Stress-strain relationship

Introduction to Stress-Strain Relationship

When it comes to physics, the phrases Stress and strain describe the forces that cause things to deform or break. Deformation is defined as the alteration of the shape of an item as a result of the application of force. Materials feel it as a result of external forces acting on them. Examples of such forces include:

• The objects are being squeezed or crushed, twisted or shear.
• Tearing.
• Pulling apart from one another.

The connection between stress and strain is a straight proportional ratio up to an elastic limit. Hooke’s law explains the link between stress and strain. Let’s first learn about Stress and strain.

What Do You Mean By Stress?

Stress in materials is defined as the restoring force per unit area resulting from external forces, uneven heating, or deformations. The breaking stress, also known as the ultimate tensile stress, is the highest amount of stress that a material can withstand before breaking. 

The Greek letter σ is used to represent this tensor quantity. Pascal or N/m²are the units of measurement. Mathematically, this may be stated as –

σ=F/A

where,

The restoring force, denoted by the letter F, is measured in Newtons or N.

A is the area of the cross-section measured in square metres.

N/m² or Pa are the units of measurement for Stress.

Types of Stress

When it comes to physics, there are several types of Stress, but they are primarily divided into two categories: 

• Normal Stress
• Tangential or Shearing Stress. 

Normal Stress 

When the deforming force is applied perpendicular to the body’s cross-sectional area, it is called Normal Stress. Stress will remain at an average level even if the length of the string or the object’s volume varies. 

Based on the magnitude of the force exerted, normal Stress is divided into two categories:

Longitudinal Stress

 Longitudinal Stress is a term used to describe when the length of the body varies due to the usual tension that is imposed. Longitudinal Stress is equal to the product of the deforming force and the cross-sectional area.

Longitudinal Stress can be further classified and separated into two categories: 

Tensile Stress

When a rubber band is stretched out, this is an example of tensile Stress in action.  

Compressive Stress

Compression is the polar opposite of tension. Creating compressive Stress is something you’ve probably done before, like squeezing a rubber ball in your hands.

Bulk Stress or volume stress

Volumetric Stress, or bulk Stress, occurs when the deforming force or applied force operates from all directions, leading to changes in the object’s volume. 

Tangential or shearing Stress 

 Shearing stress, also known as tangential Stress, occurs when a deforming force or an external force acts in a direction perpendicular to the cross-sectional area of the body under consideration. Consequently, the body’s form is altered as a consequence.

What is Strain?

Strain is defined as the total amount of deformation witnessed by the body in the direction of the applied force divided by the initial dimensions of the body. 

The following equation expresses the relationship between deformation and the length of a solid in terms of size:

ϵ=δl/L

where,

ϵ is the amount of strain caused by the Stress applied

δl represents the change in length

L is the original length of the material

The strain only defines the relative change in shape; therefore, it has no numerical value.

Types of Strain

 There are two types of strain depending on how Stress is applied.

Tensile strain

Tensile strain is defined as a change in the length of a body due to the application of tensile stress to the body.

Compressive Strain

It is the change in length of a body caused by the application of compressive stress.

Stress-strain curve

The stress-strain curve gives us a good idea about the Stress-strain relationship. Several variables influence the stress-strain curves of different materials. To understand how a material deforms with increasing shapes, we may look at these curves. This helps us to justify Hooke’s law in a specific manner.

Stress-strain curves have various areas, which are as follows:

Proportional limit

The stress-strain curve is the area that obeys Hooke’s Law. The point OA shows the proportional limit on the graph.

Elastic limit

If all of the load acting on the material is removed, it reverts to its previous location up to a point on the graph when that load was applied. If the material is stretched beyond this point, it will not return to its previous position, and a plastic deformation will begin to manifest itself in it.

Yield point 

The yield point is when a material begins to distort in a plastic manner. When the yield point is reached, permanent plastic deformation takes place. In this case, there are two yield points: the upper yield point and the lower yield point. 

Ultimate stress point 

It is the point at which a material can withstand the most significant amount of stress before failing. Failure happens once you reach this point in time.

Fracture or Breaking point

It is the point on the stress-strain curve where the material fails.

Conclusion

The stress-strain curve shows the connection between Stress and the accompanying strain. Stress and strain are directly proportional to a certain point, but only up to that point. Hooke’s law is applicable only in this linear portion of the stress-strain curve. The slope of a linear curve determines the young’s modulus of a material.

The stress-strain curve offers a comprehensive list of mechanical parameters required for engineering design. The stress-strain curve can be used to determine a material’s ability to sustain loads before it fractures under certain conditions.