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Stress vs. strain. Image Credit: Shutterstock.com/Ralf Geithe

Stress vs. Strain: What Are the Key Differences?

Xomety X
By Team Xometry
May 10, 2023
 16 min read
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Stress and strain are two of the most important concepts in materials science and engineering. Stress refers to the force applied to a material per unit area, while strain is a deformation or change in the shape of the material that results from the applied force. However, the relationship between stress and strain is not always straightforward. Different materials can exhibit very different stress-strain behaviors depending on their composition, structure, and loading conditions.

This article will explore the key differences between stress and strain and why they matter for engineering and design. We'll discuss the different types of stress and strain, how they're measured and analyzed, and how they can be used to predict the performance and failure of materials and structures. 

What Is Stress?

Stress is defined as the force per unit area that acts on a material. This property helps define how different materials behave under specific loading conditions.

Various types of stress can occur inside an object, including compressive stress, tensile stress, shear stress, and torsional stress, among others. Different symbols are used to represent each type of stress, with the Greek letter sigma (𝜎) being the primary symbol. The mathematical expression for stress is given below:

Slide 1 of 1
stress equation
stress equation
stress equation

Stress formula

Where:

  1. σ is stress, measured in N/m² or Pa
  2. F is the applied force, measured in Newtons (N)
  3. A is the cross-sectional area to which the force is applied, measured in m²

Additional symbols include 𝜎t, 𝜎c, and 𝜏, which represent tensile stress, compressive stress, and shear stress, respectively. 

Additional symbols include 𝜎t, 𝜎c, and 𝜏, which represent tensile stress, compressive stress, and shear stress, respectively. 

How Does Stress in Materials Work?

Stress within an object, structure, or material develops when an object is subjected to a deforming force. As a result of the applied force, it undergoes either elastic (reversible) or a combination of elastic and plastic (permanent) deformation. The bonds between atoms of a material resist external forces, developing an equal and opposite reaction force inside the stressed object.

Even the application of a simple tensile force, stretching a material along just one of its axes, results in reaction stresses generated in at least two dimensions, since the material is elongating in one direction and contracting in a direction normal to the applied force. The real three-dimensional stress state of an object under load is represented by a stress tensor, which describes the stress state in each of the principal directions as well as the interactions between the stresses on the principal axes.

What Is the Importance of Stress?

Stress is the reaction of a material to the application of force. We can define the observed stress under certain well-defined test conditions (e.g., yield strength is typically defined as the stress observed at 0.2% strain) as characteristics or properties of materials that can help us with selecting the right material for various applications.

There are two parameters that are very important when considering the effect of stress, stress testing, and stress analysis. Stress testing is the procedure where different forces are applied to an object to see how the object will react under different loading conditions; while stress analysis is when you take what you learned from the testing and apply it to select an optimal material or revise a design for optimal strength or durability (or at least, to meet the application's requirements). The main idea behind these methods is to test whether a material can withstand the forces it will be subjected to in real-life applications or to test for weak spots within a specific design. This is especially useful in the construction industry where structures made of concrete, for example, should be able to withstand different forces without failing. 

Stress can also be used to calculate or determine a lot of different properties, such as the elastic modulus, yield strength, ultimate strength, and fracture toughness of a material. This gives us extra information about a material which could aid in the material selection phase. 

How Is the Stress of Materials Measured?

Measuring stress directly is not possible, so instead, we must measure either the applied forces or resulting deformations. To measure deformation, it is necessary to have an understanding of the relationship between the applied forces (stresses) and the resulting deformations (strains).

Several experimental testing techniques and instruments can be used to indirectly measure the generation of stress by applied forces, such as strain gauges, extensometers, piezoelectric materials, load cells, ultrasonic testing, x-ray diffraction, and photoelasticity. 

Once the magnitude of the force is known, or measured, the stress equation (σ=F/A) can be used to calculate stress. 

Stress analysis is a valuable tool for evaluating the effects that various forces can have on an object, and it can be performed using various techniques, such as experimental testing, computational simulations, analytical mathematical modeling, or a combination of these methods. The choice of technique depends on the material being tested, the type of stress measured, and the desired level of accuracy.

