Ethan Clarke
Plastic deformation is a complex process that is challenging to study, especially in metals. It involves the interaction of various factors, including deviatoric stress components, dislocations, and slip planes, which contribute to the overall deformation. The yield stress, typically ranging from 0.05% to 0.1% of the elastic modulus, marks the transition from elastic to plastic deformation, and this process is influenced by factors such as crystal structure, grain size, and composition. The behaviour of materials during plastic deformation is described using models like the Ludwik-Hollomon and Voce equations, which account for stress-strain relationships and the effects of hardening.
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Stress-strain curve
A stress-strain curve illustrates the relationship between stress and strain for a given material. It is a useful tool for understanding the mechanical properties of materials, such as metals and ductile materials like structural steel.
The curve can be divided into several stages, each indicating different behaviour and properties. The first stage is the linear elastic region, where the material obeys Hooke's law and the stress is proportional to the strain. This region ends at the initiation point of plastic deformation, which is defined as the yield strength or upper yield point (UYP).
The second stage is the strain hardening region, which begins when the stress surpasses the yielding point. Here, the stress increases as the material elongates, and this continues until the ultimate tensile strength (UTS) is reached. The UTS is the maximum stress that the material can withstand.
Beyond the UTS, the stress increases further due to strain hardening, leading to a process called necking in ductile materials. This progressive increase in stress indicates that continued plastic deformation requires higher levels of applied stress, a phenomenon known as work hardening or strain hardening. Work hardening arises from the interaction and reduced mobility of dislocations within the material.
The stress-strain curve can be approximated using equations such as the Ramberg-Osgood equation for ductile materials, or the Ludwik-Hollomon and Voce equations for characterising the work hardening of metals. These equations consider various factors, including yield strength, ultimate strength, and elastic modulus, and the work hardening coefficient and exponent.
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Yield stress
The yield strength or yield stress is a property of a material and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, as it represents the upper limit of forces that can be applied without causing permanent deformation. For example, in engineering metals, the yield stress is used to determine the force required to make a polymer flowable.
The yield stress is usually considered to have a single value, but work hardening requires a more complex definition. Work hardening, or strain hardening, refers to the continuation of plastic deformation requiring progressively increasing levels of applied stress. The work hardening rate tends to decrease progressively with increasing strain, and this is due to the competition between the creation of new dislocations and their inhibition of mobility.
The yield stress can be determined through a tensile test, where a sample is loaded until it begins to undergo plastic strain. This can be visualised on a stress-strain curve, where the yield point is the point at which the curve indicates the limit of elastic behaviour and the beginning of plastic behaviour. However, it is important to note that for some materials, such as copolymers, there may be no apparent yield point on the stress-strain curve, and the determination of yield stress is approximate.
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Work hardening
Plastic deformation of metals is a complex phenomenon that involves various factors such as crystal structure, grain size, and dislocation interactions. Work hardening, also known as strain hardening, is a critical aspect of this process. It refers to the increase in hardness and strength of a material due to dislocation entanglements and the inhibition of their mobility.
Before work hardening occurs, the lattice of the material exhibits a regular, nearly defect-free pattern with minimal dislocations. However, as plastic deformation progresses, the number and density of dislocations within the material increase significantly. These dislocations interact and create entanglements, impeding the motion of other dislocations. This leads to an increase in the stress required to achieve further plastic deformation, resulting in enhanced strength and hardness.
The rate of work hardening, or the hardening rate, is influenced by several factors, including the initial dislocation density, the rate of dislocation generation, and the rate of dislocation annihilation. This rate plays a crucial role in understanding and predicting the mechanical behaviour of the material. For example, in metals, the work hardening rate tends to decrease as the strain increases, eventually approaching a plateau. This behaviour is a result of the competition between the creation of new dislocations and their inhibition through entanglements, as well as processes that enable their annihilation, such as climb and cross-slip.
