Hardness numbers, while derived from different testing methodologies, are generally related through their measurement of a material's resistance to permanent deformation. While no direct, universal mathematical equivalence exists across all scales, empirical relationships and conversion charts facilitate their comparison, especially for similar material types and within specific hardness ranges.
Understanding Hardness Numbers
A material's hardness fundamentally describes its resistance to localized plastic deformation, such as indentation. At its core, a hardness number is defined as the force applied by an indenter divided by the area of contact between the indenter and the specimen. The various types of hardness tests primarily differ in the shape and size of the indenter, and the magnitude of the applied force. For a specific indenter geometry and applied force, the resulting indent size directly reflects the material's resistance to plastic deformation, providing a quantifiable hardness value.
Common Hardness Scales and Their Principles
Different hardness tests have been developed to suit various materials, thicknesses, and application requirements. Each method uses a distinct approach:
- Brinell Hardness (HB/HBW): This test employs a large, hardened steel or tungsten carbide ball indenter under a high load. The Brinell hardness number is calculated by measuring the diameter of the permanent indentation left on the material's surface. It's often used for materials with rough surfaces or those that exhibit macroscopic non-homogeneity.
- Rockwell Hardness (HR): The Rockwell test measures the depth of penetration of an indenter under a minor and then a major load. It offers various scales (e.g., HRC, HRB, HRA), each using a specific indenter (diamond cone or steel ball) and load combination, making it versatile for a wide range of materials from very soft to very hard.
- Vickers Hardness (HV): Utilizing a square-based diamond pyramid indenter, the Vickers test measures the diagonals of the resulting square-shaped indentation. Its key advantage is that it can be used for almost all metals and provides a very wide hardness range, from micro-loads for thin coatings to macro-loads for bulk materials.
- Knoop Hardness (HK): Similar to Vickers, the Knoop test uses an elongated diamond pyramid indenter. This design creates a very shallow, rhombic indentation, making it ideal for measuring the hardness of very thin materials, surface coatings, or individual microstructural constituents where minimal penetration depth is desired.
The Relationship: Empirical Conversions, Not Direct Equivalence
Due to the fundamental differences in indenter geometry, applied loads, and measurement techniques, the hardness numbers from various scales are not directly interchangeable through a simple, universal mathematical formula. Instead, relationships are established through extensive empirical testing, leading to:
- Conversion Tables: Widely published tables, such as those found in ASTM E140 (Standard Hardness Conversion Tables for Metals), provide approximate conversions between different scales for specific material groups (e.g., steels, aluminum alloys, copper alloys).
- Empirical Formulas: Some specific formulas exist for narrow ranges or particular materials, often derived from regression analysis of experimental data.
It's crucial to understand these key aspects of hardness conversion:
- Approximation, Not Exact: Conversions are approximations. They are most accurate for materials with similar characteristics and within specific hardness ranges. Expect some degree of deviation from directly measured values.
- Material Dependence: The relationship between scales varies significantly depending on the material's elastic modulus, yield strength, strain hardening exponent, and other microstructural features. A conversion valid for a specific type of steel may not be accurate for an aluminum alloy or a ceramic.
- Hardness Range: Conversions are typically more reliable within the mid-range of each scale. At very high or very low hardness values, where the material's response to indentation might deviate, discrepancies can increase.
Practical Considerations for Hardness Conversion
When working with different hardness scales, consider these practical insights:
- Consult Industry Standards: Always refer to recognized industry standards (e.g., ISO 18265 or ASTM E140) for the most reliable and applicable conversion data. These standards often provide specific tables for different material classes.
- Material Specificity: Use conversion charts specifically developed for the exact material you are testing. Generic charts can lead to significant errors.
- Application Context: Understand that converted values might not always meet strict engineering specifications. When a precise hardness value is critical, it should ideally be measured directly using the specified test method.
- Load Dependence: For some materials and tests, conversions might be sensitive to the applied load, particularly in microhardness testing where material anisotropy or surface effects become more prominent.
Illustrative Hardness Conversion Table (Example for Steels)
The table below provides a highly simplified example of approximate hardness conversions for common carbon and alloy steels. Actual conversion tables are far more extensive and specific.
| Vickers (HV) | Brinell (HBW) | Rockwell C (HRC) | Rockwell B (HRB) | Approximate Tensile Strength (MPa) |
|---|---|---|---|---|
| 150 | 143 | - | 79 | 500 |
| 200 | 190 | - | 92 | 650 |
| 300 | 285 | 30 | - | 1000 |
| 400 | 380 | 40 | - | 1300 |
| 500 | 475 | 49 | - | 1650 |
| 600 | 570 | 55 | - | 2000 |
Note: This table provides approximate relationships for carbon and alloy steels and should be used for general guidance only. Consult specific material standards and comprehensive conversion tables for precise conversions.
Why Multiple Scales?
The existence of numerous hardness scales reflects the diverse requirements of material testing. No single test is optimal for all scenarios. For example, the Brinell test is excellent for heterogeneous materials, Rockwell is fast for production environments, Vickers offers precision over a wide range of loads, and Knoop is perfect for delicate or very thin samples. Each scale fulfills a specific need, and their relationships allow for a comprehensive understanding of material properties across different testing contexts.
