Positive Stress Ratios Research Articles

Multi-scale study of subsurface fatigue cracking behavior of laser-powder bed fused Inconel 718 at stress ratios and temperatures

Multi-scale subsurface fatigue cracking is a significant lifetime-limiting failure mode, not yet fully understood, of additively manufactured superalloys in mechanical applications. Here, combined with some technologies of electron-backscattered diffraction, focused Ion beam, and transmission electron microscope, a series of axial fatigue tests at different stress ratios and temperatures are conducted to investigate the fatigue failure behavior of as-built superalloy manufactured by Laser-Powder Bed Fusion. The main results show that especially in the assistance of defect (e.g., pore or inclusion) and elevated temperature, the faceted cracking related to the grain feature is a typical failure mode. It is mainly controlled by shear stress and is more popular under a positive stress ratio. Based on the analysis of dislocation structure with faceted cracking, the localized plastic deformation at 25 °C is controlled by anti-phase boundary (APB) shearing, whereas that at 650 °C is caused by a combination of APB shearing, precipitation bypassing, and stacking fault shearing mechanisms. Combined with the definition of threshold value at the crack tip, a crack nucleation life prediction approach associated with the faceted cracking characteristics is proposed, and the predicted results show a good agreement with the experimental results.

Mechanism of mean stress sensitivity in Ti-6Al-4V under different stress ratios in high cycle fatigue

Initially, this article precisely determines that the “facet” on the fracture surface of the Ti-6Al-4V alloy during high cycle fatigue (HCF) loading under positive stress ratios, as determined by white light interferometry and transmission Kikuchi diffraction (TKD), originates from cracking along the slip planes that exhibit a grain orientated α grain in the loading direction, predominantly involving shear deformation along the crystallographic planes. The article emphasizes the crack initiation mechanisms in Ti-6Al-4V alloy related to internal microstructures under positive stress ratio HCF loading, elucidating relationship between texture-induced crack initiation and growth, and anomalous mean stress sensitivity. Under positive stress ratio fatigue loading, preferentially orientated texture regions tend to generate irreversible dislocations parallel to the basal plane, gradually accumulating within multiple locations to form persistent slip bands (PSBs), which, under the influence of internal stresses, sequentially collapse and rupture, leading to nucleation of microcracks. Upon encountering unfavorably oriented texture regions or grains, PSBs or existing microcracks experience dislocation accumulation, which in turn induce grain refinement, thereby causing further crack nucleation. Consequently, microcracks, through aggregation and coalescence during the fatigue loading sequence, form the main crack, ultimately precipitating fatigue failure and engendering the anomalous mean stress sensitivity observed in the Ti-6Al-4V alloy.

Effects of stress ratio on plasticity-induced crack closure through three-dimensional advanced numerical finite element models

The plasticity induced crack closure (PICC) is a local phenomenon that substantially influences crack growth. PICC is most commonly determined by numerical models. Specifically, the vertical displacements of the nodes behind the crack front have been extensively used to obtain the PICC and the crack opening loads (Pop/Pmax). Although this procedure has been demonstrated to be adequate for positive stress ratios, this work evidences the uncertainty of such procedure to obtain PICC under negative stress ratios. For this reason, the main objective of this paper is to investigate the effect of stress ratio on PICC by 3D advanced numerical methodology. The purposed method consists of evaluating the contact pressures of all nodes behind the crack tip, from the first to the last released row of elements included on a crack propagation finite element model. Moreover, this method is tested at positive stress ratios and results show a good agreement with the CTOD method.

Numerical Analysis on Fatigue Crack Growth at Negative and Positive Stress Ratios.

The finite element method was used to investigate the effect of the stress ratio on fatigue crack propagation behavior within the framework of the linear elastic fracture mechanics theory. The numerical analysis was carried out using ANSYS Mechanical R19.2 with the unstructured mesh method-based separating, morphing, and adaptive remeshing technologies (SMART). Mixed mode fatigue simulations were performed on a modified four-point bending specimen with a non-central hole. A diverse set of stress ratios (R = 0.1, 0.2, 0.3, 0.4, 0.5, -0.1, -0.2, -0.3, -0.4, -0.5), including positive and negative values, is employed to examine the influence of the load ratio on the behavior of the fatigue crack propagation, with particular emphasis on negative R loadings that involve compressive excursions. A consistent decrease in the value of the equivalent stress intensity factor (ΔKeq) is observed as the stress ratio increases. The observation was made that the stress ratio significantly affects both the fatigue life and the distribution of von Mises stress. The results demonstrated a significant correlation between von Mises stress, ΔKeq, and fatigue life cycles. With an increase in the stress ratio, there was a significant decrease in the von Mises stress, accompanied by a rapid increase in the number of fatigue life cycles. The results obtained in this study have been validated by previously published literature on crack growth experiments and numerical simulations.