What Are the Benefits of Stress?

Stress, or more specifically stress analysis, is a very useful tool. It plays a crucial role in understanding how different materials behave under external forces. Here are some of the benefits associated with stress analysis:

  1. Design of Structures: Stress analysis is essential in designing and testing structures, such as buildings, bridges, and airplanes, to ensure they can withstand the forces they will be subjected to.
  2. Material Selection: Understanding the stress behavior of different materials helps in selecting the appropriate material for a particular application.
  3. Failure Analysis: Stress analysis can help identify the cause of material failure, which can inform improvements in design and manufacturing processes.
  4. Quality Control: Measuring stress can help ensure the quality and consistency of materials, especially in manufacturing processes where precision is crucial.
  5. Safety: Knowledge of stress can help prevent failures in structures and materials, which can have severe safety implications.

What Is Strain?

Strain is a measure of the deformation of a material under the influence of an external force. It represents the amount of deformation that occurs in a material when subjected to stress. Strain is defined as the ratio of the change in length (or other dimensions) of a material to its original length (or dimension), and is expressed as a unitless quantity or as a percentage. The equation in terms of change in a specimen’s length is given below:

Slide 1 of 1
strain equation
strain equation
strain equation

Strain formula.

  1. Strain (ε) is the fractional or percentage change in length or another dimension.
  2. L is the length of the material after an external load is applied.
  3. L0 is its original length measured in the same units as “L”.

The name for the type of strain observed is based on the name for the type of stress applied: tensile strain, shear strain, compressive strain, volumetric strain, and thermal strain. A tensile strain occurs when a material is stretched or elongated, while compressive strain occurs when a material is compressed or shortened. A shear strain is the result of stress applied in a direction parallel to the cross-section of interest. Volumetric strain relates to changes in the volume of a material due to changes in its shape or size. Lastly, thermal strain refers to the change in length or volume of a material due to temperature changes.

How Does a Strain in Materials Work?

When an external force is applied to a material, it causes deformation, which is measured as strain. The deformation behavior of the material under stress depends on various factors such as the type of material, its composition, and the magnitude, direction, and nature of the applied stresses. In general, materials can deform in three main ways under stress: 

  1. Elastic Deformation: Occurs when the material deforms under stress but returns to its original shape when the stress is removed. In other words, the material can withstand a certain amount of strain without undergoing permanent deformation. 
  2. Plastic Deformation: Occurs when the material is subjected to stress beyond its elastic limit, causing permanent deformation. The material undergoes a change in shape that is not recoverable even after the stress is removed. The amount of plastic deformation that a material can undergo before it breaks is known as its ductility.
  3. Fracture: Occurs when the applied stress exceeds the strength of the material, causing it to break or fail. The strength of a material indicates its ability to withstand stress without breaking or undergoing plastic deformation.

What Is the Importance of Strain?

Strain is an important property of materials because it provides a way to measure and understand how a material deforms under stress. When stress and strain data are acquired simultaneously, as in the stress-strain curve generated during a simple tensile test, it can be used to calculate important parameters that engineers need for application design. Some of these mechanical properties include strength, toughness, elasticity, strain energy, yield point, elongation under load, and resilience. 

How Is the Strain of Materials Measured?

Various methods can be used to measure strain. The most popular methods are strain gauges and extensometers. Both of these methods require contact between the specimen and the instrument, and both are directional. Other methods that can be used include digital image correlation (DIC), piezoelectric sensors, and acoustic emission sensors. 

What Are the Benefits of Strain?

The study of the amount of strain that a material exhibits under stress have benefits and applications in various fields. Here are some of the benefits of strain analysis:

  1. Design and Optimization of Structures: Strain measurement is essential for designing and optimizing structures that can withstand different loads and stresses. Understanding the strain behavior of different materials allows engineers to design structures that are safe, reliable, and efficient.
  2. Quality Control and Testing: Strain measurement is also used for quality control and testing of materials during manufacturing. Manufacturers can detect defects, ensure consistency, and improve the quality of their products by monitoring the strain behavior of materials.
  3. Material Characterization: Strain measurement can help in the characterization of different materials, such as metals, polymers, and composites. Researchers can understand their properties, performance, and potential applications by measuring the strain behavior of these materials.
  4. Failure Analysis: Strain measurement is also important for the failure analysis of materials and structures. Analyzing the strain behavior of a failed component allows engineers and researchers to identify the causes of failure and develop strategies to prevent it from happening in the future.

