Uncertainty Analysis of Plane Strain Fracture Toughness (KIC) Measurements of R350HT Rail Steels According to ASTM E399

Abstract

Fracture toughness is a very important mechanical attribute that affects the strength of rail steel used in high-speed rail systems. This study tests the measurement uncertainty that comes with measuring the plane strain fracture toughness (K_IC) of R350HT rail steel. We used the Single-Edge Bend (SEB) specimen to do fracture toughness testing. We used the Guide to Expressing Measurement Uncertainty (GUM)-based method to figure out how much uncertainty came from measuring the load, the crack opening displacement (COD), and the specimen’s shape and figuring out the crack length. At a 95% confidence level (k = 2), the combined standard uncertainty was found to be 0.881 MPa·m^1/2, which is the same as an expanded uncertainty of 1.761 MPa·m^1/2. The measured fracture toughness value of 40.59 ± 1.76 MPa·m^1/2 meets the standards for rail steels. The results show how important it is to include measurement uncertainty in conformity assessment methods for safety-critical railway components. They also provide an experimentally proven framework for accurate mechanical property evaluation.

1. Introduction

The mechanical performance of steels used in rail systems is critical for structural integrity and operational safety, especially in high-speed rail lines. Increased axle loads, high speeds, and environmental factors pose significant risks for the initiation and propagation of cracks in rail materials. Therefore, not only the static strength properties of rail steels, but also damage tolerance parameters such as fracture toughness, which defines their resistance to crack propagation, must be carefully evaluated [1,2].

The DIN EN 13674-1 standard describes the chemical composition, mechanical properties, heat treatment conditions, and quality requirements of all different grades of rail steels. This standard ensures not only product-based quality processes, but also the optimization of production conditions and the implementation of all requirements to produce a product of the desired quality. In light of all this, parameters such as fracture toughness, fatigue strength, fatigue crack propagation rate, and residual stress are understood to be critical properties in terms of safety [3].

Fracture toughness is a fundamental mechanical property that defines the resistance of a material to fracture in the presence of an existing crack. Fracture toughness, defined under plane strain conditions, is directly related to the microstructural properties of the material, and is widely used in the evaluation of damage mechanisms associated with crack propagation. In high-strength materials with different wall thicknesses, such as rail steels, determining stress conditions and reliably measuring the K_IC value is extremely important [4,5,6,7,8].

The EN 13674-1 standard defines minimum acceptance limits for fracture toughness values for rail steels, both for individual measurements and average values. However, considering only the measured nominal values is insufficient for conformity assessment. Uncertainties inherent in the measurement results directly affect decision rules and declarations of conformity. Measurement uncertainty is a fundamental element determining the reliability, repeatability, and traceability of experimental results [9,10].

The fracture toughness test depends on numerous parameters such as specimen geometry, loading conditions, crack length measurement, load cell calibration, and COD measurement. Each of these parameters constitutes uncertainty components that contribute to the final K_IC value at different rates. Although numerous experimental studies exist in the literature regarding fracture toughness measurements, there are only a limited number of systematic studies on the uncertainty analysis of K_IC measurements performed according to the ASTM E399 standard [4], specifically for rail steels. Although fracture toughness tests were performed in accordance with the ASTM E399 standard, references to the ASTM E1820 standard only illustrate the calculation principles and assessments related to measurement uncertainty calculation [6,7,11].

The goal of this study is to use the Measurement Uncertainty Expression Guide (GUM) method to find out how much uncertainty there is in the measurements taken during plane strain fracture toughness testing on R350HT grade rail steel according to the ASTM E399 standard. In this context, the main sources of uncertainty, such as the load cell, COD measurement system, specimen geometry, and crack length determination, were analyzed separately, and their contributions to the final K_IC value were determined. The results obtained highlight the importance of integrating measurement uncertainty into decision-making processes in conformity assessment for rail steels [7,8,9,10].

Fracture toughness testing using Single-Edge Bend (SEB) specimen is generally performed by crack opening under Mode I loading conditions. In Mode I loading, tensile stresses act perpendicular to the crack plane, creating stress concentration at the pre-crack tip and causing crack opening. The SEB specimens used in this study were subjected to Mode I loading using a three-point bending apparatus, resulting in crack opening in accordance with ASTM E399 [4,5].

