Understanding Young's Modulus

Summary

This video introduces Young's modulus, one of the key elastic constants used in engineering to describe how materials deform under load. Through the example of a tensile test, the video explains the relationship between stress and strain and how Young's modulus is determined from the elastic region of the stress-strain curve. It highlights how Young's modulus reflects material stiffness, varies between materials, and is influenced by atomic bonds. The video emphasizes the importance of Young's modulus in material selection for engineering applications, such as ensuring minimal elastic deformation in structures like bridges.

Takeaways

• 📏 Young's modulus is one of the three main elastic constants, alongside shear modulus and bulk modulus.
• 🛠️ It measures how a material deforms under loading, specifically during a tensile test where the material is stretched along its length.
• 📊 The tensile test outputs a stress-strain curve, which shows how a material deforms under different levels of stress.
• 🔄 The stress-strain curve has two main regions: the elastic region (where deformation is reversible) and the plastic region (where deformation is permanent).
• ⚖️ In the elastic region, stress and strain are proportional, and the slope of this linear region represents Young's modulus.
• 🏋️‍♂️ Young's modulus, denoted as E, is a measure of a material's stiffness—the higher the modulus, the stiffer the material.
• ⚙️ Different materials have different Young's modulus values: ceramics have the highest, metals are lower, and polymers are the lowest.
• 🔬 On the atomic level, Young's modulus is related to the strength of atomic bonds, which act like springs resisting deformation.
• 🧱 Alloyed metals, like mild steel and high carbon steel, have similar Young's modulus values despite differences in other mechanical properties, due to their atomic structure.
• 🏗️ Young's modulus is essential in engineering design, especially when minimizing elastic deformations in structures like bridges.

Q & A

What is Young's modulus and why is it important?

Young's modulus, also known as the modulus of elasticity, measures the stiffness of a material. It is crucial in engineering design because it helps predict how much a material will deform under a specific load.

How is Young's modulus measured in a tensile test?

Young's modulus is measured from the slope of the stress-strain curve in the elastic region. It represents the ratio of stress to strain, and its units are the same as stress (Pascals in SI units or psi in US customary units).

What is the difference between elastic and plastic deformation?

Elastic deformation occurs when the material returns to its original shape after the load is removed. Plastic deformation is permanent, meaning the material does not return to its original dimensions once the load is removed.

What is the significance of the elastic region in a stress-strain curve?

The elastic region in the stress-strain curve represents the range where the material will return to its original shape after the load is removed. In this region, the relationship between stress and strain is linear, following Hooke's law.

Why do different materials have different values for Young's modulus?

Different materials have different atomic structures and bonding strengths, which affect how much they deform under stress. For example, ceramics have strong atomic bonds, giving them a higher Young's modulus, while polymers have weaker intermolecular bonds and thus a lower modulus.

How does the direction of load affect Young's modulus in anisotropic materials?

In anisotropic materials like wood or composites, Young's modulus depends on the direction of the applied load. This is because these materials have different properties in different directions due to their internal structure.

How does Young's modulus relate to atomic bonding in materials?

Young's modulus is related to the strength of atomic bonds in a material. The elastic strain in a material stretches the inter-atomic bonds, and the stiffness of these bonds determines the material's resistance to deformation.

Why do mild steel and high carbon steel have similar Young's modulus values despite their different mechanical properties?

Although mild steel and high carbon steel have different mechanical properties, their Young's modulus is similar because the addition of a small amount of carbon atoms doesn't significantly affect the overall resistance of the atomic bonds to elastic deformation.

What role does Young's modulus play in engineering applications, such as bridge design?

In engineering, Young's modulus is used to select materials that minimize elastic deformation under load. For example, in bridge design, a material with a high Young's modulus is preferred to prevent excessive deflection when heavy loads pass over it.

What are typical Young's modulus values for polymers, metals, and ceramics?

Ceramics generally have the highest Young's modulus values due to their strong atomic bonds, followed by metals with moderately high values. Polymers have much lower Young's modulus values because of their weaker intermolecular bonds.

Outlines

00:00

🔍 Introduction to Young's Modulus

This paragraph introduces Young's modulus, one of the three main elastic constants used to describe how a material deforms under loading. It explains the concept through the tensile test, a common mechanical test that stretches a test piece along its length. The tensile test measures the applied load and the change in length, resulting in a stress-strain curve. The curve is divided into elastic and plastic regions, where elastic deformations are reversible and plastic ones are not. Young's modulus, or modulus of elasticity, is defined as the ratio of stress to strain in the elastic region and is a measure of material stiffness. The higher the Young's modulus, the stiffer the material and the smaller the elastic deformations for a given load. The paragraph also discusses the variation in Young's modulus values among different materials and the atomic-level explanation involving inter-atomic bonds.

