Formula and Method for the Charpy/Izod Impact Test
A pendulum impact test measures the energy a material absorbs when it fractures under a sudden, high-strain-rate blow rather than a slow, steady load. A hammer of known mass swings from a fixed release height, strikes and breaks a notched specimen at the bottom of its arc, then continues swinging up the far side. The height it fails to reach on the far side is a direct measure of the energy the specimen consumed while breaking: E = mgL(cosβ − cosα), where m is the hammer mass, L is the pendulum arm length (the radius from the pivot to the hammer's center of percussion), α is the release angle measured from the vertical rest position, and β is the rebound angle measured the same way.
How the calculation works
Before release, the hammer sits at angle α from the vertical rest position, giving it a height h₁ = L(1 − cos α) above the specimen. All of that potential energy converts to kinetic energy at the bottom of the swing, where the hammer strikes and breaks the specimen. Whatever energy remains carries the hammer up the far side to angle β, a height of h₂ = L(1 − cos β). The difference, mg(h₁ − h₂), is the energy the specimen absorbed — algebraically that simplifies to mgL(cosβ − cosα), which the calculator applies directly. Dividing that energy by the fractured cross-sectional area beneath the notch gives the impact (notch) toughness, an intensive property that lets you compare specimens of different sizes.
Common mistakes
- Angle reference confusion: both α and β are measured from the same vertical reference — the specimen's position at the bottom of the swing — not from horizontal and not from each other.
- Using the wrong length: the arm length L is the effective radius to the hammer's center of percussion, not the full pendulum length; testing-machine manuals usually list this radius next to the hammer's rated capacity.
- Forgetting to subtract the notch: toughness uses the remaining ligament area beneath the notch (commonly 80 mm² for a standard 55×10×10 mm bar with a 2 mm V-notch), not the full 10×10 mm cross-section.
- Reporting energy without temperature: Charpy energy for steels changes sharply near the ductile-to-brittle transition temperature, so a bare joule value without a stated test temperature is not comparable across labs.
Real-world applications
- Bridge, pressure-vessel, and structural steel codes specify a minimum Charpy V-notch energy at a minimum service temperature to guard against brittle fracture.
- Pipeline steel grades are qualified with a full Charpy energy-versus-temperature transition curve, not a single-point test.
- Polymer and composite impact ratings (often Izod-style) use the same pendulum-energy method to compare material toughness for enclosures and consumer products.
- Production quality control uses Charpy energy as a fast, low-cost proxy for fracture toughness where slower fracture-mechanics testing is impractical.