Investigations on fatigue properties of red sandstone under positive and negative pure bending loads

Brittle materials such as rock and concrete may be subjected to positive and negative cyclic loading effects such as earthquakes and construction disturbances, and bending damage is one of the most likely forms of damage. A four-point bending fixture was designed to conduct fatigue tests with positive and negative stress ratios under pure bending to investigate the influence of cyclic loading on the form and mechanism of damage. The fracture energy calculation equation based on crack mouth opening displacement (CMOD) was derived, and the fracture criterion based on fracture toughness and fracture energy was established, which was in good agreement with the experimental results. Under the pure bending fatigue load, the hysteresis loop of the P-CMOD curve shows a loose-dense-loose law, and the damage curve can be divided into three stages of initial, stable, and accelerated law. Stress level and stress ratio are two main factors affecting fatigue life. The fatigue life of negative stress ratios is greater than that of positive stress ratios because there is a crack closure process in negative stress ratios, which affects the fatigue life. The final damage occurs for positive stress ratio specimens when the fatigue dissipation energy is greater than the static fracture energy. Static CMOD starting and final values were introduced to define the fatigue damage variables, and a damage evolution model was established better to simulate the evolution with positive and negative stress ratios.

Calibration of Paris law constants for crack propagation analysis of damaged steel plates strengthened with prestressed CFRP

Paris law constants, C and m, are two vital parameters of the Paris law for fatigue crack propagation of steel structures. Traditionally, the constants are determined through a linear regression of experimental crack growth curve under tension-to-tension cyclic loading. However, the direct linear regression would provide the value of C with larger error under negative stress ratios (tension-to-compression cyclic loading) probably caused by prestress. This study firstly proposed a reverse-reasoning methodology to obtain and calibrate Paris law constants based on the notched specimens with non– and prestressed CFRP (Carbon Fiber-reinforced Polymer) reinforcement under a wider range of stress ratios. Finite element (FE) modeling was then performed using a combination of the programs FRANC3D and ANSYS to compute the stress intensity factors (SIF) as well as crack tip shape evolution of the respective specimens. A sensitivity analysis was also made to investigate the variety of the constants affected by crucial factors. The comparison of experimental and theoretical results confirms excellent accuracy of the proposed method. The results indicated that the constant m is stable around 3.15 and prestress effect is significant not only on reduction of effective SIF range but also on change of the constant C. Moreover, the suggested value of m and C are 3.15 and 1.08E-12 for prestressed CFRP reinforced steel structures under negative stress ratio (R ≤ 0), and are 3.15 and 2.17E-13 for the positive stress ratio (R > 0) in the unit of mm and MPa, respectively.

Embedding artificial neural networks into twin cohesive zone models for composites fatigue delamination prediction under various stress ratios and mode mixities

This paper presents for the first time a novel numerical technique for modelling fatigue delamination growth in fibre reinforced composites, which is based on coupling two twin cohesive zone models with a single-hidden-layer artificial neural network. The simulation approach proposed here can describe composites fatigue delamination under negative & positive stress ratios and the full range of mode mixities. In the modelling strategy, each segment of a composites interface is described by two twin cohesive elements, which jointly provide local fracture mechanics parameters into a feedforward single-hidden-layer neural network, without the need to know the global load R ratio. In turn, the neural network algorithm feeds the fatigue crack propagation rate da/dN back into the twin cohesive elements, which follow a static and fatigue cohesive law in a synchronous fashion. The novel modelling methodology has been implemented in an explicit finite element scheme. The modelling strategy is first verified and validated by several benchmark cases, involving mode I Double Cantilever Beam tests, mode II End Loaded Split tests with and without reversal, as well as Mixed-Mode Bending tests. A relevant application of the modelling technique is demonstrated considering a tapered laminate, which experiences non-proportional loading due to the presence of combined static tension and cyclic bending.

