publications

2026

1. A Multi-task Bayesian Optimization framework to identify a Gurson–Tvergaard–Needleman constitutive model for an MS1500 steel in hydrogen environment

   T. Grossi, A. Guazzini, L. Romanelli, and 2 more authors

   International Journal of Hydrogen Energy, Jul 2026

   Abs

   In this work, we propose a Multi-task Bayesian Optimization framework for identifying constitutive parameters of material models whose calibration typically requires significant computational effort. While the objective function is formally expressed as a residual between experimental and simulated curves of the specimen, we allow a Multi-task Gaussian Process to directly learn the entire force–displacement response. This richer representation captures more structural information than the scalar objective alone, improving predictive accuracy and efficiency. The surrogate is used iteratively to infer optimal parameter values and to adaptively select new simulation points, balancing exploration of the parameter space with exploitation of current optima. A key advantage of the approach is that the trained surrogate can be reused for new specimens, progressively reducing the number of simulations required for parameter identification. The methodology is demonstrated through a case study on the Gurson–Tvergaard–Needleman damage model, applied to MS1500 steel specimens exposed to hydrogen charging at different concentrations. To ensure that the Multi-task Gaussian Process effectively represents the simulated curves, the force–displacement data were pre-processed to exclude regions minimally influenced by hydrogen for the concentrations investigated, such as the elastic regime. The proposed approach demonstrates its effectiveness by allowing the identification of parameter values through a limited number of iterations. The results confirm the suitability of the GTN model for describing hydrogen embrittlement and suggest that the proposed methodology can be potentially extended not only to different materials, but also to other constitutive models whose parameter identification entails significant computational cost.

2. Improved residual stress evaluation with Hole-Drilling and DIC through the L-curve tool and super-resolution along depth

   T. Grossi, P. Neri, and C. Santus

   Measurement, Jan 2026

   Abs

   Full-field methods such as Electronic Speckle Pattern Interferometry (ESPI) and Digital Image Correlation (DIC) emerge as promising alternatives to strain rosette in the hole-drilling method, each with its own advantages and limitations. In particular, DIC stands out as a method requiring minimal (and cheap) specimen preparation; however, its sensitivity is approximately one order of magnitude lower than that of conventional strain gauge techniques. We address two fundamental questions. First, how can the inverse problem of the hole-drilling method be systematically approached outside the well-established framework of ASTM E837, which provides users with comprehensive guidance, including automated regularization procedures? Second, thanks to full-field measurement techniques, is it possible to retrieve stress distributions at a spatial resolution finer than the drilling step? We revisit the theoretical development of the inverse problem, aiming to directly identify the residual stresses from raw images, without intermediate pre-processing of the displacement fields. We introduce the L-curve method – well established in other scientific domains – as a rational tool for the choice of the regularization parameter. Finally, we show that, in principle, it would be possible to identify the entire stress distribution from a single drilling increment. We perform a deep rolling treatment on an aluminum specimen and compare the residual stresses identified using both a strain gauge rosette and DIC. We demonstrate that the proposed framework yields results comparable to those obtained using strain gauge rosettes, while minimizing user-dependent arbitrariness. Furthermore, we show that depth super-resolution of at least a factor of two is already achievable with current technological capabilities.

