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A phenomenological hardening model based on the extended Voce law is proposed to capture the plastic flow of a third generation aluminium-lithium alloy. The model includes a simple precipitation law, which accounts for pre-ageing plastic deformation, and a hardening law that accounts for hardening of the matrix, and for the interaction of matrix glide dislocations with anisotropic and isotropic precipitates. Flow stress evolution in solution treated, underaged, and peak-aged samples is measured through uniaxial tensile tests on specimens cut at 0∘, 45∘, and 90∘ to the rolling direction. The measured flow stress evolution in all the tempers is captured well by the model. Model parameters offer insights into the sub-structural evolution that accompanies plastic deformation.

The strength of metal matrix composites shows wide scatter on account of variability in the strengths of individual fibres. The relationship between the strength distribution of the fibres, and that of the composite is also affected by the non-linear matrix and fibre/matrix interfacial responses. The present study aims to describe the strength distribution of 2D and 3D commercial Ti/SiC composites. This is accomplished by performing Monte Carlo failure simulations of these composites, comprised of up to 128 fibres. A detailed deformation theory based model, developed and validated against experimental data in previous work, is used to calculate load redistribution in the course of each simulation. The empirical composite strength distribution obtained from the simulations follows weakest-link scaling. A stochastic model for the clustered propagation of fibre breaks, akin to a model proposed for polymer matrix composites in the literature, captures the empirical weakest-link strength distribution. A scaling relationship is derived between the composite strength and composite size for a number of reliability levels.

A detailed study concerning a novel, dynamic control strategy for mitigating thermoacoustic instability in a swirl-stabilized lean premixed, laboratory combustor configuration is presented in this paper. The mitigation strategy is realized by rotating the otherwise static swirler, which is primarily meant for stabilizing the lean premixed flame. The proposed strategy is tested over a range of bulk flow velocities, mixture equivalence ratios, and swirler rotation rates for validating the robustness of this concept. A prominent reduction in the fundamental acoustic mode amplitude by about 25dB is observed with this control technique for the cases that are studied. The physical mechanism responsible for the instability mitigation due to the rotating swirler is investigated by observing the distinct changes associated with the reacting flowfield using particle image velocimetry. An attempt is made to probe into the self-excited flame dynamics using high-speed intensified, chemiluminescence imaging and identifying the instability driving source locations from a spatial Rayleigh indices map. The rotating swirler induces vortex breakdown and increased turbulence intensity to decimate strongly positive Rayleigh indices regions (and eventually the acoustic energy source) to render quiet instability mitigated swirling flames.

The classical Chin-Hosford-Mendorf (CHM) criterion for deformation twinning is used widely in polycrystal plasticity computer simulations. It assumes that twin nuclei are abundant, and that twin propagation and growth control the realisation of deformation twins. However, recent experimental studies reported in the literature have found that nominally unfavourable twin systems are activated in grains. This has been attributed to twin nucleation in some of the unfavourable twinning systems with low Schmid factors, and its suppression in some of the nominally more favourable ones. Presently, this explanation is quantitatively examined. Full and relaxed constraint versions of the Taylor, ALAMEL, and binary tree based models, all implementing the CHM criterion are used to simulate uniaxial compression of a zirconium billet. Model predictions are compared with experimentally measured twinning statistics reported in the literature for a Zr polycrystal. The ALAMEL and binary tree models, which explicitly represent intergranular interactions, are found to capture the twinning statistics well. These observations suggest that the CHM criterion is adequate to capture twinning in Zr, provided intergranular interactions are represented in the model used to interpret the experiments.

A shear-lag and deformation-theory based model for a metal matrix composite reinforced by continuous unidirectional fibres is proposed. The model accounts for fibre and matrix cracking, matrix plasticity, and fibre-matrix interfacial sliding through seven characteristic non-dimensional parameters, which combine geometric, phase and interface properties. It allows arbitrary tensile loading and unloading history along the fibre direction, and predicts the history-dependent elastoplastic displacement, strain, and stress fields in all the fibre and matrix elements. Broken elements may be present initially, or form during the imposed loading history. Non-linear one-dimensional governing differential and algebraic equations are formulated on the basis of the model. A computationally fast solution methodology based on pseudospectral collocation is implemented. The present model is employed to predict the elastic strain profiles in a Ti/SiC composite tape near pre-existing breaks. These predictions agree well with experimental measurements reported in the literature.

Although high-temperature material response is known to be history-dependent, many models of creep crack growth assume the history-independent Norton constitutive law. Even so, these models capture the experimentally observed creep crack growth by adjusting only the damage model. This is explained presently by showing that the damage evolution ahead of a stationary crack in a material obeying a history-dependent unified creep-plasticity constitutive law due to Robinson can be 'fit' by simply adjusting the damage parameters in a model implementing Norton's law. The implication of this result to the case of propagating cracks is discussed. � 2015 Elsevier Ltd.

