On a stress-strain curve, how is Young's modulus determined?

• A. Area under the curve
• B. Maximum stress
• C. Stress at yield point
• D. Slope of initial elastic region

Answer: (D)

Young's modulus is a measure of stiffness and is defined in the elastic regime where deformation is proportional to the applied load and the material returns to its original shape. In that linear portion of the stress–strain curve, stress and strain are proportional, described by sigma = E * epsilon. The slope of that initial elastic region, d(sigma)/d(epsilon), equals the modulus E. The area under the curve relates to energy stored per volume, not stiffness; the maximum stress is the ultimate tensile strength, and the stress at yield marks the start of plastic deformation. So the slope of the initial elastic region is the correct way to determine Young's modulus.