Estimation Of Residual Stresses Research Articles

An Estimation of Local Residual Stresses in Amorphous and Crystallized Trivalent Chromium Coatings

Hard chromium coatings have demonstrated their performance for several decades, particularly for their wear and corrosion resistance properties. However, the traditional process using chromium trioxide (CrO3) is very toxic and is intended to disappear in the European Union by 2024, thanks to the REACH regulation. This study aimed to determine the residual stress of amorphous chromium deposits elaborated from baths containing trivalent chromium ions. However, the amorphous structure of these deposits does not allow the determination of residual stresses by conventional means. In this study, we propose adapting a recent method called “FIB-DIC”, which is not limited by the material’s crystalline structure compared to the classical X-ray diffraction (XRD) analysis. The method is based on the measurement of relaxation-induced displacement fields following the ablation of material on a very local scale. The results obtained by the classical (XRD) and the FIB-DIC method on crystallized heat-treated Cr(III) deposits are 296 ± 45 and 377 ± 275 MPa. Then, the FIB-DIC technique allowed us to evaluate a residual stress level of 479 ± 359 MPa for amorphous trivalent chromium coating, which has never been performed before.

Estimation of residual compressive stresses in deformed U8 steels with coarse-plate perlite by field dependences of magnetic permeability

The physical reasons for the formation of peaks of that part of the magnetic permeability, which is caused by transitions of only 90-degree domain boundaries μ90(H0) in deformed steel U8 with coarse-plate perlite when the field changes along the back of the hysteresis loop, are considered. It is shown that the orientation relations of the Patch-Pitch between single-crystal ferrite and cementite plates in U8 steel lead to the appearance of a constant angle between the magnetic moments of these plates and, consequently, to the appearance of corresponding local scattering fields. The latter can significantly affect the values of the peak fields of the curve μ90(H0). Theoretical expressions for these fields containing contributions of scattering fields that should be taken into account when determining residual compressive stresses are obtained. It is also shown that to determine the residual stresses, two expressions for peak fields are not enough, and additional experiments are needed, as which it is proposed to use the dependences of the coercive force on elastic tensile stresses. This leads to a complication of the algorithm for determining residual compressive stresses in comparison with the case of low-carbon steels. A method for estimating the values of local scattering fields in the ferrite parts of U8 steel grains with residual compressive stresses is proposed. Keywords: residual compressive stresses, deformed steel U8 with coarse-plate perlite, magnetic field, magnetization, magnetic permeability, 90-degree domain boundaries (DB), large-angle vicinity(LAV) and small-angle (SAV) grain boundaries of steel, orientation relations of the Patch-Pitch.

A mixed-finite element approach for full-field residual stress estimation

In this paper, a full-field residual stress identification technique has been presented via a mixed finite element approach from limited measured detail. Being an inverse problem, complete identification of residual stresses from incomplete measurement is always suffered by inherent ill-posedness. To control this issue, the identification problem has been formulated as an optimization problem via a Tikhonov type cost functional. The first part of this cost functional is associated with an energy norm of mismatch between predicted and measured residual stress. The second part represents the regularization term. A Lagrangian is then considered to satisfy the equilibrium constraint over the region of interest. The incorporation of Lagrangian with aforementioned cost functional provides a form which is very similar to the standard Hellinger-Reissner (HR) functional except the discrepancy term between the data. The minimization of this formulation leads to the solution of two-field mixed variational form associated with residual stress and Lagrangian variable. To show the efficacy of the proposed procedure a two-dimensional welded specimen is considered where the weld bead is assumed to be spatially varying in all direction for residual stress identification. Line scan details are also presented to examine the deviation between the actual and predicted residual stress in the heat affected zone and at the region away from the weld bead. The results indicate that the mixed finite element formulation has the capability to provide the complete information of residual stress despite of having very few information of measurement.

