Bulging Factor Research Articles

Effect of hexagonal stringer design on bulging factor and stress intensity factor of cracks in the skin of pressurized aircraft fuselage

Aircraft structural fatigue is a serious issue. Untreated, it could lead to failure. Several aircraft accidents were caused by widespread fatigue damage. For cracks in the fuselage, the stress state is due to the bulging around the crack caused by applied internal pressure. This condition is characterized by a parameter called the bulging factor; it compares the stress intensity factor of a crack in curved shell to its counterpart in a plate. Bulging factor expressions are available for longitudinal and circumferential cracks but less for slanted cracks. The underlying structure that stiffens the skin of the fuselage has a direct impact on the stress intensity factor and the bulging factor of the crack. A hexagonal grid stiffening pattern has been shown to provide sufficient stiffening to the fuselage skin while using a lesser amount of material compared to the traditional orthogonal grid design. However, the response of this grid pattern in the presence of a cracked fuselage has not been studied. The current paper aims to estimate the effect of the hexagonal grid pattern on the bulging factor and stress intensity factor of cracks of various lengths and orientations in the skin of the fuselage. Results obtained are compared to the conventional orthogonal grid stiffening pattern of a fuselage structure. Several patterns were considered. Results show that cracks of different lengths and orientations in hexagonal grid stiffened panels had stress intensity factors and bulging factors that are comparable to the base case within a margin of 2%–8%.

A comparative study of burst failure models for assessing remaining strength of corroded pipelines

This paper performs a comparative study of remaining strength assessment models for corroded pipelines. A brief review of burst prediction models is first given for defect-free pipes, including strength solutions and flow solutions of burst pressure and experimental validations. Followed is a review of corrosion assessment models that are categorized into three generations in terms of the reference stress used in each model. Those corrosion models are then evaluated in comparison to full-scale burst data, with a focus on validating the newly proposed third-generation models. Next, recent progresses are discussed, including the PRCI corrosion assessment projects, constraint effect, bulging factor and defect width effect. Major technical challenges facing the corrosion model improvement are finally discussed with regards to full-scale tests, numerical modeling, material failure criteria, and real corrosion defects.

Determination of Folias Factor for Failure Pressure of Corroded Pipeline

AbstractCorrosion assessment and burst pressure prediction of line pipes with corrosion defects are essential for the integrity assessment of steel transmission pipelines. The failure assessment methods proposed in codes or handbooks may be overly conservative or exhibit significant scatter in their predictions. In this paper, the effects of two key parameters—the flow stress and Folias bulging factor, on predicting the failure pressure of pipelines with defects are studied. The Folias bulging factor is suggested by fitting the results from finite element (FE) analysis. Then, a new prediction method for the failure pressure of pipelines with defects is proposed. The failure pressures predicted by the proposed method are in better agreement with the experimental results than the results by the other methods such as B31G, MB31G, Det Norske Veritas (DNV), and rectangular parabolic area (RPA).

Influence Law of Initial Reverse Bulging on Sheet Hydroforming Process

In order to investigating the effect of the combination of two technological parameters such as the initial bulging height and the initial bulging pressure on the sheet , the sheet hydroforming process was studied. Firstly, by using the method of numerical simulation, the sheet hydroforming process with and without the initial bulging were discussed; Secondly, the effect of both the initial bulging height and the initial bulging pressure which were based on the hydroforming with the initial bulging on the forming of the part was studied; Thirdly, the result of the simulation was verified in the experiment. It was found that when the initial bulging height is 3.75mm and the initial bulging pressure is 2MPa, the maximum thinning ratio of the sheet is 4.803% at the end of the sheet hydroforming process. According to the hydroforming process without the initial bulging factors, the maximum thinning ratio is 5.123%. It can be found that the initial bulging factors play a key role in the sheet hydroforming process. The maximum thinning ratio of the wall thickness can be decreased effectively by the appropriate initial bulging height and bulging pressure, and the forming limit can also be improved at the same time. The results of numerical simulation have a reasonable agreement with the experimental results.

