# The impact of hydrogen flakes on the uniaxial and biaxial fracture toughness of a forged ferritic steel

F C Tankoua, Á C Jacquemoud, Minh Bao Le, G. Roussel

► To cite this version:

F C Tankoua, Á C Jacquemoud, Minh Bao Le, G. Roussel. The impact of hydrogen flakes on the uniaxial and biaxial fracture toughness of a forged ferritic steel. International Journal of Fracture, 2025, 249, pp.26. 10.1007/s10704-025-00841-7. cea-05005199

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https://cea.hal.science/cea-05005199v1

Submitted on 25 Mar 2025

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# The impact of hydrogen flakes on the uniaxial and biaxial fracture toughness of a forged ferritic steel

F. Tankoua · C. Jacquemoud · M. B. Le · G. Roussel

Received: 21 October 2024 / Accepted: 3 February 2025

© The Author(s) 2025

**Abstract** This work focuses on the effects of hydrogen flakes on the fracture toughness of forged ferritic steel under uniaxial or biaxial loading conditions. The fracture toughness under uniaxial loading was investigated on CT specimens and cruciform specimens were used for the biaxial loading conditions representative of a thermal shock in a Reactor Pressure Vessel. The observed decrease in fracture toughness in the flaked material was related to the higher carbon content near the hydrogen flake. Moreover, the nature of the initial defect (fatigue crack or hydrogen flake) did not significantly affect the fracture toughness. The cruciform specimen exhibited higher fracture toughness compared to CT specimens, even in the presence of flakes. This confirmed the conservatism of standard fracture analyses used for structure integrity assessment based on a lower bound fracture toughness curve obtained from CT specimens.

**Keywords** Hydrogen flake · Fracture toughness · Uniaxial · Biaxial · Master curve

**Abbreviations**

<table><tr><td>a, c</td><td>Semi-elliptical notch depth and half-width</td></tr><tr><td>a/W</td><td>Ratio between crack size and width</td></tr><tr><td>T<sub>0</sub></td><td>Reference temperature of the Master Curves</td></tr><tr><td>CT</td><td>Compact Tensile</td></tr><tr><td>RPV</td><td>Reactor Pressure Vessel</td></tr><tr><td>PWR</td><td>Pressurized Water Reactors</td></tr><tr><td>Zone 1</td><td>Flaked region</td></tr><tr><td>Zone 2</td><td>Zone without flake near the flaked region</td></tr><tr><td>Zone 3</td><td>Large zone without flake within the flaked region</td></tr><tr><td>L, T, S</td><td>Longitudinal direction, Transverse direction and Short transverse direction</td></tr><tr><td>CMOD</td><td>Crack mouth opening displacement</td></tr><tr><td>R<sub>0</sub></td><td>Initial yield strength in the constitutive model</td></tr><tr><td>H, Q, b</td><td>Parameters of the isotropic hardening law</td></tr><tr><td>J</td><td>J-Integral</td></tr><tr><td>K<sub>J</sub></td><td>Stress intensity factor</td></tr><tr><td>K<sub>J1T</sub></td><td>Stress intensity factor with thickness correction</td></tr></table>

<footnote>F. Tankoua (✉) · C. Jacquemoud
Université Paris-Saclay, CEA, Service d'Etudes Mécaniques Et Thermiques, 91191 Gif-Sur-Yvette, France
e-mail: franck.tankoua@cea.fr</footnote>

<footnote>M. B. Le
Institut de Radioprotection Et de Sûreté Nucléaire, IRSN, PSN-EXP, SES, 92262 Fontenay-Aux-Roses, France</footnote>

<footnote>G. Roussel
BelV, 1070 Brussels, Belgium</footnote>
# 1 Introduction

After about 30 years of operation, the reactor pressure vessels (RPVs) of the Doel 3 and Tihange 2 pressurized water reactors (PWR) in Belgium were found to contain a large number of hydrogen flake defects, mainly concentrated in the circumferential planes of the core shell (or beltline). The hydrogen flakes are associated with zones of segregation of non-metallic inclusions in the low-alloy steel cylindrical forgings used to manufacture the core-shell parts of the RPVs and have been shown to have been generated during forging operations where hydrogen content control was inadequate. Independently of the analytical and experimental efforts carried out in Belgium to justify the serviceability of these RPVs, a test programme was initiated in France by the CEA and the IRSN to verify that the presence of hydrogen flakes was not symptomatic of a weaker material.

The first phase of this test programme (Jacquemoud et al. 2018) included fracture toughness Compact Test (CT) specimens. Nevertheless, the uniaxial loading conditions on CT specimens are not representative of the RPV loading conditions. In fact, under either its normal operating conditions or a pressurised thermal shock (due to the safety injection of cooling water), the RPV undergoes biaxial loadings. On the one hand, the out-of-plane stress induced by biaxial loadings theoretically increases the stress triaxiality and decreases the plastic zone size ahead of the crack tip. This leads to a higher constraint, which is negative for the fracture toughness (Ziebs et al. 1981, Dodds Jr et al. 1993, Pennell et al. 1995, Bass et al. 1999). On the other hand, the defects in the inner wall of RPV are shallow cracks, contrary to standard CT specimens with deep cracks. Larger plasticity is related to shallow defects compared to deep defects, suggesting thus a positive effect of the shallow defect on RPV. In addition, large components often benefit from the so-called structure effect, inducing higher toughness compared to the conservative values obtained on CT specimens.

