Table of contents

The microstructure of dual-phase (DP) steels typically consists of a soft ferrite matrix with dispersed islands of hard martensite phase. Due to the composite effect of ferrite and martensite, DP steels exhibit a unique combination of strain hardening, strength and ductility. A microstructure-based micromechanical modeling approach is adopted in this work to capture the tensile and cyclic plastic deformation behavior of DP steel. During tensile straining, strain incompatibility between the softer ferrite matrix and the harder martensite phase arises due to a difference in the flow characteristics of these two phases. Microstructural-level inhomogeneity serves as the initial imperfection, triggering strain incompatibility, strain partitioning and finally shear band localization during tensile straining. The local deformation in the ferrite phase is constrained by adjacent martensite islands, which locally results in stress triaxiality development in the ferrite phase. As the martensite distribution varies within the microstructure, the stress triaxiality also varies in a band within the microstructure. Inhomogeneous stress and strain distribution within the softer ferrite phase arises even during small tensile straining because of material inhomogeneity. The magnitude of cyclic plastic deformation within the softer ferrite phase also varies according to the stress distribution in the first-quarter cycle tensile loading. Accumulation of tensile/compressive plastic strain with number of cycles is noted in different locations within the ferrite phase during both symmetric stress and strain controlled cycling. The basic mode of cyclic plastic deformation in an inhomogeneous material is cyclic strain accumulation, i.e. ratcheting. Microstructural inhomogeneity results in cyclic strain accumulation in the aggregate DP material even in symmetric stress cycling.

A set of parameters for the modified embedded atom method (MEAM) potential was developed to describe the perovskite silver tantalate (AgTaO₃). First, MEAM parameters for AgO and TaO were determined based on the structural and elastic properties of the materials in a B1 reference structure predicted by density-functional theory (DFT). Then, using the fitted binary parameters, additional potential parameters were adjusted to enable the empirical potential to reproduce DFT-predicted lattice structure, elastic constants, cohesive energy and equation of state for the ternary AgTaO₃. Finally, thermal expansion was predicted by a molecular dynamics (MD) simulation using the newly developed potential and compared directly to experimental values. The agreement with known experimental data for AgTaO₃ is satisfactory, and confirms that the new empirical model is a good starting point for further MD studies.

For two-dimensional dislocation dynamics simulations under periodic boundary conditions in both directions, the summation of the periodic image stress fields is found to be conditionally convergent. For example, different stress fields are obtained depending on whether the summation in the x-direction is performed before or after the summation in the y-direction. This problem arises because the stress field of a 1D periodic array of dislocations does not necessarily go to zero far away from the dislocation array. The spurious stress fields caused by conditional convergence in the 2D sum are shown to consist of only a linear term and a constant term with no higher order terms. Absolute convergence, and hence self-consistency, is restored by subtracting the spurious stress fields, whose expressions are derived in both isotropic and anisotropic elasticity.

A stochastic model is proposed for the efficient simulation of complex three-dimensional microstructures consisting of two different phases. The model is based on a hybrid approach, where in a first step a graph model is developed using ideas from stochastic geometry. Subsequently, the microstructure model is built by applying simulated annealing to the graph model. As an example of application, the model is fitted to a tomographic image describing the microstructure of electrodes in Li-ion batteries. The goodness of model fit is validated by comparing morphological characteristics of experimental and simulated data.

We present a molecular dynamics (MD) study of the micro-spallation of lead (Pb), which corresponds to damage and liquid fragment ejection following the reflection of a strong shock wave on the free surface of the target. First, the Hugoniot and melting curves of Pb are derived by equilibrium MD simulations, and the potential function is validated by comparing these curves with experimental results. Then nonequilibrium MD simulations are conducted to study the dynamical processes of micro-spallation. Damage and ejection processes are analyzed by a binning analysis and direct observations of atom configurations. Comparisons with classical spallation simulations or experiments are made where necessary. It is found that damages in classical spallation and micro-spallation are both dominated by cavitation, i.e. nucleation and the growth and coalescence of voids. The main difference in the cavitation process of classical and micro-spallation lies in the amount and spatial distribution of void nucleation sites. Different properties in dynamical stress evolutions between micro-spallation and classical spallation are also discussed. In addition, the properties of the surface micro-spall are found to be different from those of interior micro-spall particles in some shock intensity regimes. Factors that cause such differences are studied by analyzing in detail the thermodynamics paths of different parts of the shocked target.

