113_2009_HW7 - UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering Fall 2009 MSE 113 Mechanical

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Unformatted text preview: UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering Fall 2009 MSE 113 Mechanical Behavior of Materials PROBLEM SET 7 Assigned 11/19/09 Due 12/03/09 Prof. Ritchie Problem 1 a) List four mechanisms for environmentally‐assisted cracking and describe each briefly. A steel ship (AISI 4340: σys = 215 ksi, KIC = 100 ksi√in) which sails between Nova Scotia and New York. During a pre‐voyage inspection, dock workers notice that some paint has been chipped off the hull by a foreign object during the previous voyage and there is now a small notch and a patch of rust in the bare spot. b) Find the critical crack length assuming that the fracture toughness of the local material is 10 ksi√in as a result of being exposed to the environment. c) The crack is on the hull roughly level with the water, so it gets a mix of seawater and air. Illustrate the crack environment in this corrosive environment to describe how the crack might grow. To idealize, assume it is a surface crack of length 2a and depth a into the hull. d) To slow the growth of the crack, the dock workers need to do something. They have a choice of attaching a material to the hull which will preferentially corrode, painting over the spot, or applying a voltage. Pick one solution and discuss the specifics of your choice. e) The dock workers choose to paint over the spot, but having never taken a materials science class, they don’t realize they had to clean the surface first of any rust or debris. What will likely happen when they paint over a rusty spot? Problem 2 Comment on the relationship between striation spacings on fatigue fracture surfaces and corresponding fatigue crack propagation rates (macroscopic). Problem 3 A large seel plate is used in an engineering structure. A radical mechanical engineering graduate student, intent on destroying this component, decides to cut a very sharp notch in the edge of the plate (perpendicular to the applied loading direction). If he runs away from the scene of his dastardly deed at 10 miles/hr, how far away will he get by the time his plan succeeds? Here are hallowed hints for the hunter: a) The plate is cyclically loaded uniformly from 0 to 80kN at a frequency of 100 Hz. b)The steel is 20 cm wide and 0.3 cm thick c) The yield strength is 140 MPa and the plane strain fracture toughness is 48 MPa√m, and elastic modulus is 2.114 × 105 MPa. d)The misled mechanical engineer’s mutilating mark was measured to be 1 cm long (though thickness). e) A janitor noted in subsequent eyewitness testimony that the crack was propagating at a velocity proportional to the square of the cyclic crack tip plastic zone size. (The janitor has just completed a correspondence course entitled “Relevant Observations on the Facts of Life” and was alerted to the need for such critical observations.) f) Post‐failure fractographic examination revealed the presence of fatigue striations 2.5 × 10−4 mm in width where the crack was 2.5 cm long. Problem 4 The tungsten filament of an argon‐filled light bulb operates at a temperature of 1600°C. The bending stress in the filament due to its own weight is approximately 3,000 psi. Because of the steep temperature gradient and geometrical constraints at the welds to the filament support, there is a total change in strain of approximately α∆T/2 [i.e. ∆εe + ∆εp = α∆T/2]. The filament will eventually fail, either from fatigue caused by the on‐off cycles, or because creep causes excessive sag in the filament. You can assume that failure is said to occur when the strain reaches 20%. Give expressions for the lifetime of the tube before failure by each of the two mechanisms. If the light bulb is used for a period of 8 hours each day, is it better to leave the light on when not in use (ignoring wasted energy), or to turn it off? The properties of tungsten are: E = 5 x 107 psi α = 4.5 x 10‐6 / °C εf = 0.2 at 1600°C σy = 24 ksi at 1600°C σu = 36 ksi at 1600°C See Figure 1 for creep data for tungsten. Problem 5 In a hydraulic turbine pump the actuating levers which control the position of the wicket gates are provided with notched shear pins for overload protection. During normal operation the shear pins are subjected to fluctuating shear loads which can produce fatigue crack growth out of the notches and eventual failure. The dimensions of the rectangular shear pins are shown in the sketch below. The pins are made of deep‐hardening 4340 steel which has, in the heat‐treated condition, a critical fracture toughness KIC = 67000 psi√in and a fatigue crack propagation law of da = C (ΔK ) 4 dN in mode I loading. ∆K is the range of stress intensity, da/dN is the growth rate per cycle and C = 1.7 × 10 −23 in−1 lb−4 cycle−1 is the scale factor of the crack propagation rate. Based on this available information, calculate the nominal stress amplitude for a 105 ‐cycle fatigue life in the shear pin, assuming that the shear case can be approximated by mode I loading in tension. Treat notches as cracks and assume you can use half symmetry and solve using just one notch on half the pin. Further assume it behaves as a semi‐infinite body. The pin is said the “fail” when the remaining cross‐sectional area is reduced to 1/4 that of unnotched pin area. ...
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This note was uploaded on 01/25/2010 for the course MSE 113 taught by Professor Ritchie during the Fall '09 term at University of California, Berkeley.

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