as long as a = 10 mm.
The member must resist a tension force of P = 50 kN. Determine: (a) the safety factor
against brittle fracture, (b) the safety factor against fully plastic yielding, and (c) the overall
(controlling) safety factor.
8.8 A center-cracked plate of AISI 1144 steel has dimensions, as defined in Fig. 8.12(a), of b = 50
and t = 5 mm, and it is subject to a tension force of P = 100 kN.
(a) What are the safety factors against brittle fracture and against fully plastic yielding if
the crack length is a = 10 mm?
(b) Proceed as in (a) but use a = 30 mm.
(c) Assume that this plate is an engineering component and comment on its safety for the
two different crack lengths.
8.9 A beam with a rectangular cross section has dimensions, as defined in Fig. 8.13, of b = 40
and t = 10 mm. The beam is made of 7475-T7351 aluminum and is subjected to a bending
moment of M = 900 N·m.
(a) If a through-thickness edge crack of length a = 5 mm is present, what is the safety
factor against brittle fracture?
(b) Repeat (a) for a crack length of 10 mm.
(c) What is the critical crack length for fracture?
(d) What crack length can be allowed if a safety factor of 3.0 against brittle fracture is
required?
8.10 A tension member made of 2014-T651 aluminum has dimensions, as defined in Fig. 8.12(c),
of b = 50 and t = 5 mm. A safety factor of 3.0 against failure by either brittle fracture or fully
plastic yielding is required.
(a) If there is a through-thickness crack in one edge of length a = 10 mm, what is the
highest tension force P that can be permitted in service.
(b) If the force in service is P = 5.0 kN, what is the largest crack length that can safely
exist in the member?
8.11 A rectangular beam made of ABS plastic is b = 20 mm deep and t = 10 mm thick. As shown
in Fig. 8.13(a), a bending moment M is applied, and a through-thickness edge crack may be
present. For a safety factor against brittle fracture of 2.5 in stress, what is the largest crack
length a that can be allowed if (a) M = 20 N·m, and (b) M = 5.0N·m?
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8.12 An engineering member is made of 300-M (650 C temper) steel. It is in the shape of a plate
loaded in tension and may have a crack in one edge, as shown in Fig. 8.12(c). The dimensions
are width b = 80 mm and thickness t = 20 mm, and the member must resist a tension force
of P = 150 kN. Determine the length a of the largest edge crack that can be permitted such
that the safety factor against brittle fracture is not less than 3.5, and also the safety factor
against fully plastic yielding is not less than 2.5.
8.13 An engineering member is to be made of an aluminum alloy. It is in the shape of a plate loaded
in tension that may have a crack in one edge, as shown in Fig. 8.12(c). The dimensions are
width b = 40 mm and thickness t = 4.0 mm, and the crack may be as long as a = 8.0 mm.
The member must resist a tension force of P = 7.5kN.