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By means of relaxation methods, residual stresses can be obtained by introducing a progressive cut or a hole in a specimen and by measuring and elaborating the strains or displacements that are consequently produced. If the cut can be considered a controlled crack-like defect, by leveraging Bueckner's superposition principle, the relaxed strains can be modeled through a weighted integral of the residual stress relieved by the cut. To evaluate residual stresses, an integral equation must be solved. From a practical point of view, the solution is usually based on a discretization technique that transforms the integral equation into a linear system of algebraic equations, whose solutions can be easily obtained, at least from a computational point of view. However, the linear system is often significantly ill-conditioned. In this paper, it is shown that its ill-conditioning is actually a consequence of a much deeper property of the underlying integral equation, which is reflected also in the discretized setting. In fact, the original problem is ill-posed. The ill-posedness is anything but a mathematical sophistry; indeed, it profoundly affects the properties of the discretized system too. In particular, it induces the so-called bias–variance tradeoff, a property that affects many experimental procedures, in which the analyst is forced to introduce some bias in order to obtain a solution that is not overwhelmed by measurement noise. In turn, unless it is backed up by sound and reasonable physical assumptions on some properties of the solution, the introduced bias is potentially infinite and impairs every uncertainty quantification technique. To support these topics, an illustrative numerical example using the crack compliance (also known as slitting) method is presented. The availability of the Linear Elastic Fracture Mechanics Weight Function for the problem allows for a completely analytical formulation of the original integral equation by which bias due to the numerical approximation of the physical model is prevented. [ABSTRACT FROM AUTHOR]

Thanks to the increasingly widespread additive manufacturing technology and promising properties, the use of lattice structures (LS) is becoming increasingly frequent. LS allows the components to be designed with tunable stiffness, which can unlock the control of natural frequencies. However, crucial challenges must be faced to integrate LS into the typical design process. In this work, an experimental and numerical study of LS-enabled tuning of natural frequencies in mechanical components are proposed. In a first step, the difficulties arising with the large amount of finite element method (FEM) nodes, that are required to predict LS complex shapes in detail, are overcome by modeling LS with an elastic metamaterial whose stiffness properties are determined through ad hoc finite element analyses. After that, a simplified investigation can be conducted on the modal properties of components with fixed external shape and variable internal LS filling, based on triply periodic minimal surfaces (TPMS) lattices. In those conditions, the parameters of the LS core can be tuned to control and optimize the global modal frequencies of the entire geometry. In addition, the admissible range of frequencies can be estimated. Optimized plates results are validated through an experimental test campaign on additively manufactured specimens made with laser powder bed fusion technology. The samples are hammer-tested with various boundary conditions while laser sensors measure the oscillation data of selected points. Finally, estimated and identified natural frequencies were compared. The described model is suitable to be implemented in an automated tool for designers. [ABSTRACT FROM AUTHOR]

The paper presents a method for modeling and measuring the residual stress (RS) field in axisymmetric autofrettaged elements. The method is based on the assumption that an Initial Strain Distribution (ISD), originated by the plastic strain previously induced during the autofrettage process, is the source of RSs. The ISD is the quantity to be evaluated and, after being determined, it can be used, by means of a dedicated finite element (FE) model, to evaluate the RS field in the component or in any part extracted from it. The ISD is obtained by elaborating the relaxed strains produced by cutting the autofrettaged component in incremental steps. The elaboration is based on solving a set of Fredholm's integral equations in which the unknown function is the ISD and the kernel is an Influence Function (IF) correlating the measured relaxed strain to the ISD. After a general discussion of the RS induced by the autofrettage and the effect of the plastic properties of the material under process, the methods for obtaining the relaxed strains by a rational experimental setup and the procedures for obtaining the IFs are presented and discussed. The whole methodology is applied to evaluate the RS field in a hollow cylinder for which the autofrettage was modeled by a FE simulation. The consistency of the method is verified and useful indications for the experimental activities were obtained. [ABSTRACT FROM AUTHOR]