Stress and Strain – Definition, Stress-strain Curve 2024

When you are talking about solids and various other materials, it is crucial to understand how these types of materials usually react when a force is applied. This process helps the students identify their strengths, deformations, and various other parameters acting on the objects. And to find these parameters, the stress and strain quantities are important. Here, in this article, we are going to provide a detailed guide about these aspects including how we define stress and strain, their types, and difference between stress and strain. Also let us learn about stress formula and strain formula. 

Why is it important to study stress and strain?

It is important to study the stress and strain differences and basics, and stress strain curve, all of which will help in ascertaining the amount of stress or load that a material is capable of handling before it breaks, gets distorted, or stretches. So, the study of stress and strain is all about understanding how and why certain materials are more malleable and can be easily deformed or distorted than others. 

What is Stress?

Stress is defined as the force per unit area that is observed by a material when an external force is applied. These external forces are generally uneven heating, permanent deformation, etc. These in turn help students calculate and find the plastic, elastic, and fluid behavior of each material under different forces. 

Mathematically, stress is given by,   

\(\sigma = \frac{F}{A}\)

Where, \(\sigma\) = Applied Stress 

F = Force Applied 

A = Area of Force 

Unit of stress is \(\frac{N}{ M^{2} } \)

Types of Stress

There are different types of Stress that can be applied to a material, such as   

Compressive Stress

When a force acts on a body, it causes a reduction in the volume of the said body, resulting in deformation. This type of stress is referred to as Compressive stress.

Compressive stress leads to material failure that is ultimately caused due to tension. The compressive stress from its application to brittle materials differs from that of ductile materials.

Tensile Stress

When an external force is applied per unit area on a material, and it results in the stretching of the said material, then it is described as Tensile Stress.

Tensile stress leads to elongation of any material due to external stretching force.

What is Strain?

If a body experiences deformation due to the applied external force in a particular direction, it is called strain. Moreover, the strain does not have any dimensions, as it only explains the change in the shape of the object.

The strain formula is expressed as,  

\( \epsilon = \frac{ \delta l}{L} \)

Where, \(\sigma \) = Strain due to Applied Stress

\(\delta l \) = change in length 

L = original length 

Types of Strain

Similar to stress, strain is also differentiated into Compressive Strain and Tensile Strain.   

Compressive Strain  

Compressive strain is defined as the deformation observed on an object when compressive stress acts on it. And in this type of strain, the length of the material or object generally decreases.

Tensile Strain  

The Tensile stress acting on a body or a material that causes the increase in the length of said material is referred to as a tensile strain.  

Stress-Strain Curve

This graph explains how stress and strain curves act on a body with respect to each other, as well as the different regions formed on the graph.   

Stress-Strain Curve constitutes one of the crucial studies and essentially involves the study of elastic properties of materials understood through the relationship between stress and strain, factoring in various loads. In short, any material’s stress-strain curve indicates the relationship between stress and strain. In this curve, the stress and its corresponding strain values are marked. 

Let’s understand the stress strain diagram in detail,

• The OA line represents the Proportional Limit, as it described the region, where the material or body obeys Hooke’s Law. And this line can help students to calculate Young’s Modulus, using the ratio of stress and strain.    
• Now, the AB line represents the Elastic Limit of the object, which means that after this point, the body does not retain its original shape or size, when the acting force is removed.    
• As you can guess, the BC lines describe the Yield Point. Which, when force is applied on the material, then there is complete deformation in the object, which cannot be reversed, even if the force is removed.    
• D point on the graph is the point beyond which students can observe the complete failure of the object, as it crosses the maximum stress a material can endure. This point is stated as Ultimate Stress Point.    
• E is the Fracture of Breaking Point, at which students can observe the complete failure of deformation of the object, regardless of the force whether it is applied or removed.  

The stress-strain curve typically consists of several distinct regions: 

Let us understand stress-strain curve as we try to understand the stress-strain graph better through various regions: 

• Proportional limit
• Elastic Region
• Yield point
• Stress point
• Fracture or breaking point

Elastic Region: In this region, the material deforms elastically in response to applied stress, meaning it returns to its original shape once the stress is removed. The relationship between stress and strain is linear, and this region is characterized by Hooke’s Law, which states that stress is proportional to strain. 

Yield Point: Beyond a certain stress threshold known as the yield point, the material begins to deform plastically, meaning it undergoes permanent deformation even after the stress is removed. The yield point marks the transition from elastic to plastic deformation. 

Plastic Region: In this region, the material continues to deform plastically with increasing stress, undergoing significant strain without a proportional increase in stress. Plastic deformation is irreversible, and the material’s shape changes permanently. 

Ultimate Tensile Strength: The ultimate tensile strength (UTS) is the maximum stress that a material can withstand before failure occurs. It represents the highest point on the stress-strain curve and indicates the material’s resistance to fracture under tension. 

Fracture Point: Beyond the ultimate tensile strength, the material experiences a rapid decrease in stress leading to fracture or failure. The fracture point marks the end of the stress-strain curve, indicating the material’s ultimate failure under tension. 

