Atomistic/continuum simulation of interfacial fracture Part II: Atomistic/dislocation/continuum simulation

Coupled atomistic/dislocation/continuum simulation of interfacial fracture is performed in this paper. The model consists of a nanoscopic core made by atomistic assembly and a surrounding elastic continuum with discrete dislocations. Atomistic dislocations nucleate from the crack tip and move to the continuum layer where they glide according to the dislocation dynamics curve. An atoms/continuum averlapping belt is devised to facilitate the transition between the two scales. The continuum constraint on the atomic assembly is imposed through the mechanics atmosphere along the overlapping belt. Transmissions of mechanics parameters such as displacements, stresses, masses and momenta across the belt are realized. The present model allows us to explore interfacial fracture processes under different mode mixity. The effect of atomistic zigzag interface on the fracture process is revealed: it hinders dislocation emission from the crack tip, especially under high mode mixity. The project supported by the National Natural Science Foundation of China     

A piezoelectric biaxial loading device for interfacial fracture experiments

In this paper we describe the development of a new biaxial loading device for investigating mixed-mode fracture at bimaterial interfaces. The new device makes use of piezoelectric actuators and specially arranged flexures to provide independent displacements normal and tangential to the interface. Capacitive probes and special washer load cells were used for measuring the displacements and reactive loads, respectively. A closed-loop circuit was formed with a personal computer to control the applied displacements to within 10 nm. Preliminary experiments with quartz/epoxy/aluminum sandwich specimens with cracks growing between the quartz and the epoxy found that the intrinsic toughness of this interface was 30% lower than the value for a glass/epoxy interface. Crack opening interferometry measurements having a resolution of 30 nm revealed the presence of a cohesive zone whose size was about 0.5 μm.     

基于数值模拟的混凝土系列有效断裂判据

基于ANSYS平台,对某系列混凝土断裂破坏试验的加载过程进行有限元数值模拟,获得了荷载-加力 点位移曲线.利用获得的曲线,在线性渐进叠加假定的基础上,确定了试件在失稳断裂时的临界有效裂缝长度.将模拟峰值荷载和临界有效裂缝长度代入由LEFM推导出的公式计算了考虑断裂过程区影响的有效断裂韧度.最后,通过对系列试验有效断裂韧...     

The dynamical complexity of work-hardening： a large-scale molecular dynamics simulation

We analyze a large-scale molecular dynamics simulation of work hardening in a model system of a ductile solid. With tensile loading, we observe emission of thousands of dislocations from two sharp cracks. The dislocations interact in a complex way, revealing three fundamental mechanisms of work-hardening in this ductile material. These are (1) dislocation cutting processes, jog formation and generation of trails of point defects; (2) activation of secondary slip systems by Frank-Read and cross-slip mechanisms; and (3) formation of sessile dislocations such as Lomer-Cottrell locks. We report the discovery of a new class of point defects referred to as trail of partial point defects, which could play an important role in situations when partial dislocations dominate plasticity. Another important result of the present work is the rediscovery of the Fleischer-mechanism of cross-slip of partial dislocations that was theoretically proposed more than 50 years ago, and is now, for the first time, confirmed by atomistic simulation. On the typical time scale of molecular dynamics simulations, the dislocations self-organize into a complex sessile defect topology. Our analysis illustrates numerous mechanisms formerly only conjectured in textbooks and observed indirectly in experiments. It is the first time that such a rich set of fundamental phenomena have been revealed in a single computer simulation, and its dynamical evolution has been studied. The present study exemplifies the simulation and analysis of the complex nonlinear dynamics of a many-particle system during failure using ultra-large scale computing.     

Application of split Hopkinson tension bar technique to the study of dynamic fracture properties of materials

A novel approach is proposed in determining dynamic fracture toughness(DFT) of high strength steel,using the split Hopkinson tension bar(SHTB) apparatus,combined with a hybrid experimental-numerical method.The center-cracked tension specimen is connected between the bars with a specially designed fixture device.The fracture initiation time is measured by the strain gage method,and dynamic stress intensity factors(DSIF) are obtained with the aid of 3D finite element analysis(FEA).In this approach,the dimensions of the specimen are not restricted by the connection strength or the stress-state equilibrium conditions,and hence plane strain state can be attained conveniently at the crack tip.Through comparison between the obtained results and those in open publication,it is concluded that the experimental data are valid,and the method proposed here is reliable.The validity of the obtained DFT is checked with the ASTM criteria,and fracture surfaces are examined at the end of paper.     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

3-D numerical simulation of fracture processes in heterogeneous brittle materials

By using the lattice model combined with finite element methods and statistical techniques, a numerical approach is developed to establish mechanical models of three-dimensional heterogeneous brittle materials. A special numerical code is introduced, in which a lattice model and statistical approaches are used to simulate the initial heterogeneity of material properties. The size of displacement-load step is adaptively determined so that only few elements would fail in each load step. When the tensile principal strain in an element exceeds the ultimate strain of this element, the element is considered broken and its Young's modulus is set to be very low. Some important behaviors of heterogeneous brittle materials are indicated using this code. Load-displacement curves and figures of three-dimensional fracture patterns are also numerically obtained, which are similar to those observed in laboratory tests.     

