Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum

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 Σ99 [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.     

Modeling finite deformations in trigonal ceramic crystals with lattice defects

A model is developed for thermomechanical behavior of defective, low-symmetry ceramic crystals such as α$\alpha$-corundum. Kinematics resolved are nonlinear elastic deformation, thermal expansion, dislocation glide, mechanical twinning, and residual lattice strains associated with eigenstress fields of defects such as dislocations and stacking faults. Multiscale concepts are applied to describe effects of twinning on effective thermoelastic properties. Glide and twinning are thermodynamically irreversible, while free energy accumulates with geometrically necessary dislocations associated with strain and rotation gradients, statistically stored dislocations, and twin boundaries. The model is applied to describe single crystals of corundum. Hardening behaviors of glide and twin systems from the total density of dislocations accumulated during basal slip are quantified for pure and doped corundum crystals. Residual lattice expansion is predicted from nonlinear elasticity and dislocation line and stacking fault energies.     

分子动力学方法在研究材料力学行为中的应用进展

报道近年来分子动力学方法应用于研究位错、裂纹、晶界及其相互作用方面的进展．主要包括:裂纹尖端的位错发射,位错发射的不稳定堆垛能,晶体与裂纹’几何关系对位错发射的影响,温度对位错发射的影响以及由裂纹尖端发射的位错列与不对称倾侧晶界的相互作用．报道主要以我们的工作为主,重点讨论裂纹尖端位错发射的研究结果      

Energy dissipation mechanisms in ductile fracture

The objective is to investigate energy dissipation mechanisms that operate at different length scales during fracture in ductile materials. A dimensional analysis is performed to identify the sets of dimensionless parameters which contribute to energy dissipation via dislocation-mediated plastic deformation at a crack tip. However, rather than using phenomenological variables such as yield stress and hardening modulus in the analysis, physical variables such as dislocation density, Burgers vector and Peierls stress are used. It is then shown via elementary arguments that the resulting dimensionless parameters can be interpreted in terms of competitions between various energy dissipation mechanisms at different length scales from the crack tip; the energy dissipations mechanisms are cleavage, crack tip dislocation nucleation and also dislocation nucleation from a Frank-Read source. Therefore, the material behavior is classified into three groups. The first two groups are the well-known intrinsic brittle and intrinsic ductile behavior. The third group is designated to be extrinsic ductile behavior for which Frank-Read dislocation nucleation is the initial energy dissipation mechanism. It is shown that a material is predicted to exhibit extrinsic ductility if the dimensionless parameter bρ_disl^1/2 (b is Burgers vector, ρ_disl is dislocation density) is within a certain range defined by other dimensionless parameters, irrespective of the competition between cleavage and crack tip dislocation nucleation. The predictions compare favorably to the documented behavior of a number of different classes of materials.     

Nanoindentation of polymeric thin films with an interfacial force microscope

The mechanical properties of interphase regions at bi-material interfaces can be quite different from the surrounding bulk materials. For composite materials, this interphase region is usually thin but plays an important role in their overall mechanical properties. Nanoindentation has become a commonly used experimental technique for measuring the mechanical properties of materials, especially when one of the dimensions is small. However, the extraction of reduced elastic modulus from the nanoindentation of thin films on substrates can pose challenges due to the influence of the substrate. In this study, the nanoindentation of thin films on substrates has been examined with a view to extracting the reduced modulus of thin polymer films.Thin films of (3-aminopropyl)triethoxysilane (C₉H₂₃NO₃Si, γ-APS) were deposited on silicon. An interfacial force microscope (IFM) was used to indent the γ-APS films. The effect of the substrate was studied by considering two very different thicknesses ( and ). The nanoindentation data were analyzed via contact mechanics theories and a finite element analysis that incorporated surface interactions. The analyses showed that nanoindentation experiments can provide reliable values of film modulus when the film is very different from the substrate. It was found that the commonly used rule of thumb that the indentation depth should be less than 10% of the thickness did not eliminate substrate effects for a wide range of material combinations. Instead, it is proposed that the contact radius should be less than 10% of the thickness so that contact mechanics theories for monolithic materials can be used without considering the presence of the substrate. The modulus of γ-APS polymer films and the surface energy between the tungsten tip of the IFM and γ-APS films were extracted and were related to their cure. A completely cured thick γ-APS film had a reduced modulus of . This value falls in the usual range for polymers due to the amorphous nature of the γ-APS films.     

