# What Is the Relationship Between Elastic Modulus, Stiffness, Strength and Hardness?

There are many parameters to measure materials, among which the elastic modulus, stiffness, strength and hardness are the parameters we see most, but many friends do not really understand these parameters.

Now let’s review these concepts again to re understand the relationship between them.

Table of Contents

## Modulus of elasticity

### What is the elastic modulus

Elastic model is an important performance parameter of materials.

Elastic modulus represents the elasticity of materials.

The greater the elastic modulus, the greater the elasticity of materials, and the stronger their ability to resist deformation.

In the elastic range, the stress divided by the stress becomes a positive proportional relationship, which satisfies Hooke’s law, and its ratio is the elastic modulus.

Elastic modulus is the inherent property of materials and the reflection of bonding strength between atoms, molecules or ions.

The chemical composition, crystal structure and temperature of the material affect the elastic modulus.

Generally speaking, the higher the temperature of the material, the lower the elastic modulus. For example, when forging parts, heat the parts first to reduce the elastic modulus and yield strength of the material, rather than choose to forge directly at room temperature.

### Does heat treatment affect the elastic modulus?

The heat treatment of metal materials includes overall heat treatment (annealing, quenching, tempering, normalizing) and surface heat treatment (carburizing, nitriding, high, medium and low frequency quenching, anodizing of aluminum alloy, etc.).

Heat treatment can improve the yield strength and tensile strength of materials.

No matter which heat treatment method, it has little effect on the elastic modulus, which changes by about 5%.

In engineering applications, the elastic modulus is usually used as a constant.

## Stiffness

Stiffness is the ability of parts to resist elastic deformation under the action of external forces.

The stiffness of the part is related to the geometry of the part itself (such as the stiffness of rods with different sections) and the material selection of the part itself (for the same structure, the greater the elastic modulus, the greater the stiffness of the structure).

In engineering applications, stiffness is related to the accuracy of parts, such as the spindle of machine tool.

When the machine tool is working, we don’t want the spindle of machine tool to deform after being stressed, which will affect the machining accuracy.

Therefore, when designing the spindle of machine tool, we should consider both the structure and the elastic modulus of material.

## Strength

Strength is used to measure the bearing capacity of the part itself.

For brittle materials, we use tensile or compressive ultimate strength to judge whether parts fail.

For elastic materials, we use yield strength to judge whether the parts are permanently deformed, and tensile strength to judge whether the parts are broken.

## Hardness

Hardness refers to the ability of materials to resist hard objects pressing on the surface.

Measuring hardness is to use indenters to press on the surface of parts, and judge the hardness of materials according to the indentation depth on the surface of parts.

Therefore, hardness represents the ability of a material to resist plastic deformation, and the higher the strength limit of a material is.

The hardness value is determined by the initial plastic deformation resistance and the continuous plastic deformation resistance.

The higher the strength of the material, the higher the plastic deformation resistance, and the higher the hardness value.

## Relationship between elastic modulus and hardness

There is no relationship between elastic modulus and hardness.

Hardness measures the ability of a material to resist plastic deformation, and the elastic modulus is the material constant of the material itself.

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