Alexei Volkov
When an external force is applied to a material, it causes deformation, which is measured as strain. The deformation behaviour of the material under stress depends on factors such as the type of material, its composition, and the magnitude, direction, and nature of the applied stresses. Stress and strain can be normal, shear, or a mixture, and can also be uniaxial, biaxial, or multiaxial. The stress-strain curve is a graphical representation of the relationship between stress and strain in a material. It is obtained by subjecting a sample of a material to gradually increasing levels of stress and measuring the corresponding strain that occurs. This curve is used to determine the forces required to induce plastic deformation. Plastic deformation occurs when a material is subjected to stress beyond its elastic limit, causing permanent deformation. The amount of plastic deformation that a material can undergo before it breaks is known as its ductility. Ductile materials, such as structural steel and many other metals, are characterised by their ability to yield at normal temperatures.
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What You'll Learn
Stress-strain curve
A stress-strain curve is a graphical representation of the relationship between stress and strain for a particular material. It is obtained by gradually applying load to a test sample and measuring the resulting deformation. The curve reveals important properties of the material, such as Young's modulus, yield strength, and ultimate tensile strength.
For ductile materials, including structural steel and many other metals, the stress-strain curve typically consists of several stages. The first stage is the linear elastic region, where the material undergoes elastic deformation and obeys Hooke's Law, with stress proportional to strain. This region ends at the yield point, where plastic deformation begins.
The second stage is the strain hardening region, where the stress continues to increase beyond the yield point. This region reaches a maximum at the ultimate strength point, which is the maximum stress that the material can sustain without fracture. Beyond this point, the material enters the fracture region, where the stress decreases while the work strengthening still progresses, leading to a quick development of necking and eventual fracture.
For some materials, such as steel, there may be a nearly flat region at the beginning of the curve, known as the lower yield point (LYP). This is due to the formation and propagation of Lüders bands, which are heterogeneous plastic deformations that spread along the sample. As the strain accumulates, work strengthening reinforces, and the stress continues to increase until the ultimate tensile strength is reached.
The stress-strain curve is an essential tool in engineering and materials science, providing valuable insights into the mechanical properties and behaviour of materials under different types of deformation, such as compression, stretching, torsion, and rotation. By understanding the stress-strain curve, engineers can design and select appropriate materials for various applications, ensuring optimal performance and safety.
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Plastic deformation
From a mechanical point of view, deformation can be classified into two types: elastic deformation and plastic deformation. When the external stress does not exceed the yield strength of the material, the material undergoes elastic deformation, which is non-permanent. This means that when the applied stress is removed, the material reverts to its original size and shape. In the elastic region, stress and strain increase proportionally to each other, obeying Hooke's Law.
In a polycrystal, individual grains must deform in a cooperative manner, each undergoing a complex shape change consistent with its neighbours. As plastic deformation progresses, cracks form and propagate until the material eventually fractures completely.
Steel is a ductile material that exhibits plastic deformation. It is important to consider the stress-strain curve when working with steel to understand its mechanical properties and behaviour under tensile and compressive forces.
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Elastic deformation
In engineering, deformation is the change in size or shape of an object. Deformation can be elastic or plastic. Elastic deformation is temporary and recoverable, meaning the object returns to its original shape after the force is removed. It is a self-reversing, low-stress change in shape that involves the stretching of bonds, but the atoms do not slip past each other. The relationship between stress and strain is generally linear and reversible up until the yield point, after which some degree of permanent distortion remains and is termed plastic deformation.
The stress-strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation. These curves reveal many of the properties of a material, such as Young's modulus, the yield strength, and the ultimate tensile strength. The stress-strain curve can be used to study elastic deformation in engineering strain, which is applied to materials used in mechanical and structural engineering, such as concrete and steel, which are subjected to very small deformations.
The first stage of the stress-strain curve is the linear elastic region, where the stress is proportional to the strain and the material undergoes only elastic deformation. This region obeys Hooke's Law, which states that within the proportional limit, strain is proportionate to stress. The end of this stage is marked by the initiation of plastic deformation, where the stress component is defined as the yield strength.
Ductile materials, including structural steel and many other metals, are characterised by their ability to yield at normal temperatures. They undergo elastic deformation before reaching the point of plastic deformation. This is in contrast to brittle materials such as concrete or carbon fibre, which do not have a well-defined yield point and fail while the deformation is still elastic.
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Tensile force
Tensile stress is the force exerted per unit of cross-sectional area of an object. It is responsible for the elongation of the material along the axis of the applied load. The modulus of elasticity, or elastic modulus, is a measure of the stiffness of the material. It is also known as Young's modulus.
Tensile strain is the extension per unit of the original length of an object. It is the change in the dimension with respect to the original. It is denoted by the symbol epsilon (ε) and is expressed as ε = ΔL/L.
The relationship between stress and strain can be determined through tensile testing. This involves applying a load to a test coupon and measuring the deformation, or applying a displacement and recording the force required to achieve that displacement. These tests reveal the properties of a material, such as Young's modulus, yield strength, and ultimate tensile strength.
Ultimate tensile strength (UTS) is the maximum stress that a material can withstand when a force is applied. When materials are pushed beyond UTS, they experience cracking.
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Stress-strain ratio
In engineering and materials science, a stress-strain curve illustrates the relationship between stress and strain for a given material. This relationship is determined by gradually applying load to a test coupon and measuring the resulting deformation. The stress-strain curve is a fundamental tool for understanding the mechanical properties of materials, such as steel.
For steel, the stress-strain curve can be divided into several stages, each indicating different mechanical properties. The first stage is the linear elastic region, where the material undergoes elastic deformation and returns to its original form when the external force is removed. In this region, the stress is proportional to the strain, and the slope is known as Young's modulus. The end of this stage marks the initiation of plastic deformation, with the stress component defined as the yield strength or upper yield point (UYP).
Beyond the yielding point, the stress-strain curve enters the strain hardening region. Here, the stress continues to increase as the material elongates, and the stress-strain relationship is no longer linear. This region culminates at the ultimate tensile strength (UTS), which represents the maximum stress that the material can withstand without failure.
It is important to note that the stress-strain curve for steel may exhibit a nearly flat region at the beginning, known as the lower yield point (LYP). This is due to the formation and propagation of Lüders bands, which are a result of heterogeneous plastic deformation. As the strain accumulates, work strengthening occurs, leading to an increase in stress until the ultimate tensile strength is reached.
Understanding the stress-strain curve is crucial for engineers and designers when working with materials like steel. It provides insights into the material's behaviour under different types of forces, such as tensile, compressive, and shear forces, and helps in predicting and preventing potential failures or deformations.
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Frequently asked questions
Stress is the force applied to a material that causes deformation, which is measured as strain.
Strain is the change in the dimension of a material with respect to its original form. It is the result of stress and can be calculated using the formula: ε = (L-L0) / L0.
Plastic deformation occurs when a material is subjected to stress beyond its elastic limit, causing irreversible change. This means that the material will not return to its original shape once the force is removed. Plastic deformation can be observed in ductile materials such as steel and other metals, which tend to yield and deform under stress.
