scholarly journals Analytical model for assessing fatigue limit of welded joints of ferritic-pearlitic steels

2020 ◽  
Vol 20 (3) ◽  
pp. 225-234
Author(s):  
K. A. Molokov ◽  
V. V. Novikov ◽  
A. P. German
Keyword(s):  
Crack Length ◽  
Fatigue Limit ◽  
Analytical Model ◽  
Welded Joints ◽  
Endurance Limit ◽  
Crack Tip ◽  
Analytical Dependence ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Grain Diameter

Introduction. Microdefects and zones with stress concentration in welded joints cause fatigue macrocracks. Such damage is potentially dangerous, especially if the fatigue life of the structure is almost exhausted. In this case, the crack size is close to the critical value, and it is crucial to determine its length. The paper considers the development of an engineering analytical model for assessing the critical crack length and endurance limit of welded joints with the formed grain in the structure of ferrite-pearlitic steels after welding. Materials and Methods. The theory and methods of fracture mechanics at the mesoscale are used. A simple analytical dependence is obtained, which provides determining the critical dimensions of a macrocrack for ferrite-pearlite steels without using the Griffiths formula. . The calculation results of the critical crack lengths of various steels depending on their yield strength are presented. An analytical dependence of the endurance limit calculation for the most dangerous symmetric loading cycle, according to the standard set of mechanical characteristics and the average grain diameter of ferrite-pearlite steel, is presented. Results. Structural deformation analysis of the crack propagation process has been performed. On its basis, an engineering technique for assessing the endurance limit is developed. A mathematical model that enables to calculate the endurance limit and the critical crack length in the components of welded assemblies of large-sized facilities, considering periodic loads of a symmetrical cycle, is developed. Using this model, it is possible to estimate the degree of metal sensitivity to the original characteristics (yield stress, Poisson's ratio, grain diameter, relative constriction, Young's modulus, power-law hardening coefficient, etc.).Discussion and Conclusion. Under stresses corresponding to the steel endurance limit, the critical crack opening rates of the tip and edges approach each other. Energetically, this moment approximately corresponds to the transition of the crack to an unstable state. The accumulation of one-sided plastic deformations causes the limiting state of plasticity of the region adjacent to the crack tip and its avalanche-like or sharply accelerated motion. This critical area is interrelated with the grain diameter of the material, the characteristic of critical plasticity and the critical opening at the crack tip at the fatigue limit. The proposed analytical dependences can be used to assess the residual life and the fatigue limit of welded structures, the influence of various factors on the fatigue limit of welded joints of ferrite-pearlitic steels used in mechanical engineering, shipbuilding, pipeline transport, etc

Fracture Resistance of Ship Longitudinal Members Including Fatigue Crack

2013 ◽  
Author(s):  
Yann Quéméner ◽  
Chien-Hua Huang ◽  
Chi-Fang Lee
Keyword(s):  
Fatigue Crack ◽  
Fatigue Life ◽  
Fatigue Crack Growth ◽  
Crack Length ◽  
Crack Growth ◽  
Fracture Resistance ◽  
Crack Tip ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Extreme Loads

This study investigates the fracture failure of longitudinal members including cracks. Specifically, this study employs the failure assessment diagram methodology to assess the conditions of failure at the crack tip. Based on various crack configurations, this study establishes the analytical formulations of the crack-tip condition that are validated using finite element analyses. In addition, the material toughness is expressed in terms of crack-tip opening displacement. This study evaluates the failure stress of representative cracked members as a function of the crack length. This enables determining critical crack lengths corresponding to the maximum stresses derived from extreme loads. Finally, this study uses simplified fatigue crack growth analyses to characterize the critical crack length in terms of fatigue life. For members located in the deck and bottom regions, the critical crack lengths correspond to the end of the assessed fatigue life. Therefore, the fracture resistance of the longitudinal members is satisfactory as it will not cause the premature loss of the component. This study also provides analytical formulations for crack-tip conditions that could be employed in a reliability study linking fatigue crack growth and fracture under extreme loads.

scholarly journals Analytical method for determining the critical crack length in ship structures based on structural-deformation analysis

2020 ◽  
Author(s):  
К.А. Молоков ◽  
А.И. Мамонтов ◽  
В.В. Новиков ◽  
А.П. Герман
Keyword(s):  
Crack Length ◽  
Structural Damage ◽  
Endurance Limit ◽  
Crack Opening ◽  
Structural Deformation ◽  
Deformation Analysis ◽  
Cyclic Loads ◽  
Ship Structures ◽  
Critical Crack ◽  
Critical Crack Length

Возникновение и распространение трещин в судовых конструкциях во многом зависит от напряженного состояния элементов связей, характера действующих нагрузок и структурной поврежденности металла. Поэтому важным является установление аналитических зависимостей, позволяющих непосредственно, по данным структуры металла и механическим характеристикам, определить критические размеры макротрещины для нагрузок, соответствующих пределу выносливости. В статье приводятся примеры трещинообразования в конструкциях судов, статистика появления подобных повреждений, анализируются существующие представления и подходы к решению обозначенной проблемы. Исследованиями авторов установлено, что начальная стадия образования повреждений при циклических нагрузках провоцируется, как правило, концентрацией напряжений в связях при деградации механических свойств и структуры металла. Фрагментация структуры под циклическими нагрузками резко снижает пластичность области, примыкающей к вершине развивающейся макротрещины. Накопление односторонних пластических деформаций приводит к предельному состоянию пластичности этой области и лавинообразному, или ускоренному движению трещины. Установлено, что эта критическая область имеет взаимосвязь с диаметром зерна металла, характеристикой пластичности и критическим раскрытием трещины в ее вершине на пределе выносливости. На базе структурно-деформационного анализа и линейной механики разрушения разработана инженерная методика расчета ресурса. Получена простая аналитическая зависимость, позволяющая оценить критический размер макротрещины для феррито-перлитных сталей без использования известной Гриффитсовойформулы. Возможность количественной оценки критической длины трещины на пределе выносливости имеет ключевое значение для построения инженерных методик, позволяющих вести расчет ресурса конструкций объектов морской техники. The occurrence and propagation of cracks in ship structures largely depends on the stress state of the communication elements, the nature of the existing loads and the structural damage of the metal. Therefore, it is important to establish analytical relationships that allow, directly, according to the metal structure and mechanical characteristics, to determine the critical dimensions of macrocracks for loads corresponding to the endurance limit. The article provides examples of crack formation in ship structures, statistics on the occurrence of such damage, analyzes existing ideas and approaches to solving this problem. The authors found that the initial stage of damage formation under cyclic loads is provoked, as a rule, by the concentration of stresses in the bonds during the degradation of the mechanical properties and structure of the metal. Fragmentation of the structure under cyclic loads dramatically reduces the ductility of the area adjacent to the top of the developing macrocracks. The accumulation of one-sided plastic deformations leads to a limiting state of plasticity of this region and an avalanche-like or accelerated crack motion. It has been established that this critical region is interconnected with the grain diameter of the metal, the ductility characteristic, and the critical crack opening at its apex at the endurance limit. Based on structural-deformation analysis and linear fracture mechanics, an engineering methodology for calculating the resource has been developed. A simple analytical dependence is obtained, which allows one to estimate the critical size of macrocracks for ferritic-pearlitic steels without using the well-known Griffith formula. The ability to quantify the critical crack length at the endurance limit is of key importance for constructing engineering methods that allow calculating the resource of structures of marine equipment.

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.

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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