Which of the following is a proper sequence?
Proportional limit, elastic limit, yielding, failure
Sequence: Material Behavior Under Stress
Understanding how materials respond to applied forces is fundamental in engineering. The relationship between stress (force per unit area) and strain (relative deformation) is often visualized using a stress-strain curve. This curve highlights different stages of material behavior, and knowing their correct sequence is important for predicting performance and preventing failure.
Defining Key Material Stages
The options refer to specific points or stages on a typical stress-strain curve for a ductile material:
- Proportional Limit: This is the point up to which stress ($\sigma$) is directly proportional to strain ($\epsilon$). Hooke's Law, represented as $\sigma = E\epsilon$ (where $E$ is the modulus of elasticity), holds true in this region.
- Elastic Limit: This is the maximum stress a material can endure without experiencing permanent deformation. If the stress is removed before reaching the elastic limit, the material returns to its original shape. This limit is usually very close to the proportional limit.
- Yielding: This signifies the onset of plastic (permanent) deformation. Beyond the elastic limit, the material deforms permanently even after the load is removed. Many materials show a distinct yield point, while others exhibit yielding gradually.
- Failure: This is the final stage where the material breaks or fractures due to the applied stress.
Correct Sequence Explained
The progression of material behavior under increasing tensile or compressive load follows a specific order:
- Proportional Limit: The initial phase where the stress-strain relationship is linear.
- Elastic Limit: The maximum stress reached before permanent deformation begins.
- Yielding: The point where significant plastic deformation starts.
- Failure: The ultimate point at which the material fractures.
This sequence represents the transition from elastic behavior (where deformation is temporary) to plastic behavior (where deformation is permanent), culminating in fracture. Therefore, the sequence: Proportional limit, elastic limit, yielding, failure accurately describes the stages of material response under load.
Important Questions from Stress and Strain
The ultimate tensile stress of mild steel compared to ultimate compressive stress is ______.
The total strain energy stored in a body within elastic limit is termed as
- The stress induced in a body, when suddenly loaded, is _________ the stress induced when the same load is applied gradually.
The ratio of the magnitude of the applied force to the cross-sectional area of the wire is called
A metal rod has a diameter of 8 mm and a true stress-strain relationship is given by \({\sigma } = 900 \times \epsilon^{0.6}\) is under the action of tensile loading. The minimum diameter in mm that can be achieved is:
