Non-equibiaxial Residual Stresses Research Articles

Non-equibiaxial residual stress evaluation methodology using simulated indentation behavior and machine learning

Measuring the residual stress in the components in nuclear power plants is crucial to their safety evaluation. The instrumented indentation technique is a minimally invasive approach that can be conveniently used to determine the residual stress in structural materials in service. Because the indentation behavior of a structure with residual stresses is closely related to the elastic-plastic behavior of the indented material, an accurate understanding of the elastic-plastic behavior of the material is essential for evaluation of the residual stresses in the structures. However, due to the analytical problems associated with solving the elastic-plastic behavior, empirical equations with limited applicability have been used. In the present study, the impact of the non-equibiaxial residual stress state on indentation behavior was investigated using finite element analysis. In addition, a new nonequibiaxial residual-stress prediction methodology is proposed using a convolutional neural network, and the performance was validated. A more accurate residual-stress measurement will be possible by applying the proposed residual-stress prediction methodology in the future.

A new methodology for measuring residual stress using a modified Berkovich nano-indenter

In this paper, a new methodology, based on nanoindentation, is proposed to estimate the magnitude and orientation of the principal residual stress components, in a non-equi-biaxial residual stress field at the nanoscale. The proposed method exploits the force-penetration response provided by a modified Berkovich tip that, compared to the most traditional one, is characterized by a preferential elongated size. This feature allows in estimating non-equibiaxial residual stress field since the force-penetration response changes according to the indenter orientation. No observation of the residual imprint is required. Principal stress components and orientations are estimated thanks to theoretical and finite element analysis, establishing a linear relation between stress components and load variations respect to the stress-free sample. Finite element analysis is used to calibrate the model coefficients and to verify the accuracy of this approach for isotropic metals. Obtained results revealed that the method is well suitable in estimating both tensile and compressive residual stresses with an average error lower than 6% for the first case and lower than 10% for the second one.

Tailoring of residual stresses by specific use of defined prestress during laser shock peening

The aim of the present study is to tailor laser shock peening-induced residual stresses by applying defined prestress. For this purpose, elastic prestress is introduced during laser shock peening application and subsequently released. The influence of prestress on the resulting residual stresses is investigated experimentally by a four-point bending device that allows prestressing of the specimen during laser shock peening. Furthermore, a semi-analytical model of laser shock peening, extended by a contribution accounting for the prestress, is used to determine the prestress—residual stress relationship. A linear relation between prestress and compressive residual stress is found when the resulting compressive residual stresses are in the range of 20 % – 100 % of the yield strength. Generally, tensile prestress leads to a higher magnitude and penetration depth of resulting compressive residual stress after laser shock peening. As a proof of concept, prestress was used to alter a non-equibiaxial residual stress profile into an equibiaxial one, demonstrating the applicability of prestress as an effective tool for residual stress design.

Nano-Scale Residual Stress Profiling in Thin Multilayer Films with Non-Equibiaxial Stress State.

Silver-based low-emissivity (low-E) coatings are applied on architectural glazing to cost-effectively reduce heat losses, as they generally consist of dielectric/Ag/dielectric multilayer stacks, where the thin Ag layer reflects long- wavelength infrared (IR), while the dielectric layers both protect the Ag and act as an anti-reflective barrier. The architecture of the multilayer stack influences its mechanical properties and it is strongly dependent on the residual stress distribution in the stack. Residual stress evaluation by combining focused ion beam (FIB) milling and digital image correlation (DIC), using the micro-ring core configuration (FIB-DIC), offers micron-scale lateral resolution and provides information about the residual stress variation with depth, i.e., it allows depth profiling for both equibiaxial and non-equibiaxial stress distributions and hence can be effectively used to characterize low-E coatings. In this work, we propose an innovative approach to improve the depth resolution and surface sensitivity for residual stress depth profiling in the case of ultra-thin as-deposited and post-deposition annealed Si3N4/Ag/ZnO low-E coatings, by considering different fractions of area for DIC strain analysis and accordingly developing a unique influence function to maintain the sensitivity of the technique at is maximum during the calculation. Residual stress measurements performed using this novel FIB-DIC approach revealed that the individual Si3N4/ZnO layers in the multilayer stack are under different amounts of compressive stresses. The magnitude and orientation of these stresses changes significantly after heat treatment and provides a clear explanation for the observed differences in terms of scratch critical load. The results show that the proposed FIB-DIC combined-areas approach is a unique method for accurately probing non-equibiaxial residual stresses with nano-scale resolution in thin films, including multilayers.

