Mutasem A. Shehadeh

Multiscale dislocation dynamics simulations of shock-induced plasticity in small volumes

Multiscale dislocation dynamics plasticity (MDDP) was used to investigate shock-induced deformation in monocrystalline copper. In order to enhance the numerical simulations, a periodic boundary condition was implemented in the continuum finite element (FE) scale so that the uniaxial compression of shocks could be attained. Additionally, lattice rotation was accounted for by modifying the dislocation dynamics (DD) code to update the dislocations’ slip systems. The dislocation microstructures were examined in detail and a mechanism of microband formation is proposed for single- and multiple-slip deformation. The simulation results show that lattice rotation enhances microband formation in single slip by locally reorienting the slip plane. It is also illustrated that both confined and periodic boundary conditions can be used to achieve uniaxial compression; however, a periodic boundary condition yields a disturbed wave profile due to edge effects. Moreover, the boundary conditions and the loading rise time show no significant effects on shock–dislocations interaction and the resulting microstructures. MDDP results of high strain rate calculations are also compared with the predictions of the Armstrong–Zerilli model of dislocation generation and movement. This work confirms that the effect of resident dislocations on the strain rate can be neglected when a homogeneous nucleation mechanism is included.

On the ultra-high-strain rate shock deformation in copper single crystals: multiscale dislocation dynamics simulations

Multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper single crystals that have undergone shock loading at high strain rates ranging from 1u2009×u2009106 to 1u2009×u20091010u2009s−1. Plasticity mechanisms associated with both the activation of pre-existing dislocation sources and homogeneous nucleation of glide loops are considered. Our results show that there is a threshold strain rate of 108u2009s−1 at which the deformation mechanism changes from source activation to homogeneous nucleation. It is also illustrated that the pressure dependence on strain rate follows a one-fourth power law up to 108u2009s−1 beyond which the relationship assumes a one-half power law. The MDDP computations are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models.

On the homogeneous nucleation and propagation of dislocations under shock compression

Abstract The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.

Impact of Plastic Hinge Properties on Capacity Curve of Reinforced Concrete Bridges

Pushover analysis is becoming recently the most practical tool for nonlinear analysis of regular and irregular highway bridges. The nonlinear behaviour of structural elements in this type of analysis can be modeled through automated-hinge or user-defined hinge models. The nonlinear properties of the user-defined hinge model for existing highway bridges can be determined in accordance with the recommendations of the Seismic Retrofit Manual by the Federal Highway Administration (FHWA-SRM). Finite element software such as the software SAP2000 offers a simpler and easier approach to determine the nonlinear hinge properties through the automated-hinge model which are determined automatically from the member material and cross section properties. However, the uncertainties in using the automated-hinge model in place of user-defined hinge model have never been addressed, especially for existing and widened bridges. In response to this need, pushover analysis was carried out for four old highway bridges, of which two were widened using the same superstructure but with more attention to seismic detailing requirements. The results of the analyses showed noticeable differences in the capacity curves obtained utilizing the user-defined and automated-hinge models. The study recommends that bridge design manuals clearly ask bridge designers to evaluate the deformation capacities of existing bridges and widened bridges using user-defined hinge model that is determined in accordance with the provisions of the FHWA-SRM.

Modelling the rate and temperature-dependent behaviour and texture evolution of the Mg AZ31B alloy TRC sheets

Abstract In this work, the mechanical behaviour and texture evolution of AZ31B magnesium alloy under uniaxial tensile testing are investigated at different strain rates and temperatures. A crystal plasticity model is developed and calibrated to predict the mechanical response of the AZ31B at different temperatures and strain rates. The model results show that the relative activity of the pyramidal slip increases with increasing temperature, reaching a maximum activity at 200 °C. In order to achieve the continuous increase in the relative activity of the pyramidal slip as reported in the literature, a grain boundary sliding mechanism is implemented in the crystal plasticity framework. The incorporation of the grain boundary sliding at elevated temperatures results in considerable improvement in the model’s capabilities for prediction of yielding, hardening and texture evolution.

Application of Homogenization Theory to Study the Mechanics of Cortical Bone

Homogenization theory is utilized to study the effect on the axial stiffness of secondary osteons in cortical bone due to the presence of micro porous features (e.g., lacunae, canaliculi clusters, and Haversian canals). Specifically, 2 geometric characteristics were used to describe these features within the secondary osteons: volume fraction (% porosity) and shape (circular- or elliptical-shaped). Such information was determined for each individual porous feature from an image segmentation methodology developed earlier by Hage and Hamade. For each feature, aspect ratio vectors (or arrays of ratios for each individual porous feature) were used to classify each pore inhomogeneity as cylindrical, elliptical or irregular shape. Two prominent homogenization theories were used: the Mori-Tanaka (MT) and the generalized self-consistent method (GSCM). Using the results of image segmentation, it was possible to calculate the respective Eshelby tensors of each porous feature. To calculate the isotropic stiffness tensors for matrix (Cm) and pores (Cp) the Young’s modulus and Poisson’s ratio for the matrix (Em, νm) were assigned as obtained from literature and as those of blood (Ep=10MPa, νp= 0.3), respectively. The effective elastic stiffness tensors (C*) for the secondary osteons were obtained from which axial Young’s modulus was obtained as function of volume fraction (% porosity) of each pore type and their individual shapes. The normalized axial Young’s modulus was found to 1) significantly decrease with increasing volume fraction (%) of porosity and 2) for the same % porosity, to slightly decrease (increase) with increasing ratio of circular-shaped to elliptical-shaped (elliptical-shaped to circular-shaped) porous features. These findings were validated using experimental micro-indentation study performed on secondary osteons.Copyright