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zhenek [66]
3 years ago
13

Suppose that a wing component on an aircraft is fabricated from an aluminum alloy that has a plane strain fracture toughness of

27 MPa (24.57 ksi). It has been determined that fracture results at a stress of 115 MPa (16680 psi) when the maximum internal crack length is 8.3 mm (0.3268 in.). For this same component and alloy, compute the stress level at which fracture will occur for a critical internal crack length of 5.9 mm (0.2323 in.).
Engineering
1 answer:
melamori03 [73]3 years ago
4 0

Answer:

The stress level = 133.5 Mpa

Explanation:

Given data;

Toughness = 27Mpa

Stress = 115 Mpa

Crack length = 8.3mm = 8.3 * 10^-3m

The stress level can be calculated using the formula,

б = \frac{ktc}{Y\sqrt{\pi a} }      ---------------------------------------------1

Where;

б = strain level

ktc = fracture toughness

a = surface length = 8.3 *10^-3/2 (Half of the cracked length)

Substituting into the formula, we have

But, we have to calculate the parameter Y before we can substitute into equation 1.

By making Y subject formula, we have;

Y = ktc/ (б√πa)

Y = 27/(115 *√(π * (8.3 *10^-3/2))

Y = 27/(115 *√0.0130)

Y = 27/(115 * 0.114)

Y = 27/13.131

Y = 2.1

Calculating the stress level, we substitute  into equation 1 as follows;

б = \frac{ktc}{Y\sqrt{\pi a} }

б = 27/ (2.1 *√(π * (5.9 * 10^-3/2))

    = 27/(2.1 *√(π * 0.00295))

    = 27/ (2.1 *√0.00927)

     = 27/(2.1 * 0.096)

     = 27/0.202

    = 133.5 Mpa

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Explanation:

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- The missing figure is in the attachment.

- The dimensions of member AC = ( 6 x 25 ) mm x 2

- The diameter of the pin d = 19 mm

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-  Find the axial stress in AE and the shear stress in pin C.

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- The stress in member AE can be calculated using component of force P along the member AE  as follows:

                                    stress_ac = P*cos(Q) / A_ae

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                                    cos(Q) = 4 / 5   ..... From figure ( trigonometry )

                                    A_ae = 0.006*0.025*2 = 3*10^-4 m^2

Hence,

                                    stress_ae = 2*(4/5) / 3*10^-4

                                    stress_ae = 5.333 MPa

- The force at pin C can be evaluated by taking moments about C equal zero:

                                   (M)_c = P*6 - F_eb*3

                                      0 = P*6 - F_eb*3

                                      F_eb = 0.5*P

- Sum of horizontal forces for member AC is zero:

                                      P - F_eb - F_c = 0

                                      F_c = 0.5*P

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                                     shear stress = shear force / 2*A_pin

Where, The area of the pin C is:

                                     A_pin = pi*d^2 / 4

                                     A_pin = pi*0.019^2 / 4 = 2.8353*10^-4 m^2

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                                    shear stress = 1.763 MPa

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