Brittle versus ductile transition of nanocrystalline metals

The brittle versus ductile transition for conventional metals is dictated by the competition between dislocation emission and cleavage. For nanocrystalline metals with grain size below 25 nm, however, dislocation activities are suppressed and the classic theory fails to apply. In this paper, one of the competing mechanisms that control the brittle versus ductile transition of nanocrystalline metals is found to be the grain boundary dominated creep deformation versus the grain boundary decohesion. A model is proposed to quantify the crack propagation in nanocrystalline metals. The effects of material properties, initial configuration and applied loads on the property of crack propagation are addressed. It is concluded that either the increases in the initial crack length, the applied load and the grain boundary damage, or the deterrence in creep deformation, accelerate the crack propagation, and vice versa.     

Investigating the deformation of nanocrystalline copper with microscale kinematic metrics and molecular dynamics

Atomistic simulations are employed to investigate the deformation of nanocrystalline copper and the associated strain accommodation mechanisms at 10 K as a function of grain size. Volume-averaged kinematic metrics based on continuum mechanics theory are formulated to analyze the results of molecular dynamics simulations. The metrics rely on both reference and current configurations, along with nearest neighbor lists to estimate nanoscale behavior of atomic deformation fields in nanocrystalline copper. Various deformation mechanisms are activated in the structures, and shown to depend on average grain size of the nanocrystalline structure. Furthermore, grain boundaries, along with dislocation glide, become an important source of strain accommodation as grain size is reduced. It is demonstrated that the metrics capture the contributions of various mechanisms, and provide a sense of the history of atomic regions undergoing both elastic and plastic deformation. The significance of this research is that unique kinematic signatures of the mechanisms are uncovered using certain metrics, and we are able to resolve the contributions of the deformation mechanisms to the overall strain of the structure using Green strain.     

Coupled annealing temperature and layer thickness effect on strengthening mechanisms of Ti/Ni multilayer thin films

A systematic study was performed on mechanical and microstructural properties of Ti/Ni multilayers with layer thickness from 200 nm to 6 nm and annealing temperature from room temperature to 500 °C. Based on the observed hardness evolution, a coupled layer-thickness and annealing-temperature dependent strengthening mechanism map is proposed. For as-deposited films, the deformation behavior follows the traditional trend of dislocation mediated strengthening to grain boundary mediated softening with decreasing layer thickness. For annealed films, grain boundary relaxation is considered to be the initial strengthening mechanism with higher activation temperature required for thicker layers. Under further annealing, solid solution hardening, intermetallic precipitation hardening, and fully intermixed alloy structure continue to strengthen the thin layered films, while recrystallization and grain-growth lead to the eventual softening of thick layered films. For the films with intermediate layer thickness, a strong orientation dependent hardness behavior is exhibited under high temperature annealing due to mechanism switch from grain growth softening to intermetallic precipitation hardening when changing the loading orientation from perpendicular to parallel to the layer interfaces.     

Orientation evolution in Hadfield steel single crystals under combined slip and twinning

The tensile deformation response and texture evolution of aluminum alloyed Hadfield steel single crystals oriented in the 〈1 6 9〉 direction is investigated. In this material, the strain hardening response is governed by the high-density dislocation walls (HDDWs) that interact with glide dislocations. A microstructure-based visco-plastic self-consistent model was modified to account for mechanical twinning in addition to the prevailing contribution of the HDDWs. Simulations revealed the contribution of twinning to the overall work hardening at the later stages of deformation. Moreover, both the deformation response and the rotation of the loading axis associated with plastic flow are successfully predicted even at the high-strain levels attained (0.53). Predicting the texture evolution serves as a separate check for validating the model, motivating its utilization in single and polycrystals of other alloys that exhibit combined HDDWs and twinning.     

Time-, stress-, and temperature-dependent deformation in nanostructured copper: Creep tests and simulations

In the present work, we performed experiments, atomistic simulations, and high-resolution electron microscopy (HREM) to study the creep behaviors of the nanotwinned (nt) and nanograined (ng) copper at temperatures of 22 °C (RT), 40 °C, 50 °C, 60 °C, and 70 °C. The experimental data at various temperatures and different sustained stress levels provide sufficient information, which allows one to extract the deformation parameters reliably. The determined activation parameters and microscopic observations indicate transition of creep mechanisms with variation in stress level in the nt-Cu, i.e., from the Coble creep to the twin boundary (TB) migration and eventually to the perfect dislocation nucleation and activities. The experimental and simulation results imply that nanotwinning could be an effective approach to enhance the creep resistance of twin-free ng-Cu. The experimental creep results further verify the newly developed formula (Yang et al., 2016) that describes the time-, stress-, and temperature-dependent plastic deformation in polycrystalline copper.     

