Delayed Hydride Cracking (DHC) is a hydrogen embrittlement phenomenon that may affect Zircaloy-4 fuel claddings. An experimental procedure was previously developed to measure the fracture toughness of this material using notched C-ring specimens with a precrack, for both in presence of DHC ( K_I_DHC ) and without ( K_I_C ) (François et al. 2024). Based on these experiments, and on additional experimental results on notched C-ring specimens without a precrack, a finite element model was developed to numerically reproduce the DHC phenomenon. This model couples the mechanical behavior of the material with the presence of hydrogen in solid solution and hydrides, considering the kinetics of hydrogen diffusion, and the nucleation, growth and dissolution of hydrides (HNGD model). A cohesive zone model was used for crack propagation. The numerical model successfully reproduces the experimental results and is consistent with the experimental values of K_I_DHC , crack propagation rate and incubation time at 150, and 200 ^∘C for precracked specimens and 250 ^∘C for both precracked and notched specimens. In addition, this study highlights the great influence of the swelling induced by the presence of hydrogen in solid solution and precipitated hydrides on the fracture of the material in case of DHC, and the importance to take it into account to model this phenomenon.

Spallation in ductile metals involves complex void nucleation and growth mechanisms, but the interactions between voids and the resulting statistical structure of fracture surfaces remain a persistent challenge for both experimental and theoretical modeling. This study develops a generative model to capture the statistical features of spall-induced fracture surfaces in high-purity aluminum. Aluminum samples were subjected to nanosecond laser-induced spallation, and the resulting fracture surfaces were imaged via scanning electron microscopy (SEM) and reconstructed in 3D. Individual dimples were segmented and analyzed to extract void size distributions and the spatial arrangement of nucleation sites. Boolean models and Gaussian random fields were then used to generate synthetic surfaces and compared against the experimental data using one- and two-point statistics. The analysis revealed a Poisson distribution of nucleation centers within the spall plane but significant out-of-plane spatial correlations in nucleation depth. The extended generative model successfully reproduces both the surface height distribution and the spatial covariance observed experimentally. These results emphasize the need to incorporate large-scale spatial correlations in predictive models of dynamic ductile damage. The proposed framework provides a basis for future studies of collective void growth and spall surface formation in dynamic ductile fracture.

Biodegradable magnesium alloys are promising materials for next-generation degradable vascular stents, yet their limited ductility and strong tension-compression asymmetry pose major challenges for device deployment. This study investigates the mechanical response and failure behaviour of three magnesium alloys - Mg-2Gd, Mg-4Y-3Gd, and ZX10 - under load reversals representative of stent crimping and expansion. Cyclic tension-compression tests were performed to quantify strength asymmetry, twinning/de-twinning effects, and residual ductility. A constitutive framework combining the Cazacu-Plunkett-Barlat yield criterion with a Gurson-Tvergaard-Needleman damage model was calibrated for each alloy to accurately represent cyclic plasticity and ductile failure. The validated material model was implemented into a finite element simulation of the full crimping-expansion sequence of a balloon-expandable stent. Mg-2Gd and Mg-4Y-3Gd exhibited high tensile ductility after load reversals and maintained structural integrity during simulated deployment, with moderate springback and recoil. In contrast, ZX10 showed early void nucleation, rapid damage accumulation, and premature segment failure during expansion, preventing full deployment. The modelling framework provides detailed insight into local strain paths, damage evolution, and critical design regions, enabling reliable in silico assessment of stent performance.

Ductile fracture behavior in ferritic steels is investigated using two complementary experimental databases. The first database involves a wide range of cracked and uncracked specimen geometries tested at various temperatures for a A533 (18MND5) steel, enabling a detailed analysis of the effect of stress states, particularly stress triaxiality and the Lode parameter, on damage nucleation and growth. The second database, for a WB36 (15NiCuMoNb5) steel, includes both laboratory-scale specimens and full-scale structural tests on precracked pipes at various temperatures. A gradient-enhanced energy GTN (Gurson-Tvergaard-Needleman) model incorporating a Lode-parameter-dependent nucleation function is employed to simulate ductile damage across different stress states. The model is first calibrated and validated on the A533 dataset. It is then applied to the WB36 dataset to assess its transferability from specimens to structural components. The results confirm the model's ability to accurately capture damage evolution and crack propagation, demonstrating its robustness and relevance for structural integrity assessments.