Therefore, the impact of hydrogen flakes must be assessed in biaxial loading conditions to verify that their presence does not affect the fracture toughness in the plasticity, triaxiality and crack depth conditions representative of a pressurised thermal shock. In addition, flakes in the Doel 3 and Tihange 2 RPV were not purely laminar but slightly tilted at an angle

of around 15°—20° from the wall surface. This element has to be considered too. However, no experiment can be fully representative of these real configurations. The solution is to find the best compromise. An option could be considering tensile tests on large round bars with tilted flakes to measure the material ductility in the presence of flakes in an orientation representative of the RPV ones. (Lacroix et al. 2016) showed that the high range of J reached during the test (from ~ 500 to ~ 1000 kJ/m²) would never be reached in an RPV wall even during a pressurised thermal shock. Bending tests on paral-lelepiped specimens with tilted flakes were also used to study crack interactions in (Jacquemoud et al. 2018; Lacroix et al. 2016) but the reduced thickness required on the specimen to have a through-thickness flake was not representative of the thick RPV wall and the 3D stress field. The most promising option appeared to be large cruciform specimens. In the literature, many biaxial tests have been performed on such specimen geometries (Pennell et al. 1995; Bass et al. 1999; McAfee et al. 2001). The cruciform specimen geometry introduces a far-field, out-of-plane biaxial stress in the specimen section that approximates the nonlinear stresses representative of pressurised thermal shock loading conditions. In the lower temperature range, the detrimental high constraint effect was not observed experimentally. Indeed, the fracture toughness of cruciform specimens was higher than that of standard specimens with deep cracks. Similar results were reported when applying the master curve approach on reduced-thickness cruciform specimens (Link et al. 2007; Hohe et al. 2011). This specimen geometry appeared to be a good candidate for addressing the impact of hydrogen flakes on fracture toughness in biaxial loading conditions. Its large thickness allows multiple and tilted flakes in the specimen similar to the configuration in the study case RPV.

In the present study, five-point bending tests were performed on large cruciform specimens with semi-elliptical cracks (i.e. shallow crack representative of reference defect used in safety assessment) so that both the geometry and loading conditions are representative of RPV. The novelty of these experiments is that the material contains multiple hydrogen flakes, unlike the published works on cruciform specimens focusing on homogeneous steel (Moinereau et al. 2014). The conservatism related to uniaxial standard
specimens with deep cracks was assessed in the specific case of hydrogen-flaked steel by comparing the biaxial loading tests to CT specimen tests. In parallel, tensile tests on different zones of the material were conducted to define the material constitutive law used in Finite Element simulations.

# 2 Experimental procedures

## 2.1 Material and specimen sampling

According to the goal of the present study, the investigated material is an 18MnD5 ferritic steel containing laminar hydrogen-induced flakes. It was extracted from a steam generator shell, which was discarded at the end of the forging process because of non-conformity. Indeed, to bring evidence to the study case of Doel 3 and Tihange 2 RPV, the material must be similar on various points. First, it contains flakes induced by a similar hydrogen embrittlement phenomenon that had occurred during the shell forging and degassing heat treatment process. Second, it comes from a similar (to the RPV) large forging nuclear equipment. Third, the material in the blocks dedicated to the experiments must be in the same state as the one in the component in operation, which means that the studied material has been submitted to quenching, tempering and equivalent Post Weld heat treatments.

Two blocks were dedicated to this study's experiments as indicated in Fig. 1a. The first block without flake, called the “reference block” and of 1250 × 300 × 140 mm, was taken at the bottom of the shell. The second block containing a high density of flakes, called the “flaked block” and of 1250 × 1000 × 200 mm, was extracted from the top. It should be noted that these blocks have been extracted from the same steam generator shell as the material studied by (Chaouadi et al. 2016). Therefore, the results of both experimental campaigns, in uniaxial loading conditions, could be compared and the database about fracture toughness of ferritic steels containing hydrogen-induced flakes could be completed.

The ladle chemical composition of the material is reported in Table 1.

An ultrasonic inspection confirmed that the reference block was free of flakes, unlike the flaked block containing penny-shape indication up to 10–15 mm

diameter. In the flaked block, the analysis of the ultrasonic indications on various cumulated views (Fig. 2) made it possible to map the precise positions of flakes and then to identify the areas of interest for the material characterisation. Three regions were considered in the flaked block (Fig. 2): the flaked region (zone 1), a zone without any flake near the flaked region (zone 2) and a large zone without any flake within the flaked region (zone 3). These three zones were selected for their different proximity to the flaked region to map the mechanical properties evolution in the material surrounding the flakes.

