Question

Suppose that a wing component on an aircraft is fabricated from an aluminum alloy that has a plane-strain fracture toughness of 26.0 MPa (23.7 ksi ). It has been determined that fracture results at a stress of 112 MPa (16,240 psi) when the maximum internal crack length is 8.6 mm (0.34 in.). For this same component and alloy, compute the stress level at which fracture will occur for a critical internal crack length of 6.0 mm

Answer 1

Answer: 133.88 MPa approximately 134 MPa

Explanation:

Given

Plane strains fracture toughness, k = 26 MPa

Stress at which fracture occurs, σ = 112 MPa

Maximum internal crack length, l = 8.6 mm = 8.6*10^-3 m

Critical internal crack length, l' = 6 mm = 6*10^-3 m

We know that

σ = K/(Y.√πa), where

112 MPa = 26 MPa / Y.√[3.142 * 8.6*10^-3)/2]

112 MPa = 26 MPa / Y.√(3.142 * 0.043)

112 = 26 / Y.√1.35*10^-2

112 = 26 / Y * 0.116

Y = 26 / 112 * 0.116

Y = 26 / 13

Y = 2

σ = K/(Y.√πa), using l'instead of l and, using Y as 2

σ = 26 / 2 * [√3.142 * (6*10^-3/2)]

σ = 26 / 2 * √(3.142 *3*10^-3)

σ = 26 / 2 * √0.009426

σ = 26 / 2 * 0.0971

σ = 26 / 0.1942

σ = 133.88 MPa

Answer 2

In this exercise we have to calculate the value of stress in terms of pressure, in this way we find:

133.88 MPa approximately 134 MPa

Given the information in the statement, we have:

• Plane strains fracture toughness is k = 26 MPa
• Stress at which fracture occurs is σ = 112 MPa
• Maximum internal crack length is l = 8.6 mm = 8.6*10^-3 m
• Critical internal crack length is l' = 6 mm = 6*10^-3 m

We know that the calculus the stress is:

$\sigma = K/(Y\sqrt{\pi a} )\\112 MPa = 26 MPa / Y.\sqrt{3.142 * 8.6*10^{-3})/2}\\112 MPa = 26 MPa / Y\sqrt{3.142 * 0.043}\\112 = 26 / Y.\sqrt{1.35*10^{-2}}\\112 = 26 / Y * 0.116\\Y = 26 / 112 * 0.116\\Y = 26 / 13\\Y = 2$

So using the same formula but now replacing the value of Y by 2, we have:

$\sigma = K/(Y.\sqrt{\pi a} )\\\sigma = 26 / 2 * [\sqrt{3.142 * (6*10^-3/2)}]\\\sigma = 26 / 2 * \sqrt{(3.142 *3*10^-3)}\\\sigma = 26 / 2 * \sqrt{0.009426}\\\sigma = 26 / 2 * 0.0971\\\sigma = 26 / 0.1942\\\sigma = 133.88 MPa$

See more about about stress level at brainly.com/question/1446338