Laser shock peening treatment to control and moderate fatigue crack growth in aircraft structure based on residual stress engineering approach

Laser Shock Peening (LSP) is a surface enhancement treatment which induces a significant layer of beneficial compressive residual stresses of up to several mm underneath the surface of metal components in order to improve the detrimental effects of the crack growth behavior rate in it. The aim of this thesis is to predict the crack growth behavior in metallic specimens with one or more stripes which define the compressive residual stress area induced by the Laser Shock Peening treatment. The process was applied as crack retardation stripes perpendicular to the crack propagation direction with the object of slowing down the crack when approaching the peened stripes. The finite element method has been applied to simulate the redistribution of stresses in a cracked model when it is subjected to a tension load and to a compressive residual stress field, and to evaluate the Stress Intensity Factor (SIF) in this condition. Finally, the Afgrow software is used to predict the crack growth behavior of the component following the Laser Shock Peening treatment and to detect the improvement in the fatigue life comparing it to the baseline specimen. An educational internship at the “Research & Technologies Germany – Hamburg” department of AIRBUS helped to achieve knowledge and experience to write this thesis. The main tasks of the thesis are the following: •To up to date Literature Survey related to “Laser Shock Peening in Metallic Structures” •To validate the FE model developed against experimental measurements at coupon level •To develop design of crack growth slowdown in Centered Cracked Tension specimens based on residual stress engineering approach using laser peened strip transversal to the crack path •To evaluate the Stress Intensity Factor values for Centered Cracked Tension specimens after the Laser Shock Peening treatment via Finite Element Analysis •To predict the crack growth behavior in Centered Cracked Tension specimens using as input the SIF values evaluated with the FE simulations •To validate the results by means of experimental tests

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.

Micro-FEM models based on micro-CT reconstructions for the in vitro characterization of the elastic properties of trabecular bone tissue.

This master’s thesis describes the research done at the Medical Technology Laboratory (LTM) of the Rizzoli Orthopedic Institute (IOR, Bologna, Italy), which focused on the characterization of the elastic properties of the trabecular bone tissue, starting from october 2012 to present. The approach uses computed microtomography to characterize the architecture of trabecular bone specimens. With the information obtained from the scanner, specimen-specific models of trabecular bone are generated for the solution with the Finite Element Method (FEM). Along with the FEM modelling, mechanical tests are performed over the same reconstructed bone portions. From the linear-elastic stage of mechanical tests presented by experimental results, it is possible to estimate the mechanical properties of the trabecular bone tissue. After a brief introduction on the biomechanics of the trabecular bone (chapter 1) and on the characterization of the mechanics of its tissue using FEM models (chapter 2), the reliability analysis of an experimental procedure is explained (chapter 3), based on the high-scalable numerical solver ParFE. In chapter 4, the sensitivity analyses on two different parameters for micro-FEM model’s reconstruction are presented. Once the reliability of the modeling strategy has been shown, a recent layout for experimental test, developed in LTM, is presented (chapter 5). Moreover, the results of the application of the new layout are discussed, with a stress on the difficulties connected to it and observed during the tests. Finally, a prototype experimental layout for the measure of deformations in trabecular bone specimens is presented (chapter 6). This procedure is based on the Digital Image Correlation method and is currently under development in LTM.