The specimens were located between the quarter-thickness and the three-quarter thickness of the shell so that the thickness-dependent quenching rate was similar for all of them. Their orientations were defined along the characteristic directions of the blocks: the longitudinal (L), the transverse (T) and the thickness (S) directions as indicated in Fig. 1b. The correspondence on the shell is illustrated in Fig. 1a. The orientation designations for the tensile (L or T) and CT (TL, SL or LS) specimens shown on Fig. 1b are attributed following the ASTM E399 standard (ASTM E399). The biaxial specimen orientation will be defined in details in 2.3.

## 2.2 Uniaxial specimen loading

### 2.2.1 Tensile tests

Tensile specimens with a 6 mm diameter gauge were used to determine the plastic flow behaviours of the materials. The tensile strength anisotropy was investigated in the reference block only, from tensile specimens extracted along the longitudinal (L) and the transverse (T) directions (Fig. 1b). Only the longitudinal (L) direction was considered for zone 1 and zone 2 of the flaked block. Due to the limited number of areas like zone 3, the fracture toughness characterisation was a priority and no tensile specimens were extracted from this zone. None of the specimens contained flakes.

A standard electromechanical testing machine was fitted with two laser micrometres. These two micrometres moved along the tensile axis, scanning the specimen's height in two perpendicular directions and continuously recording the diameter evolution during the test and beyond the necking. This technique allowed for a better characterisation of the material
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Schematic representation of the steam generator shell from which the reference and the flaked blocks have been extracted a and definition of the tensile and CT specimen orientations in a block according to the shell characteristic directions b</figcaption></figure>

<table><caption>**Table 1** Ladle chemical composition of the material (w%)</caption><thead><tr><th>C</th><th>Mn</th><th>Si</th><th>P</th><th>Cr</th><th>Mo</th><th>Ni</th><th>Cu</th><th>S</th><th>Fe</th></tr></thead><tbody><tr><td>0.18</td><td>1.46</td><td>0.17</td><td>0.006</td><td>0.254</td><td>0.5</td><td>0.72</td><td>0.05</td><td>0.002</td><td>bal</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Cumulated views of flake indications obtained during the ultrasonic inspection of the flaked block used to define the locations of zone 1, zone 2 and zone 3</figcaption></figure>

behaviour up to plastic instability. The stress–strain evolution calculated from the diameter reduction could be compared to standard true stress–strain curves obtained from the specimen’s global elongation.

The tests were conducted at a load-line displacement rate of 0.01 mm/s corresponding to a strain rate of $4.2 \times 10^{-6} s^{-1}$. Specimens from the reference block were tested at – 120 °C and specimens from the flaked block at – 120 °C, – 100 °C and – 80 °C.

A climatic chamber maintained a constant and homogeneous temperature during the tests.

### 2.2.2 *Fracture toughness tests*

The ductile-to-brittle transition of all zones of the material was investigated using 1/2 T-CT specimens. In the reference block, the CT specimens were cut along LS and TL orientations so the CT tensile direction corresponded to the tensile specimen’s one,
respectively longitudinal (L) and transverse (T) as illustrated in Fig. 1b. Two categories of CT specimens were extracted from the flaked block. First, specimens with standard fatigue precrack were taken along LS orientation in zone 1, zone 2 and zone 3. Second, specimens with the fatigue precrack replaced by a flake at the notch root were taken along the SL orientation. In this second case, the usual V-notch was switched for a U-notch to limit stress concentration if a flake is badly positioned (Jacquemoud et al. 2018). Due to the large variety of flake geometries, the goal was to target an average flake-length over W ratio of 0.5, consistent with the a/W ratio of the fatigue precracked specimens.

The fracture toughness tests were performed according to the guidance of the ASTM E1921 standard. CT specimens were tested inside a climatic chamber cooled by nitrogen injection. The temperature homogeneity was monitored during the test with three thermocouples welded on the specimen.

The specimens of the reference block were tested at – 140 °C. Tests on the specimens from the flaked block were conducted in the temperature range of [– 130 °C; – 80 °C]. Therefore, the reference temperature ($T_0$) was calculated using the multi-temperature method of the ASTM E1921 standard (ASTM E1921).

After the fracture toughness tests, the carbon content was measured locally on the cleavage initiation site (Jacquemoud et al. 2018). To do so, two 5-mm cylinders were extracted next to the fatigue precrack or the flake from each fractured specimen as illustrated in Fig. 3. The local carbon content for each CT specimen is the average of both trough thickness measurements

(from each cylinder) made by a carbon combustion analyser.

The second half of the fractured specimen was dedicated to fracture surface analysis with scanning electron microscopy (Fig. 3).

## 2.3 Biaxial specimen loading

Cruciform specimens were used to address the fracture toughness on biaxial loading conditions. (Bass et al. 1999) reported that a minimum thickness of around 100 mm was necessary to reach a stress field representative of RPV under pressurised thermal shock loading. The specimen geometry of this study included a 98 mm thick cruciform core illustrated in Fig. 4a and 4b and four extended arms (Fig. 4d), welded on the core to fit the five-point bending rig with a 650 mm distance between supporting plots (Fig. 4c). A semi-elliptical notch of a = 10 mm in depth and 2c = 42 mm in width was machined at the centre of the specimen.