3. Improving sustainability of cold rolling of low-carbon steels via oil free lubricants

   V. Colla, O. Toscanelli, T. Grossi, and 15 more authors

   Matériaux & Techniques, Jan 2026

   Abs

   The European steel sector is committed to improve sustainability of the whole steel production chain, from decarbonisation of major upstream processes up to all downstream operations, including rolling. In particular, in the cold rolling process, oil-in-water emulsions are usually applied to lubricate the cold rolling process of low-Carbon steel. Such emulsions present some drawbacks mainly related to emulsion bath maintenance, subsequent production stages and waste disposal. Past research works showed that in some application areas, Oil Free Lubricants (OFL) show lubricant properties that are comparable to conventional lubricants, while providing significant environmental benefits. These lubricants are formulated as aqueous dispersions of Polyalkylene Glycols (PAG), a water-soluble synthetic polymer base, combined with various additives for lubrication enhancement, corrosion protection, and oil rejection. The project entitled “Transfer of aqueous oil free lubricants into steel cold rolling practice” (Ref. RollOilFree II – G.A. No 101112433) aims at developing an Oil-Free Lubricant for the cold rolling process of low-Carbon steel for applications in the automotive and packaging sectors by assessing its performance in industrial conditions. To this aim, the project combines tests at laboratory scale and simulations with trials in an industrial pilot cold rolling mill and, finally, field trials at industrial scale. Results demonstrate that OFL01 and OFL02 represent the most promising formulations as substitutes for commercial lubricants. The paper overviews the work undertaken in the first 18 months of the project, including laboratory investigations and part of the pilot trials.

4. Integrated Multiscale Simulation Framework for Cold Rolling With Oil-Free Lubricants: Development and Preliminary Validation

   V. Colla, T. Grossi, A. Petrucciani, and 1 more author

   In AISTech 2026 — Proceedings of the Iron & Steel Technology Conference, Jan 2026

   Abs

   This work presents the preliminary prototype of Mathematical Model of Cold Rolling (MMCR) developed in the project “Transfer of aqueous oil-free lubricants into steel cold rolling practice”. MMCR integrates 1D, 2D, and micro-scale models to estimate mechanical, thermal, and tribological behavior of cold rolling processes using Oil-Free Lubricants. Key components include a Cold Rolling 1D Simulator, validated against pilot mill tests, and a micro-to-macro model bridging asperity-level simulations to continuum-scale predictions. The system demonstrates strong predictive capabilities, supports lubricant design, and is scalable to multi-stand industrial mills. This integrated approach enables efficient simulation of complex rolling conditions reducing reliance on empirical calibration

5. Digital Twins for Multiagent-Based Production and Energy Management Optimization of Integrated Steel Works

   M. Bernds, V. Colla, S. Dettori, and 13 more authors

   In AISTech 2026 — Proceedings of the Iron & Steel Technology Conference, Jan 2026

   Abs

   Decreasing carbon footprint of integrated steelworks requires the implementation of significant changes including the introduction of new process units, production modifications and the disruption of current gas and energy management, which is further challenged by the fluctuations characteristics of renewable energy sources. Therefore, existing management schemes must be altered to facilitate the transition toward C-lean processes. The contribution focuses on the first developments of the European project AgiFlex, which aims at a multi-agent-based tool addressing the listed challenges. The AgiFlex concept and the developed digital twins to be used in the multi-agent tool are presented

6. Simulation of Integrated Steel Works Transitional Pathways Toward H₂-DRI-Based Route

   T. Branca, S. Cateni, V. Colla, and 3 more authors

   In AISTech 2026 — Proceedings of the Iron & Steel Technology Conference, Jan 2026

   Abs

   Integrated steelworks transition towards hydrogen-direct reduction iron-based route is considered a promising solution for the decarbonization. However, it foresees the introduction of new units in facilities currently optimized from the point of view of the production and from the gas and energy management. The contribution focuses on the use of a module of a simulation toolkit for first stationary simulations of transitional pathways starting from a European integrated Standardized Steel Mill. The effects of the introduction of direct reduction processes and of different shares of hydrogen in reducing gas in the shaft furnace on gas and energy management are investigated.

