A method of seamlessly combining a crack tip molecular dynamics enclave with a linear elastic outer domain in simulating elastic–plastic crack advance

Molecular dynamics is applicable only to an extremely small region of simulation. In order to simulate a large region, it is necessary to combine molecular dynamics with continuum mechanics. Therefore, we propose a new model where molecular dynamics is combined with micromechanics. In this model, we apply molecular dynamics to the crack tip region and apply micromechanics to the surrounding region. Serious problems exist at the boundary between the two regions. In this study, we manage to solve these problems, and make possible the simulation of the process of crack propagation at the atomic level. In order to examine the validity of this model, we use α-iron for simulation. If the present model is valid, stress and displacement should vary continuously across the boundary between the molecular dynamics region and the micromechanics region. Our model exhibits just such behavior. This revised version was published online in August 2006 with corrections to the Cover Date.     

单晶硅预制初裂纹扩展行为的分子动力学研究

采用基于Stillinger-Weber作用势的分子动力学方法研究了单晶硅预制初裂纹前缘方向分别为[100]、[110]、[111]晶向的裂纹扩展行为.模拟结果表明:低温时裂纹尖端形成新的环状结构,温度逐渐升高后,出现母-子裂纹传播机制,裂纹前缘方向为[111]晶向的初裂纹扩展呈现出明显的取向效应.     

Transformation toughening in the γ-TiAl–β-Ti–Vsystem: Part II A molecular dynamics study

Molecular dynamics simulations of the evolution of materials in a region surrounding a crack tip were carried out for the case of a crack in a γ-TiAl phase impinging at a right angle onto the interface between a γ-TiAl phase and a metastable Ti–15V (at %) phase. The corresponding linear anisotropic solutions for the singular stress and displacement fields were used to both generate the crack in the original crystal and to prescribe the boundary conditions applied to the computational crystal during the molecular dynamics simulation runs. The atomic interactions were accounted for using appropriated embedded atom method (EAM) type interatomic potentials. The crack-tip behaviour for the two-phase γ–β material was ultimately compared with the one in the corresponding single-phase material, i.e. to the one in pure γ and the one in pure β crystals. The simulation results showed that under the same applied level of external stress, the crack tip became blunt and the crack stopped propagating in the γ-TiAl–β-Ti–15V bicrystal and in the single β-phase crystal while the crack extended by brittle cleavage in the single-phase γ crystal. The blunting process was found to be controlled by the martensitic transformation that took place in the β-phase ahead of the crack tip. Depending on the local stress conditions the crystal structure of martensite was found to be either hexagonal close packed (h.c.p.), body centred orthorhombic (b.c.o.) and/or face centred orthorhombic (f.c.o.). Finally the implications of crack tip martensitic transformation on the toughness of the materials are analysed in quantitative terms using the concept of Eshelby's conservation integral, i.e. the energy release rate. This revised version was published online in November 2006 with corrections to the Cover Date.     

Multiscale modeling of dynamic crack propagation

A multiscale approach is employed to investigate a center-cracked specimen with the purpose to redefine fracture toughness from the atomistic perspective and to simulate different modes of crack propagation. The specimen is divided into three regions: (1) far field, modeled by classical fracture mechanics, (2) near field, modeled by a multiscale field theory and analyzed by a generalized finite element method, and (3) crack tip atomic region, modeled by molecular dynamics (MD). The exact and analytical solution of the far field is utilized to specify boundary conditions at the interface between the far field and the near field. The interaction between the near field and the crack tip region is described by full-blown interatomic forces. In this work, crystals of perovskite (Barium Titanate) and rocksalt (Magnesia) have been studied. Fracture toughness is defined as a material property associated with instability of the MD simulation. Mode I, Mode II, and mixed mode fracture have been investigated and numerical results will be presented and discussed.     

Modeling of fracture behavior in polymer composites using concurrent multi-scale coupling approach

