Theory Of Critical Distances Research Articles

The applicability and the low limit of the classical fracture theory at nanoscale: The fracture of graphene

Miniaturization of mechanical structures offers excellent performances of the device while has brought problems of fracture at nanoscale. However, whether the classical fracture theory is applicable at such a small scale and what is its low limit are still challenging problems. In this paper, by conducting atomistic simulation of graphene and compared with the reported in-situ experiments, the applicable range of distance from crack tip for crack-tip stress distribution models and the low limit of crack length for fracture criterion are investigated. It is found that all crack-tip stress models are invalid within fracture process zone whose dimension is 2.5 Å away from crack tip. The energy-based fracture criteria are not applicable when the crack length is less than 8 nm due to the nonlinear stress–strain relationship, while the modified Griffith criterion can be applied to low limit of crack length 5 Å. For the stress-based fracture criterion, the stress intensity factor criterion fails when the crack length is less than 8 nm due to the decreasing size of critical K-dominant zone ΛK, while the theory of critical distances and quantized fracture mechanics can accurately predict the critical fracture stress regardless of the crack length, which can be unified by a non-local stress criterion. This work will provide a mechanical basis for the reliable application of the microelectronic devices at nanoscale.

Numerical modelling of microstructure inhomogeneity to reproduce experimentally observed scatter in fretting fatigue lifetimes

Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.

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.

Influence of material extrusion parameters on fracture mechanisms of polylactic acid under three-point bending

In this work, a thorough fracture assessment of additive manufactured specimens made by 3D printed polylactic acid (PLA) under three-point bending is presented. This polymer is widely used in additive manufacturing for numerous applications, gaining prominence in fields such as biomechanics. Prismatic fully dense specimens and lattice structure specimens with different raster orientations and densities were fabricated using the material extrusion-based additive manufacturing technique. The objective is to analyse the effect of relevant process parameters on the fracture mechanism of short beam specimens tested under three-point bending. Digital image correlation and computed tomography have been used to measure the full field displacement and internal defects, respectively. Furthermore, the theory of critical distances was applied to assess the mechanical strength of lattice structure specimens. The results have shown the strong influence of raster orientation on the mechanical strength and fracture patterns even for negative air gap values. The transition from brittle to ductile failure was observed when changing density and raster orientation. Lastly, neck-shaped defects were detected in knots of specimens manufactured with a grid pattern. Defects in grid pattern specimens appear due to the prescribed path followed by the extruder during the building process. They were the main source causing a decrease in the mechanical strength and fracture trajectories. The objective of this research is to enhance the knowledge on the mechanical response of 3D printed components and to give an in-depth failure assessment.

Tailoring the theory of critical distances to better assess the combined effect of complex geometries and process-inherent defects during the fatigue assessment of SLM Ti-6Al-4V

This work aims to apply the Theory of Critical Distances (TCD) to the fatigue assessment of additively manufactured (AM) Ti-6Al-4V material produced via the selective laser melting (SLM) process. Modified alternatives to traditional TCD methods are considered. In this sense, it is sought to develop a fatigue prediction model that is better suited to assessing the impact of multiple stress-rising features which are located in close proximity to each other. Hereby, consideration has been given to modelling process-inherent surface roughness in combination with an internally positioned artificial defect, shaped as a feature that is reminiscent of a pore. Simultaneously, the research also seeks to circumnavigate a potential issue with respect to the current TCD methodology. This concerns the matter of applying TCD practices to components whereby the area of interest for conducting stress-distance analytics is on a size scale that is smaller than that of the critical distance length parameter itself. Several different strategies were attempted as a way to try and achieve meaningful modifications to the TCD process. Results show that it is possible to overcome such challenges that can often present themselves during the fatigue appraisal of AM metal parts. In this sense, the optimal novel strategy that was experimented with returned average error margins of 13.7% or better. It is anticipated that such models may assist in further optimising the accuracy of service life evaluation for metallic AM components that are intended for industry.

Life prediction of 6201-T81 aluminum alloy wires under fretting fatigue and variable amplitude loading

Fretting fatigue tests under variable amplitude loading were performed on 6201-T81 aluminum alloy wires of an AAAC 900 MCM conductor. The loading program consisted of a three-block loading history, defined using vibration data of a transmission line located in the center-west region of Brazil. Two previously developed methodologies for life prediction of wires under fretting fatigue, based on the Theory of Critical Distances and on a master fatigue curve, were extended to variable amplitude loading conditions. The good agreement between measured and predicted lives indicated that both methodologies can be useful for fatigue analysis of wires of overhead conductors.

