# Stress and Strain-Definition, Curve, Formula, 9 Differences [PDF]

Contents

## Stress and Strain Definition

In engineering, stress has been defined as when an external force is applied to any object(made of an elastic material), they produce a change in the shape and size of the object.

Stress is defined as, the deformation force per unit area of the body or material. Stress is the internal force(per unit area) associated with the strain. It is the ratio of the force applied on the system to the per unit area of the body. To find the stress of an object which is displaced (after applying force on it). The formula is as follows

• Stress(σ)= Force(F) / (A)Cross-sectional Area
• Whereas, σ= Stress in N/M2 or Pascal.
• F= Force applied on the system which is in Newton (N).
• A= Cross-sectional area of the object in M2.

The types of stresses are as follows

• Tensile stress,
• Compressive stress,
• Torsional stress.

The Tensile stress is like pulling the material on each side or might one side as figures shown below,

The Compressive stress is like pushing the material on each side or might one side as figures shown below,

The Torsional stress is like there are two forces applied on the object and the forces are opposite to each other. The figure is shown below,

Whereas Strain is defined as the ratio of change in length to the original length of an object or body is called as Strain. Strain is the relative change in the shape or size of an object due to externally applied forces. To find the strain of an object which is displaced (after applying force on it). The formula is as follows

Strain(∈)= Change in length (Li) / Original length (L0). The standard unit of strain is dimensionless. It has no units.

• =Strain.
• Li = Change in length in Meters.
• L0 = Original length in Meters.

## Stress and Strain Curve

This curve is a behavior of the material when it is subjected to load. The stress-strain curve depends on two types of material.

##### Ductile Material
• Ductile materials are materials that can be plastically twisted with no cracks. They tend to hold the deformation that occurs in the plastic region. The ductile material is- Aluminum, Copper, Steel, and more.
##### Brittle Material
• A material is brittle if, when subjected to stress, it breaks without significant plastic deformation. Brittle materials absorb relatively little energy before fracture, even those of high strength. The brittle material is Cast Iron, Concrete, Some glass products, and more. To draw the stress-strain curve of any material the mechanical point or properties includes,
• Proportional Limit
• Elastic Limit
• Yield Point
• Ultimate Stress Point
• Breaking Point

## Stress-Strain curve for Mild steel (Ductile Material)

##### Young’s Modulus
• The Young’s modulus is defined as the ratio of the stress of the object to the strain of the object or body. Young’s Modulus= Stress / Strain. The SI unit of  Young’s Modulus is N/M2 or Pascal.
##### Limit of proportionality or Proportionality limit (A)
• The proportional limit is the point on the curve up to which the value of stress and strain remains proportional. From the diagram point, A is called the proportional limit point or it can also be known as the limit of proportionality. The stress up to this point can be also be known as proportional limit stress.
##### Elastic limit
• Elastic limit is the limiting value of stress up to which the material is perfectly elastic.
##### Yield Stress (B-C)
• B-upper yield value
• C-lower yield value

Yield stress is defined as the stress after which material extension takes place more quickly with no or little increase in load. Point (B-C) is the yield point on the graph and stress associated with this point is known as yield stress.

##### Ultimate Stress Point (D)
• Ultimate stress point is the maximum strength that material has to bear stress before breaking. It can also be defined as the ultimate stress corresponding to the peak point on the stress-strain graph.
##### Breaking Stress Point or Fracture Point (E)
• Breaking point or breaking stress or Fracture point is the point where the strength of material breaks. The stress associated with this point known as breaking strength. On the stress-strain curve, point E is the breaking stress point or Fracture point.

## Differences between Stress and Strain

• The force applied to object, the object gets displaced that is stress and Strain is the change in the form or shape of the object or physical body on which stress is applied. Stress can occur without strain, but strain cannot occur with the absence of stress. The stress and strain can be calculated. Stress has a dimensional unit but the strain has no dimensional unit
• Definition: Stress refers to the internal force per unit area that a material experiences, while strain represents the resulting deformation or elongation.
• Measurement: Stress is measured in units of force per unit area (such as pounds per square inch), while strain is dimensionless (no units).
• Types: There are several types of stress, including tensile, compressive, and shear stress. Strain can be divided into two categories, linear and shear strain.
• Effect on Material: Stress can cause a material to deform, break, or change shape. Strain measures the degree to which a material changes shape due to stress.
• Graphical Representation: The stress-strain curve provides a graphical representation of the material’s behavior under stress, showing how stress changes as strain increases.
• Formula: There is a formula relating stress and strain, which is crucial in predicting the performance of materials under different conditions.
• Applications: Understanding stress and strain is essential in designing and engineering structures that can withstand the stresses and strains they will encounter in use.
• Importance: The study of stress and strain is a crucial aspect of material science and engineering, as it helps in the selection of materials for specific applications and in predicting how materials will behave under different conditions.

## Conclusion

In conclusion, stress and strain are fundamental concepts in the field of mechanics and materials science. Stress refers to the internal force per unit area that a material experiences, while strain represents the resulting deformation or elongation. The stress-strain curve provides a graphical representation of the material’s behavior under stress, and the formula relating stress and strain is crucial in predicting the performance of materials under different conditions.

Understanding these concepts is essential in designing and engineering structures that can withstand the stresses and strains they will encounter in use. Overall, the study of stress and strain is a crucial aspect of material science and engineering.

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