Analytical Assessment of the Remaining Strength of Corroded Pipelines and Comparison With Experimental Criteria

Recently published analytical solutions for the remaining strength of a pipeline with narrow axial and axisymmetric volumetric flaws are described in this paper, and their experimental and numerical validation are reviewed. Next, the domains of applicability of each solution are studied, some simplifications suitable to steel pipelines are introduced, and an analytical model for the remaining strength of corroded steel pipelines is presented. This analytical solution is compared with the standards most widely used in the industry for assessment of corroded pipelines: ASME B31G, modified ASME, and DNV RP-F101. The empirical and analytical solutions are compared with respect to their most relevant parameters: critical (or flow) stress, flaw geometry parameterization, and Folias or bulging factor formulation. Finally, two common pipeline steels, API 5L grades X42 and X100, are selected to compare the different corrosion assessment methodologies. Corrosion defects of 75%, 50%, and 25% thickness reduction are evaluated. None of the experimental equations take into account the strain-hardening behavior of the pipe material, and therefore, they cannot properly model materials with very dissimilar plastic behavior. The comparison indicates that the empirical methods underestimate the remaining strength of shallow defects, which might lead to unnecessary repair recommendations. Furthermore, it was found that the use of a parameter employed by some of the empirical equations to model the assumed flaw shape leads to excessively optimistic and nonconservative results of remaining strength for long and deep flaws. Finally, the flaw width is not considered in the experimental criteria, and the comparative results suggest that the empirical solutions are somewhat imprecise to model the burst of wide flaws.

A model for arrest of rapid cracks in gas-pressurized ductile steel line pipe

Modifying and adding to elements of Schindler’s model, a model to predict arrest of rapidly propagating cracks in gas-pressurized steel pipe is presented. A bulging factor models the flaring of the crack flaps and contributes to the crack driving force. The crack tip, a structural hinge in each flap, a traveling neck ahead of the crack tip, and soil backfill contribute to the plastic dissipation rate. Model inputs are yield and ultimate strength, hardening exponent, crack-tip opening angle, soil density and Charpy V-Notch energy. Model predictions for steel grades ranging from X52 to X120, display modest non-conservatism.

Bulging factor of a longitudinal crack in pressurized cylindrical shell with a reinforcing layer

Bulging factor expressions for a longitudinal crack in a pressurized cylindrical shell with a reinforcing layer are developed. In this study, a parametric finite element model was constructed, validated (based on experimental data) and used to simulate various shell configurations. A Python script automates the execution, data collection and calculation of the bulging factor for 2592 configurations using the commercial code ABAQUS. Candidate expressions for the bulging factor are selected based on physical arguments and fitted using stress displacement data obtained previously; several expressions were found to be in good agreement with finite element data.

Equivalent bulging factors of internally pressurized cracked laminated composite cylindrical shell structures

Bulging factor expressions developed and available in the literature so far, are useful for damage tolerance design and characterization of internally pressurized cracked isotropic shell structures. They are not applicable to laminated composite shell structures. On the other hand, modern aircrafts and many aerospace systems are made of or partially made of laminated composite materials. Consequently, simple formulas have been developed and are presented as possibly viable means for tolerance design and characterization of cracked laminated composite shell structures under internal pressure. These simple formulas give the so-called equivalent bulging factors. Several cases of laminated composite cylindrical shells under suddenly applied internal pressures are studied. Their corresponding equivalent bulging factors are determined and presented to demonstrate the simplicity of use and their potential in damage tolerance design and characterization of internally pressurized cracked laminated composite shell structures.

Bulging factors and geometrically nonlinear responses of cracked shell structures under internal pressure

An approach based on the transverse or out-of-plane nonlinear dynamic responses at the centers of edges of cracks is being proposed as a viable alternative to bulging factors for damage tolerance design and characterization of cracked cylindrical shell structures under applied internal pressure. This approach circumvents the problems of mesh selection at the crack tip in the finite element analysis for bulging factors and provides information about the influence of crack lengths as well as crack widths on responses. The influence of crack widths on responses has been found to be significant but it is not available in bulging factors. Furthermore, existing individual bulging factor only applies to a different range of ratios of crack length to radius of shell. It is concluded that (i) the proposed approach has no limit on the range of ratios of crack length to radius of shell; (ii) conceptually, the proposed approach is simple, and (iii) computationally, the nonlinear responses at the centers of edges of cracks are relatively easy to obtain accurately and efficiently by using the mixed formulation-based shell finite elements since the present dynamic approach converges quickly at very coarse meshes.

Proposal of reference stress for a surface flaw on a cylindrical component from a review-with-comparison of the local metal loss assessment rule between API 579-1 and the p-M diagram method

The Remaining Strength Factor (RSF) approach in Part 5 of API 579-1/ASME FFS-1 is an assessment method for a cylindrical component with a local metal loss based on surface correction factors. Also, reference stress solutions that are applied in the Failure Assessment Diagram (FAD) method for a cylindrical component with a crack-like flaw are provided in Annex D using surface correction factors. In the recently-developed p-M diagram method, the reference stress solution for local metal loss evaluation in a cylindrical component is derived using bulging factors, which are similar but not identical to the surface correction factors used in API 579-1/ASME FFS-1. This paper describes the results of a comparative study among the RSF approach, reference stress solutions for the FAD method, and the p- M diagram method, in terms of plastic collapse evaluation of a cylindrical component. These results were compared with the FEA and experimental results to confirm how these estimated stresses could be validated. This study also involves recommended reference stress solutions for a cylindrical component with a crack-like flaw or a local metal loss, which should be adopted as fitness-for-service rules, and a discussion on the influence of the design margin of the construction code on allowable flaw depth.