Each cruciform core had four series of four machined slots to create a larger zone with uniform biaxial stress in the centre of the specimen where the semi-elliptical notch was located (Lebedev and Muzyka 1998). Because of machining issues on the core from the reference block, two slots on two opposite arms were longer than the original ones, as illustrated in Fig. 4a. In the flaked block, all three cores conform to the original geometry reported in Fig. 4b. They were tilted by 15° from the inner wall of the flaked block (corresponding to the inner wall of the shell) to obtain a flake orientation representative of the one observed on Doel 3 et Tihange 2 pressure vessels (Fig. 5). For each core configuration, an average of ten

<figure><img src="image_4.png" /><figcaption>**Fig. 3** Post-mortem analyses: fracture surface observation and measurement of the carbon content close to the cleavage initiation site</figcaption></figure>
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4** Cruciform specimen with a 98 mm thickness: a core geometry of the specimen from the reference block with four longer slots, b core geometry of the specimens from the flaked</figcaption></figure>

flakes (pink circles in Fig. 5) surrounded the semi-elliptical notch with the closer ones being at a distance of about 10 mm from the semi-elliptical notch front. Therefore, the interaction between the main crack (i.e. the semi-elliptical notch) and the neighbouring flakes could be addressed. It is here worth noting that the high density of flakes made it impossible to avoid flakes in and around the slots (blue circles in Fig. 5). The cruciform core from the reference block was aligned with the block surface.

Only the specimen cores represented in Fig. 4a and Fig. 4b were extracted from the reference or flaked block. The arms were machined from a standard 18MnD5 steel plate.

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>block, c five-point bending rig in the thermal chamber and d entire specimen with its arms</figcaption></figure>

The biaxial loading tests were performed on a five-point bending rig, inside a climatic chamber on a 2500 kN servohydraulic machine (Fig. 4c). The specimen balance on the bending rig was validated by sixteen strain gages positioned on the core and the arms. Prior to the fracture test, a precracking stage produced a 2 mm length fatigue crack from the semi-elliptical notch leading to an a/W ratio of 0.12. The fracture tests were conducted at a temperature of -100 °C with a prescribed load line displacement rate of 0.002 mm/s. The temperature homogeneity and stability were controlled by three thermocouples welded on the specimen close to the fatigue precrack. The crack
<figure><img src="image_9.png" /><figcaption>**Fig. 5** Position of the specimen within the flaked block. The specimen is tilted by 15° from the inner wall. The hydrogen flakes surround the elliptical notch (pink circles) and some are</figcaption></figure>

mouth opening displacement (CMOD) was measured with a clip gage during the test.

The fracture surfaces of the specimens were observed with scanning electron microscopy.

# 3 Results

## 3.1 Tensile behaviour

Standard true stress–strain curves were obtained from the global specimen elongation, estimated by applying a stiffness correction to the load-line displacement. They are reported in Fig. 6 for zone 1 (flaked material), zone 2 (near the flaked material) and the reference block. As expected, the strength gradually increases when the temperature decreases from – 80 °C to – 120 °C. In the flaked block, zone 1 (flaked region) and zone 2 (material near the flaked region) show similar behaviour, especially at low strain. In the reference block, the transverse (T) direction is stronger than the longitudinal (L) direction, suggesting an anisotropic tensile behaviour within the block. Both stress–strain curves of the reference block are significantly lower than the ones of the flaked block at – 120 °C.

The stress–strain curves of Fig. 6 are limited to strains around 15% where the laser measurement

close to the arm slots (blue circles). (Cumulative view of flakes indications through the specimen thickness)

<figure><img src="image_10.png" /><figcaption>**Fig. 6** True stress–strain curves with corrected load-line displacement for zone 1 (flaked region), zone 2 (near the flaked material) and the reference block between – 80 °C and – 120 °C</figcaption></figure>

technique can give the diameter reduction at the necking point just before the specimen fracture. Therefore, the equivalent uniaxial flow stress can be calculated using Bridgman's correction (Bridgman 1952), including the curvature radius of the necking profile measured up to high plastic strains.

The stress–strain curves obtained with the two methods are compared in Fig. 7 for the flaked material
<figure><img src="image_11.png" /><figcaption>Fig. 7 Comparison of experimental true stress–strain curves with corrected load-line displacement and Bridgman assumptions at – 100 °C on zone 1</figcaption></figure>

at – 100 °C. If both curves are similar for true strains up to 15%, the strains calculated from the laser measurements reach 80%. Therefore, these data are essential to accurately define a constitutive law for the material to be used in the finite element analysis. The grey curve in Fig. 7 represents the data interpolation made using a Young Modulus of E = 209 GPa, a Poisson ratio of v = 0.3 and an isotropic hardening (R(p)) described by Eq. 1 involving a linear contribution, an exponential Voce-type term and the yield stress (R₀).

$$R(p) = R_0 + Hp + Q(1 - \exp(-bp)) \quad (1)$$

The material parameters for the the flaked material at – 100 °C are R₀ = 600 MPa, H = 440 MPa, Q = 278 MPa and b = 16.5.

