Understanding Material Properties: Stress, Strain, and Elasticity

Unit III: Material Properties

1. Determination of the Characteristic Curve

It represents the functional relationships between the parameters characterizing a bomb. These curves show how and when a particular trip unit will act for a given time and current. A curve is represented by a band created by a minimum and a maximum value of time or current.

2. Lateral Deformation or Narrowing

It is a scale that measures how the width or space of a material is reduced due to an applied force.

3. Effort

Effort is the internal relationship of the materials when subjected to loads. It is usually expressed in intensity of force, i.e., force per unit area. The concept of effort is artificial; therefore, efforts cannot be measured experimentally. However, there are many experimental techniques used to measure deformation. If the relationship between stress and strain is known, it is possible to calculate the stress state at one point after measuring the state of deformation. The relationship between stress and strain, called the modulus of elasticity, as well as the yield stress, are determined by the structure of the molecular material. The distance between the molecules of a material under stress depends on a balance between the molecular forces of attraction and repulsion.

4. Yield

Yield strength, also known as yield stress, is the maximum stress that an elastic material can withstand without permanent deformation. If applied stresses are higher than this limit, the material undergoes permanent deformation and does not regain its original form when the loads are removed. In general, a material subjected to stresses below its yield stress is temporarily deformed according to Hooke's law. Materials subjected to stresses greater than their elastic limit exhibit plastic behavior. If the stresses continue to increase, the material reaches its breaking point. The elastic limit thus marks the boundary between the elastic field and the area of influence. More formally, this implies that in a state of uniaxial tension, the yield stress is the point from which the material enters the yield surface.

5. Elastic/Plastic Curve

The elastic/plastic curve is formed by bending the longitudinal axis of a beam, which is due to the application of transverse loads on the beam in the xy-plane. The elastic equation is the differential equation for a straight axle beam that allows you to find the concrete form of the elastic curve. Specifically, the elastic equation describes the displacement field experienced by the beam axis, from its original straight position to its curved or flexed final position.

6. Limit or Yield Point

The yield point is higher than the yield stress, where permanent deformation occurs without an increase in applied stress. It is visible in ductile materials but not in brittle and hard materials. The yield point is located at 0.2% on the graph, or by drawing a parallel line to the linear portion of the curve; where it intersects the curve is the yield point.

7. Young's Modulus or Elastic Modulus

Young's modulus is a parameter that characterizes the behavior of an elastic material, according to the direction in which force is applied. For a linear elastic and isotropic material, Young's modulus has the same value for traction and compression. It is a constant independent of the effort, as long as it does not exceed a maximum value called the yield strength. It is always greater than zero: if you pull on a bar, its length increases, it does not decrease. This behavior was observed and studied by the English scientist Thomas Young. Both Young's modulus and yield strength differ for different materials. The modulus of elasticity is a spring constant that, like the elastic limit, can be found empirically based on the tensile test of the material. In addition to this longitudinal modulus, a shear modulus can also be defined for a material.

8. Deformation: Squashed or Stretched (Axial Strain)

Axial strain is a quantity that measures the increase in length of a material when subjected to a tensile force before rupture. The elongation is expressed as a percentage (%) compared to the original length. This term is also known as elongation. In an elastic material, when the extension does not exceed the elastic limit, the material recovers its original length when the tensile stress ceases. However, if it exceeds the elastic limit, it does not regain its original length.