2. Fracture Toughness Standard Testing

The stress intensity factor (K) was calculated using standard LEFM relations, where the geometric correction factor (Y) depends on specimen geometry and crack configuration and was determined in accordance with ASTM E399 [4,12,13]:

K = Y × σ √π × a

(1)

In the SEB configuration, the applied load generates tensile stresses at the crack tip, resulting in Mode I (opening mode) fracture conditions, and the load–COD curve reflects this crack opening behavior [4,14].

Fracture toughness tests were performed using SEB specimens with straight-through wide-notch geometry in accordance with EN 13674-1 [3]. To ensure valid plane strain conditions, specimen dimensions were selected to satisfy the following requirement:

$$\begin{array}{c}a, B \ge 2.5 {\left.\left({\displaystyle \frac{K_{IC}}{{\sigma }_a}}\right.\right)}^2\end{array}$$

(2)

Crack length and specimen dimensions were defined in accordance with ASTM E399 requirements [11,15]:

$$\begin{array}{c}K={\displaystyle \frac{P}{B{W}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}f\left({\displaystyle \frac{a}{W}}\right)\end{array}$$

(3)

$$\begin{array}{c}\left({\displaystyle \raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$w$}\right.}\right)={\displaystyle \frac{\left(2+\frac{a}{W}\right)\left[0.886+4.64\left(\frac{a}{W}\right)-13.32{\left(\frac{a}{W}\right)}^2+14.72{\left(\frac{a}{W}\right)}^3-5.6{\left(\frac{a}{W}\right)}^4\right]}{{\left(1-\frac{a}{W}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}} \end{array}$$

(4)

Static tensile or bending load is applied to the pre-cracked specimen. During the test, the applied load and the corresponding crack opening distance are measured and recorded. A clip-on gage is attached to the specimen to measure the crack opening distance. Figure 1 shows an image of the specimen with our specimen and COD attached. In tests conducted to assess measurement uncertainty, an MTS 100 kN servo-hydraulic testing machine and MTS 632.03F-23 COD and MTS FWA105A 3-point bending apparatus were used. After the test, fracture toughness measurements were calculated using the MTS Test Suite software, which is prepared according to the relevant standard.

3. Results and Discussion

The measurement values were again based on the DIN EN 13674-1 standard. In determining the measurement uncertainty, the load cell of the testing machine, the axial movement of the machine, and the COD values and their calibration contributions were taken into account. A straight-through wide notch was made on the specimen before the fracture test. During the pre-crack making process, the maximum stress intensity factor applied was limited to values below 80% of the expected K_IC value, and this value was reduced to below 60% in the final part of the crack length in accordance with the ASTM E399 requirements:

$$0.55 -2.75 {\displaystyle \frac{\mathrm{M}\mathrm{P}\mathrm{a}\sqrt{m}}{s}}$$

corresponding to approximately

$$0.34-1.7 {\displaystyle \frac{\mathrm{k}\mathrm{N}}{s}}$$

for standard specimens with $B=0.5 \mathrm{W}$.

The maximum K value applied during pre-cracking should not exceed 0.8 K_IC. In the terminal pre-cracking region, this ratio should be kept below 0.6 K_IC. These conditions aim to limit plastic deformation at the crack tip and preserve a natural crack geometry [1,2,3,4,5,6,7,8,9,10,11].

The crack length is measured after fracture at the 25%B, 50%B, and 75%B positions of the fracture surfaces with an accuracy of 0.5% W, and the average of these three values is taken as the crack length (a). Figure 2 shows the crack length measurement.

The fracture surface of the tested specimen (Figure 3) exhibited trans granular cleavage characteristics, confirming brittle fracture behavior and crack propagation under the applied loading conditions.

The load–crack opening displacement (COD) curve obtained for the tested specimen is presented in Figure 4. The curve exhibits a stable linear-elastic response up to the maximum load, followed by a sudden drop, indicating brittle fracture behavior consistent with valid K_IC testing conditions [2].

The provisional fracture load (P5) was determined from the load–COD curve using the 95% secant method based on the initial linear elastic region. It should be noted that slight negative COD values at the initial stage may occur due to system compliance, seating effects, and zero-offset calibration of the COD gauge. These do not affect the determination of the linear elastic region or the calculation of P₅, which is based on slope and intersection criteria defined in ASTM E399.

$${\displaystyle \frac{P_{maks.}}{P_Q}}$$

The rate is calculated.

$${\displaystyle \frac{P_{maks.}}{P_Q}}\le 1.10$$

Then, the Provisional Fracture Toughness (K_Q) value is calculated using P_Q. If

$${\displaystyle \frac{P_{maks.}}{P_Q}}\ge 1.10$$

Otherwise, the experiment is invalid. This value can only be used in calculating the specimen strength ratio (R_SC).

$$\begin{array}{c}{R}_{SC}={\displaystyle \frac{2P_{maks.}\left(2W+a\right)}{B{\left(W-a\right)}^2{\sigma }_a}}\end{array}$$

(5)

This ratio is used only when the specimen size is insufficient for performing a fracture test; it is used to compare the toughness of specimens of similar shape and size.

