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Cross-scale method of MD-FE for modeling mechanical damage behaviors of ferrite-cementite steels
Abstract and Figures
Inspired by the experimentally observed ferrite-cementite interface damage and ferrite matrix damage, this work develops a cross-scale method using the cohesive zone model (CZM) as a bridge to study the mechanical damage behavior of ferrite-cementite steel at the micro-nano scale. The CZM parameters for the damage region of ferrite-cementite steel were obtained by molecular dynamics (MD) simulations, which were then applied to cohesive elements in the finite element (FE) framework, thus enabling crack initiation and propagation at the micro-scale. Simulation results show that the ferrite-cementite interface is more susceptible to damage resulting in cracking compared to the ferrite matrix, which is consistent with the experimental observation that there are extensive debonded voids due to interface damage. The implementation of this work provides a new way to study the micro-nano scale mechanical behavior of heterogeneous materials containing both interface damage and matrix damage.
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... Metal-based nanocomposites, known for their lightweight and high strength, have applications in industries such as automobile, shipbuilding, and aerospace [283]. Yu and Duan [284] focused on investigating the interface fracture behavior in ferritecementite steel with the combination of MD and CZM. The necessary interface parameters of CZM can be obtained from MD simulation since the traction-separation law can be captured from MD calculation. ...
The development of advanced materials like multi-phase composites has brought attention to the problem of interface fracture, leading to a focus on the study of interface fracture mechanics. Numerical methods have become predominant tools for studying interface fracture problems due to their ability to effectively model complex interface fracture processes. This article provides a comprehensive review of the historical development, current research trends, and prospects of numerical methods in interface fracture mechanics. Specifically, the most commonly-used numerical methods in interface fracture mechanics are discussed, including the finite element method, boundary element method, extended finite element method, cohesive zone model, and phase-field method. Additionally, the utilization of the generalized finite element method, scaled boundary finite element method, and molecular dynamic approaches for addressing interface fracture problems in specific cases are also highlighted. This review aims to serve as a valuable resource and reference for researchers and engineers in this field.
Rolling contact fatigue of rail steel caused by repeated contact stresses with the wheel needs to be clarified to ensure the safety of wheel-rail operation. The fatigue damage of rail steel studied from an experimental perspective provides a good phenomenon of its surface spalling in rail transportation, whereas the damage activity below the contact surface that triggers this failure phenomenon is difficult to observe. In this work, a combined plasticity model for ferrite with crystal plasticity and cementite with isotropic plasticity is proposed, which has been used to study the fatigue damage behavior of pearlitic rail steel. The results indicate that the subsurface crack propagation approximately parallel to the contact surface is the final link in the formation of the surface micropit. The downward expanding crack from the surface will meet up with the deeper internal cracks to produce macropit. As the sphericity of the grains increases from 0.145 to 0.2, the surface crack in the ferrite-cementite steel with the grain size of 50 μm extends all the way to the bottom of the upcoming macropit and lacks the micropit formation stage. In addition, the surface spalling associated with micropit connections can be delayed by increasing the cementite fraction. The presence of macropits destroys the surface integrity of rail steel, so it needs to be detected and addressed in a timely manner.
Grain boundaries (GBs) are microstructures in polycrystalline materials, which influence the mechanical properties of materials significantly. Simulation is an indispensable means to study GBs due to its high flexibility. However, the existing GB simulation models mostly focus on a single simulation scale, lack the consideration of the grain boundary misorientation angle (GBMA) characteristic and fail to describe the coupled elastic-plastic damage behavior between grains and GBs accurately. To describe the influence mechanism of GB on the mechanical behavior of materials accurately, a GBMA-considered multi-scale modeling method for polycrystalline materials is proposed in this paper. The method is based on molecular dynamics (MD), the crystal plasticity finite element method and the cohesive zone model, which considers the GBMA information at grain and atomic scales comprehensively. Firstly, a GB geometric model containing GBMA characteristic is generated at grain scale through EBSD information. Then the GB cohesive parameters are obtained at the atomic scale by MD simulation. Finally, some experiments are performed for verification, which indicates the high accuracy of the proposed method. Furthermore, three models with the same geometric shape and different grain orientation and GBMA are established to study the influence of GBMA on the mechanical properties of polycrystalline materials.
During the initial stages of hydrogen environmentally assisted cracking (HEAC), including crack incubation, initiation and microstructurally short cracking, the geometrical configuration of the microstructure greatly influences the crack growth behaviour. Therefore, there is a big incentive to generate a model which can replicate intergranular HEAC at a microstructural scale. This report provides a general framework to implement a microstructural intergranular HEAC model by using a cohesive zone approach in Abaqus. The parameters of the phenomenological model were fitted by using in-situ synchrotron tomography observations of crack initiation and propagation during HEAC of AA7449-T7651. After fitting the parameters, the real HEAC behaviour of the aluminium alloy 7449-T7651 has been replicated accurately. Several characteristic HEAC features were achieved, including crack segmentation, preferential cracking along grain boundaries with a high resolved normal stress and cracks slowing down at grain boundary triple junctions. Comparisons with experimental observations show the suitability of this approach for the prognosis of crack initiation and propagation at a microstructural scale under HEAC conditions.
We analyze the lattice dislocation trapping mechanism at the ferrite/cementite interface of the Isaichev orientation relationship by atomistic simulations combined with the anisotropic linear elasticity theory and disregistry analysis. We find that the lattice dislocation trapping ability is varied by initial position of the lattice dislocation. The lattice dislocation near the interface is attracted to the interface by the image force generated by the interface shear, while the lattice dislocation located far is either attracted to or repelled from the interface, or even oscillates around the introduced position, depending on the combination of the stress field induced by the misfit dislocation array and the image stress field induced by the lattice dislocation.
