Propagation Threshold Research Articles

On the Tolerance to Short Cracks under Fatigue and SCC Conditions

The fatigue behavior of mechanically short cracks that depart from notch tips can be mechanically modeled using sound stress analysis techniques which properly account for the notch tip stress gradient influence on their growth rates, considering the basic fatigue properties of the material, its fatigue limit and long crack propagation threshold, and all the characteristics of the notch geometry and of the loading, without the need for any data fitting parameter. This model's predictions have been validated by proper tests, and a criterion to accept tolerable short cracks has been proposed based on it. In this work, this criterion is extended to model notch sensitivity effects in environmentally assisted cracking conditions.

An Immunization Strategy Based on Propagation Mechanism

With the ubiquity of smart phones, wearable equipment, and wireless sensors, the topologies of networks composed by them change along with time. The immunization strategies in which network immune nodes are chosen by analyzing the static aggregation network topologies have been challenged. The studies about interaction propagations between two pathogens show that the interaction can change propagation threshold and the final epidemic size of each other, which provides a new thinking of immunization method. The eradication or inhibition of the virus can be achieved through the spread of its opposite party. Here, we put forward an immunization strategy whose implementation does not depend on the analysis of network topology. The immunization agents are randomly placed on a few of individuals of network and spread out from these individuals on network in a propagation method. The immunization agents prevent virus infecting their habitat nodes with certain immune success rate. The analysis and simulation of evolution equation of the model show that immune propagation has a significant impact on the spread threshold and steady-state density of virus on a finite size of BA networks. Simulations on some real-world networks also suggest that the immunization strategy is feasible and effective.

Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the underlying component ensemble. This explains why convolutional LDPC ensembles, originally introduced by Felström and Zigangirov, perform so well over this channel. We show that the equivalent result holds true for transmission over general binary-input memoryless output-symmetric channels. More precisely, given a desired error probability and a gap to capacity, we can construct a spatially coupled ensemble that fulfills these constraints universally on this class of channels under belief propagation decoding. In fact, most codes in this ensemble have this property. The quantifier universal refers to the single ensemble/code that is good for all channels but we assume that the channel is known at the receiver. The key technical result is a proof that, under belief-propagation decoding, spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble. We conclude by discussing some interesting open problems.

English

This paperwork describes a comprehensive statistical assessment of rain gauge and satellite- based monthly and annual rainfall measurements over Nigeria during the period of 2001 to 2010. Two statistical methods were empolyed for inter-comparison and validation of the Tropical Rainfall Measuring Mission - TRMM 3B43 V7 rainfall product. TRMM was selected because of the recently developed algorithms to estimate 3D rain distribution from the visual spectrum radiance, radar and microwave sensors. The results of the continuous statistical assessment of the rainfall algorithms show good agreement with rain gauge measurement in term of correlation coefficient and improved mean error tests. The geometric mean of correlation coefficient from all the locations for annual, monthly, wet and dry period are 0.43, 0.79, 0.64, and 0.41 respectively. The categorical analysis assessment is based on the International Telecommunication Union for Radio-communication (ITU-R) recommended threshold for radio propagation. The results of Accuracy and FBI for ITU-R recommendation threshold of 1 to 10% percentage error for radio propagation applications are 0.629 and 0.901 for annual while that of monthly are 0.558 and 0.416. The overall performance of the TRMM based rainfall assessment is encouraging but more improvement is still needed for accurate and sufficient global rainfall estimation. Key words: TRMM 3B43 V6, satellite data, cross-validation, categorical statistics, radio propagation, ITU-R.

Effect of submillimeter size holes on the fatigue limit of a high strength tool steel

ABSTRACTThe very high cycle fatigue and small fatigue crack growth behaviour of a generic tool steel material for diesel fuel injector application are described. The small crack growth tests for the tool steel material with and without the hardening heat treatment revealed the mechanisms of crack propagation and threshold behaviour. Based on the small fatigue crack propagation threshold value, an elastic plastic fracture mechanics methodology for the prediction of the endurance limit of specimens with submillimeter holes is proposed. The advantages of the new methodology are discussed in relation to existing methodologies for endurance limit prediction of specimens with small holes.

On the application of a micromechanical small fatigue crack growth model to predict fretting fatigue life in AA7075-T6 under spherical contact

This work presents a method for assessing the fretting fatigue life by estimating the fatigue crack growth rate from the regime of microcracks to the final failure, which is achieved using a two-threshold small fatigue crack growth model. The propagation thresholds are associated with the interaction of the "monotonic plastic zone" and the "cyclic plastic zone" with the microstructure of the material. The predicted fatigue life and the estimated non-propagating cracks agree very well with the experimental fretting fatigue tests with spherical contact in 7075-T6 aluminium alloy.

