A machine element is subjected to a variable bending moment with:The empirical material constants of the fatigue crack growth rate are:0.08inOmax = σ in ksiOmin = -25 ksi.C=2x10-12 (in/cycle)/(ksivin)mm = 3.An edge crack with length of 0.005-in. has been discovered in the machine element.It is known that the critical length of the edge crack is 0.1 in. Estimate the maximum bendingmoment σ in ksi to obtain a useful life of 1 million of cycles.0.005 in0,08 in

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Answered: A machine element is subjected to a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A material, in region II of fatigue loading follows Paris relationship given byda/dN (m/cycle) = 1 x 10-8 (δK)2.2The stress range applied δσ = 100 MPa. The number of cycles required for a crack to grow from 2mm to 8mm will be 4723 cycles 3723 cycles 2723 cycles 1723 cycles
Is the Paris power law (Eq. 10-3) relevant for all conditions of fatigue crack growth?
Problem 4. A large flat plate is subjected to constant-amplitude uniaxial cyclic tensile and compressive stresses. Compute the final critical surface crack length if the fatigue life must be a minimum of 7.0 x 10^5 cycles. Assume the initial maximum edge surface crack length of 1.80 mm and a maximum tensile stress of 160 MPa. Assume m = 1.8 and A = 7.5 x 10^-13 in MPa and meter units. Assume Y = 1.25.
8.a) Calculate the theoretical fracture strength of a brittle material wherein fracture occurs by propagation of an elliptically shaped 0.25 mm surface crack with a 1.2 × 10-3 mm tip radius under an applied 1200 MPa stress. b) If the specific surface energy for a material is 0.30 J/m2 and its elastic modulus is 69 GPa, calculate the minimum stress required for propagation of a surface crack 0.05 mm in length. Based on this calculation, estimate the materials fracture toughness.
The manufacturer of a product that is subjected to repetitive cycles has specified that the product should be removed from service when any crack reaches 15% of the critical crack length required to cause fracture. Consider a crack that is initially 0.02 mm long in a material with a fracture toughness of 55 MPaÖ The product is continuously cycled between compressive and tensile stresses of 300 MPa at a constant frequency. Assume external cracks for which f=1.12. The materials constant for these units are n = 3.4 and C= 2 X 10-11. What is the critical crack length required to cause fracture? How many cycles will cause product failure?
Some 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?
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of +140 MPa, and a minimum stress of – 70 MPa.find out the R-ratio for this cyclic loading.
Consider a steel plate with a through-thickness edge crack like the one shown in Fig. 6.21f. The plate width (W) is 75 mm, and its thickness (t) is 12.0 mm. Furthermore, the plane-strain fracture toughness and yield strength values for this material are 80 MPa m1/2 and 1200 MPa, respectively. If the application in which the plate is used is expected to cause a stress of 300 MPa along the axis perpendicular to the crack, would you expect failure to occur if the crack length a is 15 mm? Explain.
The Kic value of a steel is M within a square root of 186 MPa. If the stress to which the steel is exposed is 800 MPa, what is the maximum crack length that can be tolerated? (Take Y = 1.1)
A single edge-cracked plate of AISI 4130 Steel of Table 8.1 has dimensions, as defined in Fig 8.12(c), of b = 45 mm and t = 5.0 mm, (large h), and is subjected to a tension force of P = 81 kN. Inspection of the plate shows crack length a = 4.5 mm. a. Determine the safety factor against brittle fracture, Xk. b. Determine the safety factor against fully plastic yielding, X'o. c. Determine the safety factor on crack length, Xa.
A shaft is loaded in bending and torsion such that Ma = 70 N * m, Ta = 45 N * m, Mm = 55 N * m, and Tm = 35 N * m. For the shaft, Su = 700 Mpa, the true fracture strength is 1045 MPa, and a fully corrected endurance limit of Se = 210 MPa is assumed. Let Kf = 2.2 and Kfs = 1.8. With a design factor of 2.0 determine the minimum acceptable diameter of the shaft using: a. DE-Goodman criterion b. DE-Morrow criterion c. DE-Gerber criterion d. DE-SWT criterion Discuss and compare the results.
A crack has been discovered along the edge of a reinforcing rib in titanium housing. The rib is 0.5 inches thick and 4.0 inches wide. The crack extends completely through the thickness and is about 1.20 inches long. If the housing is subjected to static loading only, and the maximumestimated loading produces a tensile load along the rib axis of 50,000 Ib, should the housing be removed from service? The housing material exhibits a yield strength of 150 ksi and a plane strain fracture toughness of 50 ksi in1/2.

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