Study of Notched MEMS Specimen: Elasto-Plastic Modeling and Experimental Testing

This paper investigates the effect of stress and strains concentration, due to the notch presence, on the elasto-plastic behavior of gold microstructures subjected to tensile loading under electrostatic actuation. A kinematic model for the test microstructure which relates the experimentally measured deflection to the induced stress in the central specimen with applied electrostatic load is developed. The local maximum stress and strains at the notch root are analytically estimated using the Neuber’s rule and verified through a detailed non-linear coupled-field electric-structural finite element method (FEM)-based analysis. Several experimental tests are carried out to analyze the accumulation of plastic strain and the consequent development of plastic hinges induced in the central notched specimen due to repeated cyclic tensile loading by measuring the corresponding deflection with each loading cycle. The comparison between the failure condition observed experimentally in the test notched specimens and the FEM-based simulation results shows that the notch acts as stress and strains raiser fostering the initiation and expansion of plastic hinges in the thin film gold specimen which can lead to the specimen breakdown.

Low cycle fatigue behavior of circumferentially notched specimens made of modified 9Cr–1Mo steel at elevated temperature

During service, notched designed components such as steam generators in the nuclear power plant usually experience fatigue damage at elevated temperatures, due to the repeated cyclic loadings during start-up and shut-down operations. Under such extreme conditions, the durability of these components is highly-affected. Besides, to assess the fatigue life of these components, a reliable determination of the local stress-strain at the notch-tips is needed. In this work, the maximum strains of circumferentially notched cylindrical specimens were calculated using the most commonly known analytical methods, namely Neuber's rule, modified Neuber's rule, Glinka's rule, and linear rule, with notch root radius of 1.25, 2.5, and 5 mm, made of modified 9Cr–1Mo steel at 550 °C, and subjected to nominal stress amplitudes of ±124.95, ±149.95, and ±174.95 MPa. The calculated local strains were compared to those obtained from Finite Element Analysis (FEA). It was found that all the analytical approximations provided unreliable local strains at the notch-tips, resulting in an overestimation or underestimation of the fatigue life. Therefore, a mathematical model that predicts the fatigue lives for 9Cr–1Mo steel at elevated temperature was proposed in terms of the applied stress amplitude and the fatigue stress concentration factor. The calculated fatigue lifetimes using the proposed model are found to be in good agreement with those obtained experimentally from the literature with relative errors, when the applied stress amplitude is ±149.95 MPa, are of 1.97%,–8.67%, and 13.54%, for notch root radii of 1.25, 2.5, and 5 mm, respectively.

A Study On Low Cycle Fatigue Life Assessment of Notched Specimens Made of 316LN Austenitic Stainless Steel

The local strains obtained from the best known analytical approximations namely; Neuber's rule, Equivalent Strain Energy Density method, and linear rule, were compared to those resulting from finite- element analysis. It was found that apart from Neuber's rule with elastic stress concentration factor Kt, all the mentioned methods underestimate the local strains for all notch root radius, strain amplitudes level, at room temperature, and 550°C. Neuber's rule with Kt slightly overestimates the maximum strains for 1.25mm notch-root radius at high-temperature. Based on the analytically and numerically obtained notch root strains, the fatigue lives were estimated using the Coffin-Manson-Basquin equation. Besides, a numerical assessment of fatigue lives was estimated based on Brown-Miller and maximum shear strain equations. It was found that all these methods considerably underestimate the fatigue lives for all notch root radius, strain amplitude level, and under both temperature conditions. A new method was suggested, for which only the applied strain amplitude is needed to calculate the fatigue life of notched components. It was revealed that the suggested-method provides a good fatigue life prediction at a high-temperature loading state.

Ratcheting Prediction at the Notch Root of Steel Samples Over Asymmetric Loading Cycles

The present study intends to evaluate local ratcheting and stress relaxation of medium carbon steel samples under various asymmetric load levels by means of two kinematic hardening rules of Chaboche (CH) and Ahmadzadeh-Varvani (A-V). The Neuber's rule was coupled with the hardening rules to predict ratcheting and stress relaxation at the vicinity of the notch root. Stress-strain hysteresis loops generated by the CH and A-V models were employed to simultaneously control ratcheting progress over stress cycles and stress relaxation at notch root while strain range kept constant in each cycle. The higher cyclic load levels applied at the notch root accelerated shakedown over smaller number of cycles and resulted in lower relaxation rate. The larger notch diameter of 9 mm on the other hand induced lower stress concentration and smaller plastic zone at the notch root promoting ratcheting progress with less materials constraint over loading cycles compared with notch diameter d = 3 mm. Predicted ratcheting results through the A-V and CH models as coupled with the Neuber's rule were found in good agreements with the experimental data. The choice of the A-V and CH hardening rules in assessing ratcheting of materials was attributed to the number of terms/coefficients and complexity of their frameworks and computational time/central processing unit (CPU) required to run a ratcheting program.

Neuber’s rule accounting for the material nonlinearity influence on the stress concentration of the laminated composites

Since holes comprise the necessary features of many structural components, a comprehensive understanding of the behavior of composite plates containing an open hole is a crucial step in their design process. In the present manuscript, an extensive numerical study has been conducted in order to investigate the effects of material nonlinearity on the stress distribution and stress concentration factors in unidirectional and laminated composite materials. To attain this objective, various models with different configurations were studied. In unidirectional composites, the maximum deviation of stress distribution around the hole (from the linear solution) happens in 45° lamina in which includes a high level of shear stress. However, the maximum difference in the stress concentration factor occurs in 15° lamina and is 15.1% at the onset of failure. In composite laminates, the maximum deviation of nonlinear stress concentration factor from the linear solution is reported 24.3% and it occurs in [+45/−45] s laminate. In the last section, Neuber’s rule is employed to find the stress concentration factors of the laminated composites, with a reasonable accuracy.

On the Applicability of Neuber’s Rule for Low-Cycle Fatigue

Neuber’s rule is commonly applied in fatigue analysis to estimate the plasticity of purely elastic FEA results. In certain cases, this is more efficient than running elastic-plastic models. However, the applicability of Neuber’s rule is not well understood for complex models and may not always be appropriate. In this paper, the applicability of Neuber’s rule is investigated. The background of Neuber’s rule is discussed, theoretical limitations are derived, and algorithmic outlines of the procedures are presented. Neuber’s plasticity correction procedure is applied to both the Ramberg-Osgood elastic-plastic constitutive relation and the advanced Chaboche isotropic/kinematic nonlinear hardening relation. Throughout the manuscript, the aspects of each model are discussed from an educational perspective, highlighting each step of the implementation in sufficient detail for independent reproduction and verification. This level of detail is often absent from similar publications and, it is hoped, may lead to the wider dissemination of Neuber’s rule for plasticity correction. The final component of the paper presents a multiaxial correction of the Chaboche hardening model. To the best of the authors’ knowledge, this is the first published application of Neuber’s rule to the multiaxial plasticity correction of the Chaboche combined isotropic/kinematic hardening model. Examples are used to illustrate the behavior of the method and to present some of the commonly overlooked components when assessing the applicability of Neuber’s method.