Experimental investigation and estimation of compressive residual stress of ball burnished rare earth based magnesium alloy

The present study focuses on the experimental investigation and optimization of compressive residual stress on ball burnished Mg Ze41A alloy. The optimum compressive residual stress value of −182 MPa is obtained at burnishing force of 50 N, speed of 1200 r/min, feed of 150 mm/min and 4 number of passes. Burnishing force and speed are found to be the most sensitive parameters in affecting the compressive residual stress, followed by number of passes and burnishing feed. The demarcation lines in residual stress-burnishing maps of Mg Ze41A alloy are non-parallel and non-uniform, indicating significant interactions among burnishing parameters. Ball burnishing process imparted desired amount of work hardening, which resulted in homogenized ( σx1 = σx2) and isotropic stress ( σ1 = σ2) state. Additionally, the fuzzy logic model has been deployed to estimate the compressive residual stress values at different burnishing conditions. Fuzzy logic model estimated the results with an error of 6.11%. The results demonstrate that ball burnishing process is an effective method in inducing compressive residual stresses on Mg alloy. The outcome of this study can be of great help in enhancing the fatigue performance of small size products.

Fast numerical estimation of residual stresses induced by laser shock peening

The aim of this paper is to develop a model allowing a fast first approximate estimation of the elastic–plastic stress wave propagation caused by a laser impact and the resulting residual stress field. We start by modeling the stress wave propagation, adopting a 1D uniaxial modeling, reducing the behavior of the specimen to the axis of the laser impact, excluding any edge effects caused by the edges of the laser spot. The plastic strain field resulting from this propagation can in turn be used to compute the residual stresses, by making use of an analytic modeling in the case of an infinite planar plate. The accuracy of the 1D model is assessed by comparing it to finite elements simulations, acting as a reference solution, for several materials and laser spot diameters. The results show that the stress wave propagation from the 1D model is close to identical to the reference solution. The residual plastic and stress fields from the finite elements model present a uniaxial distribution on a large portion of the laser spot, except for the very edge and spot center. The comparison between the 1D model and the reference solution shows a good match, indicating that the 1D model can be used for a fast approximation the mechanical fields created by a laser impact for laser spot diameters larger than 2 mm.

Comparison of Ensemble and Base Learner Algorithms for the Prediction of Machining Induced Residual Stresses in Turning of Aerospace Materials

Estimation of residual stresses is important to prevent the catastrophic failures of the components used in the aerospace industry. The objective of this work is to predict the machining induced residual stresses with bagging, boosting, and single-based machine learning models based on the design and cutting parameters used in turning of Inconel 718 and Ti6Al4V alloys. Experimentally measured residual stress data of these two materials was compiled from the literature including the surface material of the cutting tools, cooling conditions, rake angles as well as the cutting speed, feed, and width of cut to show the robustness of the models. These variables were also grouped with different combinations to clearly show the contribution and necessity of each element. Various predictive models in machine learning (AdaBoost, Random Forest, Artificial Neural Network, K-Neighbors Regressor, Linear Regressor) were then applied to estimate the residual stresses on the machined surfaces for the classified groups using the generated data. It was found that the AdaBoost algorithm was able to predict the machining induced residual stresses with the mean absolute errors of 18.1 MPa for IN718 alloy and 31.3 MPa for Ti6Al4V by taking into account all the variables while artificial neural network provides the lowest mean absolute errors for the Ti6Al4V alloy. On the other hand, linear regression model gives poor agreement with the experimental data. All the analyses showed that AdaBoost (boosting) ensemble learning, and artificial neural network models can be used for the prediction of the machining induced residual stresses with the small datasets of the IN718 and Ti6Al4V materials.

A computational framework based on FEA, ML and GA for estimation of welding residual stresses

The present work describes a computational framework based on finite element (FE) analysis and machine learning (ML) and genetic algorithm (GA) to accurately estimate and minimize the residual stresses in welding. The FE analysis comprises of sequentially coupled thermal and mechanical analyses that are nonlinear due to temperature-dependent thermal/mechanical properties. In the FE analysis, the effective stress function (ESF) algorithm is used for accurate computation of the temperature-induced elasto-plastic stress field during welding. The ESF algorithm accounts for the large variation of yield curves due to temperature changes in welding. To improve the accuracy of the thermal and mechanical analyses, an optimization process combining supervised machine learning and binary coded genetic algorithm is utilized. This optimization technique is implemented to derive an accurate phase-change model for the thermal FE analysis of SS304, which is otherwise a burdensome and costly task to obtain from calorimetric experiments. The results obtained through the derived phase-change model are validated through welding time-temperature distribution reported for a welding experiment in literature. The same optimization process is further used to obtain a set of weld operating conditions (such as weld voltage, current, welding speed, and the gap between plates) for SS304 that reduce the tensile residual stresses. It is found that the accurate estimation and reduction of welding residual stresses can be realized by using the present computational framework. • A detailed FE analysis is presented for the estimation of residual stresses in welding. • ESF algorithm implemented in the FE analysis is found very useful. • An optimization methodology is proposed based on machine learning and genetic algorithm. • Proposed optimization scheme is used to estimate the phase-change model and weld parameters. • Accuracy in estimation of welding temperature field is improved and tensile residual stress is minimized to a certain extent.

