Non-local crystal plasticity model with intrinsic SSD and GND effects

A strain gradient-dependent crystal plasticity approach is presented to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. In order to be capable of predicting scale dependence, the heterogeneous deformation-induced evolution and distribution of geometrically necessary dislocations (GNDs) are incorporated into the phenomenological continuum theory of crystal plasticity. Consequently, the resulting boundary value problem accommodates, in addition to the ordinary stress equilibrium condition, a condition which sets the additional nodal degrees of freedom, the edge and screw GND densities, proportional (in a weak sense) to the gradients of crystalline slip. Next to this direct coupling between microstructural dislocation evolutions and macroscopic gradients of plastic slip, another characteristic of the presented crystal plasticity model is the incorporation of the GND-effect, which leads to an essentially different constitutive behaviour than the statistically stored dislocation (SSD) densities. The GNDs, by their geometrical nature of locally similar signs, are expected to influence the plastic flow through a non-local back-stress measure, counteracting the resolved shear stress on the slip systems in the undeformed situation and providing a kinematic hardening contribution. Furthermore, the interactions between both SSD and GND densities are subject to the formation of slip system obstacle densities and accompanying hardening, accountable for slip resistance. As an example problem and without loss of generality, the model is applied to predict the formation of boundary layers and the accompanying size effect of a constrained strip under simple shear deformation, for symmetric double-slip conditions.     

Additions of substituted phenylthiyl radicals to substituted α-methylstyrenes : Ground state and transition state electronic effects

The radical addition of substituted thiophenols to α-methylstyrene and substituted α-methylstyrenes has been investigated at 70°. Relative reactivities of pairs of thiophenols competing with individual alkenes can be utilized to obtain Hammett correlations. The interplay of substituent effects in alkene and thiyl radical leads to examples of non-linear rho values. Rationales for this behavior will be offered in terms of variable contributions from ground state and transition state electronic factors as well as in terms of possible mechanistic changes.     

Pyridylpyrrolides as alternatives to cyclometalated phenylpyridine ligands: synthesis and characterization of luminescent zinc and boron pyridylpyrrolide complexes

The synthesis, structure, and properties of six luminescent pyridylpyrrolide complexes and the first structural characterization of pyridylpyrrolide metal complexes are reported. A series of new zinc complexes, bis(pyridylpyrrolyl)zinc, (R2PyrPy)2Zn (R = Me, Et, iPr, tBu, and Ph), that vary in their substituents on the pyrrole ring (Me, Et, iPr, tBu, and Ph), were prepared. Pyrrole substitution produced small structural changes in the complexes and affected the fluorescence properties very little. The zinc complexes were found to be luminescent, emitting at 495 nm (Phi = 0.32, 0.32 0.31, 0.19 and 0.57, respectively). A boron analog, (Me2PyrPy)BF2, was prepared and was found to share the luminescent properties with the zinc complexes, emitting at 505 nm (Phi = 0.22), but not their water-sensitivity. A total of four crystal structures are reported, tBu2PyrPyH, (Me2PyrPy)2Zn, (tBu2PyrPy)2Zn, and (Me2PyrPy)BF2. tBu2PyrPyH crystallizes as a doubly hydrogen bonded dimer with non-coplanar pyridine and pyrrole rings. The solid-state structures of (Me2PyrPy)2Zn and (tBu2PyrPy)2Zn revealed that despite the large change in steric bulk, the two compounds have very similar structures. The structure of (Me2PyrPy)BF2 showed changes that are expected with the interaction between a smaller atom (B as compared to Zn). Molecular orbital calculations were performed on Me2PyrPyH, (Me2PyrPy)BF2, and (Me2PyrPy)2Zn using Gaussian 98 methods. It was found that the main transition (HOMO-LUMO) for all three molecules is a pi-->pi* transition and that in the inorganic complexes, the metal atom (zinc or boron) present has very little effect on transition, evidence that the optical properties are largely ligand based and that the B or Zn atom's main effect is lowering of the LUMO relative energy.     

Quantification of Three-Dimensional Surface Deformation using Global Digital Image Correlation

A novel method is presented to experimentally quantify evolving surface profiles. The evolution of a surface profile is quantified in terms of in-plane and out-of-plane surface displacements, using a Finite Element based Global Digital Image Correlation procedure. The presented method is applied to a case study, i.e. deformation-induced surface roughening during metal sheet stretching. The surface roughness was captured in-situ using a confocal optical profiler. The Global Digital Image Correlation method with linear triangular finite elements is applied to track the three-dimensional material movement from the measured height profiles. The extracted displacement fields reveal the full-field kinematics accompanying the roughening mechanism. Local deviations from the (average) global displacements are the result of the formation, growth, and stretching of hills and valleys on the surface. The presented method enables a full-field quantitative study of the surface height evolution, i.e. in terms of tracked surface displacements rather than average height values such as Root-Mean-Square or height-height correlation techniques. However, the technique does require that an initial surface profile, i.e. contrast, is present and that the contrast change between two measurements is minimal.     

