Final answer:
The FSP vs Δy graph curves due to the nonlinear behavior of materials when subjected to larger forces while still in the elastic region. Upon further increase in force, permanent deformation occurs leading up to fracture with criticial changes in the slope indicating material limits.
Step-by-step explanation:
The question is asking about the shape of the force versus displacement (FSP vs Δy) graph for materials. The correct explanation for why the graph is curved for small displacements is nonlinear behavior of materials (Option b). When a material is subjected to small forces, the relationship between the force applied and the deformation it causes can be linear, which is represented as a straight line on a graph (Hooke's law region). However, for larger forces, the material starts to behave in a non-linear way, which is reflected as a curve on the graph. This curve indicates that the material is still in the elastic region, where if the force is removed, the material will return to its original shape. Beyond this elastic limit, larger forces can cause permanent deformation until fracture occurs.
As forces increase, the slope of the graph changes, indicating different levels of stiffness within the material. From the provided information, the specific point of the graph where it is noted that a small increase in force causes a large increase in displacement (ΔL) is near the fracture point of the material, demonstrating the material's critical limit to elastic behavior and the onset of permanent deformation.