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.     

On the transformation toughening of a crack along an interface between a shape memory alloy and an isotropic medium

In this study, a bilinear cohesive zone model is employed to describe the transformation toughening behavior of a slowly propagating crack along an interface between a shape memory alloy and a linear elastic or elasto-plastic isotropic material. Small scale transformation zones and plane strain conditions are assumed. The crack growth is numerically simulated within a finite element scheme and its transformation toughening is obtained by means of resistance curves. It is found that the choice of the cohesive strength t₀ and the stress intensity factor phase angle φ greatly influence the toughening behavior of the bimaterial. The presented methodology is generalized for the case of an interface crack between a fiber reinforced shape memory alloy composite and a linear elastic, isotropic material. The effect of the cohesive strength t₀, as well as the fiber volume fraction are examined.     

A micromechanical continuum model for the tensile behavior of shape memory metal nanowires

We have previously discovered a novel shape memory effect and pseudoelastic behavior in single-crystalline face-centered-cubic metal (Cu, Ni, and Au) nanowires. Under tensile loading and unloading, these wires can undergo recoverable elongations of up to 50%, well beyond the recoverable strains of 5-8% typical for most bulk shape memory alloys. This phenomenon only exists at the nanoscale and is associated with a reversible lattice reorientation driven by the high surface-stress-induced internal stresses. We present here a micromechanical continuum model for the unique tensile behavior of these nanowires. Based on the first law of thermodynamics, this model decomposes the lattice reorientation process into two parts: a reversible, smooth transition between a series of phase-equilibrium states and a superimposed irreversible, dissipative twin boundary propagation process. The reversible part is modeled within the framework of strain energy functions with multiple local minima. The irreversible, dissipative nature of the twin boundary propagation is due to the ruggedness of strain energy curves associated with dislocation nucleation, glide, and annihilation. The model captures the major characteristics of the unique behavior due to lattice reorientation and accounts for the size and temperature effects, yielding results that are in excellent agreement with the results of molecular dynamics simulations.     

Effect of load triaxiality on polymorphic transitions in zinc oxide

Molecular dynamics (MD) simulations and first-principles calculations are carried out to analyze the stability of both newly discovered and previously known phases of ZnO under loading of various triaxialities. The analysis focuses on a graphite-like phase (HX) and a body-centered-tetragonal phase (BCT-4) that were observed recently in - and [0 0 0 1]-oriented nanowires respectively under uniaxial tensile loading as well as the natural state of wurtzite (WZ) and the rocksalt (RS) phase which exists under hydrostatic pressure loading. Equilibrium critical stresses for the transformations are obtained. The WZ → HX transformation is found to be energetically favorable above a critical tensile stress of 10 GPa in nanowires. The BCT-4 phase can be stabilized at tensile stresses above 7 GPa in [0 0 0 1] nanowires. The RS phase is stable at hydrostatic pressures above 8.2 GPa. The identification and characterization of these phase transformations reveal a more extensive polymorphism of ZnO than previously known. A crystalline structure–load triaxiality map is developed to summarize the new understanding.     

A model for the thermorheological behavior of viscoelastic fluids

Using a power-law ansatz for the temperature dependence of the shear modulus on the level of internal variables, the thermorheological behavior is modeled for viscoelastic fluids of a special group of rheological constitutive equations (rate-type models). The model parameter introduced characterizes thermoelastic contributions. The relation between the model parameter and the physical quantities appearing in deformation processes is discussed. Based on the chosen temperature dependence of the shear modulus, thermodynamically consistent equations like the nonlinear rheological constitutive equation and the temperature equation are derived. The special cases of entirely entropy and energy elastic fluids are also considered. The thermorheological behavior (exo-, - or endothermal processes) of a viscoelastic fluid in a stress-growth experiment followed by relaxation is analyzed with respect to the model parameter.     