2025

1. NeuberNet: a neural operator solving elastic-plastic partial differential equations at V-notches from low-fidelity elastic simulations

   T. Grossi, M. Beghini, and M. Benedetti

   Nature Communications Engineering, Dec 2025

   Abs

   Abstract We present NeuberNet, a nonlinear manifold decoder that learns a family of operator mappings on the domain of reentrant corners between far-field displacement boundary conditions obtained with low-fidelity elastic simulations and the high-resolution stress and strain fields that stem from the elastic-plastic axisymmetric solid mechanics equations, under the only assumptions of small-scale plasticity and bilinear isotropic hardening. We envision NeuberNet as a data-driven application of the substructuring principle in solid mechanics, engineered to simulate complex geometries by employing plastic material behavior only in the vicinity of stress raisers where nonlinearities are most likely to occur. We provide practical guidelines for mesh resolution in the initial low-fidelity elastic simulations; we show how NeuberNet can detect violations of the small-scale plasticity assumption, signaling the need for full-scale nonlinear models when required; finally, we show that NeuberNet can perform zero-shot inference on 3D problems with axisymmetric geometries and non-symmetric boundary conditions.

2. Constitutive Modeling of Creep–Fatigue Interaction in 1Cr-1Mo-0.25V Steel for Hold-Time Testing

   F. Bucciarelli, A. Guazzini, T. Grossi, and 2 more authors

   Metals, Sep 2025

   Abs

   In the field of energy production, creep–fatigue interaction is a typical failure mode that might compromise the structural integrity of both rotating equipment and pressure vessels. Common design practices approach the problem in a conservative way by using high safety factors, which typically results in additional costs for manufacturing companies. The aim of this article, in the framework of continuum damage mechanics approaches, is to present a novel fatigue damage-based constitutive law. The presented law is directly inspired by well-assessed creep-based rules, suggesting a similarity in the behavior. On the other hand, creep deformation and damage are calculated with a more recent approach. The identification of the model parameters was carried out by interpreting experimental results obtained from low-cycle fatigue and creep relaxation tests performed on a commonly used ferritic–martensitic steel for power generation rotor forgings. To validate the proposed models, they were used to estimate material life consumption when the material was subjected to fully reversed axial loading conditions with hold time under tensile load. Different loading conditions at different total strain ranges and hold times were simulated, and good agreement was found between the predicted and experimental life, thus confirming the validity of the proposed models.

3. NeuberNet: a neural operator solving elastic-plastic PDEs at V-notches from low-fidelity elastic simulations

   T. Grossi, M. Beghini, and M. Benedetti

   Research Square Preprint, Mar 2025
4. Cyclic-elastic behavior in plastically pre-strained lattice structures

   I. Senegaglia, G. Macoretta, T. Grossi, and 1 more author

   Procedia Structural Integrity, Mar 2025

   Abs

   The study investigates the evolution of elastic behavior in lattice structures subjected to cyclical loading after pre-straining to various levels of plastic deformation. Triply Periodic Minimal Surface (TPMS) gyroid lattice specimens were fabricated using the Laser Powder Bed Fusion (L-PBF) technique and subjected to controlled steps of compressive pre-straining, inducing plastic deformations. Subsequently, the specimens underwent cyclic loading-unloading tests to characterize their elastic behavior. Stress-strain curves were monitored throughout the testing to determine the apparent elastic modulus ( E *) at each cycle. The results demonstrate that E* of pre-strained lattices are not static. The initial cycles after pre-straining exhibit a change in stiffness, with the E * initially increasing depending on the pre-strain level. This behavior is attributed to the morphology of the lattice itself, which is more sensible to local hardening due to an evident bending-dominated mechanical response. Over slight plastic strains, the elastic modulus stabilizes, reaching a new stiffening-to-plastic strain evolution. The magnitude of this shift and the experimental response’s dispersion are found to not be dependent on the pre-strain level.

