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Problems

Problems.

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Problems

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  1. Problems Problem 1:20 inc.in width and 0.050 inc. İn thickness of a plate is fixed at one end and pulled from the other end with a force of 36000 lbs. The fracture toughness of this plate made of steel is KIC = 50 ksi(in) ½ . When the plate contains the center crack, calculate the critical crack length before fracture occurs. Answer 1 : a=0.60 inc (15.2mm) , 2a=1.20 inc (30.4 mm) Dokuz Eylül University, Mechanical Engineering Department Prof. Dr. M. Evren TOYGAR

  2. Problem 2:The width of the plate made of low carb is 4 in. And the tensile stress applied to this plate is 32 ksi. Calculate the value of the minimum fracture toughness to be tolerated for the plate with a 2 mm crack with edge notch. • Answer 2 : 19.4 MPa(m)1/2 • Problem 3:Plates with dimensions of 180-350 mm from two different A and B steels are subjected to a pull load of P = 45000 N. If the minimum crack size is 2.5 mm with non-destructive control and the minimum weight in design is taken into consideration, which steel should be selected? • A steel : yield strength = 91 N/mm2 , fracture toughness = 364 N/mm 3/2 • B steel : yield strngth = 103.5 N/mm2 , fracture toughness = 174 N/mm 3/2 • Answer 3: A steel must be choosen. Dokuz Eylül University, Mechanical Engineering Department Prof. Dr. M. Evren TOYGAR

  3. Problem 4:The width and thickness of a plate containing center crack are w = 6 inc. and B = 0.2 inc, respectively. The maximum applied loadis Pmax = 41 kips and the yield stress value is ys = 50 ksi. For this system that contains a center crack as 2a = 2 in; • a) calculate the fracture toughness parameter, • b) calculate the size of the plastics zone that occurs during the fracture. • Answer 4: a) 64.9 ksi(in)1/2. b) The length of the plastic zone is equal to the length outside the crack. Dokuz Eylül University, Mechanical Engineering Department Prof. Dr. M. Evren TOYGAR

  4. Problem 5:On a plate containing an edge crack, β = 1.12. R curves representing the resistance of the material to fracture progression for plane stress is • Here, the fracture toughness is 50 MN/m3/2elastic modulus is2*105 MN/m2 . is the amount of steady cracks going forward. Initial crack length is ai = 10 cm Therefore, a) calculate stable crack growth, b) calculate fracture stress. ai is the initial crack length, ac is the final crack length • Answer 5: a) ac = 0.13m, b) fr = 150.65 MPa Dokuz Eylül University, Mechanical Engineering Department Prof. Dr. M. Evren TOYGAR

  5. Problem: 6150 MPa stressis applied to a plate. The fracture toughness of the material is given as 80 MPam . According to this, • a) calculate the critical length of the center crack in the plate, • b) calculate the energy release rate. • Note : E = 207 GPa’ dır. • Problem 7: Bir A tensile sample is 10 mm wide and the half of a crack length is a = 0.3 mm long. When the applied tensile stress reaches 450 MPa on this sample, the crack propagates suddenly. The elastic modulus is given as 200 GPa • a) when there is a center crack, • b) when there is a edge crack, • Calculate the fracture toughness. Dokuz Eylül University, Mechanical Engineering Department Prof. Dr. M. Evren TOYGAR

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