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Tensile-plate anchorage (TPA) is widely used in steel cable-stayed bridges. However, due to the complex geometry of the anchorage, the stress concentration area will appear under the action of the dynamic load, leading to fatigue failure. In this paper, taking a cable-stayed bridge as an example, the theoretical analysis and experimental investigation of the fatigue performance of TPA are performed. At first, a full-bridge finite element model was set up to obtain the severest cable force and cable force amplitude under fatigue load. Then the fatigue test of 1:1.5 specimen was carried out. The maximum principal stress of TPA was 32.24 MPa and the maximum deformation was 1.6 mm. During the loading process, TPA was in elastic working state. After 2 million fatigue load cycles, no cracks were found. At last, the fatigue performance of TPA was analyzed with the theory of critical distances (TCD). The results of the theoretical analysis and fatigue test show that the fatigue performance of TPA could satisfy the use requirement. [ABSTRACT FROM AUTHOR]

During the last few decades, the requirements for modern machine elements in terms of size reduction, increasing the energy efficiency, and a higher load capacity of standard and non-standard gears have been very prevalent issues. Within these demands, the main goals are the optimization of the gears' tooth profiles, as well as the investigation of new tooth profile designs. The presented design idea is based on the optimal solutions inspired by nature. Special attention is paid to the new design of the tooth root zones of spur gears in order to decrease the stress concentration values and increase the tooth root fatigue resistance. The finite element method is used for stress and strain state calculations, and the particular gear pair is modeled and optimized for these purposes. For tooth root strength analysis, the estimations are based on the theory of critical distances and the stress gradients obtained through finite element analysis. The obtained stress gradients have shown important improvements in the stress distribution in the transition zone optimized by biomimetics. An analysis of the material variation influence is also performed. Based on the investigations of a particular gear pair, a significant stress reduction of about 7% for steel gears and about 10.3% for cast iron gears is obtained for tooth roots optimized by bio-inspired design. [ABSTRACT FROM AUTHOR]

The study shows that the combination of several finite elements with different deformation models of continuum (elastic, elastic-plastic, isotropic and orthotropic) at common nodes makes it possible to predict complex nonlinear deformation of fibrous composites. There is considered only elastic deformation in the built-in libraries of anisotropic materials in well-known commercial FEA packages. Calculations of nonlinear mechanical behavior and failure under loading in the warp/weft and diagonal directions were performed on the example of fibreglass plastic STEF. Complex behavior of STEF is shown to be described by combining three phases with simple constitutive models: two brittle monotropic (imitate dry warp and weft fibers) and one isotropic elastic-plastic (imitate polymer). To determine the elasticity and fracture parameters of each model, it is proposed to apply experimental STEF stress-strain diagrams in the warp/weft and diagonal directions. The failure criteria for the above mentioned models are independent and are recorded in terms of strain. The strain mapping and damage development in STEF near the hole was studied by DIC and acoustic emission methods. ANSYS Workbench (Autodyn) software, critical distance theory, and failed finite element erosion technology were used to evaluate the fracture load of tensile specimens with a hole. The results of fracture loads and inelastic deformation fields calculations are in good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

The purpose of this work is to analyze the stress-raisers that affect the tensile strength and fatigue resistance of GFRP parts using the point and line methods of the theory of critical distances (TCD) to obtain a quantitative measure of the defect size that can be tolerated by the composite before it fails. In the course of the work, a method combining TCD and the Weibull function was developed. In the course of the work, GFRP structural fiberglass for electrical purposes was tested under uniaxial quasi-static and cyclic loading with digital image correlation (DIC) and acoustic emission (AE), as well as a numerical simulation of deformation. The studied specimens were plain (without a stress-raiser) and notched (V-shaped) with different notch root radii and depths. The results were used to determine the material critical distances. In this case, two approaches to TCD were used: line (LM) and point (PM) methods. To analyze the experimental results, finite element modeling was applied using the ANSYS software package. As a result, the linearized maximum principal stresses were obtained on the central line passing through the top of the stress raiser. Thus, the values of the critical distances of the material were determined by PM and LM. Based on the data obtained, the sizes of permissible defects in the studied fiberglass were established that do not affect the tensile and fatigue strength of the material. The paper illustrates the cumulative energy, peak amplitudes, and distributions of the frequency of the spectral maximum of acoustic emission signals obtained after the destruction of specimens by fatigue test. Evolutions of deformation fields on the specimen surface were recorded using a Vic-3D contactless optical video system and the DIC. [ABSTRACT FROM AUTHOR]

The repair of structural elements for the prestressing of reinforced concrete is necessary when existing prestressing wires are damaged or after a certain period of time. The objective of this paper is to describe the methodology for the life assessment of corroded prestressing wires, sampled from prestressed concrete elements after a few decades of use. The aim of the presented research was to determine the real properties of corroded wire in terms of the evaluation of remaining load capacity using the Theory of Critical Distances (TCD). The methodology also includes spatial 3D characterization of corroded surfaces, determination of mechanical properties, and Finite Element Analysis (FEA) of a model of wire with corrosion pits. The final goal of the presented methodology is to enable more efficient evaluation of repair range and options for the elements of mechanical prestressing systems within various structures. The results and conclusions indicate that the developed methodology, based on the interdisciplinary approach and implementation of state-of-the-art methods, has a high applicability potential for both static and fatigue fracture prediction in the case of prestressed wires. The proposed method has a huge potential for simple and fast prediction of the life assessment of engineering structures, particularly for damaged elements with arbitrary geometry features. [ABSTRACT FROM AUTHOR]

