Question

Problem 3 [35 marks] An inspection of a failed thin walled pressure vessel (cylinder with closed ends) shows through- the-thickness cracks in the axial (or longitudinal) direction. The length of the cracks varies from 10 mm to 25 mm. The pressure vessel has radius R = 1.5 m, wall thickness t = 30 mm, and was manufactured from aluminium with fracture toughness properties Kịc = 50 MPa m12. a) Determine the pressure at which the vessel is expected to have failed by brittle fracture. Give your answer in MPa. [20 marks] b) What is the critical length (2ac) of through-the-thickness circumferential cracks (oriented in the hoop direction) when the inner pressure reaches 10 MPa. Give your answer in mm. [15 marks]

Answer 1

Sata from the giren question 0 Coack length radies = 10 mm to 25mm Radius = 1.5m Thickness = 30mm KIC= somparm @ poesure of the versel : using the equation = єү, та Ka Pd Ylira lut the values. Assume (Y=1) and putling ps land) x Thai Pi = / 4X50 X 0.03 X 3.0 T X0-01 6 3.0 욺 X 10.031 2X01 176 2x 5.681 Pi=11•362 mpa = 25 X16 m2 Now subs titoleAg -25 mm - P2= ) (4X50 X0:03) Tx0.025 2x 0.078 2 X 0.229

- 2x 3.584 P2 = 7. 168 mpa 6 Ks Ta ka Pd sta { Choop 6 he 20 2+ x = a 2 X 50 X 0.03 2 3 (30) x 0.318 - a (0.15€ x 0.318 - a $ 0.01% 0.318 - a 0.06318 = a Ac = 3.18x10m lac= 3.18 mm half length of the crack 1206 = 6-36mm This is the critical full length of the coack for the pressure - lompa -0-