Final answer:
The calculated value of engineering stress being much lower than true stress in a shear test is False, as true stress tends to be higher due to the decrease in cross-sectional area during material deformation.
Step-by-step explanation:
The statement that the calculated value of engineering stress is much lower in comparison to the true stress in a shear test is False. In the context of shear testing, engineering stress and true stress are terms used to describe the measurement of stress on a material. Engineering stress is calculated by dividing the force applied by the initial cross-sectional area of the material, whereas true stress is calculated using the current cross-sectional area, which may change during deformation.
Shear stress is caused by forces that act parallel to the surface of the material, as denoted by the symbol F. The measure of shear stress is the magnitude of F divided by the surface area A where the shearing force is applied. The shear modulus, denoted by S, is the proportionality constant that relates shear stress to shear strain, and its use is elucidated by Equation 12.33.
With respect to the shear test, under large strains, the true stress tends to be greater than the engineering stress because the cross-sectional area of the material decreases as it is deformed, leading to higher stress values when using the true stress calculation. Therefore, the original statement is incorrect since the calculated value of engineering stress is not lower than true stress, rather it is the other way around when significant deformation occurs.