When materials face forces, they experience stress and strain. Stress is the internal force per unit area, while strain is the resulting deformation. Understanding these concepts helps us grasp how materials behave under different loads.
Calculating stress, strain, and elastic modulus 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
- Stress refers to the internal force per unit area within a material, measured in Pascals (Pa) or Newtons per square meter (N/m²)
- Tensile stress occurs when a material is stretched or pulled apart, causing the material to elongate (rubber band)
- Compressive stress occurs when a material is compressed or pushed together, causing the material to shorten (spring)
- Bulk stress occurs when a material is subjected to uniform pressure from all directions, causing a change in volume (deep-sea submersible)
- Shear stress occurs when a material is subjected to forces that cause adjacent layers to slide past each other (deck of cards)
- Strain describes the deformation or change in shape of a material due to an applied force
- Tensile strain occurs when a material is stretched, causing an increase in length (stretching a rubber band)
- Compressive strain occurs when a material is compressed, causing a decrease in length (squeezing a sponge)
- Bulk strain occurs when a material undergoes a change in volume due to uniform pressure (inflating a balloon)
- Shear strain occurs when a material undergoes angular deformation due to shear stress (bending a book)
Calculations for stress and strain
- Stress can be calculated using the formula $\text{Stress} = \frac{F}{A}$, where $F$ is the force applied to the material in Newtons and $A$ 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 $\text{Strain} = \frac{\Delta L}{L_0}$, where $\Delta L$ is the change in length of the material in meters and $L_0$ 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%
- Elastic modulus (Young's modulus) is a measure of a material's stiffness or resistance to elastic deformation, calculated using the formula $\text{Elastic modulus} = \frac{\text{Stress}}{\text{Strain}}$ 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
- Elastic limit is the maximum stress a material can withstand without permanent deformation
- Materials that experience stress below their elastic limit 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)
- Plastic deformation 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 (cast iron)
- Ductile materials can undergo significant plastic deformation before fracturing, such as many metals at room temperature (copper, aluminum)
Material behavior under stress
- Yield point is the stress level at which a material begins to deform plastically
- Fracture occurs when a material completely fails and separates into pieces due to excessive stress
- Viscoelasticity is a property of materials that exhibit both viscous and elastic characteristics when undergoing deformation
- Creep is the tendency of a solid material to slowly deform permanently under the influence of persistent mechanical stresses