If the condition is met, K_Q:

$$\begin{array}{c}{K}_Q= {\displaystyle \frac{P_Q}{B{W}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}f\left({\displaystyle \raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$W$}\right.}\right)\end{array}$$

(6)

$$\begin{array}{c}f\left({\displaystyle \raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$W$}\right.}\right)={\displaystyle \frac{\left(2+\frac{a}{W}\right)\left[0.0886+4.64\left(\frac{a}{W}\right)-13.32{\left(\frac{a}{W}\right)}^2+14.72{\left(\frac{a}{W}\right)}^3-5.6{\left(\frac{a}{W}\right)}^4\right]}{{\left(1-\frac{q}{W}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}} \end{array}$$

(7)

It can be calculated using the equations. At this stage, another check is performed to determine whether the test is valid. In this check,

$$a,B\ge 2.5{\left({\displaystyle \frac{K_Q}{{\sigma }_a}}\right)}^2$$

All tests were conducted on SEB specimen for train rails, as specified in ASTM E399 according to DIN EN 13674-1. Since we performed the test with applied bending load, only the calibration value along this axis was included in the measurement uncertainty calculations. However, when testing a compact CT specimen used for train wheels, a tensile force will be applied, requiring calibration accordingly, and these aspects must be considered in the measurement uncertainty calculations. Similarly, since the test will continue with a certain load after the formation of a pre-crack, the traverse movement of the device must also be included in the calibration [3].

The sensitivity analysis reveals that the dynamic loading precision, governed by PID control parameters, directly correlates with the pre-crack tip sharpness, which is a primary input in the uncertainty budget. The long duration of K_IC testing necessitates sustained metrological stability to ensure the technical validity of the final data [11].

The sensitivity analysis indicates that dynamic loading precision, governed by PID control parameters, directly affects pre-crack tip sharpness, which is a key contributor to the uncertainty budget. The long duration of K_IC testing requires sustained system stability to ensure data validity [9,10].

In this study, repeatability-related uncertainties were treated as Type A, while instrument calibration, resolution, and manufacturer specifications were considered as Type B contributions.

COD Measurement Accuracy Uncertainty, L0

Rectangular distribution:

U_ver-L0 = 1 mm

$$\begin{array}{c}{u}_{ver\text{-}L0}={\displaystyle \frac{U_{ver\text{-}L0}}{\sqrt{3}}}\end{array}$$

(8)

The standard uncertainty associated with verification was calculated as $u_{ver\text{-}\mathrm{L}0}=0.577 \mathrm{m}$m, assuming a rectangular probability distribution of 0.577 mm.

Uncertainty Arising from COD Gauge Resolution, L0

Rectangular distribution:

$${\mathrm{d}}_{\mathrm{L}0}=0.0001 \mathrm{m}\mathrm{m}$$

$$\begin{array}{c}{u}_{res\text{-}L0}={\displaystyle \frac{d_{L0}}{2\sqrt{3}}} \mathrm{mm}\end{array}$$

(9)

The standard uncertainty due to measurement resolution was determined as $u_{res\text{-}\mathrm{L}0}$ assuming a rectangular distribution.

Uncertainty Arising from COD Gauge Calibration, L0

Normal distribution:

$$U_{cal\text{-}L0}=0.17 \mathrm{m}\mathrm{m}$$

$$\begin{array}{c}{u}_{cal\text{-}L0}={\displaystyle \frac{U_{cal\text{-}L0}}{2}} \end{array}$$

(10)

The standard uncertainty associated with calibration was determined as ${\mathit{u}}_{\mathit{c}\mathit{a}\mathit{l}\text{-}\mathbf{L}0}=0.085$ mm based on the calibration certificate.

Total uncertainty for COD gauge:

$$\begin{array}{c}{u}_{L0}=\sqrt{{u^2}_{ver\text{-}L0}+{u^2}_{res\text{-}L0}+{u^2}_{cal\text{-}L0}}\end{array}$$

(11)

The combined standard uncertainty associated with $L_0$ was calculated as $u_{\mathrm{L}0}=0.692 \mathrm{m}$m.

