Length Scale Dependent Deformation Research Articles

A method to extract slip system dependent information for crystal plasticity models

A tool to implement a length scale dependency to classical crystal plasticity simulations is presented. Classical crystal plasticity models do not include a size effect; therefore, the size of the grain does not influence the simulated deformation. Classical crystal plasticity advancements have been through the inclusion of stress or strain gradient based constitutive models to improve the simulation of length scale dependent deformation. However, this tool presents an alternative to implementing a length scale, where the influence of slip pile-up in the form of dislocations at grain boundaries as a potential to explaining the Hall-Petch effect in materials. This is achieved by calculating the slip distance in adjacent grains for each slip system, by assuming the total slip length spans the grain in the slip direction. These calculations can occur in two ways. The first is the analysis occurs at the start of the simulation, therefore, only occurs once. If this approach is used, the computational cost of this tool is minute. However, if the simulations consider large deformations, during which it is expected that the grains are going to undergo large rotations, then it would be advantageous to the have the tool recalculate the information during the analysis. Consequently, the computational cost would depend on the resolution of the modelled geometry, the number of grains, and the number of slip systems. The tool also provides a capability to develop constitutive models based on complex grain boundary features which can be implemented in classical crystal plasticity models and gradient based crystal plasticity models. The described calculation process is implemented through a Fortran subroutine, which has been designed to be easily used in crystal plasticity simulations. The presented tool also includes Python code designed to link with microstructures built using DREAM.3D to extract the required input data to the Fortran subroutine.The proposed tool is not limited to classical crystal plasticity formulations, instead the data extracted and outputted from the Fortran subroutine can be used to serve alternative purposes in both stress and strain gradient crystal plasticity models.The proposed tool can be modified to extract additional data to that presented.The slip distance in the adjacent grain, the distance from the grain boundary of the current calculation point, and the interaction between slip systems between grains can be used in any crystal plasticity constitutive models.

Length-scale dependent deformation, strengthening, and ductility of fcc/fcc Ni/Al nanolaminates using micropillar compression testing

The deformation and strengthening behaviors of face-centered cubic/face-centered cubic (fcc/fcc) nickel (Ni)/aluminum (Al) nanolaminates were systematically investigated in uniaxial compression tests using micropillars with a varied range of individual layer thickness h from 5 nm to 100 nm. The deformation behavior of micropillar samples of Ni/Al nanolaminates was strongly dependent on the individual layer thickness of Ni and Al, where at larger h the deformation of micropillars took place first by plastic deformation of the Al layers and proceeded to dislocation pileup–based Hall–Petch (H-P) strengthening, which further nucleated in the Ni layers. The deformation behavior of the Ni/Al nanolaminates transitioned from dislocation-dominated homogeneous co-deformation with multiple shearing in Ni and Al layers and grain boundary–mediated massive fractures in the Ni layers at larger h to stress-concentrated broken interfaces and valleys with plastic barreling due to layer shearing and smaller fractures in the Ni and Al layers at smaller h. With decreasing h from 100 nm down to 5 nm, the Ni/Al micropillars exhibited a gradual transition from lower to higher strain hardening, and the strain-hardening rate reached a peak at h = 20 nm; while it started declining with further decreasing of h. The yield strength (σ0.2%) and flow strength (σ8%) of the Ni/Al micropillars reached the peak of ~1.93 GPa and ~2.35 GPa, respectively, with decreasing h to 10 nm. The confined layer slip (CLS) strengthening mechanism operated well at h = 10 nm, whereas H-P strengthening model was applicable for h = 20–100 nm, and surprisingly the strengthening at h = 5 nm was independent of h. Interestingly, significant strain softening was observed at h = 5 nm due to the severe plastic deformation at the broken interfaces, interfacial sliding of layers, and defects related to the presence of intermixed Ni and Al layers at the interface, and valleys between the islands of stacked constituent layers.

Geometry- and Length Scale-Dependent Deformation and Recovery on Micro- and Nanopatterned Shape Memory Polymer Surfaces.

Micro- and nanoscale surface textures, when optimally designed, present a unique approach to improve surface functionalities. Coupling surface texture with shape memory polymers may generate reversibly tuneable surface properties. A shape memory polyetherurethane is used to prepare various surface textures including 2 μm- and 200 nm-gratings, 250 nm-pillars and 200 nm-holes. The mechanical deformation via stretching and recovery of the surface texture are investigated as a function of length scales and shapes. Results show the 200 nm-grating exhibiting more deformation than 2 μm-grating. Grating imparts anisotropic and surface area-to-volume effects, causing different degree of deformation between gratings and pillars under the same applied macroscopic strain. Full distribution of stress within the film causes the holes to deform more substantially than the pillars. In the recovery study, unlike a nearly complete recovery for the gratings after 10 transformation cycles, the high contribution of surface energy impedes the recovery of holes and pillars. The surface textures are shown to perform a switchable wetting function. This study provides insights into how geometric features of shape memory surface patterns can be designed to modulate the shape programming and recovery, and how the control of reversibly deformable surface textures can be applied to transfer microdroplets.

