Wheeler Model Research Articles

Retardation mechanisms and modeling of fatigue crack growth of a high-strength steel after single overload

This study investigated the retardation mechanisms and modeling methodology for the fatigue crack growth (FCG) of a high-strength Q500qE steel after a single overload. Different stress ratios (R = 0.1, 0.3, and 0.5) and overload ratios (OLR = 1.5, 2.0, and 2.5) were considered as key parameters. The digital image correlation (DIC) testing technique was used to capture the deformation at the crack tip during the tests. The crack closure response in the crack wake region was investigated using a virtual extensometer. The results show that, under an identical stress ratio, the fatigue life was increased as the OLR increased. The FCG was completely arrested when OLR reached 2.5 when R ≥0.3. Under an identical stress ratio, the residual strain before the crack tip and the residual deformation in the crack wake region increased with the rise of the overload ratio after a single overload. It’s found that the FCG was retarded or completely arrested due to the constraint of the crack tip plastic zone caused by single overload. Finally, a modified Wheeler model was proposed to predict the FCG rate based on the measured plastic zone size at the crack tip, and the predicted results agree well with the experimental findings.

A new method for prediction of fatigue crack propagation life under variable amplitude spectrum loading

This paper proposes a new method for predicting propagation lives for through-thickness cracks under variable amplitude mode-I spectrum fatigue loads. Only the crack opening, i.e., the increasing parts of the load cycles within spectrum profiles are considered for cycle counting and computing their stress ratios. Moreover, a cycle-by-cycle analysis is also performed throughout the spectrum to compute the so-called Spectrum Overload Index (SOL-Index), which is a multiplier applied on stress intensity factor range used within different crack growth retardation models, in which effects of stress ratio are also included. The SOL-Index is calculated using the average of peak loads for all cycles within the spectrum and their percent deviations from the peaks’ average value. Simulation results using the proposed cycle counting method, the integrated crack growth model and the SOL-Index are compared with those from multiple experiments under two different loading spectrums and another study in the literature. The results show that usage of Wheeler's model embodying the Forman or Walker equation and the SOL-Index together yields the closest results to the experiments.

Model-model Pengembangan Kurikulum di Sekolah

This research explores the curriculum development model in schools. This research, sometimes referred to as a type of library research, or library research, involves research or obtaining materials from various sources such as magazines, books, articles, and others that are relevant to the problem. to be solved. The output of this research is curriculum development, namely the process of curriculum planning and design by curriculum developers, and the activities carried out so that it becomes teaching materials and reference materials to achieve national education goals. In designing the curriculum, teachers can choose from several models including: Tyler model, Taba model (converter model), Wheeler model, Skillback dynamic model. Curriculum development procedures include curriculum planning, curriculum organization, personnel records, and curriculum management. Curriculum implementation is the process of putting ideas, concepts and policies into practice, so that it has an impact on changes in knowledge, skills and values. student attitude. The success of curriculum implementation depends on the availability of information about the implementation plan and the support of all resources in this implementation.

The Effect of Overload Block Size on Fatigue Crack Growth Life

In this study, the effect of the block overload duration on the two-dimensional crack propagation life was experimentally investigated. In the experiments, different sizes of overload cycles were applied on Compact Tension (CT) specimens machined from rolled Al-7075-T6 plates. The experiments showed that if applied block overload cycles are extended, the crack growth accelerates, because the overload cycles dominate the crack growth. In the short cycle block overload case, crack propagates slower than the case of single overload due to the plasticity-induced effect in the crack tip. After the tests, crack growth life was calculated using some models in the literature, and the results were compared with the experiments. Close results to the experiments were obtained with Wheeler model and its modifications.

