PS33.22 Mechanical Behavior of materials PS3 Due: March, 2, 2004 (Tuesday) before class (10:00am) 1. A sample of a material subjected to a compressive stress zσ is confined so that it cannot deform in the y-direction, but deformation is permitted in the x-direction, as shown below. Assume that the material is isotropic and exhibits linear-elastic behavior. Determine the following in terms of zσ and the elastic constants of the material: (a) The stress that develop in the y-direction. (b) The strain in the z-direction. (c) The strain in the x-direction. (d) The stiffness zzEεσ/'= in the z-direction. Is this apparent modulus equal to the elastic modulus E from ial test on the material? Why or why not? a uniax 2. n orthotropic material has the compliance matrix: The reciprocal relation states that: A=66554433231323221213121100000000000000000000000SSSSSSSSSSij 0SSS121212Eν=, where 1212εεν−= Eν(a) Prove the reciprocal relation. ely isotropic and has the elastic moduli: (b) A fiber composite is transvers521== EE GPa 253=E GPa 125.012=ν 33.0 a 13=ν813=G GPCalculate the strain tensor for the stress state of MPa. 3. (a) How and why would you expect the elastic modulus to vary with melting temperature? modulus of 70 GPa. An Al alloy commonly used in aero/astro of 7075 T6 Al is not much ct . (a) As temperature increases, explain how the elastic modulus changes for crystalline materials crystalline solids . Using the figures below for cases of isostress and isostrain, derive the upper and lower bounds =534350405ijσHow would you explain that, although aluminum (Al) and magnesium (Mg) have very similar melting temperatures (Tm ~650℃), they have very dissimilar elastic moduli (EAl = 70 GPa, EMg = 45 GPa)? (b) Pure Al has an elastic engineering applications is 7075 T6 Al. The designation “7075” indicates the chemical composition of the alloy: 1.6% Cu, 2.5%Mg, 5.6% Zn, 0.23 Cr, balanced Al. The designation “T6” indicates that the heat treatment of the alloy: tempered at 650℃. Despite the addition of so many alloying elements, the elastic modulusdifferent from that of the pure Al:E7075 T6=70.7GPa. Explain why alloying has little effect on E. (c) Cobalt is magnetostrictive and contracts upon exposure to a magnetic field. What is the effeof a magnetic field on the elastic modulus of Cobalt? 4and rubbers. Relate each type of behavior to fundamental properties of material. (b) Speculate on the relation between the modulus of elasticity of a group of and their respective melting points. Also relate the modulus of elasticity to the respective coefficients of thermal expansion. 5for Young’s modulus for a composite material that were given in class. 2(a) Isostrain (b)