Question

Problem 3: Composite moduli Composites are materials that are composed of two or more distinct composed of two materials with Young's modulus E, (top and bottom components) and Eb (center component), and where 0 < λ < 1. HAL (1-A)L AL Ex (3a) Suppose that the material is subjected to an average stress σχ along the x direction resulting in a strain Ex as shown in the center figure above. Find the effective Young's modulus Eer (in terms of E. E, L,A) such that σ,-Ex,x Hint: assume the displacements in each layer are the same but that the stresses are not. (3b) Similarly to the first part, suppose that the material is subjected to a stress ơy in the y direction resulting in an average strain Ey as shown in the figure to the right above. Find the effective Young's modulus E.ff (in terms of E,, E. L, A) such that ơ,-E", (3c) Let the outer material (with Young's modulus E.) be made of titanium carbide and the inner material (Young's modulus Eb) be made of A36 structural steel, and let Solution: Ex-262GPa, Ey-232GPa -0.25. Evaluate your answers above.

Answer 1

Any Pogc ひ Avea omatsal dist 2. 入し p = total loco in hosuzmw diucho,

tbed tat.n hy hali.İn, .n -7

Poy-3 ズし vwe kmow tolal

Poa efHi a 450CP Stuud A36 450企. 25) 여 200 C1-02x) 261 S GPa

Po n)