Atomistic simulation study on key factors dominating dislocation nucleation from a crack tip in two FCC materials: Cu and Al

Dislocation nucleations from crack tips in FCC copper and aluminum are studied using atomistic simulations. It is shown that the critical load for dislocation nucleation predicted by Rice’s model (Rice, 1992) based on the Peierls concept of dislocation can either be under- or over-estimated in reference to the simulation results. Such discrepancies have not been fully resolved by existing improved nucleation models, due to the complicated atomic environments at crack tips. Based on our simulation results, it is proposed that such discrepancies can be reconciled by the competition of two coupling processes at a crack tip: the tension-shear coupling, which facilitates the dislocation nucleation, and the nucleation-debonding coupling, which retards the dislocation nucleation. In addition, the two couplings are applied to explain the paradoxical observation: easy dislocation nucleation at a blunted crack tip. The present work provides a detailed picture to justify future improvements on Rice’s model for dislocation nucleation and to accurately predict intrinsic brittle to ductile transition for crystalline materials.     

Modeling of ductile fracture: Significance of void coalescence

In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain (E_c) as a function of the stress triaxiality parameter (T) and the Lode angle (θ) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface E_c(T, θ). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for E_c is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.     

Influence of misfit stresses on dislocation glide in single crystal superalloys: A three-dimensional discrete dislocation dynamics study

In the characteristic $\gamma /\gamma \prime$ microstructure of single crystal superalloys, misfit stresses occur due to a significant lattice mismatch of those two phases. The magnitude of this lattice mismatch depends on the chemical composition of both phases as well as on temperature. Furthermore, the lattice mismatch of γ and $\gamma \prime$ phases can be either positive or negative in sign. The internal stresses caused by such lattice mismatch play a decisive role for the micromechanical processes that lead to the observed macroscopic athermal deformation behavior of these high-temperature alloys. Three-dimensional discrete dislocation dynamics (DDD) simulations are applied to investigate dislocation glide in γ matrix channels and shearing of $\gamma \prime$ precipitates by superdislocations under externally applied uniaxial stresses, by fully taking into account internal misfit stresses. Misfit stress fields are calculated by the fast Fourier transformation (FFT) method and hybridized with DDD simulations. For external loading along the crystallographic [001] direction of the single crystal, it was found that the different internal stress states for negative and positive lattice mismatch result in non-uniform dislocation movement and different dislocation patterns in horizontal and vertical γ matrix channels. Furthermore, positive lattice mismatch produces a lower deformation rate than negative lattice mismatch under the same tensile loading, but for an increasing magnitude of lattice mismatch, the deformation resistance always diminishes. Hence, the best deformation performance is expected to result from alloys with either small positive, or even better, vanishing lattice mismatch between γ and $\gamma \prime$ phase.     

Chaotic diffusion in steady wavy vortex flow—Dependence on wave state and correlation with Eulerian symmetry measures

The dimensionless effective axial diffusion coefficient, D_z, calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor-Couette system, has been determined as a function of Reynolds number (R=Re/Re_c), axial wavelength (λ_z), and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when R<3.5, D_z has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when R>3.5, D_z decreases monotonically.Eulerian quantities measuring the departure from rotational symmetry, ?_θ, and flexion-free flow, ?_ν, were calculated. The space-averaged quantities and were found to have, unlike D_z, a simple unimodal dependence on R. In the low R regime the correlation between D_z and ?_θ?_ν was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of R. In the large R regime, however, the correlation simplified to for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets.A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the ‘escape basins’ (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low R regime after the breakup of all KAM tori, the outflow basin (γ_O) is larger than the inflow basin (γ_I), and both γ_O and γ_I are (approximately) independent of R. In the large R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase. This implies that the growth of the integrable core occurs at the expense of the outflow escape basin. Finally, it is shown that the variation of the weighted escape rates (γ_Or_O,γ_Ir_I) with Reynolds number was in excellent qualitative agreement with the variation of .     