ABSTRACT

Embedded statistical coupling method was originally developed to provide computational efficiency, to decrease coupling complexities, and to avoid the need to discretize the continuum model to atomic scale resolution in concurrent multi-scale modeling. An embedded statistical coupling method scheme is relatively easy to implement within a conventional finite element method code and has been tested in standard solid lattice structures. However, this method encounters difficulties when being implemented for amorphous materials like polymers, due to the fact that they lack specific ordered lattice structure and atoms may not be covalently bonded with each other, which are the requirements of common coupling schemes. Therefore, a new approach needs to be developed to resolve this problem. In this article, details of a modified embedded statistical coupling method approach for atomistic-continuum coupling developed to perform simulations of macroscale crack growth in polymers is presented. The presence of the continuum domain surrounding the molecular dynamics region allows for the application of far field loading, and prevents stress wave reflections from the external boundary impinging back on the crack tip. In our approach, a material point method, which is a meshless particle-in-cell method based on an arbitrary Euler-Lagrange scheme and has been proven to have good performance in large deformation problems, is used to model the continuum domain. It is concurrently coupled with molecular dynamics, a widely used method in atomistic simulations, using a so-called handshake region. Anchor points, the equilibrium positions of the constrained particles, which are designed to transmit displacements and forces between nanoscale and macroscale model, are defined in the handshake region. A concurrently coupled material point method-molecular dynamics simulation of crack propagation inside a polymer is performed to verify this new coupling approach, thereby providing a better understanding of the fracture mechanisms at the nanoscale to predict the macro-scale fracture toughness of a polymer system. Results are presented for concurrently coupled simulation of crack initiation and crack propagation in a di-functional cross-linked thermoset polymer, EPON 862.     

Molecular dynamics simulation of crack growth under cyclic loading

The mechanical behaviors around a crack tip for a system including both a crack and two tilt grain boundaries under cyclic loading are examined using a molecular dynamics simulation. Not only a phase transition but also the emission of edge dislocations is observed in order to relax stress concentration around a crack tip during the first loading. Then, a dislocation pile-up is formed near the grain boundary after the edge dislocations reach the grain boundary, because they cannot move beyond the grain boundary. During the first unloading, the edge dislocations emitted from the crack tip return to the crack tip and disappear in the system. We observe several vacancies generated around the crack tip and crack growth corresponding to an atomic scale during cyclic loading. Conclusively, we propose the fatigue crack growth mechanism for the initial phase of the fatigue fracture. That is, a fatigue crack propagates due to coalescence of the crack and the vacancies caused by the emission and absorption of dislocations.     

Seamless coupling of molecular dynamics and material point method via smoothed molecular dynamics

A concurrent multiscale method coupling molecular dynamics (MD) and continuum‐based material point method (MPM) is proposed. Seamless coupling is realized by utilizing smoothed molecular dynamics (SMD) method. One set of background mesh is used in SMD method. Atomic equations of motion are assembled onto mesh nodes, and atomic variables are updated with nodal increments. SMD allows much larger time step size than MD critical time step size but keeps nice global accuracy. SMD is similar to MD except for the mapping process between background mesh nodes and atoms. SMD and MPM share the feature using the background mesh to solve momentum equations and to update variables. So bridging MD and MPM via SMD is straightforward and concise. A recently proposed transition scheme based on frequency decomposition is adopted to suppress phonon reflection at MD‐SMD interface. The nodal equations in SMD–MPM interface region have contributions from both atoms and material points, which ensure the consistency between SMD region and MPM region. A multiple‐time‐step scheme is adopted for high efficiency. Numerical examples including wave propagation, bending, and crack propagation validate the proposed method, and the results show nice accuracy. The computational cost is greatly saved compared with pure MD computation. Copyright © 2017 John Wiley & Sons, Ltd.     

外应力场下NiAl合金微裂纹动态扩展的分子动力学模拟

目的 对NiAl合金中不同晶体取向的裂纹扩展动力学行为进行原子尺度研究,明晰在塑性变形过程或实际应用过程中裂尖的脆性解理和塑性变形行为,为研究NiAl合金的塑性变形行为和评估服役寿命提供理论基础。方法 建立了4种不同取向的裂尖模型,其扩展取向分别为(010)[001]、(0■1)[100]、(010)[101]、(01■)[011],用分子动力学方法对上述模型进行模拟,采用Gear算法计算原子在真实受力状态下的运动情况。结果 在NiAl合金中,微裂纹在外载作用下的裂尖反应强烈依赖于裂纹取向（裂纹面及裂纹前沿方向）。{110}裂纹面的裂纹构型易于脆性解理扩展;{100}裂纹面的裂纹构型具有一定的塑性,裂尖处可形成位错发射,位错的出现可以协调塑性变形,模拟结果与实验观察相一致。结论 裂纹的晶体取向对裂尖的马氏体相变行为有重要影响,当裂纹前沿为<100>方向时,原子在裂纹前端的{100}滑移面上运动,诱导B2相转变成L10相,产生马氏体相变,这种马氏体相变有利于相变增韧,能够促进裂尖处位错发射,可提升材料塑性和服役寿命。     

A study of the estimation method of the cutting force for a conical tool under nanoscale depth of cut by molecular dynamics

This study uses molecular dynamics to simulate the nanoscale cutting of a Cu single crystal by a conical diamond tool. Actual nanoscale straight-line cutting experiments were performed, and the experimental results are compared with the simulation results. The heaping of copper atoms is qualitatively quite consistent with the simulation result. This paper also proposes a nanoscale contact pressure factor (NCP factor) that is applicable to the probes at different tip radii. An estimation model of the cutting force for nanoscale cutting is established. This model can estimate the cutting force during actual nanoscale cutting. Actual nanoscale cutting experiments were performed for verification, and the difference between the cutting force estimated by this model and the actual force is very small.     

