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.

This study involved laboratory unidirectional (UDR) and reverse (RR) cold rolling of steel, and corresponding direct (and indirect) observations of surface (and sub-surface) microstructures. Though both processes had identical strain mode of plane strain compression (PSC), the as-rolled surface grains showed clear differences in imposed mesoscopic shear strains. Further, the surface microstructure and its orientation sensitivity differed remarkably between the two processes. RR had more dislocation density, grain misorientations and non-crystallographic microbands, but exhibited insignificant differences between different crystallographic orientations. These effects appeared significant in low carbon interstitial free (IF) steel, but noticeably less so for high strength low alloy (HSLA) grade. The crystallographic textures of both the processes were identical in the mid-thickness section. However, the surface textures differed noticeably irrespective of the steel grade. These were captured quantitatively with a crystal plasticity model, and by introducing parametrically positive (UDR) and negative (RR) local shear strains for the respective surfaces. In summary, this study established, quantitatively, the defining role of local shear strain on the developments of as-rolled microstructure and crystallographic texture of steel.

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 microstructure of an Al-Cu-Li alloy sheet is characterised in the solution treated, underaged, and peak aged tempers. Its mechanical response under uniaxial tension is measured at (Formula presented.), (Formula presented.), and (Formula presented.) along (Formula presented.), (Formula presented.), and (Formula presented.) to the rolling direction. The anisotropic stress-strain curves are interpreted using a polycrystal plasticity model, which implements three hardening modes suggested by the microstructure, viz., matrix hardening, hardening due to isotropic precipitates, and hardening due to anisotropic precipitates. Phenomenological activation theory based analysis of the work hardening suggests that the physical mechanism underlying work hardening due to anisotropic precipitates remains constant over the temperature range studied, while the mechanism underlying matrix hardening varies strongly with temperature.

Macroscopic shear bands (MSB) may develop during hot working of metallic materials. They are well-understood as a physical manifestation of flow instability, and the processing regimes wherein they form are well-charted. However, the microstructural transitions that occur between the onset of flow instability and MSB inception are not fully understood. In order to elucidate them, several aluminum alloy specimens were subjected to strip testing in a thermomechanical simulator (Gleeble™) at 298 K and 573 K. Prominent MSB were observed along the diagonals of the strip volume of only Aluminum-6 wt% Magnesium alloy specimen deformed at 573 K. Comparing the experimental grain morphology and crystallographic textures with those from plastic flow models revealed that MSB inception occurred only after ∼0.20 homogeneous plane strain deformation. However, classical flow instability was predicted at much smaller strain. This ‘delay’ was explained experimentally by showing that clusters of neighbouring severely deforming, fragmenting, mostly soft-oriented grains gradually developed due to lattice rotations along the specimen diagonals, and that MSB inception corresponded to the formation of a percolating network of such grains spanning the specimen. Further, clear experimental evidence revealed that differential dynamic recovery between hard- and soft-oriented grains was essential for MSB formation.

The two-dimensional stress fields induced by a set of infinitely many parallel edge dislocations are difficult to estimate as those of individual dislocations decay slowly. A simple numerical method to compute them is proposed. The method is based on series summation using a convergence factor, (Formula presented.) that decays rapidly with radial distance r from the field point, and letting the positive parameter (Formula presented.) numerically through Richardson extrapolation. The present method is more general than a lattice summation method with explicit spurious stress cancellation that is widely used in the literature. Furthermore, the spurious long-range stresses are cancelled in the present method without explicit evaluation.