2024

1. Numerical Analysis of a Nozzle Guided Vane Filled With Lattice Structures

   I. Senegaglia, T. Grossi, G. Macoretta, and 5 more authors

   In ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition, Aug 2024

   Abs

   Gas turbines play a critical role in industries such as power generation and aviation. Additive manufacturing has emerged as a game-changing technology for gas turbine components, offering superior design flexibility and performance enhancements. The present work provides an overview of a multistep approach for integrating lattice structures into a specific gas turbine component, the Nozzle Guide Vane (NGV), using additive manufacturing technology. The first step involves a comprehensive assessment of lattice structures’ influence on the mechanical and thermal properties of the exposed part of NGV. Through computational simulations and experiments, an ideal lattice geometry is determined, optimizing structural integrity and heat transfer properties while minimizing volume usage. The second step sets the baseline performances of the current NGV system components, which were investigated and selected for additive manufacturing analysis. The third step focuses on the overall effect of additive manufacturing capabilities in the NGV system. The fourth and final step optimizes the additive manufacturing process for fabricating gas turbine components with lattice structures. Laser Powder Bed Fusion (L-PBF) technology, united with advanced Topological Optimization analyses, and high-temperature alloys were selected to withstand the demanding gas turbine operating conditions. This multistep approach represents a significant step forward in gas turbine technology, capitalizing the advanced mechanical applications as lattice designs and additive manufacturing, aiming in enhanced performance, reduced weight, and improved efficiency. These developments hold the potential to achieve more sustainable and cost-effective energy generation and transportation systems.

2. Measuring Residual Stresses with Crack Compliance Methods: An Ill-Posed Inverse Problem with a Closed-Form Kernel

   M. Beghini, and T. Grossi

   Applied Mechanics, Jul 2024

   Abs

   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.

3. Determination of Chaboche and Bouc-Wen parameters for quenched and tempered steel

   C. Santus, L. Romanelli, T. Grossi, and 1 more author

   Journal of Theoretical and Applied Mechanics, Jul 2024

   Abs

   During cyclic loadings, metal alloys can undergo cyclic plasticity, for example, at notches. The Chaboche kinematic hardening model provides a versatile and realistic description of the material stress-strain behaviour under multiaxial cyclic loadings. In this work, the global properties, extracted from stabilized cycles of strain-controlled tests and from a force–controlled test, are employed to calculate the parameters. Alternatively, the Bouc-Wen model can provide a reliable representation of nonlinear hysteretic phenomena, and the classic nonlinear least squares approach is employed to tune its constants. The performances of the two proposed techniques are compared, and a final discussion is provided.

4. Regularization of Hole-Drilling Residual Stress Measurements with Eccentric Holes: An Approach with Influence Functions

   M. Beghini, L. Bertini, M. Cococcioni, and 3 more authors

   Journal of Materials Engineering and Performance, Apr 2024

   Abs

   The hole-drilling method is one of the most widespread techniques to measure residual stresses...

5. Towards a Reliable Uncertainty Quantification in Residual Stress Measurements with Relaxation Methods: Finding Average Residual Stresses is a Well-Posed Problem

   M. Beghini, and T. Grossi

   Experimental Mechanics, Apr 2024

   Abs PDF

   In a previous work, the problem of identifying residual stresses through relaxation methods was demonstrated to be mathematically ill-posed. In practice, it means that the solution process is affected by a bias-variance tradeoff, where some theoretically uncomputable bias has to be introduced in order to obtain a solution with a manageable signal-to-noise ratio. As a consequence, an important question arises: how can the solution uncertainty be quantified if a part of it is inaccessible? Additional physical knowledge could—in theory—provide a characterization of bias, but this process is practically impossible with presently available techniques. A brief review of biases in established methods is provided, showing that ruling them out would require a piece of knowledge that is never available in practice. Then, the concept of average stresses over a distance is introduced, and it is shown that finding them generates a well-posed problem. A numerical example illustrates the theoretical discussion Since finding average stresses is a well-posed problem, the bias-variance tradeoff disappears. The uncertainties of the results can be estimated with the usual methods, and exact confidence intervals can be obtained. On a broader scope, we argue that residual stresses and relaxation methods expose the limits of the concept of point-wise stress values, which instead works almost flawlessly when a natural unstressed state can be assumed, as in classical continuum mechanics (for instance, in the theory of elasticity). As a consequence, we are forced to focus on the effects of stress rather than on its point-wise evaluation.