The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): namely, linear elastic fracture mechanics and smooth parallel plates lubrication fluid flow inside the propagating fracture. We relax these hypotheses and investigate in details the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a fluid lag. In addition to a dimensionless toughness and the time-scale tom of coalescence of the fluid and fracture fronts governing the fracture evolution in the LHFM case, the solution now also depends on the ratio between the in-situ stress and material peak cohesive stress σo∕σc and the intensity of the flow deviation induced by aperture roughness (captured by a dimensionless power exponent). We show that the solution is appropriately described by a nucleation time-scale tcm=tom×(σo∕σc)3, which delineates the fracture growth into three distinct stages: a nucleation phase (t≪tcm), an intermediate stage (t∼tcm) and late time (t≫tcm) stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages of growth. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM predictions with shorter fracture lengths, larger widths and net pressures. These deviations from LHFM ultimately decrease at late times (t≫tcm) as the ratios of the lag and cohesive zone sizes with the fracture length both become smaller. The deviations increase with larger dimensionless toughness and larger σo∕σc ratio, as both have the effect of further localizing viscous dissipation near the fluid front located in the small rough cohesive zone. The convergence toward LHFM can occur at very late time compared to the nucleation time-scale tcm (by a factor of hundred to thousand times) for realistic values of σo∕σc encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.
Herein, micromechanical material deformation behavior of medium carbon steel—with varying cementite particle size and distribution—under monotonic tensile load is modeled. The statistical phase morphology data are collected from the microscopy images of 83% spheroidized C45EC steel. Virtual microstructures for nine different cases are constructed using Dream.3D by varying the concentrations of small, large, and bimodal cementite particles on the ferrite grain boundaries. A crystal plasticity-based numerical simulation model, i.e., DAMASK, is used to simulate the local material deformation behavior. The material model parameters for elastic–plastic ferrite and elastic cementite phases are adopted from the literature and calibrated by modifying the fitting parameters to match the experimentally observed material flow curve. It is observed that the cementite particle size and distribution in the primary phase affect the local mechanical behavior of the material. An analysis of deformation at 20% of global strain has
helped in the qualitative understanding of factors affecting the stress and strain concentration points. The evolution of stresses and strains in the least and the most stressed representative volume elements (RVEs) has provided interesting information regarding the path followed by the dislocation movement during deformation. The study has provided insight into the factors affecting the material’s global and local deformation behavior.
Grain boundary (GB) characteristics play an important role in the determination and prediction of material behavior, especially when it comes to nanocrystalline metals and ceramics. The main goal of this work is to develop a general interface model to accurately incorporate grain boundary sliding as well as intergranular fracture as two main phenomena in characterizing the grain boundary. To gain a deeper insight into the behavior of different grain boundaries, molecular dynamics (MD) simulations are utilized for mode I and mode II loadings. By adding the unloading path to the MD simulations it was possible to differentiate between different active mechanisms at the GB. Current MD investigations motivate a model which accounts for anisotropic plasticity and damage within the grain boundary to capture the complex interface behavior. Therefore, a two-surface formulation is utilized in which damage and plasticity at the interface are coupled in a thermodynamically consistent way. The parameters for the introduced interface model are determined using the MD simulations based on an embedded atom potential. Finally, the calibrated interface model is implemented into a cohesive zone (CZ) element. In order to show the applicability of the proposed interface model, several numerical studies are carried out. A volume element is selected which depicts a point in an arbitrary polycrystalline material at the macroscale. The results of these studies reveal interesting behaviors of the selected volume element which can be used, e.g., to determine the parameters of a continuum damage model at the macroscale.
Atomistic modeling is used to investigate the mechanical response to compressive and tensile straining of the Bagaryatskii orientation relationship between ferrite and cementite within pearlite. A range of interlamellar spacings and ferrite to cementite ratios are considered and values for important mechanical properties, including elastic modulus, yield stress, flow stress, and ductility, are determined. These values are fit to simple elasto-plastic models, thus allowing for the easy interpolation of states not simulated. Transverse loading can be described using simple 1-D composite theory, while longitudinal loading requires the consideration of the strain compatibility of the interface. The mechanical properties are shown to be largely dependent on the volume ratios of the cementite and ferrite, with the interlamellar spacing having an increasing role as it reaches smaller values. Additionally, the effect of the interface is discussed and characterized, including its role as a nucleation site for dislocations in both the ferrite and cementite.
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli (C
e
) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated with energy conservation and work-conjugacy due to the use of the Jaumann objective stress rate in ABAQUS nonlinear incremental analysis is viewed as a consequence of the implementation of a constitutive model that violates these requirements.
Micromechanical experiments with 3 × 3 × 6 μm3 sized micro pillars were used to examine orientation dependencies of the mechanical properties in a severely plastically deformed high strength steel and compared with the undeformed state. For the synthesis, an initially ultrafine-lamellar (UFL) fully pearlitic steel was subjected to high pressure torsion (HPT) transforming the steel into a nanolamellar (NL) composite. Both microstructural states were then tested in-situ inside a scanning electron microscope. Within the individual micro pillars, fabricated by focused ion beam milling, the ferrite and cementite lamellae were aligned parallel, normal or inclined to the loading direction. The main findings are: First, the strength and strain hardening capacity is more than doubled comparing the UFL with the NL composite. Second, an anisotropic mechanical response exists in terms of i) strain hardening capacity and ii) stress level at the onset of plateau formation. Third, deformation and localization mechanisms at large compressive strains vary with the lamellae orientation, however they are independent of the lamellae thickness.
A traction–displacement relationship that may be embedded into a cohesive zone model for
microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics (MD)
simulations. An MD model for crack propagation under steady-state conditions is developed to
analyze intergranular fracture along a flat S99 [1 1 0] symmetric tilt grain boundary in aluminum.
Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two
opposite directions along the grain boundary. In one direction, the crack propagates in a brittle
manner by cleavage with very little or no dislocation emission, and in the other direction, the
propagation is ductile through the mechanism of deformation twinning. This behavior is consistent
with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference
for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion.
A comparison with finite element calculations shows that while the stress field around the brittle
crack tip follows the expected elastic solution for the given boundary conditions of the model, the
stress field around the twinning crack tip has a strong plastic contribution. Through the definition of
a Cohesive-Zone-Volume-Element—an atomistic analog to a continuum cohesive zone model
element—the results from the MD simulation are recast to obtain an average continuum traction–displacement relationship to represent cohesive zone interaction along a characteristic
length of the grain boundary interface for the cases of ductile and brittle decohesion.
