A PMMA plate with a 25 mm (width) x 6.5 mm (thickness) cross-section has a contained crack of length 2c = 0.5 mm in the center of the specimen. If the applied load (along the 2 length direction) is 1000 N, calculate the stress intensity factor. If the fracture toughness of PMMA, K1c = 1.15 MPa.m1/2, at what load (in N) does the crack propagate?

Answer :

Answer:

LAOD = 6669.86 N

Explanation:

Given data:

width[tex] = 25 mm = 25\times 10^{-3} m[/tex]

thickness [tex]= 6.5 mm = 6.5\times 10^{-3} m[/tex]

crack length 2c = 0.5 mm at centre of specimen

[tex]\sigma _{applied} =  1000 N/cross sectional area[/tex]

stress intensity factor  =  k  will be

[tex]\sigma_{applied} = \frac{1000}{25\times 10^{-3}\times 6.5\times 10^{-3}}[/tex]

                   [tex]= 6.154\times 10^{6} Pa [/tex]

we know that

[tex]k =\sigma_{applied} (\sqrt{\pi C})[/tex]

  [tex]=6.154\sqrt{\pi (2.5\times 10^{-04})}[/tex]          [c =0.5/2 = 2.5*10^{-4}]

K = 0.1724 Mpa m^{1/2} for 1000 load

if[tex] K_C = 1.15 Mpa m^{1/2}[/tex] then load will be

[tex]Kc = \sigma _{frac}(\sqrt{\pi C})[/tex]

[tex]1.15 MPa = \sigma _{frac}\times \sqrt{\pi (2.5\times 10^{-04})}[/tex]

[tex]\sigma _{frac} = 41.04 MPa[/tex]

[tex]load = \sigma _{frac}\times Area[/tex]

[tex]load = 41.04 \times 10^6 \times 25\times 10^{-3}\times 6.5\times 10^{-3} N[/tex]

LAOD = 6669.86 N

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