Enhanced fracture energy and effects of temperature at spalling in ceramics: continuum damage modelling

Summary Enhanced fracture energy losses at spalling and the temperature dependence of the spalling strength of alumina ceramic bars are analysed on the basis of the experimental tests conducted both in room temperature and within the temperature range up to 1500°C at strain rates of some 500 s⁻¹. The experimental method and the measurements are first shortly outlined. The mechanical response of ceramic bars is modelled then as a heterogeneous distribution of brittle-elastic mesoelements undergoing continuum damage at the known strain history, corresponding to that registered in the experiments. The mesoelements are characterised by the values of initial damage randomly fluctuating within a given band-width superposed on a deterministic distribution, which corresponds to the fabrication conditions of the ceramic bars. The model has been tested in the evaluation of room-temperature experiments, its parameters: the average value of the initial damage, Young's modulus of the undamaged material and the energy absorption capacity in continuum damage are taken from the calibration fitting the experimental data. The registered energy losses at spalling, which exceed the static values of fracture energy by almost an order of magnitude, can be explained thus by the enhancement of the dissipation due to bulk damage, which is computed on the basis of the above parameters. The temperature change of the Young's modulus of the matrix material is taken as corresponding to the measured change of the uniaxial wave velocity in the bar, and corrected by the temperature change of the mass density. The analysis of the model shows that the drop in the spalling strength of the specimens with the increase of the temperature is phenomenologically related to the falling energy absorption capacity within the continuum damage mechanism. An explanation of this phenomenon is attempted, based on the grain-size-related mechanisms of the microfracture from pre-existing intergranular flaws distributed over the bulk of ceramics. Received 7 May 1999; accepted for publication 14 June 1999     

Bending solution of third-order orthotropic Reddy plates with asymmetric interfacial crack

In this paper Reddy’s third-order shear deformable plate theory is applied to asymmetrically delaminated orthotropic composite plates under antiplane–inplane shear fracture mode. A double-plate system is utilized to capture the mechanical behavior of the uncracked plate portion. An assumed displacement field is used and modified in order to satisfy the traction-free conditions at the top and bottom plate boundaries. Moreover, the system of exact kinematic conditions was also implemented into the novel plate model. An important improvement of this work compared to previous papers is the continuity condition of the shear strains at the interface of the double-plate system. Applying these conditions it is shown that the nineteen parameters of the third-order displacement field can be reduced to nine. Using the simplified displacement field the governing equations are derived, as well. The solution of a simply-supported delaminated plate is presented using the state-space model and the displacement, strain and stress fields are determined, respectively. The energy release rate and mode mixity distributions are calculated using the 3D J-integral. The analytical results are compared to those by finite element computations and it is concluded that the present model is the most accurate one among the previous plate theory-based approaches.     

镍涂层对碳纳米管/镁复合材料界面结合强度影响的分子动力学模拟

使用分子动力学模拟方法研究了镍涂覆单壁碳纳米管(SWCNTs)增强镁基复合材料的力学行为.结果表明,镍涂覆SWCNT/Mg复合材料的杨氏模量显著大于未涂覆SWCNT/Mg复合材料的杨氏模量,在碳纳米管表面修饰的Ni涂层可有效传递碳纳米管和Mg基体之间的载荷.此外,还研究了Ni涂层数对SWCNT/Mg复合材料界面结合强度的影响.对于不同Ni涂层数,即无Ni涂层、1层Ni涂层和2层Ni涂层,涂覆1层Ni和2层Ni的SWCNT从Mg基体中完全拔出后的界面结合强度分别约为无Ni涂层SWCNT/Mg复合材料界面结合强度的3.9和11.9倍.     

Development of hot dry rocks by hydraulic stimulation: Natural fracture network simulation

This paper presents an advanced computational modelling of natural fracture networks in HDR (hot dry rock) reservoirs. The model stochastically simulates discrete properties of natural fractures, utilizing multi-set orientation and fractal mathematics. The simulated fracture networks are essential for further stimulation and fluid flow studies. The model has been verified using the data of actual fracture stimulation programs conducted by Gas Research Institute and Department of Energy at the multi-site. It is validated that the simulated fracture distribution is sufficiently similar to that observed in the reservoir. This paper also examines the detrimental effects of the simulated natural fracture network on the stimulated fluid flow capacity. The effective permeability enhancement (due to hydraulic stimulation) is found almost proportional to the density of the reservoir natural fractures.     