Stress-Strain Graph

The stress-strain graph is primarily a representation of the stress-strain curve where plotting is clearly of the curve is shown. It reflects the changes caused to stress vis-à-vis the change in strain. The graphs are reference illustrations for metals in both material sciences as well as manufacturing.

The graph provides design engineers with parameters and inputs much-needed for application design. Also, many mechanical properties such as toughness, yield point, elasticity, strength, strain energy, elongation at load, and many others are understood. Through the graph, one can understand the slope and the axis.

Hooke’s Law

From the above sections, we have learned all about types of stress and strain, and their units, as well as a graphical representation of stress and strain on objects. Now let us talk about Hooke’s law of stress and strain, which plays an important role in helping us understand how stress and strain work on an object when force is applied.

According to this principle, the strain of the material is equal to the applied stress, in the elastic limit region of the said object or material. And it is represented as,

F = –k.x 

F = Force 

X = Extension of Length 

K = Spring Constant 

Difference between stress and strain

In physics, stress refers to the force that is acting per unit area of the object, whereas strain depicts the ratio of the change in an object’s dimension to its original dimension. In physical parlance, stress is equivalent to Pressure and its unit is Pascal or psi, or pounds. On the other hand, strain signifies the ratio of change in dimensions to that of the original dimension, therefore has no units of measurement. Strain, however, can be measured by strain gauges.

Stress and strain are related, but are characterized by distinct properties. Stress causes deformation, while strain can be caused by several types of stress, including tension or compression.

Difference between plain stress and plane strain

plane stress happens when the value of normal stress remains zero and the sheer stress which is seen perpendicular to the direction of the applied load is presumed zero. Plane stress is based on assumption and is measured approximately. On the other hand, plane strain is about distortion in the object that is perpendicular to the object’s plane. If plane stress is more of an approximation, then plane strain is more accurate.

Shear stress and shear strain

Shear stress is the stress that is applied parallel to the plane of the object which renders lateral distortion in the object. As far as shear strain is concerned, it reflects the magnitude of lateral strain in terms of tanθ. Shear Strain is shown as tanθ = Lateral Distortion / Perpendicular height.

Conclusion

Stress and strain are fundamental concepts that play a crucial role in understanding the mechanical behavior of materials. The stress-strain curve provides a graphical representation of this relationship, offering insights into the material’s strength, stiffness, and ductility. By studying stress and strain, engineers and scientists can design and analyze structures and materials to ensure their safety, reliability, and performance in real-world applications. 

In the above article, we have explained in detail the terms, stress and Strain, how they act, units of stress and strain, types of stress and strain, etc. This will be helpful for students to solve any kind of problems from these chapters or understand other subtopics easily from the next chapters. However, if you are still worried about how to cover many complex topics and chapters in Physics. Then the best solution for you is to join Online Coaching Platforms. Like the Tutoroot platform, which offers cost-effective online interactive classes that come with various amazing benefits for the students. Visit the Tutoroot site to learn more about these benefits. 

Frequently Asked Questions

What are the differences between Stress and Strain? define stress. 

Stress is defined as a force acting per unit area of an object, while strain is stated as the amount of relative deformation caused by the force acting on an object. Moreover, the unit of stress is NM2, while strain does not have any units as it is not dimensional. 

What is a stress-strain diagram or graph?  

The stress-strain diagram graphically represents the material’s strength and elasticity. Furthermore, the stress-strain diagram may be used to study the behavior of the materials, making it easier to comprehend their application. 

What is the stress and strain formula? 

The stress and strain formula is: stress = (elastic modulus) × strain. Strain = Δ L L = Change in Original Length. 

What is the Proportional Limit of the Stress Strain Curve? 

The proportional limit id stress-strain curve refers to the highest stress where stress and strain are directly proportional so that the stress-strain graph represents a straight line in such a way that the gradient equals the elastic modulus of the material 

What is the Elastic Limit of Stress Strain Diagram? 

The elastic limit of the stress-strain diagram illustrates the point where the behavior of the material changes from being elastic to becoming plastic. Where the stress (and therefore strain) applied to the material is lower than the elastic limit, both the stress and strain revert to zero (recover) when the load is removed. 

What is the Yield Point of the Stress Strain Diagram? 

The yield point on the stress-strain diagram represents the point of the end of elastic deformation and the beginning of permanent deformation. Before this point, the stress-strain curve stays linear, and after the yield point, it turns non-linear. 

What is the Breaking Point of the Stress Strain Curve? 

The breaking point of stress-strain curve represents the point at which the material’s failure takes place. It is also called the fracture point 

Define Stress and Strain: 

Stress is the internal force per unit area acting on a material, while strain is the measure of deformation or change in shape experienced by the material in response to applied stress. Together, stress and strain form the basis for understanding the mechanical behavior of materials and are essential concepts in engineering, physics, and materials science. 

Strain Meaning: 

Strain refers to the relative change in size or shape of a material compared to its original dimensions when subjected to external forces or loads. It quantifies the deformation experienced by the material and is expressed as a percentage or in decimal form.