Question

A crack of the length a0 = 0.02 m was discovered in the connecting rod with the cross-section of w x w (w = 0.2 m) of a steam engine shown below. The characteristics of the engine are: power 4200 hp, frequency of rotation 15 rpm, stroke 8 feet. The connecting rod experiences symmetric cyclic load with the amplitude of F = 2,611 kN. It is made of a cast iron with the following mechanical characteristics: the yield strength is ?y = 200 MPa, the fracture toughness is KIc = 40 MPa?m, the fatigue threshold stress intensity factor is ?Kth = 14 MPa?m and parameters of the Paris' relationship for the fatigue crack growth rate are m = 6.5 and A = 7 x 10^-16 m/(MPa?m)^6.5. (a) Determine the stress intensity range ?K for the crack of the size a0. (b) Determine the size of the crack af at which Kmax becomes equal to KIc. What is the significance of af? (c) Determine the number of cycles Nf required for the crack to grow from a0 to af. (Be mindful of Y and its dependence on a/w ratio. An average Y can be the first approximation.) (d) Which recommendation can you make regarding continuing or discontinuing service of the machine based on computed Nf? Hint: The analytical relationship (Dowling, p. 349) is suggested for the geometry factor Y = 0.265(1 - ?)^4 + (0.857 + 0.265?) / (1 - ?)^3/2 , where ? = a/w. (source: Ashby and Jones)

          A crack of the length a0 = 0.02 m was discovered in the connecting rod with the cross-section of w x w (w = 0.2 m) of a steam engine shown below. The characteristics of the engine are: power 4200 hp, frequency of rotation 15 rpm, stroke 8 feet. The connecting rod experiences symmetric cyclic load with the amplitude of F = 2,611 kN. It is made of a cast iron with the following mechanical characteristics: the yield strength is ?y = 200 MPa, the fracture toughness is KIc = 40 MPa?m, the fatigue threshold stress intensity factor is ?Kth = 14 MPa?m and parameters of the Paris' relationship for the fatigue crack growth rate are m = 6.5 and A = 7 x 10^-16 m/(MPa?m)^6.5.

(a) Determine the stress intensity range ?K for the crack of the size a0.
(b) Determine the size of the crack af at which Kmax becomes equal to KIc. What is the significance of af?
(c) Determine the number of cycles Nf required for the crack to grow from a0 to af. (Be mindful of Y and its dependence on a/w ratio. An average Y can be the first approximation.)
(d) Which recommendation can you make regarding continuing or discontinuing service of the machine based on computed Nf?

Hint: The analytical relationship (Dowling, p. 349) is suggested for the geometry factor
Y = 0.265(1 - ?)^4 + (0.857 + 0.265?) / (1 - ?)^3/2 ,
where ? = a/w.

(source: Ashby and Jones)

$A crack of the length a0 = 0.02 m was discovered in the connecting rod with the cross-section of w x w (w = 0.2 m) of a steam engine shown below. The characteristics of the engine are: power 4200 hp, frequency of rotation 15 rpm, stroke 8 feet. The connecting rod experiences symmetric cyclic load with the amplitude of F = 2,611 kN. It is made of a cast iron with the following mechanical characteristics: the yield strength is ?y = 200 MPa, the fracture toughness is KIc = 40 MPa?m, the fatigue threshold stress intensity factor is ?Kth = 14 MPa?m and parameters of the Paris' relationship for the fatigue crack growth rate are m = 6.5 and A = 7 x 10^-16 m/(MPa?m)^6.5. (a) Determine the stress intensity range ?K for the crack of the size a0. (b) Determine the size of the crack af at which Kmax becomes equal to KIc. What is the significance of af? (c) Determine the number of cycles Nf required for the crack to grow from a0 to af. (Be mindful of Y and its dependence on a/w ratio. An average Y can be the first approximation.) (d) Which recommendation can you make regarding continuing or discontinuing service of the machine based on computed Nf? Hint: The analytical relationship (Dowling, p. 349) is suggested for the geometry factor Y = 0.265(1 - ?)^4 + (0.857 + 0.265?) / (1 - ?)^3/2 , where ? = a/w. (source: Ashby and Jones)$

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