The application of various methods of the theory of critical distances for evaluating the cleavage failure of a quasi-brittle plate with a notch in the form of a circular hole that is subjected to uniaxial tension, uniaxial compression, and also to the combined action of tensile and compressive stresses is considered. Critical stress calculations have been performed based on the previously proposed approach, according to which the structural parameter of the nonlocal failure criterion is represented as the sum of two terms. The first of them characterizes the actual structure of the material and is a constant, while the second one reflects the formation of inelastic deformations and depends on the plastic properties of the material, sample geometry, and boundary conditions. The calculation results are compared with known experimental data. [ABSTRACT FROM AUTHOR]

The paper reviews the research results to date on critical length parameters of notched aluminum specimens with various notch radii. The Theory of Critical Distances (TCD) was applied in form of the Line Method for the determination of the critical length parameter. This parameter can be used for lifetime predictions of notched components. The output is a comparison of critical length parameters of specimens with various notch radii. Numerical calculations as well as experimentally obtained data were employed in the analysis. Fatigue experiments were performed at fatigue loading device working at ultrasonic frequency of 20 kHz. Thus we were able to reach very high number of cycles to failure. [ABSTRACT FROM AUTHOR]

This paper focuses on fatigue estimation of notched components. It discusses two major concepts – critical distance theory and solutions based on the relative stress gradient – and specific criteria related to them. It checks their quality by validating their output on own experimental data retrieved in fully-reversed tension and in fully-reversed torsion on unnotched and notched specimens manufactured from ČSN 411523 structural steel (equivalent to S355J2). The solutions based on the stress gradient provide better estimates. However, these two calculation concepts process the input data differently and use them for calibrating their parameters. Together with the limited scope of the experimental set, this has prevented the authors reaching a final verdict on ranking the estimation quality of the compared criteria. The output of our investigation shows that the solutions proposed within the concept of a relative stress gradient are currently more practical for use in the general engineering domain. • Selected methods for assessing the notch effect into fatigue analysis were tested. • Analysis carried out on own fatigue experiments of S355J2 structural steel. • In general, the relative stress gradient methods provide more acceptable results. [ABSTRACT FROM AUTHOR]

• Stress distributions in notch fatigue and fretting fatigue are compared. • The general path of the Point Method is analyzed considering stress distributions. • A rig with an accurate alignment is designed for fretting fatigue experiments. • Fretting fatigue tests of complete contacts are carried out for Ti-6Al-4V alloy. • The minimum life path is proposed for the fretting fatigue life prediction. With the improvement and success of the Theory of Critical Distances (TCD) in notch fatigue problems, the TCD, especially the Point Method (PM), combined with multiaxial fatigue criteria, has been used over the last few years to predict the fretting fatigue life. However, little attention is paid to the effect of different damage mechanisms, especially stress distribution, between the two conditions on the application of the PM. This paper aims to select a suitable path for the PM, considering various stress distributions, for the fretting fatigue life prediction of complete contacts. A new method is developed to select the suitable path of the PM for fretting fatigue life prediction. To validate the analysis, corresponding tests were carried out using an improved proving ring-like rig in a Ti-6Al-4V alloy. Predicted lives on all paths were calculated using the PM combined with different multiaxial fatigue criteria, without incorporating wear effects, and compared with experimental lives using an error bar graph. Results indicate that when the fretting wear is not considered, the minimum predicted life path is more suitable for the PM than the perpendicular and maximum predicted life paths. This suitable path is compared to the path selection in the uniaxial symmetric V-notch fatigue condition. Analysis shows that the conventional path (the notch bisector) of the PM produces the maximum predicted life for the notch fatigue condition. The cause of this different path selection of the PM in the two fatigue conditions is assumed to be the effect of the asymmetric stress distribution and fretting wear damage in the fretting fatigue condition. [Display omitted] [ABSTRACT FROM AUTHOR]

During the last few decades, the requirements for modern machine elements in terms of size reduction, increasing the energy efficiency, and a higher load capacity of standard and non-standard gears have been very prevalent issues. Within these demands, the main goals are the optimization of the gears’ tooth profiles, as well as the investigation of new tooth profile designs. The presented design idea is based on the optimal solutions inspired by nature. Special attention is paid to the new design of the tooth root zones of spur gears in order to decrease the stress concentration values and increase the tooth root fatigue resistance. The finite element method is used for stress and strain state calculations, and the particular gear pair is modeled and optimized for these purposes. For tooth root strength analysis, the estimations are based on the theory of critical distances and the stress gradients obtained through finite element analysis. The obtained stress gradients have shown important improvements in the stress distribution in the transition zone optimized by biomimetics. An analysis of the material variation influence is also performed. Based on the investigations of a particular gear pair, a significant stress reduction of about 7% for steel gears and about 10.3% for cast iron gears is obtained for tooth roots optimized by bio-inspired design.

This study aims to find suitable fatigue assessment methods for welded structures (cover plates and T‐joints) subjected to axial and bending loading. The Hot Spot Stress (HSS), 1‐mm stress (OM), Theory of Critical Distances (TCD), Stress Averaging (SA), and Effective Notch Stress (ENS) methods are evaluated in terms of accuracy and reliability. The evaluation is based on fatigue test data extracted from the literature and carried out in this study. It is found that the SA method can be used to assess the fatigue strength of cover plate joints under axial loading with relatively good accuracy and low scatter, followed by the ENS method. The HSS, TCD, SA, and ENS methods are conservative estimation methods for T‐joints under bending, while the accuracy is low. Furthermore, fatigue design curves applicable for T‐joints under bending are discussed, which can be used in the TCD method and SA method. [ABSTRACT FROM AUTHOR]

The purpose of this work is to analyze the stress-raisers that affect the tensile strength and fatigue resistance of GFRP parts using the point and line methods of the theory of critical distances (TCD) to obtain a quantitative measure of the defect size that can be tolerated by the composite before it fails. In the course of the work, a method combining TCD and the Weibull function was developed. In the course of the work, GFRP structural fiberglass for electrical purposes was tested under uniaxial quasi-static and cyclic loading with digital image correlation (DIC) and acoustic emission (AE), as well as a numerical simulation of deformation. The studied specimens were plain (without a stress-raiser) and notched (V-shaped) with different notch root radii and depths. The results were used to determine the material critical distances. In this case, two approaches to TCD were used: line (LM) and point (PM) methods. To analyze the experimental results, finite element modeling was applied using the ANSYS software package. As a result, the linearized maximum principal stresses were obtained on the central line passing through the top of the stress raiser. Thus, the values of the critical distances of the material were determined by PM and LM. Based on the data obtained, the sizes of permissible defects in the studied fiberglass were established that do not affect the tensile and fatigue strength of the material. The paper illustrates the cumulative energy, peak amplitudes, and distributions of the frequency of the spectral maximum of acoustic emission signals obtained after the destruction of specimens by fatigue test. Evolutions of deformation fields on the specimen surface were recorded using a Vic-3D contactless optical video system and the DIC.

The fracture toughness reflects the rock resistance to crack propagation, and therefore represents an important parameter for rock fracture assessments. From a strict point of view, the real fracture toughness ( K IC ) corresponds to a cracked situation in which the notch radius is theoretically equal to zero. However, most of the defects in rocks have a finite radius and, therefore, should be studied as notch-type defects. Here, the notch effect is numerically studied together with the influence of the grain size and the sorting coefficient (grain size uniformity) on the apparent fracture toughness ( K IN ). To this end, several four-point bending tests with different U-shaped notch radii, mean grain sizes and degrees of uniformity in grain size and shape have been simulated using the Discrete Element Method. In order to represent the grains of the rocks, the Voronoi tessellation is used to create randomly sized and distributed polygonal blocks. These Voronoi polygons have been defined, on the one hand, by an average edge length of 1, 2 and 3 mm, and, on the other hand, by a different number of iterations (n ) in the relaxation process during the generation of the polygons, which defines the grain size uniformity. The numerical analyses performed and the interpretation of the results show a clear notch effect in all the studied cases, as the apparent fracture toughness ( K IN ) increases with notch radius. Finally, the obtained stress fields at the notch tip have been compared to those obtained from the traditional finite element method. Highlights: Four-point bending tests with U-shaped notches simulated using the Discrete Element Method. Different notch radii, mean grain sizes and degrees of uniformity are studied. Results show a clear notch effect, increase of apparent fracture toughness with notch radius. Interpretation of the results using the Theory of Critical Distances. A linear relation between the critical distance of the rock and the grain size is observed. The critical distance slightly increases when less uniform grains are studied. [ABSTRACT FROM AUTHOR]

• Fretting fatigue tests of 42CrMo4+QT steel performed with varying bridge pad radii. • Qualitative variation in crack initiation was observed with the number of cycles. • This phenomenon was successfully modeled using elasto-plastic material behavior. • Among the 11 criteria tested, Papuga's QCP method yielded the most accurate results. This paper focuses on an experimental and numerical assessment of fretting fatigue in cyclically loaded specimens from 42CrMo4+QT steel in contact with bridge pads of the same material. Four different pad configurations were employed, varying the radii of the pad legs, to achieve various stress gradient conditions in the fatigue process zone. A qualitative change in terms of the number of contact initiation locations observed in relation to fatigue life served as one of the aspects of the evaluation of a set of 11 fatigue prediction methods. It was observed that elastic–plastic stress analysis is crucial for capturing this phenomenon. Among the tested methods, Papuga's quadratic parameter criterion (QCP) performs best in terms of risk assessment of crack initiation and prediction of its location. [ABSTRACT FROM AUTHOR]

[Display omitted] • Structural integrity assessment of materials containing notch-type defects. • Combines Failure Assessment Diagrams and the Theory of Critical Distances. • Validated on 1106 experimental results from metals and non-metals. • The methodology provides safe reasonably conservative assessments. This paper provides a comprehensive description, and the subsequent validation, of a structural integrity assessment methodology of structural materials containing notch-type defects. The approach is based on the combination of Failure Assessment Diagrams (FAD) and the Theory of Critical Distances (TCD). The former provides the general assessment tool, which is exactly the same one as that used for crack-like defects, whereas the latter provides the notch effect correction required for the analysis of this type of defects. Finally, the proposed methodology is validated on a number of metallic and non-metallic structural materials, with 1,106 experimental results on different types of testing specimens, covering four structural steels, aluminium alloys 7075-T651 and 6060-T66, PVC, PMMA, PA6, fibre-reinforced PA6, 3D printed (Fused Filament Fabrication) ABS, PLA and graphene reinforced PLA, granite and limestone. The results show how the FAD-TCD methodology provides safe reasonably conservative assessments on the mentioned structural materials in the presence of notch-type defects. [ABSTRACT FROM AUTHOR]

