Question 15. A very large, steel plate of yield stress 200 MPa and Poisson's ratio 0.3 has a crack at the centre of length 34 mm, orientated along the x-axis. If the plate is subjected to far field tensile loading of magnitude 177 MPa and is assumed to be in a state of plane stress, determine the extent of the plastic region at the crack tip, along the x-axis. You may assume Poisson's ratio is (1/3). Express your answer as an integer value of mm. Question 17 A shear pin made from a 4340 steel (0.4% C) fails by ductile fracture. It was supposed to be initially normalised, austenitised, quenched and tempered to 100% martensite to give a hardness of 5.5 GPa. The hardness was measured to be 4.5 GPa. Which of the following summaries most accurately accounts for what may have gone wrong? O Insufficiently heating the steel would result in partial austenitisation, leading to only partial martensite after quenching and a reduction in final hardness. The temper could still occur at the correct conditions and still lead to an insufficient strength and encouraging ductile failure. O Performing a full austenitisation but then cooling slower than the critical cooling rate for the alloy would allow some ferrite/pearlite to form after the martensite reaction has finished. This would be softer than the tempered martensite and so reduce the final hardness. O Assuming a full austenitisation and then cooling faster than the critical cooling rate, the hardness would exceed the required hardness. Tempering at an excessive temperature would reduce the hardness too much and also reduce the ductility, which is consistent with the mode of failure. O If the carbon content of the alloy was lower than expected then we might get incomplete austenitisation at a temperature sufficient to fully transform correct alloy, leading to retention of softer austenite at room temperature. The resulting hardness of the tempered martensite would also be lower than desired due to reduced solution strengthening by the carbon.