Fatigue life evaluation model for high-strength steel wire considering different levels of corrosion

This article studies the quantitative influences of corrosion on the fatigue life of high-strength steel wires, considering a wide variation in the degree of corrosion. A multiparameter Weibull model for corrosion-stress-life (C-S-N) is proposed, and the Goodman relation is employed to deal with the dependences of stress ranges on positive stress ratios. Fatigue data are collected from the literature for three groups with different ultimate tensile strengths and the degree of corrosion ranging from 0.18% to 18.67%. This data is then used to estimate the parameters of the Weibull model; subsequently, quantitative influences of corrosion on fatigue life for steel wires with a wide range in the degree of corrosion are illustrated and discussed. The results indicate that the influence of ultimate tensile strengths on fatigue life for corroded steel wire can be ignored, because corrosion causes crack nucleation faster, especially at lower stress ranges. The fatigue life decreases sharply as the corrosion increases, and reduction is much pronounced under a lower stress range. Negative correlation of fatigue life and corrosion increases as the stress range decreases, which further confirms that corrosion has a higher influence at lower stress ranges. The proposed model can provide quantitative evaluation on the fatigue life of steel wires at specified survival probabilities, considering a wide range in the degree of corrosion; these results can be used by engineering designers to ensure the safety for cable-supported bridges during their lifetime.

Fatigue crack growth in aluminum panels repaired with different shapes of single-sided composite patches

In this study, the effects of patch shape on the performance of bonded composite repairs on aircraft structures are investigated using experimental and numerical approaches. Fatigue tests under constant amplitude loading, with a positive stress ratio, are performed on V-notch cracked specimens using two aluminum alloys, 2024-T3 and 7075-T6 that are repaired with bonded carbon/epoxy patches. Three composite patch shapes are used: rectangular, trapezoidal, and triangular. Left- and right-oriented triangular patch shapes are used to analyze the effects of the patch orientation on the repair efficiency. Numerical models are built with these patch shapes and orientations. The stress intensity factors and adhesive stresses are computed to numerically evaluate the repair performances obtained with the different patch shapes and orientations. The experimental results demonstrate that rectangular patches provide the most efficient repair, whereas the triangular shape with a left-orientation may lead to catastrophic results, particularly with the 2024-T3 aluminum alloy. The numerical results concur with the experimental observations.

A General Damage Accumulation Model for Multiaxial, Proportional High Cycle Fatigue Loadings With Sines, Crossland and Dang Van Criteria

AbstractIn this paper, a key differential equation is proposed to formulate fatigue damage evolution in metallic alloys under multiaxial, multiblock, proportional loadings in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) regimes. This differential equation possesses two main components: one is a stress function to accommodate the adopted fatigue criterion and the other one is a characteristic damage function that serves to capture the HCF response of alloys. Two distinct characteristic damage functions with three different multiaxial fatigue criteria, namely Sines, Crossland, and Dang Van criteria, are examined to develop six (out of many possible) variants of the presented damage accumulation model. As a validation measure, Chaboche’s HCF damage model is retrieved as a specific case of the developed formalism. For model parameters identification, an ad hoc two-level identification scheme is designed and numerically verified. It is demonstrated that endurance limit, which is determined from fully reversed HCF tests (i.e., R = −1), can be identified from fatigue tests with positive stress ratio (R > 0), thus making our development quite suitable for specimens prone to buckling under compression. Another salient feature of the devised identification scheme is its capability in extracting model parameters from noisy data.

Further investigation on microstructure refinement of internal crack initiation region in VHCF regime of high-strength steels

The profile samples prepared by focused ion beam (FIB) in crack initiation region (CIR) and fish-eye (FiE) region of failed specimens subjected to rotary bending (RB) and ultrasonic axial (UL) fatigue testing with various stress ratios (R) were observed by transmission electron microscopy (TEM) with selected area electron diffraction (SAD) detection for two high-strength steels. The grain size and the thickness of nanograin layer along the crack growth path in CIR underneath fine-granular-area (FGA) were measured for the cases of R 0 and the FiE region outside CIR for either negative or positive stress ratio cases, which suggests that the formation of nanograin layer in the FGA region is due to the numerous cyclic pressing (NCP) process and the plastic deformation ahead of the crack tip may cause certain extent of microstructure deformation but is insufficient to form nanograin layer on crack surfaces.

Fatigue crack growth in wheelset axles under bending and torsional loading

In the past, unexpected failures in wheelset axles lead to catastrophic consequences. To avoid those failures inspection intervals must be defined. The definition of the inspection intervals is based on fracture mechanical approaches. In the present work, the railway axle steel 34CrNiMo6 is investigated. For this material fatigue crack growth data have been experimentally determined for a range of different negative and positive stress ratios. Furthermore, the FORMAN/METTU parameters for different probabilities of survival are identified. In wheelset axles different geometry factors influence the crack growth behaviour. Therefore, different shouldered solid shafts with transition radii and a press fit seat are designed and tested under rotating bending. Moreover, the load situation also has an influence on the crack growth. The main bending load is overlapped with torsional loading at special wheel-rail-situations. With the developed mixed mode test rig, the influence of different load situations on wheelset axles are examined.

