Proof strength at specified plastic extension (Rp, most commonly Rp0.2) is the standard yield criterion for metallic materials that do not exhibit a distinct yield point, and it is measured during a uniaxial tensile test with a verified extensometer attached to the specimen gauge length. This parameter underpins material acceptance decisions for structural steels, aluminum alloys, stainless steels, and many other metals tested in accordance with ISO 6892-1, ASTM E8/E8M, GB/T 228.1, and JIS Z 2241. This article explains the principle, instrumentation, sample requirements, test procedure, data reduction, and typical applications of extensometer-based determination of proof strength in accredited third-party laboratories.
Technical Overview
Proof strength, plastic extension (denoted Rp and subscripted with the specified plastic extension value, e.g., Rp0.2) is defined as the stress at which the plastic extension of a tensile specimen equals a specified percentage of the original gauge length. In practical terms, Rp0.2 is the stress at which the material has accumulated a permanent (plastic) elongation of 0.2 % of the gauge length. It is calculated as the force at this condition divided by the original cross-sectional area S0 of the test piece.
Many industrially important materials, such as high-strength low-alloy steels, solution-treated stainless steels, aluminum alloys, titanium alloys, and copper alloys, show a smooth, continuous transition from elastic to plastic behavior on the stress-strain curve with no visible yield plateau. For these materials, the upper and lower yield strengths (ReH, ReL) cannot be determined, so the offset proof strength Rp is used as the engineering yield criterion in product specifications, design codes, and acceptance testing.
Because Rp is defined in terms of a small extension (for a 50 mm gauge length, 0.2 % plastic extension corresponds to only 0.1 mm), its accurate determination requires direct measurement of extension within the gauge length using an extensometer. The extensometer must be verified and classified, typically to Class 1 or better according to ISO 9513 (or Class B-1 according to ASTM E83), while the force measuring system of the testing machine must comply with ISO 7500-1 or ASTM E4. Extensometer-based Rp determination is therefore a combined metrology and mechanical testing task in which instrument class, gauge length, strain rate, and alignment all directly influence the result.
Testing Samples
Determination of Rp by extensometry can be performed on virtually any metallic material that can be prepared as a tensile test piece. Typical sample forms submitted to testing laboratories include the following:
Machined Round Tensile Specimens
Turned cylindrical test pieces with parallel length, fillets, and threaded or shouldered ends. Proportional test pieces with a gauge length of L0 = 5.65 × √S0 (approximately 5 diameters) or L0 = 11.3 × √S0 are most common, in diameters such as 5 mm, 6.25 mm, 8 mm, 10 mm, 12.5 mm, and 20 mm depending on the product form and standard.
Flat Rectangular Specimens
Flat test pieces taken from sheet, strip, and plate in the rolling direction (longitudinal) or transverse direction. Because the reduced section width must remain constant, care is taken to ensure edge quality and freedom from burrs that could cause premature cracking. The extensometer gauge length is set equal to L0 within the reduced section.
Wire, Bar, and Profile Specimens
Full-section test pieces of wire, rod, and bars where the gauge length is marked directly on the as-received product. For very small sections, miniature extensometers or non-contact extensometers may be required to achieve adequate resolution of the 0.2 % offset.
Tubular Specimens
Full-section tube test pieces with plugs at the grips to prevent crushing, or flattened strap specimens where permitted by the product standard. Axial extensometers are attached to opposite sides of the tube wall to average out bending effects.
Product and Component Coupons
Coupons from castings, forgings, welded joints (base metal, weld metal, or across-weld), fastener blanks, powder metallurgy parts, and additively manufactured metals, prepared so that the gauge length is representative of the zone being evaluated.
Regardless of form, samples must be free of surface defects, decarburization, or machining damage within the gauge length, must be straightened only by agreed methods if curved, and must be identified so that orientation (longitudinal or transverse) and location relative to the product are traceable in the test report.
Testing Items
The core deliverable of this test is the proof strength at the specified plastic extension, with the most frequently reported items being:
- Rp0.2 — proof strength at 0.2 % plastic extension, the default engineering yield value for materials without a distinct yield point.
- Rp0.5 — proof strength at 0.5 % plastic extension, sometimes specified for aluminum alloys and for comparison with total-extension values.
- Rp0.1, Rp0.05, and other specified offsets — required by particular product specifications or design codes; these demand higher extensometer class and resolution because the offset is smaller.
