Influence of microstructure variability on short crack growth behavior

Fatigue life in metals is predicted utilizing regression analysis of large sets of experimental data, thus representing the material’s macroscopic response. Furthermore, a high variability in the short crack growth (SCG) rate has been observed in polycrystalline materials, in which the evolution and distributionof local plasticity is strongly influenced by the microstructure features. The present work serves to (a) identify the relationship between the crack driving force based on the local microstructure in the proximity of the crack-tip and (b) defines the correlation between scatter observed in the SCG rates to variability in the microstructure. A crystal plasticity model based on the fast Fourier transform formulation of the elasto-viscoplastic problem (CP-EVP-FFT) is used, since the ability to account for the both elastic and plastic regime is critical in fatigue. Fatigue is governed by slip irreversibility, resulting in crack growth, which starts to occur during local elasto-plastic transition. To investigate the effects of microstructure variability on the SCG rate, sets of different microstructure realizations are constructed, in which cracks of different length are introduced to mimic quasi-static SCG in engineering alloys. From these results, the behavior of the characteristic variables of different length scale are analyzed: (i) Von Mises stress fields (ii) resolved shear stress/strain in the pertinent slip systems, and (iii) slip accumulation/irreversibilities. Through fatigue indicator parameters (FIP), scatter within the SCG rates is related to variability in the microstructural features; the results demonstrate that this relationship between microstructure variability and uncertainty in fatigue behavior is critical for accurate fatigue life prediction.

Organic matter deposition/resuspension in a one-dimensional physical-biogeochemical model. A modelling study

The shallow water configuration of the gulf of Trieste allows the propagation of the stress due to wind and waves along the whole water column down to the bottom. When the stress overcomes a particular threshold it produces resuspension processes of the benthic detritus. The benthic sediments in the North Adriatic are rich of organic matter, transported here by many rivers. This biological active particulate, when remaining in the water, can be transported in all the Adriatic basin by the basin-wide circulation. In this work is presented a first implementation of a resuspension/deposition submodel in the oceanographic coupled physical-biogeochemical 1-dimensional numerical model POM-BFM. At first has been considered the only climatological wind stress forcing, next has been introduced, on the surface, an annual cycle of wave motion and finally have been imposed some exceptional wave event in different periods of the year. The results show a strong relationship between the efficiency of the resuspension process and the stratification of the water column. During summer the strong stratification can contained a great quantity of suspended matter near to the bottom, while during winter even a low concentration of particulate can reach the surface and remains into the water for several months without settling and influencing the biogeochemical system. Looking at the biologic effects, the organic particulate, injected in the water column, allow a sudden growth of the pelagic bacteria which competes with the phytoplankton for nutrients strongly inhibiting its growth. This happen especially during summer when the suspended benthic detritus concentration is greater.

A new insight in stress recovery tecniques and hessian reconstruction methods

Stress recovery techniques have been an active research topic in the last few years since, in 1987, Zienkiewicz and Zhu proposed a procedure called Superconvergent Patch Recovery (SPR). This procedure is a last-squares fit of stresses at super-convergent points over patches of elements and it leads to enhanced stress fields that can be used for evaluating finite element discretization errors. In subsequent years, numerous improved forms of this procedure have been proposed attempting to add equilibrium constraints to improve its performances. Later, another superconvergent technique, called Recovery by Equilibrium in Patches (REP), has been proposed. In this case the idea is to impose equilibrium in a weak form over patches and solve the resultant equations by a last-square scheme. In recent years another procedure, based on minimization of complementary energy, called Recovery by Compatibility in Patches (RCP) has been proposed in. This procedure, in many ways, can be seen as the dual form of REP as it substantially imposes compatibility in a weak form among a set of self-equilibrated stress fields. In this thesis a new insight in RCP is presented and the procedure is improved aiming at obtaining convergent second order derivatives of the stress resultants. In order to achieve this result, two different strategies and their combination have been tested. The first one is to consider larger patches in the spirit of what proposed in [4] and the second one is to perform a second recovery on the recovered stresses. Some numerical tests in plane stress conditions are presented, showing the effectiveness of these procedures. Afterwards, a new recovery technique called Last Square Displacements (LSD) is introduced. This new procedure is based on last square interpolation of nodal displacements resulting from the finite element solution. In fact, it has been observed that the major part of the error affecting stress resultants is introduced when shape functions are derived in order to obtain strains components from displacements. This procedure shows to be ultraconvergent and is extremely cost effective, as it needs in input only nodal displacements directly coming from finite element solution, avoiding any other post-processing in order to obtain stress resultants using the traditional method. Numerical tests in plane stress conditions are than presented showing that the procedure is ultraconvergent and leads to convergent first and second order derivatives of stress resultants. In the end, transverse stress profiles reconstruction using First-order Shear Deformation Theory for laminated plates and three dimensional equilibrium equations is presented. It can be seen that accuracy of this reconstruction depends on accuracy of first and second derivatives of stress resultants, which is not guaranteed by most of available low order plate finite elements. RCP and LSD procedures are than used to compute convergent first and second order derivatives of stress resultants ensuring convergence of reconstructed transverse shear and normal stress profiles respectively. Numerical tests are presented and discussed showing the effectiveness of both procedures.

