Historical development of Internal forces, stress, strain and strength

# Introduction

Much of what we know about the strength (the strength of a material is its ability to withstand an applied load without failure or plastic deformation) of an engineering material is gained from a laboratory test which is called tension test: in this test, a piece of any material is taken and stretched with the help of a machine and it is continued to be stretched until the material starts breaking. And after that, a curve is made between stress-strain. first of all what this term means. I’m sure if you reading this you already familiar with some of these basic terms if not here is a clue.

Stress: it is the ratio of applied force F to a cross-section area – defined as “force per unit area” means it is the amount of internal force per unit area of materials

Strain: it is the response of a system to applied stress. All I mean is this when you put force on something there will be some effect on the material because of applied force it will deform from its original shape

The stairs-strain curve is made. it this tells us a lot about materials mechanical properties and about its stability for a particular structural task. Think of the stress-strain curve as the fingerprint of engineering material. Let’s understand the development of this stress-strain curve in order to understand this concept better.

**Historical development.**

Leonardo da Vinci whom most of you remember as great painter. Yes, of course, he was a great painter. But he was also into science and he made a simple tension test. As you can see in the below image. There is not much difference between the working of this machine and advance tension machine.

How his machine is working I’m sure you get the idea by seeing that there is bucket below and another bucket with a hole in it the upper bucket is filled with sand the sand from top bucket falls on bucket below the weight of sand is an external force which causes failure if string from which lower bucket is hanged. His machine was good and working fine problem is what is concluded from this experiment. For example, he said the strength of iron wire depends on its length. Which is wrong toady we know strength is independent of length it has nothing to do with length.

Later his idea was disproven by none other than Galileo Galilei. Galileo published the worlds first detailed study of the mechanics of materials in 1638:Two New Sciences. In his experiment, he concluded that the strength of a structural element is independent of its length, disproving Leonardo’s idea. But more importantly, he showed that the strength of a material depends on its cross-section area. What is cross_section area? Well, it is the 2-dimensional area formed by cutting through an object perpendicular to its longest axis. For example, if we take a cylinder and try to find it cross-section area it would be π r2. It is the area which is perpendicular to the longest axes of the cylinder.

Based on this we can say that it doesn’t matter how long your material is its strength would be only dependent on its cross-section area. Means if you have a material of 2 m^2 and another of the same material but different cross-section area like 4 m^2. The strength would as twice strong for 4 m^2.

Later around 1650, English scientist Robert Hook tools Leonardo’s and Galileo’s experiment to the next step further. He was not much interested in the investigation of the breaking point of the material rather he investigated how long the wire (material) elongates under the full range

Of load. From zero to its breaking point. And when he plotted a graph between load elongation (deformation) on graph he observed it forms nearly a perfectly straight line. Means it shows a linear relationship. Increasing one will increase others. And today this relation between load and deformation what we call Hooke’s law. This law was fine but still, it was missing something see actually he only considered external forces acting on a material. To complete our understanding of materials we need to what happens inside the material.

In 1822, French Mathematician Augustin Cauchy made the concept of stress as the internal force divided by the cross-section area. Which is expressed in the unit of force per unit area. Which is similar to the pressure unit which is also force per unit area. But as we can see in the case of stress we considering force which develops inside the material because of external load. Stress is independent of geometry and material type: ie when a steel bar of a cross-section 10 m^2 is loaded with 10 kg of weight. The stress in the bar would be 1 kg per meter square. Cauchy also defined strain as the intensity of deformation, calculated as the amount of deformation divided by the original length of the member. Example if a member is original of 10cm and after applying load it deforms 1cm then the strain would be 1/10. In decimal, it would be 0.1. As you may have noticed strain have no units one can think it as a percentage increase in length.

Today the result of simple tension test is recorded as a stress-strain curve. this curve tells us almost everything we need to know about materials properties. This gives us that fingerprint without which it would not possible to construct this megastructure around you. Thank you