12.3 Stress, Strain, and Elastic Modulus
3 min read•june 24, 2024
When materials face forces, they experience and . Stress is the internal force per unit area, while is the resulting . Understanding these concepts helps us grasp how materials behave under different loads.
Calculating stress, strain, and lets us predict material behavior. We can determine if a material will return to its original shape or deform permanently. This knowledge is crucial for designing structures and choosing materials for various applications.
Stress, Strain, and Elastic Modulus
Concepts of stress and strain
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- Stress refers to the internal force per unit area within a material, measured in Pascals (Pa) or Newtons per square meter (N/m²)
- occurs when a material is stretched or pulled apart, causing the material to elongate ()
- occurs when a material is compressed or pushed together, causing the material to shorten ()
- occurs when a material is subjected to uniform from all directions, causing a change in volume ()
- occurs when a material is subjected to forces that cause adjacent layers to slide past each other ()
- Strain describes the or change in shape of a material due to an applied force
- occurs when a material is stretched, causing an increase in length (stretching a rubber band)
- occurs when a material is compressed, causing a decrease in length (squeezing a )
- occurs when a material undergoes a change in volume due to uniform pressure (inflating a )
- occurs when a material undergoes angular deformation due to (bending a book)
Calculations for stress and strain
- Stress can be calculated using the formula , where is the force applied to the material in Newtons and is the cross-sectional area of the material in square meters
- Example: A 100 N force applied to a material with a cross-sectional area of 0.01 m² results in a stress of 10,000 Pa or 10 kPa
- Strain can be calculated using the formula , where is the change in length of the material in meters and is the original length of the material in meters
- Example: A material with an original length of 1 m is stretched by 0.05 m, resulting in a strain of 0.05 or 5%
- () is a measure of a material's stiffness or resistance to elastic deformation, calculated using the formula and measured in Pascals (Pa) or Newtons per square meter (N/m²)
- Example: A material with a stress of 100 MPa and a strain of 0.01 has an elastic modulus of 10 GPa
Material properties and deformation
- is the maximum stress a material can withstand without permanent deformation
- Materials that experience stress below their will return to their original shape when the force is removed (rubber band)
- Materials that experience stress above their elastic limit will not return to their original shape when the force is removed (bent paperclip)
- is permanent deformation that occurs when a material is subjected to stress beyond its elastic limit
- Example: A metal wire that is bent and remains bent even after the force is removed has undergone plastic deformation
- Brittle materials undergo little or no plastic deformation before fracturing, such as glass, ceramics, and some metals at low temperatures ()
- Ductile materials can undergo significant plastic deformation before fracturing, such as many metals at room temperature (, )
Material behavior under stress
- is the stress level at which a material begins to deform plastically
- occurs when a material completely fails and separates into pieces due to excessive stress
- is a property of materials that exhibit both viscous and elastic characteristics when undergoing deformation
- is the tendency of a solid material to slowly deform permanently under the influence of persistent mechanical stresses
Key Terms to Review (58)
Aluminum: Aluminum is a lightweight, silvery-white metal that is highly malleable, ductile, and corrosion-resistant. It is the most abundant metallic element in the Earth's crust and is widely used in various industries due to its unique properties.
Balloon: A balloon is an inflatable, flexible container that is filled with a gas, typically air or helium, and is used for various purposes such as decorative displays, scientific research, and transportation. Balloons are often associated with the concepts of stress, strain, and elastic modulus in the context of physics and engineering.
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 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 Strain: Bulk strain is a measure of the deformation or change in volume experienced by a material under applied stress. It quantifies the relative change in the overall size or dimensions of a material as a result of the forces acting upon it.
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.
Bulk Stress: Bulk stress, also known as hydrostatic stress, is the uniform pressure exerted on a material or object from all directions. It is a fundamental concept in the study of stress, strain, and elastic modulus, as it describes the internal forces acting on a body in a state of equilibrium under external loading.
Cast Iron: Cast iron is a type of iron alloy that is produced by melting iron and other elements, such as carbon, silicon, and manganese, and then pouring the molten mixture into a mold to create a specific shape. It is known for its high strength, durability, and ability to retain heat, making it a popular material for various applications, including cookware, machinery, and construction.
Compressive Strain: Compressive strain is a measure of the deformation experienced by a material when it is subjected to a compressive stress. It quantifies the fractional change in the dimensions of an object under compressive loading, reflecting the material's ability to resist being squeezed or compressed.
Compressive stress: Compressive stress is the internal force per unit area that tends to reduce the length of a material along the direction of the applied force. It is measured in pascals (Pa) or newtons per square meter (N/m²).
Compressive Stress: Compressive stress is the internal force exerted on a material or structure that tends to reduce its size or compress it. It is a type of stress that acts perpendicular to the surface of an object, pushing the material inward and causing it to deform or fail under the applied load.
Copper: Copper is a reddish-brown metallic element that is an excellent conductor of heat and electricity. It is a crucial material in various applications, particularly in the context of stress, strain, and elastic modulus, which are important concepts in physics and engineering.
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.
