MSE 200 - Test 2 (Calculations)

A steel cable with a length of 10 m and 8 mm in diameter has a modulus of elasticity of 414 GPa. A force equal to 2400 N is applied. Calculate how much the cable stretches (in meters). The yield point of the material is 200 MPa. 1.) Strain in the cable is a. 1.15 b. 0.0115 c. 0.000115 2.) Final length of the cable (in meters) is a. 10.00115 b. 10.115 c. 21.5

1.) 0.000115 2.) 10.00115

A steel with a critical fracture toughness of 150 MPa.m1/2 has a yield strength of 1200 Mpa. If fracture were to take place at the yield stress, answer the following questions. 1.) Surface crack size at yielding leading to failure is a. 0.497 cm b. 0.994 cm c. 0.249 cm 2.) If the fracture toughness is increased to 300 Mpa. m1/2 , what is the stress value in MPa at which failure takes place for the same crack size. a. 2400 b. 600 c. 1200 3.) The improvement in fracture toughness is a result of a. increase in yield strength at which fracture took place b. increase in grain size in the material c. decrease in grain size in the material 4.) If the yield strength for very large grain size (d is very very large so that 1/d=0) is 200 MPa, how should the grain size be changed for the observed improvement in fracture toughness.. a. increase by a factor of 2.2 b. decrease by a factor of 4.8 c. decrease by a factor of 10

1.) 0.497 cm 2.) 2400 3.) decrease in grain size in the material 4.) decrease by a factor of 4.8

From the creep curves obtained for copper given below at temperatures of 600 and 800oC in Figure 2. Samples A and B are subjected to 600oC and load of 100 MPa and 200 MPa. Sample C is subject to temperature 800oC and load 200 MPa. The linear portions of the creep behavior are given by the markers. Determine the following. 1.) The steady state creep strain rate in units of (hour) -1 in sample A is close to a. 0.9x10-6 b. 0.4x10-6 c. 2.0x10-6 2.) Steady state creep strain rate in sample B in units of (hour) -1is close to a. 3.2x10-6 b. 0.9x10-6 c. 2.0x10-6 3.) Steady state creep strain rate in sample C in units of (hour)-1 is close to a. 3.2x10-6 b. 0.9x10-6 c. 2.0x10-6 4.) Activation energy for creep in the material is close to a. 0. 19 eV b. 0.38 eV c. 0.09 eV 5.) Total creep rupture life of sample at 800oC is a. below 6000 hr b. 9000 hr c. 12000 hr 6.) The creep exponent in this material is a. 0.5 b. 1.17 c. 1.51

1.) 0.9x10^-6 2.) 2.0x10^-6 3.) 3.2x10^-6 4.) 0.19 eV 5.) 9000 hr 6.) 1.17

The creep curves are obtained at applied stress of 200 MPa for copper given below at temperatures of 600 and 800oC in Figure 2. The sample C is subjected to creep at the same temperature but at a stress twice that is applied in sample B. Determine the following. 1.) The steady state creep strain rate in units of (hour) -1 in sample A is close to a. 1.8x10-6 b. 0.4x10-6 c. 24x10-6 2.) The sample that is subjected to creep at 600oC is the one with label a. A b. B c. neither 3.) Steady state creep strain rate in sample B in units of (hour) -1is close to a. 4.4x10-6 b. 1.8x10-6 c. 2.4x10-6 4.) Steady state creep rate in sample C in units (hour)-1 is close to a. 8x10-6 b. 0.8x10-6 c. 80x10-6 5.) Activation energy for creep in the material is close to a. 0. 7 eV b. 0.36 eV c. 1.05 eV 6.) Total creep rupture life at 800oC and 200 Mpa is a. below 6000 hr b. 7500 hr c. above 6000 hr 7.) The creep rate, in units of hr-1 , at 300 MPa and 600oC will be close to a. 1.54x10-6 b. 2.54x10-6 c. 2.0x10-6 8.) Nucleation of voids during creep takes place in polycrystalline metals at a. Surfaces b. within the grains c. at triple points