A novel combined molecular dynamics–micromechanics method for modeling of stiffness of graphene/epoxy nanocomposites with randomly distributed graphene

In this paper, by combining molecular dynamics and micromechanics methods, a new approach for prediction of the stiffness of the nanocomposites with randomly distributed nanoparticles in the macro level is presented. The molecular dynamics method is used to model the stiffness of the graphene/epoxy nanocomposites containing one layer of an aligned nano graphene embedded in epoxy resin. By considering the large sizes of the length and width of the nano graphene in comparison with its thickness and the shortcomings of the available hardware and software for simulation purposes, a new approach for modeling is also developed. This new approach, by using the moduli of different graphene sheets with different sizes embedded in a representative volume element, can predict the moduli of a real size graphene embedded in the matrix along the longitudinal, transverse and normal directions in the nano-scale. In order to consider the effect of the random distribution of graphene sheets in epoxy resin, a micromechanical approach is used. The results obtained by the molecular dynamics method are used by the micromechanics approach and the stiffness of graphene/epoxy nanocomposites with randomly distributed graphene in the macro-scale is predicted. An experimental program is conducted to evaluate the capability of the model. The result of the modeling is in a very good agreement with the experimental data.     

Path-independent integrals in fracture dynamics using auxiliary fields

“Path-independent” integrals are presented for use in fracture dynamics. One class of integrals is based on a reciprocal theorem and the other is related to the energy flow into a moving crack tip. These integrals may be used to numerically calculate the dynamic stress intensity factor in elastodynamic crack propagation problems. Several examples are presented using the release node technique to model crack propagation.     

Coarse-grained molecular dynamics simulation of nanofilled crosslinked rubber

A bead-spring model was applied to a crosslinked polymer with nanofillers for coarse-grained molecular dynamics simulation. Two nanofillers consisting 561 tightly connected beads and a crosslinked polymer with about 3000 beads were used as a simulation model. The strength of interactions between nanofiller and polymer based on the Lennard-Jones potential were varied. In order to investigate the effects of crosslinking and nanofiller on reinforcement, uniaxial elongation behavior was studied by coarse-grained molecular dynamics simulation with deformation function. From the uniaxial elongation simulation results and the analysis of polymer dynamics around nanofiller, it was confirmed that the degree of reinforcement depends on the strength of filler–polymer interaction, and one of the factors which influenced the stress was attributed to the existence of a low mobility phase around the nanofiller.     

Molecular dynamics study on low temperature brittleness in tungsten single crystals

This study employed a numerical model combining molecular dynamics and micromechanics to study the low temperature fracture of tungsten. In the simulations a pre-crack was introduced on the (110) planes and cleavage was observed along the (121) planes. Cleavage along (121) planes has also been observed in experiments. Simulations were performed with three sizes of molecular dynamic regions at 77 K, and it was found that the results were independent of the size. Brittle fracture processes were simulated at temperatures between 77 K and 225 K with the combined model. The fracture toughness obtained in the simulations showed clear temperature dependency, although the values showed poor agreement with experimental results. A brittle fracture process at 77 K was discussed considering driving forces for dislocation emissions and cleavage in an atomic scale region of the crack tip. The driving force for dislocation emissions was saturated after the first dislocation emission, whilst the driving force for cleavage gradually increased with the loading K-field. The increased driving force caused cleavage when it reached a critical value. The critical values of driving force, which were close to the theoretical strength of the materials, were not influenced by temperature. This indicates that the temperature dependency of fracture toughness is not caused by the temperature dependency of dislocation emissions, but by that of dislocation mobility.     

Crack propagation in a Tantalum nano-slab

Using molecular dynamics with an accurate many-body potential for metallic Tantalum, we studied crack propagation in a pre-notched nano-slab under uniaxial strain in a [100] direction. We study dislocation emission from the crack tip for various strain rate and temperatures, focusing on the influence of the local temperature at the crack tip on the propagation of the crack. We find a close connection between the local temperature at the crack tip and dislocation emission. This revised version was published online in June 2006 with corrections to the Cover Date.     

