Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 11, Problem 8ETSQ
To determine
The probability of surviving
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Example: the low cycle fatigue of a certain steel is given by life cycle equation-2:
(of/E)=0.005
E=0.07
b= -0.08
c= -0.7
a. What is the value of the transition fatigue life, in this case 2 N/when Ɛɛ = Ep
b. What is the total strain amplitude at the transition fatigue life?
3. Given the following fatigue data for a brass alloy:
Cycles to Failure
2 x 105
1х 106
Stress Amplitude (MPa)
310
223
191
3х 106
168
1 x 107
153
3х 107
143
1х 108
134
3х 108
127
1х 109
a.) Plot the S-N curve for this alloy.
b.) Does this material have an endurance limit? Explain.
c.) Determine the fatigue strength at 5 x 105 cycles.
d.) Determine the fatigue life for 200 MPa.
e.) If the loading in part c is uniaxial, what is the minimum diameter of a circular rod
required for this application if the maximum load is 500 kN?
A cylindrical specimen of a metal alloy 47.5 mm long and 9.72 mm in diameter is stressed in tension. A true stress of 397 MPa
causes the specimen to plastically elongate to a length of 54.3 mm. If it is known that the strain-hardening exponent for this
alloy is 0.2, calculate the true stress (in MPa) necessary to plastically elongate a specimen of this same material from a length of
47.5 mm to a length of 55.8 mm.
i
MPa
Chapter 11 Solutions
Materials Science And Engineering Properties
Ch. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 6CQCh. 11 - Prob. 7CQCh. 11 - Prob. 8CQCh. 11 - Prob. 9CQCh. 11 - Prob. 10CQ
Ch. 11 - Prob. 11CQCh. 11 - Prob. 12CQCh. 11 - Prob. 13CQCh. 11 - Prob. 14CQCh. 11 - Prob. 15CQCh. 11 - Prob. 16CQCh. 11 - Prob. 17CQCh. 11 - Prob. 18CQCh. 11 - Prob. 19CQCh. 11 - Prob. 20CQCh. 11 - Prob. 21CQCh. 11 - Prob. 22CQCh. 11 - Prob. 23CQCh. 11 - Prob. 24CQCh. 11 - Prob. 25CQCh. 11 - Prob. 26CQCh. 11 - Prob. 27CQCh. 11 - Prob. 28CQCh. 11 - Prob. 29CQCh. 11 - Prob. 30CQCh. 11 - Prob. 1ETSQCh. 11 - Prob. 2ETSQCh. 11 - Prob. 3ETSQCh. 11 - Prob. 4ETSQCh. 11 - Prob. 5ETSQCh. 11 - Prob. 6ETSQCh. 11 - Prob. 7ETSQCh. 11 - Prob. 8ETSQCh. 11 - Prob. 9ETSQCh. 11 - Prob. 10ETSQCh. 11 - Prob. 11.1PCh. 11 - Prob. 11.2PCh. 11 - Prob. 11.3PCh. 11 - Prob. 11.4PCh. 11 - Prob. 11.5PCh. 11 - Prob. 11.6PCh. 11 - Prob. 11.7PCh. 11 - Prob. 11.8PCh. 11 - Prob. 11.9PCh. 11 - Prob. 11.10PCh. 11 - Prob. 11.11PCh. 11 - Prob. 11.12PCh. 11 - Prob. 11.13PCh. 11 - Prob. 11.14P
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- A copper rod is deformed using a uniaxial tensile force of 16000 N. Deformation continues until sufficient strain hardening has occurred such that the applied force is too small to allow further deformation. After deformation, the rod has a diameter of 0.01 m and a length of 1.5 m. Assume that copper follows the strain hardening lawwith K of 310 MPa and n=0.54 Please calculate the true strain after the deformation ?arrow_forwardExample: the low cycle fatigue of a certain steel is given by life cycle equation-2: (of/E)=0.005 E=0.07 b= -0.08 c= -0,7 a. What is the value of the transition fatigue life, in this case 2 N/when E - Ep b. What is the total strain amplitude at the transition fatigue life?arrow_forwardS Figure P1.16 shows the stress-strain relations of metals A and B during ten- sion tests until fracture. Determine the following for the two metals (show all calculations and units): a. Proportional limit b. Yield stress at an offset strain of 0.002 m/m. c. Ultimate strength d. Modulus of resilience e. Toughness f. Which metal is more ductile? Why? 900 Metal A 600 Metal B 300 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Strain, m/m FIGURE P1.16 Stress, MPaarrow_forward
