12.4 Elasticity and Plasticity
3 min read•june 24, 2024
When materials are stressed, they can deform elastically or plastically. is reversible, while is permanent. Understanding these behaviors is crucial for engineers designing structures and components that can withstand expected loads without failing.
- diagrams help visualize how materials respond to applied forces. The region shows linear behavior, while the plastic region indicates permanent changes. Key points like and guide engineers in selecting materials and designing safe, reliable structures.
Elastic and Plastic Deformation
Elastic vs plastic deformation
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- Elastic deformation involves reversible changes in shape or size of a material when subjected to an applied stress below its
- Material fully recovers its original dimensions once the stress is removed (rubber band, spring)
- Plastic deformation involves irreversible changes in shape or size of a material when subjected to an applied stress beyond its
- Material permanently deforms and does not return to its original dimensions even after the stress is removed (bent paperclip, dented car bumper)
- Elastic marks the maximum stress a material can withstand without undergoing permanent deformation
- Determined by the material's intrinsic properties such as atomic bonding and crystal structure (steel vs rubber)
- Exceeding the elastic limit causes the material to transition from elastic to plastic deformation
Implications of plastic deformation
- Plastic deformation permanently alters the material's internal structure by introducing defects and dislocations
- Changes mechanical properties such as strength, , and hardness (cold-worked metals)
- phenomenon increases a material's strength and hardness due to the accumulation of dislocations during plastic deformation
- Exploited in manufacturing processes like cold rolling and wire drawing to improve material properties
- Engineers must design components to operate within the elastic limit under expected loads to avoid permanent deformation and failure
- Plastic deformation can be intentionally utilized for shaping materials through processes like forging, rolling, and extrusion (shaping clay, bending metal sheets)
- Plastically deformed materials exhibit altered properties that must be accounted for in subsequent design and manufacturing steps
- Heat treatment may be necessary to restore desired properties (annealing, tempering)
Analysis of stress-strain diagrams
- Stress-strain diagrams graphically represent a material's mechanical response to applied stress
- Stress plotted on the y-axis, strain plotted on the x-axis
- Elastic region appears as a linear portion of the where stress is directly proportional to strain
- Slope of the linear region represents the material's , a measure of its stiffness (steel vs rubber)
- describes the linear elastic behavior as
- Elastic limit corresponds to the point where the stress-strain curve deviates from linearity, indicating the onset of plastic deformation
- Elastic limit and may differ slightly due to
- Yield strength represents the stress at which a material exhibits a specified amount of plastic deformation, typically 0.2% strain
- Yield strength serves as a practical limit for many engineering applications to ensure safe and reliable operation (bridge design, pressure vessels)
- Ultimate strength represents the maximum stress a material can withstand before fracture or failure
- Corresponds to the highest point on the stress-strain curve (tensile strength)
- indicates the stress and strain at which the material fails and separates into two or more pieces
- Sudden drop in stress on the stress-strain curve signifies the fracture event (broken glass, snapped cable)
- Ductile materials exhibit significant plastic deformation before fracture, while brittle materials fracture with little plastic deformation
- Ductility is characterized by the and reduction in cross-sectional area at fracture (copper vs ceramic)
Additional Elastic Properties and Time-Dependent Behavior
- describes a material's resistance to shear deformation, relating shear stress to shear strain
- quantifies a material's resistance to uniform compression, relating pressure to volumetric strain
- combines both elastic and viscous behavior, exhibiting time-dependent strain
- Materials like polymers can show both immediate elastic response and gradual deformation over time
- refers to the slow, continuous deformation of materials under constant stress, especially at elevated temperatures
- involves the progressive weakening of materials due to cyclic loading, even below the yield strength
Key Terms to Review (40)
Brittleness: Brittleness is a material property that describes the tendency of a solid material to fracture or break under stress, without undergoing any significant prior plastic deformation. It is a characteristic of materials that are unable to absorb much energy before failure occurs.
Bulk modulus: Bulk modulus is a measure of a material's resistance to uniform compression. It is defined as the ratio of pressure increase to the resulting relative decrease in volume.