## 3.2 Fracture toughness in uniaxial loading conditions

### 3.2.1 Standard CT specimens with a fatigue precrack

The Master Curve approach was successfully used to assess the fracture toughness in the flaked and reference blocks, within the ductile to brittle transition range. The results are reported in Fig. 8 and Fig. 9. In the reference block, no significant differences were observed between the fracture toughness of specimens

<figure><img src="image_12.png" /><figcaption>Fig. 8 Fracture toughness distributions of the reference block and zone 1 (material between the flakes)</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 9 Fracture toughness distributions of zone 2 (near the flaked region) and zone 3 (large zone within the flaked region)</figcaption></figure>

tested in either LS or TL orientations, suggesting a limited fracture anisotropy. The reference temperatures obtained for LS and TL orientations were respectively T₀ = – 126 °C and T₀ = – 129 °C. Therefore a unique reference temperature of T₀ = – 128 ± 7 °C was determined using the data of both LS and LT orientations.

The reference temperature of zone 1 in the flaked block is T₀ = – 99 ± 6 °C. The statistical distribution of fracture toughness of zone 2 and zone 3 is
almost the same, with reference temperatures of respectively $T_0 = -115 \pm 6$ °C and $T_0 = -117 \pm 7$ °C.

### 3.2.2 CT specimens with a flake as crack front

Unlike fatigue precracks, which are almost straight, the flakes have irregular fronts. As a first approximation, the mean value of the flake length was used to determine the fracture toughness, as suggested by the ASTM1921 standard. A reference temperature of $T_0 = -102 \pm 7$ °C was estimated using the master curve approach. This reference temperature can be considered as a mean value that can be compared to the $T_0$ obtained on CT specimens with fatigue prepacks. The effect of the flake front straightness on the reference temperature calculation will be later discussed in **4.2.1**.

The statistical distribution of fracture toughness for the specimens with a flake is reported in Fig. 10. This result is compared to the one previously determined for the fatigue precracked specimens of zone 1 (material between the flakes). No significant difference appears between both types of specimens, which is confirmed by similar cleavage failure probabilities of specimens with a flake and a fatigue precrack (Fig. 11).

<figure><img src="image_14.png" /><figcaption>Fig. 10 Statistical distribution of the fracture toughness for CT specimens with flake and with fatigue precrack</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 11 Cleavage failure probability of CT specimens with flake and with fatigue precrack. The dashed line is the unique Weibull fit for both sets of data</figcaption></figure>

### 3.2.3 Fracture surface analyses

For almost all the specimens, cleavage fracture was the only brittle fracture mode observed on the fracture surface. Some specimens exhibited local intergranular brittle fracture, but not on the fracture initiation sites. No correlation could be made between the specimens exhibiting local intergranular fracture and the lowest fracture toughness value. Manganese sulphides were the most represented inclusions on the fracture surface. The inclusion size was smaller than 10 µm in the reference block and between 10 and 20 µm in the flaked block.

The local carbon content measured on the crack initiation site of fractured specimens is reported as an average of all specimen values for each zone in the material in Table 2. The carbon content in the reference block (0.192%) is close to the ladle carbon content (0.18%). In the flaked block, the measured mean carbon content is higher, especially in the flaked region (zone 1). This result confirms that hydrogen flakes are located in positive macrosegmentation zones.

## 3.3 Fracture toughness in biaxial loading conditions

### 3.3.1 Result on the reference block

The brittle fracture was initiated from the fatigue precrack (Fig. 12). Multiple crack initiation sites were
<table><caption>**Table 2** Reference temperature versus mean carbon content in the different zones of the material</caption><thead><tr><th>Zone</th><th>Ref. block</th><th>Zone 2<br>(near the flaked region)</th><th>Zone 3<br>(large zone in the flaked region)</th><th>Zone 1<br>(flaked region)</th><th>With flake</th></tr></thead><tbody><tr><td>% C</td><td>0.192</td><td>0.205</td><td>0.20</td><td>0.22</td><td>0.21</td></tr><tr><td>T<sub>0</sub> ± σT<sub>0</sub> (°C)</td><td>- 128 ± 7</td><td>- 115 ± 6</td><td>- 117 ± 7</td><td>- 99 ± 6</td><td>- 102 ± 7</td></tr></tbody></table>

observed around the deepest points of the fatigue precrack. The different geometry of the core in this specimen did not affect the fracture mode or initiation site. As presented by the load vs CMOD curve plotted in Fig. 13, the maximal load at the fracture occurrence was 1674 kN.

