Ethan Clarke
Elastic modulus, also referred to as Young's modulus, quantifies a material's resistance to non-permanent deformation under stress. It is a measure of a material's stiffness and is calculated by determining the slope of the elastic portion of the stress-strain curve. The elastic modulus varies across materials, with stiffer materials having a higher elastic modulus. The elastic modulus of most plastics typically ranges from 1.5 to 5 GPa, while that of metals can vary widely, generally falling between 50 and 400 GPa. Plastic deformation, on the other hand, refers to permanent deformation, which occurs after a material passes through the elastic region and its yield point.
Characteristics and Values of Plastic
| Characteristics | Values |
|---|---|
| Appearance | Plastic can be transparent, translucent, or opaque, with a smooth, glossy, matte, or textured finish. It can also come in various solid colors or patterned designs. |
| Malleability | Plastic is highly malleable and can be easily molded or shaped into basic or complex forms, even after cooling. |
| Durability | Plastic is durable and resistant to wear, tear, and impact. It has a long lifespan and does not rust or oxidize like metals. |
| Lightweight | Plastic is generally lightweight, making it advantageous for transportation and packaging. |
| Insulation | Plastic has good electrical and thermal insulation properties, making it suitable for electrical components. |
| Chemical Resistance | Plastic is resistant to chemicals, acids, and solvents, making it suitable for storing and transporting various substances. |
| Non-biodegradability | Plastic is non-biodegradable and can take hundreds of years to break down, contributing to environmental degradation and microplastic pollution. |
| Dependency on Fossil Fuels | Plastic production relies on finite fossil fuel resources, contributing to carbon emissions and resource depletion. |
| Low Melting Point | Plastic has a lower melting point compared to metal. |
| Elastic Modulus | Plastic has an elastic modulus, which quantifies its resistance to non-permanent deformation. It is calculated using the slope of the stress-strain curve in the elastic region before yielding. |
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What You'll Learn
Plastic modulus is calculated after yielding
The elastic modulus, or modulus of elasticity, is a measurement of a material's elasticity. It quantifies a material's resistance to non-permanent, or elastic, deformation. Brittle materials like plastics and metals exhibit a steeper slope and higher elastic modulus value than ductile materials like rubber.
When under stress, materials first exhibit elastic properties, deforming but returning to their previous state after the stress is removed. After passing through the elastic region and their yield point, materials enter a plastic region, where they exhibit permanent deformation even after the stress is removed.
The plastic modulus is calculated after yielding, when the material has entered the plastic region. It is used to determine the plastic or full moment strength of a section. The plastic section modulus is used for materials and structures where limited plastic deformation is acceptable and represents the section's capacity to resist bending once the material has yielded.
The plastic section modulus is calculated as the sum of the areas of the cross-section on either side of the plastic neutral axis (PNA), each multiplied by the distance from their respective local centroids to the PNA. The PNA is defined as the axis that splits the cross-section such that the compression force from the area in compression equals the tension force from the area in tension.
It is important to note that the modulus of elasticity can be calculated in various ways, and different codes use varying notations for the elastic and plastic section moduli.
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Plastic modulus is dependent on the plastic neutral axis (PNA)
Plastic modulus, also known as the plastic section modulus, is a geometric property used in structural engineering to calculate a cross-section's capacity to resist bending after yielding has occurred across the entire section. It is used for determining the plastic, or full moment, strength and is larger than the elastic section modulus, reflecting the section's strength beyond the elastic range.
The plastic neutral axis (PNA) is the dividing line between the tension and compression zones of a shape that has developed full plasticity. The PNA is defined as the axis that splits the cross-section such that the compression force from the area in compression equals the tension force from the area in tension. For sections with constant, equal compressive and tensile yield strength, the area above and below the PNA will be equal.
The plastic moment, MP, can be found by taking moments of the resultants of the tensile and compressive stresses about the neutral axis. These stress resultants act at the centroids C1 and C2 of the areas A1 and A2, respectively. The plastic moment of a beam can also be referred to as its plastic modulus of the cross-section.
The plastic section modulus, Z, is one half the area of the total shape multiplied by the distance from the centroid of the upper half of the area to the centroid of the lower half of the area. The plastic section modulus is calculated as the sum of the areas of the cross-section on either side of the PNA, each multiplied by the distance from their respective local centroids to the PNA.
Therefore, the plastic modulus is dependent on the plastic neutral axis (PNA) as the PNA defines the line between tension and compression regions of a fully developed plastic hinge section, and the plastic modulus is used to calculate the strength of a section after yielding has occurred. The PNA is also used to calculate the plastic section modulus, which is related to the plastic modulus. For symmetric shapes composed of a single material, the elastic neutral axis (ENA) and PNA are the same, but they differ for asymmetric shapes.
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Plastic deformation is permanent
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. It is important to distinguish plastic deformation from elastic deformation. Elastic deformation refers to the ability of a material to return to its original shape after being subjected to stress. Modulus of Elasticity, or Elastic Modulus, is a measurement of a material's elasticity, or resistance to non-permanent deformation.