What Are the Key Differences of Stress and Strain?

The key differences between stress and strain and listed in Table 1 below:

Table 1: Differences Between Stress and Strain
PropertyStressStrain
Property
Formula
Stress
σ=F/A
Strain
ε=L-L0/L0
Property
Units of Measurement
Stress
Pa (N/m2) or psi (lbf/in2)
Strain
Dimensionless or %
Property
Cause
Stress
External force
Strain
Deformation caused by stress
Property
Effect
Stress
Causes a material to deform or change shape, as well as affect its strength, stiffness, and other mechanical properties. If the stress is too high, it can lead to permanent deformation or even fracture of the material. Cause materials to experience fatigue, corrosion, and other forms of degradation over time.
Strain
Elastic strain is recoverable, the material will return to its original shape once the load is removed. However, if the strain exceeds the elastic limit, plastic deformation can occur, causing permanent changes in the material's shape. In extreme cases, the material can fracture or break under excessive strain. Cause changes in other material properties, such as electrical conductivity, thermal conductivity, and magnetic susceptibility.
Property
Physical behavior
Stress
Stress can cause a material to change shape, compress, stretch, or twist.
Strain
The change in the shape or size of a material due to the applied stress. Strain can be either elastic or plastic.

What Are Examples of Stress and Strain of Different Materials?

Different materials exhibit different behavior when subjected to stress and strain. Here are some examples of stress and strain of different materials:

  1. Metals: Ductile metals like stainless steel and many other alloys tend to yield and then deform under stress, while brittle metals such as high-carbon steels are more prone to fracture with minimal plastic deformation. Low-carbon steel, on the other hand, can bend under stress until it reaches a yield point where it becomes strain hardened. This makes it less ductile and more brittle, which can increase the likelihood of failure under certain conditions.
  2. Polymers: The stress-strain behavior of polymers is diverse and can be observed in Figure 1 below:
Slide 1 of 1
polymer stress-strain behavior
polymer stress-strain behavior
polymer stress-strain behavior

The Stress-Strain Behavior of Polymers.

Image Credit: https://www.e-education.psu.edu/

The red curve represents a brittle polymer, which fractures after only elastic deformation. On the other hand, the blue curve depicts a plastic polymer, with a yield point and a peak stress value. When pulled further, fracture occurs, and the stress value at that point is known as the tensile strength. Elastomers, shown in green, are a unique class of polymers with rubber-like elasticity that can return to their original shape unless extended to the point of fracture.

While stress-strain curves for some polymers may resemble those for metals, polymers have distinct mechanical properties compared to metals or ceramics. For instance, a highly elastic polymer can stretch up to 10 times its original length before breaking, while a metal may only elastically stretch up to 10% of its original length and can stretch plastically to twice its length before fracturing. Moreover, the largest elastic modulus values for polymers are considerably lower than those for ceramics and metals, as shown in Figure 2 below:

Slide 1 of 1
elastic moduli for different materials
elastic moduli for different materials
elastic moduli for different materials

Room-Temperature Elastic Moduli for Different Materials.

Image Credit: https://www.e-education.psu.edu/

Figure 3 below demonstrates that while the tensile strengths of some polymers can be comparable to those of certain ceramics, they still fall far below those of even the softest of metals:

Slide 1 of 1
different material tensile strengths
different material tensile strengths
different material tensile strengths

Tensile Strengths for Different Materials.

Image Credit: https://www.e-education.psu.edu/

How Does Stress and Strain Relate to Each Other?

