Publications
188 results found
Zheng Z, Balint D, Dunne F, 2017, Mechanistic basis of temperature-dependent dwell fatigue in titanium alloys, Journal of the Mechanics and Physics of Solids, Vol: 107, Pages: 185-203, ISSN: 0022-5096
The temperature-dependent dwell sensitivity of Ti-6242 and Ti-6246 alloys has been assessed over a temperature range from −50∘C to 390 °C using discrete dislocation plasticity which incorporates both thermal activation of dislocation escape from obstacles and slip transfer across grain boundaries. The worst-case load shedding in Ti-6242 alloy is found to be at or close to 120 °C under dwell fatigue loading, which diminishes and vanishes at temperatures lower than −50∘C or higher than 230 °C. Load shedding behaviour is predicted to occur in alloy Ti-6246 also but over a range of higher temperatures which are outside those relevant to in-service conditions. The key controlling dislocation mechanism with respect to load shedding in titanium alloys, and its temperature sensitivity, is shown to be the time constant associated with the thermal activation of dislocation escape from obstacles, with respect to the stress dwell time. The mechanistic basis of load shedding and dwell sensitivity in dwell fatigue loading is presented and discussed in the context of experimental observations.
Patel M, Waheed S, Wenman MR, et al., 2017, Discrete dislocation plasticity modeling of hydrides in zirconium under thermal cycling, MRS Advances, Vol: 2, Pages: 3353-3358, ISSN: 2059-8521
Understanding the ratcheting effect of hydrogen and hydride accumulation in response to thermal cycling is important in establishing a failure criterion for zirconium alloy nuclear fuel cladding. We propose a simple discrete dislocation plasticity model to study the evolution of the dislocation content that arises as a micro-hydride repeatedly precipitates and dissolves over a series of thermal cycles. With each progressive thermal cycle, we find a steady growth in the residual dislocation density in the vicinity of the hydride nucleation site; this corresponds to a gradual increase in the hydrogen concentration and, consequently, the hydride population. The simulated ratcheting in the dislocation density is consistent with experimental observations concerning the hysteresis in the terminal solid solubility of hydrogen in zirconium, which can be correlated to the plastic relaxation of hydrides.
Waheed S, Hao R, Bhowmik A, et al., 2017, A unifying scaling for the Bauschinger effect in highly confined thin films: a discrete dislocation plasticity study, Modelling and Simulation in Materials Science and Engineering, Vol: 25, ISSN: 0965-0393
In this study, sequential sputter deposition, diffusion bonding and focused ion beam milling are used to fabricate sapphire micropillars encapsulating a thin single crystal niobium film. A distinct Bauschinger effect is observed during the cyclic axial compression of the samples. Plain strain discrete dislocation plasticity is used to interpret the experimental results obtained for the encapsulated film-micropillar geometry. The simulations show that the experimental samples correspond to a saturated source density regime, producing the maximum Bauschinger effect for the chosen mean nucleation strength. Next, the source density and mean nucleation strength are shown to have a coupled effect on the size of the Bauschinger effect, understood in terms of the differing number of pile-ups occurring per source in the film. The coupled effect is found to be represented by the density of dislocations annihilated upon unloading: a consistent linear relationship is observed between the size of the Bauschinger effect and the annihilated dislocation density over the entire source density and nucleation strength parameter space investigated. It is found that different film orientations fulfil the same linear relationship, whereas changing the film thickness causes the slope of the linear trend to vary suggesting a length-scale dependence on reverse plasticity. Finally, all results are found to be unified by a power-law relationship quantifying the Bauschinger effect of the form ${{\rm{\Gamma }}}_{{\rm{B}}}\propto {\rm{\Delta }}{\rho }_{{\rm{ann}}}{l}^{n}$ where it is argued that the number of dislocations undergoing reverse glide in the confined film is represented by ${\rm{\Delta }}{\rho }_{{\rm{ann}}}$, the mean free path of dislocations by l and the effect of hardening processes by the exponent n. The net reverse glide is thus represented by ${\rm{\Delta }}{\rho }_{{\rm{ann}}}{l}^{n}$ which can be used as a measure of the Bauschinger effect.
