Study on Generalization of Lefort’s Approach to Critical Crack Length

2019 ◽  
Vol 827 ◽  
pp. 153-158
Author(s):  
Jana Horníková ◽  
Pavel Šandera ◽  
Stanislav Žák ◽  
Jaroslav Pokluda
Keyword(s):  
Crack Length ◽  
Critical Length ◽  
Shear Mode ◽  
Mode I ◽  
Critical Crack ◽  
Relative Level ◽  
Critical Crack Length ◽  
Transformation Procedure ◽  
Notch Stress ◽  
Analytical Formulae

The critical length aIc of a mode I crack that corresponds to a vanishing of the influence of the notch stress concentration can be approximately expressed by a formula reported by Lefort. This study aimed to generalize his approach to shear mode cracks by finding a criterion for a statistical compatibility of formulae for critical lengths of cracks. It revealed that the Lefort ́s formula describes the critical crack length aIc at which the relative level of the notch effect on the mode I SIF is less than 1%. Based on this criterion, a mathematically similar formula for the critical length aIIIc was found. A part of this study was also a development of a transformation procedure suitable for fitting the obtained SIF data by simple analytical formulae and for clear related illustrative plots of results.

Stress Intensity Factors for Cracks Emanating from a Notch under Shear-Mode Loading

2018 ◽  
Vol 774 ◽  
pp. 48-53
Author(s):  
Jana Horníková ◽  
Pavel Šandera ◽  
Stanislav Žák ◽  
Jaroslav Pokluda
Keyword(s):  
Stress Intensity ◽  
Critical Length ◽  
Shear Mode ◽  
Mode I ◽  
Mode Ii ◽  
Mode Iii ◽  
Loading Mode ◽  
Notch Stress ◽  
Notch Geometry ◽  
Mode Ii Loading

The influence of the notch geometry on the stress intensity factor at the front of the emanating cracks is well known for the opening loading mode. The critical length of the crack corresponding to a vanishing of the influence of the notch stress concentration can be approximately expressed by the formula aI,c = 0.5ρ(d/ρ)1/3, where d and ρ are the depth and radius of the notch, respectively. The aim of the paper was to find out if this formula could be, at least nearly, applicable also to the case of shear mode loading. The related numerical calculations for mode II and III loading were performed using the ANSYS code for various combinations of notch depths and crack lengths in a cylindrical specimen with a circumferential U-notch. The results revealed that, for mode II loading, the critical length was much higher than that predicted by the formula for mode I loading. On the other hand, the critical lengths for mode I and mode III were found to be nearly equal.

Determination of the Critical Length of a Subsurface Crack in a Monobloc R7T Railway Wheel Using FEM Analysis

2010 ◽  
Author(s):  
A. Jafari ◽  
J. Alizadeh K.
Keyword(s):  
Crack Length ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Critical Length ◽  
Fem Analysis ◽  
Rolling Contact ◽  
Subsurface Crack ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Railway Wheels

Based on the endeavors have been made to reduce the wear rate of the railway wheels surfaces, and increase in the axle loads and the velocity of the trains, rolling contact fatigue of the railway wheels is nowadays a considerable damage with regard to the railway wheels. The initiated cracks in the wheels are classified into surface and subsurface ones. The former are usually removed by wear, while the latter propagate gradually until reaching the critical crack length and then suddenly bring about dangerous fractures. So, in any maintenance process of a railway system, it is essential to have the critical crack length as a vital tool to determine the possibility of the critical condition occurrence in the case of identified cracks in wheels. The critical crack length is a residential value and should be determined for any railway systems. So, by using FEM, this paper models an Iranian Railways wheel having the diameter of 920mm, made of R7T material which has a subsurface crack. The wheel is in contact with UIC60 rail. After analysis of this model, rang of stress intensity factor of the crack has been calculated for the different rotation angles. Finally, the critical length of a subsurface crack in conformity with Iranian Railways has been determined based on the fracture mechanics and some approximate relations about mechanical properties. Results show that because of geometrical limitations of the wheel, a subsurface crack can cause the wheel fracture before reaching the critical length.

Crack Shape Development for Leak-Before-Break Analysis in Pipelines

2018 ◽  
Author(s):  
Kathy Zhang ◽  
Luyao Xu ◽  
James Ferguson ◽  
Dennis Zadery
Keyword(s):  
Crack Length ◽  
Crack Growth ◽  
Essential Element ◽  
Critical Length ◽  
Assessment Method ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Simplified Approach ◽  
Pressure Cycling ◽  
Leak Before Break

Surface cracks in pipelines under certain service conditions may grow due to fatigue, which is caused by pressure (cycles). The leak-before-break (LBB) assessment method is employed to avoid any catastrophic failure prior to a detectable leakage. In the LBB analysis, crack critical length is an essential element for determining the pipeline leak or rupture. The common approach regarding the evaluation of LBB is to calculate the critical crack length and through-wall length under iven pressure cycling conditions. If the critical crack length is less than the through-wall length, LBB conditions could occur and be detected if leak detection capability is high. This involves complex calculations in crack fatigue growth and could result in extensive analysis if thepipeline has a large crack population. This paper presents a simplified approach for assessing the leak-before-break of the flawed pipelines. This approach is based on industrial code API 579-1/ASME FFS-1 Fitness-For-Service. Through the investigation of effects for different parameters on crack growth, including crack initial geometry, pipeline materials, loading conditions, pipeline diameter and wall thickness, it was determined that the crack initial aspect ratio is a major factor influencing crack growth and geometry evolution. Based on these parameters, a crack fatigue growth map was developed. By comparing the behaviors of different cases, it was confirmed that the proposed method is a valid approach for the pipeline LBB analysis.