Measurement-driven, model-based estimation of residual stress and its effects on fatigue crack growth. Part 1: Validation of an eigenstrain model

The objective of this paper is to validate a measurement-driven, model-based approach to estimate residual stress (RS) in samples machined from quenched aluminum stock. Model input is derived from measurement of RS in the parent stock. Validation is performed for prismatic T-sections removed from bars at different locations. We find RS predicted agrees with RS measured, by contour and neutron diffraction methods, with root-mean-square model-measurement difference of 22 MPa. Follow-on work (in Part 2) applies the RS estimation to samples representative of aircraft structures and examines the effects of RS on fatigue crack growth in the RS-bearing samples.

Measurement-driven, model-based estimation of residual stress and its effects on fatigue crack growth. Part 2: Fatigue crack growth testing and modeling

This paper assesses the accuracy of fatigue crack growth (FCG) predictions for high-strength aluminum samples containing residual stress (RS) and complex two-dimensional cracks subjected to constant amplitude load. FCG predictions use linear-elastic, multi-point fracture mechanics. A first prediction includes RS estimated by the model described in Part 1; a second prediction includes RS measured by the contour method. FCG test data show a significant influence of RS. Ignoring the RS results in a +60% error in predicted FCG life (non-conservative). Including RS improves predictions of crack growth significantly (errors better than +26% (estimated RS) and −14% (measured RS)).

FIB-DIC Residual Stress Evaluation in Shot Peened VT6 Alloy Validated by X-ray Diffraction and Laser Speckle Interferometry.

Ga-ion micro-ring-core FIB-DIC evaluation of residual stresses in shot peened VT6 (Ti-6Al-4V) alloy was carried out and cross-validated against other non-destructive and semi-destructive residual stresses evaluation techniques, namely, the conventional X-ray diffraction and mechanical hole drilling. The Korsunsky FIB-DIC method of Ga-ion beam micro-ring-core milling within FIB-SEM with Digital Image Correlation (DIC) deformation analysis delivered spatial resolution down to a few micrometers, while the mechanical drilling of circular holes of ~2 mm diameter with laser speckle interferometry monitoring of strains gave a rough spatial resolution of a few millimeters. Good agreement was also found with the X-ray diffraction estimates of residual stress variation profiles as a function of depth. These results demonstrate that FIB-DIC provides rich information down to the micron scale, it also allows reliable estimation of macro-scale residual stresses.

Quantifying the subsurface damage and residual stress in ground silicon wafer using laser ultrasonic technology: A Bayesian approach

Dispersion nature of surface acoustic waves (SAWs) propagating along the machined surface contains key information about the elastic properties and stress state of the subsurface damage (SSD) layer. This enables the acoustical characterization of SSD. In this paper, we develop a mechanical properties and residual stress estimation technology for the machined surfaces, especially for ground silicon wafer, based on laser-excited surface acoustic waves (LSAWs). Bayesian inversion is applied to quantify nine orthotropic elastic constants and one residual stress parameter of the SSD layer together with the corresponding uncertainty estimates from dispersion data. The forward model of SAW propagation is derived based on Biot’s theory of small deformations influenced by initial stress. The solution of the inverse problem is given in terms of the posterior probability density (PPD) of the SSD model parameters. Markov chain Monte Carlo (MCMC) method is used to generate posterior samples by repeatedly solving the forward model to compute parameter uncertainties and inter-relationships. Laser ultrasonic experiments have been performed on two typical areas of the ground silicon wafer to determine the ability of the technology to characterize SSD and residual stress and the effect of grinding direction on the damage degree of SSD. The elastic constant values estimated by the proposed method can be reasonably explained by the fracture properties of single-crystal silicon. The reliability of the results is further verified via nanoindentation and micro-Raman spectroscopy.