Loadcell measurement accuracy uncertainty

Rectangular distribution:

$$U_{ver\text{-}Lu}=0.50 \mathrm{N}$$

$$\begin{array}{c}{u}_{ver\text{-}Lu}={\displaystyle \frac{U_{ver\text{-}Lu}}{\sqrt{3}}}\end{array}$$

(12)

The standard uncertainty associated with verification of the load measurement was calculated as $u_{ver\text{-}\mathrm{L}\mathrm{u}}=0.289$ N assuming a rectangular probability distribution.

Uncertainty arising from load cell resolution, Lu

Rectangular distribution:

$$d_{Lu}=0.001 \mathrm{N}$$

$$\begin{array}{c}{u}_{res\text{-}Lu}={\displaystyle \frac{d_{Lu}}{2\sqrt{3}}}\end{array}$$

(13)

The standard uncertainty associated with the resolution of the load measurement was calculated as $u_{res\text{-}Lu}=0.0003$ N assuming a rectangular probability distribution.

Loadcell calibration uncertainty

Normal distribution:

$$U_{cal\text{-}Lu}=0.2180 \mathrm{N}$$

$$\begin{array}{c}{u}_{cal\text{-}Lu}={\displaystyle \frac{U_{cal\text{-}Lu}}{2}} \end{array}$$

(14)

The standard uncertainty associated with calibration of the load measurement was calculated as $u_{cal\text{-}\mathrm{L}\mathrm{u}}=0.10900$ N based on the calibration certificate.

Total uncertainty for load cell

$$\begin{array}{c}{u}_{Lu}=\sqrt{{u^2}_{ver\text{-}Lu}+{u^2}_{res\text{-}Lu}+{u^2}_{cal\text{-}Lu}} \end{array}$$

(15)

The combined standard uncertainty associated with the load measurement was calculated as $u_{L_u}=0.3086 \mathrm{N}$ by combining the verification, resolution, and calibration uncertainty components using the root-sum-square method.

Validation (reproducibility uncertainty)

Normal distribution:

$${\delta }_N=1.97 \mathrm{M}\mathrm{p}\mathrm{a}\sqrt{m}$$

$$n=5$$

$$\begin{array}{c}{u}_N={\displaystyle \frac{{\delta }_N}{\sqrt{n}}} \end{array}$$

(16)

The repeatability-related standard uncertainty was obtained as $u_N=0.881011$ MPa·m^1/2, and the average fracture toughness value was calculated as $40.59$ MPa·m^1/2.

Profile Projector Measurement Uncertainty

Profile Projector Measurement Accuracy Uncertainty

Rectangular distribution:

$$U_{ver\text{-}P}=0.002 \mathrm{m}\mathrm{m}$$

$$\begin{array}{c}{u}_{ver\text{-}P}={\displaystyle \frac{U_{ver\text{-}F}}{\sqrt{3}}} \end{array}$$

(17)

The verification-related standard uncertainty of the displacement measurement was determined as $u_{ver\text{-}F}=0.0012$ mm.

Uncertainty Arising from the Resolution of the Profile Projector Device

Rectangular distribution:

d_P = 0.0001 mm

$$\begin{array}{c}{u}_{res\text{-}P}={\displaystyle \frac{d_F}{2\sqrt{3}}}\end{array}$$

(18)

The standard uncertainty associated with the resolution of the displacement measurement was calculated as $u_{res\text{-}P}=0.00002$ mm, assuming a rectangular probability distribution.

Profile Projector Measurement Uncertainty

Normal distribution:

$$U_{cal\text{-}P}=0.36 \mathrm{m}\mathrm{m}$$

$$\begin{array}{c}{u}_{cal\text{-}P}={\displaystyle \frac{U_{cal\text{-}P}}{2}}\end{array}$$

(19)

The calibration-related standard uncertainty of the displacement measurement was determined as $u_{cal\text{-}P}=0.18$ mm.

Total Uncertainty from the Device

$$\begin{array}{c}{u}_P=\sqrt{{u^2}_{ver\text{-}P}+{u^2}_{res\text{-}P}+{u^2}_{cal\text{-}P}} \end{array}$$

(20)

The combined standard uncertainty of the displacement measurement was determined as $u_P=0.18$ mm.