Nickel-based superalloys are critical for aerospace and power applications due to excellent high-temperature properties. These high-temperature properties are attributed to the coherently precipitated gamma prime phase in the gamma matrix. The segregation of alloying elements between the matrix and the gamma prime phase drives precipitate misfit strains and impacts material strength. This study aims at understanding the site preference of Co and Cr within the ordered gamma prime phase. The study also calculates the interaction energy between alloying additions within the ternary systems Ni–Al–Cr and Ni–Al–Co, and the quaternary system Ni–Al–Cr–Co. It is found that Co has mixed substitution behavior between the Al and Ni sites in the gamma prime phase. The results from the Ni–Al–Cr ternary system show that two Cr atoms prefer being close to each other, with the most stable configuration of the first nearest neighbors of the Al–Al site. The interaction energies calculated from the Ni–Al–Co system show that the initial distance between two Co atoms will decide whether the two Co atoms prefer Ni–Ni or Ni–Al configuration. The study on the quaternary system Ni–Al–Cr–Co reveals that the initial configuration of Cr and Co atoms will affect the final most stable configuration. The results are found to be consistent with our previous findings.

A mechanism for $(1\,0\,\bar{1}\,2)$ twin nucleation in Mg is studied in which edge 〈c〉 and mixed 〈c + a〉 lattice dislocations dissociate into a stable twin, having at least the minimum 6-layer thickness formed by three glissile twinning dislocations, plus a residual stair rod dislocation. Continuum dislocation theory is used to compute the energy of the initial and final states of the proposed dissociation process, using the twin boundary energy computed by density functional theory. For the 〈c〉 dislocation, the proposed dissociation is energetically favorable. An alternative dissociation path into partials on two $\{1\,0\,\bar{1}\,1\}$-type pyramidal planes is possible, as seen in an atomistic analysis, and the continuum analysis predicts this alternative path to be more favorable than the twin process. For the 〈c + a〉 dislocation, the continuum model also predicts that dissociation into the twinned structure is energetically favorable for 6-layer and thicker twins. In both 〈c〉 and 〈c + a〉 cases, the equilibrium twin length is predicted to increase with increasing applied resolved shear stress and grow unstably beyond a critical stress. Atomistic simulations of these processes are then performed. For 〈c〉, a twinned structure is stable under zero loading but with higher energy than the alternative dissociation on two $\{1\,0\,\bar{1}\,1\}$ planes. Under a positive applied strain of 4%, resolved on the twin plane, the twinning structure grows while under a negative applied strain of −3%, it reverts back to the alternative low-energy dissociated configuration on the pyramidal planes. For the mixed 〈c + a〉 dislocation, the atomistic models predict that the dissociation into twinning dislocations does not occur spontaneously at zero applied strain but there is a stable twinned region at finite applied loads. These results demonstrate that dislocation-assisted mechanisms for twinning in Mg, initiating from lattice dislocations with large Burgers vectors, are physically feasible, and therefore twin nucleation from grain boundaries is not necessarily the dominant mechanism of twinning in Mg.

The motion mechanism of the edge dislocation slipping in the cubic plane of Ni₃Al under an applied shear stress at different temperatures is studied. At lower temperatures, the edge dislocation moves forward smoothly, and no dislocation lock is formed. At higher temperatures, the motion mechanism of the edge dislocation is controlled by the complex Lomer–Cottrell lock mechanism. Sometimes, the complex Lomer–Cottrell lock tends to transform into a full Lomer–Cottrell lock. The energy barriers of these transformation processes are calculated, and the underlying reason for these transformation processes can be understood in terms of the energy barriers and the applied shear stress. This work gives a good explanation of the in situ observation of the edge dislocation slipping in the cube planes of Ni₃Al.

