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ABI® Measured Properties — Definitions

Scientifically cited definitions for every mechanical property determined by the ABI® test.

Yield Strength

The stress at which a material begins to deform plastically. Below the yield point, the material will deform elastically and return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible. ABI® reports yield strength at the 0.2% offset defined by ASTM E8, computed from the true stress-strain curve derived from the indentation load-displacement data.

ASTM E8/E8M — Standard Test Methods for Tension Testing of Metallic Materials; Dieter, G.E., Mechanical Metallurgy, 3rd ed., McGraw-Hill, 1986.

True Stress-Strain Curve

A graphical representation of the relationship between true stress (load divided by instantaneous cross-sectional area) and true strain (the natural logarithm of the ratio of instantaneous to original length). Unlike engineering stress-strain curves, true stress-strain accounts for the continuous change in cross-sectional area during deformation. ABI® derives this curve from multiple indentation load-unload cycles using elasticity and plasticity theories.

Haggag, F.M., 'Field Indentation Microprobe for Structural Integrity Evaluation,' U.S. Patent No. 4,852,397, 1989; Tabor, D., The Hardness of Metals, Oxford University Press, 1951.

Strain-Hardening Exponent (n)

A material constant in the Hollomon power-law relationship (σ = Kεⁿ) that describes the rate at which a metal hardens with plastic deformation. A higher n value indicates greater work hardening and typically better formability. ABI® determines n from the slope of the log-log plot of true stress versus true plastic strain derived from indentation data.

Hollomon, J.H., 'Tensile Deformation,' Transactions of AIME, Vol. 162, 1945, pp. 268–290; ASTM E646 — Standard Test Method for Tensile Strain-Hardening Exponents.

Uniform Ductility

The maximum uniform plastic strain a material can sustain before localized necking begins, corresponding to the strain at ultimate tensile strength. It is a critical measure of a material's ability to distribute deformation evenly. In ABI® testing, uniform ductility is calculated from the strain-hardening exponent, as the onset of necking instability occurs when the strain equals the strain-hardening exponent (εu = n) per the Considère criterion.

Considère, A., 'Mémoire sur l'emploi du fer et de l'acier dans les constructions,' Annales des Ponts et Chaussées, Vol. 9, 1885; Dieter, G.E., Mechanical Metallurgy, 3rd ed., McGraw-Hill, 1986.

Ultimate Tensile Strength

The maximum engineering stress a material can withstand before necking begins. It represents the peak of the engineering stress-strain curve and is a fundamental property used in structural design, material specification, and fitness-for-service assessments. ABI® determines UTS from the true stress-strain curve using the relationship between the strength coefficient, strain-hardening exponent, and the Considère necking criterion.

ASTM E8/E8M — Standard Test Methods for Tension Testing of Metallic Materials; Haggag, F.M., et al., 'Use of Automated Ball Indentation Testing to Measure Flow Properties and Estimate Fracture Toughness in Metallic Materials,' ASTM STP 1092, 1990.

Strength Coefficient (K)

The constant K in the Hollomon power-law equation (σ = Kεⁿ), representing the true stress at a true plastic strain of unity. It characterizes the overall strength level of the material in the plastic range. Together with the strain-hardening exponent, it fully defines the plastic flow behavior. ABI® determines K from the intercept of the log-log true stress versus true plastic strain relationship.

Hollomon, J.H., 'Tensile Deformation,' Transactions of AIME, Vol. 162, 1945, pp. 268–290; Haggag, F.M., U.S. Patent No. 4,852,397, 1989.

Lüders Strain

The heterogeneous plastic strain that occurs at approximately constant stress immediately after yielding in certain metals, particularly low-carbon and HSLA steels. It manifests as visible bands of localized deformation (Lüders bands) that propagate across the specimen. ABI® testing can detect and quantify Lüders strain from the plateau region in the indentation-derived stress-strain curve, which is important for pipeline grade classification and formability assessment.

Hall, E.O., 'Yield Point Phenomena in Metals and Alloys,' Plenum Press, 1970; Haggag, F.M., et al., ASTM STP 1092, 1990.

Fracture Toughness (KJc)

The critical stress intensity factor derived from J-integral values at cleavage fracture initiation, converted to its equivalent K value (KJc = √(J·E/(1−ν²))). It quantifies a material's resistance to crack propagation and is the single most critical property for structural integrity assessment of components containing flaws. ABI® determines fracture toughness using a correlation between indentation-derived flow properties and critical J-integral values, validated against destructive compact-tension specimen data.

Haggag, F.M., 'In-Situ Measurements of Mechanical Properties Using Novel Automated Ball Indentation System,' ASTM STP 1204, 1993; ASTM E1921 — Standard Test Method for Determination of Reference Temperature, T₀.

Fracture Toughness Master Curve

A statistical model defined by ASTM E1921 that describes the temperature dependence of cleavage fracture toughness in ferritic steels within the ductile-to-brittle transition region. The master curve is fully characterized by a single parameter — the reference temperature T₀ — and provides median, 5%, and 95% probability bounds for fracture toughness as a function of temperature. ABI® testing determines the master curve by computing T₀ from indentation-measured flow properties.

Wallin, K., 'The Scatter in KIc Results,' Engineering Fracture Mechanics, Vol. 19, No. 6, 1984; ASTM E1921 — Standard Test Method for Determination of Reference Temperature, T₀, for Ferritic Steels in the Transition Range.

Reference Temperature (T₀)

The temperature at which the median fracture toughness of a ferritic steel equals 100 MPa√m for a 1T (25 mm thick) specimen, as defined by ASTM E1921. T₀ anchors the master curve and enables prediction of fracture toughness at any temperature in the transition region. A lower T₀ indicates greater resistance to brittle fracture at low temperatures. ABI® determines T₀ nondestructively from room-temperature indentation tests, providing conservative estimates validated against destructive compact-tension specimen results.

ASTM E1921 — Standard Test Method for Determination of Reference Temperature, T₀, for Ferritic Steels in the Transition Range; Haggag, F.M., et al., 'Structural Integrity Evaluation Based on an Innovative Field Indentation Microprobe,' ASTM STP 1204, 1993.

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