Physics - Classical Mechanics - Tensile Stress and Strain

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Introduction

Hey it's a me again @drifter1! Today we continue with Physics and more specifically the branch "Classical Mechanics" to continue with the chapter of Equilibrium and Elasticity. In this article we will get into Tensile Stress and Strain. So, without further ado, let's dive straight into it!

Tensile Stress

Tensile stress is defined as the resistance an object has to forces tending to break it. It is equal to the force per unit area that a material can endure without tearing apart. The maximum stress that the material can stand is called the ultimate tensile stress or breaking stress.

Stress is defined by the following formula:

σ = tensile stress measured in N/m² or pascals (Pa)
F = force in newtons (N)
A = cross-sectional area in m²

Lots of mechanical properties of materials can be determined from a tensile test. When a tensile force acts on a material, the following tensile properties can be calculated:

Elastic modulus
Ultimate tensile stress (UTS)
Modulus of resilience
Fracture stress

Tensile Strain

The ratio of extension to original length is called strain and has no units. Mathematically, we can write it as following:

ε = tensile strain with no units
ΔL = extension measured in metres (m)
L = original length measured in metres (m)

Young's Modulus

Young's modulus of elasticity is defined as "The mechanical property of a material to withstand the compression or elongation with respect to its length". It is denoted as E or Y. Using Hooke's Law of elasticity, Young's modulus is defined as:

σ = tensile stress
ε = tensile strain
F = tensile force
A = cross-sectional area
L₀ = original length
L_n = new length

Poisson's Ratio

Stretching a material in one diretion it tends to get thinner, whilst compressing it tends to make it thicker in the lateral direction. Poisson's ratio is expressed as:

μ = Poisson's ratio
ε_t = transverse strain
ε_l = longitudinal or axial strain

Longitudinal (or axial) strain can be expressed as:

ε_t = longitudinal or axial strain
ΔL = change in length
L = initial length

Contraction (or transverse, lateral or radial) strain can be expressed as:

ε_l = transverse, lateral or radial strain
Δr = change in radius
r = initial radius

RESOURCES:

References

Images

Mathematical equations used in this article, where made using quicklatex.

Previous articles of the series

Rectlinear motion

Velocity and acceleration in a rectlinear motion -> velocity, acceleration and averages of those
Rectlinear motion with constant acceleration and free falling -> const acceleration motion and free fall
Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity
Rectlinear motion exercises -> examples and tasks in rectlinear motion

Plane motion

Position, velocity and acceleration vectors in a plane motion -> position, velocity and acceleration in plane motion
Projectile motion as a plane motion -> missile/bullet motion as a plane motion
Smooth Circular motion -> smooth circular motion theory
Plane motion exercises -> examples and tasks in plane motions

Newton's laws and Applications

Force and Newton's first law -> force, 1st law
Mass and Newton's second law -> mass, 2nd law
Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction
Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications
Contact forces and friction -> contact force, friction
Dynamics of Circular motion -> circular motion dynamics, applications
Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications
Contact force and friction examples -> exercises in force and friction
Circular dynamic and vertical circle motion examples -> exercises in circular dynamics
Advanced Newton law examples -> advanced (more difficult) exercises

Work and Energy

Work and Kinetic Energy -> Definition of Work, Work by a constant and variable Force, Work and Kinetic Energy, Power, Exercises
Conservative and Non-Conservative Forces -> Conservation of Energy, Conservative and Non-Conservative Forces and Fields, Calculations and Exercises
Potential and Mechanical Energy -> Gravitational and Elastic Potential Energy, Conservation of Mechanical Energy, Problem Solving Strategy & Tips
Force and Potential Energy -> Force as Energy Derivative (1-dim) and Gradient (3-dim)
Potential Energy Diagrams -> Energy Diagram Interpretation, Steps and Example
Internal Energy and Work -> Internal Energy, Internal Work

Momentum and Impulse

Conservation of Momentum -> Momentum, Conservation of Momentum
Elastic and Inelastic Collisions -> Collision, Elastic Collision, Inelastic Collision
Collision Examples -> Various Elastic and Inelastic Collision Examples
Impulse -> Impulse with Example
Motion of the Center of Mass -> Center of Mass, Motion analysis with examples
Explaining the Physics behind Rocket Propulsion -> Required Background, Rocket Propulsion Analysis

Angular Motion

Angular motion basics -> Angular position, velocity and acceleration
Rotation with constant angular acceleration -> Constant angular acceleration, Example
Rotational Kinetic Energy & Moment of Inertia -> Rotational kinetic energy, Moment of Inertia
Parallel Axis Theorem -> Parallel axis theorem with example
Torque and Angular Acceleration -> Torque, Relation to Angular Acceleration, Example
Rotation about a moving axis (Rolling motion) -> Fixed and moving axis rotation
Work and Power in Angular Motion -> Work, Work-Energy Theorem, Power
Angular Momentum -> Angular Momentum and its conservation
Explaining the Physics behind Mechanical Gyroscopes -> What they are, History, How they work (Precession, Mathematical Analysis) Difference to Accelerometers
Exercises around Angular motion -> Angular motion examples

Equilibrium and Elasticity

Rigid Body Equilibrium -> Equilibrium Conditions of Rigid Bodies, Center of Gravity, Solving Equilibrium Problems
Force Couple System -> Force Couple System, Example