Dynamic crack growth is analysed numerically for a plane strain block with an initial central crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on crack branching, and the effect of an inhomogeneity in strength, as in crack growth along or up to an interface. The effect of cohesive surface orientation on crack path is also explored, and for a range of orientations zigzag crack growth precedes crack branching. Finer mesh calculations are carried out where crack growth is confined to the initial crack plane. The crack accelerates and then grows at a constant speed that. for high impact velocities, can exceed the Rayleigh wave speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of crack growth is not constrained. The crack speed reaches about 45% of the Rayleigh wave speed, then the crack speed begins to oscillate and crack branching at an angle of about 29 from the initial crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast crack growth in brittle solids.
Stainless steels found in real-world applications usually have some C content in the base Fe-Cr alloy, resulting in hard and dislocation-pinning carbides-Fe3C (cementite) and Cr23C6-being present in the finished steel product. The higher complexity of the steel microstructure has implications, for example, for the elastic properties and the evolution of defects such as Frenkel pairs and dislocations. This makes it necessary to re-evaluate the effects of basic radiation phenomena and not simply to rely on results obtained from purely metallic Fe-Cr alloys. In this report, an analytical interatomic potential parameterization in the Abell-Brenner-Tersoff form for the entire Fe-Cr-C system is presented to enable such calculations. The potential reproduces, for example, the lattice parameter(s), formation energies and elastic properties of the principal Fe and Cr carbides (Fe3C, Fe5C2, Fe7C3, Cr3C2, Cr7C3, Cr23C6), the Fe-Cr mixing energy curve, formation energies of simple C point defects in Fe and Cr, and the martensite lattice anisotropy, with fair to excellent agreement with empirical results. Tests of the predictive power of the potential show, for example, that Fe-Cr nanowires and bulk samples become elastically stiffer with increasing Cr and C concentrations. High-concentration nanowires also fracture at shorter relative elongations than wires made of pure Fe. Also, tests with Fe3C inclusions show that these act as obstacles for edge dislocations moving through otherwise pure Fe.
Fatigue tests with rotary bending (52.5 Hz) and ultrasonic cycling (20 kHz) methods were performed, respectively on two high strength steels so as to investigate the effects of inclusion size and location on the fatigue behavior from low cycle fatigue to very-high-cycle fatigue (VHCF) regimes. Under rotary bending test, four fracture patterns were observed with respect to different locations of inclusion on fracture surface. The mean crack growth rate within FGA (fine granular area of crack origin) was estimated to give the value with the magnitude of 10–13 m/cycle for the specimens with the fracture pattern of “FGA+surface fisheye”. Under ultrasonic cycling test, the size effect of inclusions on VHCF was investigated with two groups of specimens. One is with the inclusion size between 20 and 60 μm and the other is with the inclusion size between 10 and 30 μm. The results show that large inclusions lowered the proportion of net FGA at given stress levels and led to the shortening of VHCF life. The degradation of VHCF strength caused by the increase of inclusion size is ascribed to the decrease of the critical stress of FGA formation for large inclusions.
Large plastic deformation and ductile damage in precipitation hardening aluminum alloy AA7075 is driven by plastic flow in the vicinity of particles as well as fracture and decohesion of second phase particles embedded in the matrix. The current work investigates the deformation and damage characteristics of Fe-rich intermetallic particles, and η and θ precipitates in AA7075-O sheet. A multiscale model simulation methodology is presented and applied to analyze large-scale plastic deformation and damage characteristics. The methodology utilizes nanoscale molecular dynamics simulation to obtain matrix-particle interface strength properties and Weibull statistics to capture experimental fracture characteristics of particles. The above sub-models are incorporated within a 2-D real particle microstructure-based finite element model to conduct a comparative study of the roles of decohesion and fracture in the development of plasticity and void damage in AA7075-O sheet. In addition, in-situ SEM uniaxial tensile tests are carried out to assess the effectiveness of the simulation methodology and to compare the experimental and numerical results. Post-test high resolution X-ray computed tomography (HR-XCT) was also carried out to qualitatively observe particle-induced voiding in the material. The numerical methodology is shown to capture well the experimental trends in damage evolution of the individual particles. It is observed that particle damage is a function of inherent particle properties, their morphological features, and matrix strain localization characteristics. Larger-size Fe-rich particles are observed to undergo damage at an earlier stage, and consequently, affect the strain localization characteristics the most. In contrast, η precipitates are found to be most resistant to particle damage, followed by θ precipitates. Higher stresses inside strain localization bands, caused increased void damage initiation and growth of η and θ precipitates. Overall, particle fracture is observed to be marginally higher compared to particle decohesion, irrespective of the particle type.
Ultra high performance concrete with coarse aggregates (CA-UHPC) exhibits complicated damage and failure mechanisms due to intricate interactions of irregular mesoscale phases, including random aggregates, fibres, mortar, and interfaces. This work proposes a 3D numerical framework to investigate the complex cohesive fracture of CA-UHPC at mesoscale for the first time. Automatic algorithms are proposed to model realistic aggregates, mortar, aggregate-mortar interfaces and steel fibres in large quantities. Zero-thickness cohesive interface elements are automatically inserted in the mortar and on the aggregate surfaces to capture potential cracks, and an efficient non-conforming methodology is developed to model the fibre-mortar bond-slip behaviour using orientation-dependent pullout force-slip relations. The proposed models are validated using typical uniaxial tension tests, and elucidate that the progressive interactions of aggregate barrier, interfacial cracking and fibre bridging govern the early cracking, strain-hardening behaviour, fibre activation and final crack networks. Quantitative analyses are performed to optimize the mechanical properties of CA-UHPC: as the aggregate content increases, there are more torturous crack surfaces and fewer activated fibres with lower load-carrying capacities, but the downside of coarse aggregates can be alleviated by increasing fibre content, especially when needing aggregates to reduce carbon footprints and improve anti-shrinkage performance.
