Highly Stressed Volume Research Articles

A probabilistic stress-life model supported by weakest link principle and highly-stressed volume/surface area concepts

This article introduces a probabilistic fatigue model that combines the principles of the weakest link theory with the highly-stressed volume (HSV) or highly-stressed surface area (HSSA) concepts to estimate stress-life (P-S-N) curves for both unnotched (smooth) and notched large-scale specimens, for any prescribed failure probability. By incorporating probabilistic models, P-S-N curves corresponding to lower probabilities of failure can be obtained. The integration of HSV or HSSA with the weakest link principle enhances the estimation of fatigue strength for real elements or components, which often require testing with reduced-size specimens. The proposed model is verified by experimental fatigue data from the literature, specifically involving unnotched and notched cylindrical specimens subjected to different constant amplitude loadings. The results demonstrate the robustness and effectiveness of the model in estimating characteristic P-S-N curves at lower probabilities of failure.

Progressive highly stressed volume for size effect analysis

The tensile strength of concrete and rock is vital for structural design, but variations in measurements arise from different experiments and specimen sizes. These discrepancies are influenced by the size effect and the highly stressed volume (HSV). Previous studies have relied on empirical formulations that provided valuable insights but overlooked fracturing's impact. In this study, we develop upon these approaches, emphasizing the significance of incorporating fracturing for improved accuracy. We develop relationships between progressive HSV and tensile strength, validated by experimental data. Furthermore, we consider the size effect using an equation relating progressive HSV, fracture quantification, and tensile strength.

Notch-based probabilistic fatigue analysis of automobile transmission gear considering size effect

Notch fatigue is regarded as a major issue of damaging the structural integrity for notched components in engineering. Based on the theory of critical distance (TCD), this study proposes a novel probabilistic fatigue analysis model to quantify the influence of notch size effect on fatigue life. Specifically, Weibull distribution is integrated into TCD for probabilistic modelling, and the impact of size effect on critical distance is characterized with highly stressed volume (HSV) method and stress concentration factor (SCF). The effectiveness and superiority of the proposed model with point method (PM) and line method (LM) are verified and compared by the experimental data of En3B, TC4 and Al-7075-T6 materials respectively. Moreover, the fatigue test of notched automobile transmission gear (ATG) is conducted, and the corresponding PSN curves are estimated with the proposed model. The test data are basically scattered in the predicted PSN curves, and the results under 50% survive probability are better than the traditional TCD, which indicates the availability of predicted PSN curves and the accuracy of the proposed model.

A modified highly stressed volume (HSV) method to predict fatigue life considering the critical crack size

Fatigue life prediction is important in engineering design to ensure structural reliability. However, it is difficult to achieve an accurate fatigue life prediction from a smooth specimen to a notched specimen with the traditional Highly Stressed Volume (HSV) method, as it is based on just one empirical evaluation of the HSV. A modified HSV method is proposed in this study, which is combined with the concept of critical distance, and the critical crack size of smooth specimens is obtained by observing the fracture surface. The predicted P-S-N curves of single-notched specimens and multi-notched specimens show a good agreement with experimental data compared with the traditional HSV method and the Theory of Critical Distance method.

A probabilistic combined high and low cycle fatigue life prediction framework for the turbine shaft with random geometric parameters

Combined high and low cycle fatigue (CCF) is a common failure mode of turbine shaft. This study presents a generic procedure for probabilistic CCF life prediction, and combined with the modified highly stressed volume (HSV) method to improve a prediction framework, which considers the effect of random geometric parameters on fatigue life and establishes the dynamic relationship between key geometric parameters and life distribution. The probabilistic CCF life modeling of turbine shafts with stochastic geometric parameters is presented, whose predicted result is consistent with practical engineering. This research is of great significance for life estimation and prolongation of turbine shaft.

