Concept explainers
A fatigue test is made with a mean stress of 17,500 psi (120 MPa) and a stress amplitude of 24,000 psi (165 MPa). Calculate (a) the maximum and minimum stresses, (b) the stress ratio, and (c) the stress range.
(a)
The minimum and maximum stress.
Answer to Problem 30AAP
The maximum stress is
Explanation of Solution
Write the expression to calculate stress amplitude.
Here, the stress amplitude is
Write the expression to calculate mean stress.
Here, the mean stress is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the maximum stress is
(b)
The stress ratio.
Answer to Problem 30AAP
The stress ratio is
Explanation of Solution
Write the expression to calculate stress ratio.
Here, the stress ratio is
Conclusion:
Substitute
Thus, the stress ratio is
(c)
The stress range.
Answer to Problem 30AAP
The stress range is
Explanation of Solution
Write the expression to calculate stress ratio.
Here, the stress range is
Conclusion:
Substitute
Thus, the stress range is
Want to see more full solutions like this?
Chapter 7 Solutions
Foundations of Materials Science and Engineering
Additional Engineering Textbook Solutions
Heat and Mass Transfer: Fundamentals and Applications
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Vector Mechanics for Engineers: Statics, 11th Edition
Thermodynamics: An Engineering Approach
EBK FUNDAMENTALS OF THERMODYNAMICS, ENH
Engineering Mechanics: Statics
- The data shown in the table below were obtained from a tensile test of high-strength steel. The test specimen had a diameter of 13mm and a gage length of 50mm. At fracture, the elongation between the gage marks was 3.0mm and the minimum diameter was 10.7mm. Plot the conventional stress-strain curve for the steel and determine the propotional limit, modulus of elasticity (i.e the slope of the initial part of the stress-strain curve), yield stress at 0.1% offset, ultimate stress, percent elongation in 50mm, and percent reduction area. TENSILE-TEST DATA Load(kN) Elongation(mm) 5 0.005 10 0.015 30 0.048 50 0.084 60 0.099 64.5 0.109 67.0 0.119 68.0 0.137 69.0 0.160 70.0 0.229 72.0 0.259 76.0 0.330 84.0 0.584 92.0 0.853 100.0 1.288 112.0 2.814 113.0 Fracturearrow_forwardThe data below are for a thin steel wire suitable for use as a guitar string. Ultimate tensile stress: 1.8 x 109 Pa Young Modulus: 2.2 x 1011 Pa Cross-sectional area: 2.0 x 10-7 m2 In a tensile test, a specimen of the wire, of original length 1.5 m, is stretched until it breaks. Assuming the wire obeys Hooke’s law throughout, calculate the extension of the specimen immediately before breaking.arrow_forward2. Another cylindrical component is madeof Enfennering ceramic Al203 but with different dimensions. Here, l=30 cm and the diameter is 4 cm. Assume the same Weibull modulus of 9. Calculate the level of the tensile strength for the following probability of failures: a. Pr (V) = 0.1 b. Pr (Vo) = 0.01 c. What is the survival probability and the failure probability of this component if a stress of 200 MPa is applied?arrow_forward
- QI (a) A tensile stress is to be applied along the axis of a cylindrical steel rod that has a diameter of 7.5 mm. Given the Poisson's ratio, v is 0.30 and the modulus of elasticity, E of the steel is 207 GPa. Determine the magnitude of the load required to produce a 2.5 x10³ mm change in diameter if the deformation is entirely elastic. (b) Referring to the tensile test data tabulated in Table 1, answer the following questions: i. Select with justification the material that will experience the greatest percent reduction in area. ii. Select with justification which material is the strongest. Table 1. Tensile stress-strain data for several hypothetical metals Material Yield Tensile Strain at Fracture Elastic Strength Strength Fracture Strength Modulus (МРа) (MPa) (MPa) (GPa) A 310 340 0.23 265 210 100 120 0.40 105 150 C 415 550 0.15 500 310 D 700 850 0.14 720 210 E Fracture before yielding 650 350arrow_forwardDraw a typical stress vs strain tensile test curve for the following materials (two seperate graphs) and label the axis. A ductile metallic test specimen that is stretched to failure displaying a characteristic yield point and show the following parts on the curve. 1- Yield point 2- Ultimate Tensile Strength 3- Breaking point 4- Elastic Region 5- Plastic Region 6- Necking regionarrow_forwardTwo different materials designated A, and B, are tested in tension using test specimens having diameters of 0.505 cm and gage lengths of 2.0 cm (Figure 1). At failure, the distances between the gauge length marks are 2.13 cm (sample A) and 2.48 cm (sample B). Also, at the failure cross-sections, the diameters are found to be 0.484 cm (sample A) and 0.398 cm (sample B), respectively. i. Calculate the percent elongation and percent of area reduction in each specimen. a. Sample A b. Sample B ii. Classify each material as brittle or ductile using your judgement.arrow_forward