Measurement Uncertainty from the Testing Device

Measurement Accuracy Uncertainty from the Device, t

Rectangular distribution:

$$U_{ver\text{-}t}\mathrm{ }=\mathrm{ }0.2\mathrm{ }\mathrm{m}\mathrm{m}$$

$$\begin{array}{c}{u}_{ver\text{-}t}={\displaystyle \frac{U_{ver\text{-}t}}{\sqrt{3}}}\end{array}$$

(21)

The verification-related standard uncertainty of the thickness measurement was determined as $u_{ver\text{-}t}=0.115$ mm.

Uncertainty Arising from the Device’s Resolution, t.

Rectangular distribution:

$$d_t=0.001 \mathrm{m}\mathrm{m}$$

$$\begin{array}{c}{u}_{res\text{-}t}={\displaystyle \frac{d_t}{2\sqrt{3}}}\end{array}$$

(22)

The resolution-related standard uncertainty of the thickness measurement was determined as $u_{res\text{-}t}=0.00029$ mm.

Uncertainty Arising from Device Calibration

Normal distribution:

$$U_{cal\text{-}t}=0.17 \mathrm{m}\mathrm{m}$$

$$\begin{array}{c}{u}_{cal\text{-}t}={\displaystyle \frac{U_{cal\text{-}t}}{2}}\end{array}$$

(23)

The calibration-related standard uncertainty of the thickness measurement was determined as $u_{cal\text{-}t}=0.085 \mathrm{m}$m.

Total Uncertainty from the Device

$$\begin{array}{c}{u}_t=\sqrt{{u^2}_{ver\text{-}t}+{u^2}_{res\text{-}t}+{u^2}_{cal\text{-}t}} \end{array}$$

(24)

Using the GUM method, the combined standard measurement uncertainty was calculated by considering load cell, COD, specimen geometry measurements, and crack length determination, as well as uncertainties arising from traverse movements of the testing apparatus. The calculated combined standard uncertainty was 0.881 MPa·m^1/2, resulting in an expanded uncertainty of 1.761 MPa·m^1/2 at a 95% confidence level (k = 2) [15,16,17,18,19].

The obtained plane strain fracture toughness mean value of 40.59 MPa·m^1/2 is within the range reported in the literature for pearlitic rail steels [20,21]. Previous studies have reported fracture toughness values typically ranging between 35 and 50 MPa·m^1/2 depending on microstructure and testing conditions. In the tests performed on five SEB specimens, the individual fracture toughness results were ${\mathrm{K}}_{\mathrm{I}\mathrm{C}}$ = 38.72, 39.91, 40.35, 41.10, and 42.87 MPa·m^1/2 (mean = 40.59 MPa·m^1/2; SD = 1.97 MPa·m^1/2), confirming compliance with the DIN EN 13674-1 acceptance limits for R350HT rail steel. These values are consistent with literature reports, which indicate that fracture toughness typically ranges between 35 and 50 MPa·m^1/2 depending on microstructure and loading conditions [6,7,20,21]. The agreement between the present results and literature confirms the reliability of the experimental procedure and specimen preparation applied in this study [6,7,22].

Measurement uncertainty evaluation in fracture toughness testing has received increasing attention in recent years, particularly for safety-critical applications [9,22]. Similar studies have shown that load measurement and crack length determination constitute dominant uncertainty sources in fracture mechanics testing [20]. The uncertainty distribution obtained in this work follows the same trend, indicating consistency with previously published uncertainty analyses [21].

The individual uncertainty components calculated above are summarized in the uncertainty budget presented in

Table 1. Uncertainty budget for plane strain fracture toughness (${\mathrm{K}}_{\mathrm{I}\mathrm{C}}$) measurement of R350HT rail steel.