Evaluation of critical distance, highly stressed volume, and weakest-link methods in notch fatigue analysis

Notch features normally lead to stress concentrations and thus present a non-legible influence on fatigue performance of critical engineering components. In this work, the predictive abilities of classic methods/theories for fatigue strength/life estimations under notch and size effects are explored and evaluated. Specifically, frameworks for fatigue strength/life estimation using the theory of critical distance (TCD), highly stressed volume (HSV) approach and weakest-link theory (WLT) are summarized, respectively, aiming to provide references for further engineering applications. Then, fatigue tests on the notched specimens of GH4169 alloy are conducted for model comparison and evaluation as well as experimental data of four other materials with different notch geometries. Results indicate that the TCD and WLT provide conservative fatigue life predictions, while the HSV approach yields better estimations on notch and size effects than the other two methods.

Flatwise to Upright Build Orientations under Three-Point Bending Test of Nylon 12 (PA12) Additively Manufactured by SLS.

This paper describes in detail a series of static tests conducted in a three-point bend configuration on three build orientations (i.e., 0°, 45°, and 90°) of additively manufactured Nylon 12 (PA12) specimens produced with a powder refresh ratio of 50%, using a benchtop industrial SLS platform, Formlabs Fuse 1. The bending strength and flexural elasticity moduli are determined following ISO 173 specifications and by employing a more complex equation that considers the influence of large deflections as per ISO 14125 indications. Statistical variability of experimental data is considered and compared to the results from the literature. Through a fractographic SEM study, the damage morphologies of tested specimens are analyzed and associated with the recorded load-deflection curves for an accurate perception of build orientation-dependent anisotropy in bending properties of AM PA12 SLS specimens. A surprising result of this investigation is that the specimens built with 45° orientation showed superior modulus elasticity in flexure but a low bending strength compared to flatwise oriented specimens. In addition, a Weibull reliability quantification of bending strength is adapted to pinpoint the effects of internal 3D printing flaws (contained within a characteristic highly-stressed volume of material) over the failure probability of the three build orientations in question.

Combined notch and size effect modeling of metallic materials for LCF using plasticity reformulated critical distance theory

Fatigue assessment of notched parts plays imperative performance in structural integrity and reliability of major equipment. The theory of critical distance (TCD) involves determining the fatigue strength of notched parts from the linear elastic stress field surrounding the notch apex. In addition, the fatigue strength of engineering part is also size dependent. Accordingly, by coupling a plasticity reformulated TCD with the weakest link theory, this study elaborates a novel scheme for probabilistic low cycle fatigue (LCF) analysis under notch and size effects. Results of fatigue tests and complementary FE analysis with the proposed model is utilized to compute highly stressed volume (HSV). Furthermore, test data of titanium alloys TC4 (Ti-6Al-4V) and TC11 (Ti-6.5Al-3.5Mo-1.5Zr-0.3Si) as well as aluminum alloy 7075-T6 are utilized for model verification. Results specify that the model predicted P–S–N curves are in good agreement with experimental data.

Evaluating size effects on fatigue life of 42CrMo4+QT steel using a statistical S-N model with highly-stressed volume and surface

A statistical S-N model based on the highly-stressed volume/surface concept is proposed for evaluating the size effects on fatigue strength of specimens from 42CrMo4+QT steel. The proposed model extends an existing physically valid model (Castillo et al. 2009) and allows the S-N curve to be extrapolated from small-scale to full-scale components. The model is validated against experimental fatigue data obtained by testing solid and hollow smooth cylindrical specimens under push-pull constant amplitude loadings. After checking that the proposed model agrees with experimental fatigue data, it is possible to apply the model to estimate the S-N curve of specimens of the highly-stressed volume up to 1802 mm3. For this case, an S-N expression is provided that can directly be used in fatigue analysis without the necessity of running a non-linear optimization.