1.) 1.8 x 10^-6 2.) A 3.) 4.4x10^-6 4.) 8x10^-6 5.) 0.36 eV 6.) below 6000 hr 7.) 2.54x10^-6 8.) at triple points

The following graph is obtained as a result of testing as a function of the thickness of the sample. The value of fracture toughness is shown as a function of ratio of thickness "t " to width "b" of the sample. Answer the following questions. (110 to 150, L shaped) 1.) The value of critical fracture toughness of the sample in MPa.m1/2 that must used for design and applications is... a. 150 b. 120 c. 110 2.) From the above results, would you expect the material to be a... a. Metal b. ceramic c. ceramic composite 3.) The region of the graph that gives a constant value of fracture toughness is called... a. Plane stress b. plane strain c. anti-plane strain 4.) If we increase the grain size of the material, would you expect the fracture toughness to... a. increase b. decrease c. not change 5.) If the magnitude of applied stress at which the crack propagated is 400 MPa, the surface crack size is... a. 2.86 cm b. 2.86 mm c. 5.72 cm 6.) If the surface crack size in the sample is 10 mm, the stress at which the sample fails by fracture is a. 621 MPa b. 1500 MPa c. 450 MPa

1.) 120 2.) metal 3.) plane strain 4.) decrease 5.) 2.86 cm 6.) 621 MPa

The dislocation density in a well annealed Cu sample is found to be 106 cm-2. The CRSS is found to be 20 MPa. Upon deformation to fracture, the dislocation density increased to 1012 cm-2. The lattice parameter of Cu is 0.36 nm and the Burgers vector of dislocations is the shortest distance between atoms. The shear modulus of Cu is 50 GPa. 1.) The flow stress at fracture in MPa is a. 420 b. 1295 c. 1695 2.) During repeated cold working to reduce the cross-section to desired value, the work piece is subjected intermittently to a. recovery b. recrystallization c. grain growth 3.) For improvement in strength of a sample in the final form with precise dimensional control, it is desirable to... a. hot work followed by cold work b. cold work followed by hot work c. only hot work

1.) 1295 2.) recrystallization 3.) hot work followed by cold work

A test bar of a sample with circular cross-section has a diameter of 1.25 cm and gage length of 5 cm. Upon applying a tensile load, the sample exhibited 0.002 plastic strain at 1700 Newtons. The maximum load during testing was 3100 Newtons occurred at a gage length of 8.5 cm. Breaking occurred at 1500 Newtons. The sample diameter at fracture was measured to be 0.42 cm. 1.) The yield strength (MPa) the material is... a. 20 b. 13.85 c. 10 Mpa 2.) The UTS (MPa) of the material is... a. 36.5 b. 25.26 c. 18.25 3.) The fracture strength (MPa) of the sample is... a. 195 b. 108 c. 93 4.) True strain at necking is... a. 0.40 b. 0.53 c.0.65 5.) The material is expected to have a crystal structure of. a. fcc b. bcc c. hcp

1.) 13.85 2.) 25.26 3.) 108 4.) 0.53 5.) fcc

A sample of steel is subjected to fatigue loading. The maximum stress is 400 Mpa and the minimum stress is -100 Mpa. The loading cycle is 0.1 seconds. The sample is subjected to fatigue test for 2000 days before the cracks could be observed on the surface. When the maximum stress is reduced to 200 Mpa and minimum stress is kept the same, the sample did not develop any cracks within a reasonable time of observations. 1.) The mean stress on the sample subjected to 2000 days of testing is... a. 200Mpa b. -50 Mpa c. 150 Mpa 2.) The number of cycles to which the sample survived in the test after 2000 days is a. 0.85x109 b. 1.73x109 c. 3.46x109 3.) The amplitude of stress to which the sample was subjected for 2000 days is a. 150 Mpa b. 500 Mpa c. 250 Mpa 4.) The endurance limit of the steel given in terms of the amplitude of stress is a. 100 Mpa b. 300 Mpa c. 150 Mpa 5.) You could safely use the steel without failure at a maximum amplitude of stress of a. 100 Mpa b. 300 Mpa c. 150 Mpa 6.) 27. The sample was shot peened to introduce a surface compressive stress of -200 Mpa. If the cyclic loading of maximum stress of 400 MPa and minimum stress of -100 MPa is applied, do you expect the steel to fail. a. yes b. no