Gurrutxaga-Lerma B, Shehadeh M, Balint, et al., 2017, The effect of temperature on the elastic precursor decay in shock loaded FCC aluminium and BCC iron, International Journal of Plasticity, Vol: 96, Pages: 135-155, ISSN: 1879-2154
This article offers a comprehensive experimental and theoretical study of the causes of thermal hardening in FCC Al and BCC Fe at high strain rates, with the aim to shed light on important mechanisms governing deformation and failures in materials subjected to shocks and impacts at very high strain rates. Experimental evidence regarding the temperature dependence of the dynamic yield point of FCC Al and BCC Fe shock loaded at 107 s−1 is provided. The dynamic yield point of Al increases with temperature in the range 125K–795K; for the same loading and temperate range, the dynamic yield point of BCC Fe remains largely insensitive. A Multiscale Discrete Dislocation Plasticity (MDDP) model of both Fe and Al is developed, leading to good agreement with experiments. The importance of the Peierls barrier in Fe is highlighted, showing it is largely responsible for the temperature insensitivity in BCC metals. The relevance of the mobility of edge components in determining the plastic response of both FCC Al and BCC Fe at different temperatures is discussed, which leads to developing a mechanistic explanation of the underlying mechanisms leading to the experimental behaviour using Dynamic Discrete Dislocation Plasticity (D3P). It is shown that the main contributing factor to temperature evolution of the dynamic yield point is not the mobility of dislocations, but the temperature variation of the shear modulus, the decrease of which is correlated to the experimental behaviour observed for both FCC Al and BCC Fe.
Li Y, Shi Z, Lin J, et al., 2017, A unified constitutive model for asymmetric tension and compression creep-ageing behaviour of naturally aged Al-Cu-Li alloy, International Journal of Plasticity, Vol: 89, Pages: 130-149, ISSN: 0749-6419
A set of unified constitutive equations is presented that predict the asymmetric tension and compression creep behaviour and recently observed double primary creep of pre-stretched/naturally aged aluminium-cooper-lithium alloy AA2050-T34. The evolution of the primary micro- and macro-variables related to the precipitation hardening and creep deformation of the alloy during creep age forming (CAF) are analysed and modelled. Equations for the yield strength evolution of the alloy, including an initial reversion and subsequent strengthening, are proposed based on a theory of concurrent dissolution, re-nucleation and growth of precipitates during artificial ageing. We present new observations of so-called double primary creep during the CAF process. This phenomenon is then predicted by introducing effects of interacting microstructures, including evolving precipitates, diffusing solutes and dislocations, into the sinh-law creep model. In addition, concepts of threshold creep stress σth and a microstructure-dependant creep variable H, which behave differently under different external stress directions, are proposed and incorporated into the creep model. This enables prediction of the asymmetric tension and compression creep-ageing behaviour of the alloy. Quantitative transmission electron microscopy (TEM) and related small-angle X-ray scattering (SAXS) analysis have been carried out for selected creep-aged samples to assist the development and calibration of the constitutive model. A good agreement has been achieved between the experimental results and the model. The model has the potential to be applied to creep age forming of other heat-treatable aluminium alloys.
Zheng Z, Balint D, Dunne F, 2017, Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue, Acta Materialia, Vol: 127, Pages: 43-53, ISSN: 1359-6454
This paper addresses the role of grain boundary slip transfer and thermally-activated discretedislocation plasticity in the redistribution of grain boundary stresses during cold dwell fatigue intitanium alloys. Atomistic simulations have been utilised to calculate the grain boundary energies fortitanium with respect to the misorientation angles. The grain boundary energies are utilised within athermally-activated discrete dislocation plasticity model incorporating slip transfer controlled byenergetic and grain boundary geometrical criteria. The model predicts the grain size effect on the flowstrength in Ti alloys. Cold dwell fatigue behaviour in Ti-6242 alloy is investigated and it is shown thatsignificant stress redistribution from soft to hard grains occurs during the stress dwell, which isobserved both for grain boundaries for which slip transfer is permitted and inhibited. However, thegrain boundary slip penetration is shown to lead to significantly higher hard-grain basal stresses nearthe grain boundary after dwell, thus exacerbating the load shedding stress compared to animpenetrable grain boundary. The key property controlling the dwell fatigue response is argued toremain the time constant associated with the thermal activation process for dislocation escape, but theslip penetrability is also important and exacerbates the load shedding. The inclusion of a macrozonedoes not significantly change the conclusions but does potentially lead to the possibility of a largerinitial facet.
Bordas SPA, Balint DS, 2017, Advances in Applied Mechanics PREFACE, ADVANCES IN APPLIED MECHANICS, VOL 50, Editors: Bordas, Balint, Publisher: ELSEVIER ACADEMIC PRESS INC, Pages: IX-X
Sutton AP, Nazarov R, Majevadia JS, et al., 2016, First-principles calculation of the elastic dipole tensor of a point defect: Application to hydrogen in α-zirconium, Physical Review B, Vol: 94, ISSN: 1550-235X
The elastic dipole tensor is a fundamental quantity relating the elastic field and atomic structure of a point defect. We review three methods in the literature to calculate the dipole tensor and apply them to hydrogen in α-zirconium using density functional theory (DFT). The results are compared with the dipole tensor deduced from earlier experimental measurements of the λ tensor for hydrogen in α-zirconium. There are significant errors with all three methods. We show that calculation of the λtensor, in combination with experimentally measured elastic constants and lattice parameters, yields dipole tensor components that differ from experimental values by only 10%–20%. There is evidence to suggest that current state-of-the-art DFT calculations underestimate bonding between hydrogen and α-zirconium.
Li N, Lin J, Balint DS, et al., 2016, Modelling of austenite formation during heating in boron steel hot stamping processes, Journal of Materials Processing Technology, Vol: 237, Pages: 394-401, ISSN: 0924-0136
A physically-based material model has been developed to describe the austenite formation in a manganese-boron steel during heating in hot stamping processes. The equations were formulated based on three austenite formation mechanisms: nucleation, growth and impingement. It is able to characterise the phase transformation process under both non-isothermal and isothermal conditions, where the effects of heating rate and soaking temperature on the austenite formation have been rationalised. Heat treatment tests of the manganese-boron steel were performed on a Gleeble 3800 subjected to various heating conditions (heating rate: 1 K/s − 25 K/s, soaking temperature: 1023 K − 1273 K). The dimensional changes of specimens associated with the phase transformation, which was measured using a high resolution dilatometer, has been quantitatively related to the volume fraction of austenite formation. The experimental data was used to calibrate and validate the equations. Good agreement between the experimental and predicted results has been obtained. Further analysis has been made to illustrate the significance of the model in applications.
Zheng Z, Balint D, Dunne F, 2016, Dwell fatigue in two Ti alloys: an integrated crystal plasticity and discrete dislocation study, Journal of the Mechanics and Physics of Solids, Vol: 96, Pages: 411-427, ISSN: 0022-5096
It is a well known and important problem in the aircraft engine industry that alloy Ti-6242 shows a significant reduction in fatigue life, termed dwell debit, if a stress dwell is included in the fatigue cycle, whereas Ti-6246 does not; the mechanistic explanation for the differing dwell debit of these alloys has remained elusive for decades. In this work, crystal plasticity modelling has been utilised to extract the thermal activation energies for pinned dislocation escape for both Ti alloys based on independent experimental data. This then allows the markedly different cold creep responses of the two alloys to be captured accurately and demonstrates why the observed near-identical rate sensitivity under non-dwell loading is entirely consistent with the dwell behaviour. The activation energies determined are then utilised within a recently developed thermally-activated discrete dislocation plasticity model to predict the strain rate sensitivities of the two alloys associated with nano-indentation into basal and prism planes. It is shown that Ti-6242 experiences a strong crystallographic orientation-dependent rate sensitivity while Ti-6246 does not which is shown to agree with recently published independent measurements; the dependence of rate sensitivity on indentation slip plane is also well captured. The thermally-activated discrete dislocation plasticity model shows that the incorporation of a stress dwell in fatigue loading leads to remarkable stress redistribution from soft to hard grains in the classical cold dwell fatigue rogue grain combination in alloy Ti-6242, but that no such load shedding occurs in alloy Ti-6246. The key property controlling the behaviour is the time constant of the thermal activation process relative to that of the loading. This work provides the first mechanistic basis to explain why alloy Ti-6242 shows a dwell debit but Ti-6246 does not.
Jonas Verschueren, Gurrutxaga Lerma B, Balint DS, et al., 2016, The injection of a screw dislocation into a crystal: atomistics vs. continuum elastodynamics, Journal of the Mechanics and Physics of Solids, Vol: 98, Pages: 366-389, ISSN: 1873-4782
The injection (creation) process of a straight screw dislocation is compared atomistically with elastodynamic continuum theory. Amethod for injecting quiescent screw dislocations into a crystal of tungsten is simulated using non-equilibrium molecular dynamics.The resulting stress fields are compared to the those of elastodynamic solutions for the injection of a quiescent screw dislocation.A number of differences are found: a plane wave emission is observed to emanate from the whole surface of the cut used to createthe dislocation, affecting the displacement field along the dislocation line (z), and introducing displacement field componentsperpendicular to the line (along x and y). It is argued that, in part, this emission is the result of the finite time required to injectthe dislocation, whereby the atoms in the cut surface must temporarily be displaced to unstable positions in order to produce therequired slip. By modelling this process in the continuum it is shown that the displacements components normal to the dislocationline arise from transient displacements of atoms in the cut surface parallel to x and y. It is shown that once these displacements areincluded in the elastodynamic continuum formulation the plane wave emission in uzis correctly captured. A detailed comparisonbetween the atomistic and continuum models is then offered, showing that the main atomistic features can also be captured in thecontinuum.
Wang Y, Mohammed IK, Balint DS, 2016, Methodology for modelling diffusion bonding in powder forging, 16th Metal Forming International Conference, Publisher: Trans Tech Publications Inc., Pages: 817-823, ISSN: 1013-9826
Interfacial bonding has a significant influence on the quality of processed components formed by powder forging. Consequently, modelling the bonding process is important for controlling the condition of the components and predicting optimum forging process parameters (e.g. forming load, temperature, load-holding time, etc.). A numerical model was developed in the present work to simulate diffusion bonding (DB) during the direct powder forging (DF) process. A set of analytical equations was derived and implemented in the finite element (FE) software Abaqus via a user-defined subroutine. The DB model was validated using a two-hemisphere compression simulation. The numerical results demonstrated that the DB model has the ability to: 1) determine the bonding status between powder particles during the forging process, and 2) predict the optimum value for key powder forging process parameters. The DB model was also implemented in a representative volume element (RVE) model which was developed in an earlier work to simulate the powder forging process by considering particle packing and thermo-mechanical effects.
Gurrutxaga Lerma B, Balint DS, Dini D, et al., 2016, A dynamic discrete dislocation plasticity study of elastodynamic shielding of stationary cracks, Journal of the Mechanics and Physics of Solids, Vol: 98, Pages: 1-11, ISSN: 0022-5096
Employing Dynamic Discrete Dislocation Plasticity (D3P), an elastodynamic analysis of theshielding of a stationary crack tip by dislocations is studied. Dislocations are generated via FrankReadsources, and make a negligible contribution to the shielding of the crack tip, whereas dislocationsgenerated at the crack tip via homogeneous nucleation dominate the shielding. Theireffect is found to be highly localised around the crack, leading to a magnification of the shieldingwhen compared to time-independent, elastostatic predictions. The resulting attenuation of KI (t)is computed, and is found to be directly proportional to the applied load and to √t.
Zheng Z, Balint D, Dunne F, 2016, Discrete dislocation and crystal plasticity analyses of load shedding in polycrystalline titanium alloys, International Journal of Plasticity, Vol: 87, Pages: 15-31, ISSN: 0749-6419
The focus of this paper is the mechanistic basis of the load shedding phenomenon that occurs under the dwell fatigue loading scenario. A systematic study was carried out using a discrete dislocation plasticity (DDP) model to investigate the effect of crystallographic orientations, localised dislocation behaviour and grain combinations on the phenomenon. Rate sensitivity in the model arises from a thermal activation process at low strain rates, which is accounted for by associating a stress- and temperature-dependent release time with obstacles; the activation energy was determined by calibrating an equivalent crystal plasticity model to experimental data. First, the application of Stroh's dislocation pile-up model of crack nucleation to facet fracture was quantitatively assessed using the DDP model. Then a polycrystalline model with grains generated using a controlled Poisson Voronoi tessellation was used to investigate the soft-hard-soft rogue grain combination commonly associated with load shedding. Dislocation density and peak stress at the soft/hard grain boundary increased significantly during the stress dwell period, effects that were enhanced by dislocations escaping from pile-ups at obstacles. The residual stress after dwell fatigue loading was also found to be much higher compared to standard fatigue loading. Taylor (uniform strain) and Sachs (uniform stress) type assumptions in a soft-hard grain combination have been assessed with a simple bicrystal DDP model. Basal slip nucleation in the hard grain was found to be initiated by high stresses generated by strong pile ups in the soft grain, and both basal and pyramidal slip nucleation was observed in the hard grain when the grain boundary orientation aligned with that of an active slip system in the soft grain. The findings of this study give new insight into the mechanisms of load shedding and faceting associated with cold dwell fatigue in Ti alloys used in aircraft engines.