A minimum plastic power principle is proposed for a rigid-viscoplastic crystalline domain subdivided into two sets of lath-shaped regions, called bands. The lattice orientation in each band is assumed uniform and to differ infinitesimally from that in the other band. The proposed minimum principle yields the slip activity in the bands and semi-analytical expressions for the misorientation axis and orientation of band boundaries. These band boundary characteristics are predicted for f.c.c. lattice orientations near the ideal rolling texture components. Surprisingly, it found that the predicted band boundary characteristics closely match those of microstructural features called cell block boundaries reported in the experimental literature, except when the dislocations of activated slip systems are known to interact very strongly. This suggests that except when precluded by strong dislocation interactions, continuum extremum principles may also govern microstructural characteristics. � 2015 Elsevier Ltd. All rights reserved.

Friction stir welds (FSWs) can be considered as an ensemble of elements of material with composite microstructures connected in series. In the present study, bead-on-plate FSW runs were made on an Al–Cu–Li alloy with varying rotation speeds ranging from 400 to 800 rpm. Microstructure of the FSW region was investigated by using optical microscope, electron backscattered diffraction (EBSD) and transmission electron microscope (TEM). Thermal stability of various precipitates was evaluated with differential scanning calorimetry (DSC) measurements. Strength variation across FSW cross sections was mapped by microhardness measurements. Average as well as local mechanical properties were evaluated using a digital image correlation (DIC) technique. Irrespective of the process parameters, FSW samples showed similar tensile and strain hardening behaviour along with serrations in stress-strain curves while local strength values showed increasing trend with rotation speed. The FSW alloy produced at intermediate rotation speed exhibited different mechanical behavior and is correlated with the resultant substantial changes in the microstructure. Strain localization occurred at the boundary of nugget zone and thermo-mechanically affected zone which led to failure of the FSW tensile specimens within weld regions. Fractography investigation revealed that the failure is initiation controlled, that is void nucleation at coarse precipitate-matrix interfaces.

Grains in f.c.c. polycrystals deform non-uniformly even under imposed homogeneous deformation and subdivide into domains of different lattice orientations. Intense non-uniformity of grain deformation produces substructural features called deformation bands and shear bands, wherein large deviations from the average lattice orientation and/or slip localization occur. Using a model of grain banding, subdivision of pure copper grains initially oriented along the �

A rigid-plastic rate-independent crystal plasticity model capable of capturing banding in single crystals subjected to homogeneous macroscopic deformation is proposed. This model treats the single crystal as a ‘stack of domains’. Individual domains deform homogeneously while maintaining velocity and traction continuity with their neighbors. All the domains collectively accommodate the imposed deformation. The model predicts lattice orientation evolution, slip distribution, strain localization and band orientation in copper single crystals with imposed plane strain deformation. In quantitative agreement with experimental observations reported in the literature, macroscopic shear banding and regular deformation banding are predicted in initially copper and rotated cube oriented single crystals, respectively, while banding is not predicted in initially Goss oriented single crystals. The model does not, however, predict the experimentally observed orientation of smaller scale dislocation boundaries such as dense dislocation walls.

Grains in f.c.c. polycrystals that accommodate imposed deformation purely byslip processes develop a multi-scale dislocation substructure that evolves with deformation.When the polycrystal is subjected to rolling deformation or to channel-die compression, oneof the elements of this substructure, called cell block boundaries, are widely reported to alignparallel to the transverse direction and close to the macroscopic plane of maximum shear. Thisobservation is explained based on standard rate-independent crystal plasticity augmented bythree hypotheses.

A novel ‘stack’ model of a rate-independent polycrystal, which extends the ‘ALAMEL’ model of Van Houtte et al. (2005) is proposed. In the ‘stack’ model, stacks of N neighboring ‘ALAMEL’ domains collectively accommodate the imposed macroscopic deformation while deforming such that velocity and traction continuity with their neighbors is maintained. The flow law and consistency conditions are derived and an efficient solution methodology based on the linear programming technique is given. The present model is applied to study plastic deformation of an idealized two-dimensional polycrystal under macroscopically imposed plane-strain tension and simple shear constraints. Qualitative and quantitative variations in the predicted macroscopic and microscopic response with N are presented. The constraint on individual ‘ALAMEL’ domains diminishes with stack size N but saturates for large N. Computational effort associated with the present model is analyzed and found to be well within one order of magnitude greater than that required to solve the classical Taylor model. Furthermore, implementation of the consistency conditions is found to reduce computation time by at least 50%.