scholarly journals Probability of the Critical Length of a Fatigue Crack Occurring at the Tooth Foot of Cylindrical Geared Wheels of the Drive System of a Fiomax 2000 Ring Spinner

2017 ◽  
Vol 25 (0) ◽  
pp. 0-0 ◽  
Author(s):  
Jacek Rysiński ◽  
Robert Drobina ◽  
Jerzy Tomaszewski
Keyword(s):  
Fatigue Crack ◽  
Fatigue Life ◽  
Crack Length ◽  
Technical Specification ◽  
Critical Length ◽  
Drive System ◽  
Test Machine ◽  
Tooth Root ◽  
Critical Crack ◽  
Critical Crack Length

In the present paper, we describe a method of determination of the probability of reaching the critical crack length at the tooth root of the cylindrical geared wheels of the drive system of the Fiomax 2000 ring spinner. The Paris-Erdogan formula was utilised for calculations of the fatigue crack length depending on the number of load cycles. Experimental investigations were performed on cylindrical geared wheels. The wheel specimens were manufactured from 1.6523 steel (UE) according to a technical specification relevant to the drive system of the ring spinner. The experiments were performed using a professional pulsator (pulsating test machine). Based upon the experiments (series of 12 tests), material constants and were calculated. These parameters were utilised in the Paris law of crack propagation for further calculations. Moreover it was also ascertained that these unknowns are related via the deterministic relationship. Therefore a function allowing for approximation of constant in dependence on exponent m was derived. In the next step, for the values of parameter chosen – belonging to the variability interval, established from experimental data – we determined the times of reaching the critical length of the fatigue crack. It was stated that the best approximation distribution describing the simulated random values of times of reaching the critical length of the tooth crack for the drive system of the ring spinner is the asymptotic Gumbel’s distribution. Knowing the distribution and number of cycles until reaching the critical crack length at the tooth root, one can evaluate the fatigue life of the damaged wheel in the ring spinner (Fiomax) drive system for the assumed probability. The goal of the present paper is evaluation of the working time of the elements of the drive system of a ring spinner until the occurrence of damage. The highest fatigue life of geared wheels was achieved within the interval (4.3 – 4.5)x 105 cycles. However, it is recommended to change of the geared wheel in case of the spotting of early symptoms of defect. For the stretching apparatus, the authors of the present paper suggest the exchange of the idler geared wheels at least once per year.

Safety Margin Optimisation by Probabilistic Analysis

2017 ◽  
Author(s):  
L. Stefanini ◽  
F. J. Blom
Keyword(s):  
Crack Length ◽  
Probabilistic Analysis ◽  
Safety Margin ◽  
Critical Length ◽  
Optimization Method ◽  
Probability Of Failure ◽  
Critical Crack ◽  
Deterministic Analysis ◽  
Critical Crack Length ◽  
Parameter Values

Deterministic assessment codes can contain large safety factors that give very conservative results. By applying probabilistic analysis to these deterministic assessments, an implicitly accepted probability of failure can be determined. The probability of failure is implicit because it is calculated with the parameter values resulting in a state that is deterministically accepted by the code [2]. When these probabilities are compared for similar deterministic assessments, the excess conservatism can be shown and possibly reduced. During the present study a probabilistic analysis of the critical crack length initiation was performed. Such analysis led to the formulation of a corrective action proposal to the Master Curve approach given in BS7910:2013 Annex J. Firstly a deterministic calculation was performed with the Kr-Lr method to define the Critical Length of a through-wall circumferential crack present in a nuclear reactor’s piping. The value of Kmat used in the Kr-Lr method was calculated for a probability of 0.05 and with T0 directly measured (T0 a unique value). The second step was to pass to probabilistic calculation. Here Kmat was calculated from both T0 directly measured and T0 estimated by Charpy-V tests (T0 as a distribution). The results from these calculations gave the probability of a crack being equal to the Critical Crack Length. Moreover, these results showed that the Tk safety margin introduced in BS7910:2013 Annex J introduce an excess conservatism. Results from the probabilistic calculations were then compared to the implicitly accepted failure probability Pf (5%) that results from deterministic analysis (T0 considered as a single value) to account for the effects of T0 distribution. An optimized Tk was then found to account for the real uncertainty of the statistical distribution. Finally, excluding a dependency on the yield stress, the Tk optimization method was generalized. A new correlation for the Tk safety margin is proposed.

scholarly journals Snow fracture in relation to slab avalanche release: critical state for the onset of crack propagation