Study on fatigue property and microstructure characteristics of welded nuclear power rotor with heavy section

Abstract The fatigue property and microstructure characteristics of the welded joint for nuclear power rotor with heavy section, were systematically reported in this paper. The welded joint microstructure is inhomogeneous for NiCrMoV rotor made by narrow gap submerged arc welding (NG-SAW), which could affect the properties in different zones of welded joint. As one of the important indicator to evaluate the running performance of welded rotor, the fatigue crack propagation behavior of the base metal (BM), weld metal (WM) and heat affected zone (HAZ) was comparatively studied. It was found that the fatigue crack propagation threshold (ΔKth) of BM was higher than that of WM and HAZ as stress ratio (R) was 0.1, but ΔKth was very close to each other as R increased. The microstructure, revealed by an optimized corrosive process, was granular bainite in WM and tempered martensite in HAZ, leading to their approximately equivalent resistance of fatigue crack propagation with BM. The experimental results showed that fatigue properties of welded joint for NiCrMoV rotor with heavy section could meet the design requirement, and also push NG-SAW into manufacturing large size rotor.

A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks

Rumor propagation is a typical form of social communication and plays a significant role in social life. In this paper, we studied the process of rumor propagation by accounting for the mechanism of forgetting in Barrat–Barthelemy–Vespignani (BBV) networks. First, we derived mean-field equations for rumor propagation based on the strength of the nodes in the propagation network. We then analyzed the stability of the model to determine whether a propagation threshold existed in the BBV networks. We also conducted numerical simulations of the BBV networks and found that rumors propagate more slowly in BBV networks than in unweighted networks. The numerical simulation results also demonstrated that as the forgetting rate increases, the rumor’s influence decreases in both BBV networks and unweighted networks. Finally, the simulation results confirmed that a threshold exists for rumor propagation in BBV networks, but that it was independent of the value of the stifling rate.

Does notch sensibility exist in environmentally assisted cracking (EAC)?

Empirical notch sensitivity factors q have been used for a long time to account for notch effects in fatigue design. This old concept has been recently modeled using sound mechanical principles to properly quantify the influence of the stress gradient around the notch tip on the fatigue behavior of mechanically short cracks. This model can be used to calculate q values from the basic fatigue resistances of the material, its fatigue limit and its crack propagation threshold, considering all the characteristics of the notch geometry and of the loading. This model predictions have been validated by proper tests, and based on this experimental evidence a criterion to accept tolerable short cracks has been proposed. In this work the mechanical principles that support this criterion are extended to account for notch effects in environmentally assisted cracking problems.

Tracking the permeable porous network during strain-dependent magmatic flow

Rheological variations have been postulated as the cause of transitions from effusive to explosive volcanic eruption style. Rheology is integrally linked to the composition and textural state (porosity, crystallinity) of magma as well as the stress, temperature and strain rate operative during flow. This study characterises the rheological behaviour and, importantly, the evolution of physical properties of two magmas (with different crystallinity and porosity) from Volcán de Colima (Mexico) — a volcanic system known for its rapid fluctuations in eruption style.Magma samples deformed in a uniaxial press at a constant stress of 2.8, 12 or 24MPa, a constant temperature of 940–945°C (comparable to upper conduit or lava dome conditions) to strains of 20 or 30% displayed different mechanical behaviour and significant differences in measured strain rates (10−2–10−5s−1). The evolution of porosity, permeability, dynamic Young's modulus and dynamic Poisson's ratio illustrate a complex evolution of the samples manifested as strain-hardening, visco-elastic, constant-rate and strain-weakening deformation. Both magmas behave as shear-thinning non-Newtonian liquids and viscosity decreases as a function of strain.We find that strain localisation during deformation leads to the rearrangement and closure of void space (a combination of pores and cracks) followed by preferentially aligned fracturing (in the direction of the maximum principal stress) to form damage zones as well as densification of other areas. In a dome setting, highly viscous, low permeability magmas carry the potential to block volcanic conduits with a magma plug, resulting in the build-up of pressures in the conduit. Above a certain threshold of strain (dependent upon stress/strain rate), the initiation, propagation and coalescence of fractures leads to mechanical degradation of the magma samples, which then supersedes magmatic flow and crystal rearrangement as the dominant form of deformation. This results in lower apparent viscosities than those anticipated for magma of such crystallinity, especially at high strain rates. In a lava dome, this could result in dome collapse and the concomitant depressurisation could trigger an explosive eruption.

Transmission dynamics feature of enterprise marketing networks

In order to understand and explain the transmission mechanism,based on propagation behavior and topology structure characteristics of enterprise marketing network and Susceptible-Infected-Removed(SIR) model,the paper introduced the indexes of node transmission rate and edge weight,and then established transmission dynamics model of enterprise marketing network.The enterprise marketing network epidemic threshold was analyzed and simulated.The results indicate that the bigger the indexes of node transmission rate and the edge weight are,the smaller the propagation threshold is,which is more helpful for product and product information transmission.Finally,the authors put forward a few suggestions from the perspectives of reducing the spread of critical value and improving actual propagation rate.

