Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes through initial yield point at P, and then strain hardens to point Q, where the loading was stopped. From point Q, the specimen was unloaded to point R, where the stress is zero. If the same specimen is reloaded in tension from point R, the value of stress at which the material yields again is ______MPa

The correct answer is 210.

Analysis of the Stress-Strain Curve from the Image:

By observing the provided stress-strain diagram:
- The initial loading path starts from the origin O.
- Point P represents the initial yield point.
The stress value at the initial yield point P is:
${\sigma }_{\mathrm{y0}}=180$ MPa
- Beyond P, the metal deforms plastically and undergoes strain hardening up to point Q.
The stress value at point Q is:
${\sigma }_Q=210$ MPa
- At point Q, the loading is stopped, and the specimen is unloaded along the path QR. The path QR is parallel to the elastic slope OP, leaving a permanent plastic strain at point R where the stress is zero.

Reloading from Point R:

- When a material is unloaded from a plastic state (point Q) and then reloaded from a zero-stress state (point R), it deforms elastically back along the unloading line RQ.
- The material will yield again only when the stress reaches the maximum stress value to which it was previously subjected during the first loading cycle.
- Consequently, the new yield stress on reloading is equal to the stress at point Q:
${\sigma }_{\mathrm{y1}}={\sigma }_Q=210$ MPa
- Therefore, the stress at which the material yields again on reloading is 210 MPa.