Because the stress-extension record obtained with the extensometer covers the full tensile test, the same setup normally yields supplementary results reported together with Rp, including:
- Rt0.5 — proof strength, total extension, at 0.5 % total extension.
- ReH and ReL — upper and lower yield strength, when the material exhibits a yield phenomenon.
- Rm — tensile strength, from the maximum force.
- E — modulus of elasticity, when the elastic line is determined over a defined stress range.
- A, Ag, Z — percentage elongation after fracture, percentage yield point extension, and percentage reduction of area.
The test report also includes metrological items essential to the validity of the Rp value: extensometer class and gauge length, testing machine force class, strain rate or stress rate used, test temperature, and the method used to construct the offset line.
Testing Methods
Governing Standards
The primary methods are ISO 6892-1 (Metallic materials — Tensile testing — Part 1: Method of test at room temperature) together with its national adoptions such as GB/T 228.1 and EN ISO 6892-1, as well as ASTM E8/E8M (Standard Test Methods for Tension Testing of Metallic Materials) and JIS Z 2241. Extensometer classification and verification follow ISO 9513 or ASTM E83, and machine force verification follows ISO 7500-1 or ASTM E4.
Apparatus and Instrumentation
- A universal testing machine with a force measuring system of at least Class 1 (ISO 7500-1) or verified to ASTM E4, sized so that the expected proof force lies within a well-calibrated range of the load cell.
- An extensometer attached within the parallel length, verified to Class 1 or better per ISO 9513, or Class B-1 or better per ASTM E83. Averaging (dual-sided) or non-contact video and digital image correlation extensometers may be used provided they are verified to the same class.
- Grips and alignment fixtures that minimize bending; alignment is preferably verified in accordance with ASTM E1012 when low-offset proof strengths are required.
- Data acquisition capable of recording force and extension at a rate sufficient to resolve the transition through the offset point, and software implementing the offset construction with a validated algorithm.
Specimen Preparation and Setup
The original cross-sectional area S0 is measured at multiple positions within the gauge length using calibrated instruments, and the smallest value is used. The original gauge length L0 is calculated and marked (commonly L0 = 5.65 × √S0 for proportional test pieces), and the extensometer gauge length Le is set equal to L0 wherever possible; if a different Le must be used, it should be as close to L0 as practicable and, per ISO 6892-1, not less than half of L0. The specimen is then gripped, the extensometer is attached symmetrically within the parallel length, and a small pre-load is applied to seat the assembly before zeroing.
Strain Rate Control
The strain rate through the elastic and transition range must be controlled and reported because proof strength is strain-rate sensitive. Under ISO 6892-1 Method A, closed-loop control maintains a strain rate of 0.00025 s⁻¹ (with 0.00007 s⁻¹ also specified for certain applications) up to and slightly beyond the proof strength, after which the rate is increased for the remainder of the test. Under Method B, or under ASTM E8/E8M stress-rate control, the stress rate in the elastic range is limited to 6–60 MPa/s for materials with an elastic modulus of at least 150 GPa, and to 2–20 MPa/s for lower-modulus materials such as aluminum and copper alloys. The test is normally conducted at room temperature within 10 °C to 35 °C unless otherwise specified.
Determination of Rp — Graphical and Computational Method
The stress-extension curve is recorded from pre-load through the plastic range. A straight line is constructed parallel to the linear elastic portion of the curve, shifted along the extension axis by the specified plastic extension (for Rp0.2, a shift of 0.2 % of the extensometer gauge length). The stress at the intersection of this offset line with the actual curve is the proof strength, and Rp = Fp / S0. Modern systems perform this construction automatically; laboratories verify the software against check values and visually inspect the fit of the elastic line before accepting the result. Where the elastic portion is not sufficiently linear — for example, materials with gradual micro-yielding — the hysteresis loop method (loading to approximately the expected Rp, unloading, and reloading) or other agreed constructions is used to establish the reference slope.
Expression and Reporting of Results
- Report the stress in MPa, generally rounded to the nearest 1 MPa, together with the subscripted offset actually used.
- State the extensometer gauge length Le, extensometer class, and verification standard.
- State the strain rate or stress rate method and values, the test temperature, and the specimen orientation.
- Report whether the result was obtained by automatic offset construction or by an alternative method, and note any deviation from the linear-elastic assumption.