Rheology and morphology of multilayer reactive polymers: effect of interfacial area in interdiffusion/reaction phenomena

The rheological behavior of multilayered reactive polymers was investigated. Dynamic mechanical experiments were performed to probe the effect of the interfacial area on the rheological behavior of a multilayered structure as compared to that of a droplet-type morphology. Polyamide (PA6)/polyethylene grafted with glycidyl methacrylate was used as a model system, and in the molten state, such a system generated a reaction between amine, carboxylic, and epoxy groups. Multilayer structures containing various amounts of both interfacial area and volume fractions of the two components were studied. Relationships between viscoelastic material functions and compositions were used to analyze the effects of bulk and reactive functions in the polyolefin phase at the interface with PA. The contribution of the interface/interphase effect was investigated along with the increase in the number of layers, and the results showed that the variation in dynamic modulus of the multilayer system was a result of both diffusion and chemical reaction. Specific experiments were carried out to separate the thermodynamic effects from the kinetic ones, and the results were rationalized by comparing the obtained data with theoretical models. Finally, the effect of the interface/interphase triggered between the neighboring layers was quantified at a specific welding time and shear rate.     

Micromechanics of fracture in a ceramic/metal composite studied by in situ fluorescence spectroscopy II: fracture mechanics analysis

Fluorescence microprobe spectroscopy was used in [1] to determine in situ microstress fields that develop during fracture in a model ceramic/metal composite. In particular, experimental and theoretical procedures were described in order to relate the experimental peak-shift to the various stress components and combinations thereof. Based on suitable micromechanical concepts, these stress maps are now used to predict quantities related to the fracture mechanics, such as (critical) stress intensity factors, R-curves, and crack-opening displacements. All predictions are compared with direct measurements of these quantities to demonstrate the feasibility and soundness of the micromechanics approach.Received: 10 September 2003, Accepted: 1 November 2003, Published online: 3 February 2004PACS: 68.37.Uv, 62.60.Mk Correspondence to: W.H. Müller     

Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls

Interest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo-spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant-property, turbulent fluid in a two-dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions. Calculations were made for a Prandtl number of 0·72 and Reynolds number based on friction velocity and channel half-height of 180 or 2800 based on channel half-height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two-point velocity correlations are given. Deficiencies are that the calculation requires many hours on a fast computer with a large high-speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.     

Fracture of bicrystal metal/ceramic interfaces: A study via the mechanism-based strain gradient crystal plasticity theory

Two continuum mechanical models of crystal plasticity theory namely, conventional crystal plasticity theory and mechanism-based crystal plasticity theory, are used to perform a comparative study of stresses that are reached at and ahead of the crack tip of a bicrystal niobium/alumina specimen. Finite element analyses are done for a stationary crack tip and growing cracks using a cohesive modelling approach. Using mechanism-based strain gradient crystal plasticity theory the stresses reached ahead of the crack tip are found to be two times larger than the stresses obtained from conventional crystal plasticity theory. Results also show that strain gradient effects strongly depend on the intrinsic material length to the size of plastic zone ratio (l/R₀). It is found that the larger the (l/R₀) ratio, the higher the stresses reached using mechanism-based strain gradient crystal plasticity theory. An insight into the role of cohesive strength and work of adhesion in macroscopic fracture is also presented which can be used by experimentalists to design better bimaterials by varying cohesive strength and work of adhesion.     

Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests

This article reports on the potential of application of LES in the calculation of turbulent two-phase flows, in the case where each phase is resolved and interfaces remain much larger than the mesh size. In comparison with single-phase flow, successful application of LES to resolve two-phase flow problems should account for the complex interaction between turbulence and interfaces. Non-linear transfers of turbulent energy across the interface have to be accurately modeled. The derivation of the complete filtered two-phase flow governing equations has been formulated to deal with turbulence at the interface in a comprehensive and practical way. Explicit filtering of 2D direct numerical simulations has been employed to evaluate the order of magnitude of the new subgrid contributions. A parametric study on the academic test case of two counter-rotative vortices and a more complex test case of phase inversion in a closed box have been utilized to perform an order of magnitude analysis of different transport mechanisms. Important features of turbulent energy transfer across the interface have been discussed. Analyses of the numerical results have been conducted to derive conclusions on the relative importance of the different subgrid scale contributions, and modeling issues and solutions are provided.     

Un modèle paramétrique d'évolution de surface pour matériaux contraints : modélisationA parametric model of surface evolution for materials under constraint; part I: modeling

We present a model describing the surface changes of an elastic preconstrained material which is valid for large deformations. The surface profile is described by a parametric curve that allows the emergence of infinite tangents and back return point as the surface evolves. The proposed model covers a number of classic models: Spencer (1994), Yang (1993), Kassner (1994), Chiu (1994). These latter models were limited to surface profiles with one-to-one representations and low amplitudes of deformation. To cite this article: M. Carrive, J. Grilhé, C. R. Mecanique 334 (2006).