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

The discrete element method (DEM) was used to model calcium-silicate-hydrate (C-S-H) at the nanoscale. The C-S-H nanoparticles were modeled as spherical particles with diameters of approximately 5 nm. Interparticle forces included traditional mechanical contact forces, van der Waals forces and ionic correlation forces due to negatively charged C-S-H nanoparticles and ion species in the nanopores. Previous work by the authors demonstrated the DEM method was feasible in studying the properties of the C-S-H nanostructures. In this work, the simulations were performed to look into the effects of nanoparticle packing, nanoparticle morphology, interparticle forces and nanoparticle properties on the deformation mechanisms and mechanical properties of the C-S-H matrix. This work will provide insights into possible ways to improve the properties of the C-S-H matrix.

Atomistic simulations play an important role in advancing our understanding of the mechanical properties of materials. Currently, most atomistic simulations are performed using relatively simple geometries under homogeneous loading conditions, and a significant part of the computer time is spent calculating the elastic response of the material, while the focus of the studies lies usually on the mechanisms of plastic deformation and failure. Here we present a simple but versatile approach called FE2AT to use finite element calculations to provide appropriate initial and boundary conditions for atomistic simulations. FE2AT allows us to forgo the simulation of large parts of the elastic loading process, even in the case of complex sample geometries and loading conditions. FE2AT is open source and can be used in combination with different atomistic simulation codes and methods. Its application is demonstrated using the bending of a nano-beam and the determination of the displacement field around a crack tip as examples.

Two twinning laws, the albite law and the pericline law, are the predominant growth twinning modes in triclinic plagioclase feldspars such as low albite, NaAlSi₃O₈, in which the aluminum and silicon atoms are in an ordered arrangement on the tetrahedral sites of the aluminosilicate framework. In the terminology used formally to describe deformation twinning in a triclinic lattice, these twin laws can be described as Type I and Type II twin laws, respectively, with the pericline twin law being conjugate to the albite twin law. In this study, twin boundaries have been constructed for low albite according to these two twinning laws and studied by molecular dynamics simulation. The results show that suitably constructed twin boundary models are quite stable for both albite twinning and pericline twinning during molecular dynamics simulation. The calculated twin boundary energy of an albite twin is significantly lower than that of a pericline twin, in accord with the experimental observation that albite twinning is the more commonly observed mode seen in plagioclase feldspars. The results of the molecular dynamics simulations also agree with conclusions from the prior work of Starkey that glide twinning in low albite is not favoured energetically.

The shear response of the $\Sigma3 \ [\bar{1}\,1\,0]$-tilt $(\bar{1}\,\bar{1}\,5)/(1\,1\,1)$ and $\Sigma9 \ [\bar{1}\,1\,0]$-tilt (1 1 5)/(1 1 1) asymmetric tilt grain boundaries (GBs) in fcc metals Cu and Al has been studied by atomistic simulation methods with the embedded atom method interatomic potentials and with a bicrystal model. It is found that the structure of the GBs studied can be well described by the coincidence site lattice (CSL) theory. Shear of these GBs at room temperature along eight different directions within the GB plane shows that these two types of GBs can transform between each other by the formation of a coherent twin boundary. The structure transformation of the GBs can also take the form of GB sliding, GB sliding–migration coupled motion, GB faceting, GB 9R structure formation, etc, depending on the shear directions adopted and the material involved (Cu or Al). The detailed structure transformation mechanisms have been analyzed with the aid of the CSL–DSC (displacement shift complete) theory. Several structure transformation paths adherent to these two types of GBs have been identified for the activation of the GB sliding–migration coupled motion. It is concluded that, although CSL–DSC theory can be applied to describe the sliding–migration coupled motion of the GBs studied, some other effects such as the shear direction within the GB plane and the bonding characteristics of the materials should also play a significant role in the shear response of these GBs.