Probabilistic assessment of fatigue crack propagation with accounting for effects of crack retardation due to overloads

The paper presents a probabilistic approach to fatigue strength assessment based on the Wheeler model that provides the opportunity to account for crack retardation due to overload in a probabilistic formulation. The probabilistic assessment is performed by Monte Carlo simulations based on random sampling. It consists of running deterministic assessments a sufficiently large number of times with different combinations of randomly sampled input data in order to build a statistical picture of the output quantities. A computer code in Matlab was developed to obtain the prior assessment of the probability of fatigue failure of a pipeline structural component. The Bayesian inference is used to update the prior assessment failure probability assessments as soon data from in-service technical inspections become available

Implementation of modified Wheeler model in peridynamic fatigue model to predict effects of overload and underload on fatigue crack growth rate

This study presents a novel peridynamic model for the prediction of fatigue crack growth rate with the effects of overload and underload. The modified Wheeler models for underload, overload and overload-underload combinations are applied to peridynamic fatigue equations. The capability of the proposed peridynamic fatigue model is demonstrated by considering fatigue crack growth on a single edge-notch plate subjected to constant amplitude loadings with overloads, underloads, and overload/underload combinations. The accuracy of the proposed peridynamic fatigue model is verified by comparing the predicted fatigue crack growth with experimental results.

How Can Termites Achieve Their Unparalleled Postembryonic Developmental Plasticity? A Test for the Role of Intermolt-Specific High Juvenile Hormone Titers

Termites are “social cockroaches” and amongst the most phenotypically plastic insects. The different castes (i.e., two types of reproductives, workers, and soldiers) within termite societies are all encoded by a single genome and present the result of differential postembryonic development. Besides the default progressive development into winged sexuals of solitary hemimetabolous insects, termites have two postembryonic, non-terminal molts (stationary and regressive; i.e., molts associated, respectively, with no change or reduction of size/morphological differentiation) which allow them to retain workers, and two terminal developmental types to become soldiers and replacement reproductives. Despite this unique plasticity, especially the mechanisms underlying the non-terminal development are poorly understood. In 1982, Nijhout and Wheeler proposed a model how this diversity might have evolved. They proposed that varying juvenile hormone (JH) titers at the start, mid-phase, and end of each intermolt period account for the developmental diversity. We tested this rarely addressed model in the lower termiteCryptotermes secundususing phase-specific pharmacological manipulations of JH titers. Our results partially support the Nijhout and Wheeler model. These data are supplemented with gene expression studies of JH-related genes that characterize different postembryonic developmental trajectories. Our study provides new insights into the evolution of the unique postembryonic developmental plasticity of termites that constitutes the foundation of their social life.

Fatigue crack propagation behavior of high-strength steel under variable amplitude loading

In this paper, aimed at high strength steel for marine structures, a series of crack propagation tests were designed and carried out, and the influence of different load forms on crack growth has been investigated. At first, a series of fatigue crack propagation experiments were designed for compact tension specimens made of AH36 High-strength steel, and the influences of overload ratio, interval of overloads, and load sequence on fatigue crack growth rate were investigated. Besides, storm model loading and superimposed loading were applied to further investigate crack growth behavior under more complex loading condition. The research indicates fatigue crack growth behavior under variable amplitude loadings deviates apparently. The difference is mainly caused by the sequence of variable amplitude loadings and the retardation/acceleration when tensile/compressive overloads are applied. Moreover, digital image correlation technique was adopted to obtain the strain fields and residual strain around crack tip. The mechanism of fatigue crack growth behavior under variable amplitude loadings was investigated by analyzing the transformation of strain fields in crack tips. Extended finite element method to calculate the plastic zone size around crack tip was proposed and verified to be accurate and applicable. In the end, the plastic zone size obtained by digital image correlation technique, which shows better accuracy, was applied to improve the modified Wheeler model, and the fatigue crack growth behavior under variable amplitude loadings was predicted by the improved modified Wheeler model, and was in good agreement with experiment results.

