## What Is Tensile Strength?

Tensile strength often termed ultimate tensile strength, is the maximum amount of load that a material can bear before its failure.

Tensile strength is the maximum value on the engineering stress-strain curve. If this stress is applied and maintained, eventually, the fracture will occur because the structure is in tension.

## Mechanism of Necking:

Consider a sample designed for a tensile test, as shown in Fig. 1(a, b). a) Dimensions of a rounded cross-section sample with two shoulders and gauge length marked inside. b) The final sample is made of Aluminum.

By applying the stress to the sample gradually, deformation will occur in the piece, which is uniform throughout the narrow region of the designed tensile specimen. When the maximum load is applied, an increase in length and decrease in cross-section at some point, i.e., necking, begins, and this is the point where after deformation is restricted, as shown in Fig 2. The fracture eventually occurs at the neck of the specimen.

Tensile strength varies from material to material, e.g., Aluminum has 50 MPa, and high-strength steel has 3000 MPa.

## Graph of Tensile Strength:

A stress-strain curve represents tensile strength.

## Mathematical relation:

The tensile strength, also known as ultimate tensile strength, is the maximum load at the failure point divided by the original cross-sectional area of the specimen. At the neck, as the cross-sectional area decreases, less force is needed to cause deformation, and engineering stress, determined by the original A_{0} area, falls.

Ultimate tensile strength (UTS) = **σ _{max} = P_{max}/ A_{0}**

Where P_{max} = maximum load, A_{0} = original cross-sectional area.

## Tensile Testing:

### Factors affecting the tensile strength of material:

There are three main factors which affect the tensile strength of the material;

#### Temperature:

Temperature is a significant factor affecting tensile strength in such a way that when temperature increases, the material’s tensile strength increases to a limit, and after that, it decreases. The decrease in tensile strength at high temperatures is due to the fact that the material become soft. Due to softness, bond strength is reduced and unable to bear larger stresses. Higher temperatures form larger grains, and dislocation density decreases; ultimately, the tensile strength decreases.

#### Defects in the Material:

The presence of defects in the material affects its strength. Vacancies in the material have less effect on tensile strength. At the same time, the interstitials and Frenkel pairs (defect in the crystal lattice, atom occupies a vacant site rather than its own) decrease the tensile strength drastically.

#### Composition of Material:

The composition of a material affects its tensile property. For example, iron has a lower tensile strength of 540MPa than its alloy (stainless steel has 621MPa). The strength of alloying elements affects the tensile strength of the material.

## What is Yield strength?

Firstly, when we apply stress on the material, it expresses elastic deformation. Applying stress develops a strain in the material that is ultimately recovered when pressure is removed. Further increasing the amount of stress on the material consequently ‘yields’ to the stress. The stress value required to start the plastic deformation is **the material’s elastic limit** under observation. Beyond the elastic limit, the plastic region is activated. The yield point can be explained as the point at which material undergoes plastic deformation, and this transition is rather abrupt. The value for stress at which the material begins to deform plastically is known as the Yield strength of the material.

## How to Find the Yield strength from stress-strain curve?

The elastic and proportional limit (level of stress above which the stress-strain relationship is non-linear) in most materials are very close, so the value of the elastic limit and proportional limit cannot be determined precisely. The measured values depend upon equipment sensitivity. So in order to determine the yield strength of the material, offset strain value (typically 0.1-0.2% of strain value at –axis) is taken. Offset strain means if the applied stress to deform the material is removed, plastic deformation of 0.2% has occurred in the material.

A line is drawn from the offset strain value parallel to the linear sequence of the stress-strain curve. This drawn line intersects the engineering stress-strain curve at some point termed as offset yield strength or yield strength of the material, as shown in Fig 5.

The point on the engineering stress-strain curve at which maximum load is applied to initiate the plastic deformation is called upper yield point S1 in fig 6.And the point at which minimum stresses are needed to maintain the plastic behaviour is known as lower yield point S2 see fig 6.

### Factors affecting Yield Strength:

#### Temperature:

The yield strength of metals decreases with the temperature rise, which plays a vital role in this mechanical property. The yield strength decreases because the dislocation density decrease and grain size become larger due to the grain growth.

#### Work hardening:

Work hardening increases the plastic deformation and yield strength of a material. Due to strain hardening, grains become elongated, the permanent deformation causes the dislocations to pile up (larger grain boundary area hinders dislocation movement), and the strength of the material is increased.

#### Grain refinement:

Fine grain size increase the yield strength of the material. The initial strain hardening increase as the grain size decrease, and thus the yield strength of the material also increases.

## Comparison of tensile strength and yield strength:

Parameters | Yield strength | Tensile strength |

Definition | Stress at the transition of elastic to plastic region | The significant pressure a material can withstand. |

Mathematical form | Swift equationσ_{s} =K_{H} (0.002)^{n}_{H} | σ_{max }= P_{max}/ A_{0} |

Methods to Measure | Offset yield Strength calculations on tensile test stress-strain curve | Tensile testing is done using hydraulic testing machine calibrated and connected to computer program from where the stress strain curve is obtained and maximum load can be calculated through formula |

Position on the Graph | At initial portion of stress-strain curve on the intersection point found by offset strain | Lies at the later portion of stress-strain curve, the maximum load value |

Extent of Plastic Deformation | Plastic deformation starts from yield point | Material is plastically deformed in tensile region |

Intensity | it requires minimum stress for deformation | It is the maximum stress needed to cause fracture |

For materials | Yield strength can be found for any material | Only for materials which do not have a yield point |

For processes | Needed for small scale activities such as rolling, forging ,milling | For larger scale activities like production of materials or construction |

Extent of Strength | It is lower than the tensile strength | Higher than the yield strength |