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2) Fatigue Behaviour & Failure (6 points) A tubular component failed in fatigue. Failure analysis included characterisation of the fracture surface. It was found that that the failure started near a small surface scratch with a depth of 0.05 mm. Assume the stress in the frame tube varies smoothly. It holds for this case R = -0.25 and the maximum stress is 400 MPa. One complete cycle takes 0.1 seconds. The tube has a diameter of 4 cm and a wall thickness of 2.5 mm. a) Take a point at the tube surface wall and sketch the stress in this point as a function of time for one loading cycle (1 point). For this material it is known: • Kic= 25 MPa.m ¹/2 • Kth=2.5 MPa.m ¹/2 Y = 1 ● m = 4 • c = 2.10-¹¹ (MPa)-4.m¹¹ b) How much is the relevant difference between the maximum and minimum stress in this case for fatigue? Explain your answer (1 point). c) Calculate the crack length when failure of the tube occurred (1 point). d) Calculate the number of cycles to failure under these conditions (1,5 point). e) Residual stresses have a strong effect on fatigue life of a construction. When do they have positive and when do they have a negative effect? Give an example of both (1,5 point).