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### Definitions of Stress, Strain and Youngs Modulus

##### Introduction

When a stretching force **(tensile force)** is applied to an object, it will extend. We can draw its force – extension graph to show how it will extend. **Note:** that this graph is true only for the object for which it was experimentally obtained. We cannot use it to deduce the behaviour of another object even if it is made of the same material. This is because extension of an object is not only dependent on the material but also on other factors like dimensions of the object (e.g. length, thickness etc.) It is therefore more useful to find out about the characteristic extension property of the material itself. This can be done if we draw a graph in which deformation is independent of dimensions of the object under test. This kind of graph is called **stress- strain curve.**

##### Stress

**Stress is defined as the force per unit area of a material.**

**i.e. Stress = force / cross sectional area:**

**where,**

**σ** = stress,

* F* = force applied, and

* A*= cross sectional area of the object.

**Units of s :** Nm -2 or Pa.

##### Strain

**Strain is defined as extension per unit length.**

**Strain = extension / original length**

**where,**

** ε **= strain,

* l_{o}* = the original length

**e** = extension = (*l-l _{o}*), and

* l* = stretched length

**Strain has no units because it is a ratio of lengths.**

We can use the above definitions of stress and strain for forces causing tension or compression.

If we apply **tensile force** we have **tensile stress** and **tensile strain**

If we apply **compressive force** we have **compressive stress** and **compressive strain.**

**A useful tip:** In calculations stress expressed in Pa is usually a very large number and strain is usually a very small number. If it comes out much different then, you’ve done it wrong!

##### Young Modulus

**Instead of drawing a force – extension graph, if you plot stress against strain for an object showing (linear) elastic behaviour, you get a straight line.**

This is because stress is proportional to strain. The gradient of the straight-line graph is the Young’s modulus, E

E is constant and does not change for a given material. It in fact represents ‘stiffness’ property of the material. Values of the young modulus of different materials are often listed in the form of a table in reference books so scientists and engineers can look them up.

**Units of the Young modulus E: Nm -2 or Pa.**

**Note:** The value of E in Pa can turn out to be a very large number. Therefore some times the value of E may be given **MNm -2** .

Introduction When a stretching force (tensile force) is applied to an object, it will extend. We can draw its force – extension graph to show how it will extend. Note: that this graph is true only for the object for which it was experimentally obtained. We cannot use it to deduce the behaviour of another object even if it is made of the same material. This is because extension of an object is not only dependent on the material but also on other factors like dimensions of the object (e.g. length, thickness etc.) It is therefore more useful to find out about the characteristic extension property of the material itself. This can be done if we draw a graph in which deformation is independent of dimensions of the object under test. This kind of graph is called stress- strain curve. Stress Stress is defined as the force per unit area of a material. i.e. Stress = force / cross sectional area: where, σ = stress, F = force applied, and A= cross sectional area of the object. Units of s : Nm-2 or Pa. Strain Strain is defined as extension per unit length. Strain = extension / original length where, ε = strain, lo = the original length e = extension = (l-lo), and l = stretched length Strain has no units because it is a ratio of lengths. We can use the above definitions of stress and strain for forces causing tension or compression. If we apply tensile force we have tensile stress and tensile strain If we apply compressive force we have compressive stress and compressive strain. A useful tip: In calculations stress expressed in Pa is usually a very large number and strain is usually a very small number. If it comes out much different then, you've done it wrong! Young Modulus Instead of drawing a force – extension graph, if you plot stress against strain for an object showing (linear) elastic behaviour, you get a straight line. This is because stress is proportional to strain. The gradient of the straight-line graph is the Young's modulus, E E is constant and does not change for a given material. It in fact represents 'stiffness' property of the material. Values of the young modulus of different materials are often listed in the form of a table in reference books so scientists and engineers can look them up. Units of the Young modulus E: Nm-2 or Pa. Note: The value of E in Pa can turn out to be a very large number. Therefore some times the value of E may be given MNm-2.