Robust approach to dynamic statistical process control

Statistical Process Control (SPC) technique are well established across a wide range of industries. In particular, the plotting of key steady state variables with their statistical limit against time (Shewart charting) is a common approach for monitoring the normality of production. This paper aims with extending Shewart charting techniques to the quality monitoring of variables driven by uncertain dynamic processes, which has particular application in the process industries where it is desirable to monitor process variables on-line as well as final product. The robust approach to dynamic SPC is based on previous work on guaranteed cost filtering for linear systems and is intended to provide a basis for both a wide application of SPC monitoring and also motivate unstructured fault detection.

Dynamic recrystallization induced by plastic deformation at high strain rate in a Monel alloy

An investigation has been made into the plastic deformation behavior of a Monel alloy deformed at high strain rate of 10(5) s(-1) by split Hopkinson bar. The results reveal that there are some equiaxed grains with an average size of 150 nm in diameter in the center of the shear bands, suggesting that this microstructure characteristics be developed by dynamic recrystallization, arising from the deformation and the rapid temperature rise in the band. Analysis shows that the plastic strain rate and the mobile dislocation density play a key role in the new crystallized grain formation and growth. Based on grain boundary energy change and diffusion mechanism, the grain growth kinetics is developed for plastic deformation at a high strain rate.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Shear Localization In Dynamic Deformation: Microstructural Evolution

Investigations made by the authors and collaborators into the microstructural aspects of adiabatic shear localization are critically reviewed. The materials analyzed are low-carbon steels, 304 stainless steel, monocrystalline Fe-Ni-Cr, Ti and its alloys, Al-Li alloys, Zircaloy, copper, and Al/SiCp composites. The principal findings are the following: (a) there is a strain-rate-dependent critical strain for the development of shear bands; (b) deformed bands and white-etching bands correspond to different stages of deformation; (c) different slip activities occur in different stages of band development; (d) grain refinement and amorphization occur in shear bands; (e) loss of stress-carrying capability is more closely associated with microdefects rather than with localization of strain; (f) both crystalline rotation and slip play important roles; and (g) band development and band structures are material dependent. Additionally, avenues for new research directions are suggested.

Ductile To Brittle Transition In Dynamic Fracture Of Brittle Bulk Metallic Glass

We report an unusual transition from a locally ductile to a pure brittle fracture in the dynamic fracture of brittle Mg65Cu20Gd10 bulk metallic glass. The fractographic evolution from a dimple structure to a periodic corrugation pattern and then to the mirror zone along the crack propagation direction during the dynamic fracture process is discussed within the framework of the meniscus instability of the fracture process zone. This work might provide an important clue in understanding of the energy dissipation mechanism for dynamic crack propagation in brittle glassy materials. (C) 2008 American Institute of Physics.

Dynamic Fracture Instability Of Tough Bulk Metallic Glass

We report the observations of a clear fractographic evolution from vein pattern, dimple structure, and then to periodic corrugation structure, followed by microbranching pattern, along the crack propagation direction in the dynamic fracture of a tough Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit.1) bulk metallic glass (BMGs) under high-velocity plate impact. A model based on fracture surface energy dissipation and void growth is proposed to characterize this fracture pattern transition. We find that once the dynamic crack propagation velocity reaches a critical fraction of Rayleigh wave speed, the crack instability occurs; hence, crack microbranching goes ahead. Furthermore, the correlation between the critical velocity of amorphous materials and their intrinsic strength such as Young's modulus is uncovered. The results may shed new insight into dynamic fracture instability for BMGs. (C) 2008 American Institute of Physics.

Comparison Of The Quasi-Static Method And The Dynamic Method For Simulating Fracture Processes In Concrete

Concrete is heterogeneous and usually described as a three-phase material, where matrix, aggregate and interface are distinguished. To take this heterogeneity into consideration, the Generalized Beam (GB) lattice model is adopted. The GB lattice model is much more computationally efficient than the beam lattice model. Numerical procedures of both quasi-static method and dynamic method are developed to simulate fracture processes in uniaxial tensile tests conducted on a concrete panel. Cases of different loading rates are compared with the quasi-static case. It is found that the inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, an unrealistic result will be obtained if a fracture process including unstable cracking is simulated by the quasi-static procedure.

