Baidurya Bhattacharya

Continuum damage mechanics analysis of fatigue crack initiation

The crack initiation period in an originally defect-free component can be a significant portion of its total fatigue life. The initiation phase is generally believed to constitute the nucleation and growth of short cracks, but the threshold crack length at which initiation occurs lacks a uniform definition. Moreover, available methods for predicting fatigue damage growth usually require an existing flaw (e.g. Paris law) and may be difficult to apply to the initiation phase. This paper presents a continuum damage mechanics-based approach that estimates cumulative fatigue damage, and predicts crack initiation from fundamental principles of thermodynamics and mechanics. Assuming that fatigue damage prior to localization occurs close to a state of thermodynamic equilibrium, a differential equation of isotropic damage growth under uniaxial loading is derived that is amenable to closed-form solution. Damage, as a function of the number of cycles, is computed in a recursive manner using readily available material parameters. Even though most fatigue data are obtained under constant amplitude loading conditions, most engineering systems are subjected to variable amplitude loading, which can be accommodated easily by the recursive nature of the proposed method. The predictions are compared with available experimental results.

Effect of randomly occurring Stone-Wales defects on mechanical properties of carbon nanotubes using atomistic simulation

The remarkable mechanical properties of carbon nanotubes (CNTs) have generated a lot of interest in recent years. While CNTs are found to have ultra-high stiffness and strength, an enormous scatter is also observed in available laboratory results. This randomness is partly due to the presence of nanoscale defects, heterogeneities etc, and?this paper studies the effects of randomly distributed Stone?Wales (SW or 5?7?7?5) defects on the mechanical properties of single-walled nanotubes (SWNTs) using the technique of atomistic simulation (AS). A Matern hard-core random field applied on a finite cylindrical surface is used to describe the spatial distribution of the Stone?Wales defects. We simulate a set of displacement controlled tensile loadings up to fracture of SWNTs with (6, 6) armchair and (10, 0) zigzag configurations and aspect ratio around six. A modified Morse potential is adopted to model the interatomic forces. We find that fracture invariably initiates from a defect if one is present; for a defect-free tube the crack initiates at quite random locations. The force?displacement curve typically behaves almost linearly up to about half way, although there is no obvious yield point. Three mechanical properties?stiffness, ultimate strength and ultimate strain?are calculated from the simulated force and displacement time histories. The randomness in mechanical behaviour resulting only from initial velocity distribution was found to be insignificant at room temperature. The mean values of stiffness, ultimate strength and ultimate strain of the tube decrease as the average number of defects increases, although the coefficients of variation do not show such a monotonic trend. The introduction of an additional defect has the most pronounced effect on the randomness in mechanical properties when the tube is originally defect free. We also find that, for a given mean number of defects in the tube, the zigzag configuration has less strength and less ultimate strain on average, but more uncertainty in its stiffness and ultimate strain, compared with the armchair tube.

A new CDM-based approach to structural deterioration

Abstract Structural deterioration often occurs without visible manifestation. Continuum damage mechanics (CDM) enables one to predict the state of damage in such situations and to estimate residual strength⧹service life of an existing structure. The accumulation of damage is modeled as a dissipative process that is governed by the laws of thermodynamics. The rate of dissipation in a deformable system, R, depends on the work done on the system and the evolution of the Helmholtz free energy, Ψ. Under certain thermodynamical conditions, the first variation of Ψ vanishes, and partial differential equations for damage growth in R prior to damage localization are obtained. This approach obviates the need of introducing arbitrary dissipation potential functions with undetermined constants in the damage growth equations. All solutions use only readily available material parameters. Assuming that damage occurs isotropically under uniaxial loading, closed-form solutions are obtained for ductile damage as a function of plastic strain, for creep damage as a function of time and for fatigue damage as function of number of cycles. The models are validated with published laboratory data.

Developing target reliability for novel structures: the case of the Mobile Offshore Base ☆

Reliability-based design criteria are usually calibrated to existing structures (of the same class) having a history of successful service. However, as the offshore industry continues to witness innovations, some novel structures clearly exceed the scope of existing design standards. A reliability-based design is attractive in such cases, but the calibration exercise is not feasible and target reliabilities need to be derived from more fundamental considerations. This paper describes a general risk-based methodology for identifying significant limit states and deriving corresponding target reliabilities for such novel structures. Reliabilities of various existing structures and available analytical methods for determining target reliabilities are reviewed. Careful consideration is given to failure consequences, both tangible and intangible, and reliabilities of intact as well as damaged structures are considered. The methodology is illustrated with the US Navys Mobile Offshore Base concept, which is a unique offshore structure in terms of function and size, and for which no precedence or industry standard exists.

Nonergodicity of the Nose-Hoover chain thermostat in computationally achievable time.

The widely used Nose-Hoover chain (NHC) thermostat in molecular dynamics simulations is generally believed to impart the canonical distribution as well as quasi- (i.e., space-filling) ergodicity on the thermostatted physical system (PS). Working with the standard single harmonic oscillator, we prove analytically that the two-chain Nose-Hoover thermostat with unequal thermostat masses approaches the standard Nose-Hoover dynamics, and hence the PS loses its canonical and quasiergodic nature. We also show through numerical simulations over substantially long times that for certain Poincaré sections, for both the equal and unequal thermostat mass cases, the bivariate distribution function of position and momentum (x,p) and of reservoir degrees of freedom (ξ,η) lose their Gaussian nature. Further, the four-dimensional x-p-ξ-η extended phase space exhibits two holes of nonzero measure. The NHC thermostat therefore does not generate the canonical distribution or preserve quasiergodicity for the PS.

