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Fracture Toughness Calculations for Steel Plates in Mechanical Engineering

Solve problems related to fracture toughness of steel plates, critical crack length, plastic zone size, and material selection. Includes calculations and answers with explanations. Suitable for mechanical engineering students.

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Fracture Toughness Calculations for Steel Plates in Mechanical Engineering

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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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