An improved atomistic simulation based mixed-mode cohesive zone law considering non-planar crack growth

A novel and improved atomistic simulation based cohesive zone law characterizing interfacial debonding is developed which explicitly accounts for the non-planarity of the crack propagation. Group of atoms in the simulation constituting cohesive zones which are used to obtain local stress and crack opening displacement data are determined dynamically during the non-planar crack growth as they cannot be determined apriori. The methodology is used to study the debonding of Σ5 (2 1 0)/[0 0 1] symmetric tilt grain boundary interface in a Cu bicrystal under several mixed mode loading conditions. Simulations show that such bicrystalline specimen exhibits three types of energy dissipative mechanisms – shear coupled GB migration (SCM) away from the crack-tips, change in spacial orientation of GB structural units rendering highly disordered grain boundary near the crack tips and brittle intergranular fracture. Which combination of these three deformation mechanism will be active influencing the degree of non-planarity of the crack propagation at various stages of loading depends on the loading mode-mixity. As the ratio of shear component of the loading parallel to the GB plane and normal to the tilt axis with respect to the normal loading increases (thereby increasing the mode-mixity), overall strain-to-failure also increases and SCM tends to become the dominant deformation mechanism. Through this framework, analytical functional forms and parameters describing cohesive laws for both normal and shear traction as a function of the mode-mixity of the loading and crack opening displacement are predicted.     

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.     

Analysis of deformation-induced crack tip toughening in ductile single crystals by nano-indentation

This paper reports on the experimental examination of the deformation characteristics near a crack tip in a cyclically work-hardened copper single crystal using a 2D surface scans with nano-indentation. The experimental methodology enables the characterization of the primary deformation field near a crack tip via the modulation of the imposed secondary deformation field by a nano-indentation. In a heavily deformed 4-point bend specimen, the measurements showed an existence of an asymptotic field around the crack tip at a distance of R ⩾ 2.5J/σ₀. The measurements also showed the qualitative details of toughness evolution within the high-gradient deformation field around the crack tip. The nature of dislocation distribution (i.e. statistically distributed vs. distributions necessitated by geometry) around the crack tip is quantified. The measurements indicate the dominance of the geometrically necessary dislocation within the finite deformation zone ahead of the tip up to a distance of R ≈ 3J/σ₀. Thereafter, it is confined in radial rays coinciding with the sector boundaries around the crack tip. These measurements elucidate the origin of the inhomogeneous hardening and the size dependent macroscopic response close to crack tip.     

Analyses of tensile deformation of nanocrystalline α-Fe2O3+fcc-Al composites using molecular dynamics simulations

The tensile deformation of nanocrystalline α-Fe₂O₃+fcc-Al composites at room temperature is analyzed using molecular dynamics (MD) simulations. The analyses focus on the effects of variations in grain size and phase volume fraction on strength. For comparison purposes, nanostructures of different phase volume fractions at each grain size are given the same grain morphologies and the same grain orientation distribution. Calculations show that the effects of the fraction of grain boundary (GB) atoms and the electrostatic forces between atoms on deformation are strongly correlated with the volume fractions of the Al and Fe₂O₃ phases. In the case of nanocrystalline Al where electrostatic forces are absent, dislocation emission initiates primarily from high-angle GBs. For the composites, dislocations emits from both low-angle and high-angle GBs due to the electrostatic effect of Al-Fe₂O₃ interfaces. The effect of the interfaces is stronger in structures with smaller average grain sizes primarily because of the higher fractions of atoms in interfaces at smaller grain sizes. At all grain sizes, the strength of the composite lies between those of the corresponding nanocrystalline Al and Fe₂O₃ structures. Inverse Hall-Petch (H-P) relations are observed for all structures analyzed due to the fact that GB sliding is the dominant deformation mechanism. The slopes of the inverse H-P relations are strongly influenced by the fraction of GB atoms, atoms associated with defects, and the volume fractions of the Al and Fe₂O₃ phases.     