The influence of H, C, N and O impurities on the energetic and mechanical stabilities of Mg and Al were studied by first-principles total energy calculations. The occupation preference and formation energy of impurities in Mg and Al were estimated. H and C decrease the energetic stability of Mg and Al, while N and O significantly increase it. In Mg, H and O prefer to occupy the tetrahedral site, while C and N tend to occupy the octahedral site. In Al, only C prefers the octahedral site, while other elements will occupy the tetrahedral site. Electronic structures were analyzed to clarify the bonding properties and stability mechanisms of H, C, N and O in Mg and Al. The bonding characteristics around the Fermi energy level respond to the influence of impurities on the stability of Mg and Al. This work shows that all the impurities form strong bonds with the host atoms, but H and C weaken the interactions between host atoms, while N and O rarely affect these kinds of interactions. It seems that these bonding characteristics are independent of the crystal structures of matrices and the valence electron configurations of the host atoms. Elastic constants of impurity-containing systems were estimated from curves of energy against strain to evaluate the mechanical stability and elastic properties of the systems considered. All the impurity-containing systems satisfy the mechanical stability criteria. The influence of impurities on the elastic properties of Mg and Al was also studied.

An ensemble averaging approach was investigated for its accuracy and convergence against time averaging in computing continuum quantities such as stress, heat flux and temperature from atomistic scale quantities. For this purpose, ensemble averaging and time averaging were applied to evaluate Hardy's thermomechanical expressions (Hardy 1982 J. Chem. Phys.76 622–8) in equilibrium conditions at two different temperatures as well as a nonequilibrium process due to shock impact on a Ni crystal modeled using molecular dynamics simulations. It was found that under equilibrium conditions, time averaging requires selection of a time interval larger than the critical time interval to obtain convergence, where the critical time interval can be estimated using the elastic properties of the material. The reason for this is because of the significant correlations among the computed thermomechanical quantities at different time instants employed in computing their time average. On the other hand, the computed thermomechanical quantities from different realizations in ensemble averaging are statistically independent, and thus convergence is always guaranteed. The computed stress, heat flux and temperature show noticeable difference in their convergence behavior while their confidence intervals increase with temperature. Contrary to equilibrium settings, time averaging is not equivalent to ensemble averaging in the case of shock wave propagation. Time averaging was shown to have poor performance in computing various thermomechanical fields by either oversmoothing the fields or failing to remove noise.

Deformation-induced heating of explosive composites is influenced by the material microstructure (i.e. porosity and particle sizes, shapes and packing), and component-specific thermomechanical properties and mass fractions. In this study, an explicit, 2D, Lagrangian finite and discrete element technique is used to examine thermomechanical fields in mixtures of explosive (HMX, C₄H₈N₈O₈) and metal particles (Al) induced by piston-supported deformation waves (piston speed 50 ⩽ U_p ⩽ 500 m s⁻¹). The mesoscale description uses a plane strain, thermoelastic–viscoplastic and friction constitutive theory to describe the motion and deformation of individual particles, and an energy consistent, penalty based method to describe inter-particle contact. The deformation response of material having an initial solid volume fraction of φ_s0 = 0.835 (porosity 1 − φ_s0 = 0.165) is characterized for different metal mass fractions and wave strengths. Transition from a strength-dominated to a pressure-dominated wave structure is predicted to occur with increasing wave strength due to the elimination of porosity. Average thermomechanical fields that define the effective wave structure differ both qualitatively and quantitatively for the two types of structures. Explosive component mass locally heated to elevated temperature behind waves is shown to be affected by the wave structure and the value of friction coefficient.

Generation of realistic grain boundaries (GBs) in bicrystals for atomistic simulations requires a search in a multidimensional space for a configuration with the atoms at the GB organized in such a way that the energy of the whole system is minimized. This paper presents a genetic algorithm that allows one to find low-energy GB configurations by optimizing three main criteria: the local arrangement of the atoms, the relative translation between the two grains that compose the GB and an overall expansion/contraction of the system. It is designed to make a wider and more effective search through the energy landscape compared with other traditional methods, giving access to more configurations and increasing the possibility of finding the global minimum in energy.