Influence of Hardening Models on the Estimation of Residual Stresses by Finite Element Modeling in Type 316LN Stainless Steel Weld Joints

Influence of Hardening Models on the Estimation of Residual Stresses by Finite Element Modeling in Type 316LN Stainless Steel Weld Joints

Nonlinear interaction of Rayleigh waves in isotropic materials: Numerical and experimental investigation

Surface treatment intensity monitoring is still an open and challenging nondestructive testing problem. For the estimation of residual stress with ultrasonic measurements, local linear and nonlinear elastic constants are needed as input. In this paper, nonlinear elastic-wave interactions (also called wave mixing or scattering) — namely, the generation of secondary ultrasonic waves in a nonlinear medium — are considered as a prospective means for near-surface nonlinear elastic parameter evaluation. The allowed interactions between bulk and surface waves, as well as the dependence of the scattering efficiency on the frequency and angle between source waves, were investigated through an analytical model, then compared with FEM simulations and experimental results. Finally, possible future steps for the development of the applied methods for the determination of near-surface higher-order elastic constants are discussed. In addition, several problem-relevant data processing procedures are presented.

Analiza zamora prednapregnutih vijčanih spojeva

This article presents Wöhler plots, or S-N curves, for use in the analysis of bolt fatigue of preloaded bolted joints. Preloaded bolts under cyclic loading have a high mean stress with a small alternating stress. This is combined with a large stress concentration at the thread root. The method of fatigue analysis presented uses S-N curves with a zero mean stress. The high mean stress experienced by the bolts is accounted for using a function to calculate a damage-equivalent stress. Notch sensitivity was considered to modify S-N curves for materials with chemical compositions encompassed within the material specifications for high strength bolts. This produced S-N curves for stress concentrations relevant to bolt threads. Curve fitting techniques were used to express these curves as a function of the equivalent stress and stress ratio. An estimate of residual stresses in bolts produced by thread rolling was made. The work provides a practical method of calculating fatigue life.

Comparison of Taguchi Method and Response Surface Methodology in Determining Optimal Parameters for Welding Two Metal Plates

Welding technology play important role in manufacturing and gas metal arc welding is one of the most popular welding methods. There are many input parameters that affect the quality of the welding seam such as welding current, welding voltage, welding speed, etc. One of the problems in controlling welding robot is determining the optimal parameters that maximize the quality of welding. There are several designs of experiment techniques can be used to get the desired results with small number of experiments. In this paper, Taguchi method and response surface methodology are chosen to estimate the value of residual stresses of the seam path of welding two metal plates. In case of response surface methodology, both Box-Behnken design and central composite design are used in determining the optimal parameters. The estimation of residual stresses is done by ABAQUS software. The comparison among the designs is done and many conclusions about the optimal parameters and mathematical model are presented.

Estimation of hardness and residual stress of finished surface by linear regression model

This study presents a novel method for estimating the surface integrity in end-milling. The mechanical properties of the machined surfaces in cutting affect the quality of the final product. In particular, hardness and residual stress often require strict control, but nondestructive inspection is not easy. This study proposes a method to estimate the hardness and residual stress of end-milled surfaces by analyzing the cutting forces measured on the machine and the tool image. The measured cutting force is analyzed to estimate the specific cutting forces and edge force coefficients. The flank wear width is measured using an on-machine measuring device installed in the machine tool. From this information, the average stresses at the primary and tertiary cutting zones are estimated. The cutting temperature in the primary cutting zone is roughly estimated by considering the shear angle theory. These state quantities are highly correlated with the dislocation density and its change on the machined surface. Therefore, hardness and residual stress are estimated based on a simple linear regression model. Parameter identification was performed based on measured hardness and residual stress in end milling experiments. The experimental results validated that the proposed method can accurately estimate hardness and residual stress.

