Question

Calculate the fracture toughness of a material for which a plate test with a central crack gives the following information W 0.5 m, B 19 mm, 2a 50 mm, failure load P 1335 kN. The yield strength is 483 MPa. Is this plane strain? Check for collapse. How large is the plastic zone at the time of fracture? Using the result of problem1,calculate the residual strength of a plate with an edge crack W 50 mm. Do the same for w = 152 mm. and a 12.2 mm. Check for collapse.

Answer 1

To calculate the fracture toughness, use the formula K = P/(W * sqrt(pi * a)). The material is likely in the plane strain regime and we can check for collapse by comparing K to Kc. The plastic zone can be approximated as a circular region with a radius r = Kc / (sqrt(pi * sigma_yield)).

Step-by-step explanation:

To calculate the fracture toughness of the material, we can use the formula K = P/(W * sqrt(pi * a)), where P is the failure load, W is the width of the plate, and 2a is the length of the crack. Substituting the given values, we have K = 1335 kN / (0.5 m * sqrt(pi * 0.05 m)).

Plane strain is defined as a condition where there is negligible deformation perpendicular to the plane of loading. For a plate with a central crack, it is typically in the plane strain regime. To check for collapse, we need to compare the fracture toughness (K) to the critical stress intensity factor (Kc).

The plastic zone is the region of the material surrounding the crack where plastic deformation occurs. At the time of fracture, the plastic zone can be approximated as a circular region with a radius given by r = Kc / (sqrt(pi * sigma_yield)), where Kc is the critical stress intensity factor and sigma_yield is the yield strength of the material.