1.) 150 Mpa 2.) 1.73x10^9 3.) 250 Mpa 4.) 150 Mpa 5.) 150 Mpa 6.) no

The following graph is obtained as a result of testing fracture toughness as a function of the thickness of the sample. The value of fracture toughness is shown as a function of ratio of thickness "t " to width "b" of the sample. Answer questions. (120 to 220, L shape) 1.) The value of critical fracture toughness of the sample that is used for design from the above graph, in the units shown is a. 160 b. 200 c. 220 2.) From these results, would you expect the material to be a metallic alloy or a ceramic material. a. ceramic b. metallic c. neither 3.) The region of the graph that gives a constant value of fracture toughness is in a. Plane stress b. plane strain c. both a and b 4.) To measure the critical fracture toughness, the sample should be... a. sufficiently thin b. sufficiently thick c. very thin 5.) If we increase the grain size of the material, would you expect the fracture toughness to... a. decrease b. increase c. not change 6.) If the crack size is increased, do you expect the critical fracture toughness to... a. decrease b. increase c. not change 7.) For the above material, a load of 1.0 GPa is applied for failure to take place. The crack size 'c' is... a. 0.17 cm b. 0.92 cm c. 0.81 cm

1.) 160 2.) metallic 3.) plane strain 4.) sufficiently thick 5.) decrease 6.) not change 7.) 0.81 cm

The following graph is obtained as a result of testing fracture toughness as a function of the thickness of the sample. The value of fracture toughness is shown as a function of ratio of thickness "t " to width "b" of the sample. Answer questions. (160 or 150 to 200, L shape) 1.) The value of critical fracture toughness of the sample that is used for design from the above graph, in the units shown is ... a. 200 b.170 c. 0.5 2.) The region of the graph that gives a constant value of fracture toughness is a. Plane stress b. plane strain c. both a and b 3.) If we reduce the grain size of the material, would you expect the fracture toughness to a. decrease b. increase c. not change 4.) For the above material, a load of 1.0 GPa is applied for failure to take place. The crack size 'a' is... a. 0.17 cm b. 0.92 cm c. 1.7 cm 5.) For the above material, a load of 0.5 GPa is applied for failure to take place. The crack size 'c' is a. 1.9 cm b. 3.7 cm c. 0.37 cm 6.) From these results, would you expect the material to be a metallic alloy or a ceramic material. a. ceramic b. metallic c. neither

1.) 170 2.) plane strain 3.) increase 4.) 0.92 5.) 3.7 6.) metallic

In a laboratory creep experiment at 1000oC, a steady state creep rate of 1.5x10-6 sec-1 is observed in nickel. When the experiments are performed under the same stress at 727oC, the observed creep rate is 1.0x10-6 sec-1 . Predict the creep rate at a service temperature of 600oC for the same applied stress. 1.) The activation energy for steady state creep in units of k (Boltzmann constant) is a. 6827.5 k b. 1890 k c. 1621.8 k 2.) The creep rate at 600oC is a. 5.5x10-6 b. 0.75x10-6 c. 0.275x10-6 3.) The activation energy for self diffusion is expected to be a. 6827.5 k b. 1890 k c. 1621.8 k

1.) 1890 k 2.) 0.75x10^-6 3.) 1890 k

A sample has been tested in plane strain fracture toughness test. A pre-crack of 1.0 cm lead to failure at a stress of 1200 Mpa. A crack of twice the size is introduced in another sample of the same alloy. 1.) The fracture toughness of the alloy in units of Mpa (m)1/2 is a. 21 b. 2.1 c.212.6 2.) The stress at which the sample fails with the new crack size (2 cm) is a. 84.8 Mpa b. 848 Mpa c. 424 Mpa 3.) The sample is made of a. ceramic b. ceramic composite c. alloy steel 4.) To improve the fracture toughness further a. Increase the grain size b. reduce the grain size c. increase the crack size

