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Materials Science & Properties Cheat Sheet
A printable reference covering stress, strain, Young’s modulus, density, toughness, hardness, and thermal expansion for grades 9-12.
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Materials science studies how a material’s structure affects its properties and performance in engineering designs. This cheat sheet helps students compare metals, polymers, ceramics, composites, and semiconductors using measurable properties. Engineers use these ideas to choose safe, efficient, and cost-effective materials for bridges, tools, vehicles, electronics, and medical devices. The most important ideas include stress, strain, stiffness, strength, toughness, hardness, density, and thermal expansion. Key formulas connect force, area, length change, volume, mass, and temperature change. A stress-strain curve shows how a material responds from elastic behavior to plastic deformation and failure. Good material selection balances performance requirements, manufacturing limits, cost, safety, and environmental impact.
Key Facts
- Stress measures internal force per area and is calculated as stress = force / cross-sectional area.
- Strain measures relative deformation and is calculated as strain = change in length / original length.
- Young’s modulus measures stiffness in the elastic region and is calculated as E = stress / strain.
- Density describes mass per volume and is calculated as density = mass / volume.
- Thermal expansion of a solid length is estimated by change in length = coefficient of linear expansion x original length x change in temperature.
- Toughness is the ability of a material to absorb energy before breaking, while hardness is resistance to scratching, indentation, or wear.
- Ductile materials deform noticeably before fracture, while brittle materials fracture with little plastic deformation.
- Material selection should match properties to the job, including strength, stiffness, weight, corrosion resistance, temperature range, manufacturability, and cost.
Vocabulary
- Stress
- Stress is the force applied to a material divided by the area over which the force acts.
- Strain
- Strain is the fractional change in shape or length of a material caused by stress.
- Young’s Modulus
- Young’s modulus is a measure of stiffness equal to stress divided by strain in the elastic region.
- Yield Strength
- Yield strength is the stress at which a material begins to deform permanently.
- Toughness
- Toughness is the ability of a material to absorb energy and deform before fracturing.
- Composite
- A composite is a material made by combining two or more materials to obtain improved properties.
Common Mistakes to Avoid
- Confusing strength with stiffness is wrong because strength describes resistance to failure, while stiffness describes resistance to elastic deformation.
- Using force instead of stress is wrong because the same force can cause different effects depending on the cross-sectional area.
- Treating elastic and plastic deformation as the same is wrong because elastic deformation is reversible, while plastic deformation is permanent.
- Assuming the densest material is always strongest is wrong because strength depends on bonding, microstructure, processing, and defects, not just mass per volume.
- Ignoring operating temperature is wrong because materials can soften, become brittle, expand, creep, or lose strength when temperature changes.
Practice Questions
- 1 A metal rod with cross-sectional area 0.002 m2 carries a tensile force of 500 N. What is the stress in the rod?
- 2 A 2.0 m polymer strip stretches by 0.010 m under load. What is its strain?
- 3 A material has stress 120 MPa and strain 0.002 in the elastic region. What is Young’s modulus?
- 4 Why might an engineer choose an aluminum alloy instead of steel for an aircraft part even if some steels are stronger?