Numerical Investigation of J-Integral on a Notched Pressure Vessel

Finite elements analysis has been performed to compute a J-integral values in a notched pressure vessel. A semi-elliptical notch was introduced in a wall of cylindrical pressure vessel with aspect ratio of notch depth to wall thickness a/w = 1/6 to 5/6, where the wall thickness was 3 mm. Two cases were examined – inner and outer notch. Numerical examinations were revealed that outer notch has much higher values of J-integral (3-4 times), all other being the same, (i.e. inner pressure and dimensions of the notch). That was explained in terms of triaxality stress state in front of notch. Namely, it was shown that inner notch has positive triaxiality stress ratio and vice-versa, outer notch revealed highly negative hydrostatic stress component ahead the notch.

The effect of compression loading on fatigue crack propagation after a single tensile overload at negative stress ratios

Experiments on fatigue crack propagation under a loading history with a single tensile overload at an overload ratio of ROL = 1.8 were performed at different baseline stress ratios of R = 0, −0.25, and −1 for aluminium alloy 2A12-O. The widely accepted fatigue crack propagation retardation due to a single tensile overload (OL) in the case of a positive stress ratio (R) was observed at R = 0. However, the retardation effect gradually decreased from R = 0 to R = −0.25 and disappeared at R = −1. These results indicate that the applied compressive load has a significant effect on the fatigue crack propagation after a single tensile overload for aluminium alloy 2A12-O. To reveal the mechanism of this effect of compression loading, a detailed elastic-plastic finite element (FE) analysis was performed. Based on the results of finite element analysis, a mechanism of additional reverse plastic damage caused by compression loading was proposed to explain the interaction of tensile overload and compressive load. The parameter of reverse plastic zone size was applied to characterize the additional reverse plastic damage. A parameter describing the effect of compression loading on fatigue crack propagation retardation due to a single tensile overload was developed. Using this parameter it was verified that the mechanism of additional reverse plastic damage is effective to explain the compression loading effect on the fatigue crack propagation retardation due to a single tensile overload.

Very high cycle fatigue of surface carburized CrNi steel at variable stress ratio: Failure analysis and life prediction

High cycle fatigue and very high cycle fatigue properties of a surface-carburized CrNi steel were examined under axial loading with stress ratios of −1 and 0. The positive stress ratio overcomes the effect of carburized layer and promotes crack initiation from the carburized layer. The morphology of fine granular area (FGA) is more distinct under the negative stress ratio with more obvious crack closure effect. Two models concerning the inclusion-fisheye failure and the inclusion-FGA-fisheye failure are proposed. The predicted fatigue lives based on the concept of crack initiation are in good agreement with experimental results.

Study on Fatigue Design Method of an Engine Component Produced by Flake Graphite Cast Iron for Different Loading Modes and Mean Stresses

In order to improve reliability of an automotive engine, a fatigue design method was studied based on the fatigue mechanisms in flake graphite cast iron. In the present study, fatigue test specimens were cut from an actual engine component. The material used showed nonlinear behavior in stress–strain relationship from lower stress level during tensile testing. Rotating bending fatigue testing and axial load fatigue testing were performed. Fatigue crack initiation and propagation behavior were observed during the fatigue tests by a replication technique. Fatigue cracking initiated from the tip of flake graphite in early stage of the total fatigue life when the applied stress was higher than the fatigue limit. On the other hand, fatigue cracking was not observed in the specimen tested with applied stress below the fatigue limit. The threshold stress intensity factor obtained with a small surface crack was lower than that obtained with a through-thickness crack. Fatigue limits under various loading conditions such as bending loading and axial loading were predicted well based on fracture mechanics using the $$ \sqrt {\text{area}} $$ parameter. Threshold stress intensity factor for a small surface crack and the maximum graphite size assumed as an initial crack were used for the prediction. Axial load fatigue tests with different stress ratios were performed. The fatigue limit diagram obtained by the fatigue tests did not follow the modified Goodman relation. On the other hand, fatigue limits prediction based on fracture mechanics approach showed good agreement with fatigue limit obtained with fatigue tests in a wider range of mean stresses σmean varying from − 150 to 50 MPa, in negative stress ratio. In case of σmean higher than 50 MPa, in a positive stress ratio, a smaller effect of stress ratio in the fatigue limit diagram was observed. It was considered that this phenomenon could be explained by the lower effect on the crack closure in a small surface crack initiated from the tip of graphite flake and also influence of local plastic behavior of the matrix around the tip of graphite flake. It can be summarized that the fracture mechanics approach is an effective way to predict fatigue limits of an engine component produced by flake cast iron in different loading conditions and in wider range of mean stress conditions.