1.) 212.6 2.) 848 Mpa 3.) alloy steel 4.) reduce grain size

In a laboratory creep experiment at 1000oC, a steady state creep rate of 1.5x10-6 sec-1 is observed in nickel. When the experiments are performed under the same stress at 800oC, the observed creep rate is 1.0x10-6 sec-1 . Predict the creep rate at a service temperature of 600oC at this stress level. When the experiment is performed with stress two times higher and temperature of 800oC, the creep rate is doubled. Answer the following. 1.) The activation energy for steady state creep in units of k (Boltzmann constant) is... a. 6827.5 k b. 2769 k c. 1621.8 k 2.) The creep rate at 600oC for the same stress level is a. 5.5x10-6 b. 0.55x10-6 c. 0.275x10-6 3.) The activation energy for self diffusion is expected to be... a. 6827.5 k b. 2769 k c. 1621.8 k 4.) The creep exponent, n , has a value of a. 0.5 b. 1.0 c. 2.0 5.) The activation energy for creep at a higher stress is expected to be... a. higher b. lower c. same

1.) 2769 k 2.) 0.55 x 10^-6 3.) 2769 k 4.) 1.0 5.) same

The following creep curves were obtained for copper at temperatures of 600 oC and 800 oC and a stress of 100 MPa for A and B and 800 oC and stress of 200 MPa for C. 1.) The activation energy (Q/k) for steady state creep is a. 2206 b. 4413 c. 8826 2.) The creep exponent is a. 0.81 b. 0.40 c. 1.62 3.) The creep rate (10-6 hr-1) in sample that is subjected to creep at 600 oC but with an applied stress of 200 MPa will be... a. 1.44 b. 0.78 c. 0.36 4.) Turbine blades that should not fail by creep are made of... a. aluminum b. nickel c. nickel aluminide 5.) The coating of ZrO2 is provided on the blades to... a. reduce the temperature of the blades b. reduce the applied stress on the blades c. both (a) and (b) 6.) Creep voids in polycrystalline alloys start a. within the grains b. at the surface c. at triple points

1.) 4413 2.) 0.81 3.) 0.78 4.) nickel aluminum 5.) reduce the temperature of the blades 6.) at triple points

A steel with a critical fracture toughness of 150 MPa.m1/2 has a yield strength of 120 Mpa. The grain size is 1 μm. If fracture were to take place at the yield stress, answer the following questions. 1.) Surface crack size at yielding leading to failure is a. 49.7 cm b. 99.4 cm c. 24.9 cm 2.) If the fracture toughness is increased to 200 Mpa. m1/2 by reducing the grain size to 0.5 μm, what is the yield stress value in MPa at which failure takes place for the same crack size. a. 240 b. 160 c. 1200 3.) If the yield strength is to be increased further to 200 Mpa, the grain size should be a. 2.99 μm b. 0.299 μm c. 4.97 μm

1.) 49.7 cm 2.) 160 3.) 0.299 um

An aluminum alloy of grain size 16 μm exhibited a yield strength of 200 Mpsi. When the grain size is reduced to 4 μm, the yield strength was 350 Mpsi. 1.) The yield strength of a single crystal with large grain size is.. a. 25 MPa b. 50 MPa c. 100 MPa 2.) If the grain size is reduced to 1 μm, the yield strength is expected to be a. 612.5 MPa b. 650 MPa c. 700 Mpa 3.) The yield strength of the same material with grain size of 2 μm is a. 47.4 MPa b. 474.3 MPa c. 4.74 MPa 4.) The ductility of aluminum with 16 μm grain size compared to that of the aluminum with grain size 2 μm is expected to be a. Lower b. higher c. same 5.) The ductility of alloy with grain size 4 μm compared to that of the alloy with grain size 16 μm will be a. same b. higher c. lower 6.) For slip to take place in the crystal, the condition to be satisfied is a. RSS<CRSS b. CRSS>RSS c. RSS>CRSS 7.) A best method to reduce grain size uniformly is a. cold working b. recrystallization after cold work c. Recovery after cold work 8.) Turbine blades with high creep resistance are made of a. small grain size polycrystalline alloy b. single crystalline alloy c. single crystalline alloy with thermal barrier coating

