Ethan Clarke
Plastic flow is a concept in physics that involves the study of plastic deformation in materials, which can be crystalline or non-crystalline. This deformation occurs when a material undergoes mechanical changes while experiencing stress or load, resulting in a flow-like movement within the material. The plastic deformation can be irreversible, with the material retaining its altered shape even after the load is removed. This phenomenon is influenced by factors such as temperature, viscosity, and the presence of dislocations within the material's structure. Plastic flow has applications in various fields, including engineering, geology, and biology, and is essential for understanding and predicting material behaviour under different conditions.
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What You'll Learn
Plastic deformation in crystalline solids
The mathematical theory of plasticity, or flow plasticity theory, employs a set of non-linear, non-integrable equations to describe the changes in strain and stress concerning a previous state and a small increase in deformation. This theory was developed by Egon Orowan, Michael Polanyi, and Geoffrey Ingram Taylor in 1934. The Tresca and von Mises criteria are commonly employed to determine whether a material has yielded, although they are inadequate for a wide range of materials.
Time-independent plastic flow in single crystals and polycrystals is defined by a critical or maximum resolved shear stress (τCRSS), which initiates dislocation migration along parallel slip planes, marking the transition from elastic to plastic deformation in crystalline materials. The critical resolved shear stress for single crystals is given by Schmid's law: τCRSS=σy/m, where σy is the yield strength, and m is the Schmid factor, which considers the angles between the slip plane direction and the applied force.
The rate of plastic deformation is initially high but eventually tapers off to a steady value, known as the shear-strain rate. This rate is influenced by temperature, with three distinct regions of critical resolved shear stress. In the low-temperature region (T ≤ 0.25Tm), a high strain rate is required to achieve high τCRSS for dislocation glide and plastic flow. In the moderate temperature region (0.25Tm < T < 0.7Tm), the thermal shear stress component disappears, and point defect impedance to dislocation migration is eliminated. In the high-temperature region (T ≥ 0.7Tm), plastic flow occurs due to thermally activated mechanisms, and the work hardening rate is low, indicating that a small shear stress can induce a large shear strain.
The shear flow stress is directly proportional to the square root of the dislocation density, indicating that hardening depends on the number of dislocations present. At small strains, the dislocation arrangement is a random 3D array, while at moderate strains, cellular dislocation structures form with heterogeneous dislocation distributions. As strains increase further, these cellular structures reduce in size until they reach a minimum.
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Plastic flow in biological structures
Plastic flow is a phenomenon observed when a material under severe stress starts to behave as a Newtonian fluid, resulting in plastic deformation. This deformation is permanent and persists even after the stress is removed. While plastic flow is commonly associated with metal-forming processes and geologic processes, it is also observed in biological structures, such as cellular materials and biological tissues.
In biological structures, plastic flow properties are evident from the cellular level up to the tissue level. Plastic deformation in biological tissues indicates damage, and if the damage is significant enough, it becomes irreversible. This is because some tissues, like cartilage and tendon, have limited self-healing capabilities due to a lower number of tissue-specific repairing stem cells in mature tissues. On the other hand, tissues like skin and bone have a higher number of stem cells capable of facilitating self-reconstruction and restoring normal mechanical properties to the injured site.
The ability of biological tissues to resist plastic flow and maintain their structural integrity is crucial. While some tissues can heal and regain their original mechanical properties, others with poor repair abilities may not recover fully. Therefore, understanding the plastic flow behaviour of biological tissues is essential for developing strategies to prevent or mitigate damage and promote effective healing processes.
The plastic flow behaviour of biological tissues can be attributed to various mechanisms. At the crystalline scale, plasticity is influenced by dislocations, which are more common in ductile metals and some crystalline materials. In brittle materials like bone, rock, and concrete, plasticity arises from slip at microcracks. In cellular materials, such as liquid foams or biological tissues, plasticity results primarily from bubble or cell rearrangements.
The study of plastic flow in biological structures involves examining the rheological properties of these materials. Rheology is the branch of physics that investigates the deformation and flow of materials under stress. By understanding how biological tissues respond to stress and deformation, researchers can gain insights into their mechanical behaviour and develop strategies to enhance their resilience and healing capabilities.
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Plastic deformation in metal-forming processes
Plastic deformation is a phenomenon observed in materials that undergo mechanical deformation while in a magnetic field. It is of great importance to the study of glacier flow and occurs in many metal-forming processes such as rolling, pressing, and forging. In the context of metal-forming processes, plastic deformation refers to the permanent change in the shape and microstructure of metals and alloys through techniques like severe plastic deformation (SPD). SPD involves subjecting materials to extensive hydrostatic pressure, high-pressure torsion, and twisting actions under high pressure, resulting in the development of ultrafine grains and desired shape changes.