A novel framework for quantifying the subject-specific three-dimensional residual stress field in the aortic wall

BackgroundQuantification of subject-specific residual stress field remains a challenge that prohibits accurate stress analysis and refined understanding of the biomechanical behavior of the aortic wall. MethodThis study presents a framework combining experiments, constitutive modeling, and computer simulation to quantify the subject-specific three-dimensional residual stress field of the aortic wall. The material properties and residual deformations were acquired from the same porcine aortic sample, so that the subject-specific residual stress field was quantified analytically. Consequently, a novel stress-driven tissue growth model was developed and incorporated in a finite element aortic model to recover the subject-specific residual stress with the help of analytical solution. We then evaluated the framework's efficacy by simulating the residual stress distribution in the aortic dissection (AD). ResultSubject-specific residual stress field of the aortic sample was quantified analytically. No appreciable discrepancy was observed between the numerically simulated and analytically derived residual stress distributions, indicating the effectiveness of the tissue growth model. Errors arising from the numerically simulated circumferential opening angle and axial bending angle were within 5% relative to experimental results, highlighting that the framework was accurate in terms of subject-specific residual stress estimation. Finally, numerical simulations recovered the buckling behavior of the intimal flap of the dissected aorta and revealed the expansion of the false lumen and compression of the true lumen as the tear propagates circumferentially. ConclusionThe proposed framework is effective in quantifying the three-dimensional subject-specific residual stress field and it is potentially applicable in more sophisticated scenarios involving residual stress.

Estimating residual stresses of silicon wafer from measured full-field deflection distribution

This paper proposes an experimental-numerical hybrid method for estimating the residual stresses in a silicon wafer from the full-field deflection measurement. In the proposed method, the measured deflection distribution is approximated using regularized least-squares based on the superposition principle. Simultaneously, the residual stresses induced with the deflection are estimated. By applying the proposed method to a deflection distribution by finite element simulation, the basic principle of the proposed method is verified. Then, the proposed method is applied to the steel plate specimens mimicking a silicon wafer. The residual stresses obtained using the proposed method are compared with the results obtained using the X-ray diffraction method, and the appropriate regularization parameter is determined. Finally, the proposed method is successfully applied to the residual stress estimation of an actual silicon wafer. Because the deflection of a silicon is often measured during the inspection process, the proposed method of using the deflection to estimate the residual stresses is useful. Therefore, the proposed method is expected to be applied to the inspection process of silicon wafers.

Design & Modelling of Double Cantilever structure by Stainless Steel 316L deposited using Additive Manufacturing Directed Energy Deposition Process

Distortion in the metal additive manufacturing due to inherent residual stress during the separation of the deposited part from the base plate is critical. Distortion gets amplified after removing it from the build platform. Internal stress in the deposited sample during the material deposition and cooling phase is crucial to estimate. Residual stress in the structure influences structural distortion. Numerical analysis of residual stress prior to deposition helps to identify inconsistent stress in the built part and helps to take required measures like optimising process parameters, base plate preheat to make it less significant. Residual stress estimation before deposition using numerical calculation plays a major role in the improvement of the built part and establishing technology for a wide application. A numerical model for thermal history and residual stress estimation has been developed for Directed Energy Deposition (DED). A standard double cantilever model was considered for physical deposition and numerical model verification. Thermal history from Finite Element (FE) Analysis was compared with the in-situ measurement. A close agreement was noticed between in situ measurement and simulation results. A double cantilever was built using austenite stainless steel 316L by the DED technique. Internal stress in the deposited part before and after a partial separation from the base plate was compared. Numerical results comparison before and after separation emphasize the impact of residual stress on distortion.

Finite element simulation of residual stresses in welded steel butt joints and their experimental verification and mitigation

The localized, intense, and moving heat source existing in welded fabrication results in residual stresses and distortion. Residual stresses remain inside the material even after the external forces or thermal gradients are removed after welding. Residual stresses decrease fatigue life of the welded joint leading to premature failures and associated distortion cause problems in fitment during assembly. Estimation of residual stresses before actual fabrication is essential for elimination or mitigation after fabrication. In this work, finite element thermomechanical analyses are carried out to estimate the levels of residual stresses of thin welded similar butt joints of 1018 steel and SS 304 steel. The numerically obtained results of the joints are compared with experimental results of identical joint geometry, welding conditions, and material properties existing in the literature. The comparison of numerically obtained thermal histories with those from experiments yielded good agreements. Longitudinal residual stresses are found to be dominant and comparison of these longitudinal stresses with experimental data also found to be in good agreements. Further, the levels of residual stresses are computed with three different preheat temperatures (600°C, 700°C and 800°C) to study the effect of preheating temperature in the mitigation of residual stresses. It has been found that the peak value of longitudinal stress decreased considerably with preheat temperature. Increasing preheat temperature has a marginal reduction in the peak value of longitudinal stress.