• The theory of critical distances is used for predictions of fatigue lifetime of notched samples. • The critical distances are modified by the stress concentration factors of assessed notches. • The approach is verified on experimental data measured on three types of steels. • The predictions matched the experimental results well. The theory of critical distances is used for evaluation of effects of notches on load-bearing capacity of notched components under static or cyclic fatigue loading. The theory can also be used to predict the fatigue life of notched components. One of the assumptions for a reliable prediction is that the critical distance is independent of the notch geometry and its stress concentration level. The study shows that the critical distance depends not only on the number of cycles to failure (under fatigue loading), but also on the notch radius. In this case, direct use of the critical distance leads to unreliable predictions. The study quantifies the relation between the model notch (from which the critical distance is determined) and the predicted notch by means of the ratio of their stress concentration factors. The predictions modified by the ratio of stress concentration factors provide results that are in satisfactory agreement with the experimental data. The predictions were made and verified on the basis of fatigue data measured on two stainless steels 1.4306 and 1.4307, and high strength structural steel S690QL. Smooth and notched specimens were tested on an ultrasonic fatigue machine in a symmetrical tension–compression mode. The results were evaluated in the regions of high cycle and very high cycle fatigue. [ABSTRACT FROM AUTHOR]

The repair of structural elements for the prestressing of reinforced concrete is necessary when existing prestressing wires are damaged or after a certain period of time. The objective of this paper is to describe the methodology for the life assessment of corroded prestressing wires, sampled from prestressed concrete elements after a few decades of use. The aim of the presented research was to determine the real properties of corroded wire in terms of the evaluation of remaining load capacity using the Theory of Critical Distances (TCD). The methodology also includes spatial 3D characterization of corroded surfaces, determination of mechanical properties, and Finite Element Analysis (FEA) of a model of wire with corrosion pits. The final goal of the presented methodology is to enable more efficient evaluation of repair range and options for the elements of mechanical prestressing systems within various structures. The results and conclusions indicate that the developed methodology, based on the interdisciplinary approach and implementation of state-of-the-art methods, has a high applicability potential for both static and fatigue fracture prediction in the case of prestressed wires. The proposed method has a huge potential for simple and fast prediction of the life assessment of engineering structures, particularly for damaged elements with arbitrary geometry features.

Open circular holes are an important design feature, for instance in bolted joint connections. However, stress concentrations arise whose magnitude depends on the material anisotropy and on the defect size relative to the outer finite plate dimensions. To design both safe and light-weight optimal structures, precise means for the assessment are crucial. These can be based on analytical methods providing efficient computation. For this purpose, the focus of the present paper is to provide a comprehensive stress and failure analysis framework based on analytical methods, which is also suitable for use in industry contexts. The stress field for the orthotropic finite-width open-hole problem under uniform tension is derived using the complex potential method. The results are eventually validated against Finite-Element analyses revealing excellent agreement. Then, a failure analysis to predict brittle crack initiation is conducted by means of the Theory of Critical Distances and Finite Fracture Mechanics. These failure concepts of different modelling complexity are compared to each other and validated against experimental data. The size effect is captured, and in this context, the influence of finite width on the effective failure load reduction is investigated. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to accurately obtain fatigue life prediction for the key components of a turning mechanism using the improved theory of critical distances (TCD). The irregularly shaped rotating arm is the central stressed part of the turning mechanism, which contains notches. It has been found that TCD achieves good results in predicting the fatigue strength or fatigue life of notched components with regular shape but is less commonly used for notched components with irregular shape. Therefore, TCD was improved and applied broadly to predict the fatigue life of an irregularly shaped rotating arm. Firstly, the notch depth and structure net width parameters were introduced into the low-order and low-accuracy classical TCD function to obtain a novel stress function with high computational efficiency and high accuracy, whereas the stress concentration factor was introduced to modify the length of critical distance. Secondly, the improved TCD was used to predict the fatigue strength of notched components with regular shape, and its accuracy was demonstrated by a fatigue experiment. Finally, the improved TCD was applied to predict the fatigue life of an irregularly shaped rotating arm. The deviation between prediction results and experimental results is less than 18%. The results demonstrate that the improved TCD can be applied effectively and accurately to predict the fatigue life of key components of turning mechanisms. [ABSTRACT FROM AUTHOR]

Fatigue strength of welded joints is typically independent of the parent material static strength; however, there are two exceptions from this rule—post-weld treated joints and high-quality joints. The reason for both is the absence of sharp weld transitions. Thus, fatigue life is not fully governed by fatigue crack propagation but also by fatigue crack initiation. This is intensified by the fact that crack initiation behaviour is proportional to static strength properties. Commonly, this effect is not accounted for by design guidelines and typical fatigue assessment methods for welded joints. This study hence investigates the applicability and accuracy of different local fatigue assessment methods for high-quality welded joints made of high-strength steel. For this purpose, fatigue test results of S500 structural steel joints with weld toe and weld root failure are assessed using a variety of local approaches and then compared to the nominal stress approach. Finally, the transferability of results to large-scale structures are discussed and recommendations are given for practical applications.

This work aims to assess the fracture of U-notched limestone samples subjected to mixed mode I + II loading conditions with a predominant mode I influence, both at room temperature and at 250 °C. This analysis is based on the use of the Theory of the Critical Distances, and more specifically on the use of the Line Method, considering both an analytical and a numerical approach for the definition of the stress fields. An experimental campaign of almost 400 three-point bending tests has been performed as a basis for the fracture assessment of the limestone, using Single Edge Notched Bend (SENB) specimens with notch radii varying from 0.15 mm up to 15 mm, different temperature conditions and variable loading positions. The Theory of Critical Distances has successfully been applied to study the experimental results. The analytical and numerical stress fields for pure mode I fracture assessments provide similar accurate results both at 23 °C and 250 °C. Similarly, the mixed mode (I + II) fracture assessments allow the critical distance (L ) to be characterised for different mode mixities ( M e ), using the stress field around the notch tip obtained from the numerical models. Comparing the values of the critical distance against the mode mixity in isolation, a slight decrease of L is observed as it approaches pure mode I conditions ( M e = 1). However, if the results are analysed separately for each notch radius, L seems to be relatively constant with M e . In parallel, a certain influence of the notch radius on the critical distance is appreciated, which shows an increment both at 23 °C and 250 °C. [ABSTRACT FROM AUTHOR]

In this paper, the coupled Finite Fracture Mechanics criterion is extended to assess the finite fatigue life of orthotropic notched laminated composites. The approach is validated through a comprehensive experimental program conducted on laminated composites under tension-tension cyclic loading conditions with two distinct lay-ups. For a given loading ratio, fatigue tests on plain and cracked specimens are first performed to provide the model inputs, the critical cyclic stress and stress intensity factor amplitudes. Fatigue tests on samples weakened by circular holes of two different radii are then used for blind predictions. Accurate predictions of the number of cycles to failure are achieved without the need for inverse calibration of material properties or deviation from standard testing procedures. Finally, a parametric study is performed to investigate the hole radius effect. It is worth mentioning that the proposed approach is general and can be applied to any notched geometry. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] • High frequency fatigue data were measured on smooth and notched samples made of 304L steel. • The critical length parameter was derived from experimental data based on critical distance theory. • The critical length parameter serves for lifetime predictions of notched samples and components. • The length parameter increases from 0 to 2.5 mm with increasing applied stress amplitude. In this paper, the fatigue data of smooth and notched specimens are evaluated using the method based on the theory of critical distances. This method is suitable for predictions of the fatigue lifetime of notched specimens using the axial stress distributions, the length parameter, and experimental data measured on smooth specimens. The critical length parameter l c r is determined from the relationship between two fatigue curves (one generated by testing smooth specimens and the other generated by testing specimens with a model notch). Experimental fatigue data are obtained using an ultrasonic fatigue pulsator at a frequency of 20 kHz and a load stress ratio R = −1. The paper describes the dependence of the critical length parameter for different notch radii on the number of cycles to fracture, as well as on the applied stress amplitude. The obtained results prove the possibility of using the critical length parameter for fatigue life prediction of notched specimens. [ABSTRACT FROM AUTHOR]

This work aims to evaluate the capability of the theory of critical distances (TCD) to predict the static failure of U-notched AISI 420 martensitic stainless steel specimens with different geometric features under pure bending loading. Theoretical estimates of the stress intensity factor during fracture onset were calculated according to the line (LM) and point methods (PM), which consider the characteristic length L, inherent strength σ0, and notch tip radius ρ. Initially, L and σ0 were determined on the basis of the material’s properties (i.e., fracture toughness KIc and ultimate tensile strength σu,t), resulting in imprecise estimates. Conversely, L and σ0 determined using the appropriate analysis of linear–elastic stress fields ahead of notches with different sharpness provided highly accurate predictions. The microscopic study of fractured specimens ensured better comprehension of the results. Moreover, the accurate values of L and σ0 were used to predict the failure of V-notched specimens.

The main objective of this paper is to accurately obtain fatigue life prediction for the key components of a turning mechanism using the improved theory of critical distances (TCD). The irregularly shaped rotating arm is the central stressed part of the turning mechanism, which contains notches. It has been found that TCD achieves good results in predicting the fatigue strength or fatigue life of notched components with regular shape but is less commonly used for notched components with irregular shape. Therefore, TCD was improved and applied broadly to predict the fatigue life of an irregularly shaped rotating arm. Firstly, the notch depth and structure net width parameters were introduced into the low-order and low-accuracy classical TCD function to obtain a novel stress function with high computational efficiency and high accuracy, whereas the stress concentration factor was introduced to modify the length of critical distance. Secondly, the improved TCD was used to predict the fatigue strength of notched components with regular shape, and its accuracy was demonstrated by a fatigue experiment. Finally, the improved TCD was applied to predict the fatigue life of an irregularly shaped rotating arm. The deviation between prediction results and experimental results is less than 18%. The results demonstrate that the improved TCD can be applied effectively and accurately to predict the fatigue life of key components of turning mechanisms.

