The Effect of Residual Stresses on the Critical Crack Length Predicted by the Griffith Theory

1963 ◽  
Vol 30 (4) ◽  
pp. 613-616 ◽  
Author(s):  
W. E. Jahsman ◽  
F. A. Field
Keyword(s):  
Stress Distribution ◽  
Residual Stresses ◽  
Crack Length ◽  
Strain Energy ◽  
Glass Plate ◽  
Uniform Stress ◽  
Unstable Crack ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Griffith Theory

The Griffith theory for unstable crack length is modified to take into account the effect of residual (self-equilibrating) stresses. An expression relating the uniform stress, physical properties of the material, critical crack length, and the equilibrating strain energy is derived for a general stress distribution. This expression is used to develop a criterion for spontaneous cracking due to residual stresses alone. A specific numerical example for a parabolic residual-stress distribution in a glass plate is carried out in some detail.

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.

Analysis of the Influence of Mechanical Properties on the Residual Stress in Offshore Chain Links Using the Finite Element Method

2003 ◽  
Author(s):  
Pedro M. Calas Lopes Pacheco ◽  
Paulo Pedro Kenedi ◽  
Jorge Carlos Ferreira Jorge ◽  
Augusto M. Coelho de Paiva
Keyword(s):  
Mechanical Properties ◽  
Residual Stress ◽  
Finite Element ◽  
Stress Distribution ◽  
Structural Integrity ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Mechanical Component ◽  
Operational Life ◽  
Chain Links

Production offshore units have a relative long operational life (about 20 years), during which are submitted to the ocean adverse environment loading produced by the combination of wind, waves and currents. This complex loading history can promote the nucleation and propagation of cracks in mooring line components. The presence of defects establishes a critical situation that can lead to catastrophic failures. In spite of residual stress plays a preponderant part in the structural integrity of a mechanical component, the presence of residual stress is not considered in traditional design of these mechanical components. Therefore, is fundamental to develop new and more precise methodologies for assessing the structural integrity of mooring components. The present contribution regards on modeling and simulation of the residual stress distributions in studless chain links using a tri-dimensional elastoplastic finite element model with large displacements. In the analysis three material conditions, associated with different mechanical properties, were considered. The results indicate that the presence of residual stresses modify significantly the stress distribution in the component. Also, residual stress distribution depends on the mechanical properties of the chain link material. The structural integrity of the mechanical component was studied using the concept of critical volume associated to the material volume susceptible to a certain critical crack size. This methodology permits the evaluation of the critical crack length distribution related to brittle fracture of the component.

scholarly journals Validating modeled critical crack length for crack propagation in the snow cover model SNOWPACK

2019 ◽  
Author(s):  
Bettina Richter ◽  
Jürg Schweizer ◽  
Mathias W. Rotach ◽  
Alec van Herwijnen
Keyword(s):  
Crack Length ◽  
Snow Cover ◽  
Field Experiments ◽  
Detection Method ◽  
Probability Of Detection ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Avalanche Forecasting ◽  
Snow Stratigraphy ◽  
Abstract Data

Abstract. Data on snow stratigraphy and snow instability are of key importance for avalanche forecasting. Snow cover models can improve the spatial and temporal resolution of such data, especially if they also provide information on snow instability. Recently, a new stability criterion, namely a parameterization for the critical crack length, was implemented into the snow cover model SNOWPACK. To validate and improve this parameterization, we therefore used data from three years of field experiments performed close to two automatic weather station above Davos, Switzerland. Monitoring the snowpack on a weekly basis allowed to investigate limitations of the model. Based on 145 experiments we replaced two variables of the original parameterization, which were not sufficiently well modeled, with a fit factor thereby decreasing the normalized root mean square error from 1.80 to 0.28. With this fit factor, the improved parameterization accounts for the grain size resulting in lower critical crack lengths for snow layers with larger grains. This also improved an automatic weak layer detection method using a simple local minimum by increasing the probability of detection from 0.26 to 0.91 and decreased the false alarm ratio from 0.89 to 0.47.

scholarly journals Validating modeled critical crack length for crack propagation in the snow cover model SNOWPACK

2019 ◽  
Vol 13 (12) ◽  
pp. 3353-3366 ◽  
Author(s):  
Bettina Richter ◽  
Jürg Schweizer ◽  
Mathias W. Rotach ◽  
Alec van Herwijnen
Keyword(s):  
Grain Size ◽  
Crack Propagation ◽  
Crack Length ◽  
Snow Cover ◽  
Field Experiments ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Avalanche Forecasting ◽  
Weak Layer ◽  
Snow Stratigraphy

Abstract. Observed snow stratigraphy and snow stability are of key importance for avalanche forecasting. Such observations are rare and snow cover models can improve the spatial and temporal resolution. To evaluate snow stability, failure initiation and crack propagation have to be considered. Recently, a new stability criterion relating to crack propagation, namely the critical crack length, was implemented into the snow cover model SNOWPACK. The critical crack length can also be measured in the field with a propagation saw test, which allows for an unambiguous comparison. To validate and improve the parameterization for the critical crack length, we used data from 3 years of field experiments performed close to two automatic weather stations above Davos, Switzerland. We monitored seven distinct weak layers and performed in total 157 propagation saw tests on a weekly basis. Comparing modeled to measured critical crack length showed some discrepancies stemming from model assumption. Hence, we replaced two variables of the original parameterization, namely the weak layer shear modulus and thickness, with a fit factor depending on weak layer density and grain size. With these adjustments, the normalized root-mean-square error between modeled and observed critical crack lengths decreased from 1.80 to 0.28. As the improved parameterization accounts for grain size, values of critical crack lengths for snow layers consisting of small grains, which in general are not weak layers, become larger. In turn, critical weak layers appear more prominently in the vertical profile of critical crack length simulated with SNOWPACK. Hence, minimal values in modeled critical crack length better match observed weak layers. The improved parameterization of critical crack length may be useful for both weak layer detection in simulated snow stratigraphy and also providing more realistic snow stability information – and hence may improve avalanche forecasting.

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.

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