2023

1. Tuning Modal Behavior Of Additively Manufactured Lattice Structures

   M. Beghini, T. Grossi, G. Macoretta, and 5 more authors

   Journal of Engineering for Gas Turbines and Power, Dec 2023

   Abs

   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 the present work, an experimental and numerical study of LS-enabled tuning of natural frequencies in mechanical components is proposed. In a first step, the difficulties arising with the large amount of 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 (L-PBF) 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.

2. Revealing systematic errors in hole drilling measurements through a calibration bench: the case of zero-depth data

   M. Beghini, T. Grossi, C. Santus, and 1 more author

   Journal of Theoretical, Computational and Applied Mechanics, Oct 2023

   Abs

   An accurate estimation of the measurement error in the hole drilling method is needed to choose an appropriate level of regularization and to perform a sensitivity analysis on the stress results. The latest release of ASTM E837 standard for the hole drilling method includes a procedure aimed at estimatingthe standard deviation of the random error component on strain measurements, proposed by Schajer. Nevertheless, strain measurements are also affected to some extent by systematic errors which are not included in the estimation and need to be compensated. For example, an error in the rosette gage factor orin the identification of the zero-depth datum systematically affects all strain measurements in a strongly correlated fashion. This paper describes a calibration bench, designed to superimpose a reference bending stress distribution on a given specimen while simultaneously performing a hole drilling measurement.Since the reference solution is known a priori and shares the measurement instrumentation, the hole geometry and the stepping process with the actual residual stress distribution, the bench provides the user with a direct validation of the obtained accuracy. In addition, strategies aimed at compensating systematicerrors can be tested on the reference solution and then applied on the residual stress evaluation. The imperfect hole geometry and drilling alignment are proven to cause a significant underestimation of stresses near the surface, as they lead to an incorrect identification of the zero-depth datum. It is shown that this effect can be corrected through the proposed calibration bench.

3. Elastic–plastic analysis of high load ratio fatigue tests on a shot-peened quenched and tempered steel, combining the Chaboche model and the Theory of Critical Distances

   C. Santus, L. Romanelli, T. Grossi, and 4 more authors

   International Journal of Fatigue, Sep 2023

   Abs

   This study aimed to predict the uniaxial fatigue strength of shot peened notched specimens made of 42CrMo4 quenched and tempered steel. The Chaboche kinematic hardening rule was employed to model the cyclic plastic behaviour of the tested samples and the evolution of the residual stresses, which were measured with X-ray diffraction and then reproduced through a finite element software with a novel proposed procedure. This latter introduced a distribution of eigenstrains to reproduce the initial residual stresses and a hardening of the material to replicate the residual stresses measured after the loading for a run-out specimen. The Theory of Critical Distances combined with the Smith-Watson and Topper multiaxial fatigue criterion were then employed to predict the fatigue strength resulting in a good level of accuracy.

4. Validation of a strain gauge rosette setup on a cantilever specimen: Application to a calibration bench for residual stresses

