Question

A linear elastic material is subjected to differing strains. At a strain of 0.2%, the stress is 36 MPa whereas at a strain of 0.75%, the stress is 128 MPa. a) (5 points) Determine the stress in this material at a strain of 0.58% (use linear interpolation) 5, 1. b) (5 points) what is the Young's modulus (elastic modulus) of this material? Use proper units mce

Answer 1

5)a) When strain=0.2%=0.002, stress=36 MPa, ie. stress/strain=0.002/36*10⁶=1.8*10¹⁰ N/m².

Also when stress=0.75%=0.0075,stress=128 MPa, i.e again stress/strain=1.8*10¹⁰ N/m². i.e.stress/strain =constant=Young's Modulus.

Therefore when strain=0.58%=0.0058,stress=1.8*10¹⁰*0.0058=104 MPa.

b)Young's Modulus of this material=stress/strain=1.8*10¹⁰ N/m².