It is a common wisdom that metallic materials become brittle once being deformed quickly. However, here we reveal an abnormal strain-rate-induced brittle-ductile-delamination transition in a widely used pearlitic steel with unique structure of alternative arrangement of nanoscale ductile ferrite and brittle cementite through extensive molecular dynamics simulations. In contrast to the brittle cleavage fracture in conventional crystalline alloys, the brittle fracture in pearlitic steel at relatively low strain rate is mediated by the nanoscale cavitation ahead of crack tip, akin to the widely observed fracture mode in metallic glasses. As the strain rate increases, fracture mode transforms to a dislocation nucleation mediated ductile mechanism. At extremely high strain rate, it is found that the fracture mode turns to be collective delamination at the interfaces, leading to a surprising "delamination toughening". The abnormal brittle-to-ductile transition with increasing deformation rate is physically rationalized by a mechanistic model, which is based on a scenario of energetic competition between the interface cleavage and the dislocation nucleation in the vicinity of crack tip. Once the strain rate exceeds a critical value, fracture transitions to dislocation nucleation dominated. When strain rate increases to extremely high values, there is no enough time for either crack propagation or dislocation nucleation, and the collective delamination of interfaces occurs which involves only instantaneous bond breaking at weakly bonded regions, i. e. the interface. The unravelled phenomenon challenges the conventional knowledge of materials deformation and failure which might shed light on coordinating unanticipated utilities of the ultrastrong pearlitic steels in extreme environments.
Thermostats/barostats that maintain temperature/pressure as constant (on average) in molecular dynamics (MD) simulations are essential for simulating isothermal-isochoric (NVT) or isothermal-isobaric (NPT) systems. In order to simulate accurate physical properties, thermostats/barostats need not only sample a correct NVT/NPT ensemble but also minimally disturb the particles’ (Newtonian) dynamics. In other words, the NVT/NPT simulations need to yield accurate physical properties (dynamics properties included, e.g. diffusivity and viscosity) and also their fluctuations. However, few studies have studied in-depth the effects of thermostats/barostats on a comprehensively wide range of simulated properties. In this work, commonly used thermostats, e.g. Andersen, stochastic dynamics (SD), Berendsen, V-rescale and Nosé-Hoover thermostats, and barostats, e.g. Berendsen and Parrinello-Rahman barostats, with different coupling strengths were studied to see whether they can yield accurate simulated properties and fluctuations. The theoretical values of physical properties’ fluctuations were calculated via statistical mechanics to provide a comparison benchmark for MD simulations. Particularly, the accuracy of thermostats was studied in the context of NPT or non-equilibrium molecular dynamics (NEMD) simulations, which has long been overlooked. Berendsen thermostat/barostat suppresses the fluctuations of energy/volume (due to the exponential decay of deviation of the simulated temperature/pressure from the target value) and yields inaccurate simulated properties. In addition, Andersen and SD thermostats perturb the particles’ dynamics so violently (due to the random component in the algorithm) that they fail to accurately simulate dynamics properties. Overall, Nosé-Hoover/V-rescale thermostat, and Parrinello-Rahman barostat with moderate coupling strength are recommended for common NVT/NPT production simulations. NPT or NEMD simulations would require more efficient (or stronger coupling) thermostats than NVT equilibrium molecular dynamics (EMD) to maintain the simulated temperature close to the target.
The mechanical behaviour and failure mechanism of highly particle-filled polymer composites (HPFPCs) with different particle morphologies over a wide range of strain rates (0.0001 /s to 1000 /s) and temperatures (-40°C to 100°C) are investigated using the nonlinear finite element method. The relevant micro-mechanical constitutive laws have been developed to characterize the mechanical performances of HPFPCs. The effects of particle shape and particle volume fraction (PVF) on the crack path and mechanical behaviour (peak strength and effective modulus) of HPFPCs are illustrated. Compared with the actual and circular particle shaped structures, the polygonal particle shaped structure shows the most stable crack path and possesses the highest peak strength and the lowest effective stiffness in corresponding PVF. It indicates that the fracture resistance of the polygonal particle shaped structure is better than the particle structure with smooth particle surfaces, especially when dealing with high strain rate problems. A sequence of failure mechanisms of HPFPCs with different particle morphologies can be observed. At higher strain rates of 100 /s and 1000 /s and lower temperatures of -40°C and -20°C, besides the interfacial debonding as the main crack path, the fracture of the extended binder filaments and the flow of small particles with extended binder matrix can be observed. While, at lower strain rates of 0.0001 /s and 0.001 /s and higher temperatures of 80°C and 100°C, micro-cracks are more scattered through the model as the binder matrix becomes more ductile. Besides, the effective stiffness is more sensitive to the particle shape at higher strain rates, while the peak strength becomes more sensitive to the particle shape at lower strain rates.
The adhesion strength of thermal barrier coatings (TBC) is governed by the interphase between the top coat (TC) and the thermally grown oxide (TGO). In most existing continuum work, the thermomechanical property of this interphase is either ignored or described using rudimentary methods. To address this deficiency and determine reliable thermomechanical properties for that interphase, we conducted comprehensive molecular dynamics (MD) simulations of the three affected interphases: TC, TGO and the cohesive interphase between them. Three aspects of the work were examined. First, we conducted extensive research to carefully select the Coulomb-Buckingham interatomic potential parameters needed for the accurate description of TC and TGO atomistic systems. Second, Young's modulus (E), coefficient of linear thermal expansion (α) and thermal conductivity (κ) were determined using MD simulations. Third, the results from MD simulations were used in finite element (FE) model to determine the continuum behaviour of the 3-phases of the TBC. The results show that at TC/TGO interphase, a cohesive bond is formed, and that Young's modulus of the interphase decreases with increased temperature. Our results further reveal that the thermal expansion of YSZ is restricted by α-Al2O3 at the interphase. Additionally, we show that the thermal resistance at the interphase is negligible. Lastly, the results obtained from the newly proposed MD-FE framework show that the assumption of line interphase will grossly overestimate the effective stiffness of YSZ/α-Al2O3 system.
Mechanical heterogeneity refers to the spatial inhomogeneity of the mechanical properties in materials, which is a common feature of composites consisting of multiple distinct phases. Generally, the effects of mechanical heterogeneity on the overall properties of the composites, such as stiffness and strength, are thought to follow the rule of mixture. Here, we investigate the cracking behavior of composite plates under impact and found that the rule of mixture may break down in describing the cracking resistance of composites with high stiffness heterogeneity. Our results show that the resistance of a composite plate, which consists of two phases of distinct stiffnesses, against dynamic cracking strongly depends on the hybridizing manner of the two phases. When the stiff phase is dispersed in the compliant matrix, the resulting composite plate exhibits superior cracking resistance compared to the monolithic plates made of either phase. In contrast, if the compliant phase is dispersed in the stiff matrix, the resulting composite plate displays reduced cracking resistance and thus higher absorption of the impact energy as compared to the monolithic controls. Our work provides an approach to harnessing the dynamic fracture by controlling the stiffness heterogeneity, which would be of great value to the design and fabrication of the protective armors and energy-absorbing shields.
