During a creep test (constant stress equal to 3.5 MPa) a material has an initial strain of 10 and a strain of 2 x 10* after 30 days. The same material was also submitted to a relaxation test (constant strain equal to 1.5 x 104). During the relaxation test, determine the stress after 30 days. Assume that the material follows the Maxwell model. 4
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- Q.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.An aluminium specimen with an initial gauge diameter d, = 10 mm and gauge length, 1, = 100 mm is %3D subjected to tension test. A tensile force P= 50 kN is applied at the ends of the specimen as shown, resulting in an elongation of 1 mm in gauge length. The Poisson's ratio (µ) of the specimen is Take shear modulus of material, G = 25 GPa. Consider engineering stress-strain conditions. PMaterial A has a Poisson’s ratio of 0.35 and Material B has a Poisson’s ratio of 0.25. Assume that cylindrical specimens having the same dimensions were prepared from both materials and they were tested under uniaxial tension (below the yield stress of both materials). At the same longitudinal strain, the final diameter of the Material A becomes less than the final diameter of the Material B. Is it true or false?
- 6.46 For some metal alloy, a true stress of 345 MPa e (50,000 psi) produces a plastic true strain of 0.02. How much does a specimen of this material elongate when a true stress of 415 MPa (60,000 psi) is applied if the original length is 500 mm (20 in.)? Assume a value of 0.22 for the strain-hardening exponent, n.A wire of circular cross section is wound around a drum of 500 mm diameter. Ewire 100 GPa. If the normal stress in the wire material is not to exceed 50 MPa, the radius of the wire cross section must beQ.24 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. The R-ratio (minimum stress to maximum stress) for this cyclic loading is (round off to one decimal place)
- 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?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.At an axial load of 22 kN, a 15-mm-thick × 50-mm-wide polyimide polymer bar elongates 5.7 mm while the bar width contracts 0.15 mm. The bar is 245-mm long. At the 22-kN load, the stress in the polymer bar is less than its proportional limit. Determine Poisson’s ratio.
- A thin-wall tube, made of a unidirectional graphite/epoxy lamina with a fiber direction 0 to its axis, is loaded in torsion (Tr) as shown in the figure. Use the Max Stress, Max Strain, Modified Tsai-Hill, Tsai-Wu and Hashin-Rotem failure criteria, to sketch the ultimate value of tr as a function of the fiber orientation angle 0 (0°<0<180°). Indicate the failure modes regions. Given that: (G=985Mpa ; (o= 690Mpa ; (o) = 29Mpa ; (o) =98Mpa ; (r2) = 49Mpa E, = 294GPA ; E, = 6.4GPA ; G, = 4.9GPA ; v =0.23GPA ; v = 0.01GPA %3D %3D ActQ.7 A cylindrical shell 4 m in diameter, is made of 20 mm thick steel plates. The efficiency of longitudinal joint and circumferential joint are 0.88 and 0.7 respectively. If the maximum permissible tensile stress in the plate is 120 MPa, the safe pressure for the shell is (a) 2.12 MPa (b) 0.84 MPa (c) 1.05 MPa (d) 1.68 MPaWhich of the following statements is incorrect? Both the grain boundary and bulk diffusion creep mechanism lead to elongated grains. For linear creep, the creep exponent in the steady-state creep rate equation is around 1. S-N curves are a plot of the stress versus the number of cycles to failure. The relaxation modulus is a time-dependent elastic modulus used for viscoelastic polymers. Crystalline polymers show a large drop in the relaxation modulus around the glass transition temperature.