Tests on cruciform specimens were modelled by using the finite element method on Cast3M software, with implicit integration scheme. Three-dimensional meshes made of quadratic, eight-node elements (47,500 total) were used. One-quarter of the specimen was modelled, together with the usual symmetry conditions. The mesh and the boundary conditions applied for the calculation are detailed in Fig. 14. The fatigue crack geometry experimentally measured on the fracture surface was used in the model. The constitutive equation identified on the flaked block tensile tests was used for all simulations since tensile data of the reference block was not available at -100 °C (Fig. 6). First, finite element simulations are required to calculate the stress intensity factor at fracture as no standard is available for such geometries, unlike the ASTM standards for CT specimens. Second, they are used to predict the stress and plastic strain field around the crack tip and along the crack front to compare the stress triaxiality and plastic state on CT and cruciform specimens.

The model prediction is in good agreement with the experiment (Fig. 13). The J integral at fracture onset

was calculated using G-theta procedure of Cast3M. The stress intensity factor values $K_J$ could be therefore estimated using equation [2]. The crack length correction was applied with the recommendations of the ASTME1921 standard. The standard formulation was adapted in equation [3] for the case of a part-through-wall elliptical defect, as proposed in (Moinereau et al. 2014). The corrected stress intensity factor obtained for the reference block was $K_{J1T} = 290 \text{ MPa.m}^{0.5}$.

<figure><img src="image_16.png" /><figcaption>**Fig. 13** Load vs CMOD curve of the biaxial test at -100 °C in the reference block. The dashed line is a finite element model prediction</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Fig. 12** Brittle fracture of the specimen from the reference block. Multiple initiation sites from the fatigue precrack ($a = 14.3$, $c = 23.5$ mm)</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 14 Mesh and boundary conditions applied for the fine element simulation of five point bending test on the cruciform specimens</figcaption></figure>

$$K_J = \sqrt{\frac{JE}{(1 - v^2)}} \qquad (2)$$

$$K_{J1T} = 20 + [K_J - 20] \left( \frac{\text{cracklength}}{25} \right)^{1/4} \qquad (3)$$

### 3.3.2 Result on the flaked block

Only one specimen exhibited the brittle fracture initiation expected on the fatigue precrack. For the two other specimens, the brittle fracture initiated on the machined slots. In that case, flake alignments on the surface of slots were responsible for the premature fracture. The load vs CMOD curves of the tests are presented in Fig. 15. The three curves are similar except for the fracture onset. The two specimens that failed on the slots showed an earlier fracture occurrence with maximal loads at fracture onset of 1100 kN and 1335 kN. The maximal load is higher (1825 kN) when the fracture initiates on the fatigue precrack.

The fracture surface presented in Fig. 16 corresponds to the specimen with fracture initiation on the fatigue precrack. The indications of flakes behind the fatigue crack front validate the good positioning of the specimen. Multiple crack initiation sites were also observed on the fatigue precrack. For the two other specimens, post-mortem loading was applied to break the specimens, so that the geometry of the initial fatigue precrack could be determined for numerical modelling.

The model predictions are in good agreement with the experiments (Fig. 15). As it was done for the

<figure><img src="image_19.png" /><figcaption>Fig. 15 Load vs CMOD curves of the three biaxial tests at -100 °C in the flaked block. The dashed line is a finite element model prediction</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 16 Brittle fracture of the specimen within the flaked block. Multiple initiation sites from the fatigue precrack (a = 13.8, c = 22 mm)</figcaption></figure>
reference block, the values of K<sub>J1T</sub> were estimated for
the three specimens, at fracture initiation. A maximal
value of K<sub>J1T</sub> = 160 MPa.m<sup>0.5</sup> was determined for the
specimen with fracture initiation on the fatigue
precrack. For the specimens that failed on the slots,
the K<sub>J1T</sub> values calculated on the fatigue precrack at
fracture onset were around 100 MPa.m<sup>0.5</sup>. (Fig. 16).

4 Discussion

4.1 Linking the fracture toughness with the carbon
content

An increase in local carbon content was measured
around the flakes. The material of zone 1, which is
between the flakes, has the highest carbon content
(Table 2). It decreases for the materials farther from
the flakes, in zone 2 and zone 3, which have almost
similar levels of carbon content. The reference block
that does not contain flakes has the lowest level of
carbon.

To separate the effects of the heat treatment and the
carbon content on the mechanical property analyses,
the quenching rate was similar for each material zone.
The higher carbon content led to slightly higher tensile
properties, in particular for the flaked region (zone 1)
compared to the reference block. The yield strength
and ultimate tensile stress increase with the carbon
content has been demonstrated in (Jacquemoud et al.
2018). The carbon content has a greater impact on the
fracture toughness than on tensile properties, with a T₀
reference temperature 15 °C higher in zone 1 (be-
tween the flakes) than in other zones of the flaked
block and 30 °C higher between the flakes than in the
reference block. This evolution of T₀ with the carbon
content is similar to the results obtained by Framatome
(Delvallée-Nunio et al. 2018) in the macrosegregation
zones of three EPR RPV vessel heads in ferritic steel
with similar chemical composition, as illustrated in
(Jacquemoud et al. 2018). Nevertheless, the reference
temperature of T₀ = -99 °C measured in zone 1 for
the flaked material, when converted to RT_T0
(-79.6 °C) (Technical Reports Series 429 of IAEA)
remains much lower than the maximal specified value
of RT_NDT in RCC-M for this material, which is used
for nuclear component design.

The same conclusions could be dropped for the
biaxial specimens, with a fracture toughness of

K<sub>J1T</sub> = 290 MPa.m<sup>0.5</sup> for the reference block contain-
ing a lower level of carbon whereas the fracture
toughness decreases to K<sub>J1T</sub> = 160 MPa.m<sup>0.5</sup> for the
flaked block with a higher level of carbon.

Intergranular fracture or coarse inclusions were not
observed on the fracture initiation sites of the spec-
imens with the lowest fracture toughness in neither
uniaxial nor biaxial loading conditions. This suggests
that the lowest fracture toughness values might result
from the embrittlement of the microstructure related to
the higher carbon content.

4.2 Role of the flakes on the fracture toughness

4.2.1 Comparison between CT specimens with fatigue
precrack and with flake

The fracture toughness of CT specimens with standard
fatigue precrack was compared to CT specimens with
hydrogen flake as a starter in Fig. 10, considering in
both cases the crack (or flake) mean length for the
fracture toughness calculation.

Nevertheless, the irregularity of the crack front on
CT specimens with flake makes the ASTM E1921
standard not strictly applicable. The crack front
curvature requirements were not met. Consequently,
further analyses were performed using minimal and
maximal crack lengths. The reference temperatures
obtained were respectively T<sub>0max</sub> = -96 °C and
T<sub>0min</sub> = -108 °C, where the value obtained with a
mean crack length was T<sub>0mean</sub> = -102 °C, suggesting
a limited effect of the crack front irregularity com-
pared to the scatter in fracture toughness at these
temperatures. This was confirmed by (Jacquemoud
et al. 2018) using extended finite elements to analyse
the same data set. The reference temperature, calcu-
lated when the flake fronts were accurately modelled,
remained close to T<sub>0max</sub>, suggesting that the impact of
the irregular shape of the flake front was negligible, as
previously considered by (Lacroix 2016).

Therefore, this validates the use of mean values to
compare the reference temperatures of CT specimens
with standard precracks and flakes. Since T₀ values are
very close (T₀ = −102 ± 7 °C and T₀ = −99 ±
6 °C) for both specimen configurations, it can be
concluded that the flakes behave as cracks in uniaxial
loading conditions, and they do not make the material
less resistant to fracture. (Chaouadi et al. 2016), who
carried out independently the first material
characterization of the same steam generator shell, drew a comparable conclusion.

### 4.2.2 Effect of flakes on biaxial fracture toughness

Cruciform specimens were used to investigate the effect of multiple tilted flakes on fracture toughness in biaxial loading conditions. Even if the geometry of the specimen had already been tested and validated in another study (Moinereau et al. 2014), it was found to be less appropriate for flaked material where the flakes could interact with the arm slots of the specimen. The stress concentration reached during the test around the slots where high enough to trigger crack initiation from the flakes located in this area. Pop-in-like sounds were noticed during the test, suggesting crack propagation and arrests. According to the distribution of flakes around the arm slots, a merging of the little cracks initiated on flakes could occur, leading to the brittle fracture of the arms. Therefore, the premature brittle fracture that occurred on the arms slots of two over three cruciform specimens was not representative of the loading expected on pressure vessels. The stress concentration induced by the slots might not be reached in the real structure. Moreover, the loading within the arm slots is uniaxial, which is covered by the analysis made on CT specimens. Regardless, a $K_j$ value of 100 MPa.m$^{0.5}$ has been reached on the fatigue precrack without any cleavage initiation. 100 MPa.m$^{0.5}$ being the mean toughness on CT specimens at this temperature, this result shows that fracture toughness in biaxial loading conditions is surely higher than in uniaxial ones.

The comparison between fracture toughness on biaxial and uniaxial loading conditions is reported in Table 3. For the reference block without flakes, the test temperature of – 100 °C in biaxial loading

conditions is almost 30 °C greater than the reference temperature $T_0$ estimated on CT specimens. The biaxial fracture toughness of 290 MPa.m$^{0.5}$ is much higher than the uniaxial fracture toughness of CT specimens, even for 99% of failure probability. According to (Bass et al. 1999) the onset of loss of containment in the cruciform specimen is reached near a stress intensity factor of approximately 200 MPa.m$^{0.5}$. The small ductile tearing zones (less than 200 µm), observed at some locations on the fatigue precrack front, confirmed that the test was performed higher in the ductile to brittle transition temperature range and the plasticity level was higher. This could explain the much higher value observed for the biaxial test in the reference block. For the flaked block, the test temperature of -100 °C corresponds to the reference temperature of the material estimated on CT specimens. The fracture toughness of 160 MPa.m$^{0.5}$ in biaxial loading conditions is higher than the uniaxial fracture toughness, even at 99% failure probability. This result validates the conservation of the usual RPV fracture analysis based on standard CT specimens toughness in the ductile to brittle transition, even in the presence of multiple hydrogen flakes.

Finally, to understand the beneficial effect of biaxial loading on cruciform specimens compared to CT specimens, the evolutions of stress triaxiality and plastic strain at the crack tip within both specimens were compared at – 100 °C (Fig. 17 and Fig. 18). For the same J-integral value, the stress triaxiality and therefore the constraint within cruciform specimens is lower compared to CT specimens. In the literature, many parameters (T, Q, A2 and $\lambda$) were introduced to quantify the constraint within specimens. They all lead to the same conclusion. (Qian et al. 2018, Cao et al. 2018 and Chen et al. 2023) reported that a lower

<table><caption>**Table 3** Summary of fracture toughness on uniaxial and biaxial loading conditions at – 100 °C</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Biaxial fracture toughness</th><th colspan="4">Uniaxial fracture toughness on CT</th></tr><tr><th>5% of failure probability</th><th>50% of failure probability</th><th>95% of failure probability</th><th>99% of failure probability</th></tr></thead><tbody><tr><td>Reference block</td><td>290 MPa.m<sup>0.5</sup></td><td>90 MPa.m<sup>0.5</sup></td><td>150 MPa.m<sup>0.5</sup></td><td>210 MPa.m<sup>0.5</sup></td><td>230 MPa.m<sup>0.5</sup></td></tr><tr><td>Flaked block (zone 1)</td><td>160 MPa.m<sup>0.5</sup></td><td>60 MPa.m<sup>0.5</sup></td><td>100 MPa.m<sup>0.5</sup></td><td>130 MPa.m<sup>0.5</sup></td><td>150 MPa.m<sup>0.5</sup></td></tr></tbody></table>
<figure><img src="image_21.png" /><figcaption>**Fig. 17** Evolution of the stress triaxiality value during loading at -100 °C. Comparison between uniaxial tests on CT specimens and biaxial tests on cruciform specimens</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. 18** Evolution of the equivalent plastic strain value during loading at -100 °C. Comparison between uniaxial tests on CT specimens and biaxial tests on cruciform specimens</figcaption></figure>

constraint resulted in a higher toughness, which was confirmed in this study too. An opposite tendency was observed for the evolution of the equivalent plastic strain, with the highest values for the cruciform specimens typical of shallow crack configuration with larger plastic zones. This result is in good agreement with (Tankoua et al 2022) who reported a delay of the brittle fracture with plastic deformation. Both stress

triaxiality and plastic strain at the crack tip could explain the higher fracture toughness obtained on cruciform specimens.

Crack interaction was not studied here, only the influence of the presence of surrounding flakes on initiation has been investigated. Nevertheless, in the flaked block, tilted flakes induce a shear component of stress leading to higher stress concentration on the fatigue precrack and consequently a higher value of the maximum fracture toughness. This phenomenon was not considered in the simulations as the flakes have not been modelled. Therefore, the biaxial fracture toughness of 160 MPa.m<sup>0.5</sup> is a conservative value.

## 5 Conclusions

The effect of hydrogen flakes on fracture toughness was investigated for uniaxial and biaxial loading conditions comparing both reference and flaked materials.

* On standard CT specimens, the fracture toughness variation in the reference and the flaked blocks was related to the difference in carbon content measured on the fracture surface. The higher the carbon content, the higher the reference temperature $T_0$. Consequently, zone 1 between the hydrogen flakes exhibiting the highest carbon level, has the lowest fracture toughness. The same conclusions apply to biaxial loading conditions.

* The presence of a hydrogen flake instead of a fatigue crack in CT specimens does not significantly modify the reference temperature $T_0$. Isolated flakes in CT specimens behave as fatigue precracks showing a similar statistical distribution of the fracture toughness.

* The fracture toughness of cruciform specimens is considerably higher than the fracture toughness of CT specimens for both reference and flaked materials at -100 °C. The positive effect of a lower constraint level combined with a shallow crack (larger plasticity) is confirmed even if it is less important on flaked material compared to the reference one. The presence of multiple flakes ahead of the fatigue precrack, at a minimum distance of 10 mm, does not cancel the positive
effect. This confirms the conservatism of the fracture analysis based on standard CT specimens.

* Additional tests in biaxial loading conditions may be required on the flaked material to confirm the positive effect observed on fracture toughness. However, another geometry should be considered to avoid the premature brittle fracture that occurred on the arm slots of some cruciform specimens, when alignments of hydrogen flake were located around the slots.

**Acknowledgements** IRSN and CEA are thankful to M. Claude BENHAMOU and M. Pierre JOLY from Framatome who provided the material of the study and expertise that assisted the research. They are also grateful to BEL V for its financial support in the second phase of the test programme. CEA-LIST involvement in the ultrasonic examinations is gratefully acknowledged.

**Author contributions** F. Tankoua: Methodology, testing & analysis, writing original draft, writing review & editing. C. Jacquemoud: Methodology, testing & analysis, writing original draft, writing review & editing. MB. Le: Methodology, review & editing. G. Roussel: Methodology, review & editing.

**Data Availability** No datasets were generated or analysed during the current study.

## Declarations

**Conflict of interest** The authors declare that they have no conflict of interest relevant to the content of this article.

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