This study investigates the effect of strain rate on hydrogen embrittlement in ferritic-pearlitic E355 steel sub-size tensile specimens. Micrometer-scale damage analysis was performed using 3D X-ray tomography. Tests were conducted using an optical extensometry at varying strain rates in air and a 100 bar gas hydrogen atmosphere, including interrupted tests before rupture to capture damage states. Hydrogen reduces ductility, with losses reaching up to 62.8% at slower strain rates. At moderate strain rate, 5 x 10-4 s-1, surface damage manifests as brittle, flat ellipsoidal cracks perpendicular to the tensile axis, while the bulk retains ductile damage with prolate voids aligned longitudinally. Hydrogen-enhanced internal shearing leads to damage coalescence via slant fracture of the ligament between surface cracks and internal voids. At low strain rates (1 x 10-5 s-1), deeper hydrogen diffusion induces brittle flat ellipsoidal cracks both at the surface and in the bulk.

A miniaturized Ring Notched Bend test (mRNB) was developed as a means to assess the fracture toughness of thin-walled tubes. The fracture resistance curve (J-R curve) was derived from both the load-CMOD curve and the load-LLD curve, utilizing a single specimen technique. Following the procedures proposed in the ASTM E1820 standard [1], the elastic unloading methods were employed for the load-CMOD curve. Alternatively, the normalization method was utilized to analyze the load-LLD curve when CMOD measurements was not possible. However, for the application of this methodology to the mRNB test, the standard lacks the necessary functions, including the compliance function, the geometric stress intensity function, and the plastic factor, to process the test results. In this study, the finite element analysis was used to determine the geometric functions required for crack length evaluation during the test, as well as the elastic and plastic components of the J-integral, whether derived from the load-CMOD or load-LLD curve. This methodology was applied to experimentally investigate the crack growth resistance and damage of two types of ODS (Oxide Dispersion Strengthened) steel tubes, (containing specifically 9%Cr and 14%Cr), which are considered candidate materials for fuel claddings of future fast-neutron reactors.

The effect of strain-hardening on ductile crack growth is explored based on a small scale yielding finite element approach using an advanced nonlocal Gurson model. A focus is put on considering high strain hardening exponent n up to 0.5, while classical literature is often limited to n = 0.2, in order to encompass materials like stainless steels as well as several modern TRIP-TWIP alloys and high entropy alloys. First, J2 plasticity-based simulations are performed to set the static crack reference. These simulations provide a hint about the origin of the increase of fracture toughness with increasing n, connected to much smaller finite strain zones at a given loading level quantified by the value of the J integral. In addition, it is found that above n similar to 0.3, the opening stress does not attain a maximum value at a distance equal to one to two crack openings but keeps increasing towards the surface of the blunted crack tip. Then, Gurson-based simulations are used to determine the JR curve for different n and initial porosity, and associated quantities related to crack initiation such as JIc, critical crack tip opening displacement Sc, and fracture process zone length. As already found in earlier studies, both JIc and Sc increase with increasing n, although the effect is much more marked on JIc. The origin of this first-order effect is unraveled by looking at the stress triaxiality, damage, and plastic strain fields. Even though the near crack tip stress triaxiality increases with n, the associated lower plastic strain at a fixed distance to the crack front leads to much lower void growth rates and delays void coalescence. As a important side result, the simulations appear very sensitive to an accurate fine-tuning of the adjustment factors entering the Gurson model at high strain hardening, pointing towards the intrinsic limitations of the model when n is large. This study confirms the interest in developing alloys with large strain hardening capacity, not only with respect to tensile properties but also in view of enhancing the ductile fracture toughness.

The state of maturity of the micromechanics of ductile fracture is such that it is possible, today, to simulate extensive crack growth in 3D using a sophisticated physics-based description of the mechanisms of nucleation, growth and coalescence of voids within a non-local formulation. Here, different phenomena related to ductile crack growth are addressed in the context of fracture mechanics specimens. Structural integrity assessment of many critical components does indeed rely on predictive models of crack growth from pre-existing sharp defects. Two similar extended Gurson models are used, after comparison to cross-verify their numerical implementation, to generate results about the effect of plate thickness, plastic anisotropy and strain hardening. The variation of the fracture toughness increasing and then decreasing with thickness down to the plane strain regime is captured owing to the 3D nature of the simulations that captures the crack tip necking phenomenon. The non-local formulation introduces a length scale that sets the range over which the fracture toughness depends on thickness. Surprizingly, the thickness effect disappears when using homothetic geometries. The effect of plasticity anisotropy is shown to be particularly important when a crack grows in sheets exhibiting significant crack tip necking by impacting among other the plastic dissipation in the neck. A large strain hardening capacity enhances very much the fracture toughness, an effect that is amplified in 3D when crack tip necking takes place. These findings constitute only a limited set of answers to many remaining questions in the important field of ductile tearing, setting an ambitious roadmap for the years to come to the solid mechanics community. These questions are particularly important in the context of modern technologies such as H2 storage, additive manufacturing, new high strength metallic alloys development, and generation IV nuclear fission and fusion reactors to name a few.