In the process of deep underground resource development and utilization, the surrounding rock mass is not only affected by high temperatures, but also dependent on the dynamic stress environment. In this paper, the dynamic impact loading tests were carried out on the cracked straight-through Brazilian disc (CSTBD) granite specimens after heat treatment using the spilt Hopkinson pressure bar (SHPB) system. The effects of temperature and loading mode on the dynamic fracture toughness, fracture growth path, strain distribution, and fracture angle were analyzed. The results showed that, the fracture toughness of CSTBD granite specimen under dynamic loading decreases gradually as the mixed coefficient increases. The pure mode II fracture toughness is linearly related to that of pure mode I. High temperatures shows a negative effect on the fracture property of granite. Dynamic fracture toughness decreases with the increase of temperature, first gently (25∼400 °C) and then sharply (400∼800 °C). Under dynamic loading, the main crack initiates from the pre-crack tip, accompanied by obvious strain concentration, and then extends gradually to the loading end. The fracture angle of the main crack presents a generally increasing trend with the increase in loading angle, but is not closely related to the temperature of heat treatment.
Since the classical molecular dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interatomic potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interatomic potentials.
Program Summary
Program Title: Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)
CPC Library link to program files: https://doi.org/10.17632/cxbxs9btsv.1
Developer's repository link: https://github.com/lammps/lammps
Licensing provisions: GPLv2
Programming language: C++, Python, C, Fortran
Supplementary material: https://www.lammps.org
Nature of problem: Many science applications in physics, chemistry, materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from atomic to mesoscale to macroscopic.
Solution method: The LAMMPS code uses neighbor lists, parallel spatial decomposition, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Størmer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addition, LAMMPS supports a wide range of interatomic potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features.
Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the LAMMPS code.
References
[1]S. Plimpton. Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys., 117:1–19, 1995.
[2]L. Verlet. Computer experiments on classical fluids: I. Thermodynamical properties of Lennard–Jones molecules. Phys. Rev., 159:98–103, 1967.
The main objective of this study is to predict the deformation behavior, strain localization, and forming limits of ferrite-pearlite steels by incorporating the contributions of the microstructural characteristics and mechanical properties of the underlying microstructure. A realistic microstructure-based micromechanical approach in the framework of the crystal plasticity (CP) model was carried out using the periodic representative volume element (RVE) generated from the scanning electron microscopy (SEM) image. The homogenized stress-strain curve of the realistic RVE was validated with the experimental data with an error of less than 6.71% at large strains. Afterward, the initial microstructural inhomogeneity criterion was applied to the realistic RVE under various loading paths to predict the forming limit diagram (FLD), which compared with the experimental results of the Nakazima-stretch forming test. Consequently, the contributions of the pearlite volume fraction and the microstructural morphology were studied by extending this approach to the synthetic microstructures with various pearlite volume fractions. In conclusion, the microstructure-level inhomogeneity at the microscopic level results in intense stress/strain partitioning and strain localization, emerging in the form of micro-localized deformation bands. Moreover, it has been found that the local deformation pattern at the micron-scale significantly depends on the microstructural morphology and loading direction.
Nickle-titanium (NiTi) alloys are widely considered as one of the most intelligent materials with great commercial values. This study focuses on investigating the grain size (GS) effect on crack propagation of polycrystalline NiTi alloys through molecular dynamics (MD) simulations combined with cohesive zone model (CZM). The GS distribution is statistically achieved by electron backscatter diffraction experiment, while the Voronoi tessellation is applied to characterize the microstructures. MD modeling is conducted to determine the traction-separation (T-S) law of CZM. The plastic behavior and phase transition are examined as well. Subsequently, the characteristic parameters extracted from the T-S law are embedded into the cohesive elements along grain boundaries, and then the intergranular fracture of NiTi alloys with various grain sizes are reproduced by conducting finite element simulations. Interestingly, an unexpected subcritical crack growth (SCG) is found during the simulations, and its mechanism is explored at the atomic scale. Moreover, the critical stress intensity factor (KIC) of compact tension specimens with average grain size from 17 to 45 μm is predicted. It is discoverable that the SCG duration and KIC increase as the grains become coarsened. Besides, the internal toughening mechanism of GS is probed from the aspects of stress-induced martensitic transformation and crack-path configuration. A comparison between numerical results and published experimental data demonstrates that this hybrid method could be used to successfully simulate the crack growth behavior.
We used molecular dynamics simulations to investigate the relationship between mechanical properties and deformation mechanisms in CoCrFeMnNi alloys having different compositions. According to deformation twinning activity, the deformation mechanisms in the different CoCrFeMnNi compositions under tensile loading can be classified into three major categories: easy-shear (ES), inter-locks (IL) and bulk hexagonal closed packed (hcp) transformation (BH). We found that the compositions with ES were more likely to rupture early because of the short and fragmented twins. The compositions following the IL pattern promoted the movement of interlocking stacking faults in the twin boundaries that could prolong tensile deformation. Moreover, BH could further increase ductility because the hcp transformation could absorb and dissipate the stacking faults. Experimental observations of immobile stacking-fault networks that impede dislocation motion and further provide preferred sites for the formation of the hcp phase were commonly found in the ES, IL and BH patterns. The calculated intrinsic stacking fault energies of CoCrFeMnNi and CoCrFeNi were consistent with the experimental measurements. The combination of high unstable stacking fault energy with the formation of the IL pattern results in high strength and high ductility in the CoCrFeMnNi HEA system.
In this work, based on the traction-separation (T-S) constitutive relations extracted from molecular dynamics (MD) simulations, a peridynamics (PD) model is proposed to investigate the crack propagation behavior of the polycrystal BBC-Fe under mode I loading condition. MD simulation is carried out to give an insight into the cracking process and fracture mechanism according to the analysis of atomic configuration and stress distribution. The atomic stress at the crack tip with respect to the opening distance is tracked during the steady cracking stage to provide a stable T-S relation. The fracture parameters of single crystal Fe are obtained via the MD simulation, based on which the PD parameters are obtained through an energy equivalent method. After that, a PD approach combined with cohesive zone model (CZM) is proposed to study the mode I fracture in polycrystal Fe. A good agreement has been found between the proposed PD model and the classical CZM based on a quasi-static splitting test of a single Fe crystal. Subsequently, PD simulations are performed concerning the dynamic propagation of cracks in a polycrystal Fe. What’s more, the effect of grain size, the grain boundary strength and the horizon size of PD on the fracture characteristics are examined. It can be concluded that the T-S relation originated from classical cohesive theory can be regarded as an effective bridge between the MD and PD. This work provides a new thought to study the fracture behavior of polycrystals from the atomic deformation mechanism to micro-fracture description.
