(a)
The critical crack length for alloy steel plate for the applied stress.
(a)
Answer to Problem 52SEP
The critical crack length for alloy steel plate for the applied stress is
Explanation of Solution
Write the expression for the critical length.
Here, the fracture toughness of the material is
Conclusion:
Substitute
Thus, the critical crack length for alloy steel plate for the applied stress is
(b)
The crack length.
The largest allowable initial crack length.
(b)
Answer to Problem 52SEP
The crack length is
The largest allowable initial crack length is
Explanation of Solution
Write the expression for the crack length of the alloy steel plate.
Write the expression for the stress range for the steel.
Here, the maximum compressive stress is
Write the expression for the fatigue life in cycles.
Here, the initial crack length is
Conclusion:
Substitute
Here, the minimum tensile stress is
Substitute
Here, the fatigue constant are
Substitute
The crack length is
The largest allowable initial crack length is
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Chapter 7 Solutions
Foundations of Materials Science and Engineering
- A tie rod made of quenched and tempered 4340 steel is used as a critical linkage in an industrial apparatus. The rod is subjected to an alternating cyclic tensile/compressive stress from 550 MPa to -550 MPa. An inspection of the rod revealed a 3.5 mm deep edge crack on the surface of the rod. Please answer the following question for the rod given the properties in the table and curve below and fracture toughness of 55 MPa√m. (NOTE: Y=1.12 for edge crack and use “a” not “2a” for the length of the crack) 1. What is the minimum crack size that would cause instantaneous fast fracture at the current maximum axial tensile loading, assuming plane strain conditions apply? If the resolution limit of the flaw detection apparatus were 1.5 mm, would this flaw be subject to detection? Show calculations to back up your conclusions.arrow_forwardA component made of 7075-T6 aluminum alloy has an edge crack of 1.4 mm in length. Plane strain fracture toughness of this alloy is given as 27 MPavm. Geometrical factor of the crack is given as 1.2. (a) If this alloy is subjected to uniaxial tensile stress of 380 MPa, determine whether sudden brittle fracture occurs or not. (b) Calculate the maximum allowable crack size for this component in order not to be failed in brittle manner under a stress of 1000 MPa (Density of steel 7.85 g/cm³, 9.80665 N = 1 kg). Modulus of elastisity, GPa Ultimate tensile Yield strength, Alloy strength, MPa MPa 2014 Al alloy Bronze (92Cu-8Sn) High carbon steel Pure Titanium 97 186 380 72 110 152 380 615 215 240 330 107arrow_forwardA copper material with initial length of 305 mm, a tension load (stress) of 276 MPa was applied to the material. Assume elastic behavior was observed during the test. use Hooke’s law to calculate the final length of the material at the fracture point. Note: The modules of elasticity (E=110 Gpa)arrow_forward
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- 1 Q 4 N Current Attempt in Progress 30¹ F1 A specimen of a 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa m (50 ksi vin.) is exposed to a stress of 978.0 MPa (141800 psi). Assume that the parameter Y has a value of 1.18. - Your answer is partially correct. @ 2 (a) If the largest surface crack is 0.9 mm (0.03543 in.) long, determine the critical stress o. i 1608.13 (b) Will this specimen experience fracture? W S Yes v eTextbook and Media Hint Save for Later 38 command F2 # 3 E D 80 F3 X C $ 4 R MPa 000 000 F4 F % 5 V F5 T G 6 B MacBook Pro Y H & 44 N U 8 J Attempts: 1 of 5 used en l M 9 K DD F9 0 < H I -O L Submit Answer A F10 P V . t C F11 { command option [ + " = ? |arrow_forwardAn 820 MPa (145,000 psi) stress is applied to a specimen of 4341 steel alloy, which has a plane strain fracture toughness of 45MPa squareroot (m). If the greatest surface crack is 0.95 mm (0.03 in) long, will this specimen fracture as a result? Assume that the parameter Y is 1.22.arrow_forwardSome aircraft component is fabricated from an aluminium alloy that has a plane strain fracture toughness of 35 MPa√m. It has been determined that fracture results at a stress of 250 MPa when the maximum (or critical) internal crack length is 2.0 mm. For this same component and alloy, show that whether fracture will or will not occur if the stress level is at 325 MPa and the maximum internal crack length is 1.0 mm.arrow_forward
- An annealed-steel specimen has a 0.750 in. diameter and a 12.000 in. gage length. Maximum load is reached at 60,000 lbs and fracture occurs at 30,000 Ibs. For this steel, E= 360 x 10° psi. (a) Draw a sketch of stress-strain diagram for a typical steel in tension? (b) What is the ultimate tensile strength (UTS)? (c) Why does fracture occur at a lower load than the maximum load? (d) What is the elongation when a tensile stress of 30,000 psi is applied? A 400-mm-long rod with a diameter of 4.5 mm is loaded with a 5000-N weight. If the diameter decreases to 3.5 mm, compute the final length of the rod. 3. 4. A steel rod 1.5 m long and 75 mm x 75 mm in cross-section is subjected to a tensile force of 160 kN. Determine the elongation of the rod, if modulus of elasticity for the rod material is 900 GPa. 5. A hollow cylinder 4.5 m long has an outside diameter of 80 mm and inside diameter of 60 mm. If the cylinder is carrying a load of 75 kN, find the stress in the cylinder. Also find the…arrow_forwardSome aluminum aircraft components have a KIc = 35 MPa(m)1/2. It has been determined that failure occurs at a stress of 250 MPa when the critical internal crack length is 2 mm. Will this component achieve failure at a stress of 325 MPa when the critical internal crack length is 1.1 mm?arrow_forwardThe figure below shows the tensile engineering stress-strain behavior for a steel alloy. (a) What is the modulus of elasticity? (b) What is the yield strength at a strain offset of 0.002? (c) What is the tensile strength? Stress (MPa) 600 500 400 300 200 100 T I 0.00 Stress (MPa) 0.04 500 400 300 200 100 0.000 0.08 0.002 Strain 0.004 Strain 0.12 I 0.006 0.16 0.20 In the previous problem, A load of 85,000 N (19,100 lbf) is applied to a cylindrical specimen of the steel alloy that has a cross-sectional diameter of 15 mm (0.59 in.). (a) Will the specimen experience elastic and/or plastic deformation? Why? (b) If the original specimen length is 250 mm (10 in.), how much will it increase in length when this load is applied?arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning