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The stress state near the notch affects fatigue damage directly, but quantifying the stress field is difficult. The purpose of this study is to provide a mathematical description method of the stress field near the notch to achieve a reliable assessment of the fatigue life of notched specimens.

Firstly, the stress distribution of notched specimens of different materials and shapes under different stress levels is investigated, and a method for calculating the stress gradient impact factor is presented. Then, the newly defined stress gradient impact factor is used to describe the stress field near the notch, and an expression for the stress at any point along a specified path is developed. Furthermore, by combining the mathematical expressions for the stress field near the notch, a multiaxial fatigue life prediction model for notched shaft specimens is established based on the damage mechanics theory and closed solution method.

The stress gradient factor for notched specimens with higher stress concentration factors (V60-notch, V90-notch) varies to a certain extent when the external load and material change, but for notched specimens with relatively lower stress concentration factors (C-notch, U-notch, stepped shaft), the stress gradient factor hardly varies with the change in load and material, indicating that the shape of the notch has a greater influence on the stress gradient. It is also found that the effect of size on the stress gradient factor is not obvious for notched specimens with different shapes, there is an obvious positive correlation between the normal stress gradient factor and the normal stress concentration factor compared with the relationship between the shear stress gradient factor and the stress concentration factor. Moreover, the predicted results of the proposed model are in better agreement with the experimental results of five kinds of materials compared with the FS model, the SWT model, and the Manson–Coffin equation.

In this paper, a new stress gradient factor is defined based on the stress distribution of a smooth specimen. Then, a mathematical description of the stress field near the notch is provided, which contains the nominal stress, notch size, and stress concentration factor which is calculated by the finite element method (FEM). In addition, a multiaxial fatigue life prediction model for shaft specimens with different notch shapes is established with the newly established expressions based on the theory of damage mechanics and the closed solution method.

Material extrusion additive manufacturing processes inevitably produce bead-shaped surface patterns on the walls of parts, which create stress concentrations under load. This study aims to investigate the influence of such stress concentrations on the strength along the build direction (“Z-strength”).

This work consists of two main parts – an experimental demonstration to show the significance of stress concentrations on the Z-strength, followed by numerical modeling to evaluate the theoretical stress concentration factors (k_t) for such shapes. Meso-scale finite element analysis (FEA) was performed to evaluate k_t at the roots of the intersecting bead shapes. The critical bead shape parameters influencing k_t were identified, and parametric FEA studies were performed on different bead shapes by varying the normalized parameters.

The experimental results showed that up to a 40% reduction in the effective Z-strength could be attributed only to the presence of surface bead shapes. Bead overhang and root radius were identified as critical shape parameters influencing k_t. The results of the parametric FEA studies were used to generate a single empirical equation to determine k_t for any bead shape.

Predictive models for Z-strength often focus on crystallization kinetics and polymer chain interdiffusion to predict interlayer adhesion strength. The authors propose that the results of such studies must be combined with surface bead-shape induced stress concentration factors to obtain the combined, “effective” Z-strength.

The purpose of this paper is to evaluate the effect of film cooling holes on the vibration characteristics of a turbine blade, and provide the design basis for the blade, which may reduce computing costs.

Modal analysis of the blades with and without film cooling holes is performed to evaluate the effect of film cooling holes on its natural frequency. Harmonic analysis of the blade is performed to calculate the stress concentration factors of film cooling holes for different modes.

The frequency differences between two blades with and without film cooling holes are insignificant, while the differences of the vibration stress cannot be neglected. For the first three modes of the blades, the stress concentration factor is sensitive to the hole’s shape and position on the blade. With the help of the stress concentration factor defined in this work, the concentration of stresses induced by different film cooling holes can be accurately described when evaluating HCF life of the turbine blade.

The effect of film cooling holes on a turbine blade's natural frequencies was confirmed to be insignificant and the stress concentration factors around the holes are calculated. Therefore, the simplified model of the blade without film cooling holes can be used to evaluate the natural frequencies and vibration stress, which saves a lot of time and cost.

Additive manufacturing (AM) enables the production of lightweight parts with complex shapes and small dimensions. Recent improvements in AM techniques have allowed a significant growth of AM for industrial applications. In particular, AM is suitable for the production of materials shaped in lattice, which are very attractive for their lightweight design and their multi-functional properties. AM parts are often characterised by geometrical imperfections, residual porosity, high surface roughness which typically lead to stress/strain localisations and decreasing the resistance of the structure. This paper aims to focus on the study of the effects of geometrical irregularities and stress concentrations derived from them.

In this paper, several technique were combined: 3D tomography, experimental tests, digital image correlation and finite elements (FE) models based on both the as-designed and the as-manufactured geometries of lattice materials. The Digital Image Correlation technique allowed to measure local deformations in the specimen during the experimental test. The micro-computed tomography allowed to reconstruct the as-manufactured geometries of the specimens, from which the geometrical quality of the micro-structure is evaluated to run FE analyses.

Experimental and numerical results were compared by means of a stress concentration factor. This factor was calculated in three different specimens obtained from three-different printing processes to compare and understand their mechanical properties. Considering the as-designed geometry, it is not possible to model geometrical imperfections, and a FE model based on an as-manufactured geometry is needed. The results show that the mechanical properties of the printed samples are directly related to the statistical distribution of the stress concentration factor.

In this work, several techniques were combined to study the mechanical behaviour of lattice micro-structures. Lattice materials obtained by different selective laser melting printing parameters show different mechanical behaviours. A stress concentration factor can be assumed as a measure of the quality of these mechanical properties.

It is well known that notches have a deleterious influence on the fatigue strength of parts. A constant, the sensitivity index, is commonly used to relate the fatigue stress concentration factor to the elastic stress concentration factor. The author outlines a simpler hypothesis, which he claims to be a more reliable guide to fatigue behaviour in notches. Briefly it assumes that the elastic stress concentration factor gives the reduction in the fatigue strength due to the notch, but because of the local nature of the stress concentration, the endurance limit is increased according to a simple law. This increase in the fatigue strength depends on the smallness of the notch.

Inverse distance weighted (IDW) functions are utilized to make models of heterogenous materials such as functionally graded materials (FGM) in computer aided design (CAD). However, the use of IDW function based FGM for stress concentration reduction is scarcely available in the literature. The present work aims to analyze and reduce the stress concentration around a circular hole in IDW function-based finite FGM panel under biaxial loading.

Extended finite element method (XFEM) model was prepared using MATLAB to investigate the effect of geometrical and material parameters on the stress concentration factor (SCF). The obtained results of IDW FGM are compared with homogeneous material as well as two different FGMs based on the power-law function.

It was observed that the IDW function based FGM is simple in material modeling, conformal with all domain boundaries and shows lower stress concentration in comparison with the homogeneous material case. While comparing IDW FGM with power-law based FGMs, it was observed that the IDW FGM has least values of stress concentration for low d/W (diameter of the hole to panel width ratio) and is comparable with power-law based FGMs for high d/W.

It can be stated that IDW FGM is highly suitable for stress concentration reduction in finite panels with d/W = 0.5, which can further be intended for obtaining optimum hole and panel designs.

The purpose of this paper is to investigate the effect of pressure angle, and module of spur gear teeth on stress concentration factor, using photoelasticity method, and numerical MSC/NASTRAN finite element package.

The stress concentration factor is determined as a ratio between maximum stress (determined in the fillet radius by photoelastic and finite element methods), and nominal stress (calculated by a common standard formulas). In order to specify the geometric parameters (height and thickness) of gears, both standard Deutsches Institut für Normung (DIN)/Japanese Gear Manufactures Association (JGMA), and five other non‐standard approaches are used.

The results show that the stress concentration factor increases by decreasing the pressure angle. In addition, the values which are obtained by finite element analyses exhibit more uniformity than photoelastic method.

An accurate determination of stress concentration factors will limit both over and under design of the gears.

The results show that one of the suggested non‐standard approaches gives the highest stress concentration factor than the standard approaches.

