Solve Example 15.2 for the condition that d = 200 mm and 2c = 50 mm.Example 15.2 Brittle F...

Solve Example 15.2 for the condition that d = 200 mm and 2c = 50 mm.

Example 15.2 Brittle Fracture for Combined Tension and Bending

A hook similar to that shown in Figure E15.2 is part of a scarifier used to dig up old road beds before replacing them. Let the tool be made of AISI 4340 steel and heat-treated to the properties indicated in Table 15. 1. The dimensions of the tool are as follows: d = 250 mm, 2c = 60 mm, and the width of the rectangular cross section is t = 25 mm. Determine the magnitude of the fracture load P for a crack length of

(a) a = 5 mm and

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(b) a = 10 mm.

FIGURE E15.2

Solution:

Note that both the width t and crack length a satisfy Eq. 15.29; therefore, the hook is assumed to be loaded in the brittle state. At a section through the crack, the hook is subjected to combined axial load (Case 4 of Table 15.2) and bending (Case 6 of Table 15.2). Since a linear elastic analysis is assumed, the state of stress for combined loading can be obtained by superposition of the two states of stress for the two types of loading. Thus,

σf(λ) = σ1f1(λ) + σ2f2(λ)

(a) When a = 5 mm, λ = a/2c = 0.083. From Table 15.2 for Cases 4 and 6, we obtain f1(λ) = 1.22 and f2(λ) = 1.02. Therefore,

This is substituted in the relation

t. give

 

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(b) When a = 10 mm, λ = 0.167 and

 

Table 15.1:

TABLE 15.1 KIC Critical Stress Intensity Factor (Fracture Toughness)a

aRoom temperature data.

 (15.29)

Case 4 of Table 15.2:

TABLE 15.2 Stress Intensity Factors KI

Case 6 of Table 15.2:

TABLE 15.2 Stress Intensity Factors KI