Deck of Cards: A deck of cards is a standard set of playing cards that typically consists of 52 cards divided into four suits - spades, hearts, diamonds, and clubs. The deck is a fundamental tool used in various card games and can be utilized to illustrate concepts related to stress, strain, and elastic modulus in the context of physics.
Deep-Sea Submersible: A deep-sea submersible is a specialized underwater vehicle designed to operate at great depths, often reaching thousands of meters below the ocean's surface. These highly advanced machines allow researchers and explorers to study the unique ecosystems and geological features found in the deep ocean.
Deformation: Deformation is the change in shape or size of an object due to applied forces. It can be temporary (elastic) or permanent (plastic) based on the material properties and magnitude of the force.
Deformation: Deformation is the change in the shape or size of an object due to the application of a force or stress. It is a fundamental concept in physics that describes how materials respond to external forces, and it is essential for understanding various topics, including friction, collisions, and the behavior of solids under stress.
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 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.
Elastic Modulus: The elastic modulus, also known as Young's modulus, is a measure of a material's stiffness and its ability to resist deformation under stress. It quantifies the relationship between the stress applied to a material and the resulting strain or deformation within the material's elastic range.
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.
Elasticity Limit: The elasticity limit, also known as the yield point, is the maximum stress a material can withstand before it begins to deform plastically and lose its ability to return to its original shape and size. This concept is crucial in understanding the behavior of materials under stress, as it defines the boundary between elastic and plastic deformation.
Fracture: A fracture is the breaking or cracking of a hard material, such as bone or a solid object, due to the application of stress or force that exceeds the material's strength. It is a crucial concept in the context of understanding stress, strain, and elastic modulus in physics.
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.
I-beams: I-beams are structural elements with an I-shaped cross-section, designed to bear high loads. Their geometry provides a high moment of inertia, making them efficient in resisting bending and deflection.
Modulus: Modulus, or elastic modulus, is a measure of a material's ability to resist deformation under stress. It quantifies the stiffness of a material.
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.
Normal pressure: Normal pressure is the component of force per unit area exerted perpendicular to the surface of an object. It is a crucial factor in understanding how forces are distributed across surfaces in static equilibrium.
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 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.
Pressure: Pressure is the force exerted per unit area. It is typically measured in Pascals (Pa) or atmospheres (atm).
Rubber Band: A rubber band is a loop of elastic material, typically made from natural or synthetic rubber, that is used to store mechanical energy and provide a restoring force when stretched or deformed. It is a common everyday object that demonstrates the principles of stress, strain, and elastic modulus in the context of physics.
Shear: Shear refers to the deformation of a material where parallel planes slide past one another. It occurs when forces are applied tangentially to a surface.
Shear modulus: The shear modulus is a measure of a material's ability to resist shear deformation. It quantifies the ratio of shear stress to shear strain.
Shear Strain: Shear strain is a measure of the deformation of a material or structure when subjected to a shear stress. It quantifies the angular change in the shape of an object due to the application of a force that causes the material to slide in opposite directions parallel to the face of the object.
Shear stress: Shear stress is a type of stress that occurs when forces are applied parallel or tangential to a material's surface, causing layers within the material to slide past each other. It is calculated as the force applied divided by the area over which it acts.
Shear Stress: Shear stress is the component of stress coplanar with a material cross-section. It is the stress that arises from the force pushing one part of a material in one direction and another part in the opposite direction. Shear stress is a crucial concept in the understanding of stress, strain, and elastic modulus, as well as viscosity and turbulence in fluid dynamics.
Sponge: A sponge is a porous, marine invertebrate animal that lacks specialized organs and tissues. It is characterized by a skeletal structure that provides support and a means of filtering water to obtain food and oxygen.
Spring: A spring is an elastic object that stores mechanical energy when it is stretched or compressed. It is a device that can store and release energy, and it is commonly used in various mechanical systems to provide force, absorb shock, or control motion.
Strain: Strain is the measure of deformation representing the displacement between particles in a material body. It is dimensionless and often expressed as a fraction or percentage.
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.
Tensile strain: Tensile strain is the measure of deformation representing the elongation of a material under tensile stress. It's calculated as the change in length divided by the original length.
Tensile Strain: Tensile strain is a measure of the deformation of a material subjected to tensile stress, which is the force acting to elongate or stretch the material. It quantifies the relative change in the length of an object when a tensile force is applied, providing insight into the material's response to applied stress.
Tensile stress: Tensile stress is the internal force per unit area that resists elongation or stretching in a material when an external force is applied. It is calculated as the force divided by the cross-sectional area perpendicular to the force.
Tensile Stress: Tensile stress is a type of stress that occurs when a material is subjected to pulling or stretching forces, causing it to experience internal forces that try to pull the material apart. It is a fundamental concept in the study of stress, strain, and elastic modulus.
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.
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.
Volume stress: Volume stress is the type of stress applied uniformly in all directions on a body, resulting in a change in its volume. It is mathematically expressed as the ratio of force exerted to the surface area over which it acts.
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 Point: The yield point is the point on a stress-strain curve where a material transitions from elastic deformation to plastic deformation. It marks the stress level at which a material begins to permanently change shape without the ability to return to its original form.
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 elastic modulus, is a measure of the stiffness of a solid material. It quantifies the relationship between tensile stress and strain in a material.
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.