Improvement of indentation technique for measuring general biaxial residual stresses in austenitic steels

Investigations on engineering structures show that residual stresses in combination with external loads can cause failure in loads that are less than the design threshold. Due to the applicability of austenitic steel in important industries (such as oil pipelines), accurate measurement of residual stress in this material is very important. Indentation is a new method for estimating residual stress. In this paper, by performing a large number of finite element simulations, the accuracy of residual stress measurements in austenitic stainless steels using indentation was studied by performing a large number of finite element simulations. Three different models (Suresh's, Wang's and Lee and Kwon's model) were investigated and it was found that the Lee and Kwon's model has a more accurate prediction of residual stress values in austenitic steels.Based on these numerical simulations and by studying how the residual stress measurement error of Lee and Kwon's model changes according the stress ratio, a method is suggested to correct this error and calculate the real amount of non-equibiaxial residual stresses in austenitic steels. The procedure is significantly reducing the error of residual stress measurement (from about 50% to less than 10%) and has been verified by conducting experimental test on a sample made from austenitic steel.

Evaluation of Non-Equibiaxial Residual Stresses in Metallic Materials via Instrumented Spherical Indentation

Residual stresses, existed in engineering structures, could significantly influence the mechanical properties of structures. Accurate and non-destructive evaluation of the non-equibiaxial residual stresses in these structures is of great value for predicting their mechanical performance. In this work, investigating the mechanical behaviors of instrumented spherical indentation on stressed samples revealed that non-equibiaxial residual stresses could shift the load-depth curve upwards or downwards and cause the residual indentation imprint to be an elliptical one. Through theoretical, experimental, and finite element (FE) analyses, two characteristic indentation parameters, i.e., the relative change in loading curvature and the asymmetry factor of the residual indentation imprint, were found to have optimal sensitivity to residual stresses at a depth of 0.01R (R is the radius of spherical indenter). With the aid of dimensional analysis and FE simulations, non-equibiaxial residual stresses were quantitatively correlated with these two characteristic indentation parameters. The spherical indentation method was then proposed to evaluate non-equibiaxial residual stress based on these two correlations. Applications were illustrated on metallic samples (AA 7075-T6 and AA 2014-T6) with various introduced stresses. Both the numerical and experimental verifications demonstrated that the proposed method could evaluate non-equibiaxial surface residual stresses with reasonable accuracy.

Developing a method in measuring residual stress on steel alloys by instrumented indentation technique

Indentation technique is a new method for measuring residual stress, widely used due to its simplicity of use, in-situ applicability, and nano-to-macro range of measurements. In this technique, the stresses are computed from experimentally obtained force-displacement diagrams using different models with various capabilities, proposed by some researchers. Lee's model has been proposed for non-equibiaxial residual stresses' state. In this study, the accuracy of Lee’s model was numerically scrutinized for measuring residual stress on steel specimens with a wide range of mechanical properties. Also, by performing a large number of finite-element simulations, calculation of the errors, and data analysis a function was proposed to obtain the amount of error in Lee’s model. Using the proposed relations, the accuracy of Lee’s model in measuring non-equibiaxial residual stresses on steel specimens was significantly improved.

Measuring Nonequibiaxial Residual Stresses and Mechanical Properties Using Knoop Indentation

Abstract A proper knowledge of the mechanical properties and residual stresses of materials has a significant role in the prediction of engineering failures. Indentation is a simple, nondestructive test that is capable of estimating both residual stresses and mechanical properties. In frequent studies, the response of materials during the indentation process has been used as a key parameter to distinguish different substances. Here, a state-of-the-art method with no undesirable restriction is suggested to attain the work hardening exponent, yield strength, and planar nonequibiaxial residual stresses. In the current work, an extensive series of Knoop indentation simulations were performed using two indenter angles. Subsequently, a precise observation was made in order to find existent relationships. A local method was employed based on characteristics of similar materials to obtain stress-free sample parameters through a genetic algorithm, and then another error function was defined in order to measure the yield strength and work hardening exponent. After the determination of the mechanical properties and the stress-free sample’s parameters, a particular and precise categorization was made. Then, neural network analysis was employed to derive planar residual stresses. Experimental validation was conducted using six types of aluminum and steel specimens. The results confirmed a good agreement between the test data and those predicted using the suggested procedure.

