Understanding the Stress-Strain curve is the main concept in engineering and materials science. It represents the relationship between the stress applied and resulting strain.
In this article we will learn the mechanics of stress-strain curve, understanding the properties of a material to know about material selection, to design the product under safety and to solve complex engineering challenges
What is Stress-Strain Curve?
Stress-Strain Curve is a graphical representation of materials response to any external force. This curve provides understanding of the Mechanical properties i.e. ultimate strength, yield strength, ductility, elasticity etc. and these properties plays a vital role in material selection, Quality assurance and Design engineering.
The resulting graph provides different material phases during stress and each phase provides us information that how a particular material will act under that particular loading/stress. This thing helps a lot an engineer or a manufacturer to choose a good material for his work. The stress-strain curve is obtained by tensile testing in this graph the stress (force per unit area) is plot on y-axis while the strain on x-axis. The material behavior is observed by applying different stresses and through this curve the designing and material selection becomes easy, safe and efficient.
Types of Stress
Stress is defined as internal force per unit area and depending upon the stress applied, stress is primarily divided in to three types which are given below:
Tensile
It is a stress that experienced by a material when a force is applied to pull it apart (elongating the material). It is represent by a Greek letter (σ) and is equal to the force applied per unit area.
σ = F/A
Compressive
This stress is experienced when a force is acting inward i.e. compacting the material. Compressive stress is define force per unit area. Compressive stress mostly occurs in load bearing applications i.e. structural supports, columns and foundations. Compressive stress mostly occurs in load bearing applications i.e. structural supports, columns and foundations.
σ = F/A
Shear Stress
Shear stress is also a type of stress experienced, when a force is applied parallel to material surface causing sliding of one layer of material to another. Shear stress occurs in application where the material resists the force in sliding manner. It is represented by:
τ = F/A
Types of Strain
Strain is defined as the measure of deformation that occurs when a material comes under stress. It is also primarily divided in to two types:
Tensile Strain
Tensile strain occurs when a material comes under tensile stress. Applying the force in the direction causes it to stretch (elongating the material).
Tensile strain (ϵ) = ΔL/L
Where ΔL is the change in length
And L is the original length
Compressive Strain
Compressive strain occurs when a material is subjected to compressive stress, force is acting inward (decreasing the length)
Compressive strain = ΔL/L
Where ΔL is the decrease in length
Stages of the Stress-Strain Curve
Stages in stress-strain curve determine the behavior of material under applied stress. These stages provide a detail view of materials mechanical properties across several stages of deformation. Each stage of the curve determines the specific material behavior from the starting point to failure of a material. The stages of the stress strain curve is as following
Elastic Region
It is the initial stage of the stress-strain curve, when the deformation of the material is proportional to the load applied and eventually returns to its original shape when load is removed. This behavior determines Hooke’s law which states that stress is directly proportional to strain with in elastic region.
Hooke’s Law
It is a basic principle of mechanics which define the behavior of material with in the elastic region. Stress and strain are both proportional i.e. increase in stress tends to increase in strain and vice versa. The relationship between stress and strain is represented as:
σ=E⋅ϵ
Yield Point
Yield point is a point in stress-strain curve that above this point the material undergoes permanent deformation. It is mid-point between elastic region and plastic region, until unless when a material is under elastic region it comes back to original shape after removal of stress but when it crosses yield point it started to permanent deform.
Plastic Region
It is a phase in which material undergoes permanent deformation, It comes after yield point. In this region stress strain relationship is not linear anymore and also the material doesn’t obey Hooke’s law in plastic region.
Ultimate Tensile Strength (UTS)
Ultimate Tensile Strength is a critical property in stress-strain curve which shows the maximum amount of strength a material can bear before failure. It is essential property for engineers and material manufacturer to know about it during designing components subject to tensile load. UTS is given by
UTS= Fmax / Ao
Necking and Fracture
It is a final stage in stress-strain curve graph, it occurring after ultimate tensile strength has reached. In this stage the material started to undergo localized deformation and at last leading to failure. Necking and Fracture is also a crucial phase which determines engineers material limit, predict failure mode and to make necessary safety factors in design.
Interpretation of the Curve
The interpretation of the stress-strain curve is very crucial; it gives a detail view of the materials mechanical properties and behavior of the material under load. By examining each phase of stress-strain curve, material scientists and engineers gain understanding in to materials property strength, ductility, material failure etc.
Young’s Modulus
Young’s Modulus is a significant material property that describes material stiffness or resistance to elastic deformation under loading condition. It is also known as modulus of elasticity. Young’s Modulus is a critical limiting factor in materials science and engineering, used to design components and structure, predict deflection and stability and optimize material selection.
Young’s Modulus is given by:
E= σ/ϵ
Ductile vs. Brittle Behavior
Ductility and brittle behavior are both materials properties, It shows how material responds to stress and strain.
