PROBLEM 8.20 8.20 The fatigue data for a ductile cast iron are given as follows: Stress Amplitude Cycles to Failure [MPa (ksi)] 248 (36.0) 1 × 105 236 (34.2) 3 × 105 224 (32.5) 1 × 106 213 (30.9) 3 × 106 201 (29.1) 1 × 107 193 (28.0) 3 × 107 193 (28.0) 1 × 108 193 (28.0) 3 × 108 (a) Make an S–N plot (stress amplitude versus logarithm cycles to failure) these data. (b) What is the fatigue limit for this alloy? (c) Determine fatigue lifetimes at stress amplitudes of 230 MPa (33,500 psi) and 175 MPa (25,000 psi). (d) Estimate fatigue strengths at 2 105 and 6 106 cycles. Solution (a) The fatigue data for this alloy are plotted below. (b) The fatigue limit is the stress level at which the curve becomes horizontal, which is 193 MPa (28,000 psi). (c) As noted by the set of dashed lines, the fatigue lifetime at a stress amplitude of 230 MPa is about 5 “A” 105 cycles (log = 5.7). From the plot, the fatigue lifetime at a stress amplitude of 230 MPa (33,500 psi) is about N 50,000 cycles (log = 4.7). At 175 MPa (25,000 psi) the fatigue lifetime is essentially an infinite number of cycles N since this stress amplitude is below the fatigue limit. (d) As noted by the set of dashed lines, the fatigue strength at 2 105 cycles (log = 5.3) is about 240 N “B” MPa (35,000 psi); and according to the set of dashed lines, the fatigue strength at 6 106 cycles (log = 6.78) is N “C” about 205 MPa (30,000 psi).
PROBLEM 8.20 8.20 The fatigue data for a ductile cast iron are given as follows: Stress Amplitude [MPa (ksi)] Cycles to Failure 248 (36.0) 1 × 105 236 (34.2) 3 × 105 224 (32.5) 1 × 106 213 (30.9) 3 × 106 201 (29.1) 1 × 107 193 (28.0) 3 × 107 193 (28.0) 1 × 108 193 (28.0) 3 × 108 (a) Make an S–N plot (stress amplitude versus logarithm cycles to failure) these data. (b) What is the fatigue limit for this alloy? (c) Determine fatigue lifetimes at stress amplitudes of 230 MPa (33,500 psi) and 175 MPa (25,000 psi). (d) Estimate fatigue strengths at 2 105 and 6 106 cycles. Solution (a) The fatigue data for this alloy are plotted below. (b) The fatigue limit is the stress level at which the curve becomes horizontal, which is 193 MPa (28,000 psi). (c) As noted by the “A” set of dashed lines, the fatigue lifetime at a stress amplitude of 230 MPa is about 5 105 cycles (log N = 5.7). From the plot, the fatigue lifetime at a stress amplitude of 230 MPa (33,500 psi) is about 50,000 cycles (log N = 4.7). At 175 MPa (25,000 psi) the fatigue lifetime is essentially an infinite number of cycles since this stress amplitude is below the fatigue limit. (d) As noted by the “B” set of dashed lines, the fatigue strength at 2 105 cycles (log N = 5.3) is about 240 MPa (35,000 psi); and according to the “C” set of dashed lines, the fatigue strength at 6 106 cycles (log N = 6.78) is about 205 MPa (30,000 psi).
SOLUTION_ASSIGNMENT_CH8.docx