Several effects of melt viscosity on the nature ofC p —T data aboveT g for acrylate,methacrylate, and hydrocarbon polymers

Using objective computerized statistical procedures, we have examined high precisionC _p data by DSC reported by Wunderlich and Gaur for a series of alkyl acrylate and methacrylate polymers. Although they claimed the data to be linear inT aboveT _g , our results do not support the linear model. One or two endothermic slope changes are revealed aboveT _g in lowT _f polymers (T _f < 20 °C) and at least one exothermic slope change in highT _f polymers (T _f > 20 °C).T _f is the flow temperature of Ueberreiter. Both the first endotherm and the first exotherm occur near (1.22 ± 0.07)T _g , suggesting aT _ll type phenomenon.T _ll varies as \(1/\bar M_n \) . The first exotherm is associated by us with wetting of the DSC pan by molten polymer on the first heating of particulate highT _f polymers. The rate of wetting, and presumably the magnitude of the exotherm, depends in part on the ratio,γ/η, whereγ is surface tension andη is melt viscosity of the molten polymer. Sinceγ is relatively constant, the molecular weight and temperature dependence for rate of wetting resides inη, which depends on \(\bar M_w \) . For \(\bar M_n > > \bar M_c \) , a second exothermic event caused by sintering, and also controlled by η, may be present. The interactive roles of \(\bar M_n ,\bar M_w ,\bar M_w /\bar M_n \) ;M _c (entanglement molecular weight); particle size, and heating rate onC _p —T behaviour are delineated for the first time. LowT _f hydrocarbon polymers, namely atactic polyalphaolefins,C ₃ ,C ₅ ,C ₆ ; PIB; and dienes, PBD and cis-PI, exhibit single or double endotherms. Other results on highT _f polymers showing exothermic effects, notably PS, PnBMA and polyglycidylmethacrylate are cited.     

A first-principles measure for the twinnability of FCC metals

Twinnability is the property describing the ease with which a metal plastically deforms by twinning relative to deforming by dislocation-mediated slip. In this paper a theoretical measure for twinnability in face-centered-cubic (fcc) metals is obtained through homogenization of a recently introduced criterion for deformation twinning (DT) at a crack tip in a single crystal. The DT criterion quantifies the competition between slip and twinning at the crack tip as a function of crack orientation and applied loading. The twinnability of bulk material is obtained by constructing a representative volume element of the material as a polycrystal containing a distribution of microcracks and integrating the DT criterion over all possible grain and microcrack orientations. The resulting integral expression depends weakly on Poisson's ratio and significantly on three interfacial energies: the stacking-fault energy, the unstable-stacking energy and the unstable-twinning energy. All these four quantities can be computed from first principles. The weak dependence on Poisson's ratio is exploited to derive a simple and accurate closed-form approximation for twinnability which clarifies its dependence on the remaining material parameters. To validate the new measure, the twinnability of eight pure fcc metals is computed using parameters obtained from quantum-mechanical tight-binding calculations. The ranking of these materials according to their theoretical twinnability agrees with the available experimental evidence, including the low incidence of DT in Al, and predicts that Pd should twin as easily as Cu.     

Modelling of laminated microstructures in stress-induced martensitic transformations

This paper is concerned with micromechanical modelling of stress-induced martensitic transformations in crystalline solids, with the focus on distinct elastic anisotropy of the phases and the associated redistribution of internal stresses. Micro-macro transition in stresses and strains is analysed for a laminated microstructure of austenite and martensite phases. Propagation of a phase transformation front is governed by a time-independent thermodynamic criterion. Plasticity-like macroscopic constitutive rate equations are derived in which the transformed volume fraction is incrementally related to the overall strain or stress. As an application, numerical simulations are performed for cubic β₁ (austenite) to orthorhombic γ₁′ (martensite) phase transformation in a single crystal of Cu-Al-Ni shape memory alloy. The pseudoelasticity effect in tension and compression is investigated along with the corresponding evolution of internal stresses and microstructure.     