Fatigue crack growth of butt welded joints subjected to mixed mode loading and overloading

Since welded joints in structures are known to be critical regions for crack initiation and growth, study of fatigue crack growth behavior of welded joints under various loading scenarios are essential. In present study, two groups of experiments were conducted. At first, fatigue crack growth behavior of Al5083 butt welded joint subjected to mixed mode loading with constant amplitude has been studied. Afterwards, fatigue crack growth behavior of butt welded joints subjected to mixed mode single overload has been investigated. The sensitivity of the crack growth retardation behavior to post-welding heat treatments was also studied. Considering the effect of residual stress on fatigue crack growth, a modification to the Wheeler model was proposed to improve the accuracy of retardation prediction after applying a mixed mode overload.

Experimental Study on the Fatigue Crack Growth and Overload Effect in Medium Density Polyethylene

The fatigue crack growth behavior of medium-density polyethylene (MDPE) under constant amplitude load was experimented on plate specimens. The effect of additional imposed single overload was also researched. An optimized crack front marking method was developed to obtain the actual crack front shape of polymer materials in fatigue crack growth, which was successfully applied to the studied MDPE. The results showed that the retardation of fatigue crack growth evidently appeared after the tensile overload was applied, which was similar to metallic materials. The passivation of the wedge-shaped plastic zone was a primary cause to crack retardation. The theory based on residual stress was introduced to describe the retardation effect, and the plastic zone size of crack tip was calculated by the Dugdale model. The Wheeler model was successfully used to fit the decreased crack growth rate.

Fatigue crack growth modelling of Fão Bridge puddle iron under variable amplitude loading

This study addresses the fatigue crack growth behaviour of a material from an old riveted steel bridge, the Portuguese Fão Bridge, based on an experimental program of constant and variable amplitude loading tests. The material under consideration is a centenary puddle iron, for which information on fatigue crack growth under variable amplitude loads is not available in the literature. Additionally, the experimental program aimed at analysing the fracture surfaces of the specimens through observations under Scanning Electron Microscopy (SEM), and correlate their characteristics with macroscopic fatigue crack growth behaviour. Furthermore, a crack closure analysis was performed using electrical strain gauges applied on the back face of the CT specimens. The fatigue crack propagation along the parallel to the rolling direction (L) revealed to be higher when compared with the transverse direction (T). The experimental data obtained in this study were compared with existing fatigue crack propagation models, such as the Paris model with linear damage accumulation, according to Miner’s rule, as well as with more complex crack propagation models, with capacity for modelling retardation effects of single overloads. The Paris model with linear damage accumulation, despite its simplicity, led to the best predictions for the generality of variable amplitude random block loading. The original Wheeler model is enough to correlate the crack propagation data under overloads, since the application of more sophisticated models would not be justified by the extremely high scatter observed in these old materials.

Two engineering models for predicting the retardation of fatigue crack growth caused by mixed mode overload

The effect of mixed mode overload on the retardation of pure mode I cyclic loading has been investigated experimentally on Al5083-H111. Two models for extension of the Wheeler retardation model are proposed in order to calculate retardation of fatigue crack growth subjected to mixed mode overload. The first proposed model can predict retardation with high precision. The second proposed model is a simplified form of the first one and does not contain more experimental constants than the Wheeler model so, it may be more practical. The application of the proposed models has been examined for another material and testing conditions.

Effect of overload on fatigue crack growth behavior of thin copper foil

Smart stress-memory patch (SSMP) which consists of electrodeposited copper foil has been proposed as a sensor to measure fatigue loading for structural health monitoring in previous researches. In this study, the fatigue crack growth behavior of the copper foil was examined under constant amplitude loading with single overload and variable amplitude loading in order to evaluate the applicability of SSMP to the actual loading conditions. Under the overload condition, the fatigue crack growth rate gradually decreased after the overload and reached a minimum value, and then recovered to the baseline. Since the retardation behavior was different from one of thick specimen, a new model to quantify the crack growth in the thin specimen was proposed based on a modified Wheeler model. The proposed model successfully reproduced the fatigue crack growth curve under the single overload condition. Additionally, the proposed model was extended to the variable amplitude loading conditions by including cycle-by-cycle calculation procedure. The results showed that the fatigue crack growth behavior can be represented by the proposed model under the variable amplitude loading condition. Therefore, the feasibility of applying SSMP to actual loading conditions was demonstrated.