Numerical study of the effect of yield strain and stress ratio on the measurement accuracy of biaxial residual stress in steels using indentation

Investigations into engineering structures show that residual stresses in combination with external loads can cause failure in loads which are below the design threshold. As a result, the exact study of the magnitude and distribution of these stresses is an important topic in mechanical engineering. Indentation is a new method for estimating residual stress. To measure non-equibiaxial residual stresses, there is only one reliable method presented by Lee et al. In this paper, the effect of yield stress and different values of residual stress on the accuracy of residual stress measurements in steels with similar work hardening behavior was studied by performing a large number of finite element simulations.Based on these numerical simulations and by studying how the residual stress measurement error of Lee and Kwon’s model changes according the stress ratio and the yield strain, a method is suggested to correct this error and calculate the real amount of non-equibiaxial residual stresses. The procedure is significantly reduces the error of residual stress measurement (from more than 100% to less than 10%) and has been verified by conducting experimental indentation.

Effect of Laser Peening Process Parameters and Sequences on Residual Stress Profiles

Laser Peening (LP) is a surface modification technology that can induce high residual stresses in a metallic material. The relation between LP process parameters, in particular laser sequences, as well as pulse parameters and the resulting residual stress state was investigated in this study. The residual stress measurements, performed with the hole drilling technique, showed a non-equibiaxial stress profile in laser peened AA2024-T3 samples with a clad layer for certain parameter combinations. Shot overlap and applied energy density were found to be crucial parameters for the characteristic of the observed non-equibiaxial residual stress profile. Furthermore, the investigation showed the importance of the advancing direction, as the advancing direction influences the direction of the higher compressive residual stress component. The direction of higher residual stresses was parallel or orthogonal to the rolling direction of the material. The effect was correlated to the microstructural observation obtained via electron backscattered diffraction. Additionally, for peening with two sequences of different advancing directions, the study showed that the order of applied advancing directions was important for the non-equibiaxiality of the resulting residual stress profile.

Numerical investigation of spherical indentation on elastic-power-law strain-hardening solids with non-equibiaxial residual stresses

Abstract

Generalised residual stress depth profiling at the nanoscale using focused ion beam milling

The study of Residual Stress is gaining more and more attention due to its importance in design for structural integrity. At present a lot of emphasis is placed on understanding the origins of mechanical failure that lie at the nano-/micron-scale. This leads to the evident need for evaluating residual stress distributions at increasingly smaller scales, and the search for modern tools capable of accomplishing this task. Prior state-of-the-art methodologies mostly required expensive and time-consuming sample preparation and examination processes to evaluate residual stress, e.g. the study of thin TEM lamellae. The recent advent of Focused Ion Beam methods opened up methods suitable for direct application at sample surface, yet allowing the observation and quantification of stress relief phenomena at the nano-scale. In the last decade, technical aspects of FIB-based method(s) have seen significant development. On the other hand, the calculation framework employed to analyse the experimental outcome remained largely conventional, in most inconvenient for high precision analysis of challenging problems.In the present paper, the eigenstrain-based method previously presented by the authors for the depth-resolved evaluation of equi-biaxial residual stress, is generalised to non-equi-biaxial distributions of residual stress. This extends the applicability of the method to a much wider class of problems. The use of cylindrical ring-core shape in FIB-DIC analysis allows reconstructing the full in-plane residual stress tensor as a function of milling depth. We report formulae for calibrated influence functions that have very broad applicability, and can be used in the overwhelming majority of cases. Their derivation is based on an extensive set of FEM simulations that allowed reliable identification of the limitations of this approach, and highlight the importance of making appropriate selection of ring-core diameter(s). Finally, experimental validation of the method is presented that involves the reconstruction a known non-equibiaxial residual stress depth profile, confirming the validity and reliability of the present approach.