2017 ◽  
Vol 11 (1) ◽  
pp. 217-228 ◽  
Author(s):  
Johan Gaume ◽  
Alec van Herwijnen ◽  
Guillaume Chambon ◽  
Nander Wever ◽  
Jürg Schweizer
Keyword(s):  
Crack Propagation ◽  
Slope Angle ◽  
Critical Length ◽  
Snow Layer ◽  
Critical Crack ◽  
Critical Crack Length ◽  
New Model ◽  
Avalanche Forecasting ◽  
Weak Layer ◽  
Recent Developments

Abstract. The failure of a weak snow layer buried below cohesive slab layers is a necessary, but insufficient, condition for the release of a dry-snow slab avalanche. The size of the crack in the weak layer must also exceed a critical length to propagate across a slope. In contrast to pioneering shear-based approaches, recent developments account for weak layer collapse and allow for better explaining typical observations of remote triggering from low-angle terrain. However, these new models predict a critical length for crack propagation that is almost independent of slope angle, a rather surprising and counterintuitive result. Based on discrete element simulations we propose a new analytical expression for the critical crack length. This new model reconciles past approaches by considering for the first time the complex interplay between slab elasticity and the mechanical behavior of the weak layer including its structural collapse. The crack begins to propagate when the stress induced by slab loading and deformation at the crack tip exceeds the limit given by the failure envelope of the weak layer. The model can reproduce crack propagation on low-angle terrain and the decrease in critical length with increasing slope angle as modeled in numerical experiments. The good agreement of our new model with extensive field data and the ease of implementation in the snow cover model SNOWPACK opens a promising prospect for improving avalanche forecasting.

Impact of PWSCC and Current Leak Detection on Leak-Before-Break Acceptance

2005 ◽  
Author(s):  
Gery Wilkowski ◽  
Rick Wolterman ◽  
Dave Rudland
Keyword(s):  
Fatigue Crack ◽  
Crack Length ◽  
Flow Path ◽  
Critical Crack ◽  
Cracking Behavior ◽  
Critical Crack Length ◽  
Crack Morphology ◽  
Actual Flow ◽  
The Difference ◽  
Morphology Parameters

This paper assesses the effect of using primary water stress corrosion cracking (PWSCC) crack morphology parameters (roughness, number of turns, and actual flow path/pipe thickness) in determining the difference in the leakage crack length, and how the difference in the leaking crack lengths changes typical margins from past LBB submittals and published reports. Several past LBB submittal cases were selected; in addition, cases from generic LBB reports published by EPRI were also selected. The results of the analyses showed that the past submittals by nuclear steam system supply (NSSS) companies frequently used the surface roughness comparable to an air-fatigue crack with no turns and the actual flow path equal to the thickness of the pipe. This condition would give the shortest possible leakage flaw length. The roughness, number of turns, and actual flow path to thickness ratio for PWSCC cracks were determined from photomicrographs of service-removed cracks. When using the PWSCC crack morphology parameters that corresponded to the crack growing parallel to the long direction of the dendritic grains (V.C. Summer and Ringhals cases), then the leakage flaw length increased 69 percent over the air-fatigue crack length at the same leak rate. Using the same critical crack length as was used in the initial LBB submittals and the published documents, the margins on the crack length changed from 1.77 to 6.0 for the initial submittals (which we also reproduced) to 0.88 to 2.74 from our calculations for a PWSCC crack. If the crack grew in the buttered region of the bimetallic weld, then based on metallographic sections from service-removed flaws, there would be a more tortuous flow path. For this crack condition, in all but one case, the margins on the normal operating versus N+SSE crack lengths were below the safety factor of two required for LBB approval. The average margin decreased from 3.39 for the air-fatigue crack to 1.55 for the PWSCC crack growing transverse to the long direction of the dendritic grains. This was about an additional 20 percent decrease in the margin from the case of having the PWSCC grow parallel to the long direction of the dendritic grains. These results show that LBB is difficult to satisfy for PWSCC susceptible pipe using the current SRP 3.6.3 LBB approach. This LBB assessment did not consider the possible development of a long circumferential surface crack, which would be more detrimental to LBB behavior. Such cracking behavior would violate the LBB screening criterion.

Fracture of Flat and Curved Aluminum Sheets With Stiffeners Parallel to the Crack

1961 ◽  
Vol 83 (1) ◽  
pp. 32-38 ◽  
Author(s):  
J. Frisch
Keyword(s):  
Crack Propagation ◽  
Crack Length ◽  
Uniaxial Tension ◽  
Radius Of Curvature ◽  
Appreciable Effect ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Crack Location ◽  
Aluminum Sheets ◽  
Curved Panels

The mode of crack propagation and failure in relatively large 2024-T3 aluminum sheets reinforced with stiffeners parallel to the crack direction has been investigated. Curved specimens with a 69-in. radius of curvature as well as flat panels were subjected to uniaxial tension perpendicular to a simulated crack to study the effects of curvature, crack location, and stiffener spacing. Increase in strength due to stiffening particularly in the curved panels was observed although these specimens exhibited considerable lower crack strength than flat ones. For the specimens tested, crack location as well as variations of stiffener spacing from 3 to 12 in. had no appreciable effect on either critical crack length or failure stress.

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