Relationship between refined Griffith criterion and power laws for cracking

Rice [J. Mech. Phys. Solids 26 (1978) 61] proposes a refined Griffith criterion, at any local crack front, where G is the Irwin's energy release rate, γ is the surface free energy and is the rate of crack advance. The refined version implies that the entropy production inequality should holds locally rather than globally from the thermodynamic point of view. Within the irreversible thermodynamic framework developed by Rice [J. Mech. Phys. Solids 19 (1971) 433; Constitutive Equations in Plasticity, 1975, p. 23], it is revealed in this paper that the entropy production inequality holds for each internal variable if its rate is a homogeneous function in its conjugate force. It is further shown that widely-used power laws for crack growth are just certain homogeneous kinetic rate laws, so it is concluded that the power laws directly lead to the refined Griffith criterion.     

Application of the γ-Reθ Transition Model to Simulations of the Flow Past a Circular Cylinder

Based on the finite volume method, the flow past a two-dimensional circular cylinder at a critical Reynolds number (Re = 8.5 × 10⁵) was simulated using the Navier-Stokes equations and the γ-Re_θ transition model coupled with the SST k ? ω turbulence model (hereinafter abbreviated as γ-Re_θ model). Considering the effect of free-stream turbulence intensity decay, the SST k ? ω turbulence model was modified according to the ambient source term method proposed by Spalart and Rumsey, and then the modified SST k ? ω turbulence model is coupled with the γ-Re_θ transition model (hereinafter abbreviated as γ-Re_θ-SR model). The flow past a circular cylinder at different inlet turbulence intensities were simulated by the γ-Re_θ-SR model. At last, the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers were each simulated by the γ-Re_θ-SR model, and the three flow states were analyzed. It was found that compared with the SST k ? ω turbulence model, the γ-Re_θ model could simulate the transition of laminar to turbulent, resulting in better consistency with experimental result. Compared with the γ-Re_θ model, for relatively high inlet turbulence intensities, the γ-Re_θ-SR model could better simulate the flow past a circular cylinder; however the improvement almost diminished for relatively low inlet turbulence intensities The γ-Re_θ-SR model could well simulate the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers.     

Cyclic behavior of extruded magnesium: Experimental, microstructural and numerical approach

The present study aims at determining the influence of cyclic straining on the behavior of pure extruded magnesium. For this purpose, tensile, compressive and cyclic tests are performed (small plastic strains are applied (Δε^p/2 = 0.1% and 0.4%). Deformation mechanisms (slip and twin systems) have been observed by TEM and the different critical resolved shear stress (CRSS) have been determined. Based on microscopic observations, a crystal-plasticity-based constitutive model has been developed. The asymmetry between tensile and compressive loadings mainly results from the activation of hard slip systems in tension (such as 〈a〉 pyramidal and prismatic and 〈c + a〉 pyramidal glides) and twinning in compression. It is shown that basal slip is very easy to activate even for small Schmid factors. Numerical simulations reveal that untwinning in tension subsequent to compression must be considered to correctly fit the experimental S-shaped hysteresis curves. TEM observations indicate also intense secondary slips or twins inside the mother twins under cyclic conditions, so that twinning in compression and dislocation glide in tension are affected by cycling. The polycrystalline model allows to predict slip activities and twin volume fraction evolutions.     

A dislocation-based constitutive law for pure Zr including temperature effects

In this work, a single crystal constitutive law for multiple slip and twinning modes in single phase hcp materials is developed. For each slip mode, a dislocation population is evolved explicitly as a function of temperature and strain rate through thermally-activated recovery and debris formation and the associated hardening includes stage IV. A stress-based hardening law for twin activation accounts for temperature effects through its interaction with slip dislocations. For model validation against macroscopic measurement, this single crystal law is implemented into a visco-plastic-self-consistent (VPSC) polycrystal model which accounts for texture evolution and contains a subgrain micromechanical model for twin reorientation and morphology. Slip and twinning dislocations interact with the twin boundaries through a directional Hall–Petch mechanism. The model is adjusted to predict the plastic anisotropy of clock-rolled pure Zr for three different deformation paths and at four temperatures ranging from 76 K to 450 K (at a quasi-static rate of 10⁻³ 1/s). The model captures the transition from slip-dominated to twinning-dominated deformation as temperature decreases, and identifies microstructural mechanisms, such as twin nucleation and twin–slip interactions, where future characterization is needed.