Uncertainty Component	Symbol	Constant/ Varying	Input Value	Distribution	Divisor	Standard Uncertainty	Unit	Type (A/B)
COD verification	$u_{ver\text{-}{L}_0}$	Constant	Uver-L0 = 1	Rectangular	$\sqrt{3}$	0.577	mm	B
COD resolution	${\mathrm{u}}_{\mathrm{r}\mathrm{e}\mathrm{s}\text{-}\mathrm{L}0}$	Constant	dL0 = 0.0001	Rectangular	$2\sqrt{3}$	0.00003	mm	B
COD calibration	$u_{cal\text{-}L0}$	Constant	Ucal-L0 = 0.17	Normal	2	0.085	mm	B
Combined COD uncertainty	$u_{L0}$	-	-	-	-	0.692	mm	-
Loadcell verification	$u_{ver\text{-}Lu}$	Constant	Uver-Lu = 0.50	Rectangular	$\sqrt{3}$	0.289	N	B
Loadcell resolution	$u_{res\text{-}Lu}$	Constant	dLu = 0.0001	Rectangular	$2\sqrt{3}$	0.0003	N	B
Loadcell calibration	$u_{cal\text{-}Lu}$	Constant	Ucal-Lu = 0.2180	Normal	2	0.1090	N	B
Combined Loadcell uncertainty	$u_{Lu}$	-	-	-	-	0.3086	N	-
Profile Projector verification	$u_{ver\text{-}P}$	Constant	Uver-P = 0.002	Rectangular	$\sqrt{3}$	0.0012	mm	B
Profile Projector resolution	$u_{res\text{-}P}$	Constant	dP = 0.0001	Rectangular	$2\sqrt{3}$	0.00002	mm	B
Profile Projector calibration	$u_{cal\text{-}P}$	Constant	Ucal-P = 0.36	Normal	2	0.18	mm	B
Combined Profile Projector uncertainty	$u_P$	-	-	-	-	0.18	mm	-
Testing Device verification	$u_{ver\text{-}t}$	Constant	Uver-t = 0.2	Rectangular	$\sqrt{3}$	0.115	mm	B
Testing Device resolution	$u_{res\text{-}t}$	Constant	dt = 0.001	Rectangular	$2\sqrt{3}$	0.00029	mm	B
Testing Device calibration	$u_{cal\text{-}t}$	Constant	Ucal-t = 0.17	Normal	2	0.085	mm	B
Combined Testing Device uncertainty	$u_t$	-	-	-	-	0.143	mm	-
Validation (reproducibility)	$u_N$	Varying	δN = 1.97, n = 5	Normal	$\sqrt{n}$	0.881011	MPa·m1/2	A
Combined Standard uncertainty	$u_c$	-	-	-	-	0.88	MPa·m1/2
Expanded uncertainty (95%, k = 2)	U	-	-	-	-	1.761	MPa·m1/2

in accordance with the GUM methodology.

The uncertainty budget shows that the dominant contribution arises from repeatability and load-related measurements, while resolution effects remain negligible. The combined standard uncertainty obtained from all contributions leads to an expanded uncertainty of 1.761 MPa·m^1/2 at a 95% confidence level (k = 2).

The reproducibility (validation) uncertainty was evaluated based on repeated fracture toughness measurements conducted on $n=5$ specimens prepared and tested under the same conditions. The standard deviation of the obtained $K$ values was calculated as ${\delta }_N=1.97$ MPa·m^1/2. Following the GUM approach, the Type A standard uncertainty associated with repeatability was then obtained as $u_N={\delta }_N/\sqrt{n}=0.881$ MPa·m^1/2. This term represents the combined effect of specimen-to-specimen variability and test repeatability and was included in the uncertainty budget as the validation contribution [16,17,18,19].

The results indicate that incorporating measurement uncertainty enhances the reliability of fracture toughness evaluation by providing a quantitative basis for result interpretation and decision-making.

4. Conclusions

In this study, the measurement uncertainty of plane strain fracture toughness (K_IC) for R350HT rail steel was systematically evaluated in accordance with ASTM E399 using the GUM framework. The contributions of critical parameters, including load cell calibration, COD measurement system, crack length determination, fracture surface evaluation, specimen geometry, and experimental repeatability, were individually quantified and combined into a comprehensive uncertainty budget.

The average fracture toughness value was determined as 40.59 MPa·m^1/2, with an expanded uncertainty of ±1.761 MPa·m^1/2 (k = 2, 95% confidence level). The sensitivity analysis indicates that the dominant uncertainty components arise from crack length measurement and COD system calibration. Sensitivity analysis revealed that the dominant uncertainty contributions originate from crack length measurement and COD system calibration, demonstrating the strong influence of measurement accuracy and calibration on K_IC evaluation. These findings underscore the necessity of maintaining rigorous metrological traceability across the entire measurement chain.

Furthermore, this study demonstrates that incorporating an uncertainty budget provides a robust basis for decision rules in conformity assessment. Especially for safety-critical components like R350HT rail steels, quantifying the expanded uncertainty is essential to minimize the risk of false acceptance (consumer’s risk) during material qualification. In conclusion, the proposed framework offers a validated approach for improving the reliability and international comparability of fracture mechanics data in accredited testing environments.