On couple-stress elasto-plastic constitutive frameworks for glassy polymers

Various experimental studies have revealed length scale dependent deformation of different materials at micron and sub-micron length scales. In metals, such length scale dependent deformations are considered to be associated with geometrically necessary dislocations arising from an increase in strain gradients related to non-uniform plastic deformation. Recent experiments, however, have shown that the nature of length scale dependent deformation in polymers is quite different from metals as in polymers size effects have been observed in pure elastic as well as in elasto-plastic deformation. It is shown in this study that similar to metals, size effects in polymers can be associated with an increase in higher order displacement gradients with decreasing length scale. However, the experimental results discussed here reveals that, in contrast to metals, these higher order displacement gradients are mainly of elastic nature even when glassy polymers deform elasto-plastically. Taking the effects of these elastic higher order displacement gradients into account, a couple-stress theory is developed to predict size effect in glassy polymers with elasto-plastic deformation.

On thresholds in the indentation size effect of polymers

Length scale-dependent deformation in polymers has been observed by various research groups in the last years. Here, the indentation size effect of polymers is studied where the hardness increases with decreasing indentation depth. As a model polymer, polydimethylsiloxane (PDMS) of two different cross-link densities is studied as it has been found in previous studies to exhibit very strong indentation size effects. It is found that there is an upper threshold in the indentation depth range of 17.9 and 41.6 μm, respectively, below which the indentation size effect can be observed and above which the hardness does not change with the indentation depth. Similar phenomena can be determined for other polymers, however, at much smaller length scales.

Length scale dependent deformation in natural rubber

ABSTRACTStrong length scale dependent deformation has been previously observed in the elastomer polydimethylsiloxane by indentation type experiments at micro‐ to nanometer length scales with a sharp conical tip. To examine if other nonsilicone based elastomers exhibit similar length scale dependent deformation behavior, natural rubber has been chosen in this study. Performing indentation type tests with a nanoindentation system, the universal hardness and the elastic modulus are determined at different probing depths ranging from about 90 to 5 μm to characterize length scale dependent deformation behavior in natural rubber. The testing with a Berkovich tip resulted in an amazing increase in the universal hardness with decreasing probing depth indicating that the deformation mechanisms at the micrometer length scales are significantly different as compared to those at the macroscopic length scales. The observed length scale dependent deformation is associated with an increase in rotation gradients with decreasing probing depth. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 42683.

Axisymmetric couple stress elasticity and its finite element formulation with penalty terms

Length scale dependent deformation in polymers has been reported in the literature in different experiments at the micron and submicron length scales. Such length scale dependent deformation behavior can be described using higher order gradient theories. A numerical approach for axisymmetric problems is presented here where a couple stress elasticity theory is employed. For the numerical formulation, a penalty finite element approach is proposed and implemented with C0 axisymmetric elements. In this approach, rotations are introduced as nodal variables independent of nodal displacements, and the penalty term is used to minimize the difference in rotations determined from nodal displacements and nodal rotations. Numerical simulations are performed on different examples to assess the performance of the suggested approach. In particular, a circular cylinder with spherical inclusions and the interaction of the inclusion with the boundary are studied. It is found that with the length scale parameter the distance with which the free boundary affects the stress state of the inclusion increases as well.

Length scale-dependent deformation behavior of nanolayered Cu/Zr micropillars

The mechanical behavior of incoherent Cu/Zr multilayers was studied in uniaxial compression experiments using micropillars with individual layer thicknesses (h) ranging from 5 to 100nm. The deformation behavior of these micropillars are size dependent, transiting from dislocation dominated symmetrical slip at large h to shear localization induced by asymmetric slip and grain boundary mediated deformation at small h. During compression studies the multilayer micropillars exhibit a transition from strain hardening to shear softening at small h, and work softening at greater h. A maximum strain hardening rate is observed at a critical h of 20nm, which was explained in terms of a transition from dislocation interactions to cross-slip of dislocations. The mechanical strength of the micropillars is also dependent on h, which was quantitatively analyzed using the confined layer slip model. In addition, the influence of pillar diameter on the mechanical behavior is also investigated. The effect of extrinsic size on the deformation mechanisms is discussed with respect to the intrinsic size effect with variation in h.

Toward Understanding Size-Dependent Plasticity of Nanolayered Metallic Composites

Deformation and fracture behaviors of Cu/Au and Cu/Cr multilayered composites with different length scales were investigated by using instrumented-indentation and three-point-bending methods. It is found that with decreasing the length scale (layer thickness and grain size), both multilayers tend to produce plastic instability via localized shear banding under indentation load in spite of high hardness they have, while quasi-brittle fracture under relatively low fracture stress prevails at three-point-bending test. Especially, the compressive flow stress and the tensile fracture stress exhibit inverse trend of variation with the length scales, which implies different mechanisms. Such length scale dependent deformation and plasticity were analyzed concerning size and interface effects under different stress state.

543 Ni 基スーパーアロイの寸法依存性変形挙動のモデル化と数値シミュレーション

543 Ni 基スーパーアロイの寸法依存性変形挙動のモデル化と数値シミュレーション