Is notch sensitivity a stress analysis problem?

Semi–empirical notch sensitivity factors q have been widely used to properly account for notch effects in fatigue design for a long time. However, the intrinsically empirical nature of this old concept can be avoided by modeling it using sound mechanical concepts that properly consider the influence of notch tip stress gradients on the growth behavior of mechanically short cracks. Moreover, this model requires only wellestablished mechanical properties, as it has no need for data-fitting or similar ill-defined empirical parameters. In this way, the q value can now be calculated considering the characteristics of the notch geometry and of the loading, as well as the basic mechanical properties of the material, such as its fatigue limit and crack propagation threshold, if the problem is fatigue, or its equivalent resistances to crack initiation and to crack propagation under corrosion conditions, if the problem is environmentally assisted or stress corrosion cracking. Predictions based on this purely mechanical model have been validated by proper tests both in the fatigue and in the SCC cases, indicating that notch sensitivity can indeed be treated as a stress analysis problem.

Study on the Rationality and Validity of Probit Models of Domino Effect to Chemical Process Equipment caused by Overpressure

Overpressure is one important cause of domino effect in accidents of chemical process equipments. Some models considering propagation probability and threshold values of the domino effect caused by overpressure have been proposed in previous study. In order to prove the rationality and validity of the models reported in the reference, two boundary values of three damage degrees reported were considered as random variables respectively in the interval [0, 100%]. Based on the overpressure data for damage to the equipment and the damage state, and the calculation method reported in the references, the mean square errors of the four categories of damage probability models of overpressure were calculated with random boundary values, and then a relationship of mean square error vs. the two boundary value was obtained, the minimum of mean square error was obtained, compared with the result of the present work, mean square error decreases by about 3%. Therefore, the error was in the acceptable range of engineering applications, the models reported can be considered reasonable and valid.

Windowed Decoding of Spatially Coupled Codes

Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as for finite lengths, since degree-2 variable nodes that result in high error floors can be completely avoided. However, to realize the promised good performance, one needs large blocklengths. This in turn implies a large latency and decoding complexity. For the memoryless binary erasure channel, we consider the decoding of spatially coupled codes through a windowed decoder that aims to retain many of the attractive features of belief propagation, while trying to reduce complexity further. We characterize the performance of this scheme by defining thresholds on channel erasure rates that guarantee a target erasure rate. We give analytical lower bounds on these thresholds and show that the performance approaches that of belief propagation exponentially fast in the window size. We give numerical results including the thresholds computed using density evolution and the erasure rate curves for finite-length spatially coupled codes.

A new semi-empirical law for variable stress-ratio and mixed-mode fatigue delamination growth

A new semi-empirical equation that describes the fatigue delamination growth in fibre reinforced toughened epoxies is presented and validated against data available in the literature. The new law accounts for the simultaneous effects of the stress-ratio and mode-mixity on the interlaminar crack propagation. If delamination propagation thresholds are ignored, the proposed semi-empirical equation allows describing interlaminar crack propagation employing only three material dependent parameters, whereas alternative models presented in the literature require four. If reliable threshold data are available from experimental tests, the new semi-empirical law can be extended to a unified description of stress-ratio, mode-mixity and thresholds effects using six material dependent parameters.

Longitudinal nonlinear wave propagation through soft tissue

In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated strain-rates introduced at the end of the structure where the load is applied. In addition, it is shown that when steep wave fronts are generated in the nonlinear viscoelastic material, energy dissipation is focused in those wave fronts implying deposition of energy in a highly localized region of the material. Novel mechanisms for brain tissue damage are proposed based on the results obtained. The first mechanism is related to the dissipation of energy at steep wave fronts, while the second one is related to the interaction of steep wave fronts with axons encountered on its way through the structure.

Estimation of Notch Sensitivity and Size Effect on Fatigue Resistance

This paper addresses the problem of high cycle fatigue resistance associated to notches and the role of short crack propagation in the fatigue notch sensitivity quantified by the notch factor kf. An integrated fracture mechanics approach is proposed to estimate the fatigue notch sensitivity, by including the effect of both blunt and sharp notches.Whether fatigue strength at a given life is controlled by crack initiation (very blunt notches, kf = kt), by microstructuraly short cracks (blunt notches, kf <kt), or by mechanically short crack propagation (sharp notches, kf <<kt), depends on the stress concentration kt, the notch length D and the material threshold to crack initiation ΔσeR, to short crack propagation ΔKth and to long crack propagation ΔKthR.The approach includes the prediction of the fatigue crack propagation threshold for short cracks, previously developed to analyze the short crack behavior in metallic materials with or without blunt notches, and is integrated adding the influence of sharp notches and accounting for the controlling parameters. It estimates the fatigue resistance of the component by comparing the threshold for fatigue crack propagation as a function of crack length, ΔKth, with the applied ΔK for the given configuration. Estimations for results reported in published bibliography are presented.The proposed fracture mechanics approach allows accounting for the effects of notch acuity, notch size and intrinsic material fatigue properties on fatigue notch sensitivity. It opens the door to a new simple method for predicting fatigue notch sensitivity and fatigue strength of components with geometric concentrators by using parameters that can be easily measured or estimated, without the necessity of any fitting parameter.