   M. Beghini, T. Grossi, and C. Santus

   Materials Today: Proceedings, Jun 2023

   Abs

   It is commonly known that the most difficult part of measuring residual stresses through diffraction or relaxation methods is the high sensitivity of the results to input errors, such as noise in the strain data. Then, quantifying and minimizing stress uncertainties is at least as important as the residual stress results themselves. Results are often validated by leveraging different measurement techniques, although each method is somehow specialized at detecting residual stresses at different locations and length scales. This leads to a fundamental lack of ground truth data and an inherent difficulty in detecting biases. The authors have introduced a calibration bench that facilitates the application of a well-known bending stress distribution on a specimen while conducting residual stress measurements using either the Hole-Drilling Method (HDM) or X-ray Diffraction (XRD). By leveraging Bueckner’s superposition principle, the bench allows for determination of both the residual stress distribution and the reference stress distribution through a single experimental setup. This approach not only enables direct evaluation of accuracy but also identification of any procedural systematic errors, as the reference stress distribution is known with a high degree of certainty. In this work, a detailed characterization of the stress and strain fields generated by the externally applied load was pursued. Then, the calibration bench was used to perform a validated characterization of residual stresses produced by two shot peening treatments, through both XRD and HDM. Additionally, both techniques were employed to verify the recognized bending stresses, thereby validating the findings of the residual stress measurements.

5. Tuning Modal Behaviour of Additively Manufactured Lattice Structures

   M. Beghini, T. Grossi, G. Macoretta, and 5 more authors

   In Volume 11B: Structures and Dynamics — Emerging Methods in Engineering Design, Analysis, and Additive Manufacturing; Fatigue, Fracture, and Life Prediction; Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration, Jun 2023

   Abs

   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 the present work, an experimental and numerical study of LS-enabled tuning of natural frequencies in mechanical components is proposed. In a first step, the difficulties arising with the large amount of 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 Selective Laser Melting (SLM) 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.

6. Ill-Posedness and the Bias-Variance Tradeoff in Residual Stress Measurement Inverse Solutions

   M. Beghini, T. Grossi, M.B. Prime, and 1 more author

   Experimental Mechanics, Mar 2023

   Abs PDF

   Background Relaxation methods determine residual stresses by measuring the deformations produced by incremental removal of a subdomain of the specimen. Measured strains at any given increment, determined by the cumulative effect of the relieved stresses, appear as an integral equation, which must be inverted to obtain residual stresses. In practice, stress distributions are discretized by a finite-dimensional basis, to transform the integral equations into a linear system of equations, which is often ill-conditioned. Objective This article demonstrates that the problem is actually ill-posed and comes with an inherent bias-variance tradeoff. Methods The hole drilling method is used as an example application, and the practical effects of ill-posedness are illustrated. Results Traditional regularization of the solution by limiting the resolution of the discretization reduces solution variance (noise) at the expense of increased bias and often results in the ultimately harmful practice of taking fewer data points. A careful analysis including the alternate Tikhonov regularization approach shows that the highest number of measurements should always be taken to reduce the variance for a given regularization scheme. Unfortunately, the variability of a regularized solution cannot be used to build a valid confidence interval, since an unknown bias term is always present in the true overall error. Conclusions The mathematical theory of ill-posed problems provides tools to manage the bias-variance tradeoff on a reasonable statistical basis, especially when the statistical properties of measurement errors are known. In the long run, physical arguments that provide constraints on the true solution would be of utmost importance, as they could regularize the problem without introducing an otherwise unknown bias. Constraining the minimum length scale to some physically meaningful value is one promising possibility.

7. Ill-posedness and the bias-variance tradeoff in residual stress measurement inverse solutions

   M. Beghini, T. Grossi, M. B. Prime, and 1 more author

   Mar 2023

   Abs

   Background: Relaxation methods determine residual stresses by measuring the deformations produced by incremental removal of a subdomain of the specimen. Measured strains at any given increment, determined by the cumulative effect of the relieved stresses, appear as an integral equation, which must be inverted to obtain residual stresses. In practice, stress distributions are discretized by a finite-dimensional basis, to transform the integral equations into a linear system of equations, which is often ill-conditioned. Objective: This article demonstrates that the problem is actually ill-posed and comes with an inherent bias-variance tradeoff. Methods: The hole drilling method is used as an example application, and the practical effects of ill-posedness are illustrated. Results: Traditional regularization of the solution by limiting the resolution of the discretization reduces solution variance (noise) at the expense of increased bias and often results in the ultimately harmful practice of taking fewer data points. A careful analysis including the alternate Tikhonov regularization approach shows that the highest number of measurements should always be taken to reduce the variance for a given regularization scheme. Unfortunately, the variability of a regularized solution cannot be used to build a valid confidence interval, since an unknown bias term is always present in the true overall error. Conclusions: The mathematical theory of ill-posed problems provides tools to manage the bias-variance tradeoff on a reasonable statistical basis, especially when the statistical properties of measurement errors are known. In the long run, physical arguments that provide constraints on the true solution would be of utmost importance, as they could regularize the problem without introducing an otherwise unknown bias. Constraining the minimum length scale to some physically meaningful value is one promising possibility.