Bulk Modulus: Bulk modulus is a measure of a material's resistance to uniform compression. It quantifies how much a material's volume decreases when subjected to a given increase in pressure, and is an important parameter in understanding the behavior of solids, liquids, and gases under compression.
Bulk strain: Bulk strain is the measure of deformation representing the fractional change in volume of a material under uniform pressure. It is calculated as the change in volume divided by the original volume.
Bulk stress: Bulk stress is the type of stress experienced by a material when it undergoes a uniform change in pressure, resulting in a change in volume. It is also known as volumetric or hydrostatic stress.
Compression Test: A compression test is a mechanical test used to evaluate the compressive strength and behavior of materials, particularly solids and rigid structures. It measures how a material or object responds to compressive forces applied to it.
Creep: Creep is the tendency of a solid material to slowly move or deform permanently under the influence of mechanical stresses. It is an important consideration in the design and analysis of structures and materials that are subjected to long-term loading or elevated temperatures.
Ductility: Ductility is the ability of a material to undergo plastic deformation, or to be drawn into a wire, without fracturing or breaking. It is a crucial property in the context of stress, strain, and elasticity, as well as the transition between elastic and plastic behavior in materials.
Elastic: Elasticity is the property of a material to return to its original shape after being deformed when the applied stress is removed. It is described quantitatively by the elastic modulus.
Elastic Deformation: Elastic deformation is a type of material response where a solid object or structure undergoes temporary changes in shape or size when subjected to an applied force, but returns to its original form and dimensions when the force is removed. This reversible deformation is a key characteristic of materials exhibiting elasticity.
Elastic limit: The elastic limit is the maximum stress that a material can withstand without permanently deforming. Beyond this point, the material will not return to its original shape when the stress is removed.
Elastic Limit: The elastic limit is the maximum stress a material can withstand before it begins to deform permanently. It marks the boundary between the elastic and plastic regions of a material's stress-strain curve, where the material will return to its original shape and size if the stress is removed.
Elasticity: Elasticity is a material property that describes the ability of a substance to deform under stress and then return to its original shape and size when the stress is removed. It is a fundamental concept in physics and engineering that governs the behavior of materials under various loading conditions.
Elongation: Elongation refers to the increase in length or dimension of an object or material when subjected to an applied force or stress. It is a fundamental concept in the study of elasticity and plasticity, which describe the behavior of materials under various loading conditions.
Fatigue: Fatigue is a state of physical and/or mental exhaustion that can impair an individual's ability to perform tasks effectively. It is a complex phenomenon that arises from a combination of physiological, psychological, and environmental factors, and can have significant implications in the context of elasticity and plasticity in materials.
Fracture Point: The fracture point is the point at which a material or structure experiences a complete loss of integrity, leading to a break or separation. This term is particularly relevant in the context of elasticity and plasticity, as it represents the critical stress or strain threshold beyond which a material can no longer withstand deformation and fails catastrophically.
Hooke's Law: Hooke's law is a fundamental principle in physics that describes the linear relationship between the force applied to an elastic object and the resulting deformation or displacement of that object. It is a crucial concept that underpins the understanding of various physical phenomena, including work, conservative and non-conservative forces, potential energy diagrams and stability, stress, strain, and elasticity, as well as simple harmonic motion.
Limit: A limit represents the maximum extent to which a material can be deformed without undergoing permanent deformation. It is the threshold beyond which elasticity ceases and plasticity begins.
Microplastic Deformation: Microplastic deformation refers to the microscopic-level changes in the shape and structure of plastic materials under the application of stress or external forces. This phenomenon is particularly important in the context of understanding the behavior and properties of plastics at the smallest scales, which is crucial for applications ranging from material science to environmental studies.
Necking: Necking is a phenomenon that occurs in materials under tensile stress, where a localized reduction in cross-sectional area develops, leading to the formation of a 'neck' in the material. This process is a critical aspect of the transition from elastic to plastic deformation in materials.
Newton per Square Meter: The newton per square meter (N/m²) is the unit of measurement for pressure, which is the force applied perpendicular to a surface divided by the area of that surface. This unit is crucial in understanding the concepts of stress, strain, and elasticity in the context of physics.
Pascal: A pascal (Pa) is the SI unit of pressure, defined as one newton per square meter. It is used to quantify internal pressure, stress, Young's modulus, and tensile strength.