Numerical Study of Cracked Titanium Shell under Compression

In many industrial conditions, light thin titanium shells are well used under various severe loading conditions. It is of interest to know the real conditions that govern the instability of a cracked panel subject to buckling loads in order to conserve as maximum as possible the strength of the structure. Several parameters can be varied in order to achieve this objective. The aim of this study is to determine the evolution of these parameters in order to achieve optimal crack propagation conditions while keeping these parameters within “reasonable” limits of physical and economic feasibility. For the purpose of the current study the considered structure can be regarded as thin cylindrical shell of radius r, thickness t with an initial through crack of length a. The titanium cylindrical shell is sealed on one edge and compression is applied on the other. An additional applied pressure can generates a stress and deformation field around the crack tip that has bending stresses and membrane stresses and appears as a bulge around the crack area. This paper give details of a simulation with FEA numerical analysis that determine governing instability conditions of a Titanium shell under particular loading conditions and to put in light the effect of bulging on the stress intensity factor at the crack tips. This bulging factor measures the severity of the stress intensity in the bulged crack compared to a plane shell subjected to equivalent loading conditions.

The stress-strain fields at crack tip in axially cracked cylindrical shells and the calculation of stress intensity factors

A perturbation solution for stress-strain fields (including modes I, II, III) at crack tip in axially cracked cylindrical shells is given. The analysis, using 10th-order differential equations which take the transverse shear deformations into account, involves perturbation in a curvature parameter λ2, (λ2=[12(1-v2)]1/2a2/Rh). Stress intensity factors for finite size cylindrical shells under bending and internal pressure loading are evaluated. A good accuracy can be obtained without using fine meshes in a region near the crack tip. Besides, the influence of the finite size and the shearing stiffness on bulging factors, which are commonly used in engineering, are analyzed.

Brittle Fracture Initiation in Line Pipes Estimated from Surface Crack COD

The brittle fracture initiation from the surface crack in the large diameter pipe subjected to inner pressure is treated from the practical point of view. The crack opening stretch model is applied to the surface crack and the ligament of the crack is subjected for the crack closure force.The hydrostatic tests are carried out for two kinds of pipes. One is a heavy wall and large diameter pipe, API 5 L X 70 grade, 940 mm in outer diameter and 39. 2 mm in wall thickness. Another is a relatively thin wall and small diameter pipe, API 5 L X 65 grade, 508 mm in outer diameter and 12. 7 mm in wall thickness. The test pipes have various notches, which are ma. chined by electrical discharge. And the crack closure force is experimentally determined from the notch tip COD, which is directly measured by the clip gage installed on the center of the notch tip, by use of the Dugdale Model with regard to the bulging factor for the pipes.Consequently crack tip COD of the surface crack center is calculated by the proposed crack opening stretch model. And corresponding to the defect size, the required fracture toughness to prevent the brittle fracture initiation from the surface crack of the pipes subjected to inner pressure is estimated.

Fracture of longitudinally cracked ductile tubes

Various bulging factor and plasticity correction factor formulations are discussed and a new plasticity correction factor leading to a simple failure law is proposed. Failure stresses predicted by the usual LEFM formula corrected for plasticity are shown to be identical with the Dowling and Townley two-criteria approach if the relevant parameters are chosen in a suitable manner. Burst tests on AISI 304 stainless steel tubes performed at the Joint Research Centre, Ispra are described. The strengthening effect of the sealing patch was taken into account by replacing the Folias bulging factor by a smaller empirical factor determined by Bernard and Henry from fatigue crack growth tests. A flow stress \\ ̄ gs and a toughness K c were derived which apply to the prediction of the onset of stable crack growth in 304 stainless steel tubes at room temperature. For other ductile materials and temperatures tentative formulae are proposed.

The bulging factor, a fungistatic antibiotic produced by a streptomyces strain, with evidence of an active water-excreting mechanism in fungi.

SUMMARY: The ‘bulging factor’, a new antibiotic with a chemical nature related to streptothricin, is produced by a Streptomyces strain and was isolated as reineckate and picrate. A study on its mode of action resulted in the development of a plate technique for assaying bulging factor activity. Evidence is presented in support of a theory about the existence of an active water-excreting mechanism in fungi susceptible to the bulging factor.