A coupled molecular dynamics and extended finite element method for dynamic crack propagation

A multiscale method is presented which couples a molecular dynamics approach for describing fracture at the crack tip with an extended finite element method for discretizing the remainder of the domain. After recalling the basic equations of molecular dynamics and continuum mechanics, the discretization is discussed for the continuum subdomain where the partition‐of‐unity property of finite element shape functions is used, since in this fashion the crack in the wake of its tip is naturally modelled as a traction‐free discontinuity. Next, the zonal coupling method between the atomistic and continuum models is recapitulated. Finally, it is discussed how the stress has been computed in the atomic subdomain, and a two‐dimensional computation is presented of dynamic fracture using the coupled model. The result shows multiple branching, which is reminiscent of recent results from simulations on dynamic fracture using cohesive‐zone models. Copyright © 2009 John Wiley & Sons, Ltd.     

Simulation of failure processes with the variational multiscale method

In the present contribution a multiscale method for the modeling an simulation of failure and crack propagation is presented. Thereby, the variational multiscale method initially introduced by Hughes provides the methodological multiscale framework. The basis of this method is a decomposition of the solution into coarse scale and fine scale contributions, the latter incorporating the local behaviour. The method involves the propagation of cracks at finite strains. A twoscale approach, macro-meso, is adopted and both scales are discretized with finite elements whereby certain locality assumptions are prescribed to the mesoscopic solution. At the fine scale an evolving mesostructure induced by crack propagation is taken into account. The multiscale framework implies naturally a refined discretization in the area of the crack tip. Nevertheless, when crack propagation is modelled, the crack direction should not depend on the discretization. To prevent constant remeshing a discretization with discontinuous elements at the fine scale is applied. The applicability of the method to simulate multiscale failure processes at finite strains is demonstrated by numerical examples.     

Molecular dynamics‐smoothed molecular dynamics (MD‐SMD) adaptive coupling method with seamless transition

Smoothed molecular dynamics (SMD) method is a recently proposed efficient molecular simulation method by introducing one set of background mesh and mapping process into molecular dynamics (MD) flow chart. SMD can sharply enlarge MD time step size while maintaining global accuracy. MD‐SMD coupling method was proposed to improve the capability to describe local atom disorders. The coupling method is greatly improved in this paper in two essential aspects. Firstly, a transition scheme is proposed to avoid artificial wave reflection at the interface of MD and SMD regions. The new transition scheme has simple formulation and high efficiency, and the wave reflection can be well suppressed. Secondly, an adaptive scheme is proposed to automatically identify the regions requiring MD simulation. Two adaptive criteria, the centro‐symmetry parameter criterion and the displacement criterion, are also proposed. It is found that both the two criteria can achieve good accuracy but the efficiency of the displacement criterion is much better. The coupling method does not demand reduction in mesh size near the interface, and a multiple time stepping scheme is adopted to ensure high efficiency. Numerical results including wave propagation, nano‐indentation, and crack propagation validate the method and show nice accuracy. Copyright © 2016 John Wiley & Sons, Ltd.     

DUCTILE TEARING SIMULATION BASED ON A LOCAL ENERGETIC CRITERION

It is well known that the tearing resistance curve J–Δa is not a material property and that probably the energy dissipation rate is preferable to the integral J to characterize crack growth. The G parameter represents the energy dissipated in plasticity and fracture and, under certain conditions, this parameter could be used directly as a critical value for a criterion based on an energy release rate calculated near the crack tip to simulate propagation. Indeed, we see that a local energy release rate could be calculated near the crack tip to take account only of that portion of energy which participates in the fracture.
We applied this approach to simulate the crack growth for CT specimens with and without side grooves in a 20  MnMoNi 55 ferritic steel, and compared the results with Rousselier's model.     

超高分子量聚乙烯架桥纤维与裂缝的交互微观力学

使用拉曼光谱研究了架桥纤维与裂缝微观力学,以超高分子量聚乙烯(UHMWPE)纤维为例,将纤维搭桥试样进行微拉伸试验,着重分析架桥纤维的止裂作用和架桥纤维/环氧树脂界面的应力分布,并对不同位置架桥试样的裂缝扩展速度和应力分布进行分析,并进一步运用剪切滞后模型,对架桥纤维在不同拉伸载荷下的应力分布进行了拟合分析,结果表明:架桥纤维能够分散部分外载应力,对于裂纹扩展具有显著的止裂作用。在低于UHMWPE纤维最大应变拉伸时,发现在裂缝中心位置处架桥纤维所承受的应力最大,其应力不超过2GPa,而基体树脂的应力可达到12GPa,架桥纤维/基体界面的应力传递达不到100%。以UHMWPE为架桥的应力传递模型呈"正抛物线"型,应力分布存在于粘结区、脱粘区和架桥区。