Measuring ductile fracture toughness for materials requires the specimen size to be large enough for the tests to be valid. The presented work investigates the size related fracture behavior of as-received and aged 316 L(N) stainless steel through an experimental approach. It focuses on the effects of the thickness and size of the specimens on the evaluated toughness. Compact tension (CT) specimens (thicknesses from 4 to 50 mm) and double edge notched tensile (DENT) specimens (thicknesses from 2 to 5 mm) were used. At as-received state, CT tests lead to a nonmonotonic evolution of fracture toughness with a maximum at a critical thickness. At aged state, there is no significant thickness effect as all tests are valid. The essential work of fracture measured with DENT specimens appears to be equivalent to J0.2$$ {J}_{0.2} $$ and consequently extends the nonmonotonic evolution of the fracture toughness at small thicknesses.

Tests on cracked CT and SENT specimens (152 tests) extracted from a nuclear pressure vessel steel (18MND5) were conducted between C and C together with tests on smooth and notched bars. Tests on tensile bars were used to calibrate a temperature-dependent hardening law. Tests on cracked specimens that exhibited brittle failure only were analyzed using the Beremin model. Special care was taken to evaluate local stresses using enhanced mixed finite elements. The Beremin model was able to represent the entire database provided the reference failure stress increases with temperature. Finally, the results were also interpreted using the Master Curve approach, which was adapted to account for different stress states using the -parameter.

The integration of hydrogen into natural gas pipelines presents challenges due to Hydrogen Embrittlement (HE), requiring critical material selection and testing methods. One such test is the Disk Pressure Test (DPT), which consists in pressurizing a clamped disk to failure. However, failure happens often at the clamping zone, making analysis difficult. This study aims to develop new disk geometries to control failure location while maintaining the test setup. Using two steel grades (a vintage X52 pipeline steel and a modern E355 modified steel with potential for pipeline use), new disk geometries were tested under helium and hydrogen at various pressure rise rates. Results show successful displacement of failure away from the clamping zones, demonstrating the effectiveness of the new geometries. Hydrogen embrittlement is demonstrated by comparing failure pressures under helium and hydrogen at various pressure rise rates. Using both material testing and simulation, this study provides insights into hydrogen embrittlement.

Delayed hydride cracking (DHC) is a hydrogen embrittlement phenomenon that may potentially occur in Zircaloy-4 fuel claddings during dry storage conditions. An experimental procedure has been developed to measure the toughness of this material in the presence of DHC by allowing crack propagation through the thickness of a fuel cladding. Notched C-ring specimens, charged with 100 wppm of hydrogen, were used and pre-cracked by brittle fracture of a hydrided zone at the notch root at room temperature. The length of the pre-crack was measured on the fracture surface or cross-sections. Additionally, a finite element model was developed to determine the stress intensity factor as a function of the crack length for a given loading. Two types of tests were conducted independently to determine the fracture toughness with and without DHC, K_I_DHC and K_I_C , respectively: (i) constant load tests at 150 ^∘ C, 200 ^∘ C, and 250 ^∘ C; (ii) monotonic tests at 25 ^∘ C, 200 ^∘ C, and 250 ^∘ C. The results indicate the following: (1) there is no temperature influence on the DHC toughness of Zircaloy-4 between 150 and 250 ^∘ C ( K_I_DHC∈[ 7.2;9.2] MPa √(m) ), (2) within this temperature range, the fracture toughness of Zircaloy-4 is halved by DHC ( K_I_C∈[ 16.9;19.7 ] MPa √(m) ), (3) the crack propagation rate decreases with decreasing temperature and (4) the time before crack propagation increases as the temperature and loading decrease.

