Damage localization using experimental modal parameters and topology optimization

This work focuses on the developement of a damage detection and localization tool using the Topology Optimization feature of MSC.Nastran. This approach is based on the correlation of a local stiness loss and the change in modal parameters due to damages in structures. The loss in stiness is accounted by the Topology Optimization approach for updating undamaged numerical models towards similar models with embedded damages. Hereby, only a mass penalization and the changes in experimentally obtained modal parameters are used as objectives. The theoretical background for the implementation of this method is derived and programmed in a Nastran input file and the general feasibility of the approach is validated numerically, as well as experimentally by updating a model of an experimentally tested composite laminate specimen. The damages have been introduced to the specimen by controlled low energy impacts and high quality vibration tests have been conducted on the specimen for dierent levels of damage. These supervised experiments allow to test the numerical diagnosis tool by comparing the result with both NDT technics and results of previous works (concerning shifts in modal parameters due to damage). Good results have finally been archieved for the localization of the damages by the Topology Optimization

Deformed SPDE models with an application to spatial modeling of significant wave height

A non-stationary Gaussian random field model is developed based on a combination of the stochastic partial differential equation (SPDE) approach and the classical deformation method. With the deformation method, a stationary field is defined on a domain which is deformed so that the field becomes non-stationary. We show that if the stationary field is a Mat'ern field defined as a solution to a fractional SPDE, the resulting non-stationary model can be represented as the solution to another fractional SPDE on the deformed domain. By defining the model in this way, the computational advantages of the SPDE approach can be combined with the deformation method's more intuitive parameterisation of non-stationarity. In particular it allows for independent control over the non-stationary practical correlation range and the variance, which has not been possible with previously proposed non-stationary SPDE models. The model is tested on spatial data of significant wave height, a characteristic of ocean surface conditions which is important when estimating the wear and risks associated with a planned journey of a ship. The model parameters are estimated to data from the north Atlantic using a maximum likelihood approach. The fitted model is used to compute wave height exceedance probabilities and the distribution of accumulated fatigue damage for ships traveling a popular shipping route. The model results agree well with the data, indicating that the model could be used for route optimization in naval logistics.Comment: 22 pages, 12 figure

Mechanical behaviour of fibre metal laminates based on self-reinforced composites for impact applications

Lightness and appropriate mechanical response of materials are currently demanded in many applications related to transportation (automotive, aeronautic). Depending on the component, an appropriate mechanical behaviour may consist in having either damage tolerance or energy dissipation capacity. In this regard, it is essential to understand the mechanical behaviour of the materials in order to succeed in the selection of them and the design of components. Fibre metal laminates (FMLs) are multilayer systems consisting of stacked metal sheets and thin plates of composite material. Among FMLs, the ones based on self-reinforced composites (SRCs) have demonstrated they can offer an excellent response to low and high velocity impact loadings in terms of impact energy dissipating capacity when compared to thermosetting matrix-based systems. The main objective of this thesis is to study the mechanical behaviour of fibre metal laminates based on SRCs. Within this general objective, three partial subobjectives are established: - To select the most appropriate SRC-FML, between an Al-based one and a Mg-based one, in terms of energy dissipation capacity under low-velocity impacts. - To characterise the mechanical behaviour of the plain SRC and to evaluate its influence in the mechanical response of the FML based on the strain rate. - To develop a constitutive model of the mechanical behaviour of the SRC. The results reveal that the Al/SRPP-FML is the most appropriate in terms of energy dissipation capacity under low-velocity impacts. After that, the characterisation of the plain SRPP shows that, when the material is submitted to both tensile and shear stresses solicitations, it presents irreversible strains, hysteresis phenomena under cyclic loads, a rate-dependent behaviour and a stiffness varying with the strain. Besides, its influence in the mechanical response of the FML is considerable. Then, a constitutive model of the mechanical behaviour of the SRC is proposed. The model is based on the combination of a elastoplastic model and a fractional viscoelastic model. The numerical-experimental correlation demonstrates that the model is capable of predicting accurately both the cyclic tensile and shear behaviours of the SRPP

Quantitative non-destructive testing

The work undertaken during this period included two primary efforts. The first is a continuation of theoretical development from the previous year of models and data analyses for NDE using the Optical Thermal Infra-Red Measurement System (OPTITHIRMS) system, which involves heat injection with a laser and observation of the resulting thermal pattern with an infrared imaging system. The second is an investigation into the use of the thermoelastic effect as an effective tool for NDE. As in the past, the effort is aimed towards NDE techniques applicable to composite materials in structural applications. The theoretical development described produced several models of temperature patterns over several geometries and material types. Agreement between model data and temperature observations was obtained. A model study with one of these models investigated some fundamental difficulties with the proposed method (the primitive equation method) for obtaining diffusivity values in plates of thickness and supplied guidelines for avoiding these difficulties. A wide range of computing speeds was found among the various models, with a one-dimensional model based on Laplace's integral solution being both very fast and very accurate

On the formulation of hereditary cohesive-zone models

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The thesis presents novel formulations of hereditary cohesive zone models able to capture rate-dependent crack propagation along a defined interface. The formulations rely on the assumption that the measured fracture energy is the sum of an intrinsic fracture energy, related to the rupture of primary bonds at the atomic or molecular level, and an additional dissipation caused by any irreversible mechanisms present in the material and occurring simultaneously to fracture. The first contribution can be accounted for by introducing damage-type internal variables, which are to be driven by a rateindependent evolution law in order to be coherent with the definition as intrinsic energy. It is then proposed that the additional dissipation can be satisfactorily characterised by the same continuum-type material constitutive law obeyed by the interface material considered as a continuum: it is postulated that the dimensional reduction whereby a three-dimensional thin layer is idealized as a surface does not qualitatively alter the functional description of the free energy. The specific application considered is mode-I crack propagation along a rubber interface. After focusing on viscoelasticity as a suitable candidate to reproduce rubber’s behaviour, firstly the most common relaxation function, namely a single exponential term, is considerd after which the attention is turned to the use of fractional calculus and the related fractional integral kernel. A comparison with experimental results is presented. A shortcoming of the proposed approach is then noted, in that certain features of experimentally measured responses (i.e.the non-monotonicity of the critical energy-release rate with respect to crack speed) will be shown to be out of reach for the described modelling paradigm. A novel micromechanical formulation is then sketched in an attempt to qualitatively understand the phenomenon. An additional interface damaging mode is introduced, physically inspired by the desire to reproduce the formation of fibrils in a neighbourhood of the crack tip. Fibril formation is then driven by a variational argument applied to the whole of the interface, yielding its non-local character. Upon the introduction of an anisotropic fracture energy, motivated by experimental considerations, it is noted how the model can predict a non-monotonic energy-release rate vs crack speed behaviour, at least for a simple loading mode.Dunlop Oil & Marine Ltd and EPSR

Study on Time-Dependent Behavior of Granite and the Creep Model Based on Fractional Derivative Approach Considering Temperature

Based on mineral components and the creep experimental studies of Three Gorges granite and Beishan granite from different regions of China at various temperatures, the strength and creep property of two types of granites are compared and analyzed. Considering the damage evolution process, a new creep constitutive model is proposed to describe the creep property of granite at different temperatures based on fractional derivative. The parameters of the new creep model are determined on the basis of the experimental results of the two granites. In addition, a sensitivity study is carried out, showing effects of stress level, fractional derivative order, and the exponent m. The results indicate that the proposed creep model can describe the three creep stages of granite at different temperatures and contribute to further research on the creep property of granite