The fracture assessment of notched components based on cracked components approaches leads to over‐conservative failure predictions. In the research literature, several approaches are proposed to overcome this problem using an apparent fracture toughness, KmatN. Nevertheless, most of these approaches are based on deterministic assumptions despite the large and variable scatter exhibited by KmatN for different notch radii (ρ) or temperatures (T). This paper proposes a methodology for deriving a probabilistic KmatN−ρ field including the effect of temperature on the failure of notched components. First, the theory of critical distances is applied to transform each apparent fracture toughness into the equivalent fracture toughness for ρ = 0. Then, the temperature is supposed to act as a scale effect in the Weibull cumulative distribution function of the equivalent fracture toughness, and the corresponding scale effect function is derived. Finally, the applicability of the proposed methodology is illustrated by an example using two ferritic‐pearlitic steels: S275JR and S355J2. [ABSTRACT FROM AUTHOR]

• Notch stress field affected by residual thickness/width is studied. • The proposed TSFM improves the prediction accuracy compared to TCD. • TSFM required the elastic stress field of notch and S - N expression. The notch stress fields in current studies are mainly not affected by the residual thickness/width at notch root. The Theory of Critical Distances (TCD) has been widely applied in notch fatigue analysis. However, fatigue tensile experiment results show that TCD has limitation in surface-notched specimens with finite residual thickness and side-notched specimens with finite residual width. Under the assumption that the total stress field should be considered in determining the effective stress σ eff , we proposed the total stress field method (TSFM). It has advantages in prediction accuracy and convenience of finite residual thickness/width notched specimen (FRT/WNS). [ABSTRACT FROM AUTHOR]

Many design scenarios of components made of polymer materials are concerned with notches as representative constructive details. The failure hazard assessment of these components using models based on the assumption of cracked components leads to over-conservative failure estimations. Among the different alternative approaches proposed that are based on the apparent fracture toughness, KcN is considered. In so doing, the current deterministic underlying concept must be replaced by a probabilistic one to take into account the variability observed in the failure results in order to ensure a reliable design. In this paper, an approach based on the critical distance principle is proposed for the failure assessment of notched EPOLAM 2025 CT samples with each different notch radii (ρ) including a probabilistic assessment of the failure prediction. First, each apparent fracture toughness is transformed into the equivalent fracture toughness for ρ=0 based on the critical distances theory. Then, once all results are normalized to the same basic conditions, a Weibull cumulative distribution function is fitted, allowing the probability of failure to be predicted for different notch radii. In this way, the total number of the specimens tested in the experimental campaign is reduced, whereas the reliability of the material characterization improves. Finally, the applicability of the proposed methodology is illustrated by an example using the own experimental campaign performed on EPOLAM 2025 CT specimens with different notch radii (ρ).

This paper aims to investigate the accuracy of the Theory of Critical Distances (TCD) in estimating static strength of notched additively manufactured PLA as both notch sharpness and infill angle vary. The TCD takes as its starting point the assumption that the extent of damage under static loading can be assessed successfully by using two different material parameters, i.e. (i) a critical distance whose length is closely related to the material microstructural features and an inherent (i.e., a defect free) material strength. Plain and notched specimens of 3D-printed PLA were manufactured horizontally by making the deposition angle vary in the range 0-90. Using the TCD in the form of the Point Method, failures were predicted by directly post-processing the linear-elastic stress fields estimated through the well-known analytical solutions due to Glinka and Newport. Independently of the notch sharpness, the estimates being obtained were found to be highly accurate, falling within an error interval of about 20%. This result fully supports the idea that the TCD can successfully be used in situations of practical interest to design against static loading notched components of additively manufactured PLA by directly post-processing the results from simple linear-elastic Finite Element (FE) models.

The aim of this work is to evaluate wear effects on life prediction for components subjected to fretting conditions. Therefore, fretting fatigue FE simulations have been carried considering the geometry update due to the material removal and results were compared to both experimental data and FE simulations where wear was neglected. Well known multiaxial fatigue criteria in association with the Theory of Critical Distances (TCD) have been used to estimate life. Results have shown that, for the data assessed, where fretting fatigue tests were conducted on a Ti-6Al-4V alloy under partial slip conditions, considering wear effects might slightly increase the accuracy of life estimates. However, this improvement may not be worth the increase in the computational cost in such analysis. • Fretting fatigue life assessment considering wear is carried out for Ti-6Al-4V. • Life estimates considering and neglecting wear are compared to experiments. • Considering wear slightly improve the quality of the results for partial slip. • Accounting wear may not justify its high computational cost for partial slip regime. [ABSTRACT FROM AUTHOR]

Highlights • Local linear-elastic stresses allow notch fatigue to be assessed accurately. • Material length parameters are successful in estimating uniaxial/multiaxial fatigue lifetime of notched metals. • The MWCM/PM and the SED approach can be applied by post-processing linear-elastic FE results. Abstract This paper assesses the accuracy and reliability of the Theory of Critical Distances (TCD) and the Strain Energy Density (SED) approach in estimating the lifetime of plain and notched specimens subjected to cyclic loading. To validate the two approaches for plain and notched components under uniaxial and multiaxial fatigue loading, a large bulk of experimental data taken from the literature was re-analyzed, with the state variables, i.e. the stress distributions and the strain energy density, being calculated via the Finite Element (FE) method. The results obtained demonstrate that both the TCD and the SED approach can provide highly accurate fatigue life estimation. In addition, these two approaches require little computational effort and little calibration information to be implemented and used for fatigue design in situations of practical interest. [ABSTRACT FROM AUTHOR]