Notch fatigue behavior of a titanium alloy in the VHCF regime based on a vibration fatigue test

The notch fatigue behavior of a titanium alloy TC17 in the very high cycle fatigue (VHCF) regime is investigated by a vibration-based bending fatigue test. A complete S-N relation of notched specimens with high resonance frequencies is obtained, covering the lifetime up to 109 cycles, and the fracture surfaces are observed. The results show the TC17 exhibits relatively high fatigue notch sensitivity. Several fatigue crack initiation mechanisms relevant to the notch are then revealed. Furthermore, a notch fatigue prediction model based on a modified theory of critical distance is proposed by introducing a special weight function, which is demonstrated to have good prediction accuracy.

Anisotropy and internal flaws effects on fatigue response of notched 3D-printed PLA parts

In this study, the fatigue strength of notched 3D printed polylactic acid (PLA) samples were examined experimentally, considering the notch shapes, raster patterns, and internal voids/flaws between the filaments. Three different raster patterns were considered, which were 0˚, 45˚, and 90˚, and three different notch shapes were considered. The samples were subjected to five different cyclic loads ranging from 40 % to 80 % of the samples' ultimate tensile strength with a load ratio of 0.1. Results revealed that filaments could act as sharp cracks in the case of 90º raster orientation. However, this effect in the cases of 0º and 45º was slightly smaller. Machine learning techniques including linear, polynomial and random forest (RF) regression models have been utilized for fatigue life predictions of the samples. R-squared values were utilized to compare the accuracy of the regression models. Among the regression models, polynomial regression best predicted fatigue lives of the notched samples with the R-squared value equal to 92 %. Predicted results with machine learning techniques were then compared with those obtained through an analytical approach by employing critical distance theory and using stress field and stress gradient distributions obtained from numerical simulations. It was found that all machine learning models except linear regression at high load levels predicted better than an approach based on analytical and numerical methods.

Fatigue strength assessment of cover plate joints subjected to axial and bending loading

AbstractThis study investigates stress‐based fatigue assessment methods to determine their applicability to welded cover plate joints subject to axial and bending loading. The nominal stress (NS), hot spot stress (HSS), 1 mm stress (OM), effective notch stress (ENS), theory of critical distances (TCD), and stress averaging (SA) methods are covered, and their accuracy and reliability are evaluated. To the best of the authors' knowledge, there is limited fatigue test data available for cover plate joints subjected to bending loading. In this study, fatigue tests are performed with cover plate joints under axial and bending loading. Evaluation of the fatigue assessment methods is based on the test results. It is observed that for axial loading, the ENS and OM method have the highest accuracy. For bending, the OM method is non‐conservative, and the other methods are overly conservative. Using design curves recommended for thin‐walled welded joints subjected to bending highly improves accuracy.

Life Assessment of Corroded Wire for Prestressing

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.

On reformulating the theory of critical distances to predict strength of notched plain concrete beams under mode I and mixed mode loading

The theory of critical distances (TCD), due to its appealing characteristics, has been successfully used in the past to predict the strength of brittle as well as ductile materials, weakened by the presence of stress risers, under both static and fatigue loading. In this work, the TCD’s unique features are exploited and the point method is reformulated to predict the strength of notched plain concrete beams of different sizes under mode I and mixed mode quasi-static loading. The fracture process zone, which is responsible for the non-linearity of concrete, is considered through the concept of an effective elastic crack. A power law is proposed to relate the effective crack length to the geometrical properties. The material characteristic length, required for application of TCD, is correlated with the maximum aggregate size. The resulting formulation is found to yield satisfactory prediction of static strength of notched plain concrete beams, wherein the geometric dimensions of the beam, tensile strength and maximum aggregate size of the concrete mix are the only input parameters. The proposed formulation is validated using a probabilistic analysis of various experimental results available in the literature.