Plastic deformation occurs when a material is subjected to tensile, compressive, bending, or torsion stresses that exceed its yield strength. This results in permanent distortion, such as elongation, compression, buckling, bending, or twisting. At the atomic level, plastic deformation occurs when atoms are displaced a sufficient distance from their initial position, causing chemical bonds to break and reform, transforming elastic energy into chemical potential energy.
In crystalline materials, plasticity is caused by dislocations, or irregularities in the crystal structure. These dislocations allow planes of atoms to slip past each other, resulting in a permanent change of shape. In amorphous materials, such as polymers, plastic deformation occurs when the material is pulled in tension, opening up regions of free volume and causing a hazy appearance known as crazing.
Plastic deformation is observed in a wide range of materials, including metals, soils, rocks, concrete, and foams. However, the mechanisms responsible for plastic deformation can vary depending on the material. For example, in metals, plastic deformation occurs due to the collective motion of dislocations gliding on specific slip planes. In soils, plastic behaviour is caused by the rearrangement of clusters of adjacent grains.
Understanding the plastic deformation behaviour of materials is crucial in engineering and manufacturing processes. By controlling factors such as temperature, acceleration, and drag force, the permanent deformation of materials can be managed to prevent product failure and ensure desired product characteristics.
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Plastic modulus is used in structural engineering
Plastic modulus, or plastic section modulus, is a key concept in structural engineering. Structural engineering involves the application of physics and mechanics to design man-made structures that can withstand the loads imposed on them. The plastic modulus is used to calculate a material's ability to resist bending once it has yielded and entered the plastic range, where permanent deformation occurs.
The plastic modulus is used in structural engineering to ensure that structures can safely bear the required loads without significant or unacceptable deformation. This is known as the limit state design method. Engineers compare the plastic moment strength against factored applied moments to ensure the structure's integrity. The plastic modulus is particularly relevant for structures that need to withstand extreme loads, such as those caused by earthquakes or explosions.
In the design of steel structures, for example, the plastic modulus is used to determine the strength of lateral elements and connections post-elastic behaviour. This is known as the plastic hinge model, where the beam becomes a plastic hinge once it reaches yield stress. By encouraging plastic hinges at prescribed locations, engineers can design structures that exhibit ductile behaviour under above-strength load limits.
The plastic modulus is also used to enhance the efficiency and cost-effectiveness of large beams with predictable loading conditions. By strategically adjusting the section modulus along the length of the beam, engineers can optimise its performance. This technique is particularly useful in applications such as cranes, aeronautical structures, and space structures, where relying solely on calculations may be insufficient.
The calculation of the plastic modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as the axis that divides the cross-section such that the compression force from the area in compression equals the tension force from the area in tension. The plastic modulus is calculated differently from the elastic modulus, and there are various equations for determining the plastic modulus for different shapes, such as I-beams and rectangles.
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Plastic modulus is calculated differently in the US and Australia
Elastic Modulus, also known as Modulus of Elasticity or simply Modulus, is a measurement of a material's elasticity. It quantifies a material's resistance to non-permanent, or elastic, deformation. Materials will first exhibit elastic properties when under stress: the stress causes them to deform, but the material will return to its previous state after the stress is removed. After passing through the elastic region and through their yield point, materials enter a plastic region, where they exhibit permanent deformation even after the tensile stress is removed.
The Elastic Modulus is calculated by finding the slope of the straight-line portion of a stress-strain curve. The formula for this is:
Modulus = (σ2 - σ1) / (ε2 - ε1)
Where stress (σ) is force divided by the specimen's cross-sectional area and strain (ε) is the change in length of the material.
The Plastic Modulus, on the other hand, is calculated differently. It is based on the stress-strain curve after yielding. The Plastic Modulus assumes that the entire section of the material yields.
While the specific details of how the Plastic Modulus is calculated were not found in the search results, one source mentions that it involves first finding the plastic neutral axis (PNA), which is the axis about which there is an equal amount of area above and below. The next step is to find the centroids of the areas above and below the PNA independently and then multiply the total area of the section by the distance between these two centroids.
Interestingly, there appears to be a difference in how the Plastic Modulus is referred to in the US compared to Australia. In the US, S is used to refer to the Elastic Section Modulus, while Z is used for the Plastic Modulus. In Australia, it seems to be the other way around. However, this difference in nomenclature does not seem to affect the actual calculation methods, which are consistent across both countries.
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Frequently asked questions
The elastic modulus of plastic is typically between 1.5 and 5 GPa, depending on the polymer type and formulation.
The elastic modulus, also known as Young's modulus, is a measure of a material's stiffness or resistance to elastic (non-permanent) deformation under stress.
The elastic modulus is calculated by determining the slope of the elastic portion of the stress-strain curve.
The elastic modulus is the measurement before yielding, while the plastic modulus is the measurement after yielding.