Interaction between a screw dislocation and a viscoelastic piezoelectric bimaterial interface

The complex variable method is employed to derive analytical solutions for the interaction between a piezoelectric screw dislocation and a Kelvin-type viscoelastic piezoelectric bimaterial interface. Through analytical continuation, the original boundary value problem can be reduced to an inhomogeneous first-order partial differential equation for a single function of location z = x + iy and time t defined in the lower half-plane, which is free of the screw dislocation. Once the initial, steady-state and far-field conditions are known, the solution to the first order differential equation can be obtained. From the solved function, explicit expressions are then derived for the stresses, strains, electric fields and electric displacements induced by the piezoelectric screw dislocation. Also presented is the image force acting on the screw dislocation due to its interaction with the Kelvin-type viscoelastic interface. The derived solutions are verified by comparing with existing solutions for the simplified cases, and various interesting features are observed, particularly for those associated with the image force.     

Continuum interpretation of virial stress in molecular simulations

The equivalence of the virial stress and Cauchy stress is reviewed using both theoretical arguments and numerical simulations. Using thermoelasticity problems as examples, we numerically demonstrate that virial stress is equivalent to the continuum Cauchy stress. Neglecting the velocity terms in the definition of virial stress as many authors have recently suggested, can cause significant errors in interpreting MD simulation results at elevated temperatures (T > 0 K).     

Residual stresses in thin film systems: Effects of lattice mismatch,thermal mismatch and interface dislocations

This paper explores the mechanisms of the residual stress generation in thin film systems with large lattice mismatch strain, aiming to underpin the key mechanism for the observed variation of residual stress with the film thickness. Thermal mismatch, lattice mismatch and interface misfit dislocations caused by the disparity of the material layers were investigated in detail. The study revealed that the thickness-dependence of the residual stresses found in experiments cannot be elucidated by thermal mismatch, lattice mismatch, or their coupled effect. Instead, the interface misfit dislocations play the key role, leading to the variation of residual stresses in the films of thickness ranging from 100 nm to 500 nm. The agreement between the theoretical analysis and experimental results indicates that the effect of misfit dislocation is far-reaching and that the elastic analysis of dislocation, resolved by the finite element method, is sensible in predicting the residual stress distribution. It was quantitatively confirmed that dislocation density has a significant effect on the overall film stresses, but dislocation distribution has a negligible influence. Since the lattice mismatch strain varies with temperature, it was finally confirmed that the critical dislocation density that leads to the measured residual stress variation with film thickness should be determined from the lattice mismatch strain at the deposition temperature.     

Effect of projectile nose shape,impact velocity and target thickness on deformation behavior of aluminum plates

The present study deals with the experimental and numerical investigations of aluminum target plates impacted by blunt, ogive and hemispherical nosed steel projectiles. The projectiles were normally impacted on the target plates of 0.5, 0.71, 1, 1.5, 2, 2.5 and 3 mm thicknesses at different velocities with the help of a pneumatic gun. Effect of projectile nose shape, impact velocity and plate thickness on the deformation of the target plates was studied. Hemispherical nosed projectile caused highest global deformation (dishing) of the target plates. Ogive nosed projectiles were found to be the most efficient penetrator for the case of plates of thicknesses 0.5, 0.71, 1.0 and 1.5 mm. For the case of plates of thicknesses 2.0, 2.5 and 3.0 mm however, blunt nosed projectiles required least energy to perforate the target plates. The ballistic limit velocity of hemispherical nosed projectiles was found to be highest as compared to the other two projectiles. Finite element analysis of the problem was carried out using ABAQUS finite element code. Results of the numerical analysis were compared with the experiments and good correlation between the two was found.     

Irreversible thermodynamics of triple junctions during the intergranular void motion under the electromigration forces

A rigorous reformulation of internal entropy production and the rate of entropy flow is developed for multi-component systems consisting of heterophases, interfaces and/or surfaces. The result is a well-posed moving boundary value problem describing the dynamics of curved interfaces and surfaces associated with voids and/or cracks that are intersected by grain boundaries. Extensive computer simulations are performed for void configuration evolution during intergranular motion. In particular we simulate evolution resulting from the action of capillary and electromigration forces in thin film metallic interconnects having a “bamboo” structure, characterized by grain boundaries aligned perpendicular to the free surface of the metallic film interconnects. Analysis of experimental data utilizing previously derived mean time to failure formulas gives consistent values for interface diffusion coefficients and enthalpies of voids. 3.0 × 10⁻⁶ exp(−0.62 eV/kT) m² s⁻¹ is the value obtained for voids that form in the interior of the aluminum interconnects without surface contamination. 6.5 × 10⁻⁶ exp(−0.84 eV/kT) m² s⁻¹ is obtained for those voids that nucleate either at triple junctions or at the grain boundary-technical surface intersections, where the chemical impurities may act as trap centers for hopping vacancies.     

Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression

Fractures in natural rocks have an important effect on the strength and failure behavior of rock mass, which are often evaluated in rock engineering practice. The theoretical evaluation of mechanical behavior of fractured rock mass has no satisfactory answer due to the role of confining pressure and crack geometry. Therefore, in this paper, conventional triaxial compression experiments were carried out to study the strength and failure behavior of marble samples with two pre-existing closed cracks in non-overlapping geometry. Based on the experimental results of a number of triaxial compression tests, the effect of crack coalescence on the axial supporting capacity and deformation property were investigated with different confining pressures. The results show that intact samples and flawed samples (marble with pre-existing cracks) have different deformation properties after peak stress, which change from brittleness to plasticity and ductility with the increase of confining pressure. The peak strength and failure mode are found depending not only on the geometry of flaw, but also on the confining pressure. The strength of flawed samples shows distinct non-linear behavior, which is in a better agreement with non-linear Hoek–Brown criterion than linear Mohr–Coulomb criterion. For a kind of rock that has been evaluated as a Hoek–Brown material, a new evaluation criterion is put forward by adopting optimal approximation polynomial theory, which can be used to confirm more precisely the strength parameters (cohesion and internal friction angle) of flawed samples. For intact samples, the marble leads to typical shear failure mode with a single fracture surface under different confining pressures, while for flawed samples, under uniaxial compression and a lower confining pressure (σ₃ = 10 MPa), tests for coarse and medium marble (the coarse and medium refer to the grain size) exhibit three basic failure modes, i.e., tensile mode, shear mode, and mixed mode (tensile and shear). Shear mode is associated with lower strength behavior. However, under higher confining pressures (σ₃ = 30 MPa), for coarse marble, the axial supporting capacity is not related to the geometry of flaw. The friction among crystal grains determines the strength behavior of coarse marble. For medium marble, the failure mode and deformation behavior are dependent on the crack coalescence in the sample. The present research provides increased understanding of the fundamental nature of rock failure under conventional triaxial compression.     

Dislocation loop nucleation and plastic deformation of nanocrystalline materials

We propose a three-dimensional model of plastic deformation of a mechanically loaded nanocrystalline material by means of heterogeneous nucleation of loops of complete and partial lattice dislocations and by means of grain boundary dislocations on the already formed dislocation loops. We calculate and compare the energy variations characterizing various versions of dislocation loop nucleation. We discover three basic regions of variation of nanocrystalline material grain dimensions which are characterized by their own types of loop nucleation. We also study the role played by loop nucleation in plastic and superplastic deformations of nanocrystalline materials.     

Mechanics of very fine-grained nanocrystalline materials with contributions from grain interior, GB zone, and grain-boundary sliding

In this paper, we formulated an atomically-equivalent continuum model to study the viscoplastic behavior of nanocrystalline materials with special reference to the low end of grain size that is typically examined by molecular dynamic (MD) simulations. Based on the morphology disclosed in MD simulations, a two-phase composite model is construed, in which three distinct inelastic deformation mechanisms disclosed from MD simulations are incorporated to build a general micromechanics-based homogenization scheme. These three mechanisms include the dislocation-related plastic flow inside the grain interior, the uncorrelated atomic motions inside the grain-boundary region (the GB zone), and the grain-boundary sliding at the interface between the grain and GB zone. The viscoplastic behavior of the grain interior is modeled by a grain-size dependent unified constitutive equation whereas the GB zone is modeled by a size-independent unified law. The GB sliding at the interface is represented by the Newtonian flow. The development of the rate-dependent, work-hardening homogenization scheme is based on a unified approach starting from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity through replacement of the Maxwell viscosity of the constituent phases by their respective secant viscosity. The developed theory is then applied to examine the grain size- and strain rate-dependent behavior of nanocrystalline Cu over a wide range of grain size. Within the grain-size range from 5.21 to 3.28 nm, and the strain rate range from 2.5 × 10⁸ to 1.0 × 10⁹/s, the calculated results show significant grain-size softening as well as strain-rate hardening that are in quantitative accord with MD simulations [Schiotz, J., Vegge, T., Di Tolla, F.D., Jacobsen, K.W., 1999. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60, 11971–11983]. We have also applied the theory to investigate the flow stress, strain-rate sensitivity, and activation volume over the wider grain size range from 40 nm to as low as 2 nm under these high strain rate loading, and found that the flow stress initially displays a positive slope and then a negative one in the Hall–Petch plot, that the strain-rate sensitivity first increases and then decreases, and that the activation volume first decreases and then increases. This suggests that the maximum strain rate sensitivity and the lowest activation volume do not occur at the smallest grain size but, like the maximum yield strength (or hardness), they occur at a finite grain size. These calculated results also confirm the theoretical prediction of Rodriguez and Armstrong [Rodriguez, P., Armstrong, R.W., 2006. Strength and strain rate sensitivity for hcp and fcc nanopolycrystal metals. Bull. Mater. Sci. 29, 717–720] on the basis of grain boundary weakening and the report of Trelewicz and Schuh [Trelewicz, J.R., Schuh, C.A., 2007. The Hall–Petch breakdown in nanocrystalline metals: a crossover to glass-like deformation. Acta Mater. 55, 5948–5958] on the basis of hardness tests. In general the higher yield strength, higher strain rate sensitivity, and lower activation volume on the positive side of the Hall–Petch plot are associated with the improved yield strength of the grain interior, but the opposite trends displayed on the negative side of the plot are associated with the characteristics of the GB zone which is close to the amorphous state.     