In elastically inhomogeneous solid materials, the presence of strains causes changes in both morphology and phase equilibria, thereby changing the mechanical and chemical properties. For any given initial phase- and grain-structure, it is difficult to determine experimentally or analytically these changes in properties. Phase-field models coupled with micro elasticity theory can be used to predict the morphological and chemical evolution of such strained systems, but their accuracy with respect to interfacial excess contributions has not been tested extensively. In this study, we analyse three existing phase-field schemes for coherent two-phase model systems and a Cu₆Sn₅–Bct-Sn system. We compare the chemical composition and stress state obtained in the simulations with analytical values calculated from Johnson's (Johnson 1987 Metall. Trans. A 18 233–47) model. All schemes reproduce the shift in chemical composition, but not the strains. This deviation is due to excess interfacial energy, stresses, and strains not present in the analytical results, since all three schemes are based on assumptions different from the stress and strain relations at equilibrium. Based on this analysis, we introduce a new scheme which is consistent with the analytical calculations. We validate for the model system that this new scheme quantitatively predicts the morphological and chemical evolution, without any interfacial excess contributions and independent of the diffuse interface width.

The interatomic interaction potential of tungsten and thorium crystals and those of hypothetical tungsten and thorium alloys within the embedded atom approach are considered. The corresponding Ansatz functions are fitted against full potential linear augmented plane wave data of real tungsten- and thorium- and hypothetical tungsten-thorium-crystals. The result is interatomic potentials, ready for use within classical molecular dynamics schemes. A cross check of the resulting force scheme derived by comparison of ab initio and classical molecular dynamics data is provided. Furthermore, we used the potentials to calculate the phonon dispersion relations, which then serve as an additional check.

Electron and x-ray diffraction are well-established experimental methods used to explore the atomic scale structure of materials. In this work, a computational method is implemented to produce virtual electron and x-ray diffraction patterns directly from atomistic simulations without a priori knowledge of the unit cell. This method is applied to study the structure of [0 1 0] symmetric tilt low-angle and large-angle grain boundaries in Ni. Virtual electron diffraction patterns and x-ray diffraction 2θ line profiles show that this method can distinguish between low-angle grain boundaries with different misorientations and between low-angle boundaries with the same misorientation but different dislocation configurations. For large-angle Σ5 (2 1 0), Σ29 (5 2 0) and Σ5 (3 1 0) coincident site lattice [0 1 0] symmetric tilt grain boundaries, virtual diffraction methods can identify the misorientation of the grain boundary and show subtle differences between grain boundaries in the x-ray 2θ line profiles. A thorough analysis of the effects of simulation size on the relrod structure in the electron diffraction patterns is presented.

We construct two new area-preserving projections, which map regular hexagons and regular triangles onto circles. Combination of these projections with the inverse Lambert equal-area projection from the disc to the two hemispheres of a sphere provide bi-directional conversions between uniform planar grids with three-fold and six-fold rotational symmetry and corresponding uniform grids on the sphere. An application example is given for the representation of the channeling-modified back-scattered electron yield for hexagonal titanium.

An assessment of the ponderomotive effect contributions to the kinetics of single contact growth during sintering is carried out. A considerable free surface electromigration during microwave sintering in a polarized electromagnetic field is determined at inter-particle interfaces. It is shown that the electromigration flux reaches its maximum near the inter-particle contact edge and it is equivalent to the compressive stress acting on the contact between particles. The compressive stress is proportional to the intensity of the electric field at the inter-particle neck and inversely proportional to the ratio of the grain boundary and surface diffusivities. The electromigration matter transport can substantially accelerate the shrinkage rate during microwave sintering in comparison with conventional sintering.

The plastic deformation of body-centered cubic iron at low temperatures is governed by slip behavior of $\case{1}{2}\langle 1\,1\,1 \rangle$ screw dislocations. Their non-planar core structure gives rise to a strong temperature dependence of the yield stress and overall plastic behavior that does not follow the Schmid law common to most close-packed metals. In this work,we carry out a systematic study of the screw dislocation behavior in α-Fe by means of atomistic simulations using a state-of-the-art magnetic bond-order potential. Based on the atomistic simulations of the screw dislocations under various external loadings, we formulate an analytical yield criterion that correctly captures the non-Schmid plastic response of iron single crystals under general loading conditions. The theoretical predictions of operative slip systems for uniaxial loadings agree well with available experimental observations, and demonstrate the robustness and reliability of such atomistically based yield criterion. In addition, this bottom-up approach can be directly utilized to formulate dislocation mobility rules in mesoscopic discrete dislocation dynamics simulations.

