Solid Deformation

Dhristi JEE 2022-24

Matter has three forms: solids, liquids, and gases. They differ in the way ions, molecules, and atoms are arranged in them. Solid is characterized by tightly packed particles that are not free to move around within the substance. A solid can change its shape when pressure is applied to it. The change might be very little for some structures like a building or very large in objects like a spring. This article will look into what is deformation and what are the different types of deformation that can happen in a solid. Let us first define deformation.

Deformation Definition 

What forces act on a solid object affects the spacing of atoms within the solid to a small extent. This change in spacing changes the external structure or shape and size of the solid, and it is termed as deformation of solids. 

Stress and Its Types

Stress is considered as a force that produces strain when it acts on an object or material. The unit of stress is force/area (for example, lb/in2) since the stress is applied over an area. The pressure is a special type of stress where forces are acting in equal magnitude from all directions. But if the force from all directions is not equal, then we get differential stress. There are mainly three types of stress:

  • Tensile Stress 

This is also called extensional stress, which causes the material (to which stress is applied) to stretch. An example is the stretching of a rubber band.

  • Compressive Stress 

This kind of stress results in the object being squeezed or squashed. An example is when you squeeze a ball; you are applying compressive stress.

  • Shear Stress 

The deforming stress acts tangentially to the object's surface and the result in either slippage or translation of the object.

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Features of Deformation in Solids 

  • When stress is applied to a solid, a deformation occurs, which gives rise to internal intermolecular forces in the solid that oppose the forces being applied.

  • If the applied forces are not so strong, then the internal molecular forces can resist the stress, and the object can acquire a new equilibrium state. Once the load is removed, the object then comes back to its original state.

  • If the force is very large, there could be permanent deformation of solids or even a complete structural failure.

  • The type of deformation that a solid undergoes depends on its material, size, geometry, and forces.

Types of Deformation of Solids

A strain is defined as a change in the size, shape, or volume of an object. Strain could also be in the form of any movement of the material, including titling and translation. 

Solids can undergo various types of deformation as described below:

  • Elastic deformation - This kind of deformation is reversible, and the object returns to its original size and shape once the applied force is removed. 

  • Linear elastic deformation is given by Hooke’s law that states that the amount a body extends is directly proportional to the force applied on it provided the elastic limit of the object is not exceeded. The deformation formula according to Hooke’s law is; σ = E * ε, where σ is the force applied, E is the spring or elastic constant (called young’s modulus), and ε is the extension or resulting strain.

  • The elastic constant is measured as force per unit extension, and its unit is N m-1. It is denoted by the gradient of the graph drawn by force against the extension. 

  • When the material reaches its yield strength, its elastic range ends, and plastic deformation begins.

  • Stress = Force/cross-sectional area

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  • Plastic or ductile deformation - This is an irreversible kind of deformation that starts as elastic deformation, and the object can partially return to its original state till this stage. A material like soft thermoplastic has a large plastic deformation range. Some ductile metals like gold, silver, and copper also have a large range of plastic deformation. Materials with minimal plastic deformation ranges are rubber, hard, thermosetting plastics, and ceramics. Plastic deformation can be of different types under tensile stress:

    • Strain hardening region - Due to the movement of atoms, the material becomes harder.

    • Necking region - After the ultimate strength is reached, there is a reduction in the cross-sectional area of the specimen. At this point, the material can no longer tolerate the maximum stress, and there is a rapid increase in the strain in the object.

    • Fracture - This indicates the end of plastic deformation where the material breaks.

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Young’s Modulus

Young’s modulus is a fundamental property of all materials which is unchangeable. However, it is dependent on pressure and temperature. Young’s modulus is also called the elastic modulus, and in simple words, it describes the stiffness of the material, i.e., how easily you can bend or stretch the material. The name “Young’s modulus” comes from 18th-century English physicist and physician Thomas Young. Young’s modulus describes the elastic properties of a material undergoing compression or tension in only one direction. It indicates a material’s ability to withstand length changes when it is undergoing lengthwise compression or tension. Mathematically it is expressed as:

Young’s modulus = stress/strain = (F * L0)/(A * (Ln - L0)) 

Or, F/A = Y * (ΔL/L0)

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Where L0 is the original length, Ln is the new length, F is the force applied, and A is the cross-sectional area of the metal bar.

Young’s modulus is measured in pascal and 1 Pascal = Nm-2

FAQs on Solid Deformation

Q1. What is Strain Energy with Respect to Solid Deformation?

Ans: When forces act on an object to change its shape, the object is under strain. In a strained state, there is energy stored in the object in the form of potential energy. This specific type of energy is referred to as elastic potential energy or strain energy. For example, a stretched wire, compressed gases, twisted elastic bands all possess strain energy. 

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Q2. What is the Classification of Materials Based on their Elastic Properties?

Ans: Materials are divided into two classes based on how they relatively behave under stress:

  • Brittle materials - These materials display a tiny region of ductile behavior before they fracture. A brittle fracture happens in them without plastic deformation. Some of the brittle materials are rock, glass, cast iron, graphite, ceramic, and a few alloys with very low plasticity.

  • Ductile materials - Ductile materials exhibit a large region of ductile behavior before they can fracture. In such materials, a large plastic deformation happens before fracturing. Some examples are rubber, plastic, and some soft metals like aluminum and copper.

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