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ENGR 6441 Assignment 2

Due on Oct. 14th, 2011

Question 1: A material; with a plane strain fracture touchness of KIC=61 MPa.m1/2 has a central crack in a very wide panel. If ϭys=1520 MPa and assuming a safety factor N = 2: a) Compute the critical crack length during cycling loading. (Assume that plain strain condition prevails and A=1.) b) If the initial flaw length is 2.5 mm, how many loading cycles (from zero to the design stress) could the panel endure? Assume that fatigue crack growth rates varied with the stress intensity factor range raised to fourth power (m=4). The proportionality constant A may be taken to be 1.1 x 10-39. Question 2 For a certain high-temperature alloy, failure was reported after 3500 hours at 650oC when subjected to a stress of 310 MPa. If the same stress were applied at 705oC, how long would the sample be expected to last? Assume the material constant needed for this computation to be 20.

Question 3

Creep can occur via several different mechanisms in amorphous and crystalline materials, each with their own activation energy Q. Typically, there is an Arrhenius behavior to this creep response, with an exponential prefactor that is particular to the material considered and on the operating mechanism. a) You are running two separate creep experiments on polycrystalline Ni, one at o o 527 C and the other at 532 C. You observe that dε/dt increases by a factor of 1.5 for the sample tested at the higher temperature. What is the activation energy Q for this creep mechanism? o b) What do you think the mechanism at 532 C could be, and why? Note that the actual grain size d and stress magnitude need not be stated to figure this out, but you can use deformation mechanism maps to narrow down your options. c) You are running these tests because you would like to develop a new polycrystalline Ni alloy for Boeing aircraft engines. The Ni parts will be under a constant stress of about 1.3 o GPa due to centrifugal forces, and a temperature of about 1100 C. Which creep mechanism are you most concerned about, and how do you propose to modify the polycrystalline Ni alloy to minimize creep rates for this application?

Question 4: A nickel superalloy single crystal turbine blade is used in a high performance jet engine. The strain rate during steady state creep for the blade is given by:

ϵ. = 3.7x10-48 ϭn e(-Q/RT) s-1 Where n is the creep exponent and Q is the activation energy for creep. Experiments are carried out to determine Q which is found to be 240 kJ mol-1. Young’s modulus for the blade is 214 GPa. a) From the following experimental data obtained at a constant temperature of 1273 K determine the value of n. Strain rate x10-6 (s-1) Stress level (MPa) 250 0.12 280 0.26 300 0.38 320 0.55 340 0.81 360 1.20

b) If n = 6 and the engine is expected to last for 100 hrs. and the clearance between the 20 cm long blade and the housing is 0.8 mm (after thermal expansion has been taken into account) estimate whether the engine will survive the design time if the blade is at a constant temperature of 8000C and a stress of 300 MPa. c) If the blade cooling system fails after 91 hours raising the blade temperature to 9000C for the last 9 hours what difference will this make? d) If the engine is run at higher revs during climbing giving stresses in the blade of 350 MPa, for an average time of 2 hrs. out of the 100 while at a constant temperature of 8000C, (without cooling failure) what will be the overall length of the blade after the 100 hrs.? Question 5 The most common strengthening mechanisms are strain hardening, solid solution, precipitation, dispersion, martensite formation, composites. Discuss the effectiveness of these strengthening mechanisms with respect to fatigue.

Question 6 Discuss high temperature deformation of metals. What are the two significant softening mechanisms?

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Due on Oct. 14th, 2011

Question 1: A material; with a plane strain fracture touchness of KIC=61 MPa.m1/2 has a central crack in a very wide panel. If ϭys=1520 MPa and assuming a safety factor N = 2: a) Compute the critical crack length during cycling loading. (Assume that plain strain condition prevails and A=1.) b) If the initial flaw length is 2.5 mm, how many loading cycles (from zero to the design stress) could the panel endure? Assume that fatigue crack growth rates varied with the stress intensity factor range raised to fourth power (m=4). The proportionality constant A may be taken to be 1.1 x 10-39. Question 2 For a certain high-temperature alloy, failure was reported after 3500 hours at 650oC when subjected to a stress of 310 MPa. If the same stress were applied at 705oC, how long would the sample be expected to last? Assume the material constant needed for this computation to be 20.

Question 3

Creep can occur via several different mechanisms in amorphous and crystalline materials, each with their own activation energy Q. Typically, there is an Arrhenius behavior to this creep response, with an exponential prefactor that is particular to the material considered and on the operating mechanism. a) You are running two separate creep experiments on polycrystalline Ni, one at o o 527 C and the other at 532 C. You observe that dε/dt increases by a factor of 1.5 for the sample tested at the higher temperature. What is the activation energy Q for this creep mechanism? o b) What do you think the mechanism at 532 C could be, and why? Note that the actual grain size d and stress magnitude need not be stated to figure this out, but you can use deformation mechanism maps to narrow down your options. c) You are running these tests because you would like to develop a new polycrystalline Ni alloy for Boeing aircraft engines. The Ni parts will be under a constant stress of about 1.3 o GPa due to centrifugal forces, and a temperature of about 1100 C. Which creep mechanism are you most concerned about, and how do you propose to modify the polycrystalline Ni alloy to minimize creep rates for this application?

Question 4: A nickel superalloy single crystal turbine blade is used in a high performance jet engine. The strain rate during steady state creep for the blade is given by:

ϵ. = 3.7x10-48 ϭn e(-Q/RT) s-1 Where n is the creep exponent and Q is the activation energy for creep. Experiments are carried out to determine Q which is found to be 240 kJ mol-1. Young’s modulus for the blade is 214 GPa. a) From the following experimental data obtained at a constant temperature of 1273 K determine the value of n. Strain rate x10-6 (s-1) Stress level (MPa) 250 0.12 280 0.26 300 0.38 320 0.55 340 0.81 360 1.20

b) If n = 6 and the engine is expected to last for 100 hrs. and the clearance between the 20 cm long blade and the housing is 0.8 mm (after thermal expansion has been taken into account) estimate whether the engine will survive the design time if the blade is at a constant temperature of 8000C and a stress of 300 MPa. c) If the blade cooling system fails after 91 hours raising the blade temperature to 9000C for the last 9 hours what difference will this make? d) If the engine is run at higher revs during climbing giving stresses in the blade of 350 MPa, for an average time of 2 hrs. out of the 100 while at a constant temperature of 8000C, (without cooling failure) what will be the overall length of the blade after the 100 hrs.? Question 5 The most common strengthening mechanisms are strain hardening, solid solution, precipitation, dispersion, martensite formation, composites. Discuss the effectiveness of these strengthening mechanisms with respect to fatigue.

Question 6 Discuss high temperature deformation of metals. What are the two significant softening mechanisms?

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