Experimental studies have shown that electrolyte-emerged nanoporous metals with nano-wire-resembling ligaments as building blocks can undergo considerable dimensional changes when a potential difference is applied. The primary actuation mechanism is the electric double-layer charging of the internal surface. To study the fundamental physical mechanism, we explore the charge-induced deformation of a gold nanowire using atomistic simulations. The excess charge is taken into account by modifying the embedding function of the surface embedded atom method as informed by density functional theory calculations. Our atomistic simulations indicate that the charge-induced deformation increases considerably for reduced cross-sectional dimensions of the wire, and depends sensitively on the crystallographic orientation. We found that anisotropy-driven surface distortions play an important role in transducing the atomistic charge-induced forces into dimensional changes. To capture the fundamental mechanisms, we present a simple analytical model for the charge-induced strain of gold nanowires that is found to be in excellent agreement with the atomistic simulations.

Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) is a high-energy explosive with high sensitivity. The heat dissipation of the HMX/additive interface is a key issue in understanding the hot spot formation and desensitizing mechanism of mixture explosive. In this work, we derive new formulae to calculate the heat dissipation rate for a set of HMX/additive interfaces, and build a physical model to describe the energy dissipation time and distance in mixture explosive. Four kinds of additives are considered: 1,3,5-triamino-2,4,6-trinitrobenzene, graphite, paraffin and fluoropolymers. At low strength loading, we prove that the heat dissipation rate is proportional to the square of frequency, and suggest a way to decrease the sensitivity of the explosive. At medium strength loading, the viscosity coefficient and friction coefficient of interface are calculated. The desensitizing abilities of additives to HMX are discussed systematically.

In this paper, buckle-driven delamination between thermal barrier coatings (TBCs) and a polynomial curved substrate is theoretically analyzed under thermal loading. First, based on the one-dimensional flat blister mode, a theoretical model for buckle-driven delamination of a polynomial curved coating blister is established. Second, a finite element model of the TBCs with an interface initial crack on different polynomial curved substrates is built to investigate the influence of temperature and the initial substrate morphology on the energy release rate and mode mixity, which agrees well with the results from the theoretical prediction. Finally, the influence of crack length, coating thickness and substrate morphology on the buckle-driven mechanism is analyzed and discussed. The results will provide important guidance for characterizing and designing curved TBCs of thermal protection structures.

Hybrid bearings comprising ceramic balls and steel rings exhibit increased wear-resistance and a reduced coefficient of friction (COF) compared with standard steel bearings. Using plasma-enhanced chemical vapour deposition (PECVD) coatings to modify the surface properties, the performance of these bearings can be further improved. Fluorine-containing amorphous hydrogenated carbon (a-C : F : H) films are well suited to this purpose. To study the influence of such coatings on the friction characteristics of key parts of hybrid bearings, a model of an a-C : F : H film was constructed and employed in molecular dynamics simulations of two slabs sliding past each other, lubricated by water. With one slab being pulled by a virtual spring, the perpendicular force (load) was kept constant using a barostat. For comparison, a system of two silicon dioxide (cristobalite) slabs and a mixed system consisting of a cristobalite slab and an a-C : F : H slab were investigated. Our results indicate a linear dependence of the friction force on the perpendicular force. With an increasing amount of water between the slabs, the COFs decrease. A decrease in temperature leads to an increased COF, while a decrease in the relative velocity of the slabs does not influence the COF between two a-C : F : H slabs, but reduces the COF for the other two systems. Our results for the COF and its dependence on temperature and relative sliding velocity generally agree well both with experiments and with simulations for similar systems reported in the literature.

The bulk effects of hydrogen on the kinematics, thermodynamics, and kinetics of plasticity and damage evolution were derived based on the constitutive equations of the Bammann continuum plasticity and Horstemeyer damage mechanics framework. From nanoscale atomistic simulation results and existing experimental observations, the Horstemeyer–Gokhale void/crack nucleation rate was modified to account for hydrogen effects. The continuum damage framework was implemented into a user material code and applied in finite element simulations. The finite element results showed close comparisons with the experimental data from Kwon and Asaro who charged smooth and notched spheroidized 1518 steel specimens with hydrogen.