At which point in a material's stress-strain curve does permanent deformation begin?

The yield point is the correct answer because it is the stage in a material's stress-strain curve where it begins to exhibit permanent deformation. Prior to reaching the yield point, materials deform elastically, meaning they will return to their original shape once the applied stress is removed. However, once the yield point is surpassed, the material transitions into a plastic deformation region, where changes to the shape remain even after the stress is no longer applied.

This characteristic is important in engineering because understanding the yield point allows designers and engineers to select materials that can safely withstand expected loads without permanent damage. The concepts of elastic limit and fracture point do relate to the behavior of materials under stress but define different behaviors: the elastic limit is where elastic deformation stops, and the fracture point indicates where the material ultimately fails and breaks. Ultimate strength refers to the maximum stress a material can withstand before failure, but does not specifically indicate where permanent deformation starts.