This paper attempts to study the microstructural stress-strain evolution and strain localization in the ferrite-pearlite steel by high-resolution experimental-numerical integrated testing. Ferrite crystal orientations measured by electron backscatter diffraction (EBSD) were mapped onto precise scanning electron microscopy (SEM) micrographs of ferrite and cementite lamellar morphologies. Furthermore, in-situ SEM tensile testing was employed to map strains during the deformation using digital image correlation (DIC) at high spatial resolutions. Finally, spectral solver-based crystal plasticity (CP) simulations loaded by the local SEM-DIC boundary conditions were performed and compared to the experimental data. Crucially, all microstructure data was carefully aligned, and strains were filtered to the same spatial resolution, measured to be as small as ∼75 nm. This integrated methodology yields new insights in the high degree of plastic strain partitioning between ferrite grains and pearlite colonies, and ferrite and cementite lamellae inside pearlite. One-to-one experimental-numerical comparison augmented with the numerical variation of the ferrite constitutive model, pearlite interlamellar spacing, and lamellar orientation reveals how the ferrite-cementite strain partitioning and the onset of strain localization depend on the morphology and distribution of ferrite grains and pearlite colonies. Importantly, this comparison showcases the limitations of state-of-the-art simulations in their capability to predict specific mechanisms and correct degrees of strain heterogeneity.
Gradient nanostructured metals attract extensive attention due to their excellent mechanical properties, while they are prone to microcracks during forming and servicing process and eventually develop into a sudden fracture. Actually, experimental studies show that microcracks occurred in both the grain boundary (GB) and the intragrain, but most of the current reports only focus on the GB cracking, very limited work has studied the intragranular cracking. In this paper, the crystal plasticity finite element method (CPFEM) and cohesive zone model (CZM) are combined to study the cracking mechanism of polycrystalline aluminum (Al) with different grain-gradient structures under tensile load, where molecular dynamics (MD) method is used to determine the cohesive parameters of the intragrain and GB. The results not only show the crack initiation and propagation process of polycrystalline Al with different grain-gradient structures, but also reveal the mechanism of intragrain fracture, GB fracture and crack transgranular. The grain-gradient distribution with optimal comprehensive performance is obtained. Moreover, it is also found that the initial microcracks with different positions, numbers and angles have a great influence on the cracking mechanism and effective properties of the whole material. This study provides a solid theoretical basis for improving the quality and operation life of metal parts.
Nickle-titanium (NiTi) alloys are widely accepted to be one of the most favored engineering materials for use in the structural community. In this work, the formulation and application of a multiscale approach combined with cohesive zone model (CZM) and molecular dynamics (MD) were proposed to investigate the crack propagation of NiTi alloys. The Voronoi tessellation was employed to represent microstructures of such polycrystalline materials. MD simulations were performed to achieve the traction-separation law in the CZM with various initial micro-cracks. The resultant characteristic parameters were embedded in cohesive elements along grain boundaries and in grains, and in turn both intergranular and transgranular fracture were simulated by implementing the finite element analysis with failure criteria. Consequently, the stress intensify factor of compact tension specimens was predicted, and further the relationship between the microstructure and fracture toughness was explored. The results show that there is a reasonable agreement between numerical results and published experimental data, highlighting the adequacy of the new analytical method for reproducing the cracking behavior across micro-, meso-, and macro-scales.
In this work, microstructure dependent impact-induced failure of hydroxyl-terminated polybutadiene (HTPB)–cyclo-tetra-methylene-tetra-nitramine (HMX) energetic material samples is studied using the cohesive finite element method (CFEM). The CFEM model incorporates experimentally measured viscoplastic constitutive behavior, experimentally measured interface level separation properties, and phenomenological temperature increase due to mechanical impact based on viscoplastic and frictional energy dissipation. Nanoscale dynamic impact experiments were used to obtain parameters for a strain-rate dependent power law viscoplastic constitutive model in the case of bulk HTPB and HMX as well as the HTPB–HMX interfaces. An in situ mechanical Raman spectroscopy (MRS) setup was used to obtain bilinear cohesive zone model parameters to simulate interface separation. During analyses, the impact-induced viscoplastic energy dissipation and the frictional contact dissipation at the failed HTPB–HMX interfaces is found to have a significant contribution toward local temperature rise. Microstructures having circular HMX particles show a higher local temperature rise as compared to those with diamond or irregularly shaped HMX particles with sharp edges indicating that the specific particle surface area has a higher role in temperature rise than particle shape and sharp edges. Regions within the analyzed microstructures near the HTPB–HMX interfaces with a high-volume fraction of HMX particles were found to have the maximum temperature increase.
Grain boundaries play a pivotal role in dictating the deformation behavior of crystalline materials. Modeling their effects within the framework of physically based crystal plasticity approaches demands a multiscale description of the underlying phenomena. This work puts-forth a two-scale atomistic to crystal plasticity approach for determining the deformation behavior of a ductile face-centered cubic material. The approach uses atomistic computations to quantify the activation energies for nucleation of partial dislocations from a grain boundary under tensile loading. To this end, embedded-atom method based atomistic simulations involving nudged elastic band method are utilized to compute stress-dependent activation parameters of the grain boundary. The extracted parameters are then used as input to the flow rule of crystal plasticity at higher length scale, which is based on transition state theory. At this scale, the grain boundaries are explicitly accounted for by assigning a finite thickness and are differentiated from their bulk counterparts by prescribing distinct flow parameters extracted from atomistic simulations. The predictive capabilities of the proposed methodology are then assessed by performing numerical simulations on uniaxial tensile behavior of Ni bicrystal and validating them from the published experiments and computations available in the literature. This research paradigm can be pushed forward by incorporating more complex grain boundary behaviors at higher length scales while preserving the richness provided by atomic scales.