Investigation of the statistical and geometrical size effect on the fatigue strength of EN-GJL-300 under consideration of the graphite morphology

Grey cast iron (GJL) is one of the most important materials for numerous components in car, utility vehicle and ship engines, power generation units and machine beds in various branches of mechanical engineering. In order to optimize the design of grey cast iron components for applications subjected to cyclic loading, a precise knowledge of the fatigue mechanisms is necessary. In the framework of a research project, the statistical and geometrical size effect on the fatigue strength of EN-GJL-300 is investigated. The statistical size effect describes the relationship between the fatigue strength and a changing stressed volume or surface and can be expressed with the highly stressed volume (HSV) of the component. The geometrical size effect instead takes into account the influence of a stress gradient e.g. due to notches on fatigue strength. Knowledge of the statistical and geometrical size effect allows the transfer of the fatigue strength from small specimens with different notch factors to complex large-scale components. For the investigation, unnotched and notched specimens with different highly stressed volumes are removed from cast samples as well as from a gearbox housing to determine the cyclic material behavior by stress controlled axial fatigue tests. The investigations are complemented by metallographic analyses to describe the influence of the graphite morphology on fatigue strength. The data obtained in this study serve as a contribution to the development of a design and lifetime assessment concept enabling an estimation of the local lifetime of the component as a function of the highly stressed volume and the local microstructural properties.

Combined TCD and HSV approach for probabilistic assessment of notch fatigue considering size effect

Transforming fatigue data from tested smooth specimens to notched components needs to take both notch and size effects into account. In the present study, a novel methodology for combined notch and size effects modeling is proposed based on critical distance theory and highly stressed volume (HSV) modified Weibull distribution for probabilistic fatigue assessment of notched components. In particular, a model parameter accounting for size effect is proposed based on HSV approach. Experimental data of Al 2024-T351 notched specimens were utilized for validation of the proposed model. Results indicate that almost all tested lives are within the predicted P–S–N curves with 90% survival probability.

Validation Study on the Statistical Size Effect in Cast Aluminium

Imperfections due to the manufacturing process can significantly affect the local fatigue strength of the bulk material in cast aluminium alloys. Most components possess several sections of varying microstructure, whereat each of them may inherit a different highly-stressed volume (HSV). Even in cases of homogeneous local casting conditions, the statistical distribution parameters of failure causing defect sizes change significantly, since for a larger highly-stressed volume the probability for enlarged critical defects gets elevated. This impact of differing highly-stressed volume is commonly referred as statistical size effect. In this paper, the study of the statistical size effect on cast material considering partial highly-stressed volumes is based on the comparison of a reference volume V 0 and an arbitrary enlarged, but disconnected volume V α utilizing another specimen geometry. Thus, the behaviour of disconnected highly-stressed volumes within one component in terms of fatigue strength and resulting defect distributions can be assessed. The experimental results show that doubling of the highly-stressed volume leads to a decrease in fatigue strength of 5% and shifts the defect distribution towards larger defect sizes. The highly-stressed volume is numerically determined whereat the applicable element size is gained by a parametric study. Finally, the validation with a prior developed fatigue strength assessment model by R. Aigner et al. leads to a conservative fatigue design with a deviation of only about 0.3% for cast aluminium alloy.

Probabilistic Estimation of Fatigue Strength for Axial and Bending Loading in High-Cycle Fatigue.

In this paper, the sensitivity to the type of loads (axial and bending loading) of selected construction materials (AW6063 T6 aluminum alloy, S355J2+C structural steel, and 1.4301 acid-resistant steel) in high-cycle fatigue was verified. The obtained S-N fatigue characteristics were described by a probabilistic model of the 3-parameters Weibull cumulative distribution function. The main area of research concerned the correct implementation of the weakest link theory model. The theory is based on a highly-stressed surface area and a highly-stressed volume in the region of the highest stresses. For this purpose, an analytical model and a numerical model based on the finite element method were used. The model that gives the lowest error implemented in specific test conditions was determined on the basis of high-cycle fatigue analysis. For the analyzed materials, it was a highly-stressed volume model based on the weakest link theory.