Constraint corrected cycle-by-cycle analysis of crack growth retardation under variable amplitude fatigue loading

Various models exist to predict load interaction effects on fatigue crack growth in variable amplitude loading conditions. Stress overloads have the potential to strongly retard or even arrest a propagating fatigue crack. Whereas global analysis methods (making use of equivalent quantities) allow to describe stochastic loading scenarios, describing the effects of deterministic overloads requires cycle-by-cycle analysis techniques. Within this category, plastic zone models have proven to be effective and pragmatic in terms of calibration. Current models, however, do not account for the effect of crack tip constraint on the plastic zone size, whose estimation is a requirement. This paper develops a novel (“extended”) crack growth formulation based on the traditional plastic zone based Wheeler’s model, taking into account the effect of out-of-plane constraint (plane stress versus plane strain). Calibration of the model requires characterization of shut-off overload ratios for different stress intensity factor levels. The “extended Wheeler” model gives better agreement with experimental tests results than the original and modified Wheeler model.

Effect of single overload on fatigue crack growth in QSTE340TM steel and retardation model modification

To analyze the effect of single tensile overload on fatigue crack growth behavior, a series of experiments have been conducted under different load ratios and overload ratios on QSTE340TM automobile steel. The results showed that the application of overload extended the fatigue life of the specimens in all cases. The fatigue crack growth rate curves presented different patterns between the case load ratio R = 0.7 and the cases R = 0.1, 0.3, 0.5. Difference between the trends of the closure load and the fatigue crack growth rate in the cases R = 0.1, 0.3, 0.5 was found and discussed. The images of fracture surface were obtained by Scanning Electron Microscope. A new effective stress intensity factor expression was proposed and discussed. A combined model based on both the residual stress effect and the plasticity-induced crack closure effect was proposed by modifying the Wheeler model and applying the new effective stress intensity factor expression. The proposed model gave reliable estimates of QSTE340TM steel for all overload cases and two other materials from references.

Origins of sports car marketing: early 20th Century British cycle-cars

PurposeThe aim of this study is to explore the attempts by early twentieth century cyclecar manufacturers in the UK and USA to segment the personal transportation market and to position early cyclecars through the development of unique product attributes and advertising. More specifically, the authors speculate about early twentieth century British cyclecar marketing strategies that implicitly recognized a sports car segment and positioned cyclecar brands to meet the needs of that segment.Design/methodology/approachThe primary source material for this research is a sample of 205 print ads and articles from the early twentieth century (1912-1921) specialty magazines devoted to cyclecars in the UK and USA. We combine the content analysis of the sample of ads with a critical reading and interpretation of a sub-sample of those same ads.FindingsBetween 1910 and 1921, a new form of personal transportation was developed that combined the technology of motorcycles with the utility of automobiles. Known as “cyclecars”, these vehicles were typically constructed from off-the-shelf motorcycle parts and assembled in small batches by a myriad of manufacturers. Current scholarship suggests that the cyclecar craze of the 1910s ended with the introduction of low cost “real” automobiles such as the Ford Model T, Austin 7 and Morris Oxford. We use the content analysis of cyclecar advertisements to construct a brand-positioning map of this emerging segment of the transportation market. We argue that while the core cyclecar positioning was in direct competition with small economically positioned cars such as the Ford Model T, a significant part of the market, primarily centered in the UK, could be considered as for sports cars. That segment of the cyclecar market, along with the development of cyclecars into urban delivery vehicles, continued over time and has re-emerged today in a range of three-wheeled sports cars, including the updating and continuation of the British Morgan 3 Wheeler model which was launched during the heyday of cyclecars.Research limitations/implicationsThe authors can only speculate about the impact of the Ford Model T in this study. Further research on that issue is needed.Originality/valueThis is the first historical study of cyclecar marketing. Most of what little has been published about cyclecars focuses on their design and technology.