• The TCD has been applied to predict the EAC behaviour of X80 and S420 steels. • Fracture tests were carried out under cathodic polarization conditions. • The study has been completed with Finite Elements simulations and SEM analysis. • The TCD provides accurate predictions of KN IEAC. This paper provides a methodology, based on the Theory of Critical Distances (TCD), for the hydrogen embrittlement analysis of steels in cracked and notched conditions. The TCD has been successfully employed in fracture and fatigue analysis, but it has not yet been applied under environmentally assisted cracking conditions. The point method and the line method, both belonging to the TCD, have been applied to two steels (X80 and S420) following an experimental programme composed of C(T) specimens containing defects with notch radii varying from 0 mm up to 2 mm. Fracture mechanics tests were carried out at 6 · 10−8 m/s of constant displacement rate under cathodic polarization conditions (5 mA/cm2). The aqueous environment has been prepared following the Pressouyre's method. The study, which has been completed with finite element simulation analysis, reveals that the TCD provides accurate predictions of the hydrogen embrittlement behaviour of these steels in notched conditions. [ABSTRACT FROM AUTHOR]

In the present work, we propose a robust calibration of some bi‐parametric multiaxial fatigue criteria applied in conjunction with the theory of critical distances (TCD). This is based on least‐square fitting fatigue data generated using plain and sharp‐notched specimens tested at two different load ratios and allows for the estimation of the critical distance according to the point and line method formulation of TCD. It is shown that this combination permits to incorporate the mean stress effect into the fatigue strength calculation, which is not accounted for in the classical formulation of TCD based on the range of the maximum principal stress. It is also shown that for those materials exhibiting a low fatigue‐strength‐to‐yield‐stress ratio σfl,R = −1/σYS, such as 7075‐T6 (σfl,R = −1/σYS = 0.30), satisfactorily accurate predictions are obtained assuming a linear‐elastic stress distribution, even at the tip of sharp notches and cracks. Conversely, for any materials characterized by higher values of this ratio, as quenched and tempered 42CrMo4 (σfl,R = −1/σYS = 0.54), it is recommended to consider the stabilized elastic‐plastic stress/strain distribution, also for plain and blunt‐notched samples and even in the high cycle fatigue regime still with the application of the TCD. [ABSTRACT FROM AUTHOR]

Highlights • Fatigue life predictions were performed in wires with geometric discontinuities. • S-N curves were produced to calibrate and to validate the numerical methodology. • A new approach to evaluate the equivalent stress in the Volume Method is proposed. • The effect of the fatigue process zone size in the life predictions is evaluated. Abstract The aim of this work is to predict fatigue life of aluminum alloy wires 6201-T81 containing geometric discontinuities using the Theory of Critical Distances (TCD). These wires were taken from a 900 MCM All Aluminum Alloy Conductor (AAAC 900 MCM) used in overhead power transmission lines. The equivalent stress was evaluated by means of the Point Method (PM) and the Volume Method (VM), based on the maximum principal stress (σ 1). Regarding the latter method, a new approach to evaluate the equivalent stress inside a material volume defined by the shape of a sphere is presented. The relation between the critical distance and the number of cycles to failure was calibrated using two distinct methodologies: the first one uses two S-N curves, one curve of a plain wire and the other of a notched wire; the second methodology also uses two S-N curves, however, in this case, both curves refer to wires containing different geometric discontinuities. Therefore, S-N curves of wires containing artificial geometric discontinuities like holes and notches were produced, both to calibrate the critical distance relation and to validate the life predictions. When the life estimations were performed based on the first calibration, the results were considered not satisfactory. However, when the second calibration was used, almost all the predictions were inserted within scatter bands regarding the experimental data used to calibrate the model. The authors believe that the difference in accuracy between predictions obtained by the two calibration methods could be related to a statistical size effect associated to the fatigue process zone size. [ABSTRACT FROM AUTHOR]

Abstract: The Theory of Critical Distances (TCD) is the name that has been given to a group of design methodologies that all make use of a material length scale parameter to postprocess the local linear‐elastic stress fields in the vicinity of the crack initiation locations. The aim of the present investigation is to check whether the simple linear‐elastic TCD is successful in predicting static strength of notched components made of 3D‐printed polylactide (PLA). PLA is a thermoplastic aliphatic polyester that is produced from renewable biodegradable resources. The accuracy and reliability of the TCD in estimating the static strength of additively manufactured (AM) PLA were assessed against a large number of experimental results generated by testing, under tensile loading as well as under bending, AM notched specimens containing different geometrical features (open notches included). The TCD was seen to be highly accurate, its systematic use resulting in estimates falling mainly within an error interval of about 20%. This result is certainly very relevant since it demonstrates that the linear‐elastic TCD can be used successfully to design against static loading notched components of AM PLA by directly postprocessing the results from simple linear‐elastic Finite Element (FE) models. [ABSTRACT FROM AUTHOR]

This paper validates a methodology for the estimation of critical loads in tubular beams containing notch-type defects. The methodology is particularized for the case of Al6060-T66 tubular cantilever beams containing U-shaped notches. It consists in obtaining the stress field at the notch tip using finite element analysis (FEA) and the subsequent application of the theory of critical distances (TCD) to derive the corresponding critical load (or load-bearing capacity). The results demonstrate that this methodology provides satisfactory predictions of fracture loads.