On the Statistical Size Effect of Cast Aluminium.

Manufacturing process based imperfections can reduce the theoretical fatigue strength since they can be considered as pre-existent microcracks. The statistical distribution of fatigue fracture initiating defect sizes also varies with the highly-stressed volume, since the probability of a larger highly-stressed volume to inherit a potentially critical defect is elevated. This fact is widely known by the scientific community as the statistical size effect. The assessment of this effect within this paper is based on the statistical distribution of defect sizes in a reference volume compared to an arbitrary enlarged volume . By implementation of the crack resistance curve in the Kitagawa–Takahashi diagram, a fatigue assessment model, based on the volume-dependent probability of occurrence of inhomogeneities, is set up, leading to a multidimensional fatigue assessment map. It is shown that state-of-the-art methodologies for the evaluation of the statistical size effect can lead to noticeable over-sizing in fatigue design of approximately . On the other hand, the presented approach, which links the statistically based distribution of defect sizes in an arbitrary highly-stressed volume to a crack-resistant dependent Kitagawa–Takahashi diagram leads to a more accurate fatigue design with a maximal conservative deviation of to the experimental validation data. Therefore, the introduced fatigue assessment map improves fatigue design considering the statistical size effect of lightweight aluminium cast alloys.

Fatigue strength characterization of Al-Si cast material incorporating statistical size effect

Cast aluminium components may exhibit material imperfections such as shrinkage and gas pores, or oxide inclusions. Therefore, the fatigue resistance is significantly influenced by the size and location of these inhomogenities. In this work, two different specimen geometries are manufactured from varying positions of an Al-Si-Cu alloy casting. The specimen geometries are designed by means of shape optimization based on a finite element analysis and exhibit different highly-stressed volumes. The numerically optimized specimen curvature enforces a notch factor of only two percent. To enable the evaluation of a statistical size effect, the length of the constant testing region and hence, the size of the highly-stressed volume varies by a ratio of one to ten between the two specimen geometries. Furthermore, the location of the crack initiation is dominated by the comparably greatest defects in this highly-stressed volume, which is also known as Weibull’s weakest link model. The crack initiating defect sizes are evaluated by means of light microscopy and modern scanning electron microscope methods. Finally, the statistical size effect is analysed based on the extreme value distribution of the occurring defects, whereby the size and location of the pores is non-destructively obtained by computed tomography (CT) scanning. This elaborated procedure facilitates a size-effect based methodology to study the defect distribution and the associated local fatigue life of CPS casted Al-Si lightweight components.

Statistical size effect on multiaxial fatigue strength of notched steel components

Fatigue strength assessment of large-scale structures and components is usually performed on the basis of experimental results from small-scale specimens. A proper transfer from small specimens to large-scale structures requires the consideration of size and stress-gradient induced micro supports effects, which depend on material to loading type. This paper investigates statistical size effects on the fatigue strength of notched electroslag remelted 50CrMo4 steel components under uniaxial and multiaxial loadings. Firstly, stress-based micro support concepts utilizing uniaxial small-scale tests are applied to enable an accurate fatigue design of notched steel parts. Then, the notched large-scale specimens, as representatives for an engineering component, are tested under uniaxial transverse and rotating bending as well as multiaxial loading for validation purpose. Secondly, stress-based methods with highly-stressed surface area and volume are applied in order to consider the fatigue support and statistical size effects. The estimated fatigue strength at the high-cycle regime shows a sound conformity to the large-scale experiments with a maximum deviation of 7.4% in case of the surface, and of 4.3% by the volume approach. The results of the present investigation also reveal that a certain upper threshold value is required for the highly-stressed volume concept in advance in order to ensure a proper fatigue strength assessment. The threshold value is not required for the surface approach and thus, it is found to be more feasible to an engineering purpose, especially in case of surface-initiated fatigue failure modes.