05:01

🏗️ Engineering Applications of Young's Modulus

The second paragraph discusses the practical implications of Young's modulus in engineering, emphasizing its importance in material selection to minimize elastic deformations. It uses the example of constructing a bridge, explaining that a material with a low Young's modulus would lead to significant deflection under load, which is undesirable. The paragraph also addresses the atomic-level model to explain why different types of steel, despite having different mechanical properties, have similar Young's modulus values. This is due to the small percentage of carbon atoms added to iron not significantly affecting the resistance to increasing atomic spacing. The paragraph concludes by inviting viewers to share interesting facts about Young's modulus and promising more educational content in future videos.

Keywords

💡Young's Modulus

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in the linear elastic region of the stress-strain curve. In the video, it is described as crucial for understanding how a material deforms under tensile loading, with higher Young's modulus values indicating stiffer materials that resist elastic deformation more effectively.

💡Tensile Test

The tensile test is a mechanical test that stretches a material sample uniaxially to measure its response to stress and strain. The video uses this test to introduce Young's modulus, explaining how the stress-strain curve is generated by measuring the load applied to a material and its deformation. This test helps determine the material's elastic and plastic properties.

💡Stress-Strain Curve

The stress-strain curve is a graphical representation of the relationship between the applied stress on a material and the resulting strain (deformation). The curve is divided into two main regions: the elastic region, where deformation is reversible, and the plastic region, where permanent deformation occurs. The video emphasizes that Young's modulus is the slope of the linear portion in the elastic region of this curve.

💡Elastic Region

The elastic region of the stress-strain curve is where the material deforms linearly and reversibly. When the applied stress is removed, the material returns to its original shape. In the video, this region is highlighted as critical for defining Young's modulus, as it measures how much a material can stretch without permanent deformation.

💡Plastic Region

The plastic region on the stress-strain curve describes where a material undergoes permanent deformation. When stress is applied beyond the elastic limit, the material deforms and does not return to its original shape even after the load is removed. The video discusses this as the point where atomic bonds are rearranged, leading to permanent structural changes.

💡Hooke's Law

Hooke's Law defines the linear relationship between stress and strain in the elastic region, where the material obeys a proportionality constant known as Young's modulus. In the video, Hooke's Law is mentioned to explain how stress and strain are directly proportional in the elastic region for many materials, as long as the material does not exceed its elastic limit.

💡Anisotropic Materials

Anisotropic materials have properties that vary depending on the direction of the applied load. The video explains how materials like wood and carbon fiber have different Young's modulus values based on the direction of the force applied. This concept highlights that material stiffness can change depending on orientation, making it important for engineering designs involving such materials.

💡Inter-atomic Bonds

Inter-atomic bonds are the forces holding atoms together within a material. These bonds behave like tiny springs, and their stiffness determines a material's Young's modulus. The video uses this analogy to explain how elastic deformation is resisted by these bonds, making them key to understanding why different materials have different stiffness and elastic properties.

💡Plastic Deformation

Plastic deformation refers to the permanent change in shape a material undergoes when subjected to stress beyond its elastic limit. Unlike elastic deformation, plastic deformation does not reverse when the load is removed. The video differentiates between elastic and plastic behavior, showing that atomic rearrangements cause plastic deformation, making it a key consideration in material strength.

💡Material Selection

Material selection refers to the process of choosing materials with suitable properties for a specific engineering application. The video discusses how Young's modulus is a key factor in this process, as selecting a material with appropriate stiffness is crucial to minimizing unwanted elastic deformation, such as in the construction of bridges or other structures.

Highlights

Introduction to Young's modulus, one of the three main elastic constants along with shear and bulk modulus, used to describe material deformation under loading.

Explanation of the tensile test, a uniaxial test that stretches a test piece along its length to measure the applied load and change in length.

The primary output from the tensile test is the stress-strain curve, which shows how a material deforms under different stress levels.

The stress-strain curve is split into two regions: the elastic region (linear) and the plastic region (non-linear).

In the elastic region, the material returns to its original dimensions after load removal, while in the plastic region, permanent deformation occurs.

Young's modulus is introduced as the ratio of stress to strain in the elastic region, representing how stiff a material is.

Young's modulus is measured as the slope of the stress-strain curve in the elastic region, with units in Pascals (SI) or psi (US customary units).

The higher the Young's modulus, the stiffer the material and the smaller the elastic deformations for a given applied load.

Young's modulus varies between materials; ceramics have high values, metals have lower values, and polymers have the lowest values.

Young's modulus is influenced by the strength of atomic bonds, where elastic deformation results from increased spacing between atoms.

