The correct answer is option 'B' - curvature is infinite.

Explanation:
A plastic hinge is a phenomenon that occurs in structural elements when they undergo plastic deformation. It is a location where the material has yielded and the deformation becomes permanent. Plastic hinges usually occur in beams and columns under excessive loads or during extreme events like earthquakes.

Plastic Hinge and Curvature:
When a plastic hinge forms in a structural element, it indicates that the material has reached its plastic limit and will not regain its original shape. At the location of a plastic hinge, the curvature of the element becomes infinite.

Curvature is a measure of how much a curve deviates from being a straight line. It is defined as the reciprocal of the radius of curvature. In other words, curvature is inversely proportional to the radius of curvature.

At the location of a plastic hinge, the radius of curvature becomes zero because the material has yielded and undergone permanent deformation. Therefore, the curvature becomes infinite.

Significance of Infinite Curvature:
Infinite curvature at a plastic hinge signifies that the structural element has undergone significant deformation and has lost its ability to carry additional load. It indicates that the element has reached its ultimate capacity and cannot sustain any more load without further damage.

Other Options:
- Option 'A' - radius of curvature is infinite: This is incorrect because the radius of curvature becomes zero at a plastic hinge, not infinite.
- Option 'C' - moment is infinite: This is incorrect because the moment at a plastic hinge is not infinite. It is the bending moment that causes the plastic deformation and the formation of the hinge.
- Option 'D' - flexible stress in infinite: This is incorrect because the stress at a plastic hinge is not infinite. The material has reached its yield point and is subject to the yield stress, but it is not infinite.

In conclusion, the correct answer is option 'B' - curvature is infinite. At the location of a plastic hinge, the curvature becomes infinite, indicating significant plastic deformation and loss of load-carrying capacity.