Prediction of the size effect in concrete structures using an analytical approach to the weakest link and localization method (WL2)

This paper proposes a refined Weibull effective volume (WEV) approach in order to model the size effect in concrete structures. Both the Highly Stressed Volume (HSV) and Weibull Weakest Link and Localization (WL2) methods are presented. An analytical probabilistic approach to running WL2 is then developed, knowing that this method takes into account the energetic-statistical size effect. The approach employed recognizes the inelastic phase before the peak load; it provides an analytical and fast estimation of the structural tensile strength at various scales. This approach depends on a scale length, which accounts for the spatial randomness of the concrete tensile strength, and is identified on a series of concrete specimens under uniaxial tension by use of an inverse analysis. The Weibull modulus estimation is also discussed herein. Moreover, it is shown that the analytical probabilistic approach to WL2 implementation yields the size effect prediction in both average and dispersion for various experimental series, from laboratory tests to large massive structures. The experimental test series discussed in this paper consists of concrete specimens under uniaxial tension and 3-point bending loading.

Fatigue assessment of a notched member under combined LCF and HCF loading

Steam turbine last stage blades can experience a wide range of load spectra during their lifetime, which involves both Low Cycle Fatigue (LCF) and High Cycle Fatigue (HCF) phenomena.In the paper a numerical model is proposed for considering this specific load spectrum in the fatigue life assessment of turbine blade components made of high strength precipitation-hardening steels.The method is based on cyclic isothermal stress and strain controlled fatigue test results of notched and un-notch specimen up to the HCF-regime. Moreover, stress controlled tests on notched specimens with different stress ratios were performed in order to evaluate the influence of mean stress and to derive a local Haigh diagram. The Highly Stressed Volume (HSV) has been used to transfer characteristic fatigue properties from specimens to a critical area (notched part) of a turbine blade. Furthermore, the real operating conditions of the component were used to allow the application of Palmgren-Miner damage rule.An ad-hoc MATLAB® software has been developed for the post-process of Finite Element Analysis (FEA) results, in particular for the automatic calculation of the HSV on the critical areas of the component. The proposed fatigue model has been finally applied on a real case study (blade dovetail) using appropriate safety margins for reliable design assessment.

Size effect of test specimens on tensile splitting strength of concrete: general relation

A broad experimental program was carried out on cubes, cylinders and prisms (loaded transversally or longitudinally) of sizes usually used in laboratory testing. For casting, concrete mixes of various compositions were used. The 1600 results obtained were evaluated by mathematical statistical methods. The volume of test specimens was substituted either by the size of the corresponding fracture area or by the size of the highly stressed volume (HSV) in their loaded cross-section. The absolute values of the tensile splitting strength were converted to relative values (depending on the basic size of the fracture area or on the highly stressed volume). For mathematical expression of the relationships between these quantities, an exponential function was used. This relation enables to convert the test results obtained on specimens of different sizes and shapes to the strength of the basic size specimen. This is important for the test results obtained on samples taken from finished structures, as these samples are usually of different sizes.

Effects of highly stressed volume on fatigue strength of austempered ductile irons

The relationship between fatigue strength and highly stressed volume was investigated with various combinations of specimen configurations and loading modes for austempered ductile irons (ADIs) in different heat treatments. Fatigue specimens were prepared in different notch geometries with stress concentration factors ranging from 1 to 2.64. High-cycle fatigue experiments were conducted in both rotating-bending and axial loading to determine the relevant stress–life curves. Experimental results indicate that the fatigue strength of ADI is higher when austempered at 360°C in comparison to that austempered at 300°C due to the greater toughness present. The fatigue limit in rotating-bending is higher than that in axial loading because of a smaller volume of high stress. ADI austempered at 300°C is more susceptible to notch effects on fatigue strength due to its harder, more brittle matrix structure. The fatigue limit of ADI is generally decreased with an increase in the volume of material subjected to high stress. A prediction equation for the fatigue limits of ADIs at different heat-treated conditions is established in terms of highly stressed volume and toughness.