Elastic deformation is reversible because it involves changes in atomic spacing, unlike plastic deformation, which involves atomic rearrangement.

Polymers have weaker inter-molecular bonds than ceramics and metals, leading to lower Young's modulus values.

Alloyed metals, like mild steel and high carbon steel, have different yield strengths but similar Young's modulus values due to similar atomic bond resistance.

Young's modulus is crucial in engineering design, where minimizing elastic deformations is often a key objective.

In structures like bridges, selecting materials with high Young's modulus ensures small elastic deformations under large loads.

Transcripts

Welcome back to the Efficient Engineer channel everyone!

In this video we're going to talk about Young's modulus,

one of the three main elastic constants

along with shear modulus and bulk modulus, which are used to describe how

a material deforms under loading.

Let's introduce Young's Modulus using the tensile test.

The tensile test is a very common mechanical test which takes a

test piece and stretches it along its length. It is a uniaxial test meaning

that it applies a load in one direction only, as shown here.

During the test, the test machine measures the applied load

and the change in length of the test piece.

The main output from the tensile test is the stress-strain curve, which

describes how much the material we're testing will deform for different levels

of applied stress. Watch how the stress strain curve evolves as we perform a

tensile test on our test piece, which in this case is made of steel.

The test ends when the material fractures.

We can observe that the stress-strain curve is

split into two regions - the elastic region, where the curve is linear,

and the plastic region.

If the applied stress is low and we remain in the elastic region,

the original dimensions of the component will be completely recovered when the

applied load is removed. For larger stresses that take us into the plastic region,

permanent plastic deformation will remain after the applied load is removed.

In the elastic region the stress-strain curve is a straight line

for most materials. This means the strain is proportional to the applied stress.

Hookes law gives us the relationship between stress and strain in this linear elastic region.

The ratio between stress and strain is Young's modulus, also

called the modulus of elasticity, which we denote with the letter E.

It has the same units as stress, so psi in US customary units and Pascals in SI units.

We can also measure Young's modulus as the gradient of the slope in the elastic region.

Young's modulus is essentially a measure

of how stiff a material is. The higher the Young's modulus, the stiffer of

material and so the smaller the elastic deformations will be for a given applied load.

If we perform tensile tests for a few different materials we will notice

that the slope of the stress-strain curve is different for each of them.

Different materials can have vastly different values for Young's modulus.

For anisotropic materials like wood or composites such as carbon fiber the

value of Young's modulus will depend on the direction in which the load is applied.

This graph shows the range of typical Young's modulus values for

polymers, metals and ceramics

In general ceramics have higher values of Young's modulus, metals have slightly

lower values, and polymers have much lower values.

Understanding what is happening at the atomic level can give us a better

understanding of Young's modulus.

On an atomic level a materials Young's modulus is closely related to the

strength of the bonds between its atoms.

We can imagine these inter-atomic bonds

as tiny springs connecting adjacent atoms. Elastic strain is the result of an

increase in spacing between the atoms of the material, and is resisted by the

strength of the inter-atomic bonds, or the stiffness of the little springs in our model.

This is very different to the mechanism behind plastic deformation,

which involves rearrangement of the position of the atoms.

This is why elastic deformations are

reversed when the load is removed

but plastic deformations are not.

I mentioned earlier that Young's modulus is smaller for polymers than it is for

ceramics and metals. This is because it is the weaker inter-molecular bonds in

polymers that determine the material stiffness, rather than the stronger

atomic bonds.

Looking at things on the atomic level can also help explain why differences in

Young's modulus for alloyed metals tend to be small.

Let's take the example of carbon steel.

Mild steel and high carbon steel have quite different mechanical properties.

Their yield strengths for example are very different.

And yet they have very similar Young's modulus values,

which at first glance might seem surprising.

We can explain it using our inter-atomic bonds model. Mild steel has

a carbon content of up to 0.25% and high carbon steels can have a

carbon content of up to 0.95%.

Adding such a small number of additional carbon

atoms to the existing iron atoms isn't enough to significantly affect the

overall resistance to increasing the spacing between atoms, and so the Young's

modulus is very similar for mild steel and for high carbon steel, despite some

of their other mechanical properties being very different.

Young's modulus is a crucially important

material property when it comes to engineering. In engineering design,

a common objective for many different applications is to keep elastic

deformations as small as possible, which means that Young's modulus is a key

parameter that needs to be considered in the material selection process.

Take the example of a bridge.

If we construct a bridge from a material with a low

Young's modulus it will deflect a large amount when something crosses it, which

is probably not the desired response.

Selecting a high stiffness material would ensure that elastic deformations

remain small for large loads.

That concludes this brief introduction to Young's modulus. If you have any

interesting facts about Young's modulus, let me know in the comments.

And stay tuned for more videos!