**Definition of Modulus of elasticity:** The axial stress ratio to the axial strain of the material in the elastic deformation stage is called the Modulus of elasticity (Also called Young's Modulus).

The Modulus of elasticity can be regarded as an index to measure the difficulty of elastic deformation of the material. The larger the value, the greater the stress causes the material to undergo a certain elastic deformation. The greater the material's stiffness, the elasticity occurs under particular pressure. The smaller the deformation.

### The role of Modulus of elasticity

Modulus of elasticity is an important performance parameter of engineering materials. From a macro perspective, the Modulus of elasticity measures an object's ability to resist elastic deformation. It manifests the bonding strength between atoms, ions or molecules from a microscopic point of view.

All factors that affect the bonding strength can affect the material's elastic Modulus. Such as bonding method, crystal structure, chemical composition, microstructure, temperature, etc. Due to different alloy compositions, additional heat treatment conditions, other cold plastic deformations, etc., Young's modulus value of metal materials may fluctuate by 5% or more.

But in general, the Modulus of elasticity of metal materials is an index of mechanical properties that is not sensitive to the organization. Alloying, heat treatment (fibrous structure), cold plastic deformation, etc., have little influence on elasticity. External factors such as temperature and loading rate have little effect on it. Therefore, the Modulus of elasticity is a constant in general engineering applications.

### Impact on the production of ultrasonic equipment

Ultrasonic transducers and ultrasonic equipment too large or too small will affect the equipment's efficiency and service life. Modulus of elasticity is a mechanical property index that is not sensitive to tissue, but the parameters of different batches of products from other manufacturers will still be different. Therefore, in the manufacturing process of ultrasonic equipment, it is necessary to detect the Modulus of elasticity of the metal materials used.

### The relationship between Modulus of elasticity and stress

**E** is the modulus of elasticity

**σ** is the stress

**ε** is the strain

### Calculation of elastic Modulus of isotropic material

Anisotropic material has only one Modulus of elasticity. An orthotropic material like titanium has three principal moduli of elasticity. The Modulus of elasticity may also depend on the raw stock's size, decreasing with temperature.

For an isotropic material, if the thin-wire wave speed is known, then the modulus of elasticity can be calculated from -

\begin{align} \label{eq:12301a}

E &= \rho \, {c_{tw}}^2

\end{align}

E = modulus of elasticity (Young's modulus)

ρ = density

c_{tw} = thin-wire wave speed

**Here are some values of E for the most commonly used materials.**

- Mild steel- E= 200 GPa
- Cast iron E= 100 GPa
- Aluminium E= 70 GPa
- Nickel E=210 GPa
- Iron E=91 GPa
- Titanium E=108 GPa

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