When a material is subjected to an external load, it undergoes deformation. Stress is a measure of the internal resistance of a material to this deformation. Instantaneous stress refers to the stress that occurs when the load is applied suddenly and with a high rate of change, while gradually applied load refers to a load that is applied slowly and steadily.
The statement that instantaneous stress developed due to sudden loading is twice that of a gradually applied load is not always true in all cases. It depends on the material behavior and the loading conditions. However, in certain scenarios, this relationship can hold true, and here's the explanation for it:
Elasticity: When a material is loaded gradually, it has time to adjust and distribute the load throughout its structure more evenly. In the elastic region (i.e., where the material behaves elastically), the deformation is directly proportional to the applied load. So, when the load is applied slowly, the deformation is small, and the stress is relatively low.
Inertia effects: When a load is applied suddenly and with high intensity, there might be some inertial effects. Inertia causes the material to resist sudden changes in motion. As the load is applied quickly, the material might not have enough time to respond and distribute the load, resulting in a localized concentration of stress.
Wave propagation: A sudden load application can create stress waves that propagate through the material. These stress waves can cause additional internal stresses beyond the initial applied load, contributing to higher instantaneous stress.
Strain rate sensitivity: Some materials exhibit strain rate sensitivity, which means their mechanical properties, including their stress-strain relationship, can change with the rate at which the load is applied. Under high strain rate conditions (such as in sudden loading), the material may behave stiffer, resulting in higher stress values.
It's important to note that if the material is loaded beyond its elastic limit, it might undergo plastic deformation, where it will not return to its original shape once the load is removed. In such cases, the relationship between instantaneous stress and gradually applied load becomes more complex and cannot be simply expressed as twice or any specific factor.
In conclusion, the idea that instantaneous stress developed due to sudden loading is twice that of a gradually applied load is a simplified statement and is valid only in specific cases and materials. In real-world engineering scenarios, it is essential to consider the material's behavior, the loading conditions, and the rate of application to understand and predict stress accurately. Engineers use detailed material testing and analysis to account for these factors in their designs and calculations.