A new simulation strategy to model hydrogen embrittlement based on a multi-field finite element using displacements, pressure, volume variation, nonlocal damage variables and lattice hydrogen concentration as unknowns is proposed. The material is described using a modified GTN model, which includes the description of hydrogen enhanced decohesion (HEDE). The finite element problem is solved using a fully implicit formulation. Numerical problems related to volumetric locking are solved using a mixed pressure/volume variation formulation. The use of the mixed formulation allows a straightforward evaluation of the pressure gradient, which drives hydrogen diffusion. Mesh size dependence is solved using an implicit gradient nonlocal formulation. Two variables are used to represent damage: the plastic volume variation and the accumulated plastic strain, controlling nucleation. The model is used to simulate an existing experimental database (Moro et al., 2010; Briottet et al., 2012) including tensile, fracture toughness and pressurized disk tests. The model, after adjusting the various coefficients, can represent the main experimental findings: the effect of deformation rate on the failure of tensile specimens, the transition from surface to internal fracture with increasing deformation rate, the sharp toughness drop under hydrogen (CT specimen), the fracture location and the effect of the pressurization rate in the case of the tests on disks.

In the present study, several parameters related to crack morphology in the case of hydrogen embrittlement were estimated by X-ray computed tomography and correlated with the macroscopic mechanical responses (J-integral and tearing modulus) obtained from the fracture mechanics tests. Even when the hydrogen content was high up to 4.00 wt ppm, unstable premature fracture did not immediately occur, and a certain crack-growth resistance could be confirmed. The three-dimensional crack morphology was not continuous with the formation of un-cracked ligaments in the uncharged specimen. In contrast, the hydrogen-related intergranular crack propagated more continuously with a smaller crack opening-displacement. The J-integral value monotonically increased with increasing estimated values of the surface area divided by the projected surface area on the macroscopic crack plane, indicating that crack meandering and branching increased the fracture energy. We defined crack-propagated thickness (standard deviation of the crack surface area at each section (parallel to the macroscopic crack plane) divided by the crack surface area) as a parameter representing crack meandering. The tearing modulus increased as the crack-propagated thickness increased, suggesting that crack meandering also increased the crack-growth resistance.

The mechanical behaviour of 316L stainless steel single crystal is characterised at room temperature and 300°C. Elasticity moduli at room temperature are obtained with resonant ultrasound spectroscopy. Their dependence on temperature is calibrated with molecular dynamics simulations. The plastic behaviour is characterised by tensile tests on millimetre-sized single crystal specimens and compression tests on micrometre-sized single crystal specimens. A constitutive model of crystal plasticity based on dislocation density hardening at finite strains is developed and implemented in an open-source material subroutine compatible with several finite element (FE) and fast Fourier transform (FFT) solvers. Tensile curves at room temperature and 300°C are used to calibrate the interaction coefficients for self and coplanar dislocation interactions. The dislocation mean free path for obstacle dislocations and the annihilation distance are also calibrated. The calibrated model predicts tensile curves in excellent agreement with experimental data. In addition, the predicted plastic strain fields are in good agreement with the experimental fields obtained by digital image correlation. Semi-quantitative agreement between simulation and experimental data is obtained for micro-compression tests without further calibration of the model. Finally, an extension to polycrystals with grain size effects is finally proposed. The predicted strain hardening behaviour is compared with experimental data on stainless steel polycrystals.

Intergranular cracks in the uncharged specimen were arrested at low-angle prior austenite grain boundary (PAGB) segments of several micrometers. In contrast, even small, low-angle PAGB segments with sub-micrometer sizes impeded the propagation of hydrogen-related intergranular crack. At the hydrogen-related quasi-cleavage crack tip, the crystallographic orientation changed abruptly, and deformation microstructures developed, including the formation of low-energy dislocation structures. A certain degree of crack growth resistance (intrinsic crack growth resistance) in the hydrogen-related fractures could be attributed to the intense localized plastic works involved in the arrest of intergranular cracks and the propagation of quasi-cleavage cracks.

The failure strain of a tube is a function of the biaxial strain ratio (axial strain/hoop strain) to which it is subjected. The relationship between failure strain and the strain ratio can be determined experimentally using expansion due to compression tests with a tensile load (EDCT), in which a ductile pellet placed inside the tube is compressed axially so it expands in diameter and imposes a hoop strain on the tube. At the same time, a tensile load on the ends of the tube creates an axial strain. This study investigates the capabilities and limitations of EDCT tests using two devices that allow experiments to be performed on a standard tensile testing machine. The first device applies an axial force on the ends of the sample, and the second device applies an axial displacement. Tests on zirconium alloy tubes confirmed that the failure strain is dependent on the strain ratio and the metallurgical state of the material. EDCT tests can produce a range of strain ratios, but there is an upper limit on the strain ratio that can be obtained, and it is dependent on the plastic behaviour of the sample and the friction conditions between the components.