Quality Assurance Considerations
Key contributors to measurement uncertainty include extensometer calibration error at small extensions, gauge length setting accuracy, specimen alignment-induced bending, strain rate variations, gripping effects, and temperature. Laboratories control these through periodic verification of the extensometer and load cell, pre-test zero and drift checks, alignment verification, duplicate testing for statistical monitoring, and participation in interlaboratory comparisons.
Applications
Extensometer-based Rp determination is applied across nearly every sector that relies on metallic materials, including:
- Structural steel products such as high-strength low-alloy plates, sections, and hollow sections, where product standards specify minimum Rp0.2 values for design and acceptance.
- Pipeline and pressure equipment materials, where proof strengths feed directly into allowable-stress calculations and code compliance for vessels, boilers, and piping.
- Automotive sheet and light metal alloys, including aluminum body sheet and chassis components, for formability and crash-relevant strength qualification.
- Aerospace materials such as aluminum alloys, titanium alloys, superalloys, and forged parts, where tight limits on Rp0.2 control design margins.
- Stainless steels in the solution-treated condition, which have no yield plateau and rely on Rp0.2 in both wrought and cast product specifications.
- Fasteners and hardware, where specified property classes require proof stress verification on machined or full-size test pieces.
- Welded fabrications, comparing base metal, weld metal, and cross-weld proof strengths for welding procedure and welder qualification.
- Heat treatment validation, incoming material inspection, supplier qualification, failure analysis, research and development, and statistical process control of metallurgical production.
In all of these contexts, the extensometer-measured Rp value serves as the contractual and regulatory measure of the onset of permanent deformation, making it one of the most frequently requested items in mechanical testing laboratories worldwide.
FAQ
What exactly does Rp0.2 mean?
Rp0.2 is the stress at which the specimen has undergone a plastic (permanent) extension equal to 0.2 % of the original gauge length. It is obtained from the force divided by the original cross-sectional area at the point where the stress-extension curve intersects a line drawn parallel to the elastic slope and offset by 0.2 % extension.
Why is the 0.2 % offset convention used?
For materials without a distinct yield point, there is no single stress at which yielding "begins." The 0.2 % offset was adopted historically as a small, easily measured, and reproducible engineering definition of yielding that correlates with practical design limits. Other offsets (0.1 %, 0.5 %) are used where specifications require them.
What is the difference between Rp0.2, Rt0.5, and yield strengths ReH/ReL?
Rp0.2 is based on plastic extension only, while Rt0.5 is based on total extension (elastic plus plastic). ReH and ReL are the upper and lower yield strengths that exist only when the material shows an obvious yield plateau, such as in many mild steels. For continuous-yielding materials, Rp is the applicable parameter.
Which extensometer class is required for Rp testing?
ISO 6892-1 requires at least a Class 1 extensometer per ISO 9513 for proof strength determination, and Class 0.5 is recommended when smaller offsets such as Rp0.1 or Rp0.05 are needed. Under ASTM E8/E8M, a Class B-1 extensometer per ASTM E83 or better is required for yield-type properties.
Can non-contact video or DIC extensometers be used?
Yes, provided they are verified and classified to the same accuracy class as a contact extensometer and the gauge length is measured and set correctly. Non-contact systems are particularly useful for small specimens, high-temperature tests, and materials sensitive to knife-edge contact.
Does the extensometer gauge length affect the Rp result?
The offset is defined as a percentage of the gauge length, so Le must be known and reported. Best practice, and the requirement of the standards wherever practical, is to set Le equal to the original gauge length L0 so that the result is directly comparable and consistent with product specifications.
Why is strain rate control so important for Rp?
Proof strength increases with strain rate for most metals. The standards therefore specify narrow rate ranges (for example 0.00025 s⁻¹ under ISO 6892-1 Method A) to ensure reproducibility, and the rate actually used must be stated in the test report.
What if the stress-extension curve has no clear straight elastic portion?
When the initial slope is not linear, for instance in materials with early micro-plasticity or after a pre-load that has already yielded the specimen, the standards allow alternative constructions such as the hysteresis loop method, in which the specimen is unloaded and reloaded to establish the elastic slope, or other methods agreed between the parties.
How is the result rounded and judged against specifications?
Rp is normally rounded to the nearest 1 MPa (or as specified by the product standard) and compared with the specified minimum value. A result is acceptable only when all metrological conditions — extensometer class, machine class, strain rate, temperature, and specimen preparation — were within the limits of the governing test method.