Study of Local Fatigue Methods (TCD, N-SIF, and ESED) on Notches and Defects Related to Numerical Efficiency

The fatigue strength of structural components is strongly affected by notches and imperfections. Both can be treated similarly, as local notch fatigue strength methods can also be applied to interior defects. Even though Murakami’s √area approach is commonly used in the threshold-based fatigue design of single imperfections, advanced concepts such as the Theory of Critical Distances (TCD), Notch Stress Intensity Factors (N-SIF), or Elastic Strain Energy Density (ESED) methods provide additional insight into the local fatigue strength distribution of irregularly shaped defects under varying uniaxial load vectors. The latter methods are based on the evaluation of the elastic stress field in the vicinity of the notch for each single load vector. Thus, this work provides numerically efficient methods to assess the local fatigue strength by means of TCD, N-SIF, and ESED, targeting the minimization of the required load case count, optimization of stress field evaluation data points, and utilization of multi-processing. Furthermore, the Peak Stress Method (PSM) is adapted for large opening angles, as in the case of globular defects. In detail, two numerical strategies are devised and comprehensively evaluated, either using a sub-case-based stress evaluation of the defect vicinity with an unchanged mesh pattern and varying load vector on the exterior model region with optimized load angle stepping or by the invocation of stress and strain tensor transformation equations to derive load angle-dependent result superposition while leaving the initial mesh unaltered. Both methods provide numerically efficient fatigue post-processing, as the mesh in the evaluated defect region is retained for varying load vectors. The key functions of the fatigue strength assessment, such as the evaluation of appropriate planar notch radius and determination of notch opening angle for the discretized imperfections, are presented. Although the presented numerical methods apply to planar simulation studies, the basic methodology can be easily expanded toward spatial fatigue assessment.

Application of Methods of the Theory of Critical Distances to Estimate the Fracture of Quasi-Brittle Materials with Notches

Application of Methods of the Theory of Critical Distances to Estimate the Fracture of Quasi-Brittle Materials with Notches

Fretting fatigue lifetime estimation for heterogeneous material using critical distance with mesh control

Fretting fatigue has a wide range of applications in many fields, which have high requirements for accurate prediction of their lifetime. In this paper, the theory of critical distance using volume method and mesh control approach are applied to predict the fretting fatigue lifetime. Considering the existence of heterogeneity and defects in the material, the homogenization method and sub-model technique is used to directly investigate the influence of defects on stress, strain and fatigue lifetime. It is found that the computational cost can be reduced dramatically due to the use of mesh control approach. The prediction accuracy is improved through the implementation of the Unit Cell (UC) models based on a sub-modelling technique. Meanwhile, the Representative Volume Element (RVE) is applied for the estimations of fretting fatigue lifetimes using homogenization method taking into account the heterogeneity of material.

High Cycle Fatigue Life Prediction of Single-Crystal Specimen Based on TCD Method and Crystal Plasticity Theory

This paper performs a comprehensive investigation on the high cycle fatigue (HCF) life prediction of turbine blade with film cooling holes. The modified theory of critical distance (MTCD) method is proposed to estimate the fatigue life of the specimen considering the notch sensitivity coefficient and multiaxial stress effect. Then, two types of specimens were designed with regard to the single-hole and multihole conditions. Afterwards, the dangerous path and fatigue life of the two specimens were achieved implementing the MTCD method. Then, the experiments and failure analysis were carried out. The results show that the stress concentration and multiaxial stress resulting from the film cooling holes are the primary reasons that the cracks originated. Meanwhile, the dangerous path of the single-hole specimen is quite different from the multihole specimen due to the interhole interference. Finally, most of the calculated fatigue life is within the twice error band of the tested life.

High cycle fatigue life prediction model based on crystal plasticity and continuum damage mechanics for Ni-based single crystal superalloys under a multiaxial stress state

A high cycle fatigue life prediction model based on continuum damage mechanics, crystal plasticity and critical distance theory is developed. A novel damage evolution law for anisotropic Ni-based single crystal materials built on continuum damage mechanics is proposed. The crystal plasticity framework was introduced to take into account the particular characteristics of high cycle fatigue. The critical distance theory was innovatively applied to the structure of film cooling holes to predict the lifetime for materials under a multiaxial stress state. High cycle fatigue tests considering drilling technology, stress ratio and creep time were performed using Ni-based single crystal superalloy plates with film cooling holes. The constitutive equations were implemented into a finite element framework to simulate the high cycle fatigue properties of Ni-based single crystal superalloys, and the results of numerical calculations were compared with experimental observations. It was demonstrated that the constitutive formulations proposed in the present study can be used to model the mechanical behavior of Ni-based single crystal superalloys under a multiaxial stress state. The life prediction errors are found to be within the factor-of-three scatter band. The fatigue life of the specimen with ultrafast laser drilled film cooling holes is larger than that with electrostream machined film cooling holes under the same test conditions. The fatigue strength of the specimen with film cooling holes at a stress ratio R = 0.95 is higher than that at a stress ratio R = -1. The life of the specimen with film cooling holes is found to decrease with increasing creep time before high cycle fatigue. The γ/γ'-microstructure evolution in the specimens with film cooling holes is related to the kinetics of the stress redistribution during the fatigue process. A minimum stress level is essential for rafting to occur. The damage distribution for the plate model is in line with the crack initiation location and propagation region of the specimen.