8. Residual stress measurements on a deep rolled aluminum specimen through X-Ray Diffraction and Hole-Drilling, validated on a calibration bench

   M. Beghini, T. Grossi, C. Santus, and 2 more authors

   IOP Conference Series: Materials Science and Engineering, Feb 2023

   Abs

   Residual stress measurements are notably affected by a high sensitivity to errors in input data. Measurements should then be presented together with an estimation of their accuracy. A common strategy is to carry out more measurements and/or to compare the results of different techniques. However, error contributions due to biases could be dangerously left unseen. In a previous work, the authors presented a calibration bench which can impose a known bending stress distribution on a specimen while simultaneously performing X-Ray Diffraction (XRD) or Hole-Drilling Method (HDM) residual stress measurements. Since the external load can freely be applied and removed, the superposition principle can be exploited to simultaneously identify either the reference bending stress distribution or the actual residual stress distribution, with the same experimental setup. A deep rolling treatment was measured and analyzed on the calibration bench with both XRD and HDM. First, residual stresses on the surface were evaluated with XRD measurements, then electrochemical material removal was performed to investigate stresses at higher depths. After that, HDM measurements were carried out and compared with the results of XRD. Both methods were also used to identify the known bending stresses, providing an additional validation of the residual stress results.

9. Investigation of Chaboche and Bouc–Wen Parameters of Quenched and Tempered Steel and Comparison of Model Predictive Capabilities

   C. Santus, L. Romanelli, T. Grossi, and 5 more authors

   Applied Sciences, Feb 2023

   Abs

   The aim of this paper is to model the elastic–plastic uniaxial behaviour of a quenched and tempered steel. The common Chaboche isotropic kinematic hardening model (CIKH) is introduced, and a physics-based procedure is proposed to determine its parameters. This procedure is based on strain- and stress-controlled tests and is focused on the stabilized cycles. The imposed cycle properties are the hysteresis area, the stress range, the slope at the inversion points, obtained from the stabilized cycles of strain-controlled tests, and the ratcheting rate extracted from a stress-controlled test. The novelty of the algorithm is to determine the hardening parameters from the global properties of the cycle rather than imposing a pointwise fitting, which is also implemented to calculate the parameters for a comparison. The Bouc–Wen model showed great flexibility in describing nonlinear behaviours, corresponding to different physical phenomena, through an appropriate tuning of its parameter values. In this paper, another optimization approach is developed to estimate the Bouc–Wen coefficients and accurately describe the same experimental cycles. The performances of the Bouc–Wen model are compared with the predictions of the Chaboche model, and a discussion comparing the techniques used to reproduce cyclic plastic behaviour is provided.

10. A computationally fast and accurate procedure for the identification of the Chaboche isotropic-kinematic hardening model parameters based on strain-controlled cycles and asymptotic ratcheting rate

    C. Santus, T. Grossi, L. Romanelli, and 2 more authors

    International Journal of Plasticity, Jan 2023

    Abs

    The Chaboche isotropic-kinematic hardening (CIKH) model provides a versatile and realistic description of the material stress–strain behavior under generic multiaxial cyclic loadings...

