P. J. Guruprasad

A phenomenological model of size-dependent hardening in crystal plasticity

A phenomenological model of plastic deformation is proposed, which captures the size-dependence of plastic flow strength and work-hardening in pure FCC crystalline materials. Guided by discrete dislocation dynamics analyses, the treatment is based on two structural variables determining the mechanical state of the material. A complete description of plastic behaviour is achieved, giving two inherently different statements for the evolution of structure, supplemented by a new kinetic equation, which specifies the hardening law in differential form at fixed structure. Evolution of the first state variable is set by phenomenology; it accounts for the cardinal bulk phenomena of athermal hardening and dynamic recovery, in addition to geometric storage. The second state variable is kinematically determined so that an evolution equation need not be formulated explicitly in rate form. The model formulation leaves the classical treatment of dynamic recovery unaltered. However, since there is virtually no experimental data on the temperature and strain-rate dependence of plastic flow at the micron scale, emphasis is laid on athermal behaviour. In this limit, the model equations are integrated, following specified strain paths to give the flow strength at the current structure. Model predictions are assessed through comparison with results from discrete dislocation analyses of geometrically similar crystals subject to compression.

Direct Experimental Observations on Concurrent Microstructure and Magnetic Property Developments in Non-Grain Oriented Electrical Steel

Non-grain oriented electrical steel, with minor in-grain orientation gradients, was subjected to interrupted tensile deformations and concurrent microtexture, magnetic property and residual stress measurements. After the upper yield point, clear signatures of mechanical stress relief were observed. Changes in orientation gradients led to annihilation of low-angle (1 to 3 deg) boundaries. Prior deformation compressive residual stresses became tensile and magnetic properties improved. Beyond an optimum true strain of 0.01, this boundary annihilation ceased, compressive stresses were generated, and magnetic properties degraded.

Relating Residual Stress and Substructural Evolution During Tensile Deformation of an Aluminum-Manganese Alloy

Interrupted tensile tests were coupled with ex situ measurements of residual stress and microtexture. The residual stress quantification involved measurements of six independent Laue spots and conversion of the interplanar spacings to the residual stress tensor. A clear orientation-dependent residual stress evolution emerged from the experiments and the numerical simulations. For the orientations undergoing negligible changes in ρGND (density of geometrically necessary dislocation), the residual stress developments appeared to be governed by the elastic stiffness of the grain clusters. For the others, the evolution of the residual stress and ρGND exhibited a clear orientation-dependent scaling.

Modeling of active fiber composite for delamination sensing

In order to demonstrate the feasibility of Active Fiber Composites (AFC) as sensors for detecting damage, a pretwisted strip made of AFC with symmetric free-edge delamination is considered in this paper. The strain developed on the top/bottom of the strip is measured to detect and assess delamination. Variational Asymptotic Method (VAM) is used in the development of a non-classical non-linear cross sectional model of the strip. The original three dimensional (3D) problem is simplified by the decomposition into two simpler problems: a two-dimensional (2D) problem, which provides in a compact form the cross-sectional properties using VAM, and a non-linear one-dimensional (1D) problem along the length of the beam. This procedure gives the non-linear stiffnesses, which are very sensitive to damage, at any given cross-section of the strip. The developed model is used to study a special case of cantilevered laminated strip with antisymmetric layup, loaded only by an axial force at the tip. The charge generated in the AFC lamina is derived in closed form in terms of the 1D strain measures. It is observed that delamination length and location have a definite influence on the charge developed in the AFC lamina. Also, sensor voltage output distribution along the length of the beam is obtained using evenly distributed electrode strip. These data could in turn be used to detect the presence of damage.

Orientation-Dependent Developments in Misorientation and Residual Stress in Rolled Aluminum: The Defining Role of Dislocation Interactions

AbstractOrientation-dependent developments in misorientation and residual stress, in rolled aluminum, were quantified experimentally and simulated numerically. The latter involved analysis using a crystal plasticity finite element model, accounting for anisotropies in slip system hardening but neglecting near-neighbor interactions, and discrete dislocation dynamics of the single crystals. Both were successful in capturing the experimental patterns of orientation dependence. Numerical simulations, without slip transfer across the neighboring grains, thus established the defining role of dislocation interactions in establishing orientation-sensitive microstructural evolution.

WAVE PROPAGATION IN THIN PRETWISTED ANISOTROPIC STRIPS

This paper presents an asymptotically exact cross-sectional framework coupled with spectrally formulated one-dimensional (1-D) finite element model for the study of wave propagation in thin pre-twisted anisotropic strips. The cross-sectional model used here is based on the dimensional reduction of laminated shell theory to nonlinear 1-D theory using the variational asymptotic method (VAM). A linearized version of this model (zeroth-order asymptotic analysis) is used in the development of a 1-D spectral finite element (SFE) for a pre-twisted strip. Within this modeling framework, an exact dynamic stiffness matrix is derived, as the governing equations are solved using the exact interpolating functions in frequency-wavenumber domain. Compared to regular three-dimensional (3-D) finite element (FE) analysis, this model requires less computation cost since single element is sufficient to capture the frequency response of the strips. For numerical validation of the model, the natural frequencies of the strip without delamination are compared to the data available in literature. Finally, the developed framework is used to simulate wave propagation due to modulated sinusoidal pulse input.

Evolution of geometrically necessary dislocation density from computational dislocation dynamics

This paper presents a method for calculating GND densities in dislocation dynamics simulations. Evolution of suitably defined averages of GND density as well as maps showing the spatial nonuniform distribution of GNDs are analyzed under uniaxial loading. Focus is laid on the resolution dependence of the very notion of GND density, its dependence upon physical dimensions of plastically deformed specimens and its sensitivity to initial conditions. Acknowledgments Support from the National Science Foundation (CMMI-0748187) is gratefully acknowledged.

Closed-form non-linear sectional analysis in the presence of delamination

A non-linear sectional analysis is presented for a composite strip with small pretwist in the presence of delamination. Variational Asymptotic Method (VAM)is used as a tool for dimensional reduction of laminated shell theory to a non-linear one-dimensional (1D)theory. Study is performed to investigate the influence of delamination on trapeze effect, which is important in rotor blades. As the developed procedure gives the nonlinear stiffness of the strip at any given cross-section,degradation in the non-linear stiffness due to the presence of delamination can be used as data to detect damage. Hence the developed model has a potential application in structural health monitoring of rotorcraf flexbeams.