A variational multiscale constitutive model for nanocrystalline materials

This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The constitutive models of both phases are formulated in a small strain framework and extended to finite deformation by use of logarithmic and exponential mappings. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor-type homogenization where a log-normal grain size distribution is assumed. It is shown that the proposed model is able to capture the inverse Hall-Petch effect, i.e., loss of strength with grain size refinement. Finally, the predictive capability of the model is validated against experimental results on nanocrystalline copper and nickel.     

Effect of projectile nose shape on the ballistic resistance of ductile targets

Three-dimensional numerical simulations were carried out to study the ballistic resistance of ductile targets subjected to normal impact by the projectiles. 12 mm thick Weldox 460 E steel targets were impacted by 20 mm diameter conical nosed projectiles and 1 mm thick 1100-H12 aluminum targets were impacted by 19 mm diameter ogive nosed projectiles. The internal nose angle of conical projectile was varied (33.4°–180°) and found to have significant effect on the ballistic limit of 12 mm thick Weldox 460 E steel target. Similarly, the caliber radius head (CRH) of ogive nosed projectile was varied (0–2.5) and found to have significant effect on the ballistic limit of 1 mm thick 1100-H12 aluminum target. The ballistic limit of 12 mm thick Weldox 460 E steel target increased almost linearly with the decrease in the projectile nose angle. While the ballistic limit of 1 mm thick 1100-H12 aluminum target increased as the CRH increased from 0 to 0.5 and with further increase in CRH to 1.0, 1.5, 2.0 and 2.5 its values were found to drop quite significantly. ABAQUS/Explicit finite element code was used to carry out the numerical simulations.     

Dynamic response of tubular dielectric elastomer transducers

In this paper, a numerical model for the dynamic response of tubular dielectric elastomer transducers is presented and validated with experimental results for the first time. Dielectric elastomers (DE) are soft polymer based smart materials that can be potentially employed in applications such as actuation, sensing and energy harvesting (Kornbluh, 2004, Carpi et al., 2005, Waki et al., 2008). In our previous work, the quasi-static response of tubular DE transducers was studied (Goulbourne et al., 2007, Son and Goulbourne, 2009). Here, a numerical model is developed to predict the dynamic response of tubular DE transducers. Inertia effects are included in our previous static model which yields a system of partial differential equations. The results of the dynamic response of the tubular DE transducers are obtained by numerically solving the simplified partial different equations using a finite difference scheme. The capacitance change induced by the dynamic deformation of the tubular DE is also calculated by a simple electrostatic model, illustrating dynamic passive sensing.Several tubular DE transducer samples (VHB 4905 and silicone) were fabricated and an experimental setup was developed to investigate the dynamic response by measuring capacitance and radial deformation. In the sensing experiments, a sweep of dynamic pressure profiles (0–5 Hz) are applied. It is observed that silicone transducers have a larger dynamic sensing range. In the actuation experiments, the deformation of the silicone actuator is monitored while a voltage signal (4.5 kV) is applied from 0 to 30 Hz. The silicone actuator shows a good actuation response. The comparison between numerical and experimental results for the DE transducers shows an overall error of 3%.