# ELASTIC PROPERTIES OF SOLID

Elastic composition or elasticity is the property of a solid material to restore its original shape and size after being removed from the force that deform it.

### CONTENT

Concept Of Elasticity

Hooke’s Law

Definition of Elastic Limit

Yield point

Tensil Stress

Tensil Strain

Young Modulus

### Concept of Elasticity

In physics and materials science, elasticity is the ability of the body to resist distorted effects and restore to its original size and shape when that effect or force is removed. When a sufficient load is applied to a solid object, the solid object will deform; if the material is elastic, the object will return to its initial shape and size after removal. This is the opposite of plasticity, in plasticity, an object cannot do this, but remains in its deformed state.

For different materials, the physical reasons for elastic behavior may be completely different. In metals, when a force is applied (energy is added to the system), the atomic lattice changes size and shape. When the force is removed, the lattice will return to its original low energy state. For rubber and other polymers, elasticity is caused by the stretching of the polymer chain when a force is applied.

Elasticity is a measure of the sensitivity of one variable to changes in another variable, the most common is that this sensitivity is a quantitative change relative to changes in other factors (such as price). In business and economics, price elasticity refers to the degree to which individuals, consumers, or producers change their demand or supply in response to changes in price or income. It is mainly used to assess changes in consumer demand caused by changes in the price of goods or services.

### Hooke’s Law

Hook’s law points out that the force required to deform an elastic object should be proportional to the distance of deformation, no matter how large the distance is. This is called perfect elasticity, in which a given object, no matter how strongly deformed, will be restored to its original shape. This is just an ideal concept; most materials with elasticity maintain pure elasticity in practice, and plastic (permanent) deformation occurs only after very small deformation.

### Definition of Elastic Limit

To a more or less extent, most solid materials exhibit elastic behavior, but for any given material, the size of the force and the accompanying deformation are limited, where elastic recovery is possible. This limit is called the elastic limit and is the maximum stress or force per unit area that a solid material may produce before permanent deformation occurs. Stress beyond the elastic limit can cause the material to yield or flow.

For such materials, the elastic limit marks the end of the elastic behavior and the beginning of the plastic behavior. For most brittle materials, stress beyond the elastic limit will lead to fracture, almost no plastic deformation. The elastic limit significantly depends on the type of solid under consideration; for example, steel rods or steel wires can only elastically extend about 1% of their original length, while for strips of certain rubber materials, up to 1,000% elastic extension can be achieved.

However, steel is much stronger than rubber, because the tensile force required to achieve maximum elastic extension in rubber is smaller than the tensile force required for steel (about 0.01). The elastic properties of many solids under tension lie between these two extremes.

### Yield point

The yield point is defined as a relatively large amount of deformation of the material that exceeds the force, a small increase in tensile force. The yield point is the point on the stress-strain curve, indicating the limit of the elastic behavior and the beginning of the plastic behavior.

Below the yield point, the material will deform elastically and return to its original shape when the applied stress is removed. Once through the yield point, part of the deformation will be permanent and irreversible, called plastic deformation. Yield strength is usually used to determine the maximum allowable load of mechanical components, because it represents the upper limit of the force that can be applied without permanent deformation. In some materials (such as aluminum), nonlinear behavior begins gradually, making it difficult to determine the exact yield point.

In this case, the offset yield point(or proof stress)is taken as the stress where 0.2% plastic deformation occurs. Submission is a gradual failure mode, unlike the final failure, which is usually not catastrophic. In solid mechanics, the yield point can be specified by the three-dimensional main stress of the yield surface or yield criterion.

### Tensil Stress

Tensile stress (σ)is the resistance of an object to the force that may tear it. It is calculated based on the highest tension the object in question is subjected to without tearing, and is measured in Newton/square millimeter, but initially expressed in tons/inch. Tensile stress can be defined as the size of the force applied along the elastic rod, which is divided by the cross-sectional area of the rod in a direction perpendicular to the applied force. Stretching means that the material is under tension, and there is a force acting on it to try to stretch the material.

Stress is the force per unit area of a material, thus:

Tensile Stress = Force / Cross-sectional Area

Tensile stress measures the strength of a material; therefore, it refers to the force trying to pull apart or stretch the material. Many mechanical properties of the material can be determined by tensile testing. Tensile stress can also be called normal stress or tension. When the applied stress is less than the tensile strength of the material, the material is completely or partially restored to its original shape and size.

When the stress is close to the tensile strength value, the material has begun to flow plasticly and quickly forms a contraction area called the neck, which is the point at which it breaks. Tensile stress accelerates the corrosion process and leads to intergranular corrosion of steel and intergranular stress-induced corrosion cracking. Therefore, the stress will reduce the mechanical properties and overall strength of the corroded steel.

### Tensil Strain

Tensile strain is defined as deformation or elongation of a solid due to the application of tensile force or stress. In other words, when the applied force tries to “stretch” the body, a tensile strain is generated when the length of the body increases. Tensile strain can be expressed mathematically by the following formula:

ε = ΔL / L

Where:

ε = Tensile strain

ΔL = Change in length

L = Original length

### Young Modulus

The elastic modulus of tensile stress is called Young’s modulus; the elastic modulus of bulk stress is called the bulk modulus; the elastic modulus of shear stress is called the shear modulus. Note that the relationship between stress and strain is an observational relationship measured in the laboratory.

Young’s Modulus The elastic modulus in Young’s modulus or tensile or compression (i.e. negative tension) is a mechanical property that measures the tensile or compression stiffness of a solid material when a longitudinal force is applied. It quantifies the relationship between tensile/compressive stress (force per unit area) and axial strain

Young’s modulus, a numerical constant named for Thomas Young, an 18th-century British physician and physicist, describes the elastic properties of a solid that undergoes stretching or compression in only one direction, such as in the case of a metal rod, which returns longitudinally to its original length after being stretched or compressed.

Young’s modulus is a measure of the ability of a material to withstand length changes under longitudinal stretching or compression. Sometimes called elastic modulus, Young’s modulus is equal to longitudinal stress divided by strain. Stress and strain can be described as follows in the case of the metal rod under tension.

Previous Post