18.6:
Hooke’s Law
Hooke's law states that stress applied to a material is directly proportional to the strain it experiences within the elastic limit. For ductile materials, the elastic limit often aligns with the yield point.
The proportionality constant, known as the modulus of elasticity, has the same units as that of stress since strain is a dimensionless quantity.
The physical properties of structural metals are affected by the manufacturing process used. The stress-strain diagrams of pure iron and three different grades of steel show significant variations in yield strength, ultimate strength, and rupture point.
However, they possess the same modulus of elasticity: their stiffness within the linear range is the same. So, if a high-strength steel is substituted for a lower-strength steel in a structure having the same dimensions, it will have an increased load-carrying capacity.
In isotropic materials, like metals, the Stress-strain relationship is independent of load direction. However, for anisotropic materials, such as fiber-reinforced composites, elasticity moduli differ significantly in the directions parallel and perpendicular to the fibers, resulting in different resistances to loading.
18.6:
Hooke’s Law
Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
The implementation of Hooke's law holds true until the material reaches its proportional limit. Beyond this point, the stress-strain relationship becomes nonlinear. This limit often coincides with the yield point for materials that are ductile in nature. However, identifying this limit for other types of materials can be challenging due to the non-linearity of the stress-strain relationship.
Materials are categorized into two main types based on mechanical characteristics, such as isotropic and anisotropic. Isotropic materials, such as metals, exhibit consistent properties regardless of the direction of the load. As such, their stress-strain relationship, including the modulus of elasticity, remains constant irrespective of the direction of the applied stress. On the other hand, anisotropic materials like fiber-reinforced composites display mechanical properties that depend on the load's direction. These materials consist of fibers of a robust material embedded within a softer matrix. The moduli of elasticity along directions parallel and perpendicular to the fibers differ significantly, resulting in varying resistances to load. The maximum strength of these materials can be achieved when the fibers align in the same direction as the load.