Direct Stress-Strain Measurements from Bulged Membranes Using Topography Image Correlation

This paper discusses an experimental method to characterize thin films as they are encountered in micro-electronic devices. The method enables the measurement of the stress and strain of pressure deflected bulged membranes without using a priori defined bulge equations. An enrichment to the Global Digital Image Correlation method is detailed to capture the membrane strain and curvature while robustly dealing with acquisition noise. The accuracy of the method is analyzed and compared to the standard bulge test method. The method is applied to a proof of principle experiment to investigate its applicability and accuracy. Additionally, it is shown for two experimental cases that the method provides accurate results, although the bulge equations do not hold.     

A Uni-Axial Nano-Displacement Micro-Tensile Test of Individual Constituents from Bulk Material

For both single-phase and multiphase metallic materials, it is necessary to understand the mechanical behavior on the grain-size scale in detail to get information that is not obtainable from macro-scale mechanical characterizations. This paper presents a methodology for uniaxial tensile testing of micro-specimens isolated from a bulk material. The proposed concept of multiple parallel micro-tensile specimens at the tip of a macro-sized wedge reduces the alignment work and offers an easy way for specimen handling. The selection of site-specific specimens is based on detailed microstructural and crystallographic characterization. Three kinds of representative specimens are presented to illustrate the wide range of application of the methodology for a variety of materials. Accurate, reproducible measurement of force (2.5 μN resolution) and displacement (~10 nm resolution) is demonstrated, while accurate alignment (in-plane rotational and out-of-plane tilt misalignment of <0.2°) limits the stress due to bending to <0.2% of the imposed uni-axial stress. Combined with detailed material characterization on both sides of the micro-specimens, this method yields detailed insights into the micro-mechanics of bulk materials which is hard to obtain from traditional macro-mechanical tests.     

An implicit tensorial gradient plasticity model – Formulation and comparison with a scalar gradient model

Many rate-independent models for metals utilize the gradient of effective plastic strain to capture size-dependent behavior. This enhancement, sometimes termed as “explicit” gradient formulation, requires higher-order tractions to be imposed on the evolving elasto-plastic boundary and the resulting numerical framework is complicated. An “implicit” scalar gradient model was thus developed in Peerlings [Peerlings, R.H.J., 2007. On the role of moving elastic–plastic boundaries in strain gradient plasticity. Model. Simul. Mater. Sci. Eng. 15, 109–120] that has only C⁰ continuity requirements and its implementation is straightforward. However, both explicit and implicit scalar gradient models can be problematic when the effective plastic strains do not have smooth profiles. To address this limitation, an implicit tensorial gradient model is proposed in this paper based on the generalized micromorphic framework. It is also demonstrated that the scalar and tensorial implicit gradient models give similar results when the effective plastic strains fluctuate smoothly.     

Non-local energetics of random heterogeneous lattices

In this paper, we study the mechanics of statistically non-uniform two-phase elastic discrete structures. In particular, following the methodology proposed in Luciano and Willis (2005) [Journal of the Mechanics and Physics of Solids 53, 1505-1522], energetic bounds and estimates of the Hashin-Shtrikman-Willis type are developed for discrete systems with a heterogeneity distribution quantified by second-order spatial statistics. As illustrated by three numerical case studies, the resulting expressions for the ensemble average of the potential energy are fully explicit, computationally feasible and free of adjustable parameters. Moreover, the comparison with reference Monte-Carlo simulations confirms a notable improvement in accuracy with respect to approaches based solely on the first-order statistics.     

Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation

A strain gradient dependent crystal plasticity approach is used to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. Material points are considered as aggregates of grains, subdivided into several fictitious grain fractions: a single crystal volume element stands for the grain interior whereas grain boundaries are represented by bi-crystal volume elements, each having the crystallographic lattice orientations of its adjacent crystals. A relaxed Taylor-like interaction law is used for the transition from the local to the global scale. It is relaxed with respect to the bi-crystals, providing compatibility and stress equilibrium at their internal interface. During loading, the bi-crystal boundaries deform dissimilar to the associated grain interior. Arising from this heterogeneity, a geometrically necessary dislocation (GND) density can be computed, which is required to restore compatibility of the crystallographic lattice. This effect provides a physically based method to account for the additional hardening as introduced by the GNDs, the magnitude of which is related to the grain size. Hence, a scale-dependent response is obtained, for which the numerical simulations predict a mechanical behaviour corresponding to the Hall-Petch effect. Compared to a full-scale finite element model reported in the literature, the present polycrystalline crystal plasticity model is of equal quality yet much more efficient from a computational point of view for simulating uniaxial tension experiments with various grain sizes.