Stress-strain relationship explained

Introduction

Every object when in linear motion experiences some form of load due to applied force during the motion that acts upon the object. The object that experiences this gives an opposite reaction to the loads, this is described as mechanical properties.

For an object that is subjected to any sort of compression or tension such as carrying balls rolls, shafts that are mounted vertically or fastening and joining of any hardware into the body. Here the property of mechanical stress and strain plays an important role. It helps in determining whether the object can withstand these types of loads.

Stress:

It is the force applied to an object which is divided in terms of its cross-sectional area.

σ = F/A

Where , F = force.

A = cross sectional area.

Stress is nothing but the distribution of the force that is applied when the object is loaded. When there is the distribution of the forces internally it balances the reaction. The distribution may or may not be uniform. The uniformity completely depends on the object.

Some commonly used  measurements of stress are:

Psi (pounds per square inch) =lbs/in2.

Pascals – Newtons per square metre (Pa = N/m2)

 kPa = Kilopascals — one thousand or 10 to power 3 Newtons per square metre.

Types of stress:

• Tensile stress.

It is the force applied to the cross section of an area of an object, which increases the length of the object. This type of stress makes the object thinner and longer. Ductile materials can withhold this type of stress as ductility is the property in which a metal can be drawn into thin wires. For brittle metals, it is difficult to manage this type of stress.

Tensile stress is used to calculate certain properties:

• Elastic modulus: It records the stiffness of an object.
• Ultimate tensile stress: It is the measure of how much stress can an object withstand by loading.
• Modulus resilience: It is the maximum amount of energy that material can absorb within elastic limit (per unit volume).
• Fracture stress: It is the total force an object can withstand until it reaches the point of breaking.

Compressive stress

It is the force applied to the cross section of an area of an object, which decreases the length of the object. This type of stress makes the object thicker and shorter. The force applied by the compressive stress is responsible for the Deformation of the object which reduces the volume of the material. 

When compressive stress is applied the ductile materials compress and there is no breakage but when a brittle material is supplied with this type of stress the fracture as there is a sudden release of the internal energy stored.

Strain:

Strain is determined when the amount of deformation experienced by the object in the direction of the applied force is divided by the object’s initial dimension.

ε = dl / lo

where,

dl = change of length (m, in)

lo = initial length (m, in)

ε = strain (no unit)

Ways to deform solids using external force/ types of strain

1. By applying tensile stress, when tensile stress is applied the body changes with respect to length. The length increases, the object turns thinner and longer. This is called tensile strain.

1. By applying compressive stress, when an object is compressed, there is some force acting up against it which helps in deformation. This is called compressive strain.
   
   
2. Shearing forces/stress cause deformation. When two objects are provided with two equal opposite forces parallel to the cross-sectional area there is a tangential force that is developed and this is referred to as the shearing stress.

τ = Fp / A

where,

τ = shear stress (Pa (N/m2)

Fp = shear force applied parallel to the cross-sectional area(N)

A = area (m2)

Relation between strain and stress using the stress-strain curve: 

While trying to understand the solids and their relation of Mechanical properties information regarding their elastic properties is of most importance. The elastic properties of the objects or materials are studied using the stress strain relationship under different loading circumstances. 

An object’s stress- strain curve gives its stress – strain relationship accurately. by using the stress – strain curve will be able to understand the elastic properties and the mechanical properties of an object. 

Explanation of the stress-strain curve:

1. Proportional limit

Many materials show proportional relativity between stress and strain, which is referred to as Hooke’s law. In the proportional limit of the curve, the object/material follows Hooke’s law. The slope obtained from the curve in the proportional limit is referred to as the young’s modulus.

Young’s modulus or modulus of elasticity is the measure of the stiffness of the material and the factor that gives us a note on the reaction of the material on the load.

2. Elastic limit 

The point in which the material returns to its original form, any deformation formed due to stress and strain is reversed when the load is removed. The elastic limit and proportional limit are roughly equivalent for many known materials. Beyond this limit, the material cannot return back to its original position, and plastic deformation occurs later.

3. Yield point

At this point, strain increases rapidly than stress and it is referred to as strain hardening. The material experiences some permanent deformation in this stage. For materials that do not have a defined yield point, an offset yield point is utilized to determine the permanent deformation. Draw a line that crosses the strain axis at 0.002 and travels parallel to the stress-strain line that is slope equals to E, to find the offset yield point. This line intersects the stress-strain curve at the offset yield point.

4. Ultimate Stress Point

The point at which the material can hold the maximum amount of stress after which, it will break or fail.

5. Fracture or Breaking Point

The point beyond which the material cannot hold the stress anymore, it breaks or fails or fractures. It starts to fall from this particular point.

Conclusion:

Stress and strain are the two force concepts that allow us to understand how any material or object acts when an external force is applied to it. We use many external forces to shape the solids as to how we want them to be, but knowing how much of the force should be added we need to understand the stress-strain curve and calculate all the required values.

Stress and strain were calculated using the initial cross-sectional area and length. As a result, it’s known as an “engineering stress-strain diagram.” However, a material’s cross-sectional area and length vary when it deforms. A “true stress-strain diagram” is a stress-strain diagram that uses the instantaneous values of cross-sectional area and length to determine stress and strain.

Because the discrepancies between the engineering and real versions are very minimal below the material’s yield point, the engineering stress-strain diagram is suitable for most applications.