J.2Estimation of uncertainty

IS 1608:2005, Metallic Materials — Tensile Testing at Ambient Temperature

Last Updated 29 Oct 2026

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J.2.1 Material independent parameters

The manner in which errors from a variety of sources should be added together has been treated in considerable detail [4] and more recently guidance has been given on assessing precision and uncertainty in two ISO documents, ISO 5725-2 and the Guide to the expression of uncertainty in measurement.

In the following analysis the conventional least mean squares approach has been used.

The tolerances for the various testing parameters for tensile properties are given in table J.1 together with expected uncertainty. Because of the shape of the stress-strain curve, some of the tensile properties in principle can be determined with a higher degree of precision than others, e.g., the upper yield strength $R_{\mathrm{eH}}$ is only dependent on the tolerances for measurement of force and cross sectional area, whilst proof strength, $R_{\mathrm{p}}$ , is dependent on force, strain (displacement), gauge length and cross-sectional area. In the case of reduction in area, Z, the measurement tolerance for cross-sectional area both before and after fracture needs to be considered.

Table J.1 — Summary of maximum admissible measurements uncertainties for determining tensile test data

Parameter	Tensile properties, % error
Parameter	R_eH	R_eL	R_m	R_p	A	Z
Force	1	1	1	1
Strain¹) (displacement)	—	—	—	1	1
Gauge length, L_o¹)	—	—	—	1	1
S_o	1	1	1	1	—	1
S_u	—	—	—	—	—	2
Expected uncertainty	±√2	±√2	±√2	±√4	±√2	±√5
(error summation using least-mean squares)

Assuming a class 1 extensometer calibrated in accordance with ISO 9513.

J.2.2 Material dependent parameters

For room temperature tensile testing, the only tensile properties significantly dependent upon the materials response to the straining rate (or stressing rate) control parameters are $R_{\mathrm{eH}}, R_{\mathrm{eL}}$ and $R_{\mathrm{p}}$ . Tensile strength, $R_{\mathrm{m}}$ , can also be strain rate dependent, however in practice it is usually determined at a much higher straining rate than $R_{\mathrm{p}}$ and is generally less sensitive to variations in strain rate.

In principle, it will be necessary to determine any material's strain rate response before the total error budget can be calculated. Some limited data are available and the following examples may be used to estimate uncertainty for some classes of materials.

Typical examples of data sets used to determine materials' response over the strain rate range specified in this International Standard are shown in tables J.2 and J.3 and a summary of materials' response for proof stress for a number of materials measured under strain rate control is given in table J.2. Earlier data on a variety of steels measured under a set stressing rate are given in the seminar paper[5].

Table J.2 — Examples of variation in room temperature proof stress over the strain rate range permitted in this International Standard

Material	Nominal composition	R_p0,2 Mean value	Proof stress strain rate response	Equivalent tolerance
Material	Nominal composition	MPa	%	± %
Ferritic steel
Pipe steel	Cr-Mo-V-Fe(bal)	680	0,1	0,05
Plate steel (Fe 430)	C-Mn-Fe(bal)	315	1,8	0,9
Austenitic steel
(X5 Cr Ni Mo 17-12-2)	17Cr, 11Ni-Fe(bal)	235	6,8	3,4
Nickel Base Alloys
Ni Cr 20 Ti	18Cr, 5Fe, 2Co-Ni(bal)	325	2,8	1,4
Ni Cr Co Ti Al 25-20	24Cr, 20Co, 3Ti, 1,5Mo, 1,5Al-Ni(bal)	790	1,9	0,95

J.2.3 Total measurement uncertainty

The material-dependent response of proof strength over the permitted strain rate range specified in table J.2 may be combined with the material independent parameters specified in table J.1 to give a total estimate of uncertainty for the various materials indicated, as shown in table J.3.

For the purpose of this analysis, the total value of the variation in proof strength over the strain rate range permitted in the standard has been halved and expressed as an equivalent tolerance, i.e. for X5 Cr Ni Mo 17-12-2 stainless steel, the proof strength can vary by 6,8 % over the permitted strain rate range so it is equivalent to a tolerance of ± 3,4 %. Therefore for X5 Cr Ni Mo 17-12-2 stainless steel, the total uncertainty is given by:

$\pm \sqrt{2^{2}+3,4^{2}}=\pm \sqrt{15,6}=\pm 3,9 \%$

Table J.3 — Examples of total expected measurement uncertainty for room temperature proof strength determined in accordance with this International Standard

Material	R_po,2 Mean value	Values from table J.1	Values from table J.2	Total expected measurement uncertainty
Material	MPa	±%	%	±%
Ferritic steel
Pipe steel	680	2	0,05	√4,0 = 2,0
Plate steel	315	2	0,9	√4,8 = 2,2
Austenitic steel
X5 Cr Ni Mo 17-12-2	235	2	3,4	√15,6 = 3,9
Nickel base alloys
Ni Cr 20 Ti	325	2	1,4	√6,0 = 2,4
Ni Cr Co Ti Al 25-20	790	2	0,95	√4,9 = 2,2