4. The microstructure of a low carbon steel (Steel A) is shown below. MnS inclusions are marked by arrows. These inclusions will serve as cracks embedded in the steel if fractured. The stress required to cause the fracture of MnS inclusions can be calculated using Equation 1, in which Co is the elongated length of an inclusion in meter. Assume that yield strength of the steel is 400 MPa. 50m Microstructure of a low carbon steel with inclusions (marked by arrows) 4,000,000.00 Equation 1 = Pa According to fracture mechanics (to be learnt in the 2nd half of the term), the stresses present in a small zone, often called plastic zone, ahead the crack tip can be either biaxial or triaxial, even though the plate structure is subjected to uniaxial loading. The biaxial stress condition is found when the structure is a thin plate, while triaxial stress condition is present when the structure is a thick plate. The principal stresses in the plastic zone are listed in Table 1. Answer the following questions: 1 Table 1 Loading conditions applied Loading conditions in the plastic zone ahead of the crack tip in a plate structure Principal stress 01 02 03 A (Bi-axial) (simulating the 3 Plastic zone stresses present in the plastic zone ahead of the crack tip in a thin plate structure) B (Tri-axial) (simulating the stresses present in the plastic zone ahead of the crack tip in a thick plate structure) 0.660 a. Determine if the inclusions could be fractured when the plate is loaded to a stress just to cause the material in the plastic zone to start plastic deformation. [6; 2 for fracture stress + 2 for each case] b. Determine the minimum size of inclusions that could be fractured under the loading condition in a) [4; 2 for each case] 1 50m Microstructure of a low carbon steel with inclusions (marked by arrows) 4,000,000.00 Equation 1 Pa According to fracture mechanics (to be learnt in the 2nd half of the term), the stresses present in a small zone, often called plastic zone, ahead the crack tip can be either biaxial or triaxial, even though the plate structure is subjected to uniaxial loading. The biaxial stress condition is found when the structure is a thin plate, while triaxial stress condition is present when the structure is a thick plate. The principal stresses in the plastic zone are listed in Table 1. Answer the following questions: 1 Plastic zone Table 1 Loading conditions applied Loading conditions in the plastic zone ahead of the crack tip in a plate structure A (Bi-axial) (simulating the stresses present in the plastic zone ahead of the crack tip in a thin plate structure) B (Tri-axial) (simulating the stresses present in the plastic zone ahead of the crack tip in a thick plate structure) Principal stress 02 03 b b 0 0.660 a. Determine if the inclusions could be fractured when the plate is loaded to a stress just to cause the material in the plastic zone to start plastic deformation. [6; 2 for fracture stress + 2 for each case] b. Determine the minimum size of inclusions that could be fractured under the loading condition in a) [4; 2 for each case] c. The inclusions appear to be oriented in one direction (rolling direction of the plate) and assume that the fracture of one largest inclusion in the plastic zone could lead to the fracture of the entire plate structure. Answer the following questions and justify your answers: i. Would you expect the stress to cause the fracture of the plate be very different from test to test, assuming the crack geometry and plate dimensions are kept the same from test to test? [2] HINT: it is random which inclusions happen to be in the plastic zone in any given test ii. Would you expect a large difference in ductility, a measure of resistance to tensile fracture, if you perform tensile tests on the same plates without a crack? [2] d. Draw some conclusions on how microstructural dimensions and geometry of the second phases present in the material affect the strength and the fracture of materials differently? [2] e. The resistance to fracture is often correlated to the area under the stress-strain curve. Briefly discuss whether the correlation can be justified for materials with inclusions. [2] 2