The purpose of this paper is to develop basic principles of deterministic structural integrity assessment of a component with a crack- or notch-like defect by including safety factors against fracture and plastic collapse in criteria equations of linear and nonlinear fracture mechanics.

The safety factors against fracture are calculated by demanding that the applied critical stress should not be less than the yield stress of the material for a component with a crack or a notch of the acceptable size. Structural integrity assessment of the engineering components damaged by crack- or notch-like defects is discussed from view point of the failure assessment diagram (FAD). The methodology of the FAD has been employed for the structural integrity analysis and assessment of acceptable sizes of throw-thickness notch in a plate under tension and surface longitudinal notch-like defects in a pressure vessel.

Basic equations have been presented to calculate the safety factor against fracture for critical values of the stress intensity factor, crack tip opening displacement (CTOD), the J-integral and the FAD as well as to estimate an acceptable (safe) region for an engineering component with a crack- or notch-like defect of the acceptable size. It was shown that safety factors against fracture depend on both the safety factor against plastic collapse and employed fracture mechanics criterion. The effect of crack/notch tip constraint is incorporated into criteria equations for the calculation of safety factors against fracture.

The deterministic method of fracture mechanics is recommended for structural integrity assessment of a component with a crack- or notch-like defect by including safety factors against fracture and plastic collapse in criteria equations of linear and nonlinear fracture mechanics.

In order to obtain the relationship between the geometry and stress concentration of load-bearing welded joints, the fatigue design method of welded structures based on stiffness coordination strategy is studied.

Based on the structural stress theory, a new method for anti-fatigue design of welded structures oriented to stiffness coordination strategy is proposed, and the detailed implementation process of this method is given. This method is also called the three-stage anti-fatigue design method for welded structures, which includes three stages, namely, identification, analysis and relief of stress concentration.

Through the experimental analysis of welded joints in IIW standard, the effectiveness of stiffness coordination in welded joint design is proved. The method is applied to the design of welded parts and products, and the feasibility of the method in alleviating the phenomenon of stress concentration and improving the fatigue resistance of welded structures is verified.

In this study, based on the principle of coordinated design of weld stiffness, a three-stage anti-fatigue design method of welded structure is proposed. The method has practical value for the optimization design and anti-fatigue performance improvement of welded structure in engineering products.

This paper aims to present the novel stacked machine learning approach (SMLA) to estimate low-cycle fatigue (LCF) life of SAC305 solder across structural parts. Using the finite element simulation (FEM) and continuous damage mechanics (CDM) model, a fatigue life database is built. The stacked machine learning (ML) model's iterative optimization during training enables precise fatigue predictions (2.41% root mean square error [RMSE], R² = 0.975) for diverse structural components. Outliers are found in regression analysis, indicating potential overestimation for thickness transition specimens with extended lifetimes and underestimation for open-hole specimens. Correlations between fatigue life, stress factors, nominal stress and temperature are unveiled, enriching comprehension of LCF, thus enhancing solder behavior predictions.

This paper introduces stacked ML as a novel approach for estimating LCF life of SAC305 solder in various structural parts. It builds a fatigue life database using FEM and CDM model. The stacked ML model iteratively optimizes its structure, yielding accurate fatigue predictions (2.41% RMSE, R² = 0.975). Outliers are observed: overestimation for thickness transition specimens and underestimation for open-hole ones. Correlations between fatigue life, stress factors, nominal stress and temperature enhance predictions, deepening understanding of solder behavior.

The findings of this paper highlight the successful application of the SMLA in accurately estimating the LCF life of SAC305 solder across diverse structural components. The stacked ML model, trained iteratively, demonstrates its effectiveness by producing precise fatigue lifetime predictions with a RMSE of 2.41% and an “R²” value of 0.975. The study also identifies distinct outlier behaviors associated with different structural parts: overestimations for thickness transition specimens with extended fatigue lifetimes and underestimations for open-hole specimens. The research further establishes correlations between fatigue life, stress concentration factors, nominal stress and temperature, enriching the understanding of solder behavior prediction.

The authors confirm the originality of this paper.