Understanding Elastic-Plastic Deformation In Materials

what does elastic perfectly plastic mean

In engineering, the transition from elastic behaviour to plastic behaviour is known as yielding. Elastic perfectly plastic materials have an elastic region and a perfectly plastic region. In physics and materials science, plasticity, or plastic deformation, is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. Elasticity, on the other hand, is a material's ability to resist deformation.

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Plastic deformation

In physics and materials science, plasticity, or plastic deformation, is the ability of a solid material to undergo permanent, non-reversible changes in shape in response to applied forces. Plastic deformation is observed in most materials, especially metals, soils, rocks, concrete, and foams. However, the mechanisms causing plastic deformation vary widely.

In engineering, the transition from elastic behaviour to plastic behaviour is known as yielding. For example, in ductile metals, tensile loading causes elastic behaviour, and each increment of load is accompanied by a proportional increment in extension. However, once the load exceeds the yield strength, the extension increases more rapidly, and when the load is removed, some degree of extension remains.

Perfect plasticity is a property of materials to undergo irreversible deformation without any increase in stresses or loads. The plasticity of a material is directly proportional to its ductility and malleability.

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Elastic deformation

The concept of elastic deformation is important in engineering, where it is studied in the context of mechanical and structural engineering. Materials such as concrete and steel are commonly subjected to small elastic deformations. Elastic deformation is also observed in metals and ceramics at low strains, where their elastic behaviour is generally linear. When metals are subjected to small loads or stresses, they undergo elastic deformation and return to their original shape once the load is removed.

The behaviour of materials during elastic deformation can be modelled and analysed using various methods. One approach is to calculate the stress due to deformation at a particular time point during a transient analysis, which can then be used for further computations. Another method involves considering the internal energy distribution on a microscopic scale, which may be irrelevant to the macroscopic deformation problem. Additionally, the slip system, which includes the slip plane and slip direction, plays a crucial role in understanding the strength of metallic biomaterials and their resistance to deformation.

It is worth noting that the term "perfectly elastic" has different interpretations. One perspective defines a perfectly elastic material as one that suffers zero deformation under any value of stress within its elastic limit. However, this definition resembles the description of a rigid body, which also experiences no deformation under stress. An alternative definition suggests that a perfectly elastic material behaves elastically throughout its entire stress-strain curve, exhibiting elastic behaviour until fracture.

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Stress-strain curve

In engineering, the transition of a material from elastic behaviour to plastic behaviour is known as yielding. Most materials considered in engineering are elastic perfectly plastic, meaning they have an elastic region and a perfectly plastic region. The elastic region is marked on the stress-strain curve only if elastic behaviour is observed.

A stress-strain curve illustrates the relationship between stress and strain for a particular material. It is a graphical representation of how a material responds to an applied force. The curve is used to determine the behaviour of materials under different conditions, such as impact loading, high pressures, and high temperatures.

The stress-strain curve for a perfectly plastic material is thought to be a horizontal line at zero, while for a perfectly elastic material, it is a straight line increasing to infinity. However, this straight line can also be an inclined straight line or a non-linear curve, as elastic bodies can be linear or non-linear.

The stress-strain curve for an elastic-perfectly-plastic material is one where the stress remains constant upon exhausting the elastic capacity of the material. This is also referred to as a rigid, strain-hardening material. An example of an elastic-perfectly-plastic material is soft steel, which, once the yield stress is reached, continues to elongate to failure without additional stress.

The bilinear hardening model is described by the stress-strain curve, where the coefficients needed for material characterisation are the Young modulus and the plastic phase modulus. When the plastic phase modulus is very small or zero, the bilinear model simulates the behaviour of perfect plasticity.

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Elastic–perfectly-plastic model

In physics and materials science, plasticity (also known as plastic deformation) is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. Most materials are "elastic perfectly plastic", meaning they have an elastic region and a perfectly plastic region. The elastic region is marked on the stress-strain curve if and only if elastic behaviour is observed.

The Elastic–Perfectly-Plastic model is a mathematical tool used to compute stress based on the current value of strain and selected internal variables. It is a simplification of the elasto-plastic model, which accounts for both elastic and plastic deformation. The elastic-perfectly plastic model assumes that once the yield stress is reached, the material continues to elongate to failure with no additional stress required. This is often observed in soft steels.

The elastic-perfectly plastic model is useful for modelling materials that exhibit a brittle response and have a marginal difference between their ultimate stress and yield stress. It is also used when the effect of hardening is limited, as it is a simpler model that does not include hardening. This model is also useful for predicting the behaviour of materials under extreme conditions, such as impact loading, high pressures, and high temperatures.

The elastic-perfectly plastic model can be simulated using the SimScale platform, which offers Bilinear, Multilinear, and Johnson-Cook parameters for modelling elasto-plastic materials. The Bilinear model can simulate a linear elastic analysis or perfect plasticity, depending on the value of the plastic phase modulus. The Multilinear model is more accurate as it takes into account the entire behavioural history of the material, and the material properties are established to be the same as the stress-strain curve obtained from a tensile test.

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Yield strength

In engineering, the transition from elastic behaviour to plastic behaviour is known as yielding. Elastic perfectly plastic materials have an elastic region and what can be estimated as a perfectly plastic region. Elasticity refers to a material's resistance to deformation. A perfectly elastic material can be defined as one that suffers zero deformation under any value of stress within its elastic limit. However, this definition is similar to that of a rigid body, which does not deform under stress. Another definition could be that a perfectly elastic material behaves elastically throughout its stress-strain curve, i.e. until fracture.

The yield strength of crystalline materials can be increased by altering dislocation density, impurity levels, and grain size. Introducing defects and impurities increases the yield stress of the material as more stress is required to move dislocations through the crystal lattice.

Frequently asked questions

Elastic perfectly plastic refers to materials that have an elastic region and a perfectly plastic region.

Some soft steels behave like elastic-perfectly plastic materials. Once yield stress is reached, the material continues to elongate to failure with no additional stress required.

Elastic deformation refers to the ability of a material to return to its original shape after a load is released. Plastic deformation, on the other hand, is a permanent, non-reversible change in the shape of a material in response to applied forces.

A perfectly elastic material can be represented by a straight line or a non-linear curve that increases to infinity.

A rigid body is defined as one that does not deform under any amount of stress, whereas a perfectly elastic body can have any value of Young's modulus and will deform under stress but return to its original shape.

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