Shear behavior of reinforced concrete slabs under concentrated load: an investigation through Sequentially Linear Analysis

ABSTRACT (italiano) Con crescente attenzione riguardo al problema della sicurezza di ponti e viadotti esistenti nei Paesi Bassi, lo scopo della presente tesi è quello di studiare, mediante la modellazione con Elementi Finiti ed il continuo confronto con risultati sperimentali, la risposta in esercizio di elementi che compongono infrastrutture del genere, ovvero lastre in calcestruzzo armato sollecitate da carichi concentrati. Tali elementi sono caratterizzati da un comportamento ed una crisi per taglio, la cui modellazione è, da un punto di vista computazionale, una sfida piuttosto ardua, a causa del loro comportamento fragile combinato a vari effetti tridimensionali. La tesi è incentrata sull'utilizzo della Sequentially Linear Analysis (SLA), un metodo di soluzione agli Elementi Finiti alternativo rispetto ai classici approcci incrementali e iterativi. Il vantaggio della SLA è quello di evitare i ben noti problemi di convergenza tipici delle analisi non lineari, specificando direttamente l'incremento di danno sull'elemento finito, attraverso la riduzione di rigidezze e resistenze nel particolare elemento finito, invece dell'incremento di carico o di spostamento. Il confronto tra i risultati di due prove di laboratorio su lastre in calcestruzzo armato e quelli della SLA ha dimostrato in entrambi i casi la robustezza del metodo, in termini di accuratezza dei diagrammi carico-spostamento, di distribuzione di tensioni e deformazioni e di rappresentazione del quadro fessurativo e dei meccanismi di crisi per taglio. Diverse variazioni dei più importanti parametri del modello sono state eseguite, evidenziando la forte incidenza sulle soluzioni dell'energia di frattura e del modello scelto per la riduzione del modulo elastico trasversale. Infine è stato effettuato un paragone tra la SLA ed il metodo non lineare di Newton-Raphson, il quale mostra la maggiore affidabilità della SLA nella valutazione di carichi e spostamenti ultimi insieme ad una significativa riduzione dei tempi computazionali. ABSTRACT (english) With increasing attention to the assessment of safety in existing dutch bridges and viaducts, the aim of the present thesis is to study, through the Finite Element modeling method and the continuous comparison with experimental results, the real response of elements that compose these infrastructures, i.e. reinforced concrete slabs subjected to concentrated loads. These elements are characterized by shear behavior and crisis, whose modeling is, from a computational point of view, a hard challenge, due to their brittle behavior combined with various 3D effects. The thesis is focused on the use of Sequentially Linear Analysis (SLA), an alternative solution technique to classical non linear Finite Element analyses that are based on incremental and iterative approaches. The advantage of SLA is to avoid the well-known convergence problems of non linear analyses by directly specifying a damage increment, in terms of a reduction of stiffness and strength in the particular finite element, instead of a load or displacement increment. The comparison between the results of two laboratory tests on reinforced concrete slabs and those obtained by SLA has shown in both the cases the robustness of the method, in terms of accuracy of load-displacements diagrams, of the distribution of stress and strain and of the representation of the cracking pattern and of the shear failure mechanisms. Different variations of the most important parameters have been performed, pointing out the strong incidence on the solutions of the fracture energy and of the chosen shear retention model. At last a confrontation between SLA and the non linear Newton-Raphson method has been executed, showing the better reliability of the SLA in the evaluation of the ultimate loads and displacements, together with a significant reduction of computational times.

Finite element modeling of the cement-bone interface beneath the tibial tray of a total knee arthroplasty: Study of the stress shielding effect (modellazione agli elementi finiti dell'interfaccia cemento-osso sotto il piatto tibiale di protesi totale di ginocchio: Analisi dello stress shielding)

The goal of this thesis was the study of the cement-bone interface in the tibial component of a cemented total knee prosthesis. One of the things you can see in specimens after in vivo service is that resorption of bone occurs in the interdigitated region between bone and cement. A stress shielding effect was investigated as a cause to explain bone resorption. Stress shielding occurs when bone is loaded less than physiological and therefore it starts remodeling according to the new loading conditions. µCT images were used to obtain 3D models of the bone and cement structure and a Finite Element Analysis was used to simulate different kind of loads. Resorption was also simulated by performing erosion operations in the interdigitated bone region. Finally, 4 models were simulated: bone (trabecular), bone with cement, and two models of bone with cement after progressive erosions of the bone. Compression, tension and shear test were simulated for each model in displacement-control until 2% of strain. The results show how the principal strain and Von Mises stress decrease after adding the cement on the structure and after the erosion operations. These results show that a stress shielding effect does occur and rises after resorption starts.