1.) 50 MPa 2.) 650 MPa 3.) 474.3 MPa 4.) higher 5.) lower 6.) RSS>CRSS 7.) recrystallization after cold work 8.) single crystalline alloy with thermal barrier coating

The endurance limit in terms of the mean or average stress applied is found to be 55 Ksi. If the maximum stress applied is 150 Ksi and minimum stress applied is -50 Ksi, Answer the following questions. 1.) The mean stress applied on the sample is a. 40 Ksi b. 65 Ksi c. 50 Ksi 2.) This material is a. nonferrous material b. mild steel c. neither 3.) Fatigue life of the material subjected to the above stress is a. determined by the S-N curve b. zero c. infinite 4.) If a tensile residual stress of 10 Ksi is present from the processing of a new sample, the sample will exhibit a. infinite life b. zero life c. limited life determined by S-N curve 5.) If a residual stress of -10 Ksi is applied, the life of the sample a. infinite life b. zero life c. limited life determined by S-N curve

1.) 50 ksi 2.) mild steel 3.) infinite 4.) limited life determined by S-N curve 5.) infinite life

A sample of gage length 2 inches has received an elongation to 2.2 inches in tension and compressed to 1.818 inches in compression. The engineering stress in tension was 6 Mpsi and 6.2 Mpsi in compression. The area of cross section initially is 2 square inches. 1.) The true stress in tension is a. 5.454 Mpsi b. 6.6 Mpsi c. 10 Mpsi 2.) The true stress in compression is a. 5.636 Mpsi b. 6.6 Mpsi c. 10 Mpsi 3.) The true strains in both tension and compression a. differ in sign and magnitude b. differ in magnitude c. differ in sign only

1.) 6.6 Mpsi 2.) 10 Mpsi 3.) differ in sign only

A test bar of aluminum with circular cross-section has a diameter of 0.505 inches. Upon applying a tensile load, the sample exhibited 0.002 plastic strain at 1700 lb and the maximum load during testing was 3100 lb; and breaking occurred at 2200 lb. The actual sample diameter at fracture was measured to be 0.169 inches. The maximum load occurred at a total strain of 0.57. (Psi= pounds/inch2) 1.) The yield strength of the material is... a. 9493 psi b. 8487 psi c. 16975 psi 2.) The UTS of the material is a. 16975 psi b. 15477 psi c. 30954 3.) The fracture strength of the sample is a. 11000 psi b. 98075 psi c. 138197 psi 4.) True strain at necking is a. 0.50 b. 0.45 c.0.1 5.) Engineering strain at necking is a. 0.57 b. 0.65 c. 0.11 6.) The power hardening exponent, n, of the material is a. 0.50 b. 0.45 c.0.1 7.) Based on the value of n , the crystal structure of the material is a. bcc b. fcc c. hcp 8.) For structural applications, the stress on the material should not exceed, a. 8487 psi b. 15477 psi c. 98075 psi

1.) 8487 psi 2.) 15477 psi 3.) 98075 psi 4.) 0.45 5.) 0.57 6.) 0.45 7.) fcc 8.) 8487 psi

A steel cable with a length of 10 m and 8 mm in diameter has a modulus of elasticity of 207 GPa. A force equal to 4800 N is applied. Calculate how much the cable stretches (in meters). The yield point of the material is 200 MPa. 1.) Stress in the cable is a. 95.496 MPa b. 954.96 c. 9.5496 2.) Strain in the cable is a. 0.461 b. 0.0461 c. 0.000461 3.) Final length of the cable (in meters) is a. 10.00461 b. 20.00962 c. 10.561 4.) Is the material subjected to plastic deformation a. Yes b. no c. may be

1.) 95.496 MPa 2.) .000461 3.) 10.00461 4.) no