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Two cylindrical vessels under internal pressure are used for this work in order to study the influence of the position and size of defects on their elastic and elastoplastic behavior. One contains two external longitudinal semi-elliptic defects of different dimensions realized diametrically opposed. The other contains the same defects but is circumferential. These defects are carried out by elect-erosion. Strain gauges are placed in the neighborhood of the defects of which the purpose is to obtain the strain distribution. This work also allows the comparison between two defects of different dimensions, which are of the same shape or different shapes. These defects are longitudinal and circumferential semi-elliptical. The position of these defects relative to the inner radius of a cylindrical pressure vessel is considered. The deformations results are discussed.

In industrial structures, pressure vessels have been a major subject of research for several decades: gas transfer pipelines and oil [

In the first geometry, we make two semi-elliptical longitudinal defects diametrically opposed by the process electron discharge machining, while the second model contains two circumferential defects diametrically opposite. These defects are instrumented with strain gauges to measure deformations. In this paper, we study four semi-elliptic defects: two longitudinal and two circumferential. To deduct the most critical between longitudinal defects and circumferential, we compare their openings deformations in the case of a purely elastic behavior.

The experimental study is performed on models consist of a cylindrical shell closed by two semi spherical fund large square radius (

To determine the mechanical characteristics of the material studied, we realized tensile tests at room temperature. The test specimens were made in the longitudinal direction of the cylinder. We performed 6 cylindrical specimens according to standard NF A 03-172 [

Mechanical characteristics | ||||
---|---|---|---|---|

Young’s modulus (bars) | Poisson’s coefficient | Yield strength at 0.2% (bars) | Tensile strength (bars) | Elongation (A %) |

2,070,000 | 0.3 | 3400 | 4400 | 35 |

Testing, pressures in the pressure vessels have been made within the School of Mines de Douai Mechanics Laboratory according to standard CODAP.

In the experimental part, the studied defects are supposed semi-elliptical through-in outer surface, circumferential or longitudinal. We note “a” the depth of the defect and “2c” their length. Each model includes two diametrically opposed defects of different sizes, so as to exploit maximum results on testing a minimum. Both defects are far enough from each other so as not to influence each other. The first cylindrical enclosure contains two longitudinal defects (

In the second cylindrical enclosure, the two defects are circumferential semi-elliptical in

The defects are realized so as to have the same ratio a/c equal to 1/4.

The cylindrical enclosure instrumented strain gauges, chain type, is put under internal pressure so that the objective is to follow the evolution of the deformations in zones near to defects. These defects are considered as notch [

Chains are placed in the model (

This cylindrical enclosure is instrumented with strain gauges according to

D1 and D2 are longitudinal defects whereas D3 and D4 are circumferential defects. Near the D1 longitudinal default, we stuck three chains: The chain C_{1} consisting in the first circumferential gauges, is located at the end of the defect and the two others (one consisting in circumferential C_{2} gauges and the other longitudinal in gauges C_{3}) are in the middle of the defect. While in neighborhood of the longitudinal defect D2, two chains gauges are glued, the first C_{4} placed in the middle of the defect, measuring longitudinal deformations and the second C_{5} measures the longitudinal strains at the bottom of the defect.

For the circumferential defect D3, four chains are stuck: two chains at the end of the defect, the first chain C_{1} consisting in circumferential gauges and the second C_{4} consists in longitudinal gauges and the other two chains (one constituted of longitudinal gages C_{2} and the other circumferential gauges C_{3}) in the middle of the defect.

Models | Defects | Orientations | Dimensions |
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M1 | D_{1} | longitudinal | a = 8 mm c = 32 mm |

D2 | longitudinal | a = 2 mm c = 8 mm | |

M2 | D3 | Circumferential | a = 8 mm c = 32 mm |

D4 | Circumferential | a = 2 mm c = 8 mm |

While for the circumferential defect D4, we placed two chains: the first C_{5} consisting in longitudinal gauges is located at the end of the defect and the second C_{6} allows also measure the longitudinal deformations.

In order to confirm results obtained by the strain gauges, the resonant piezoelectric sensors are placed near defects (

The dimension of the cylindrical shell comply with the General rules of construction of CODAP, we choose a D category of construction. The nominal stress of calculation is σ_{f} = 1470 bars. The pressure of the cylindrical shell is obtained by inverting the formula C2.1.4.2 CODAP:

With D_{m}, σ_{f}, t, z are respectively the mean diameter of the envelope, the nominal stress of calculation of the envelope’s material, the thickness of the envelope and welding coefficient (as the ring is taken in seamless tube, it will take z = 1).

The numerical application, of this equation and considering the previous data, gives a P pressure 74 bars. Pressure testing models, were performed in the laboratory of mechanical engineering from the Ecole of the Mines of Douai with water as pressure fluid. To realize the acoustic emission testing of pressure equipment, the applied pressure must be higher than the applied maximum pressure (AMP) in service (the recommended pressure is 110% of AMP). The pressurization cycles are carried out in accordance with the recommendation of the GBP [

The various stages of solicitations of specimens are:

In order to work in the elastic domain, a cylindrical shell was loaded by an internal pressure p and the circumferential strain e_{qq} was measured in the neighborhood of the longitudinal defect D1. _{qq} registered by J_{1} and J_{2} gauges of the chain C_{1} located respectively in 2 mm and 4 mm of the edge of longitudinal defect D1. We noted the plasticization of the material in J_{1} before J_{2} those is due to the stress concentrations at the bottom of the defect. The different elastic limit raised by J_{1} and J_{2} is respectively 1108 μ-strains and 766 μ-strains. Whereas in the zone of deformation the most requested in the neighborhood of defect passes in the plastic range to 40 bars in J_{1} and 42 bars in J_{2}. This proves that the material is plasticized initially at the bottom of the defect.