Pascal: Pascal is a unit of pressure, named after the French mathematician and physicist Blaise Pascal. It is a fundamental concept in physics that is closely related to the study of stress, strain, elasticity, fluids, and hydraulics.
Plastic behavior: Plastic behavior is the permanent deformation of a material after the applied stress exceeds its yield strength. Unlike elastic behavior, plastic deformation is not reversible when the stress is removed.
Plastic Deformation: Plastic deformation is a permanent change in the shape or size of a material due to the application of external forces, where the material does not return to its original form when the forces are removed. This irreversible alteration of a material's structure is a key concept in understanding the behavior of materials under stress and strain.
Poisson's Ratio: Poisson's ratio is a measure of the Poisson effect, which describes the behavior of an elastic material when it is stretched or compressed. It quantifies the relationship between the lateral contraction and the longitudinal extension or compression of a material under uniaxial stress.
Proportional Limit: The proportional limit is the maximum stress a material can withstand before it begins to deform permanently. It marks the boundary between the elastic and plastic regions of a material's stress-strain curve, where the material's response transitions from being proportional and reversible to non-proportional and irreversible.
Robert Hooke: Robert Hooke was an English scientist, natural philosopher, and architect who made significant contributions to the fields of physics, biology, and engineering. He is particularly known for his work on the concepts of elasticity and plasticity, which are fundamental to understanding the behavior of materials under stress.
Shear Modulus: The shear modulus, also known as the modulus of rigidity, is a measure of a material's resistance to shear deformation. It quantifies the relationship between the applied shear stress and the resulting shear strain in a material, indicating its stiffness and ability to withstand distortion under shear forces.
Strain: Strain is a measure of the deformation or change in shape and size of an object or material under the application of a force or stress. It quantifies the relative change in the dimensions of an object compared to its original state.
Stress: Stress refers to the internal force exerted on an object or material, causing it to deform or change shape. It is a measure of the intensity of the internal forces acting within a material or structure, and it plays a crucial role in the study of the mechanical properties of materials and the design of structures.
Stress-Strain Curve: The stress-strain curve is a graphical representation that illustrates the relationship between the stress applied to a material and the resulting strain or deformation of that material. It is a fundamental tool used in the study of the mechanical properties of materials, particularly in the context of elasticity and plasticity.
Stress-strain diagram: A stress-strain diagram is a graphical representation of the relationship between the stress applied to a material and the resulting strain. It is used to understand the material's mechanical properties, including its elasticity and plasticity.
Tensile Test: A tensile test is a fundamental mechanical test used to determine the tensile properties of a material, such as its strength, ductility, and elasticity. It involves applying a gradually increasing force to a specimen until it breaks, providing valuable information about the material's behavior under tensile stress.
Ultimate Strength: Ultimate strength, also known as tensile strength, is the maximum stress a material can withstand before failing or breaking. It represents the point at which a material reaches its maximum load-bearing capacity and can no longer sustain additional stress without undergoing permanent deformation or fracture.
Ultimate stress: Ultimate stress is the maximum stress that a material can withstand before failing or fracturing. It is a critical value in understanding the strength and durability of materials under load.
Viscoelasticity: Viscoelasticity is a material property that describes the combined viscous and elastic behavior of a substance. It is the ability of a material to exhibit both solid-like and liquid-like characteristics when subjected to deformation or stress.
Work Hardening: Work hardening, also known as strain hardening, is a phenomenon in materials science where a metal or alloy becomes stronger and more resistant to deformation as a result of plastic deformation. This process occurs when the material is subjected to mechanical stress, causing dislocations in the crystal structure to accumulate, leading to an increase in the material's strength and hardness.
Yield Strength: Yield strength is the stress at which a material begins to deform plastically. It is the point on the stress-strain curve where the material transitions from elastic to plastic behavior, marking the limit of a material's ability to recover its original shape and size upon the removal of an applied load.
Young's Modulus: Young's modulus, also known as the modulus of elasticity, is a measure of a material's resistance to elastic deformation under tensile or compressive stress. It quantifies the relationship between the stress applied to a material and the resulting strain, providing a fundamental understanding of a material's mechanical properties.