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Elastic metal. Image Credit: Shutterstock.com/Nevena Marjanovic

What Is Elastic Limit? Definition, Importance, How It Works, and Examples

Xomety X
By Team Xometry
May 10, 2023
 12 min read
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The elastic limit is a fundamental property of solid materials that determines the maximum amount of stress a material can handle before plastic deformation begins. It separates the recoverable (elastic) strain regime from the unrecoverable (plastic) strain region of the stress-strain curve. Stresses beyond the elastic limit cause material to yield and deform permanently.

This article discusses the definition of the elastic limit, its importance, and how it works. Additionally, it explains Hooke's Law and how it relates to the elastic limit of a material. Finally, the article provides a guide on how to determine the elastic limit of a material.

What Does Elastic Limit Mean?

The elastic limit is the maximum amount of stress that can be applied to a material before the onset of plastic deformation. When the stress applied to a material is below the elastic limit, the material will return to its original shape once the stress is removed from the object. Conversely, if a stress  greater than the elastic limit is applied to a material, the material will remain deformed even when the external force is removed. 

What Is the Importance of Elastic Limit?

The elastic limit is an important property of any material because it determines the amount of stress a material can withstand before suffering permanent damage. It tells us where elastic behavior stops and plastic deformation starts. This is significant because it indicates what the elastic deformation capability of a material is. Stresses beyond the elastic limit cause materials to flow or yield. For brittle materials, the stress at the elastic limit is at or close to the fracture strength, because brittle materials exhibit little or no plastic deformation.

How Does an Elastic Limit Work?

To understand how elastic limit works, let’s consider an object with an external force acting on it. When the external force is applied, the bonds holding the object's atoms together are stretched. This stretching creates an internal reaction force as the atoms resist being pulled apart. As long as the external stress remains below the elastic limit of the material, the atomic bonds are only stretched, and not broken. When the externally applied force is removed, the stretching of the atomic bonds is relieved, and the material returns to its original size and shape. In essence, the material will behave like a spring. 

On the other hand, if the applied force is more than the strength of the interatomic bonds can resist, the deformation becomes permanent. The object will no longer be able to regain its original shape after the force has been removed. This is termed plastic deformation. 

The elastic limit refers to the point where the material transitions from the elastic deformation region to the plastic deformation region, as shown in the stress-strain curve of Figure 1 below:

diagram of elastic stress-strain

Example of a Stress-Strain Diagram Showing the Elastic Limit.

Image Credit: https://whatsinsight.org/

This is the point at which permanent deformation or even failure (in brittle materials) initiates.

What Is Hooke's Law?

Hooke's Law states that within the elastic limit of a material, the strain of that material is directly proportional to the applied stress. When elastic materials are stretched, the atoms and molecules inside deform until they're under stress. When that stress is removed, they'll return to their original state.

We can express this relationship mathematically using Hooke's Law, which is written as:

F = kx

Where: 

  1. F is the force
  2. x is the extension in length
  3. k is the constant of proportionality, otherwise known as the spring constant, measured in N/m. 

How Does an Elastic Limit Relate to Hooke's Law?

Hooke's Law describes the linear relationship between the applied force (stress) and the resulting amount of deformation (strain) in a material, at stress levels below the elastic limit.

According to Hooke's Law, for small deformations, the stress and strain are proportional to each other. This linear relationship holds within the elastic limit of the material. As long as the applied stress does not exceed the elastic limit of the material, the material will deform elastically and will return to its original shape once the applied stress is removed.

How To Find the Elastic Limit of a Material?

The elastic limit for a material can be determined following these steps:

  1. Prepare a standard test sample shape that is free of any defects or damage, as these can affect the results.
  2. Apply a known amount of stress to the sample using a mechanical testing machine or similar instrument. The specific method of applying stress can vary depending on the type of material and testing method being used. However, typically the stress is gradually increased until the material begins to exhibit permanent deformation. This point where permanent deformation initiates is known as the elastic limit of the material. 
  3. Measure the resulting strain (deformation) as the stress is increased. This can be done using displacement sensors or strain gauges.
  4. Plot the results with stress on the y-axis and strain on the x-axis. This is called a stress-strain curve and will show how the sample responds to different levels of stress.
  5. Determine the point where the material starts to exhibit permanent deformation. This is the elastic limit of the material and is typically close to, or equal to, the point where the stress-strain curve transitions from linear to non-linear behavior. Be sure to record all the observations and measurements accurately for analysis.

What Is the Formula for Elastic Limit According to Hooke's Law?

Hooke's Law describes the proportional relationship between stress and strains up to the proportional limit, while the elastic limit is the point beyond which the material undergoes permanent deformation. 

The formula for Hooke's Law adapted from force units to stress units is:

σ = Eε

Where: 

  1. σ is the stress applied to the material
  2. E is Young's modulus of the material
  3. ε is the resulting strain in the material. 

The relationship between Hooke’s law and the elastic limit, however, cannot be expressed through an equation. The elastic limit is a value that is tested experimentally and not calculated through an equation. 

Can Hooke's Law Accurately Describe Material Behavior Beyond Its Elastic Limit?

No, Hooke’s Law does not accurately describe material behavior beyond its elastic limit. Hooke's Law assumes that material behaves elastically, meaning that it will return to its original shape once the applied stress is removed. Beyond the elastic limit, the material will undergo permanent deformation, meaning that it will not return to its original shape, and the relationship between stress and strain is no longer linear.

