Creep exercises You are involved in a design for high temperature alloys and have performed a rupture test of material A and B. After data analysis, you noticed that the master curve (o vs LMP) of both material A and B coincide as shown in the diagram below. Based on the rupture ↑ strength o (MPa) A+B LMP = T(C+ Int) Which material will you select if they both have same constant (CA = CB)? Which material will you select if CA CB? Motivate your answer by means of a calculation.
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- A 5-mm-thick rectangular alloy bar is subjected to ajtensile load P by pins at A and B, as shown in the figure. The width of the bar is w = 33 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: €, =710 με and ε,--255 με (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 24 kN, what is the modulus of elasticity for this specimen? Answers: (a) v= (b) E= GPaQ.1 The yield stresses (oy) have been measured using steel and aluminum specimens of various grain sizes, as follows: Material D (µm) σΥ (MPa) Steel 60.5 160 136 128 Aluminum 11.1 235 100 223 (a) Determine the coefficients o and kỵ in the Hall- Petch for these two materials. (b) Determine the yield stress in each material for a grain size of d=26 um.Consider a cylindrical metal 6 mm in diameter and 50 mm long ispulled in tension. It is known that yield strength and elastic (Young’s) Modulus of thematerial are 200 MPa and 100 GPa, respectively, and its Poisson’s Ratio is 0.3.(a) Determine whether the deformation is elastic or plastic when 6000 N is applied.(b) Calculate specimen elongation (∆l) and reduction in diameter (∆d) when 5000 N isapplied? What are the values ∆l and ∆d when the load is released?(c) If necking occurs at a load of 8850 N, determine the UTS of the metal.(d) Calculate the ductility in terms of % E.L. if the length of the specimen at fracturepoint is 56.0 mm.
- In a tensile test on a metal specimen having a cross section 20 mm by 10 mm elastic breakdown occurred at a load of 70 000 N. A thin plate madec from the same material is to be subjected to loading such that at a certain point in the plate the stresses are o,=-70 N/mm², 7.y= 60 N/mm² and o. Determine the maximum allowable values of o, using the Tresca and von Mises theories of elastic breakdown. Ans. 259 N/mm² (Tresca), 294 N/mm² (von Mises).3. Given the following fatigue data for a brass alloy: Cycles to Failure 2 x 105 1х 106 Stress Amplitude (MPa) 310 223 191 3х 106 168 1 x 107 153 3х 107 143 1х 108 134 3х 108 127 1х 109 a.) Plot the S-N curve for this alloy. b.) Does this material have an endurance limit? Explain. c.) Determine the fatigue strength at 5 x 105 cycles. d.) Determine the fatigue life for 200 MPa. e.) If the loading in part c is uniaxial, what is the minimum diameter of a circular rod required for this application if the maximum load is 500 kN?The stress–strain relation shown in Figure was obtained during the tensile test of an aluminum alloy specimen. Determine the Yield stress using an offset of 0.002 strain.
- The specimen shown is made from a 25 mm diameter cylindrical steel rod with two 38 mm outer-diameter sleeves bonded to the rod as shown. Knowing that E = 200 GPa, determine (a) the load P so that the total deformation is 0.05 mm, (b) the corresponding deformation of the central portion BC. 38 mm diameter P' 25 mm diameter B 38 mm diameter C 50 mm 75 mm 50 mmProblem 1 An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown. Axial loads are applied at the positions indicated. Aluminum Steel A=800mm2 A=1000mm2 Bronze A=700mm? 4P 2P 500mm 600mm 700mm 1. What is the maximum value of P that will not exceed the axial stress bronze of 105 MPa? 2. What is the maximum value of P that will not exceed the axial stress in aluminum of 90 MPa? 3. If P=10KN, what is the axial force to be carried by the aluminum in KN? 4. If P is 5KN, what is the axial stress of steel?2. A polymer muterial is subjected to a constant load for a set amount of time and then the load is removed. This experiment generates the stress versas time plot and the strain versus time plot shown below. Describe what is happening to the material at following locations on the strain versus time plot below: • At point A • Between point A and point B • Between point B and peint C • Between point C and peint D Briefly comment on how you would expect this strain versus time plot to change if the experiment was carried out en anather sample of the same polymer at a temperature below the polyrmer's glass transition temperature. Time, t в A D Time, t Strain, ɛ Stress, o
- Q.3. (30%) A circular aluminum tube subjected to T pure torsion by torques T has an outer radius r2 equal to 2 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 500x10-6 rad, what is the shear strain y1 at the inner surface? (b) If the maximum allowable rate of twist (0) is 0.15°/m and the maximum shear strain is to be kept at 500x10-6 rad by adjusting the torque T, what is the minimum required outer radius (r2 )min?The stress-strain relationship shown in Figure P1.13 was obtained during the tensile test of an aluminum alloy specimen. Determine the following: a. Young's modulus within the linear portion b. Tangent modulus at a stress of 310 MPa c. Yield stress using an offset of 0.002 strain d. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used? 450 300 150 0.002 0.004 0.006 0.008 Strain, m/m FIGURE P1.13 Stress, MPaThe (G-E) diagram obtained in the tensile test performed on a metal sample with a diameter of 16 mm is as follows. The loads at points A, B and C and the elongation measured on l. 16 cm gauge length were determined as follows: B A B C Load (kgf) 4800 8400 7200 Elongation (mm) 0.192 28.8 38.4 c) Calculate the fracture work and the maximum elastic energy the metal rod can store. d) Find the cross-sectional area of a 6 m long rod made of this metal such that it can carry 12 tons of load with 2 times the safety of yield strength. How long does the rod extend under this load?