A deterministic thermostat for controlling temperature using all degrees of freedom

We propose a new thermostat that uses all the phase space variables for controlling temperature and thus differs from the existing thermostats that control either the kinetic (e.g., Nose Hoover) or the configurational (e.g., Braga Travis) degrees of freedom. Our thermostat is a special case of the set of equations proposed by Kusnezov et al. [Ann. Phys. 204, 155 (1990)] and is derived using the extended system method. We show that it generates a canonical phase-space distribution. The performance of the thermostat is compared with those of Nose-Hoover kinetic thermostat and Braga-Travis configurational thermostat for a system (i) in thermal equilibrium, (ii) subjected to sudden temperature changes, and (iii) in steady state non-equilibrium under thermal conduction. We observe that all three thermostats perform similarly for systems in equilibrium. However, our thermostat performs the best in the thermal conduction problem by generating a consistent temperature profile across the conduction length. We expect this thermostat to be useful in other non-equilibrium scenarios as well.

DNA Functionalized Carbon Nanotubes for Nonbiological Applications

Functionalization of an inorganic nanomaterial like carbon nanotube (CNT) with biological macromolecules like deoxyribonucleic acid (DNA) leads to the formation of hybrid materials with fascinating properties. This article describes the structures of CNT and DNA, portrays the van der Waals force-dominant non-covalent π–π stacking interactions formed due to their self-assembly, and reviews the electronic, electrochemical, optical, and chemical properties of DNA-functionalized CNTs (DFCs). Current computational developments in simulating and predicting CNT-DNA interactions, alternate functionalization techniques, conformational changes of DNA bases, etc. are discussed. Various characterization techniques using scanning electron microscopy (SEM), scanning tunneling microscopy (STM), atomic force microscopy (AFM), UV-visible, Photoluminescence (PL) and Raman spectroscopy, etc. that help explain DFC properties are detailed. Potential applications for this hybrid material in nanoelectronics and chemical sensors as well as in chirality-based separation of metallic nanotubes from semiconducting ones are considered. The article concludes with current challenges, future directions of research, and prospective applications in this field.

Deoxyribonucleic Acid Functionalized Carbon Nanotube Network as Humidity Sensors

In this paper, deoxyribonucleic acid functionalized carbon nanotube (DFC) network has been used to develop field effect transistor (FET)-based humidity sensor. The sensor works on the principle of variation of conductance of the DFC network with change in relative humidity. Since the output signal current of the sensor increases exponentially with increase in RH, the device offers higher sensitivity especially at higher RH. The response and recovery times of this zero gate biased FET-based humidity sensor are measured to be 4 and 8 s, respectively, and offers no baseline shift during recovery, which indicates that the sensing mechanism is governed by charge transfer between the DFC and water molecules. The device is highly selective to atmospheric humidity, having no response to nitrogen and oxygen. The effect of temperature on the performance of the sensor is also studied and reported in this paper.

Bridge rating using in-service data in the presence of strength deterioration and correlation in load processes

This paper presents a probability-based methodology for load rating bridges that can accommodate detailed site-specific in-service structural deterioration and response data in a load and resistance factor rating (LRFR) format. The use of site-specific structural response allows the elimination of a substantial portion of modelling uncertainty in live load characterization. Inclusion of structural ageing allows the bridge owner the choice to rate for longer intervals than, say, the usual two-year inspection cycle. This methodology allows the live load-effect sequence on bridges to be statistically stationary with a weakened mixing-type dependence that asymptotically decreases to zero with increasing separation in time, instead of making the common assumption of independent and identically distributed sequences of live loads. In addition, uncertainties in field measurement, modelling uncertainties and Bayesian updating of the empirical distribution function are considered to obtain an extreme value distribution of the time-dependent maximum live load. Gross section loss due to corrosion occurring with a random rate governed by an exponentiated Ornstein-Uhlenbeck type stochastic noise is considered. An illustrative example utilizes in-service peak strain data from ambient traffic collected on a high-volume steel girder bridge. In-service load and ageing resistance factor rating (ISLARFR) equations corresponding to plastic collapse of critical girder cross-section over a range of service lives are developed.

Estimation of ultimate hull girder strength with initial imperfections

The estimation of the ultimate strength of the ship hull is very important for its structural safety against applied loads. Various methodologies have been developed to evaluate the ultimate hull girder capacity, for example Caldwell (1965), Paik and Mansour (1995), International Association of Classification Societies Common structural rules (IACS CSR, 2006), etc. These methods do not usually include initial imperfections like initial deflection and initial residual welding stresses in the plating between stiffeners. The IACS CSR, introduced in April 2006, suggest the analytical incremental-iterative method for determining ultimate strength estimation of ship hull, which ignores welding residual stresses. In the present study, the stress–strain relationship for stiffened plate given in IACS CSR method is extended to account for the initial imperfections. Our previous work (Vhanmane and Bhattacharya 2007) on the stress–strain relationship of plate between stiffeners under axial loads, including imperfections like initial deflection and initial residual welding stresses, is used to determine the effective width of attached plating. The proposed methodology is applied to six benchmark cases: a double hull very large crude carrier and a capesize bulk carrier under three different levels of imperfection (slight, average, and severe) for both initial deflection and residual stresses. The ultimate strengths thus obtained are compared with published results that use two different methods (idealised structural unit method and finite element analysis) and it appears that the proposed methodology is simple yet robust in estimating hull girder ultimate strength under initial imperfections.