In this paper a fracture assessment in additive manufactured acrylonitrile butadiene styrene (ABS) fracture specimens containing U-notches is performed. We performed 33 fracture tests and 9 tensile tests, combining five different notch radii (0 mm, 0.25 mm, 0.50 mm, 1 mm and 2 mm) and three different raster orientations: 0/90, 30/−60 and 45/−45. The theory of critical distances (TCD) was then used in the analysis of fracture test results, obtaining additional validation of this theoretical framework. Different versions of TCD provided suitable results contrasting with the experimental tests performed. Moreover, the fracture mechanisms were evaluated using scanning electron microscopy in order to establish relationships with the behaviour observed. It was demonstrated that 3D-printed ABS material presents a clear notch effect, and also that the TCD, through both the point method and the line method, captured the physics of the notch effect in 3D-printed ABS. Finally, it was observed that the change in the fracture mechanisms when introducing a finite notch radius was limited to a narrow band behind the original defect, which appeared in cracked specimens but not in notched specimens.

This study aimed to predict the uniaxial fatigue strength of shot peened notched specimens made of 42CrMo4 quenched and tempered steel. The Chaboche kinematic hardening rule was employed to model the cyclic plastic behaviour of the tested samples and the evolution of the residual stresses, which were measured with X-ray diffraction and then reproduced through a finite element software with a novel proposed procedure. This latter introduced a distribution of eigenstrains to reproduce the initial residual stresses and a hardening of the material to replicate the residual stresses measured after the loading for a run-out specimen. The Theory of Critical Distances combined with the Smith-Watson and Topper multiaxial fatigue criterion were then employed to predict the fatigue strength resulting in a good level of accuracy. [Display omitted] • Chaboche kinematic hardening rule to model the cyclic plastic behaviour. • Residual stresses after the shot peening reproduced with the eigenstrain technique. • Residual stresses after fatigue modelled with an increase of the material hardening. • Smith-Watson and Topper combined with the Theory of Critical Distances. • Low prediction errors of the fatigue strength assessment. [ABSTRACT FROM AUTHOR]

This work presents a methodology for life estimation of mechanical couplings subjected to fretting fatigue. In this approach, a stress-based multiaxial fatigue parameter is evaluated at a critical distance below the contact surface. The fatigue parameter is based on an improved formulation of the Modified Wöhler Curve Method, in which the shear stress amplitude is measured via the Maximum Rectangular Hull method. To apply the Theory of Critical Distances in the medium-cycle fatigue regime, the critical distance is assumed to depend on the number of cycles to failure. Available fretting fatigue data, conducted on a cylinder-plane contact configuration made of Al alloy 4% Cu, were used to assess the methodology. Most of the life estimates were within an error band given by a factor of 2.

This paper investigates the fracture properties and notch effect of PUR materials with four different densities. The asymmetric semi-circular bend specimen was adapted to perform mixed mode fracture toughness tests. This semi-circular specimen with radius R, which contains an edge crack of length a oriented normal to the specimen edge, loaded with a three point bending fixture, was proved to give wide range of mixed modes from pure mode I to pure mode II, only by changing the position of one support. Different types of notched specimens were considered for notch effect investigations and the Theory of Critical Distances was applied. It could be seen that the critical distances are influenced by the cellular structure of investigated materials

In this paper the so-called Theory of Critical Distances is reformulated to make it suitable for estimating the strength of notched metals subjected to dynamic loading. The TCD takes as its starting point the assumption that engineering materials’ strength can accurately be predicted by directly post-processing the entire linear-elastic stress field acting on the material in the vicinity of the stress concentrator being assessed. In order to extend the used of the TCD to situations involving dynamic loading, the hypothesis is formed that the required critical distance (which is treated as a material property) varies as the loading rate increases. The accuracy and reliability of this novel reformulation of the TCD was checked against a number of experimental results generated by testing notched cylindrical bars of Al6063-T5. This validation exercise allowed us to prove that the TCD (applied in the form of the Point, Line, and Area Method) is capable of estimates falling within an error interval of ±20%. This result is very promising especially in light of the fact that such a design method can be used in situations of practical interest without the need for explicitly modelling the non-linear stress vs. strain dynamic behaviour of metals.

Engineering components often contain notches, keyways or other stress concentration features. These features raise the stress state in the vicinity of their apex which can lead to unexpected failure of the component. The Theory of Critical Distances has been proven to predict accurate results, but, conventionally, requires two key ingredients to be implemented: the first is a stress-distance curve which can be obtained relatively easily by means of any finite element software, the second is two additional material parameters which are determined by running appropriate experiments. In this novel reformulation, one of these additional parameters, namely the critical distance, can be determined a priori, allowing design engineers to assess components whilst reducing the time and cost of the design process. This paper investigates reformulating the Theory of Critical Distances to be based on two readily available material parameters, i.e., the Ultimate Tensile Strength and the Fracture Toughness. An experimental data base was compiled from the technical literature. The investigated samples had a range of stress concentration features including sharp V-notches to blunt U-notches, and a range of materials that exhibit brittle, quasi-brittle and ductile mechanical behaviour. Each data set was assessed and the prediction error was calculated. The failure predictions were on average 30% conservative, whilst the non-conservative predictions account for less than 10% of the tested data and less than 2% of the non-conservative error results exceed -20%. It is therefore recommended that a safety factor of at least 1.2 is used in the implementation of this version of the Theory of Critical Distances.