After a silent period, the acoustic emission gradually changes according to the rise in pressure. A pressure of 40 bars, the acoustic activity becomes more important. What Attests the beginning of plasticization in the neighborhood of the defects and confirms the results obtained by gauges deformations.

So that the various cylindrical shells go an elastic behavior, we have chooses a pressure of 25 bars in order to be sure that our test-tubes do not undergo any plastic deformation and they behave elastically.

The internal pressure is constant during all the tests and is equal to 25 bars. We chose the same geometrical reports of the defects retained in the experimental part of two defects namely: a/t; t/R_{i}; c/a (

The deformations raised by the various chains are represented in _{1} chain is larger at the bottom of the defect than relieved by C_{2} chain in the middle of the lip of

the defect. The positive deformation at the bottom of the defect shows its opening, whereas the negative circumferential deformation shows its compression on the level of lips. The longitudinal deformation measured by the C_{3} chain shows the lip is requested in traction along the first cylindrical vessels. Considering the three curves of deformation, we confirm that the circumferential deformation is the one which controls the opening of the defect. The maximal value of 644 μdef is reached at the bottom of the defect.

We compare the longitudinal deformations taken with the free lips of both D1 and D2 defects measured with the C_{3} and C_{4} chains of the same a/c (

We noted that the longitudinal strain at the lip of defect is almost the same for both defects from J_{3} gauge. The middle of the D2 lip is almost free and has undergone a deformation of 24.79 μ-strains, whereas the middle of the D1 lip underwent a deformation of 416 μ-strains. This shows that a/c report is not only significant, but it is necessary to specify moreover the position of the semi-elliptical defect from the internal radius of the cylindrical enclosure.

In this cylindrical enclosure, we carried out two semi-elliptical external defects diametrically opposite. The chains C_{2} and C_{4} measure the longitudinal deformation, whereas the chains C_{1} and C_{3} measure the circumferential deformation (

We note that the maximum circumferential deformation, 247 μ-strain, is recorded by the C_{3} chain in the middle on the lip of the D3 defect. It is also followed by a circumferential deformation raised by the C_{1} chain. The other lip of the defect records a compression in its middle. We can conclude that the circumferential strain controls as much for the semi-elliptical circumferential defects as for the semi-elliptical longitudinal defects. Let us compare now the evolutions of the deformation between the D3 and D4 defects and check the influence of the position of the defect relative to the internal radius of the second cylindrical enclosure. For this, we will compare between the deformation raised by the C_{2} and C_{4} chains of the D3 defect and those raised by the C_{5} and C_{6} chains of the D4 defect and the evolution by finite element [

We note that the lip of D3 defect is under compression, whereas the lip of D4 defect is under traction. The defect area should be finely refined including special elements at the crack tip. A fundamental step is to calibrate and optimize the mesh. For this application is the CASTEM software that is used. But the simulation by the finite element method has shown that the two strains meet beyond the zone of disturbance.

The longitudinal deformation at the bottom of the two defects represents an extension of the cylindrical enclosure. The D3 defect is less sought with the disturbance, because it is to 8 mm of the internal radius of the cylindrical enclosure and the maximum strain is of 169 μ-strains. While the D4 defect is to 2 mm and the maximum strain is of 190 μ-strains.

C_{1} (μ-strain) | C_{2} (μ-strain) | C_{3} (μ-strain) | C_{4} (μ-strain) | C_{5} (μ-strain) | C_{6} (μ-strain) | |
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D1 defect | 644 | −45 | 416 | |||

D2 defect | 25 | 55 | ||||

D3_{ }defect | 159 | −90 | 247 | 169 | ||

D4 defect | 185 | −35 |

We note that the higher deformation is raised by the J_{2} gauge of the C_{1} chain of the D1 defect which measures a circumferential deformation at the bottom of the defect. At the same dimension, the D3 circumferential defect is requested less than the D1 longitudinal defect. For two defects of the same form (either longitudinal or circumferential) but of different dimensions, it is necessary to also take into account the position of these defects relative to the internal radius of the cylindrical enclosure. Regardless of the form of the defect; it is the deformation of circumferential opening which it is necessary to take into account for any use.

An experimental study, on cylindrical shells carrying of the semi-elliptical defects longitudinal and circumferential, was performed by using strain gauges of the neighborhoods of defect. We made the comparison between two semi-elliptical defects of the same dimension but one of them was oriented longitudinally and the other was circumferential. These defects are found in two different positions relative to the internal radius from the cylindrical enclosure. We noted that the longitudinal semi-elliptic defect is more dangerous than the circumferential through the study of circumferential opening deformation. A comparison among the strains has shown that it is the circumferential deformation at the bottom of the defect which constitutes the maximum. This work is of interesting value; it will allow us to study the effect of the harmfulness of cylindrical shells cracked with energy methods, the influence of the position and size of the cracks compared with the inner side pressure cup.