Numerical study of nonlinear interaction between a crack and elastic waves under an oblique incidence

A Finite Element (FE) model is proposed to study the interaction between in-plane elastic waves and a crack of different orientations. The crack is modeled by an interface of unilateral contact with Coulombs friction. These contact laws are modified to take into account a pre-stress _σ0${\sigma }_0$ that closes the crack. Using the FE model, it is possible to obtain the contact stresses during wave propagation. These contact stresses provide a better understanding of the coupling between the normal and tangential behavior under oblique incidence, and explain the generation of higher harmonics. This new approach is used to analyze the evolution of the higher harmonics obtained as a function of the angle of incidence, and also as a function of the excitation level. The pre-stress condition is a governing parameter that directly changes the nonlinear phenomenon at work at the interface and therefore the harmonic generation. The diffracted fields obtained by the nonlinear and linear models are also compared.     

Effect of bulk deformation and surface tension on the growth of a coherent inclusion

The object of this paper is the study of the moving boundary problem modeling the growth of a spherical solid inclusion in an infinite solid matrix. The displacement in bulk is assumed infinitesimal, while the phases are modeled as isotropic elastic bodies, and the interface structure is described by a constant surface tension. Existence of solutions is proved, and their asymptotic behavior in time is studied, with particular attention to the competition between surface tension and bulk deformation.     

Dynamics of Phase Transitions and Hysteresis in a Viscoelastic Ericksen's Bar on an Elastic Foundation

This work is a follow-up on the study [32] of interface dynamics and hysteresis in materials undergoing solid-solid phase transitions. We consider the dynamics of a viscoelastic bar with a nonmonotone stress-strain relation and viscous stress linearly proportional to the strain rate. The bar is placed on an elastic foundation with stiffness β mimicking the interaction of phases in higher dimensions. Time-dependent displacement-controlled loading of the bar results in a tilted and serrated hysteresis loop, in qualitative agreement with some experimental observations in shape-memory alloys. The model exhibits three phase transition processes: phase nucleation, interface slip and phase annihilation. Between these dynamic processes the system gets stuck in local minimizers of the potential energy. As β increases from zero, a slip-dominated solution behavior transforms to the one where slip and annihilation events are preceded by a step-by-step nucleation process. We show that this transition is caused by an interplay between the slip-favoring inertia term and the nucleation-favoring elastic foundation terms. This revised version was published online in August 2006 with corrections to the Cover Date.     

Model of the fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media

The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media. A plane symmetric problem is formulated. The zone is modeled by lines of discontinuity of the normal displacement at the interface. The exact solution of the elastic problem is found by the Wiener-Hopf method Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 13–22, October 2008.     

Interaction between edge dislocations and amorphous interphase in carbon nanotubes reinforced metal matrix nanocomposites incorporating interface effect

Dislocations mobility and stability in the carbon nanotubes (CNTs)-reinforced metal matrix nanocomposites (MMNCs) can significantly affect the mechanical properties of the composites. However, current processing techniques often lead to the formation of coated CNT (amorphous interphase exists between the reinforcement and metal matrix), which have large impact upon the image force exerting on dislocations. Even though the importance of the interphase zone formed in metal matrix composites has been demonstrated by many studies for elastic properties, the influence of interphase on the local elastoplastic behavior of CNT-reinforced MMNCs is still an open issue. This paper puts forward a three-phase composite cylinder model with new boundary conditions. In this model, the interaction between edge dislocations and a coated CNT incorporating interface effect is investigated. The explicit expressions for the stress fields and the image force acting on an edge dislocation are proposed. In addition, plastic flow occurring around the coated reinforcement is addressed. The influences of interface condition and the material properties of coated CNT on the glide/climb force are clearly analyzed. The results indicate that the interface effect becomes remarkable when the radius of the coated reinforcement is below 10 nm. In addition, different from the traditional particles, the coated CNT attracts the adjacent edge dislocations, causing pronounced local hardening at the interface between the interphase and the metal matrix under certain conditions. It is concluded that the presence of the interphase can have a profound effect on the local stress field in CNT-reinforced MMNCs. Finally, the condition of the dislocations stability and the equilibrium numbers of dislocations at a given size grain are evaluated for considering the interface effect.     

SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR (Ⅰ)—FUNDAMENTAL BEHAVIOR

The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elasto~plasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concept of `cohesive crack’ was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.     

