Ethan Clarke
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. Plastic deformation occurs when a material is subjected to stress beyond its elastic limit, causing permanent deformation. The stress-strain curve is a graphical representation of the relationship between stress and strain in a material. It is obtained by gradually applying load to a test coupon and measuring the deformation. The stress-strain curve is an important reference for metals in material science and manufacturing. It is used to determine the forces required to induce plastic deformation. Steel, for example, exhibits a nearly flat region at the beginning of the stress-strain curve, which is defined as the lower yield point (LYP). Beyond this point, plastic deformation occurs, and the increase in stress with the progress of extension results from work strengthening. Understanding the stress-strain curve is crucial for designing applications and performing operations with steel, as it allows for the determination of the forces necessary to induce plastic deformation.
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What You'll Learn
Stress-strain curve
In engineering and materials science, a 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, from which the stress and strain can be determined. These curves reveal many of the properties of a material, such as Young's modulus, the yield strength, and the ultimate tensile strength.
The first stage of the stress-strain curve is the linear elastic region. The stress is proportional to the strain, obeying Hooke's Law, and the slope is Young's modulus. In this region, the material undergoes only elastic deformation. The end of the stage is the initiation point of plastic deformation, defined as the yield strength or upper yield point.
The second stage is the strain hardening region. This region starts as the stress goes beyond the yielding point, reaching a maximum at the ultimate strength point, which is the maximal stress that can be sustained and is called the ultimate tensile strength.
For some materials, such as steel, there is a nearly flat region at the beginning of the curve. The stress of this flat region is defined as the lower yield point and results from the formation and propagation of Lüders bands. After the sample is again uniformly deformed, the increase of stress with the progress of extension results from work strengthening. As the strain accumulates, work strengthening gets reinforced, until the stress reaches the ultimate tensile strength.
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Tensile and compressive forces
Tensile forces, also known as tension forces, are those that act to elongate or stretch a material. They are typically applied externally and pull the material apart. This type of force causes deformation along the axis of the force and is the opposite of compressive forces, which act to reduce the volume of a material. Tensile forces tend to pull the atoms of a material apart and decrease the cross-sectional area of the material.
Compressive forces, on the other hand, act in the same direction as the axis of the force, causing a compressing or squashing effect. These forces make the material more compact and increase its cross-sectional area. They tend to push the atoms of a material together. For example, concrete slabs deform due to compressive forces when people, animals, or machines walk or roll over them.
Both tensile and compressive forces can occur simultaneously, as seen when a pencil is bent into a U-shape. The upper portion of the U exhibits compressive stress, while the bottom area experiences tensile stress.
The stress-strain curve is an important concept in understanding the relationship between stress and strain for a given material. It reveals properties such as Young's modulus, yield strength, and ultimate tensile strength. The curve can represent the relationship between stress and strain in any form of deformation, including compression, stretching, torsion, and rotation.
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Plastic deformation
The stress-strain curve illustrates the relationship between stress and strain, with the plastic deformation stage succeeding the linear elastic region. In the elastic region, stress and strain increase proportionally, adhering to Hooke's Law, and the material returns to its original form once the external force is removed. However, in the plastic region, the applied stress surpasses the yield point, leading to permanent deformation.
During plastic deformation, atomic bonds stretch and break, and lattice planes shear over each other. This results in macroscopic changes to the size and shape of the material without affecting the atomic arrangement. The fundamental mechanism of plastic deformation in metals is the generation and movement of dislocations, which can occur through glide or climb. In the glide movement, dislocations move along a surface defined by their Burgers vector, while in the climb movement, dislocations move outward from the glide surface.
The stress required for plastic deformation can be reduced by localising deformation through line defect movement instead of sliding the entire lattice plane. Additionally, plastic deformation in metals predominantly occurs through shearing, which involves the sliding of lattice planes over each other, enabling macroscopic changes without disrupting the atomic structure.
It is important to distinguish between ductile and brittle materials when discussing plastic deformation. Ductile materials, such as structural steel, exhibit necking deformation, where the two broken parts cannot be reassembled to form the original shape due to neck formation. On the other hand, brittle materials like concrete or carbon fibre have a less defined yield point, and their ultimate strength and breaking strength are typically the same.
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Elasticity
When an external force is applied to a material, it causes deformation or change in shape or size. This phenomenon is known as the stress-strain relationship. The stress-strain curve reveals many of the properties of a material, such as Young's modulus, yield strength, and ultimate tensile strength.
In the elastic region, the material can withstand the applied stress and return to its original shape once the stress is removed. This is in contrast to plastic deformation, where the material remains deformed even after the force is removed. The end of the elastic region is marked by the initiation point of plastic deformation, known as the yield strength or upper yield point (UYP).
For ductile materials, including structural steel and many other metals, the stress-strain curve typically exhibits a linear elastic region followed by plastic deformation. Low-carbon steel, in particular, shows a very linear stress-strain relationship up to a well-defined yield point. However, some materials like steel may exhibit a nearly flat region at the beginning of the curve, known as the lower yield point (LYP), resulting from the formation of Lüder bands.
The elastic region is crucial in understanding the behaviour of materials under stress. It helps engineers and scientists design structures and choose appropriate materials for specific applications, ensuring that the materials can withstand the expected loads without permanent deformation or failure.
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Yield strength
Mathematically, yield strength can be determined by applying a controlled, gradually increasing force to a sample with a fixed cross-sectional area until it yields or breaks. This is known as a tensile test, and the longitudinal and transverse strain is typically measured using mechanical or optical extensometers. The yield strength is then calculated using the formula that relates stress and strain, with the stress component represented by σY or SY, and the strain component denoted by ε.
The yield strength of a material is influenced by various factors, including its processing and microstructural characteristics. For crystalline materials, yield strength can be fine-tuned by altering dislocation density, impurity levels, and grain size. Introducing defects or impurities increases the yield stress by impeding dislocation motion, requiring a larger applied stress to initiate plastic deformation. This is known as Hall-Petch strengthening and is particularly evident in materials with smaller grain sizes, which offer a higher surface area to volume ratio, facilitating the buildup of dislocations at grain boundaries.
In practical terms, yield strength is a critical parameter for designing structures and mechanical components. It helps engineers and manufacturers determine the maximum allowable load a material can bear without undergoing permanent deformation. This information is invaluable for applications where a degree of flexibility or "give" is required, such as suspension bridges that must withstand the dynamic loads of vehicles and wind. By understanding the yield strength of the materials used, engineers can ensure that structures perform as intended under various applied loads while preventing catastrophic failures due to excessive deformation.
Additionally, the yield strength of materials like steel can be influenced by factors such as forging, forming, and creation methods. For instance, hot-rolled A36 steel typically exhibits a yield strength of around 220 MPa, while oil-quenched or tempered steels can achieve yield strengths of up to 1,570 MPa. Understanding these variations is essential for selecting the appropriate steel grade for specific applications, ensuring optimal performance and durability.
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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 the original. It is denoted by the symbol epsilon (ε) and can be calculated using the formula ε = (L-L0) / L0.
Elastic deformation occurs when a material deforms under stress but returns to its original shape when the stress is removed. Plastic deformation occurs when a material is subjected to stress beyond its elastic limit, causing permanent deformation.
A stress-strain curve is a graphical representation of the relationship between stress and strain in a material. It is obtained by gradually applying load to a test coupon and measuring the deformation.
The yield point is where the plastic deformation of a material is first observed. If the material is unclamped from the testing machine beyond this point, it will not return to its original length.
