# Ductile Material: Explain Ductile Material & its Properties [Gate Notes]

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Ductile material is defined as when any material is applied under pull or tensile load, it has a tendency to be drawn in the direction of pull as in the wire or thin cylindrical shape form. This property of any material is known as ductility or this kind of material is known as ductile material.

Generally, ductile material gets to this stage after the edge of the elastic limit. After the elastic limit, the material is stretched with a small stress application, this kind of stage is under the plastic zone. Hence we can say that ductile material is formed in a plastic stressed zone.

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## What is Ductile Material?

In materials science, ductile material is the material that can undergo large plastic deformations before failure, and it is one of the very important characteristics that engineers consider during design. This ability of a ductile material is known as ductility.

Ductility can be measured using a tensile test and expressed as a percentage of elongation or area reduction. The ability of a ductile material to withstand high stresses, such as those caused by significant pressure fluctuations, earthquakes, and hurricanes, without experiencing a catastrophic failure or collapse is largely dependent on its ductility.

## Theories Used For Designing Ductile Material

The theories used for designing the ductile material are maximum shear stress theory, maximum strain energy theory, and maximum shear strain energy theory. These theories are based on maximum principal stresses, minor principal stresses, yield stress, and factor of safety. These theories are as below-

### Maximum Shear Stress Theory

Maximum shear stress theory is also nominated as “Tresca, Guest, Coulomb theory. According to this theory, maximum shear stress should be less than or equal to maximum shear stress under uniaxial loading. This uniaxial loading is in the same nature as either tensile or compressive.

Maximum of [(Maximum principal stress – Minor principal stress)/2, Maximum principal stress/2, Minor principal stress/2] ≤ Yield stress/2(F.O.S)

### Maximum Strain Energy Theory

Maximum strain energy theory is also nominated as “Beltrami-Haigh Theory. According to this, total strain energy per unit volume absorbed at a point should be less than or equal to total strain energy per unit volume under uniaxial loading when the material is subjected to stress up to the elastic limit. This is termed as-

σ12+ σ2232– 2μ(σ1σ22σ3+ σ3σ1) ≤(Yield stress/F.O.S)2

### Maximum Shear Strain Energy Theory

Maximum shear strain energy theory is also nominated as “Vonmises and Huber Hencky. According to this theory, maximum shear strain should be less than or equal to maximum strain energy under uniaxial loading. This theory is also most appropriate in the case of pure shear. This is termed as-

1/2{(σ12)2 + (σ23)2 + (σ31)2 } ≤(Yield stress/F.O.S)2

## Stress-Strain Curve For Ductile Material

The stress-strain curve for ductile material is represented below. In this curve, from B point to E point is denoted as a plastic region. In this region, stress does not increase too much compared to strain increment. It means a little amount of stress increment leads to high strain deformation. The material in this zone gets converted into thin wire.

## Ductile Material Examples

In our day-to-day life, many soft materials are to be used, such as rubber, aluminum, plastic, etc. But in the construction of heavy machinery, we generally consider copper, steel, iron, magnesium alloys, and all those materials with ductile properties.

This kind of material has great resistance against ductility, but after reaching a sufficient limit of stress, pressure or temperature, it behaves like soft metal. This phenomenon of ductility helps to stop sudden failure and promotes gradual failure. Here we have provided some important ductile material examples.

• Mild steel ductile limit = Upto 400 MPa
• Copper ductile limit = Upto 193 MPa
• Glass ductile limit = Upto 7 MPa
• Wood ductile limit = Upto 70- 140 MPa
• Aluminum ductile limit = Upto 40- 700 MPa etc.
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