Deformation behavior and microstructure/texture evolution of an annealed 304 AISI stainless steel sheet. Experimental and micromechanical modeling

Different tensile tests are performed at −60 °C, on a 304 AISI stainless steel, to produce strain induced α′ martensite. Using EBSD analysis and X-ray diffraction methods, the corresponding texture and microstructure evolutions is studied, as well as the γ → α′ transformation mechanism. It is shown that α′ martensite is associated with {1 1 1}_γ faulted bands, partially ε bands, as often reported in the literature for low SFE stainless steels. As a consequence, these deformation bands play a key role in the nucleation and growth of α′ martensite. A micromechanical model is applied to simulate the deformation behavior of the stainless steel as well as the corresponding transformation kinetic and γ texture evolution. Different simulations are proposed, using various assumptions for the γ → α′ transformation mechanism. The simulation data are in better agreement with the experimental ones, when the γ → α′ transformation strain is derived from the Bowles–MacKenzie theory using the (1 1 1)_γ[−1 2 −1]_γ stacking fault shear system as lattice invariant shear.     

Model of the behavior of the mixture with different properties of the species under high dynamic loads

Within the framework of a thermodynamically equilibrium model, dynamic loading of mixtures of two and more condensed phases with different properties within the experimental error is described by using species parameters only. The behavior of alloys considered as mixtures with the same volume fractions of the species is studied. The behavior of condensed phases for solid and porous materials is described with the use of the equation of state of the Mie-Grüneisen type and with allowance for the dependence of the Grüneisen coefficient on temperature. The calculated results are compared with experimental data and available calculated results in wide ranges of parameters.     

An inhomogeneous three-phase model for the flow in aluminium reduction cells

The exact prediction of both the melts flow and metal–bath interface deformation is critical to the design of commercial aluminium reduction cells which operate steadily at high current efficiency (CE). An inhomogeneous flow model of three phases, metal, bath and gas bubbles, was established in this study. The flow in a 300 kA cell was numerically computed with the model by using the finite volume scheme, and the results reveal the relation among the motion of the three phases and prove that the globality of the flow in cells could not be neglected. An improved calculation model of CE, based on the surface renewal theory, was also developed by connecting the melts flow with the mass transfer of reduced entity at the metal–bath interface. Using the model, the local CE in the 300 kA cell was predicted, and the calculated CE value of the whole cell is reasonable.     

Size effects on the martensitic phase transformation of NiTi nanograins

The analysis of nanocrystalline NiTi by transmission electron microscopy (TEM) shows that the martensitic transformation proceeds by the formation of atomic-scale twins. Grains of a size less than about 50 nm do not transform to martensite even upon large undercooling. A systematic investigation of these phenomena was carried out elucidating the influence of the grain size on the energy barrier of the transformation. Based on the experiment, nanograins were modeled as spherical inclusions containing (0 0 1) compound twinned martensite. Decomposition of the transformation strains of the inclusions into a shear eigenstrain and a normal eigenstrain facilitates the analytical calculation of shear and normal strain energies in dependence of grain size, twin layer width and elastic properties. Stresses were computed analytically for special cases, otherwise numerically. The shear stresses that alternate from twin layer to twin layer are concentrated at the grain boundaries causing a contribution to the strain energy scaling with the surface area of the inclusion, whereas the strain energy induced by the normal components of the transformation strain and the temperature dependent chemical free energy scale with the volume of the inclusion. In the nanograins these different energy contributions were calculated which allow to predict a critical grain size below which the martensitic transformation becomes unlikely. Finally, the experimental result of the atomic-scale twinning can be explained by analytical calculations that account for the transformation-opposing contributions of the shear strain and the twin boundary energy of the twin-banded morphology of martensitic nanograins.     

Effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes

In this study, we investigate the effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes. Finite element analysis is performed using the inhomogeneous field theory of polymeric gels in equilibrium proposed by Hong et al. (2009). Periodic units consisting of 2 × 2 and 10 × 10 unit cells are analyzed under a generalized plane strain assumption. Geometrical imperfections are introduced using randomly oriented elliptical holes. The 2 × 2 unit cells show that the resulting buckling patterns are sensitive to imperfections; three different buckling patterns are obtained, and the most dominant one is the diamond plate pattern observed in experiments, which cannot be described using the model without imperfections. The 10 × 10 unit cells reveal that random imperfections are responsible for inducing homogeneous transformation into the diamond plate pattern. Furthermore, domain wall formation is simulated using a 10 × 10 unit cell model containing two elliptic holes.     