An analytical relationship between the stress intensity factor and temperature rise for a moving crack tip is proposed. Comparison of the predictions with experimental results shows good agreement in both trend and magnitude. The results reveal the potential of applying theromographical technique for assessing the behavior of crack growth.
Molecular dynamics simulations were carried out to study the effect of the loading direction on the deformation behavior of the pearlite structure with a Bagaryatsky orientation relationship at the ferrite-cementite interface. We found excellent ductility in the ferrite and pearlite nanocomposites along the loading direction, while a brittle behavior was observed along the loading direction because of the reduced number of activated slip systems. Additionally, we reveal that the ductility is improved by either increasing the temperature or reducing the interlamellar spacing.
The rupture behavior of styrene-butadiene rubbers (SBR) in the presence of a V-shape notch is investigated for the first time both experimentally and theoretically. In the experiments, V-notched samples of SBR are tested under tensile loading and their rupture displacements are determined. Afterwards and in the analytical field, the rupture loads of tested rubbers are predicted using the averaged strain energy density (ASED) criterion. The key idea of this criterion (i.e. the almost uniaxial state of stress field near the notch tip) is verified through non-linear finite element modeling. It is shown that good agreement exists between the predictions of the ASED criterion and the experimental results obtained for SBR. Moreover, the microscopic study of the ruptured surfaces of the notched SBR demonstrates its high roughness which can be attributed to the resistance of the rubber chains against the crack growth.
The high amplitude loads that are usually known as overload have different effects on fatigue behavior of the specimens. These effects depend on overload parameters, specimen geometry and applied time; whether crack exist or not. Single tensile overload was applied before crack initiation. Overloads with different ratios versus the applied load and constant amplitude loads were applied on the V-notched samples made by AA 2024-T3 to characterize the fatigue behavior. Crack growth rule and finite element analysis were employed to predict the sample behavior. Weight function methods were used to determine the effects of induced residual stress on effective range of stress intensity factor, ΔKeff. There were good agreement between predicted and experimental results which proved the capability of the used method to predict the fatigue crack initiating from the notch root in presence of the residual stresses. Results revealed that the crack initiation life was improved considerably versus the overload ratio.
Also, it was observed that the crack growth life increased by increasing the overload ratio. The improving effect of the overload on the crack initiation stage was found to be remarkably higher than its effect in growth stage.
A cohesive zone model (CZM) based on a traction–separation (T-S) relation is first developed to simulate the interfacial behavior between graphene coating and aluminum (Al) substrate. The CZM parameters, which are very difficult to obtain directly experimentally, are determined using molecular dynamics (MD) simulation. Specifically, the MD simulations under the normal and shear loadings are conducted on the graphene-coating/Al interface to derive its T-S relation and then the relevant interfacial behavior of the composite is identified. The MD results show that the behavior of the interface between graphene coating and Al substrate under normal and shear loading is temperature dependent. The maximum normal tensile stress at the interface decreases gradually while the temperature increases from 150 K to 600 K. But the maximum shear stress increases as the temperature increases from 150 K to 450 K and then decreases as the temperature increases from 450 K to 600 K. Finally, the CZM parameters are determined and then imported into a finite element (FE) model. The blister test results obtained by the FE method are in good agreement with those obtained by the MD simulations. These results suggest that the proposed approach is efficient in determining the CZM parameters of the interfacial behavior between the substrate and the ultrathin coating.
Microstructural evolution and precipitation strengthening of the newly-developed 20Cr steel were investigated in present work. Three types of precipitates, including G-phase (Ni16Ti6Si7, intermetallic silicide), Laves phase (Fe2Ti, intermetallic compound) and carbide (TiC), were observed and their crystal structures were resolved with combined electrochemical phase extraction, X-ray diffraction and transmission electron microscopy analysis. G-phase particles were observed in the grains and Laves phase occurred at grain boundaries while carbides were present at both of the two sites. A temperature-dependency sketch map for these precipitates was also plotted to illustrate the characteristics of G-particles below 750 °C, Laves phase at 850 °C~1050 °C and carbide below 1150 °C. In particular, G-phase precipitated and had the cubic-cubic orientation with the ferritic matrix, thus showing a strong aging hardening characteristic. Nanodispersion of these G-particles greatly enhanced the yield strength, which was estimated to be up to ~1700 MPa. Finally, theoretical calculations for phase equilibria, critical radius and precipitation strengthening helped to understand the precipitation thermodynamics and strengthening mechanisms for developing high-performance steel by making use of G-phase.
Based on extensive experiments at the microscopic level, it was found that the grain sizes of TA1 titanium alloys exhibited a statistical nature, and in turn, the resultant distribution was achieved by a data fit. The Monte-Carlo method was employed to obtain a model size for molecular dynamics simulations. The melting point and lattice constants of the alloys were calculated using LAMMPS software with the model dimension. A comparison of numerical results and published experimental results was presented to demonstrate that such a method provides a reasonable domain that is beneficial to molecular dynamics modeling. Afterwards, a cohesive element model along the effective simulation region was established, and then the relationship between the traction and crack opening displacement for alloys was presented. The characteristic parameters obtained from the resultant curve were utilized to embed cohesive elements, and the real-life crack propagation behavior was further mimicked through finite element analysis. The results showed that the predicted fracture toughness agreed well with the experimental data, highlighting the suitability of the new analytical approach for predicting crack growth behavior.
The interfacial behavior of composites is often simulated using a cohesive zone model (CZM). In this approach, a traction-separation (T-S) relation between the matrix and reinforcement particles, which is often obtained from experimental results, is employed. However, since the determination of this relation from experimental results is difficult, the molecular dynamics (MD) simulation may be used as a virtual environment to obtain this relation. In this study, MD simulations under the normal and shear loadings are used to obtain the interface behavior of Al/Al2O3 composite material and to derive the T-S relation. For better agreement with Al/Al2O3 interfacial behavior, the exponential form of the T-S relation suggested by Needleman [1] is modified to account for thermal effects. The MD results are employed to develop a parameterized cohesive zone model which is implemented in a finite element model of the matrix-particle interactions. Stress-strain curves obtained from simulations under different loading conditions and volume fractions show a close correlation with experimental results. Finally, by studying the effects of strain rate and volume fraction of particles in Al(6061-T6)/Al2O3 composite, an equivalent homogeneous model is introduced which can predict the overall behavior of the composite.