- 1. For the stress-strain curve shown below, please estimate the properties indicated. (a) Fracture Strain Please do your work on a separate sheet of paper, and put your answers in the boxes on the right. Be sure to include the proper symbol and units. Stress Strain 70 60 50 Stress (ksi) 240 30 20 10 70 0 0.000 60 50 Stress (ksi) 40 20 10 KULL 0 0.000 0.010 0.050 0.100 Strain (in/in) Stress Strain 0.020 0.030 Strain (in/in) 0.040 0.150 0.050 (b) Ultimate Tensile Stress (c) Fracture Stress (d) Proportional Limit (e) Elastic Modulus (1) Yield Stress (g) Tensile Toughness (Modulus of Toughness) (h) Modulus of Resiliencearrow_forwardA strain gauge mounted at a potentially critical point in a steel part has recorded the stress history shown below during 20 seconds of typical use. Identical parts have been fatigue tested under constant amplitude loading with R = -1 to give an endurance limit of 60 ksi and a fatigue strength of 140 ksi at N = 1000 cycles. The steel used has an ultimate strength of 165 ksi. Estimate the fatigue life of the part under typical use. How much will the fatigue life in problem 3 (above) be reduced if a mean stress of 10 ksi is added to the stress history given?arrow_forwardThe data shown in the accompanying table are From a tensile test of high-strength steel. The test specimen has a diameter of 0.505 in. and a gage length of 2.00 in. (see figure for Prob. 1.5-3). At fracture, the elongation between the gage marks is 0.12 in. and the minimum diameter is 0.42 in. Plot the conventional stress-strain curve for the steel and determine the proportional limit, modulus of elasticity (the slope of the initial part of thestress-strain curve), yield stress at 0.1% offset, ultimate stress, percent elongation in 2.00 in., and percent reduction in area. TENSILE-TEST DATA FOR PROB. L.5-7 Laid (lb) Elongation (in) 1000 0.0002 2000 0.0006 6000 0.0019 10,000 0.0033 12,000 0.0039 12,900 0.0041 13,400 0.0047 13,600 0.0054 13,800 0.0063 14,000 0.0090 14,400 0.0102 15,200 0.0130 16,800 0.0230 18,400 0.0336 20,000 0.0507 22,400 0.1108 22,600 Fracturearrow_forward
- tensile test uses a circular test specimen that has a gage length of 50 mm and diameter = 20 mm. During the test the specimen yields under a load of 100,000 N. The corresponding gage length = 50.5 mm. This is the 0.2% yield point. The maximum load of 180,000 N is reached at a gage length = 65 mm. Determine (a) yield strength, (b) modulus of elasticity, and (c) tensile strength. (d) If fracture occurs at a gage length of 73 mm, determine the ductility. i need clear ans by hand and solve very very fast in 20 min and thank you | DYBALAarrow_forwardA tension test was performed on a specimen having an original diameter of 12.5 mm and a gage length of 50mm. The data are listed in the table below: Complete the following: Plot the stress-strain curve. Label the y-axis every 50 MPa, and the x-axis every 0.05 mm/mm. Plot the linear portion of the stress-strain curve (first 5 points). Label the y-axis every 50 MPa, and the x-axis every 0.001 mm/mm. Determine the approximate Modulus of Elasticity Determine the approximate Ultimate Stress Determine the approximate Fracture Stress Determine the approximate Modulus of Resilience Determine the approximate Modulus of Toughness Other Requirements: Provide an example hand-written calculation showing how you calculated one point on the curve. Remember to properly label your plots and provide axis labels with units. Hand sketched plots will not be accepted. Use Excel or similar software.arrow_forwardExample: Convert the change in length data in Table 3-2 to engineering stress and strain and plot a stress-strain curve Homework- help Table 3-2 The results of a tensile test of a 0.505 in. diameter aluminum alloy test bar, initial length (1o) = 2 in. Calculated LTO Load (Ib) Change in Length (in.) Stress (psi) Strain (in./in.) 0.000 1000 0.001 0.0005 4,993 14,978 24,963 34,948 37,445 39,442 39,941 39,691 37,944 3000 0.003 0.0015 5000 0.005 0.0025 7000 0.007 0.0035 7500 0.030 0.0150 7900 0.080 0.0400 8000 (maximum load) 0.120 0.0600 7950 0.160 0.0800 7600 (fracture) 0.205 0.1025arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY