Size Effects In Plasticity Research Articles

Effect of particle density on microplastics transport in artificial and natural porous media

The occurrence and persistence of microplastics (MPs) in natural environments are of increasing concern. Along with this, the transport of MPs in sediments has been investigated mainly focusing on the effect of plastic size and shape, media size effect, and solution chemistry. Yet, the influence of particle density is only partially understood. Therefore, column experiments on the transport of variably buoyant MPs in saturated natural sediments and glass beads were conducted, and transport parameters were quantified using a two-site kinetic transport model with a depth-dependent blocking function (the amount of retained MPs does not decrease at a constant rate with increasing depth, the majority of MPs were retained near the column inlet). Neutral, sinking, and buoyant MPs within the same size range were selected, with stable water isotope applied as conservative tracer to explore water and MP movement in the tested sediments. The results showed that 95.5 ± 1.4% of sinking MPs remained in columns packed with gravel, followed by buoyant and neutral MPs, thus indicating that particle density does affect MP mobility. Similar recovered amounts of MPs were found in columns packed with glass beads, indicating that tested sediment types do not affect the deposition behavior of MPs. The breakthrough curves of MPs were accurately described by the selected model. However, the simulated retention profiles overestimated the observed MP amount in layers closest to the column inlet. The coupled experimental and modeled results suggest an enhanced retention of sinking MPs, while neutrally and buoyant MPs exhibit a higher mobility in comparison. Thus, neutral or buoyant MPs can potentially pose a higher contamination risk to subsurface porous media environments compared to sinking MPs. Discrepancies between observed and simulated retention profiles indicate that future model development is needed for advancing the MP deposition as affected by particle density.

Effect of Strain Gradient on Elastic and Plastic Size Dependency in Polycrystalline Copper

This study unveils the presence of size effect not only in the plastic regime but also in the elastic regime under strain gradient. This discovery emerges from a comprehensive set of experiments encompassing micro-cantilever bending and micro-pillar compression tests. Subsequent finite element analysis serves to not only expose the limitation of classical continuum theory but also to effectively demonstrate the enhanced predictive capabilities of couple stress theory in both elastic and plastic size effects. To incorporate couple stress theory, a systematic and rigorous finite element analysis-based optimization was devised to determine length scale parameters, which are additional material properties in couple stress theory. The resulting length scale parameters for polycrystalline copper were found to be 0.536 and 0.669µm in the elastic and plastic regimes, respectively. The study also explores the physical interpretation of these length scale parameters in both regimes.

Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

Strain gradient plasticity has been the subject of extensive research in the past 40 years in order to model size effects in metal plasticity, on the one hand, and provide finite width shear bands in the simulation of localization phenomena, on the other hand. However, the use of the emerging models is still limited to academic applications and has not yet been adopted by industry practitioners. The present paper systematically reviews the pros and the cons of gradient plasticity at finite strains based on the gradient of scalar plastic variables, in particular the gradient of the cumulative plastic strain. It proposes benchmark tests addressing both size effect modeling and plastic strain localization simulation. It includes new analytical solutions for validation of FE implementation. It focuses on the micromorphic approach to gradient plasticity, as a convenient method for implementation in FE codes. New features of the analysis include the comparison of three distinct formulations of rate-independent gradient plasticity at finite deformations, based on the multiplicative decomposition of the deformation gradient and on quadratic potentials with respect to gradient terms. The performance of micromorphic and Lagrange-multiplier-based strain gradient plasticity models is evaluated for various monotonic and cyclic loading conditions including confined plasticity in simple glide and tension, bending and torsion at large deformations. Limitations are pointed out in the case of bending and torsion, which can be overcome for instance by the use of the gradient of equivalent plastic strain model.

Modeling the indentation size effects of polymers, based on couple stress elasticity and shear transformation plasticity

This work attempts to construct models which can describe the size effects in modulus and hardness of polymers measured by indentation tests. Firstly, the origin of size effects in the procedure of nanoindentation is analyzed. The finding of the literature that the indentation size effects of polymers are of significant elastic nature is further discussed and confirmed. The elastic size effects are described by a model, through introducing a model of elastic unloading load with consideration of couple stress elasticity into the Oliver-Pharr indentation approach. The accordingly proposed modulus model and hardness model agree excellently with a large amount of experimental data obtained from literatures. The models show that the elastic size effects of polymers and their experimental observations are mainly determined by the molecular structures. The fitting results verify that the size effects in indentation hardness of polymers with complex molecular structures are significantly elastic. It is postulated that the plastic size effects in indentation hardness of polymers are only derived from their glassy components. A shear transformation plasticity formula of glassy polymers recently proposed by literature is slightly extended to characterize the size dependent deformations in indentation tests. A hardness model with consideration of size effects is accordingly obtained and agrees well with related experimental data.

Effects of surface curvature and dislocation dynamics: Dynamical deformation mechanisms for uniaxial compression tests at the nanoscale

The understanding of size effects in micro-crystal plasticity has been in-part based on controlled uniaxial mechanical testing of crystalline micropillars that may be monitored in-situ, using modern microscopy approaches. Nevertheless, it has always been clear that mechanics and materials science are not ideally decoupled in uniaxial micropillar compression, thus agreement between experiments and theory remains challenging. We present a theoretical analysis of the uniaxial compression of micropillars with curved top free surfaces, in consistency with modern experimental thresholds. By using coupled Finite Element and Discrete Dislocation Dynamics simulations we investigate the effect of the small curvature to dislocation microstructure evolution at constant displacement rate. The uniaxial compression of flat micropillars is shown to be consistent with existing literature, with homogeneous stress build up and random activation of sources inside the volume. However, in the presence of a small top-surface micropillar curvature, there are significant dynamical effects on dislocation mechanisms and an overestimate of strain at yielding that leads to large errors on capturing elastic compression moduli and avalanche noise characteristics. Characteristically, for 10 nm-high isotropic curvature, large (>100MPa) stress drops emerge in the average stress, that become larger as the initial dislocation density increases, in direct contrast to expectations and findings for ideally flat micropillars.

Development of the Concurrent Multiscale Discrete-Continuum Model and Its Application in Plasticity Size Effect

A concurrent multiscale model coupling discrete dislocation dynamics to the finite element method is developed to investigate the plastic mechanism of materials at micron/submicron length scales. In this model, the plastic strain is computed in discrete dislocation dynamics (DDD) and transferred to the finite element method (FEM) to participate in the constitutive law calculation, while the FEM solves the complex boundary problem for DDD simulation. The implementation of the whole coupling scheme takes advantage of user subroutines in the software ABAQUS. The data structures used for information transferring are introduced in detail. Moreover, a FE mesh-based regularization method is proposed to localize the discrete plastic strain to continuum material points. Uniaxial compression tests of single crystal micropillars are performed to validate the developed model. The results indicate the apparent dependence of yield stress on sample size, and its underlying mechanisms are also analyzed.

Grain size effect of FCC polycrystal: A new CPFEM approach based on surface geometrically necessary dislocations

A multiscale modeling methodology involving discrete dislocation dynamics (DDD) and crystal plasticity finite element method (CPFEM) was used to study the grain size effect in FCC polycrystalline plasticity. The developed model is based on the dislocation density storage-recovery framework and is expanded to the scale of slip systems. DDD simulations were used to establish a constitutive law incorporating the main dislocation mechanisms that are involved in the strain hardening process observed in monotonically deformed FCC polycrystals. This was achieved by calculating the key features controlling the accumulation of the forest dislocation density within the grains and the polarized dislocation density at the grain boundaries during plastic deformation. The model was then integrated with a CPFEM model at the polycrystalline aggregate scale to compute short- and long-range internal stresses within the grains. These simulations quantitatively reproduced the deformation curves of the FCC polycrystals as a function of grain size. Because of its predictive ability to reproduce the Hall–Petch effect in a physically justified approach, the proposed framework has significant potential for further applications.

Computational rate-independent strain gradient crystal plasticity

Size effects in metal plasticity are widely accepted, and different theoretical approaches to handle the phenomenon are developing in the literature. The present work considers the Fleck and Willis (2009b) framework, and creates a new gradient enhanced rate-independent crystal plasticity FE-implementation. The study considers both energetic and dissipative gradient hardening and strengthening, and adopts a general form of the gradient enhanced effective slip rate. Monotonic and cyclic shearing of an infinite crystal slab containing a single slip system at an angle of 90° to the loading direction is a first benchmark case. A second case considers combined shear and tension in 2D of a constrained HCP single crystal. The HCP crystal is loaded in its basal plane by a so-called butterfly deformation path that inflicts repeated loading and unloading of the three crystallographic slip systems. Finally, the evolution and interaction of multiple plastic zones are demonstrated by considering a notched tensile sample. A direct comparison to visco-plastic (rate-dependent) simulations confirms that the proposed crystal plasticity framework forms a rate-independent limit for the gradient enhanced Fleck–Willis theory. The model response also reduces to that of conventional crystal plasticity in the limit of zero length parameters.

Effective mobility of BCC dislocations in two-dimensional discrete dislocation plasticity

Two-dimensional discrete dislocation plasticity (2D-DDP) has shown to be a powerful tool for studying micro-plasticity problems such as size effects in single crystals, fracture of bimaterial interfaces, delamination of thin films, fatigue crack growth etc. The power of 2D-DDP lies in the application of edge dislocation dipoles as the vehicle for plastic slip: the loss of accuracy in the description of dislocation structures is counter-balanced by its simplicity and the possibility to reach larger plastic strains. The constitutive rules for dislocation evolution in 2D-DDP used so far are tuned to FCC crystals and need to be modified to be used for BCC materials. One of the key challenges in extending the method to BCC materials is that, contrary to FCC, the mobilities of edge and screw dislocations in BCC crystals differ vastly from each other, so that the screw mobility will be rate limiting the plastic slip. Thus, a method is required to map the edge and screw mobilities of dislocation loops into an effective mobility to be used in 2D. To do so, we here propose a 3D-to-2D procedure that is based on the notion of conservation of in-plane plastic strain rate. The consequence of this approach is that the effective 2D mobility for FCC crystals is not simply equal to the uniform mobility of a dislocation loop, as has been assumed by all 2D models to date, but also on the size of edge dipoles. In order to assess the consequences of this departure from the current literature, we considered a few key problems involving plasticity size effects and crack growth, and compared the predictions assuming constant mobility versus the proposed effective mobility. After observing that, overall, the predictions do not deviate substantially, we proceed with application of the 3D-to-2D procedure to compute the effective 2D mobility for BCC materials based on their edge and screw mobilities. The validation of the approach is done by comparison of the predicted rate sensitivity of polycrystalline iron with the experimental rate sensitivity at room temperature, which are found to be in fairly good agreement.

Modelling the cyclic torsion of polycrystalline micron-sized copper wires by distortion gradient plasticity

ABSTRACT In this contribution, we show that the distortion gradient plasticity recently proposed by our group, characterised by a higher-order plastic potential leading to reliable predictions under non-proportional loading, can predict experimental data of literature on the cyclic torsion of copper wires of diameter ranging from 18 to 42 . To reach our goal, we plug our recent constitutive proposal in a framework that we have previously developed for the torsion problem, which is based on the pivotal theory established in 2004 by Gurtin, relying on Nye's dislocation density tensor to describe size effects in micron-scale metal plasticity. We implement the new model in a finite element code and identify its parameters by resorting to the Coliny evolutionary algorithm within the software Dakota.

Scale-dependent pop-ins in nanoindentation and scale-free plastic fluctuations in microcompression

Abstract

Study on The Effects of Plastic as Admixture on The Mechanical Properties of Cement-Sand Bricks

Cement-sand bricks is one of the building materials that being used as alternative for a low-cost house in Malaysia. Nowadays, many researchers have been researching for green and sustainable materials to replace conventional building materials. In this paper, plastic bottle has been studied as a new alternative admixture in cement-sand brick production. The objective of this research is to determine the effect of plastic size on mechanical properties of cement-sand bricks. The lab testing used for this research are compressive strength and water absorption tests. Based on the findings, the bigger size of plastic added into the brick mixture, the higher compressive strength can be achieved. This is due to the plastic can increase the structural integrity of the cement-sand brick. Also, the bigger size of plastic added into the mixture, lower rate of water absorption was obtained. This may be due to plastic help in reducing the volume of void of the cement-sand brick. Further studies are needed to improve the cement-sand brick production with plastic as admixture material.

Understanding of plasticity size-effect governed mechanical response and incomplete die filling in a microscale double-punch molding configuration

Direct replication of microscale patterns onto metal surfaces by compression molding with patterned dies is used to fabricate metal-based structures for microsystem applications. Micron scale plasticity governs both the mechanical molding response and the geometric fidelity of replicated patterns. Microscale molding replication offers a technologically relevant example in which various plasticity size effects manifest themselves and control the effectiveness of the fabrication process.Microscale compression molding of a single-crystal Al specimen was studied by combining experimentation with conventional and strain gradient plasticity finite element simulations. In the single-punch molding configuration, single rectangular punches with different widths and lengths were used. In the double-punch configuration, two identically-dimensioned rectangular punches with a spacing in between were used. Under single-punch molding at the micron scale, both the absolute punch width as well as the length-to-width ratio affected the characteristic molding pressure. Under double-punch molding, both the measured characteristic molding pressure and the material flow to fill the gap between the two rectangular punches exhibited a significant dependence on the spacing to punch-width ratio and—when this ratio was fixed—on the absolute spacing between punches. The present study elucidates the impact of plasticity size effects on the efficacy of pattern replication by molding at the micron scale.

From Statistical Correlations to Stochasticity and Size Effects in Sub-Micron Crystal Plasticity

Metals in small volumes display a strong dependence on initial conditions, which translates into size effects and stochastic mechanical responses. In the context of crystal plasticity, this amounts to the role of pre-existing dislocation configurations that may emerge due to prior processing. Here, we study a minimal but realistic model of uniaxial compression of sub-micron finite volumes. We show how the statistical correlations of pre-existing dislocation configurations may influence the mechanical response in multi-slip crystal plasticity, in connection to the finite volume size and the initial dislocation density. In addition, spatial dislocation correlations display evidence that plasticity is strongly influenced by the formation of walls composed of bound dislocation dipoles.

An analytical model for the flat punch indentation size effect

An analytical approximation for the indentation size effect (ISE) due to plane strain flat punch nanoindentation is derived. The flat punch ISE differs from that observed for self-similar (pointed) and spherical indenters in a number of ways: (1) the contact area does not change; (2) the contact pressure depends on two length scales not just one (the punch width and the indentation depth); (3) the profile of the punch is not differentially continuous, resulting in singular plastic strain gradients at the sharp edges, such that (4) the shape and connectivity of the plastic zones change with indentation depth and punch width, resulting in (5) changes in the proportion of the deformation accommodated by elasticity and plasticity are important, meaning that a fully elastoplastic model is required. Complete loading-unloading curves are modelled, with the calibration of geometrical parameters from finite element strain gradient plasticity simulations. As the punch width decreases, it is observed that there are increases in the indentation pressure, the relative size of the plastic zone(s) and the elastic component of the deformation. These predictions are found to compare favourably with experimental measurements in the literature. The model is extended to incorporate the consequence of imposing natural limitations on the maximum dislocation density at the edges. It is suggested that observable changes in the plastic zone morphology with the ISE make this an experimentally interesting area for the validation of size effects in plasticity.

Interfacial plasticity governs strain delocalization in metallic nanoglasses

Abstract

An analysis of the influence of grain size on the strength of FCC polycrystals by means of computational homogenization

The effect of grain size on the flow stress of FCC polycrystals is analyzed by means of a multiscale strategy based on computational homogenization of the polycrystal aggregate. The mechanical behavior of each crystal is given by a dislocation-based crystal plasticity model in which the critical resolved shear stress follows the Taylor model. The generation and annihilation of dislocations in each slip system during deformation is given by the Kocks-Mecking model, which was modified to account for the dislocation storage at the grain boundaries. Polycrystalline Cu is selected to validate the simulation strategy and all the model parameters are obtained from dislocation dynamics simulations or experiments at lower length scales and the simulation results were in good agreement with experimental data in the literature. The model is applied to explore the influence of different microstructural factors (initial dislocation density, width of the grain size distribution, texture) on the grain size effect. It is found that the initial dislocation density, ρi, plays a dominant role in the magnitude of the grain size effect and that dependence of flow stress with an inverse power of grain size (σy−σ∞∝dg−x) breaks down for large initial dislocation densities (>1014 m−2) and grain sizes dg> 40 μm in FCC metals. However, it was found that the grain size contribution to the strength followed a power-law function of the dimensionless parameter dgρi for small values of the applied strain (< 2%), in agreement with previous theoretical considerations for size effects in plasticity.

Combining Single- and Poly-Crystalline Measurements for Identification of Crystal Plasticity Parameters: Application to Austenitic Stainless Steel

Crystal plasticity finite element models have been extensively used to simulate various aspects of polycrystalline deformations. A common weakness of practically all models lies in a relatively large number of constitutive modeling parameters that, in principle, would require dedicated measurements on proper length scales in order to perform reliable model calibration. It is important to realize that the obtained data at different scales should be properly accounted for in the models. In this work, a two-scale calibration procedure is proposed to identify (conventional) crystal plasticity model parameters on a grain scale from tensile test experiments performed on both single crystals and polycrystals. The need for proper adjustment of the polycrystalline tensile data is emphasized and demonstrated by subtracting the length scale effect, originating due to grain boundary strengthening, following the Hall–Petch relation. A small but representative volume element model of the microstructure is identified for fast and reliable identification of modeling parameters. Finally, a simple hardening model upgrade is proposed to incorporate the grain size effects in conventional crystal plasticity. The calibration strategy is demonstrated on tensile test measurements on 316L austenitic stainless steel obtained from the literature.

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.

Mechanical properties and plasticity size effect of Fe-6%Cr irradiated by Fe ions and by neutrons

The mechanical behaviour of Fe6%Cr in the un-irradiated, self-ion irradiated and neutron irradiated conditions was measured and compared. Irradiations were performed to the same dose and at the same temperature but to very different damage rates for both methods. The materials were tested using nanoindentation and micromechanical testing, and compared with microstructural observations from Transmission Electron Microscopy (TEM) and Atom Probe Tomography (APT) reported elsewhere. Irradiated and un-irradiated micro-cantilevers with a wide range of dimensions were used to study the interrelationships between irradiation hardening and size effects in small-scale plasticity. TEM and APT results identified that the dislocation loop densities were ∼2.9 × 1022m−3 for the neutron irradiated material and only 1.4 × 1022m−3 for the ion irradiated material. Cr segregation to loops was only found for the neutron-irradiated material. The nanoindentation hardness increase due to neutron irradiation was 3 GPa and that due to ion irradiation 1 GPa. The differences between the effects of the two irradiation types are discussed, taking into account inconsistencies in damage calculations, and the differences in PKA spectra, dose rate and transmutation products for the two irradiation types.