The simplest way that stress and strain are related to each other is that one causes the other: stress causes strain. The parameter that describes the relationship is Young's modulus. Another way that stress and strain relate is through the material's elastic modulus, which is a measure of the material's stiffness. The elastic modulus relates the stress applied to a material to a resulting strain. The relationship between stress and strain is described by Hooke's law, which states that the stress applied to a material is directly proportional to the strain that results, as long as the material is behaving elastically. This relationship is only valid up until the elastic limit of a material. Mathematically, this can be expressed as:

Slide 1 of 1
stress-strain relationship
stress-strain relationship
stress-strain relationship

Stress-strain relationship.

Where:

  1. σ is stress
  2. E is the elastic modulus
  3. ε is strain 

It's important to note that Hooke's law only applies to materials that are behaving elastically. They return to their original shape and size when the stress is removed. If the material is stressed beyond its elastic limit, it will undergo plastic deformation, and Hooke's law no longer applies.

What Comes First, Stress or Strain?

Stress comes first in the sense that it is the cause, and strain is the effect. When a force is applied to a material, it stretches the bonds between the material's atoms. When the amount of force stretches the bonds too far, some of them realign with other atoms, resulting in deformation of the material, or strain. Therefore, stress is the initial force applied to the material, while a strain is the resulting deformation of the material due to the stress.

To fully understand the behavior of a material under load, both stress and strain must be considered together, as they are interdependent. The relationship between stress and strain is described by the material's elastic modulus, which relates the stress applied to a material to a resulting strain.

Is Stress Cause of Strain?

Yes, stress is the cause of strain. When a force is applied to a material, it creates an internal resistance, which is stress. The stress causes the material to deform, which is the strain. Therefore, stress is the initial force applied to the material, while a strain is the resulting deformation of the material due to the stress.

Can Stress Cause a Material To Deform or Change Shape?

Yes, stress can cause a material to deform, either temporarily (elastic deformation) or permanently (plastic deformation). When an external force is applied to a material, the material will deform in response to that force. The amount of deformation depends on the magnitude and direction of the stress, as well as the material's properties, such as its stiffness and strength.

Is Strain a Measure of the Deformation That a Material Undergoes in Response to Stress?

Yes, strain is a measure of the deformation that a material undergoes in response to stress. When a material is subjected to stress, it experiences a change in shape or size. Strain is a measure of the extent of this deformation and is defined as the ratio of the change in length or shape of a material to its original length or shape. Therefore, strain is a measure of the amount of deformation that a material undergoes due to the applied stress.

What Is a Stress-Strain Curve?

A stress-strain curve is a graphical representation of the relationship between stress and strain in a material. It is obtained by subjecting a sample of a material to gradually increasing levels of stress and measuring the corresponding strain that occurs in the material. Figure 4 below is an example of a stress-strain curve:

Slide 1 of 1
stress-strain diagram
stress-strain diagram
stress-strain diagram

Example of a Stress-Strain Diagram.

Image Credit: https://www.linearmotiontips.com/

Stress-strain diagrams is commonly used to analyze the behavior of a material throughout its loading until failure. Each material exhibits a unique stress-strain pattern that design engineers can use to extract important mechanical properties such as strength, toughness, elasticity, yield point, strain energy, resilience, and ductility. This information is crucial for designing applications and performing operations like extrusion, rolling, and bending, as it allows for the determination of the forces required to induce plastic deformation.

The stress-strain curve typically has two parts: the elastic region and the plastic region. In the elastic region, the material deforms in response to the applied stress, but the deformation is not permanent. The material returns to its original shape and size when the stress is removed. The relationship between stress and strain in this region is linear, and the slope of the line is called Young's modulus or the elastic modulus of the material.

In the plastic region, the materials’ deformation  in response to the applied stress is permanent, meaning that the material does not recover when the stress is removed. The relationship between stress and strain in this region is nonlinear. It depends on the properties of the material, such as its yield strength, ultimate strength, and ductility.

Summary

This article presented stress vs. strain, explained what each is, and discussed their key differences. To learn more about stress vs. strain, contact a Xometry representative.

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Xomety X
Team Xometry
This article was written by various Xometry contributors. Xometry is a leading resource on manufacturing with CNC machining, sheet metal fabrication, 3D printing, injection molding, urethane casting, and more.