Millar TM, Patel Y, Wang H, et al., 2016, An investigation of cutting resistance in stretched polymer films, 21st European Conference on Fracture (ECF), Publisher: ELSEVIER SCIENCE BV, Pages: 190-196, ISSN: 2452-3216
An investigation is made into the fracture properties of polymer films and laminates under cutting by a sharp tool and lateral tension under pure shear conditions. The method involves use of a sharp razor blade applied to the crack tip of polymer films which are also stretched orthogonal to the direction of the blade. The reaction force is measured as the cutting tool cuts the material and the force from applying a lateral strain is measured. The analysis and tests assume quasi-static conditions. The method is applied to a polyester film and three polyester laminates.Steady-state cutting forces are observed from cutting tests and loads at crack initiation are observed from lateral stretching tests. With fracture mechanics analysis the energy contributions from cutting and tearing are used to determine apparent fracture properties from the experimental results. It is observed that the cutting and tearing tests yield similar fracture toughness properties for the three tested polyester laminates, despite the different crack tip geometry at the point of crack growth. However, significantly larger fracture toughness values are measured from tearing tests versus cutting tests for the tested polyester film.
Junyi L, Ruffini V, Balint D, 2016, Measuring the band structures of periodic beams using the wave superposition method, Journal of Sound and Vibration, Vol: 382, Pages: 158-178, ISSN: 0022-460X
Phononic crystals and elastic metamaterials are artificially engineered periodic structures that have several interesting properties, such as negative effective stiffness in certain frequency ranges. An interesting property of phononic crystals and elastic metamaterials is the presence of band gaps, which are bands of frequencies where elastic waves cannot propagate. The presence of band gaps gives this class of materials the potential to be used as vibration isolators. In many studies, the band structures were used to evaluate the band gaps. The presence of band gaps in a finite structure is commonly validated by measuring the frequency response as there are no direct methods of measuring the band structures. In this study, an experiment was conducted to determine the band structure of one dimension phononic crystals with two wave modes, such as a bi-material beam, using the frequency response at only 6 points to validate the wave superposition method (WSM) introduced in a previous study. A bi-material beam and an aluminium beam with varying geometry were studied. The experiment was performed by hanging the beams freely, exciting one end of the beams, and measuring the acceleration at consecutive unit cells. The measured transfer function of the beams agrees with the analytical solutions but minor discrepancies. The band structure was then determined using WSM and the band structure of one set of the waves was found to agree well with the analytical solutions. The measurements taken for the other set of waves, which are the evanescent waves in the bi-material beams, were inaccurate and noisy. The transfer functions at additional points of one of the beams were calculated from the measured band structure using WSM. The calculated transfer function agrees with the measured results except at the frequencies where the band structure was inaccurate. Lastly, a study of the potential sources of errors was also conducted using finite element modelling and the errors in the
Kardoulaki E, Lin J, Balint D, et al., 2016, A study on the effect of stress state on damage evolution in hot deformation of free cutting steels using double notched bars, Philosophical Magazine, Vol: 96, Pages: 2176-2203, ISSN: 1478-6435
The effect of stress state on the initiation of damage for leaded free cutting steel has been investigated under hot rolling conditions. Double notched (DN) circumferential tension samples were designed and used to simulate damage development at different stress states and deformation conditions using a Gleeble (3800) thermal-mechanical testing system. Two DN sample geometries with varying notch profiles were used to account for different states of stress. To simulate the conditions of hot rolling the samples were tested at high temperatures (900–1200 °C) and moderate strain rates (0.1–1 s−1). After testing to failure, which normally occurs at one notch of the specimen, the unfailed notch of each sample was sectioned to examine the sites where damage occurs since the material has been captured in a state very close to failure. Two of the cases examined have shown definitive damage paths occurring from ‘outside–in’ for a sharp notch deformed at T = 900 °C and from ‘inside–out’ for a blunt notch tested at T = 1200 °C for the same strain rate of 0.1 s−1. The experimental results of the failure initiation sites were compared with computed values of the stress fields around the notch profiles, obtained from FE analysis using a set of viscoplastic constitutive equations calibrated for free cutting steel. The temperature profiles from high temperature mechanical testing were used in the FE calculations of the stress state.
Junyi L, Balint DS, 2016, Optimal shunt parameters for maximising wave attenuation with periodic piezoelectric patches, Journal of Intelligent Material Systems and Structures, Vol: 28, Pages: 108-123, ISSN: 1045-389X
Elastic metamaterials, which have huge potential in wave guiding and attenuation applications, can be built from structures with periodic piezoelectric patch arrays. Passive shunts offer the benefits of simplicity and low cost. In this paper, the effects of the magnitude and phase angle of the shunt impedance on the attenuation constant of a beam with periodic piezoelectric patch arrays were studied in order to determine the optimal shunt that produces the widest and most effective band gaps. The attenuation constants were found to be large when the phase angle is Formula rad and when the magnitude decreases exponentially with the excitation frequency. This corresponds to a negative capacitance circuit, which is the optimal shunt for such systems. The attenuation constant of the system reduces significantly when the impedance deviates from the optimal value suggesting other circuits are less effective. The impedance and band structure of resistive–inductive (R-L), negative capacitance and resistive shunts were investigated. As expected, the negative capacitance circuit produces a large band gap, while the R-L circuit only produces a band gap around its natural frequency. The transmissibilities of a finite system with these circuits demonstrated that vibration transmissions are low within the band gaps. Furthermore, the stability of the negative capacitance circuit built using a dual-output second-generation current conveyor (DO-CCII) was examined by studying the pole diagrams. The system was found to be stable in ideal conditions but unstable when parasitic effects are considered. This suggests that the stability of the system is an important consideration for the implementation of this strategy and the different negative impedance converter designs available in the literature should be studied to find a suitable circuit configuration.
Li N, Lin J, Balint D, et al., 2016, Experimental characterisation of the effects of thermal conditions on austenite formation for hot stamping of boron steel, Journal of Materials Processing Technology, Vol: 231, Pages: 254-264, ISSN: 0924-0136
The formation of austenite in manganese-boron steels during selective heat treatment has great significance in the application of innovative hot stamping processes. Heat treatment tests were designed according to the thermal cycle of industrial heating and hot stamping processes and were conducted on a Gleeble 3800 thermomechanical testing system. Specimens were subjected to non-isothermal (heating rates: 1 K/s–25 K/s) and isothermal (soaking temperatures: 1023 K–1173K) temperature profiles. A high-resolution dilatometer was employed to detect the dimensional change of the specimens associated with austenitization. The dilatometric measurement was quantitatively related to the volume fraction of austenite. By analysing the evolution curves of austenite fraction, the effects of heating rate and temperature on the progress of austenite formation under both non-isothermal and isothermal conditions were investigated and characterised, improving the current understanding of the mechanisms that control austenite formation in manganese-boron steels.
Junyi L, Balint DS, 2016, A parametric study of the mechanical and dispersion properties of cubic lattice structures, International Journal of Solids and Structures, Vol: 91, Pages: 55-71, ISSN: 1879-2146
Xu Y, Balint DB, Dini DD, 2016, A method of coupling discrete dislocation plasticity to the crystal plasticity finite element method, Modelling and Simulation in Materials Science and Engineering, Vol: 24, ISSN: 1361-651X
A method of concurrent coupling of planar discrete dislocation plasticity (DDP) and a crystal plasticityfinite element (CPFE) method was devised for simulating plastic deformation in large polycrystals withdiscrete dislocation resolution in a single grain or cluster of grains for computational efficiency;computation time using the coupling method can be reduced by an order of magnitude compared toDDP. The method is based on an iterative scheme initiated by a sub-model calculation, which ensuresdisplacement and traction compatibility at all nodes at the interface between the DDP and CPFEdomains. The proposed coupling approach is demonstrated using two plane strain problems: (i)uniaxial tension of a bi-crystal film and (ii) indentation of a thin film on a substrate. The latter was alsoused to demonstrate that the rigid substrate assumption used in earlier discrete dislocation plasticitystudies is inadequate for indentation depths that are large compared to the film thickness, i.e. theeffect of the plastic substrate modelled using CPFE becomes important. The coupling method can beused to study a wider range of indentation depths than previously possible using DDP alone, withoutsacrificing the indentation size effect regime captured by DDP. The method is general and can beapplied to any problem where finer resolution of dislocation mediated plasticity is required to studythe mechanical response of polycrystalline materials, e.g. to capture size effects locally within a largerelastic/plastic boundary value problem.
