The part of the stress-strain curve where the Hooke's Law is valid is
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Hooke's Law (\( \text{stress} \propto \text{strain} \)) is valid in the linear portion of the stress-strain curve, typically from the origin to the proportional limit (here, OA).
Hooke's Law states that stress is directly proportional to strain, which is valid in the linear elastic region of the stress-strain curve. In the given stress-strain graph:
- The x-axis represents strain, and the y-axis represents stress.
- Point O is the origin, A is within the linear region, B is the elastic limit, C is beyond the elastic limit, and D is in the plastic region.
- The region where stress is proportional to strain (a straight line) is from O to A.
Thus, Hooke's Law is valid in the region OA.
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Approach Solution -2
The portion of the stress-strain curve where Hooke's Law is valid corresponds to the region where stress is directly proportional to strain. This is the initial linear region of the graph.
From the graph, this linear relationship is clearly shown in the segment O to A.
In this region, the material obeys Hooke's Law: \( \sigma = E\epsilon \), where:
\( \sigma \) is stress,
\( \epsilon \) is strain,
\( E \) is Young's modulus.
Beyond point A, the graph deviates from linearity, indicating the end of elastic behavior and the beginning of plastic deformation.