- Consider an S-590 alloy component as shown in following figure that is subjected to a stress of 200 MPa (29,000 psi). At what temperature will the rupture lifetime be 509 h?arrow_forwardQuestion No.2 Figure P1.16 shows the stress-strain relations of metals A and B during ten- sion tests until fracture. Determine the following for the two metals (show all calculations and units): a. Proportional limit b. Yield stress at an offset strain of 0.002 m/m. c. Ultimate strength d. Modulus of resilience e. Toughness f. Which metal is more ductile? Why? 000 -Metal A S 600 -Metal B 300 0.00 a.02 0.04 0.06 0.08 0.10 0.12 0.14 Strain, mim FIGURE P1.16 Stress, MPaarrow_forwardQ.1 The yield stresses (oy) have been measured using steel and aluminum specimens of various grain sizes, as follows: Material D (µm) σΥ (MPa) Steel 60.5 160 136 128 Aluminum 11.1 235 100 223 (a) Determine the coefficients o and kỵ in the Hall- Petch for these two materials. (b) Determine the yield stress in each material for a grain size of d=26 um.arrow_forward
- PROBLEM 4: As shown in the diagram shown, there is a gap of 0.5 mm between the rods at 10°C. Determine the stress in each rod if the temperature is raised to 150°C. The properties of each material are shown in the diagram. 0.5 mm FINAL ANSWERS 300 mm -250 mm MPa O alum O steel MPа Aluminum Stainless steel A = 2000 mm2 E = 75 GPa a = 23 × 10-6°C A = 800 mm? E = 190 GPa 17.3 x 10-6/°Carrow_forwardQuestion No.2 Figure P1.16 shows the stress-strain relations of metals A and B during ten- sion tests until fracture. Determine the following for the two metals (show all calculations and units): a. Proportional limit b. Yield stress at an offset strain of 0.002 m/m. c. Ultimate strength d. Modulus of resilience e. Toughness I. Which metal is more ductile? Why? 900 -Metal A E 600 Metal B 300 0.00 a02 004 a.06 0.08 0.10 0.12 014 Strain, matm FIGURE P1.16 Strees, MPaarrow_forwardA single crystal of a metal is oriented for a tensile test such that its slip plane normal makes an angle of 64.0° with the tensile axis. Three possible slip directions make angles of 30°, 48°, and 78° with the same tensile axis. (a) Which of these three slip directions is most favored? i (b) If plastic deformation begins at a tensile stress of 1.3 MPa (188.6 psi), determine the critical resolved shear stress for this metal. i MPаarrow_forward
- Time len A material has the stress-strain behavior shown in the Figure below. Calculate the toughness (T) of this material. given that S1=195 Mpa; S2=243.75 Mpa; El=0.19; E2=0.38 E1 Strain E2 Stress - Strain diagram of a metal alloy OA.T= 18.52 Mpa O B.T= 92.62 Mpa O C.T= 37.05 Mpa O D.T= 60.21 Mpa Stress (Mpa) 3arrow_forwardA steel plate used for polymer forming is to be bent into a circular shape having an inside radius of 10 m. What maximum thickness can be used for the plate if the normal stress is not to exceed 267 MPa? Assume that the modulus of elasticity for the steel is 201 GPa.arrow_forwardA 5-mm-thick rectangular alloy bar is subjected to ajtensile load P by pins at A and B, as shown in the figure. The width of the bar is w = 33 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: €, =710 με and ε,--255 με (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 24 kN, what is the modulus of elasticity for this specimen? Answers: (a) v= (b) E= GPaarrow_forward
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