The work hardenability of a material can be predicted by analyzing a stress-strain curve or through hardness tests. Additionally, analytical equations like the Ludwik-Hollomon equation and the Voce equation are used to characterize work hardening in metals. While work hardening can be beneficial in certain applications, it is sometimes avoided by using specialized alloys and heat treatments to prevent metal fatigue and maintain ductility.
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Plastic strain
Plastic deformation is a phenomenon observed in materials such as metals, where they undergo irreversible changes in shape and structure when subjected to external forces or stresses. This is in contrast to elastic deformation, where the material returns to its original shape once the load is removed. The point at which elastic deformation ends and plastic deformation begins is known as the yield point or yield stress. At this stage, the material's behaviour changes from elastic to plastic, and any further straining will contain both elastic and plastic components.
The yield stress is the stress level at which a material begins to exhibit plastic deformation. It is usually considered a single value, typically ranging from 0.05 to 0.1% of the material's elastic modulus for most metals. However, it is important to note that the yield stress is not a fixed value and can vary depending on various factors such as crystal structure, grain size, composition, and temperature.
Plastic deformation is characterised by the creation and movement of dislocations within the material's crystal lattice. Dislocations are defects or irregularities in the arrangement of atoms or molecules. As the material is deformed, these dislocations move and interact with each other, leading to the formation of slip planes and persistent slip bands. This results in a permanent change in the material's shape and properties.
The behaviour of materials during plastic deformation can be described using stress-strain curves, which plot stress against strain. The stress-strain curve for a ductile metal typically includes regions of elastic deformation, plastic deformation, and hardening. The hardening phase, also known as work hardening or strain hardening, occurs as a result of the increasing interaction and tangling of dislocations, which reduces their mobility over time. This leads to a progressively increasing level of applied stress required to continue the deformation.
The plastic behaviour of materials can be mathematically modelled using equations such as the Ludwik-Hollomon equation and the Voce equation. These equations take into account factors such as applied stress, yield stress, plastic strain, and work hardening coefficients. By utilising these models, engineers can predict and analyse the plastic deformation characteristics of different materials, ensuring their effective use in various engineering applications.
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Ductility levels
Ductility is the ability of a material to withstand plastic deformation without rupture. It is a measure of the percent elongation of a material under tensile stress, which is defined as the maximum elongation of the gage length divided by the original gage length. Ductile materials show large deformation before fracture, while the lack of ductility is termed brittleness.
The ductility of a material is an important factor in engineering and manufacturing. It defines the suitability of a material for certain manufacturing operations, such as cold working, and its ability to absorb mechanical overload. Metals that are used for engineering purposes are normally required to have ductility levels (plastic strains to failure) of at least several per cent.
The ductility of a material can be quantitatively assessed using the percent elongation at break, which is given by the following equation:
> {\displaystyle \%\mathrm {EL} ={\frac {\text{final gauge length - initial gauge length}}{\text{initial gauge length}}}={\frac {l_{\mathrm {f} }-l_{0}}{l_{0}}}\cdot 100}
Where {\displaystyle q} is the relative elongation in percent.
The ductility of metals can be altered by changing conditions, such as temperature and impurities. An increase in temperature will increase ductility, while a decrease in temperature will have the opposite effect. Minor additions of impurities to metals can also cause a change from ductile to brittle behaviour.
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Frequently asked questions
Plastic deformation is when a material undergoes a permanent change in shape or size due to an applied force.
The yield point, or elastic limit, is the point on the stress-strain curve at which the behaviour of a material changes from elastic to plastic.
Young's modulus is a measure of the stiffness of a material. It defines the stiffness of a material during unloading.
Work hardening, also known as strain hardening, is the phenomenon where the yield stress of a material increases with increasing plastic deformation. This is due to the creation and interaction of dislocations within the material.
Necking is a highly localized deformation that can occur in ductile metals under tensile loading after they have reached their ultimate strength. During necking, the nominal stress drops below the ultimate strength while the nominal strain continues to increase.
