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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.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) AtB LMP = T(C+ Int) Which material will you select if they both have same constant (CA= CB)? Which material will you select if C < C? Motivate your answer by means of a calculation.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.
- 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 XA 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= GPaAn 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. P
- Two triangular wedges are glued together as shown in the figure. The stress acting normal to the interface, o, is MPa. 100 MPa 100 MPa on 45% 100 MPa -100 MPaStress-strain behavior of a ductile and a brittle material is given in below. Which material absorbs more energy and why? Stress, o Brittle DuctileThe brass shell (αb511.6 3 10–6/°F) is fully bonded to the steel core (αs56.5 3 10–6/°F). Determine the largest allowable increase in tem-perature if the stress in the steel core is not to exceed 8 ksi.
- Example: the low cycle fatigue of a certain steel is given by life cycle equation-2: (of/E)=0.005 E=0.07 b= -0.08 c= -0,7 a. What is the value of the transition fatigue life, in this case 2 N/when E - Ep b. What is the total strain amplitude at the transition fatigue life?A solid 45 mm diameter beryllium copper (E = 131 GPa; α = 17.0 × 10−6 /°C) rod is stress free when securely attached to the unyielding supports shown in the figure below. If the compressive normal stress in the rod must not exceed 450 MPa, what is the maximum temperature increase (rounded down to the nearest degree) that can be allowed for the rod? Use L1 = 300 mm.Solid shaft made of cast iron shown in the figure, T = 400 lb. It is subject to flick torque. Determine the smallest radius that will not generate strength loss according to the theory of greatest normal stress? The cast iron sample tested in tensile has a stress of 20 µm axim um.