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.

Determination of Local Stresses and Strains within the Notch Strain Approach: The Efficient and Accurate Calculation of Notch Root Strains Using Finite Element Analysis

For the service life estimation of metallic components under cyclic loading according to strain-based approaches, a simulation of the elastic-plastic stress–strain path at the point of interest is necessary. An efficient method for determining this stress–strain path is the use of the load–notch-strain curve, as this is also implemented within the FKM guideline nonlinear. The load–notch-strain curve describes the relationship between the load on the component and the local elastic-plastic strain. On the one hand, this can be estimated from loads or theoretical elastic stresses by using notch root approximations. On the other hand, this can be determined in a finite element analysis based on the elastic-plastic material behaviour. This contribution describes how this latter option is carried out in general and how it can be optimised in such a way that the FEA requires significantly less calculation time. To show the benefit of this optimisation, a comparative calculation on an exemplary geometry is carried out.

Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations

An estimation of the elastic-plastic stress state using elasticity-theoretical input data is an essential part of the service life estimation with the local strain approach in general and a German guideline based on it, in particular. This guideline uses two different notch root approximations (an extended version of Neuber’s rule and an approach according to Seeger and Beste) for this estimation. Both require the implementation of Newton’s method to be iteratively solved. However, many options are left open to the user concerning implementation in program code. This paper discusses ways in which notch root approximation methods can be implemented efficiently for use in software systems and elaborates an application recommendation. The following aspects and their influence on the computational accuracy and performance of Newton’s method are considered in detail: influence of the formulation of the root finding problem, determination of the derivative required for Newton’s method and influence of the termination criterion. The investigation shows that the advice given in the abovementioned guideline indeed leads to a conservative implementation. By carefully considering the investigated aspects, however, the computational performance can be increased by approximately a factor of 2–3 without influencing the accuracy of the service life estimation.

Stress Triaxiality and Lode Angle Parameter Characterization of Flat Metal Specimen with Inclined Notch

The stress state has an important effect on the deformation and failure of metals. While the stress states of the axisymmetric notched bars specimens are studied in the literature, the studies on the flat metal specimen with inclined notch are very limited and the stress state is not clearly characterized in them. In this paper, digital image correlation and finite element simulations are used to study the distribution of strain and stress state, that is stress triaxiality and Lode angle parameter. Flat specimen with inclined notch was tested to extract the full field strain evolution and calculate stress state parameters at three locations: specimen centre, notch root and failure starting point. It is found that compared with the centre point and the notch root, the failure initiation point can better characterize the influence of the notch angle on the strain evolution. Conversely, the centre point can more clearly characterize the effect of the notch angle on stress state, since the stress states at the failure point and the notch root change greatly during the plastic deformation. Then the calculated stress state parameters of the flat metal specimen with inclined notch at the centre point are used in Wierzbicki stress state diagram to establish a relationship between failure mode and stress state.

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.

Evaluation of Monkman–Grant strain as a key parameter in ductility exhaustion damage model to predict creep rupture of grade 92 steel

Conventional strain-based numerical prediction assumes that failure occurs when ductility is exhausted or accumulation of creep strain reaches the critical failure strain. Due to instability at the onset of rupture, the failure strain value appears to be scattered and leads to the erroneousness in prediction. In this paper, a new local constraint-based damage model incorporating the Monkman–Grant ductility, as a measure of strain during uniform creep deformation stage, was implemented into a Finite Element (FE) model to predict the creep damage and rupture of Grade 92 steel under uniaxial and multiaxial stress states. The prediction was applied on plain and notched bar specimens with various notch acuities. The uniaxial stress-dependent Monkman–Grant (MG) failure strain was adopted in the FE to simulate the influence of the constraints which were induced by the creep damage. The implication of reduced failure strain in long-term creep time on the rupture prediction is discussed. The multiaxial MG failure strain of the notched bar, which has a lower value than uniaxial failure strain due to the geometrical constraint, was estimated based on the linear inverse relationship between normalised MG failure strain and normalised triaxiality factor. It was found that the results obtained from the proposed technique were in good agreement with the experimental data within the scatter band of ± factor of 2. It was shown that MG failure strain can be used as an alternative to strain at fracture. MG strain outweighed strain at fracture because the determination of its value only required short-term testing to be performed. In most cases considered in the present investigation, the rupture-type fracture was predicted, however, there was evidence that under high constraint and low stress, stable crack propagation occurred before fracture. The location of the maximum creep damage was found to be dependent on the creep time, geometry or acuity level of the specimen. For sharp notch specimen, the failure was initiated near the notch root, however, as the notch radius increased, the initiation location moved further away towards the specimen centre.

Strain Energy Density as Failure Criterion for Quasi-Static Uni-axial Tensile Loading

Strain energy density is successfully used as criterion for failure assessment of brittle and quasi-brittle material behavior. This work investigates the possibility to use this method to predict the strength of V-notched specimens made of PMMA under static uniaxial tensile load. Samples are characterized by a variability of notch root radii and notch opening angles. Notched specimens fail with a quasi-brittle behavior, albeit PMMA has a nonlinear stress strain curve at room temperature. The notch root radius has most influence on the strength of the specimen, whereas the angle is less relevant. The value of the strain energy density is computed by means of finite element analysis, the material is considered as linear elastic. Failure prediction, based on the critical value of the strain energy density in a well-defined volume surrounding the notch tip, show very good agreement (error <15%) with experimental data.