Mahesh Sivasambu

The evolution of mechanical and damage fields, and the time to failure of material points ahead of a stationary crack in a compact tension specimen are computed using finite element simulations for a linear elastic/power law creeping material. These are compared with predictions obtained from fields based on two fracture mechanics based load-parameters: the steady-state C∗, and the time-corrected C(t). The finite element calculations predict opening stresses in the crack plane that are non-monotonic in the time interval 0 ≤ t≤ t1, where t1 denotes the time to transition from small-scale creep to extensive creep. This is in contradiction to the monotonic ‘self-similar’ decay of stress with time given by the C(t) field. Consequently, damage rates and times to failure of material points ahead of a crack are calculated using the finite element stress-field, and the C(t)-based stress-field diverge considerably. These observations suggest that the creep damage rates derived on the basis of self-similarly decaying opening stress fields may be severely inaccurate.

A shear-lag model of hybrid materials is developed. The model represents an alternating arrangement of two types of aligned linear elastic fibres, embedded in a linear elastic matrix. Fibre and matrix elements are taken to fail deterministically when the axial and shear stresses in them reach their respective strengths. An efficient solution procedure for determining the stress state for arbitrary configurations of broken fibre and matrix elements is developed. Starting with a single fibre break, this procedure is used to simulate progressive fibre and matrix failure, up to composite fracture. The effect of (1) the ratio of fibre stiffnesses, and (2) the ratio of the fibre tensile strength to matrix shear strength, on the composite failure mechanism, fracture energy, and failure strain is characterised. Experimental observations, reported in the literature, of the fracture behaviour of two hybrid materials, viz., hybrid unidirectional composites, and double network hydrogels, are discussed in the framework of the present model.

Components such as bladed rings, and bladed disks fabir-icated out of titanium matrix composites were extensively explored in the two decades since about 1990 as light weight replacements for conventional superalloy blades and disks in the intermediate hot stages of gas turbines. One of the challenges, which has hindered their adoption is the relative unreliability of the composite components; nominally identical Ti composite specimen display a much larger variability in strength than their superalloy counterparts. In the present work, we have quantified the reliability of Ti matrix composites by developing a detailed micromechanical-statistical model of their failure. The micromechanical model resolves fibres, matrix, and the interface, and accounts for such failure modes as fibre breakage, matrix cracking, matrix plasticity, interfacial sliding, and debonding. It also accounts for mechanical interaction between these various failure modes. The mechanical model’s predictions are validated against synchotron X-ray measurements reported in the literature, both after loading, and unloading. Using the detailed micromechanical model, Ti matrix composite was simulated following a Monte Carlo framework. These simulations yield the empirical strength distribution of the Ti matrix composite, and insights into the dominant failure mode. The latter allows the construction of a stochastic model of composite failure. The stochastic model can be used to determine safe working loads as a function of composite size for any desired reliability level.

Pilgering is a complex incremental manufacturing process for seamless tubes. In this work, a miniature physical simulator for pilgering was designed and fabricated. This miniature simulator employs a grooved roll-die and a mandrel and can impose controlled reductions in both tube diameter and wall thickness. Pilgering deformation over a range of ratios of reductions in wall thickness and in tube diameter, known as the Q-factor, was imposed on hemi-cylindrical zirconium alloy specimens. The influence of the Q-factor on the microstructure and deformation texture of the deformed specimens was quantified. A polycrystal plasticity calculation based on the binary tree model was used to simulate texture evolution during the simulated pilgering process. The computer model quantitatively captured the variation with Q of the Kearns factors, as measured in the physically simulated specimen. The small differences noticed between the predicted and experimental final textures point to unaccounted transverse components of the flow field. These observations suggest that physical and/or computer simulations can form the basis of a rapid methodology for tool selection to realize prescribed post-pilgering textures.

Monte-Carlo simulations of the fracture of elastic unidirectional model fibre composites are an important tool to understand composite reliability. On account of being computationally intensive, fracture simulations reported in the literature have been limited to simulation patches comprised of a few thousand fibres. While these limited patch sizes suffice to capture the dominant failure event when the fibre strength variability is low (synthetic fibres), they suffer from edge effects when the fibre strength variability is high (natural fibres). On the basis of recent algorithmic developments based on Fourier acceleration, a novel bisection based Monte Carlo failure simulation algorithm is presently proposed. This algorithm is used to obtain empirical strength distributions for model composites comprised of up to 2 20≈ 10 6 fibres, and spanning a wide range of fibre strength variabilities. These simulations yield empirical weakest-link strength distributions well into the lower tail. A stochastic model is proposed for the weakest-link event. The strength distribution predicted by this model fits the empirical distributions for any fibre strength variability.

Parameters of five popular continuum damage models are fit to match their creep rate and time to rupture predictions with that of a validated micro-mechanisms based model at a high nominal stress for an austenitic stainless steel. Their predictions are then compared with that of the micro-mechanisms based model at lower stress levels. The creep-strain rate and time to failure predictions of the model due to Wen et al. (Eng Fract Mech 98:169–184, 2013) best agrees with that of the micro-mechanisms based model in the regime of dominance of creep deformation processes. At still lower stress levels, where cavitation-rate is determined by diffusion processes, the Wen et al. model predictions of creep lifetimes become excessively non-conservative. A correction based on a formula due to Cocks and Ashby (Prog Mater Sci 27:189–244, 1982) has been proposed for this regime.

The stress state in a shear-lag model of a unidirectional fiber composite with an arbitrary configuration of fiber breaks is obtained by the weighted superposition of the stress state due to a single broken fiber. In a periodic patch comprised of N fibers located at the points of a regular lattice, a method to determine the stress state due to a single break was proposed by Landis et al. (J Mech Phys Solids 48(3):621–648, 2000). This method entails the determination of the eigenspace of an N× N matrix, at a computational cost of O(N3). In the present work, an alternative algorithm is proposed. This algorithm exploits the circulant structure of the matrix describing the inter-fiber interactions. The asymptotic computational complexity of the present algorithm equals that of the discrete Fourier transform: O(Nlog N). Run times of the present method with the eigensolution based method are compared, and shown to be very favorable for the present method, even for small N. Power-law scaling of the overloads due to a single break to much larger distances than previously possible has been verified using the present method.

Monte Carlo simulations of the failure of unidirectional fibre composites typically require numerous evaluations of the stress-state in partially damaged composite patches. In a simulated composite patch comprised of N fibres, of which Nb fibres are broken in a common cross-sectional plane transverse to the fibre direction, the stress overloads in the intact fibres are given by the weighted superposition of the unit break solutions associated with each of the breaks. Determining the weights involves solving Nb linear equations, and determining overloads in the intact fibres requires matrix-vector multiplication. These operations require O(Nb3), and O(NNb) floating point operations, respectively. These costs become prohibitive for large N, and Nb; they limit Monte Carlo failure simulations to composite patches of only a few thousand fibres. In the present work, a fast algorithm to determine the overloads in a partially damaged composite, requiring O(Nb1/3NlogN) floating point operations, is proposed. This algorithm is based on the discrete Fourier transform. The efficiency of the proposed method derives from the computational simplicity of weighted superposition in Fourier space. Computations of the stress state ahead of large circular clusters of breaks in composite patches comprised of about one million fibres are used to demonstrate the efficiency of the proposed algorithm.

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.

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.