Kaye MC, Balint D, Lin J, et al., 2016, Test-piece design for experimental and numerical evaluation of damage in relation to spatial triaxial stress inversion, International Journal of Damage Mechanics, Vol: 26, Pages: 588-607, ISSN: 1530-7921
This work examines the effect of stress state on the nucleation and growth of damage during hot deformation of free cutting steel. A test-piece was designed to emulate stress states similar to those found in hot rolling. The novelty of the new design is its ability to maintain a constant spatial stress state during deformation, allowing a true correlation of the damage mechanism to the stress triaxiality; previous sample geometries had a large variation in stress during plastic deformation, which made it impossible to relate an observed damage mechanism to a particular stress state using a single sample. Continuum damage equations were calibrated using uniaxial tensile tests and implemented into finite element models of compressive test-pieces. The stress distributions in each test-piece geometry were compared and a single test-piece design was chosen with an optimised triaxial stress distribution. The test-piece was deformed at elevated temperatures, sectioned and the microstructure was evaluated. The combination of stress state and strain computed via finite element analysis was compared to the damage produced across the test-piece section. The predictions of the damage equations were compared to the results of physical tests and used to identify appropriate damage models. The effect of stress state on damage was evaluated, which can be used to update and improve existing material models. The stress triaxiality was found to be the dominant factor for damage around inclusions, with a minimum stress triaxiality required for damage growth to occur.
Zheng Z, Balint D, Dunne F, 2016, Rate sensitivity in discrete dislocation plasticity in hexagonal close-packed crystals, Acta Materialia, Vol: 107, Pages: 17-26, ISSN: 1873-2453
The origin of the rate-sensitive behaviour of plasticity over strain rate regimes from 10−5 to 105 s−1 has been assessed with reference to three key mechanisms: dislocation nucleation, time of flight (dislocation mobility) and thermally activated escape of pinned dislocations. A new mechanistic formalism for incorporating thermally activated dislocation escape into discrete dislocation plasticity modelling techniques is presented. It is shown that nucleation and dislocation mobility explain rate-sensitive behaviour for strain rates in the range 102 to 105 s−1, but cannot do so for significantly lower strain rates, for which thermally-activated dislocation escape becomes the predominant rate-controlling mechanism. At low strain rates, and for a model Ti alloy considered at 20 °C, the strong experimentally observed rate-sensitive behaviour manifested as stress relaxation and creep is shown to be captured well by the new thermal activation discrete dislocation plasticity model, which otherwise simply cannot be captured by nucleation or mobility arguments. Increasing activation energy leads to a higher energy barrier and as a consequence, a higher dislocation escape time. Conversely, increasing obstacle spacing tends to diminish the thermal activation time.
Gurrutxaga Lerma B, Balint DANIEL, Dini DANIELE, et al., 2015, Elastodynamic image forces on dislocations, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 471, ISSN: 1364-5021
The elastodynamic image forces on edge and screw dislocations in the presence of a planar-free surface are derived. The explicit form of the elastodynamic fields of an injected, quiescent screw dislocation are also derived. The resulting image forces are affected by retardation effects: the dislocations experience no image force for a period of time defined by the arrival and reflection at the free surface of the dislocation fields. For the case of injected, stationary dislocations, it is shown that the elastodynamic image force tends asymptotically to the elastotatic prediction. For the case of injected, moving dislocations, it is shown that the elastodynamic image force on both the edge and the screw dislocations is magnified by inertial effects, and becomes increasingly divergent with time; this additional effect, missing in the elastostatic description, is shown to be substantial even for slow moving dislocations. Finally, it is shown that the elastodynamic image force of an edge dislocation moving towards the surface at the Rayleigh wave speed becomes repulsive, rather than attractive; this is suggestive of instabilities at the core of the dislocation, and likely resonances with the free surface.
Mercer C, Lee J, Balint DS, 2015, An investigation of the mechanical fatigue behavior of low thermal expansion lattice structures, International Journal of Fatigue, Vol: 81, Pages: 238-248, ISSN: 1879-3452
A study of the mechanical fatigue behavior of a Ti–6Al–4V lattice structure designed to exhibit controlled thermal expansion has been performed. Comparison of S–N curves generated under both zero-tension and fully reversed cyclic loading has determined that the fatigue resistance of the lattice is substantially poorer than that of the constituent Ti–6Al–4V material for the same remote applied (macroscopic) stress. In addition, the effect of beta annealing the as-received mill-annealed alloy was also to reduce fatigue life in both the lattices and parent material. This effect is due to significant microstructural changes that occurred during heat treatment. Increasing the stress ratio (σmin/σmax) of the cyclic waveform from −1 to 0 had a similar effect. An analytical model has been developed to predict the fatigue life of the lattice structures from the S–N curves of the parent material, by determining the relationship between the macroscopic stresses acting on the lattice structure and the local stresses. The local stresses were then used in a multiaxial fatigue model to determine the fatigue life. The analytical model is able to predict the fatigue life with reasonable accuracy and minimal cost. The Findley multiaxial fatigue parameter for the parent material and lattice structures can be fitted with a power law equation and appears to fall onto a single curve, suggesting the local behavior within the lattice material is similar to the parent material. The analytical tools developed in this study can be hugely beneficial to the design of these lattice structures in the aerospace and communications industries.
Gurrutxaga Lerma BENAT, Balint DS, Dini D, et al., 2015, The mechanisms governing the activation of dislocation sources in aluminum at different strain rates, Journal of the Mechanics and Physics of Solids, Vol: 84, Pages: 273-292, ISSN: 1873-4782
This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 101 s−1 to 1010 s−1 in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 106 s−1, and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 106 s−1, the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 108 s−1, suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×107 s−1 homogeneous nucleation becomes the dominant generation mechanism.
Gurrutxaga-Lerma B, Balint DS, Dini D, et al., 2015, The Role of Homogeneous Nucleation in Planar Dynamic Discrete Dislocation Plasticity, Journal of Applied Mechanics-Transactions of the ASME, Vol: 82, ISSN: 1528-9036
Homogeneous nucleation of dislocations is the dominant dislocation generation mechanismat strain rates above 108 s1; at those rates, homogeneous nucleation dominates theplastic relaxation of shock waves in the same way that Frank–Read sources control theonset of plastic flow at low strain rates. This article describes the implementation ofhomogeneous nucleation in dynamic discrete dislocation plasticity (D3P), a planarmethod of discrete dislocation dynamics (DDD) that offers a complete elastodynamictreatment of plasticity. The implemented methodology is put to the test by studying fourmaterials—Al, Fe, Ni, and Mo—that are shock loaded with the same intensity and astrain rate of 1010 s1. It is found that, even for comparable dislocation densities, the latticeshear strength is fundamental in determining the amount of plastic relaxation a materialdisplays when shock loaded. [DO
Junyi L, Balint DS, 2015, An inverse method to determine the dispersion curves of periodic structures based on wave superposition, Journal of Sound and Vibration, Vol: 350, Pages: 41-72, ISSN: 1095-8568
Phononic crystals and acoustic metamaterials have unique properties, such as the existence of band gaps, which give them huge potential in many applications, such as vibration isolation, acoustic cloaking, acoustic lensing, and more. Many methods have been proposed to determine the band structure of these materials but almost all require a model of the structure. In this paper, an inverse method to calculate the band structure of one dimensional periodic structures based on Bloch wave boundary conditions and wave superposition is introduced. The proposed method only requires the frequency responses measured at a small number of points within the structure. This allows the band structures to be determined experimentally using simple equipment, like a shaker and accelerometers. The band structure of a simple bi-material beam was calculated in this study as a demonstration of the method, and the results were found to be in agreement with calculations made using the transfer matrix method. The proposed method was then extended to predict the response of a finite periodic bi-material beam with arbitrary boundary conditions using only the band structure and components of the eigenvectors; some resonance peaks were observed within the band gaps and these were found to be caused by the reflection of the waves at the boundaries. The effects of the number of unit cells on the transmissibility of a beam were investigated. It was found that the transmissibilities within the band gaps can be estimated to be directly proportional to the number of unit cells. Lastly, an attempt was made to extend the method to two and three dimensional periodic structures and the wave superposition method was found to be able to measure a portion of the dispersion surface of two dimensional structures with a fair degree of accuracy, especially at lower bands. Errors and scatter are present at high frequencies caused by more waves significantly affecting the responses of the system. This issue can
Gurrutxaga-Lerma B, Balint DS, Dini D, et al., 2015, Attenuation of the dynamic yield point of shocked aluminum using elastodynamic simulations of dislocation dynamics, Physical Review Letters, Vol: 114, Pages: 1-5, ISSN: 0031-9007
When a metal is subjected to extremely rapid compression, a shock wave is launched that generates dislocations as it propagates. The shock wave evolves into a characteristic two-wave structure, with an elastic wave preceding a plastic front. It has been known for more than six decades that the amplitude of the elastic wave decays the farther it travels into the metal: this is known as “the decay of the elastic precursor.” The amplitude of the elastic precursor is a dynamic yield point because it marks the transition from elastic to plastic behavior. In this Letter we provide a full explanation of this attenuation using the first method of dislocation dynamics to treat the time dependence of the elastic fields of dislocations explicitly. We show that the decay of the elastic precursor is a result of the interference of the elastic shock wave with elastic waves emanating from dislocations nucleated in the shock front. Our simulations reproduce quantitatively recent experiments on the decay of the elastic precursor in aluminum and its dependence on strain rate.
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