Hooke's Law is only applicable within the proportional limit of a material, where the stress and strain are proportional and the material behaves elastically. Beyond the elastic limit, the material's behavior becomes more complex and may involve plastic deformation, yielding, or fracture, depending on the specific material and the magnitude of the applied stress.

What Is an Example of an Elastic Limit?

An example of an elastic limit is the elastic limit of steel, which is 8 x108 N/m2. 

Does Steel Have a High Elastic Limit?

Yes. Steel has a relatively high elastic limit of about 8 x108 N/m2, depending on the grade. It can withstand a significant amount of stress before undergoing plastic deformation. This property makes steel highly desirable in applications where strength and durability are required, such as in building construction, bridges, and heavy machinery.

Is it Possible to Consider That Titanium Has a High Elastic Limit?

Yes, it is fair to say that Titanium (Ti) has a high elastic limit. The elastic limit of titanium can vary depending on the specific alloy and processing method used. The elastic modulus of Ti alloys ranges from 55 to 114 GPa, which is about half that of steel but is still considered high for a lightweight metal. A higher elastic modulus means that the elastic limit of titanium and its alloys will also be fairly high, even though it is not one of the materials with the highest known elastic limits. 

What Material Has a Low Elastic Limit?

There are several materials with low elastic limits. Materials with low elastic limits are those that are more prone to permanent deformation or plastic deformation when subjected to stress. These materials will deform under relatively low stresses and will not return to their original shape once the stress is removed. Some examples of materials with low elastic limits include:

  1. Polymers Such as Rubber or Plastic: These materials have low elastic limits and can undergo significant deformation under stress.
  2. Glass: Although glass is a hard and brittle material, it has a low elastic limit. It is prone to cracking or shattering under stress.

What Are the Factors That May Affect the Elastic Limit of a Material?

The elastic modulus is an intrinsic property of a material and there are not a lot of factors that can change it. However, factors that can affect the elastic properties of a material include:

  1. Fatigue: Fatigue can be described as a gradual reduction in the load-bearing capacity of a material as a crack propagates through the load-bearing region. The connected material remains at full strength but only contributes to the undamaged area. As the crack spreads, the load-bearing area decreases, resulting in a reduction in the effective stiffness of the region. This can cause the material to deflect more if pulled apart, giving the impression of a reduced modulus. However, the material's elastic modulus does not change. Rather, it is the gross behavior of the load-bearing member that is affected by the presence of the crack. This means that  the apparent elastic limit changes because the internal x-sectional area that stress is applied to is decreasing. But the actual elastic limit does not change. 
  2. Pressure: Pressure affects the elastic constants and related properties. The effect of pressure on the elastic limit is non-linear. 
  3. Change of Length: The change of length i.e , ∆l has an effect on the elastic limit, as strain is the ratio of change of length to initial length of material.
  4. Elongation: The elongation of the material is inversely proportional to Young’s modulus.
  5. Composition: The composition of a material can greatly affect its mechanical properties, including its elasticity, and ultimately its elastic limit. When alloying elements are added to materials, it can cause variations in their elastic properties. The extent to which the elasticity increases or decreases depends on the type of impurity that is introduced.
  6. Temperature: Temperature has an effect on the elasticity of materials. Generally, the elasticity is lower at higher temperatures and vice versa. 
  7. Exposure to Environmental Factors: Exposure to certain chemicals or environments, such as corrosion, can also affect a material's elastic limit.
  8. Surface Defects: The presence of surface defects, such as cracks or scratches, can lower the elastic limit of a material.

What Are the Advantages of Elastic Limit?

The advantages of understanding the elastic limit of materials are listed below:

  1. The elastic limit provides valuable information about the behavior of materials under stress. This information can be used to improve the design and performance of structures and components.
  2. Knowing the elastic limit helps engineers and designers select the best material for a specific application by providing information about the material's ability to withstand stress without undergoing permanent deformation. This can lead to improved performance and reliability of products and structures.

What Are the Disadvantages of Elastic Limit?

The disadvantages of an elastic limit are as follows:

  1. Sets a limit on the amount of stress a material can withstand before it undergoes permanent deformation or failure. This can make the material unsuitable for high-stress applications or environments.
  2. Can limit design flexibility by constraining the choice of materials that can safely withstand expected stresses while also meeting other design criteria, such as weight, cost, and appearance.

What Is the Difference Between an Elastic Limit and Yield Strength?

The elastic limit is the maximum stress a material can endure without sustaining permanent deformation. It is the point on a stress-strain curve beyond which the material cannot return to its original shape when the stress is removed. It is the stress beyond which the material's elasticity is permanently lost, and it begins to exhibit plastic deformation.

Yield strength, on the other hand, is the stress at which a material begins to exhibit plastic deformation. The yield strength is generally taken as the stress where 0.2% plastic strain has occurred, in order to standardize and make it easy to compare materials that do not have well-defined yield points. 

What Is the Difference Between an Elastic Limit and a Proportional Limit?

The elastic limit and the proportional limit are two different concepts related to the behavior of materials under stress. The elastic limit is the maximum stress that a material can be stretched without undergoing permanent deformation after the stress is removed. In other words, if the stress applied to a material does not exceed its elastic limit, the material will return to its original shape after the stress is removed, with no permanent deformation.

The proportional limit, on the other hand, is the maximum stress at which a material exhibits a linear relationship between stress and strain. In other words, up to this point, the material behaves elastically, and the strain is directly proportional to the applied stress. Once the proportional limit is exceeded, the material begins to deform plastically, and the relationship between stress and strain becomes non-linear.

Summary

This article presented elastic limit, explained what it is, and discussed how it works and provided examples of it To learn more about elastic limit, 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.

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