Knoop Hardness Number (HK): Microhardness for Brittle Materials and Thin Coatings
The Knoop hardness number (HK) quantifies the resistance of brittle materials and thin coatings to indentation by an elongated diamond pyramid. Unlike the square-based Vickers indenter, the Knoop diamond has an aspect ratio of about 7:1, producing a shallow indentation with a long diagonal. This geometry minimises cracking and substrate influence, making HK a preferred metric for ceramics, glasses, hard carbides, and surface-engineered layers.
Keep the Vickers article handy to compare testing parameters, and use the force converter when configuring microhardness loads.
Definition and Calculation
HK formula and units
The Knoop hardness number is defined as the applied test load divided by the projected area of the indentation. Testing standards express the load P in kilogram-force and the long diagonal L in millimetres, giving HK = 14.229 × P / L². The constant 14.229 reflects the indenter’s projected-area factor of 0.070 279. When machines report load in newtons, convert using P = F / 9.806 65; equivalently, multiplying HK (in kgf·mm⁻²) by 9.807 yields the value in megapascals for direct comparison with stress-based design calculations. Because the indentation is shallow, the measurement reflects near-surface hardness without significantly penetrating underlying substrates.
Comparing HK and HV values
For isotropic materials, Knoop and Vickers numbers correlate closely. Empirical relations such as HK ≈ 0.927 HV provide quick conversions, though exact factors depend on anisotropy and load. Testing standards often require reporting both HK and HV when qualifying coatings, enabling benchmarking across laboratories. When converting to SI pressure units, multiply HK by 9.807 to obtain megapascals, aligning results with stress-based design calculations discussed in the Young’s modulus overview.
Historical Development
Origin of the Knoop test
The Knoop indenter was developed in 1939 by Frederick Knoop and colleagues at the U.S. National Bureau of Standards. Their goal was to characterise brittle materials and thin layers that fractured under traditional Vickers indentation. By stretching the indenter along one axis, they reduced penetration depth while maintaining measurable diagonals. The approach quickly gained traction in glass science, dental research, and metallography.
Standardisation and widespread adoption
ASTM E384 and ISO 4545 govern Knoop microhardness testing, detailing indenter specifications, load ranges (typically 10 g to 1 kg), and measurement procedures. Advances in automated microhardness testers and digital imaging software have improved repeatability, enabling high-throughput mapping of hardness gradients in advanced materials. Today, HK appears alongside nanoindentation metrics in quality control and research publications.
Testing Concepts and Best Practices
Load selection and indentation spacing
Proper load selection balances measurable indentation size with minimal cracking. Softer coatings may require loads below 25 g, whereas dense ceramics tolerate heavier loads without spalling. Indent spacing should exceed three times the long diagonal to avoid interaction between plastic zones. Surface preparation is crucial: polishing to 0.25 µm diamond finish reduces roughness that could distort the elongated impression.
Imaging and measurement accuracy
Knoop impressions are measured along the long diagonal using optical microscopes or digital cameras. Calibration with stage micrometers ensures scale accuracy. Automated image analysis improves repeatability, but operators must verify edge detection on brittle materials where cracks or chipping can mislead algorithms. Reporting should include both diagonals, load, dwell time, and any observed cracking to provide full context for HK values.
Applications in Modern Materials Engineering
Ceramics and glass
Engineers use Knoop hardness to evaluate alumina, zirconia, silicon carbide, and glass formulations. The elongated imprint minimises catastrophic cracking, enabling comparative studies of grain size, sintering conditions, and dopants. Dental enamel and restorative ceramics are routinely characterised with HK to assess wear resistance and acid etching protocols.
Thin films and diffusion coatings
Thermal barrier coatings, PVD nitride layers, and carburised surfaces demand shallow penetration tests. Knoop hardness maps reveal gradients in hardness through multilayer stacks, guiding process adjustments for turbine blades, cutting tools, and microelectronics. Pairing HK data with sheet resistance measurements provides a fuller picture of film performance.
Additive manufacturing and research labs
Additively manufactured metals and ceramics often exhibit anisotropic microstructures. Knoop testing can orient the long diagonal along specific microstructural directions, exposing directional dependencies in hardness. Researchers combine HK with nanoindentation and microscopy to validate heat treatment schedules and post-processing techniques.
Importance for Quality Assurance and Design
Process control and certification
Aerospace, medical device, and semiconductor suppliers rely on Knoop hardness to certify coatings and substrates. Documented HK values support process qualification reports, while statistical process control charts highlight drift in heat treatments or deposition parameters. When combined with modulus and toughness data, hardness informs wear predictions and failure analyses.
Design integration and modelling
Designers incorporate HK-derived yield proxies into finite element models of contact events, such as ball-on-disc wear tests or indentation of microcomponents. Converting HK to stress units allows coupling with elastic-plastic material models, ensuring simulations align with empirical performance. Multi-physics analyses that link hardness with thermal or electrical behaviour benefit from shared datasets with tools like the spring force calculator to verify fixture mechanics.
By mastering the Knoop scale, engineers gain a sensitive probe for near-surface mechanical properties, enabling durable designs in demanding environments from turbine engines to biomedical implants.