Crack initiation and early growth behavior of TC4 titanium alloy under high cycle fatigue and very high cycle fatigue

Abstract

Subcycle fatigue crack growth formulation under positive and negative stress ratios

A new fatigue crack growth model at the subcycle scale is proposed for both positive and negative stress ratios. The term “subcycle” refers to the crack growth modeling within a cyclic loading duration rather than the classical cycle averaged crack growth rate (i.e., da/dN). The proposed model includes two major components: a subcycle crack growth rate function and a crack opening stress estimation algorithm for tension–tension and tension–compression cyclic loading. The subcycle crack growth rate function is proposed based on existing in situ scanning electron microscopy testing results. Following this, separation of far field crack contact and near tip crack contact are discussed for both positive and negative stress ratios. A simple linearized model is proposed to estimate the crack opening stress. The developed simplified crack opening stress estimation model is compared with several other models available from open literatures. Next, the proposed subcycle fatigue crack growth methodology is validated with several sets experimental data for various metallic materials under different positive and negative stress ratios. Some discussions and conclusions are drawn based on the proposed model.

Fatigue crack growth at negative stress ratios: On the uncertainty of using ΔK and R to define the cyclic crack tip load

At negative stress ratios, the cyclic crack tip loading cannot be defined by ΔK and R. Little attention has been paid on this issue and most of the existing fatigue crack growth data at negative stress ratios is treated in the same way as positive stress ratios. The aim of this note is to call attention on this topic and to sensitize the reader for possible uncertainties in life time prediction. Simple examples are discussed which show that neither reversal crack tip plasticity nor the crack growth rate is controlled by Kmax and R at negative stress ratios. Instead the parameter σtip seems to be a controlling parameter for minimum crack tip load at negative stress ratios. A discussion is provided with the focus on transferring the findings to other specimen or structures. Perspectives for the treatment of negative stress ratios in the context of fatigue crack growth are briefly discussed.

Prognostic analysis of fastener joints in straight attachment lugs

PurposeMany failures of aircraft structural components in the past were attributed to cracks emanating from joints, which are identified as the most critical locations. In cases using the recently emerging structural health monitoring (SHM) systems, continuous monitoring needs be carried out at many major joint locations. The purpose of this paper is to develop computational techniques for fastener joints, including the possible change in contact conditions and change in boundary values at the pin-hole interface. These techniques are used for the prognostic analysis of pin-loaded lug joints with rigid/elastic pin subjected to fatigue loading by estimating the residual life of the component at any given instance to assist the SHM systems.Design/methodology/approachStraight attachment lug joints with rigid/elastic push-fit pin and smooth pin-hole interface are modelled in commercial software MSC PATRAN. In each case, the joint is subjected to various types of fatigue load cycles, and for each type of cycles, the critical locations and the stress concentrations are identified from the stress analysis. Later, for each type of fatigue cycle, the number of cycles required for crack initiation is estimated. A small crack is located at these points, and the number of cycles required to reach the critical length when unstable crack growth occurs is also computed. The novelty in the analysis of life estimations is that it takes into account possible changes in contact conditions at the pin-hole interface during load reversals in fatigue loading.FindingsThe current work on fastener joints brings out the way the load reversals leading to change in contact conditions (consequently changing boundary conditions) are handled during fatigue loading on a push-fit joint. The novel findings are the effect of the size of the hole/lug width, elasticity of the material and the type of load cycles on the fatigue crack initiation and crack growth life. Given other parameters constant, bigger size hole and stiffer pin lead to lesser life. Under load controlled fatigue cycles, pull load contributes to significant part of fatigue life.Originality/valueThe analysis considers the changing contact conditions at the pin-hole interface during fatigue cycles with positive and negative stress ratios. The results presented in this paper are of value to the life prediction of structural joints for various load cycles (for both pull-pull cases, in which the load ratios are positive, and pull-push cycles, where the load ratios are negative). The prognostic data can be used to effectively monitor the critical locations with joints for SHM applications.