Cycle-by-cycle simulation of variable amplitude fatigue crack propagation

In variable amplitude fatigue of high strength low alloy (HSLA) steel components, overloads can severely retard subsequent crack propagation for a number of cycles. In order to be able to predict fatigue crack propagation with a reduced degree of conservatism, retardation has to be taken into account. Of all numerical models that have been developed over time, crack tip plasticity models are selected based on the need for a detailed and fast cycle-by-cycle simulation of high cycle. After introducing the load interaction zone concept, common to all crack tip plasticity models, the Wheeler and Willenborg models are discussed, implemented and compared to experimental data. It is concluded that the Modified Wheeler model provides the most promising results, whereas the main limitation of Willenborg models is the need for extensive experimental data.

Effect of single tensile overload on fatigue crack growth behavior in DP780 dual phase steel

The purpose of this study was to analyze the effect of single tensile overload on fatigue crack growth (FCG) behavior in DP780 dual phase steel. The compact tension samples were tested under constant amplitude load and overload condition. The results showed that all the material conditions responded favorably to the single tensile overloads; the magnitude and extent of crack retardation was amplified due to an increase in overload ratio (OLR) and a longer crack length at overload application. The error between the overload affected crack growth increment and the magnitude of overload monotonic plastic zone size decreased about 30% after introducing the factor (n−1)/(n+1) into Irwin model. A plastic zone size factor was used to modify the Wheeler model to calculate the FCG rate during retardation period after an overload, the predicted results were in good agreement with the experimental data. During the application of an overload, a crescent moon shaped damage zone was formed ahead of the crack tip characterized by cleavage surfaces, tearing ridges, dimples and voids. The fracture morphology after crack front reformation was severely damaged due to the premature contact of the crack flanks. Crack branching was not significant interaction effect for the crack growth retardation under overload.

Fatigue and Fracture behaviour of AZ31b Mg alloy plastically deformed by Constrained Groove Pressing in the Presence of Overloads

Within the class of lightweight metallic materials, magnesium alloys are gaining popularity mainly thanks to abundant supply and high specific strength. A weakness of Mg alloys is their poor formability at room temperature. For this reason, in recent years thermo-mechanical treatments have often been sought that would improve this aspect. One particular way towards the combination of better formability (ductility) and strength is through grain refinement by means of Constrained Groove Pressing (CGP). The use of a pair of matching dice having groove-like geometry, coupled with controlled process temperature, allows promoting microstructural refinement and achieving sub-micron grain size in the processed plates.The purpose of the present study was to characterise the resulting fine-grained material in plate form in terms its fatigue fracture behaviour. Compact tension samples were machined and subjected to cyclic tensile loading to monitor fracture propagation and extract their Fatigue Crack Growth Rate (FCGR) behaviour as a function of the applied crack tip Stress Intensity Factor range. Firstly, as a reference sample an as-received material plate was tested at the loading ratio R=0.1. Subsequently, CGP-processed fine-grained material was tested at R=0.1 and R=0.7, and subjected to anomalous load that included overload (50% increase in the maximum load) and, in the specific case of R=0.1, underload (reversal of the sign of minimum load from tension to compression).These studies provided the critically needed input for the development of new approaches to the evaluation of the apparent fracture resistance of the material processed by CGP under variable amplitude loading (i.e. overload and underload) essential for accurate fatigue life prediction for a broad variety of applications. By combining the Walker model accounting for the mean stress effect and a modified Wheeler model for crack growth retardation due to the application of a single overload, a new predictive approach was formulated.

Tidal and centripetal stress in a model human falling deep into a Kerr black hole

I calculate the tidal and centripetal stress in the Misner–Thorne–Wheeler model human—a rigid prism—falling into a high-spin supermassive Kerr black hole at a constant, near-equatorial latitude with high energy, enough to surmount the radial potential barrier near the throat of the black hole. The stress in the model human would be nonlethal.