Ductile materials are the one that goes under plastic deformation before failure. These materials can sustain considerable strain without breaking. Ductile materials have long plastic region, Necking before failure and have high toughness.
Brittle materials are those that undergo failure with little stress without going in to plastic region. They fail suddenly after reaching their elastic limit. Brittle material have short or no plastic region, abrupt fracture and have low toughness. Glass, ceramics and some cast irons are example of brittle material.
Resilience and Toughness
Resilience and toughness are both significant material properties that describe measures of energy absorption. They both represent different material property and assessing at different point on the stress-strain curve.
Resilience is the property of a material to absorb energy under loading and to release that energy upon unloading. Mainly it is a material capacity to absorb and release energy with in the elastic region. Rubber is highly resilient material.
While the toughness is the total amount of energy store in a material before fracture, it includes both elastic and plastic region. Tough materials can resist high loads and absorb significant energy without fatal failure. Steel is a high tough material.
Benefits of Understanding the Stress-Strain Curve
Understanding the stress-strain curve is very essential; it provides understanding of material performance, guide in designing, safety and reliability, material selection etc. The detail of understanding of stress strain curve is discussed below
Material Selection
It is the most critical part in designing and engineering to choose best material as economical vise, safety vise, and work vise. In these situations stress-strain curve provides a complete property of a material, so anybody can choose the best material for his work.
Safety and Reliability
Safety and Reliability is considered as the most important thing in any industry or anywhere, and there’s no compromise can be bearable on both things. And it’s only possible when you have the understanding of stress-strain curve, which helps you to know how much loading is safe for particular material.
Optimization in Manufacturing
To achieve higher efficiency, enhance product quality and reduce cost and improving manufacturing process is the main goal of all industry .This is only possible when you have the knowledge of all the materials properties and this can only be done by understanding of stress-strain curve.
Applications of the Stress-Strain Curve
By examining stress-strain curve, material scientist and engineer get to know all the properties of material. This thing helps them in a variety of places because of its importance it has a variety of applications. Some of them are discussed below:
Structural Engineering
Stress-strain curve plays a crucial role in structural engineering. It helps in material selection for load bearing components, establishing safety margins and load limit, predicting deformation and deflection of structural members, evaluating ductility and failure modes, assessing fatigue and durability in cyclic loading, designing impact-resistant structure, quality assurance and material testing etc.
Biomechanics
In bio mechanics this tool helps in how biological tissues and biomaterial responds to forces, stresses and strains helps in implants, medical instruments and prosthetics. It also helps in understanding soft tissue mechanics, Designing biocompatible implants, modeling bone and cartilage behavior etc.
Aerospace and Automotive Engineering
The need of this industry demands materials which are light weight, durable and able to resist extreme conditions and environmental stresses. Stress-strain curve is essential in Aerospace and automotive engineering because of Material selection for light weight design, Crash worthiness and impact resistance, Fatigue and durability analysis, structural integrity and safety margin etc.
Manufacturing and Quality Control
It is a vital tool in manufacturing and quality control providing all the material property and components behavior during processing, manufacturing, shaping and performance testing. While the main applications in manufacturing and quality control is Material selection and specification, process optimization in metal forming, quality control and compliance testing, determining formability and workability etc.
Conclusion
Understanding the stress strain curve is crucial in engineering, material science, industries and in material testing areas. Stress-strain curve provide information regarding properties of material such as yield strength, plastic region, ultimate strength, ductility, elasticity, toughness etc. To understand stress-strain curve helps in optimize material performance, achieve cost effective and sustainable solution in complex engineering problems and also to ensure product safety.
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FAQ’s
1. How is the Stress-strain Curve Measured During a Tensile Test?
It is the basic experiment to determine mechanical properties of a material such as strength, ductility, elasticity, yield strength and ultimate tensile strength. The step by step explanation of how stress-strain curve is measured mentioned below
- Prepare the material to test
- Fit the material in the Testing Machine
- Apply Load(stress)
- Record the strain
- Calculate the Values
- Plot the graph
- now at last Analyze Properties from the Curve
2. How does the Stress-strain Curve Differ Between Ductile and Brittle Materials?
The ductile and brittle material have different stress-strain curve. This shows that they have different material behavior and properties.
Ductile materials are the one which have plastic region with sustainable elongation and have the property of energy absorption before failure e.g. steel .while the brittle material are the one which have no plastic region and suddenly fracture after a short elongation e.g. glass. Because of these properties ductile material are use in areas where absorption of energy is required and brittle material is used where stiffness and complete strength is needed.
3. How do Stress-strain Curves Help in Predicting Material Failure During Product Design and Testing?
Stress-strain curve acts vital role in predicting material failure during product design and testing, as the graph shows all the proprieties of a material including its strengths, plastic limit, elastic limit, ductility and failure. So if anybody has the knowledge of stress-strain graph then they can easily predict the material failure during product design or testing.