Transmission of a screw dislocation across a coherent, non-slipping interface

Current research on nanocrystalline metals and nanoscale multilayer thin films suggests extraordinary plastic strength is due to confinement of slip to individual grains or layers. To assess the magnitude of confinement, a Peierls model of slip transmission of a screw dislocation across a coherent, non-slipping interface is presented. The results reflect that large interfacial barriers to transmission are generated by rapid fluctuations in dislocation line energy near the interface due to elastic modulus mismatch, stacking fault energy mismatch, and antiphase boundary energy for transmission into an ordered phase. Coherency stress is predicted to dramatically alter the dislocation core configuration and impart additional strength regardless of the sign. Contributions to strength are not additive due to nonlinear coupling via the dislocation core configuration. The predicted barrier strength for a coherent (0 0 1) Cu/Ni interface is comparable to atomistic (EAM) results but larger than estimates from hardness data.     

Mixed-mode interfacial adhesive strength of a thin film on an anisotropic substrate

The mixed-mode interfacial adhesion strength between a gold (Au) thin film and an anisotropic passivated silicon (Si) substrate is measured using laser-induced stress wave loading. Test specimens are prepared by bonding a fused silica (FS) prism to the back side of a 〈1 0 0〉 Si substrate with a thin silicon nitride (Si_xN_y) passivation layer deposited on the top surface. A high-amplitude stress wave is developed by pulsed laser ablation of a sacrificial absorbing layer on one of the lateral surfaces of the FS prism. Due to the negative non-linear elastic properties of the FS, the compressive stress wave evolves into a decompression shock with fast fall time. Careful selection of the incident angle between the pulse and the FS/Si interface generates a mode-converted shear wave in refraction, subjecting the Si_xN_y/Au thin film interface to dynamic mixed-mode loading, sufficient to cause interfacial fracture. A detailed analysis of the anisotropic wave propagation combined with interferometric measurements of surface displacements enables calculation of the interfacial stresses developed under mixed-mode loading. The mixed-mode interfacial strength is compared to the interfacial strength measured under purely tensile loading.     

Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes

This paper investigates the transverse and torsional wave in single- and double-walled carbon nanotubes (SWCNTs and DWCNTs), focusing on the effect of carbon nanotube microstructure on wave dispersion. The SWCNTs and DWCNTs are modeled as nonlocal single and double elastic cylindrical shells. Molecular dynamics (MD) simulations indicate that the wave dispersion predicted by the nonlocal elastic cylindrical shell theory shows good agreement with that of the MD simulations in a wide frequency range up to the terahertz region. The nonlocal elastic shell theory provides a better prediction of the dispersion relationships than the classical shell theory when the wavenumber is large enough for the carbon nanotube microstructure to have a significant influence on the wave dispersion. The nonlocal shell models are required when the wavelengths are approximately less than 2.36×10⁻⁹ and 0.95×10⁻⁹ m for transverse wave in armchair (15,15) SWCNT and torsional wave in armchair (10,10) SWCNT, respectively. Moreover, an MD-based estimation of the scale coefficient e₀ for the nonlocal elastic cylindrical shell model is suggested. Due to the small-scale effects of SWCNTs and the interlayer van der Waals interaction of DWCNTs, the phase difference of the transverse wave in the inner and outer tube can be observed in MD simulations in wave propagation at high frequency. However, the van der Waals interaction has little effect on the phase difference of transverse wave.     

A fully anisotropic single crystal model for high strain rate loading conditions with an application to α-RDX

In this paper, we develop a fully anisotropic, nonlinear, thermodynamically consistent model for single crystals under high rates of loading with thermodynamically consistent decoupling of the stress tensor into hydrostatic and deviatoric components. A new slip resistance model, which accounts for the main high-pressure mechanisms arising at the microscale including the effects of phonon drag, has been developed. When applied to α-RDX single crystals, the model is capable of predicting the salient elastic-plastic wave characteristics observed in gas gun experiments which include stress relaxation behind the elastic wave, elastic wave decay and increasing separation between the elastic and plastic waves with propagation. At lower pressures, slip activity is observed to occur over a longer period of time resulting in a distinct elastic plastic wave, which is missing at higher pressures.