Intrinsic-crack modelling of the notch fatigue limit of a solid with an elliptical-cylindrical or a spheroidal cavity

Based on an approximate stress-intensity factor for a crack emanating from an elliptical-cylindrical or spheroidal cavity, the El Haddad intrinsic-crack method for modelling the notch fatigue limit of a solid containing a cavity has been extended from a straight through-crack or a circular crack to a wider range of cavity shapes. Thus, predictions of the notch fatigue limit have been presented for elliptical cylinders, ranging from a through-crack to a circular cylinder, and for limiting cases of spheroids, viz. the circular crack and the sphere. These predictions have been shown to be in good to excellent agreement with those based on the theory of critical distances.

The application of the Theory of Critical Distances to nonhomogeneous materials

AbstractThe Theory of Critical Distances (TCD) has undoubtedly represented a breakthrough in the brittle failure assessment of engineering materials containing defects, crack, or notches. The basic idea on which the simplest formulation of the TCD is based is to evaluate an effective stress at a characteristic distance from the tip of the defect/crack/notch and compare it with an inherent fracture strength. Is the critical distance related to the material (micro) structure? Whereas a correlation was already proved for homogeneous materials, the current attention to nonhomogeneous ones has brought the question back to the fore. The goal of the present work is therefore twofold: (i) to extend the use of the TCD, through the simple yet effective Point Method (PM), for the static failure assessment of inhomogeneous materials, such as cellular, biological, and additively manufactured (AM) materials; and (ii) to look for a correlation between critical distance and internal (micro) structure.

Investigation of the processes of deformation of glass-reinforced plastics with a stress concentrator using the theory of critical distances

In the course of the work, a series of tensile tests were carried out on flat samples of STEF structural fiberglass for electrical purposes. In addition to the experiment, numerical simulation of the tensile processes of these samples was carried out. The studied samples were strips without stress concentrators and with a concentrator in the form of V-shaped cuts with different rounding radii at the top of the concentrator and the depth of the cut. The results obtained were used to determine the material constants according to the theory of critical distances. Two approaches of the theory of critical distances were used: linear and point. To analyze the experimental results, finite element models were built using the ANSYS software package and numerical simulation was carried out, which resulted in the obtained linearized maximum principal stresses on the central line passing through the top of the stress concentrator. Based on the results of the work, the values of the critical distances of the composite were determined, obtained using the point and linear methods and the finite element method. The results obtained can be used to predict the strength characteristics of real products with complex geometry, as well as damaged structural elements.

Fatigue life assessment of imperfective cast steel components in the medium-cycle regime by stress- and energy-based concepts

Manufacturing process-based imperfections, such as shrinkage porosities, severely limit the fatigue strength of cast steel components. Due to the complexly shaped spatial geometry of such defect structures, the application of local fatigue assessment concepts is recommendable. This work applies the Theory of Critical Distances (TCD) to assess the fatigue life of imperfective cast steel components made of G12MnMo7-4+QT in the medium-cycle regime. Based on a calibration procedure utilizing generalized S-N curves of plain and notched specimens at various load ratios, the relationship between the critical distance LM and the number of cycles to failure Nf is parametrized first. At second, the implemented planar framework is validated with specimens featuring a different notch geometry. The presented linear-elastic methodology is furthermore extended to arbitrarily shaped spatial imperfections, resulting in reasonable predictions of experimentally derived fatigue life results. Moreover, a strain energy density-based fatigue assessment methodology is formulated, introducing a relationship between the control radius Rc and Nf. The yielded fatigue strength assessment values correspond to the results of the initially implemented TCD-framework. Concluding, the presented stress- and energy-based concepts depict engineering-feasible methodologies to assess the fatigue life of cast steel components affected by complexly shaped shrinkage imperfections.