Determination of directionality of nonequibiaxial residual stress by nanoindentation testing using a modified Berkovich indenter

Abstract

Directionality of residual stress evaluated by instrumented indentation testing using wedge indenter

In instrumented indentation testing (IIT), residual stress can be evaluated by shift in indentation load-depth curves for stress-free and stressed states. Although the average surface residual stress is able to be evaluated with Vickers indenter, in order to know stress directionality, another indentation tests with two-fold symmetric indenter, for example, Knoop indenter, are needed. As some necessities for evaluating nonequibiaxial residual stress within small indent area, we suggest a novel way to evaluate directionality of residual stress, p, using wedge indenter characterized by two parameters, edge length and inclined angle. We develop wedge-indentation-mechanics model based on predetermined conversion factors which are determined by IITs for various uniaxial stressed states combining with finite element analysis simulations. By utilizing the developed model, directionality of residual stress is evaluated through two serial wedge IITs with respect to principal directions. We find good agreements between applied residual stress and residual stress evaluated by the developed model for biaxial tensile stress states.

Prediction of residual stress components and their directions from pile-up morphology: An experimental study

Abstract

Modeling and experimental verification for non-equibiaxial residual stress evaluated by Knoop indentations

Surface residual stress is usually characterized by two parameters; (1) magnitude and (2) direction of two principal residual stresses. We propose a novel way to evaluate these parameters by instrumented indentation testing (IIT) using a Knoop indenter, which has two-fold symmetry. Non-equibiaxial surface stress causes a shift from residual stress in the force-indentation depth curve of IIT that depends on the Knoop indentation in-plane angle between residual stress and long diagonal of Knoop indenter. We develop a theoretical model to evaluate surface residual stress using only experimental parameters obtained by four Knoop IITs at 45° rotated angles, by introducing mathematical definition of conversion factor, a, which ratio of normal and parallel conversion factors was known as constants (~0.34) on previous studies. We verify this model by Knoop IITs on four metallic cruciform samples in which the surface residual stress is controlled by bending. Experimental results of principal stress and direction show good agreements with applied stress and directions.

Optimization of indirect magnetoelectric effect in thin-film/substrate/piezoelectric-actuator heterostructure using polymer substrate

Indirect magnetoelectric effect has been studied in magnetostrictive-film/substrate/piezoelectric-actuator heterostructures. Two different substrates have been employed: a flexible substrate (Young's modulus of 4 GPa) and a rigid one (Young's modulus of 180 GPa). A clear optimization of the indirect magnetoelectric coupling, studied by micro-strip ferromagnetic resonance, has been highlighted when using the polymer substrate. However, in contrast to the rigid substrate, the flexible substrate also leads to an a priori undesirable and huge uniaxial anisotropy which seems to be related to a nonequibiaxial residual stress inside the magnetostrictive film. The “strong” amplitude of this nonequibiaxiallity is due to the large Young's modulus mismatch between the polymer and the magnetostrictive film which leads to a slight curvature along a given direction during the elaboration process and thus to a large magnetoelastic anisotropy.

Evaluation of nonequibiaxial residual stress using Knoop indenter

Abstract

ICONE19-43348 MEASUREMENT OF NON-EQUIBIAXIAL RESIDUAL STRESS FIELD BY INDENTATION TECHNIQUE USING ASYMMETRIC INDENTER

The instrumented indentation technique (IIT) has received much attention as an alternative evaluation method for nondestructive measurement of residual stresses in recent years. In the past, however, the measurement of residual stresses by indentation technique has been limited to an equibiaxial residual stress states because of a symmetric indenter used in this method. In the present study, the effects of the shapes of asymmetric indenters on differences in indentation loads between a stress-free state and residual stress states are discussed by theoretical approaches. These approaches are progressed by focusing on the effect of deviator residual stresses. A method for evaluating non-equibiaxial residual stress field are proposed by using these results. In addition, the proposed method is applied to bead-on-welded plate. The evaluation results by the proposed method are in agreement with the evaluation results by X-ray diffraction method.

Numerical approaches and experimental verification of the conical indentation techniques for residual stress evaluation

Conical indentation methods to determine residual stress are proposed by examining the finite element solutions based on the incremental plasticity theory. We first note that hardness depends on the magnitude and sign of residual stress and material properties and can change by up to 20% over a specific range of elastic tensile and compressive residual stress, although some prior indentation studies reported that hardness is hardly affected by residual stress. By analyzing the characteristics of conical indentation, we then select some normalized indentation parameters, which are free from the effect of indenter tip rounding. Adopting dimensional analysis, we present practical conical indentation methods for the evaluation of elastic/plastic equi- and nonequi-biaxial residual stresses. The validity of developed approaches is confirmed by applying them to the experimental evaluation of four-point bending stress.