Estimating the fatigue behavior of welded joints in the VHCF regime

PurposeThe present work aims to deal with a very high cycle fatigue (n=109 cycles) of gas metal arc welded joints, subjected to a multiaxial and non‐proportional loading. Different design codes and recommendations can greatly reduce the analysis effort in the design of welded structures providing a suitable balance between computational accuracy and ease of use for many industrial applications. However, various assumptions have to be made in a conservative way making this approach less accurate. This paper deals with a refined fatigue assessment, which considers the most important aspects for welded joints and provides an accurate lifetime prediction of welded structures.Design/methodology/approachFor an accurate prediction of the total lifetime of welded components the information about the material state and the welding induced residual stresses on weld toes is essential. If the surface condition after welding is poor in this area, which is usually the case, the presence of defects can be assumed and the fatigue crack nucleation process can be neglected. The microstructural threshold for initial crack propagation can be therefore used as a lower bound for the fatigue limit prediction.FindingsBased on the results from the simulation of a welding process and a post‐weld heat treatment in combination with a fracture mechanics approach, this work successfully attempts to reproduce a fatigue behavior, which was observed at the fatigue tests of the multi‐pass single bevel butt weld.Originality/valueThe proposed approach is able to predict accurately the fatigue strength of welded structures and to achieve the full cost and weight optimization potential for industrial applications.

Modified Kitagawa Diagram and Transition from Crack Nucleation to Crack Propagation

Kitagawa-Takahashi diagram combines the endurance limit of a smooth specimen and the crack propagation threshold in a fracture mechanics specimen into single diagram thus providing the connection between the stress or strain-life and damage tolerance approaches. The diagram is modified by considering that (a) fatigue requires two independent load-parameters for unambiguous description, (b) long crack growth behavior defines the material resistance under constant stress amplitudes along with the associated R-ratio effects, (c) remote applied stresses and localized plasticity-effects can be combined to provide the total mechanical force opposing the material resistance leading to crack initiation, growth and failure describable in the diagram, (d) localized plasticity contributes to internal stresses that either augment or retard the remote stresses, and finally (e) the magnitude and gradient of these internal stresses determine the condition for propagation and/or non-propagation of the incipient cracks that form either at pre-existing stress concentrations or in situ formed stress concentrations due to localized plasticity. Localized plasticity forms the basis for the additional crack tip driving forces in either accelerating or decelerating crack growth kinetics thereby providing conditions for either crack arrest with resulting non-propagating cracks or for continuous uninterrupted crack growth. Internal stresses are generated during fatigue damage in the form of dislocation pile-ups, intrusions and extrusions. The analysis shows that critical magnitude and gradient of the internal stresses are required for an incipient crack to grow continuously, failing which crack arrest can occur. The methodology is based on separating the mechanically introduced crack tip driving forces vs the material resistance; the later can be extracted from long-crack growth data under constant amplitudes. Analysis of incipient short cracks growing under the elastic-plastic notch tip stress fields are analyzed systematically for various elastic stress concentrations, K t, and notch-tip radii, ρ. A general formulation is developed based on the calculations that can be incorporated into the unified life predication model that is being developed.

Instrumented end notched flexure – Crack propagation and process zone monitoring Part II: Data reduction and experimental

A mode II instrumented end notched flexure three point bending (ENF) adhesion test is described. The adhesive joint consists of two aluminium alloy (AW7075-T6) plates bonded with a structural epoxy adhesive (Hysol® EA 9395™). Strain gauges are attached to the outer surface (backface) of the substrates in the lengthwise direction to measure local surface strain during crack propagation. Simultaneously, load/displacement measurements are performed. Two cases were investigated. The first was static: the joint was loaded below the crack propagation threshold. In the second, applied load above the threshold led to crack propagation. The former test confirmed the predicted load transfer mechanism between bonded and unbonded parts of the joint. In the second case, the crack front process zone was revealed in situ in mode II, we believe for the first time. These new results permitted validation of simple or refined analytical/numerical models including those of the cohesive zone. In addition, the backface strain gauge monitoring technique exhibited unexpected mode I contributions, quantitatively evaluated. Finally, R-curves are presented, as estimated with various standard models and compared with that postulated, where the process zone is accounted for.