2022

1. Torsional-loaded notched specimen fatigue strength prediction based on mode I and mode III critical distances and fracture surface investigations with a 3D optical profilometer

   C. Santus, L. Romanelli, T. Grossi, and 5 more authors

   International Journal of Fatigue, Aug 2022

   Abs

   Torsional and axial fatigue tests were performed on steel 42CrMo4+QT and aluminium alloy 7075-T6...

2. A calibration bench to validate systematic error compensation strategies in hole drilling measurements

   M. Beghini, T. Grossi, C. Santus, and 1 more author

   Jul 2022

   Abs

   <p>An accurate estimation of the measurement error in the hole drilling method is needed to choose an appropriate level of regularization and to perform a sensitivity analysis on the stress results. Latest release of ASTM E837 standard for the hole drilling method includes a procedure aimed at estimating the standard deviation of the random error component on strain measurements, proposed by Schajer. Nevertheless, strain measurements are also affected to some extent by systematic errors which are not included in the estimation and need to be compensated. For example, an error in the rosette gage factor or in the identification of the zero-depth point systematically affects all strain measurements in a strongly correlated fashion. This paper describes a calibration bench, designed to superimpose a reference bending stress distribution on a given specimen while simultaneously performing a hole drilling measurement. Since the reference solution is known a priori and shares the measurement instrumentation, the hole geometry and the stepping process with the actual residual stress distribution, the bench provides the user with a direct validation of the obtained accuracy. In addition, strategies aimed at compensating systematic errors can be tested on the reference solution and then applied on the residual stress evaluation. Two bias correction strategies are discussed and validated on a 7075-T651 aluminum specimen. It is observed that the imperfect hole geometry and drilling alignment lead to a significant underestimation of stresses near the surface. With the proposed bench, it is shown that this effect can be corrected. </p>

3. A calibration bench to validate systematic error compensation strategies in hole drilling measurements

   M. Beghini, T. Grossi, C. Santus, and 1 more author

   Jul 2022

   Abs

   An accurate estimation of the measurement error in the hole drilling method is needed to choose an appropriate level of regularization and to perform a sensitivity analysis on the stress results. Latest release of ASTM E837 standard for the hole drilling method includes a procedure aimed at estimating the standard deviation of the random error component on strain measurements, proposed by Schajer. Nevertheless, strain measurements are also affected to some extent by systematic errors which are not included in the estimation and need to be compensated. For example, an error in the rosette gage factor or in the identification of the zero-depth point systematically affects all strain measurements in a strongly correlated fashion. This paper describes a calibration bench, designed to superimpose a reference bending stress distribution on a given specimen while simultaneously performing a hole drilling measurement. Since the reference solution is known a priori and shares the measurement instrumentation, the hole geometry and the stepping process with the actual residual stress distribution, the bench provides the user with a direct validation of the obtained accuracy. In addition, strategies aimed at compensating systematic errors can be tested on the reference solution and then applied on the residual stress evaluation. Two bias correction strategies are discussed and validated on a 7075-T651 aluminum specimen. It is observed that the imperfect hole geometry and drilling alignment lead to a significant underestimation of stresses near the surface. With the proposed bench, it is shown that this effect can be corrected.

4. X-Ray Diffraction and Hole-Drilling residual stress measurements of shot peening treatments validated on a calibration bench

   M. Beghini, T. Grossi, C. Santus, and 3 more authors

   In ICSP14–14th International Conference on Shot Peening, Jul 2022

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   The inverse problem of determining residual stresses from diffraction or relaxation methods is notoriously affected by a high sensitivity to errors in input data...

5. Procedura di determinazione dei parametri di chaboche di un acciaio con comportamento elasto-plastico in regime di fatica ad alto numero di cicli

   C. Santus, L. Romanelli, T. Grossi, and 3 more authors

   In Atti della conferenza AIAS2022, Jul 2022

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   High-strength metal alloys usually have a purely elastic behaviour during high-cycle fatigue regime...