Young’s modulus

Introduction

Young’s modulus

One of the most important engineering tests is the bending or fracture of an object or material, and a characteristic showing that it is Young’s modulus. It is the unchanged-able fundamental property of a material.  This is a measure of how easy the material is to stretch or deform. In this article, we will get into the details of how to calculate young’s modulus and what to infer from the result it gives us. We will also learn about the elemental properties of solid. It is also called elastic modulus or tensile modulus.

Understanding and defining Young’s modulus

To define Young’s modulus we can say that it is the mechanical property of a material that allows it to withstand pressure and expand, with respect to its length. It is denoted by E or Y.

 This is the standard mechanical measurement of elastic solids that are linear such as rods and wires. There are other numbers too that give an estimate of the elasticity of the object. For example,There are different numbers that provide us with a proportion of elastic properties of a material, similar to Bulk Modulus and shear modulus, but young’s modulus is the most commonly used value, in fact, it tells us about the elasticity of a material or if it fails (that is permanent deformation).

 The modulus of elasticity defines the relationship between force (force at each point) and elongation (lift depending on the object). Young’s modulus is named on Thomas Young the British scientist. Solid objects will deform when the load is applied. If it is elastic, the body will return to its original shape after removal. Most tools are linear and slightly wider. Tensile modulus works with linear elastic devices.

 Bend or break?

Wires follow Hooke’s law. When a force F is applied, it will increase a certain distance x. This is easily given by the equation  F = kx. k is the stiffness of the spring, but the elongation of the wire depends on the cross-section, length and material of the wire. 

 The modulus of elasticity (E) is the characteristic of the elongation and deformation of a material and is defined as the ratio of tensile stress (σ) to tensile strain (ε). Tension is the force applied per unit area (σ = F / A), and strain  is the elongation per unit length (ε = dl / l).

Young’s Modulus Formula: E= stress/strain = σ/ε = Fl/dl*A

Notations Used In The Young’s Modulus Formula

• E is Young’s modulus in Pa
• 𝞂 is the uniaxial stress in Pa
• ε is the strain or proportional deformation
• F is the force exerted by the object under tension
• A is the actual cross-sectional area
• dl is the change observed in length after the load is applied.
• l  is the original length 

 The Stress-Strain Curve

You can use Young’s modulus to determine the body’s elasticity or maximum limit to which it can bend before ultimate failure. This is because it measures the resistance of a body to bend.

 Figure: Stress Vs Strain Graph

The stress-strain diagram may vary depending on the type of material. 

1. Brittle materials are usually very durable because they can withstand heavy loads without being overstretched.
2. Plastic materials have a wide range of elasticity, and their dependence on stress and deformation is linear, but the initial direction change (elastic limit) makes the material lose linearity and the material cannot return to its original shape. The second peak is the tensile strength, which represents the maximum stress that the material can withstand before it breaks. Plastic is not very strong, but it can withstand heavy loads. 

The modulus of elasticity is determined by the slope of the line in the stretch diagram.

 Young’s Modulus Factors

The modulus of elasticity, E, is one of the most important characteristics of solid material because it is a characteristic of a material and represents its stiffness. It is defined as the ratio of normal stress to elongation within the proportional limit. Therefore, based on the definition, we can conclude that the Young’s Modulus Factors are-

• Stress: The more stress a material can bear the higher it’s Young’s Modulus will be
• Strain: the less strain it faces or less change in length the material experiences due to stress applied, the higher will be young’s modulus
• Elongation: Inversely proportional to the modulus of elasticity
• Influence of temperature: Generally speaking, the elastic properties of materials decrease with the increase of temperature
• The influence of impurities: Adding impurities to a metal can increase or decrease its elasticity, if the contaminant has a higher elasticity than the added material, the elasticity will increase, and if the dirt is less elastic than the material, its elasticity will decrease

 The last two points have nothing to do with young’s modulus, but only with elasticity.

Importance of Young’s Modulus in industry and academia

Knowing the modulus of elasticity of steel makes it inherently harder than wood or polystyrene because it is less likely to deform under load. The modulus of elasticity is also used to determine the degree of deformation of a material under a given load. Hence the lower Young’s modulus of the material, the greater the elongation of the body. For objects such as clay and wood, this elongation may change within the sample itself. Some clay specimens deformed more than others, and the steel bars experienced the same deformation from beginning to end. The modulus of elasticity is very important to doctors and scientists because it knows this constant when a structural implant deforms. In this way, they can learn how to mechanically design parts for the body.

Conclusion:

Young’s modulus is a quantified measurement that defines the elasticity of a linear body. It can be calculated by judging the change in length when a certain load is applied and plotting a graph. The slope of this graph gives us Young’s modulus; this graph is called the Stress-Strain curve. Young’s modulus is the inherent property of a material. It depends on various factors. It is extremely useful as it helps engineers to sort the material required to build bridges, buildings, tools etc. Studying the material’s properties helps prevent failures. As you will study further in universities, failure analysis is an integral part of engineering. Studying disasters helps them to be prevented in future.