Sequential decision making in general state space models

Many problems in control and signal processing can be formulated as sequential decision problems for general state space models. However, except for some simple models one cannot obtain analytical solutions and has to resort to approximation. In this thesis, we have investigated problems where Sequential Monte Carlo (SMC) methods can be combined with a gradient based search to provide solutions to online optimisation problems. We summarise the main contributions of the thesis as follows. Chapter 4 focuses on solving the sensor scheduling problem when cast as a controlled Hidden Markov Model. We consider the case in which the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. In sensor scheduling, our aim is to minimise the variance of the estimation error of the hidden state with respect to the action sequence. We present a novel SMC method that uses a stochastic gradient algorithm to find optimal actions. This is in contrast to existing works in the literature that only solve approximations to the original problem. In Chapter 5 we presented how an SMC can be used to solve a risk sensitive control problem. We adopt the use of the Feynman-Kac representation of a controlled Markov chain flow and exploit the properties of the logarithmic Lyapunov exponent, which lead to a policy gradient solution for the parameterised problem. The resulting SMC algorithm follows a similar structure with the Recursive Maximum Likelihood(RML) algorithm for online parameter estimation. In Chapters 6, 7 and 8, dynamic Graphical models were combined with with state space models for the purpose of online decentralised inference. We have concentrated more on the distributed parameter estimation problem using two Maximum Likelihood techniques, namely Recursive Maximum Likelihood (RML) and Expectation Maximization (EM). The resulting algorithms can be interpreted as an extension of the Belief Propagation (BP) algorithm to compute likelihood gradients. In order to design an SMC algorithm, in Chapter 8 uses a nonparametric approximations for Belief Propagation. The algorithms were successfully applied to solve the sensor localisation problem for sensor networks of small and medium size.

Dynamic mode I perturbation solution for a moving crack unsteadily

Rice et al. (Jounal of Mechanics and Physics of Solids 42, 813-843) analyze the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of Willis er al. (Journal of the Mechanics and Physics of Solids 43, 319-341), of dynamic mode I weight functions for a moving crack, we address that problem solved by Rice ei al. in the 3D context of elastodynamic theory. Oscillatory crack tip motion results from constructive-destructive interference of stress intensity waves. Those waves, including system of the dilatational, shear and Rayleigh waves, interact on each other and with moving edge of crack, can lead to continuing fluctuations of the crack front and propagation velocity. (C) 1997 Elsevier Science Ltd.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

Evolution of thermoplastic shear localization and related microstructures in Awl/SiCp composites under dynamic compression

The localized shear deformation in the 2024 and 2124 Al matrix composites reinforced with SiC particles was investigated with a split Hopkinson pressure bar (SHPB) at a strain rate of about 2.0x10(3) s(-1). The results showed that the occurrence of localized shear deformation is sensitive to the size of SiC particles. It was found that the critical strain, at which the shear localization occurs, strongly depends on the size and volume fraction of SiC particles. The smaller the particle size, the lower the critical strain required for the shear localization. TEM examinations revealed that Al/SiCp interfaces are the main sources of dislocations. The dislocation density near the interface was found to be high and it decreases with the distance from the particles. The Al matrix in shear bands was highly deformed and severely elongated at low angle boundaries. The Al/SiCp interfaces, particularly the sharp corners of SiC particles, provide the sites for microcrack initiation. Eventual fracture is caused by the growth and coalescence of microcracks along the shear bands. It is proposed that the distortion free equiaxed grains with low dislocation density observed in the center of shear band result from recrystallization during dynamic deformation.

Effect of Fe content on the thermal stability and dynamic mechanical behavior of NdAlNiCu bulk metallic glasses

The dependence of microstructure and thermal stability on Fe content of bulk Nd60Al10Ni10Cu20-xFex (0 less than or equal to x less than or equal to 20) metallic glasses is investigated by means of differential scanning calorimetry (DSC), X-ray diffraction (XRD) and high-resolution transmission electron micrograph (HRTEM). All samples exhibit typical amorphous feature under the detect limit of XRD, however, HRTEM results show that the microstructure of Nd60Al10Ni10Cu20-xFex alloys changes from a homogeneous amorphous phase to a composite structure consisting of clusters dispersed in amorphous matrix by increasing Fe content. Dynamic mechanical properties of these alloys with controllable microstructure are studied, expressed via storage modulus, the loss modulus and the mechanical damping. The results reveal that the storage modulus of the alloy without Fe added shows a distinct decrease due to the main a relaxation. This decrease weakens and begins at a higher temperature with increasing Fe content. The mechanism of the effect of Fe addition on the microstructure and thermal stability in this system is discussed in terms of thermodynamics viewpoints. (C) 2004 Elsevier B.V. All rights reserved.

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.