The mathematical theory of plasticity, or flow plasticity theory, describes the set of changes in strain and stress with respect to a previous state and a small increase in deformation. This theory explains the plastic deformation of ductile materials in terms of dislocation migration and the transition from elastic to plastic deformation behaviour in crystalline materials. The critical resolved shear stress (CRSS) defines the initiation of dislocation migration, with the Schmid factor considering the angles between the slip plane direction and the applied force.
The plastic deformation of metals is commonly caused by the glide of dislocations driven by shear stresses. In polycrystals, individual grains must deform cooperatively, undergoing complex shape changes consistent with their neighbours. The work hardening rate, or the true stress-true strain relationship, tends to decrease with increasing strain due to the competition between the creation and inhibition of dislocation mobility. The yield stress and work hardening characteristics are influenced by various factors, including crystal structure, grain size, and composition.
Metal-forming processes can involve a range of temperatures, from cold to hot deformation, to achieve grain refinement. Techniques such as equal channel angular pressing (ECAP) and direct/indirect extrusion methods are used to produce ultrafine grains in materials like magnesium alloys. These processes result in complex stress states and high defect densities, ultimately refining the microstructure and enhancing mechanical properties.
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Plastic deformation in glacier flow
Plastic deformation refers to the irreversible deformation of a material. In the context of glacier flow, plastic deformation refers to the movement of ice within a glacier in response to stresses caused by the mass of the ice and gravitational forces. This movement results in the internal deformation of the glacier, causing it to flow or advance.
Glaciers and ice sheets display a wide range of structures that provide valuable information about past and present ice dynamics. By studying these structures, scientists can gain insights into the underlying principles of glacier flow. Early pioneers in the field of structural glaciology, such as James Forbes and John Tyndall, laid the groundwork for understanding glacier flow by drawing comparisons between glacier structures and the deformational characteristics of rocks.
The rate of plastic deformation in glacier flow is influenced by factors such as temperature and stress. In the low-temperature region, a higher strain rate is required to initiate plastic flow. As the temperature increases, the thermal shear stress component decreases, and plastic flow becomes more prevalent. Additionally, the shear flow stress is directly proportional to the square root of the dislocation density, indicating that the hardening of the ice is dependent on the number of dislocations present.
The understanding of plastic deformation in glacier flow has important implications for studying the dynamics of glaciers and ice sheets. By analyzing the structures and deformation patterns within glaciers, scientists can gain insights into the past and present behavior of these massive ice formations. This knowledge contributes to our understanding of glacier movement, equilibrium, and the complex interactions between ice, rock, and the underlying terrain.
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Plastic deformation in rock folding
Plastic deformation refers to the irreversible change in form of a material under stress. In the case of crystalline solids, plastic deformation causes no change in volume. This phenomenon is observed in both metal-forming processes and geologic processes.
Rock folding is one such geologic process that occurs under extremely high pressures and elevated temperatures deep in the Earth's crust. Rocks exposed to these conditions can undergo plastic deformation, resulting in folding, stretching, compression, and bending. This occurs without fracturing, as the rock contorts and changes shape gradually. The folds can be classified as either anticlines or synclines. Anticlines tend to arch upward, while synclines arch downward. The oldest beds are found at the core of an anticline. A partial fold where only one side bends in a different direction is called a monocline.
The type of rock determines the type of deformation. For instance, under similar confining pressures, halite (rock salt) is more susceptible to ductile deformation than granite, which is more likely to fracture. Igneous and metamorphic rocks tend to be stronger and thus resist deformation to a greater extent than sedimentary rocks.
The geometry of folds can be reconstructed by geologists through a series of measurements and observations. This includes measuring the strike and dip of exposed strata, determining the direction in which the beds become younger, and identifying any structural deformations within the rocks. By applying the principles of geometry and trigonometry to this data, geologists can determine the orientation of the axial plane and whether the fold plunges.
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 with respect to a previous state and a small increase in deformation. The Tresca and von Mises criteria are commonly employed to determine whether a material has yielded. However, these criteria have proven inadequate for a wide range of materials, necessitating the use of alternative yield criteria.
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Frequently asked questions
Plastic deformation is when a material undergoes mechanical deformation while in a magnetic field. The process of deformation may result from hydrostatic pressure, shock impact, or directed tectonic stress.
Internal plastic flow is the study of how materials behave under stress. It involves the examination of how molecules and larger particles experience forces that cause them to slide along each other, developing resistance from internal molecular/particle friction.
Internal plastic flow can be observed in metal-forming processes such as rolling, pressing, and forging, as well as in geologic processes like rock folding and rock flow within the Earth's crust under high pressure and temperature conditions.
