Alexei Volkov
Plastic deformation is the ability of a solid material to undergo a permanent change in shape, form, or texture in response to applied forces. This is a common phenomenon observed in most materials, especially metals, soils, rocks, concrete, and foams. While the plastic deformation of a material is dependent on several factors, the question of whether or not it changes volume when its length changes is an intriguing one. This query delves into the intricate relationship between the dimensions of an object and the underlying physics that govern its behaviour. By exploring this topic, we can gain a deeper understanding of the transformations that occur within materials subjected to various forces and the resulting impact on their volume.
| Characteristics | Values |
|---|---|
| Plastic deformation | Permanent alteration of shape, form, or texture of a material due to stress |
| Plastic deformation process | Strain hardening, necking, and fracture |
| Plastic deformation in metals | Slip and twinning |
| Plastic deformation volume change | No volumetric change during plastic deformation |
| Plastic deformation energy | Minimum energy required to deform material is ΔU (change in internal body energy) + W (mechanical work done on the sample) + Q (heat effect associated with deformation) |
| Plastic deformation in amorphous materials | Amorphous materials like polymers contain a large amount of free volume and can be stretched to increase this free volume |
| Plastic deformation in polycrystals | More stress is required in polycrystals than in single crystals due to the presence of grain boundary defects |
| Plastic deformation assumptions | No voids, material at room temperature, no additional strain energy, negligible change in volume due to dislocation density, negligible change in volume due to grain boundary density |
| Plastic deformation and Poisson's ratio | Poisson's ratio of 0.5 implies no volumetric change during plastic deformation |
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Plastic deformation
At the crystalline scale, plasticity in metals is often a consequence of dislocations, which are defects in the crystal structure. These dislocations allow planes of atoms to slip past each other, resulting in a permanent change of shape. The mathematical theory of plasticity, or flow plasticity theory, uses a set of non-linear, non-integrable equations to describe the changes in strain and stress relative to a previous state and a small increase in deformation. When the stress exceeds a critical value, the material undergoes irreversible deformation.
In polycrystals, plasticity differs from that of single crystals due to the presence of grain boundary (GB) planar defects, which impede dislocation migration along activated slip planes. This results in a higher work hardening rate in polycrystals compared to single crystals. Additionally, the physical mechanisms causing plastic deformation can vary widely, with different mechanisms such as dislocation motion, vacancy motion, twinning, phase transformation, or viscous flow of amorphous materials contributing to the overall deformation.
In amorphous materials, the concept of dislocations does not apply due to the lack of long-range order. These materials, such as polymers, contain a large amount of free volume or wasted space. When subjected to tension, these regions open up, leading to a hazy appearance known as crazing, where fibrils form within the material in regions of high hydrostatic stress. Despite the absence of dislocations, amorphous materials can still undergo plastic deformation when the bending moment exceeds the fully plastic moment.
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Poisson's ratio
Mathematically, Poisson's ratio (ν) is the negative ratio of transverse strain to axial strain. In simpler terms, it is the ratio of the amount of transversal expansion or contraction to the amount of axial compression or elongation experienced by a material under an applied load. Poisson's ratio can be calculated using equations that take into account the changes in height and diameter of a sample after applying a compressive force.
The behaviour of materials under loading is critical in engineering applications. For example, when a rubber band is stretched, it becomes thinner in the transverse direction, exhibiting a positive Poisson's ratio. Conversely, certain materials, known as auxetic materials, display a negative Poisson's ratio, meaning they expand in the transverse direction when stretched. This unusual behaviour is observed in some crystalline materials and is being explored for new aspects in material design.
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Crazing
Crazes are similar to cracks in that they are wedge-shaped and formed perpendicular to the applied stress. However, crazes differ from cracks as they can support stress and contain plastic that is stretched in a highly oriented manner perpendicular to the plane of the craze. They are also parallel to the applied stress direction. Crazes can transmit load between their two faces through the fibrils.
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Dislocation
Plastic deformation refers to the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. This phenomenon is observed in most materials, especially metals, soils, rocks, concrete, and foams. At the atomic level, plastic deformation occurs through a slip or
The mathematical theory of plasticity, known as flow plasticity theory, uses a set of non-linear, non-integrable equations to describe the changes in strain and stress. When the stress exceeds a critical value, the material undergoes plastic deformation. This critical stress can be tensile or compressive, and it can be determined using criteria such as the Tresca and von Mises criteria. However, these criteria have limitations and may not be applicable to all materials.
While plastic deformation typically occurs at a constant volume, there may be local increases or decreases in volume on either side of a dislocation, with a net change of zero. The energy required for plastic deformation can affect the number of voids present, but the overall change in volume is generally assumed to be negligible. This assumption is often made in plasticity models, where it is also assumed that the material has recovered to room temperature and no additional strain energy is being stored, which would otherwise result in a change in volume.
It is important to distinguish between engineering stress and strain, which are based on initial dimensions, and true stress and strain, which account for changes in sample geometry during deformation. Plastic strains in ductile materials can exceed 100%, highlighting the significant deformation capacity of materials in the plastic regime.
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Plastic volumetric contraction
In the case of concrete, plastic shrinkage refers to the moisture loss and contraction that occur before the concrete sets. This shrinkage is caused by the evaporation of water from the concrete paste, leading to a reduction in volume and the formation of cracks on the surface. The rate of evaporation, which depends on factors such as air temperature, concrete temperature, relative humidity, and wind speed, influences the extent of plastic shrinkage. Additionally, concrete with lower water content is more susceptible to plastic shrinkage.
The concept of plastic volumetric contraction is also relevant in the field of engineering. During tensile testing, materials like mild steel exhibit volume changes during elastic deformation but show no change in volume during plastic deformation. This behavior is influenced by factors such as Poisson's ratio, which implies that a value of 0.5 results in no volumetric change during tensile stretching or compressive contraction.
Furthermore, plastic volumetric contraction can occur in materials with a distinct plastic region. This contraction is associated with the progressive collapse of air voids, leading to the generation of plastic volumetric strain. The mathematical theory of plasticity, or flow plasticity theory, employs non-linear and non-integrable equations to describe the changes in strain and stress concerning a previous state and incremental deformation.
It is important to note that the assumptions made in plasticity models, such as the constant-volume assumption, may not always accurately represent physical reality. These assumptions include neglecting the introduction of voids, assuming the material has returned to room temperature, and disregarding the storage of additional strain energy. While these assumptions simplify calculations, they may not capture the complex behavior of materials during plastic deformation and volumetric contraction.
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Frequently asked questions
Plastic deformation is the permanent alteration of shape, form, or texture of a material due to stress. This deformation is typically assumed to occur at a constant volume, especially in metals. However, this may not hold true for ceramics, which can densify under stress at high temperatures.
Plastic deformation is an irreversible process where a material undergoes a non-reversible change of shape in response to applied forces. It is characterized by a strain-hardening region, necking region, and eventual fracture.
Plastic deformation occurs when a shear stress exceeds a critical value, causing permanent changes in atomic positions. This typically happens along gliding planes, where crystals slide and translate permanently.
Plastic deformation is observed in most materials, including metals, soils, rocks, concrete, and foams. It is particularly common in ductile materials, where plastic strains can exceed 100%.
While plastic deformation typically assumes a constant volume, the specific volume change depends on the Poisson's ratio. A Poisson's ratio of 0.5 implies no volumetric change during tensile stretching or compressive contraction.