A model of a rigid-plastic rate-independent polycrystalline aggregate wherein sub-aggregates are represented as the nodes of a binary tree is proposed. The lowest nodes of the binary tree represent grains. Higher binary tree nodes represent increasingly larger sub-aggregates of grains, culminating with the root of the tree, which represents the entire polycrystalline aggregate. Planar interfaces are assumed to separate the sub-aggregates represented by nodes in the binary tree. Equivalence between the governing equations of the model and a standard linear program is established. The objective function of the linear program is given by the plastic power associated with polycrystal deformation and the linear constraints are given by compatibility requirements between the sub-aggregates represented by sibling nodes in the binary tree. The deviatoric part of the Cauchy stress in each sub-aggregate is deduced as linear combinations of the Lagrange multipliers associated with the constraints. It is shown that the present model allows a generalization of Taylor’s principle to polycrystals. The proposed model is applied to simulate tensile, compressive, torsional, and plane-strain deformation of copper polycrystals. The predicted macroscopic response is in good agreement with published experimental data. The effect of the initial distribution of the planar interfaces separating the sub-aggregates represented by the binary tree on the predicted mechanical response in tension, compression and torsion is studied. Also, the role of constraints relaxation in simulations of plane strain compression is investigated in detail.

A hierarchical model of a polycrystalline aggregate of rigid viscoplastic grains is formulated, and a robust and efficient computational algorithm for its solution is proposed. The polycrystalline aggregate is modeled as a binary tree. The leaves of the binary tree represent grains, and higher tree nodes represent increasingly larger sub-aggregates of grains. The root of the tree represents the entire polycrystalline aggregate. Velocity and traction continuity are enforced across the interface between the children of each non-leaf node in the binary tree. The hierarchical model explicitly models intergranular interactions but is nevertheless comparable in computational effort to the mean field models of polycrystal plasticity. Simulations of tensile, compressive, torsional, and plane strain deformation of copper lead to predictions in good agreement with experiments, and highlight the interconnection between grain deformations and intergranular constraints. It is inferred from the results that a hybrid mean field/hierarchical model represents a computationally efficient methodology to simulate polycrystal deformation while accounting for intergranular interactions.

The evolution of in situ elastic strain with cyclic tensile loading in each phase of a single Al 2O3-fiber/aluminum-matrix composite was studied using neutron diffraction (ND). An analytical model appropriate for metal matrix composites (MMCs) was developed to connect the measured axial strain evolution in each phase with the possible micromechanical events that could occur during loading at room temperature: fiber fracture, interfacial slipping, and matrix plastic deformation. Model interpretation showed that the elastic strain evolution in the fiber and matrix was governed by fiber fracture and interface slipping and not by plastic deformation of the matrix, whereas the macroscopic stress–strain response of the composite was influenced by all three. The combined single-fiber composite model and ND experiment introduces a new and quick engineering approach for qualifying the micromechanical response in MMCs due to cyclic loading and fiber fracture. 12 13 14 15 16 17 18 19

We present a shear-lag stress analysis methodology which accounts for both matrix strain-hardening plasticity and interfacial slip in a single fiber metal matrix composite (MMC) subjected to uniaxial tensile loading and unloading along the fiber direction. The fiber may either be broken or intact. Among other things, the model predicts residual stress and strain distribution after a cycle in the fiber and matrix. The development of the model is motivated by the recent measurement by Hanan et al. [Mater. Sci. Eng. A, in press], of elastic strain evolution with loading in each phase of an Al2O3/Al composite using neutron diffraction. The model also estimates two crucial in situ material parameters using these measurements, which cannot be obtained from bulk tests: the frictional threshold of the interface, and the in situ yield point of the matrix. With these parameters, the predicted elastic strain evolution with loading is in excellent agreement with the experimental data.

The basic objective of the work reported in this paper is to extend a nine-node degenerated shell element developed earlier for stress analysis to the free vibration analysis of thick laminated composites. The nine-noded degenerated shell element is preferable to conventional solid elements for the modeling and analysis of laminated composite shell structures since the shell element works for both thick and thin shells. An enhanced interpolation of the transverse shear strains in the natural coordinates is used in this formulation to produce a shear locking free element and an enhanced interpolation of the membrane strains in the local coordinates is used to produce a membrane locking free element. The interpolation functions used in formulating the assumed strains are based on the Lagrangian interpolation polynomials. Various numerical examples are analyzed and their results are compared with the existing exact solutions where available and the numerical solutions calculated from other shell finite element formulations, to benchmark the current formulation. � 2006 Elsevier Ltd. All rights reserved.