The adhesive properties of Fe(110)/Fe(110) and Fe3C(001)/Fe(110) countersurfaces have been investigated by using classical molecular dynamics simulations. The simulation results show that Fe3C/Fe exhibits a relatively lower adhesion compared to the Fe/Fe. Additionally, the temperature dependence of the adhesive properties between 300–700 K has been examined. The results demonstrate that, with increasing the temperature, the values of the adhesion force and the work of adhesion continuously decrease in the case of Fe3C/Fe; they initially slightly increase up to 500 K then decrease in the case of Fe/Fe. Furthermore, the effect of lattice coherency between Fe/Fe has been examined and found to slightly reduce the adhesion. These results explain how carbides improve galling resistance of tool steel observed during dry sliding.
The hybrid multiscale method bridging the atomistic and mesoscopic scale is proposed in the current study, which combines the concurrent generalized particle (GP) dynamics method and the bottom-up hierarchical cohesive zone model (CZM) with embedded traction-separation law. The primary purpose is to transfer the GP-obtained physical parameters to the upper mesoscale finite element method (FEM) to investigate the meso- and microscopic crack propagation. The local fracture energy, stress and opening relationships under tension loading during steady-state crack propagation are extracted from the three-scale GP model. In this procedure, the scale duality technique is conducted using the GP analog, which can allow material to exist as particles via a lumping process and allows them to decompose into atoms at crack tips and interfaces. Crack extension resistance is detected by coordination vector (CV) snapshots, and energy release rates in the subdomain are used to evaluate the material behavior against the crack propagation when the current crack tip grows. Using the unique cohesive element length, four-scale tension specimen FE models are designed to reveal the accuracy of the intrinsic correlation between the atomistic and mesoscopic scale under a stress intensity factor to study the brittle body-centered cubic (BCC)-Fe fracture behavior. The result appears reasonable and encouraging.
In this study, we find microstructure mechanisms and stress distributions around the crack-tip of an intergranular fracture process in bicrystal nickel are strongly dependent on temperature by using a molecular dynamics (MD)-based cohesive zone model (CZM). At a lower temperature, deformation twinning occurs in the two opposite directions along the grain boundary, and the crack propagation eventually forms an intergranular fracture. As the temperature increasing, deformation twinning is becoming increasingly hard to occur around the crack-tip along the grain boundary but more readily to generate the slip bands, and the crack propagation will not form intergranular fracture along the grain boundary. Moreover, based on the calculation of CZM, the slip bands are stronger to prevent intergranular crack growth than deformation twinning around the crack-tip, and a high stress is found in the region of microstructure evolution near the crack-tip. The present results may provide useful information for understanding intergranular fracture mechanisms and stress distributions at the atomic-scale.
A representative volume element (RVE)-based strategy for modeling the hardening and failure behavior of a ferritic pearlitic steel at different length scales mesoscale and microscale is presented. At first, pearlite properties were considered to be isotropic and homogeneous. Micrographs taken on the undeformed material were transformed to a finite element mesh by using the software OOF2, a public domain FE-analysis software created at the National Institute of Standards and Technology (NIST) for the investigation of microstructures. Boundary conditions of the RVE were defined based on the macroscopic deformation history of a region of interest of an axisymmetric impact extrusion part. Crack initiation in pearlite is modeled within the extended finite element method (XFEM) framework. Pearlite cracking modeled at the mesoscale corresponds well to the observed cracks on SEM-micrographs. In a further approach, the crystallographic orientation of ferrite as well as various distributions of cementite lamellae were considered to take the inhomogeneous structure of the pearlite into account. For this purpose, in the framework of RVE computation, a spectral solver of the code DAMASK (Dusseldorf Advanced Material Simulation Kit, an open source crystal plasticity general purpose solver) was applied to model strain localizations at grain level. X-ray measurements were carried out to determine the orientation of ferrite grains and to determine the parameters of the applied crystal plasticity material model (critical resolved shear stress and slip hardening parameters). Investigations showed that the orientations of cementite lamellae have a significant influence on strain localization. The concept of coupling the FE-method to simulate the macroscopic behavior of the material and the spectral solver to achieve a high resolution of the microstructure in the framework of RVE computations leads to an efficient strategy regarding computational time and modeling of the microstructure.
Microstructural aspects have fundamental influences on the fatigue crack characteristics of materials. In this paper, effects of inclusions, grain boundaries (GBs) and grain orientations on the fatigue crack initiation and propagation behavior in a 2524-T3 aluminum alloy have been investigated using in-situ scanning electron microscope (SEM) fatigue testing and electron back scattering diffraction (EBSD). The results show that, potential fatigue cracks tend to nucleate along coarse and closely spaced inclusion particles or high-angle GBs. Coarse inclusion particles drastically accelerate local crack growth rates. A model of series crack growing stages is given based on the observation of initiation and growth of cracks at the inclusion region. GBs serve to impede the crack tip from propagation and cause large angle crack deflections, which greatly affects local crack propagation behaviors. In addition, fatigue crack shows a strong tendency to propagate transgranularly grains with high Schmid factors (SFs) and avoid grains with low SFs.
The thermal expansion of Fe-carbides Fe7C3 and Fe3C was measured above and below the ferromagnetic transition in a temperature range of 297–911 K by in situ X-ray diffraction enhanced by synchrotron radiation. The coefficient of thermal expansion was estimated as α = a0 + a1T. The results for paramagnetic phases are a0 = 3.1 × 10−5 K−1 and a1 = 1.2 × 10−8 K−2 for Fe7C3 and a0 = 3.9 × 10−5 K−1 and a1 = 1.2 × 10−8 K−2 for Fe3C. The ferromagnetic phases show linear relations with V298K = 371.9 Å3, a0 = 0.91 × 10−5 K−1 and a1 = 0 for Fe7C3 and V298K = 155.2 Å3, a = 0.86 × 10−5 K−1 and a1 = 0 for Fe3C. Our obtained results indicate that the coefficients of thermal expansion, that were calculated by high-pressure equations of state for Fe-carbides, appeared to be high-precision and consistent with the data obtained at 0.1 MPa.