Pressure-induced Bending Research Articles

Bend-free design of ellipsoids of revolution using variable stiffness composites

Shells are commonly used in many structural applications due to their high specific load carrying capabilities. One of the most interesting features of shell structures is that they can resist external transverse loads by developing membrane stresses in the small deformation regime yet, in general, also generate inefficient bending deformations and stresses. In this study, a composite ellipsoid shell of revolution, under internal pressure, is designed for zero bending and curvature change. To this end, the stiffness properties of elliptical composite shell structures are tailored by fibre steering. A new definition for a bend-free state, independent of internal pressure, is presented. Based on this definition, the internal pressure-induced bending state of an isotropic ellipsoidal shell of revolution is compared with its tailored composite counterpart. Results show that up to a specific level of ellipticity, a bend-free state is achievable by fibre steering in elliptical composite shells of revolution. Finally, a failure study is performed to assess the potential improvement of the maximum allowable internal pressure by bend-free design.

Limit load solutions for elbows with circumferential through-wall crack under the pressure-induced bending restraint effect

A typical pipe finite element model is made by assuming there is internal pressure with a single crack located in the middle of the pipe where both ends are constraint-free. In reality, however, both ends are constrained by their connections to components such as the pressure vessel or pump. Furthermore, due to the complexity of the pipe system, it also experiences a self-constraint effect. This is called the pressure-induced bending restraint effect, and is known to affect the fracture mechanics parameters at the crack tip. Some studies exist on the pressure-induced bending restraint effect of straight pipes, but none have focused on elbow pipe and junction between straight pipe and elbow.This study suggests limit load solutions for elbow and their jointing regions with circumferential through-wall cracks under the pressure-induced bending restraint effect. The relevant equations can be used to estimate the maximum withstand load evaluation of a highly ductile pipe, and can also be used to estimate the elasto-plastic fracture mechanics parameters using the reference stress method.

Pressure-sensitive strain sensor based on a single percolated Ag nanowire layer embedded in colorless polyimide

This paper presents the fabrication of an elastomer-free, transparent, pressure-sensitive strain sensor consisting of a specially designed silver nanowire (AgNW) pattern and colorless polyimide (cPI). A percolated AgNW network was patterned with a simple tandem compound circuit, which was then embedded in the surface of the cPI via inverted layer processing. The resulting film-type sensor was highly transparent (~93.5% transmittance at 550nm) and mechanically stable (capable of resisting 10000 cycles of bending to a 500µm radius of curvature). We demonstrated that a thin, transparent, and mechanically stable electrode can be produced using a combination of AgNWs and cPI, and used to produce a system sensitive to pressure-induced bending. The capacitance of the AgNW tandem compound electrode pattern grew via fringing, which increased with the pressure-induced bending applied to the surface of the sensor. The sensitivity was four times higher than that of an elastomeric pressure sensor made with the same design. Finally, we demonstrated a skin-like pressure sensor attached to the inside wrist of a human arm.

A pressure-induced bending sensitive capacitor based on an elastomer-free, extremely thin transparent conductor

An elastomer-free, extremely thin, and transparent pressure-induced bending sensitive capacitor is achieved by using a combination of silver nanowires and polyvinyl butyral.

Effective applied moment in circumferential through-wall cracked pipes for leak-before-break evaluation considering pipe restraint effects

In the leak-before-break (LBB) design of nuclear power plants, crack opening displacement (COD) is an essential element for determining the length of the leakage size crack. Recent researches regarding the evaluation of COD have indicated that the current practice of the LBB evaluation without consideration of the pressure induced bending (PIB) restraint overestimates COD, which in turn gives non-conservative results. Under a free-ended boundary condition, however, the applied moment at cracked section also can be overestimated, which has conservative effects on LBB evaluation. Therefore, it is necessary to evaluate pipe restraint effects on the applied moment as well as on COD to keep the constancy. In this paper, an evaluation method for the effect of the PIB restraint on COD and an effective applied moment (=crack driving force) at cracked section was developed. Both the linear elastic and elastic–plastic behaviors of the crack were considered. By comparing the behaviors with 3-D finite element analysis results from earlier studies, it was confirmed that the proposed methods make accurate estimations of the PIB restraint effect on COD. Next, the applicability of the proposed method to other types of external loading conditions was examined.

Dynamic and structural properties of orthorhombic rare-earth manganites under high pressure

We report a high-pressure study of orthorhombic rare-earth manganites AMnO3 using Raman scattering (for A = Pr, Nd, Sm, Eu, Tb and Dy) and synchrotron X-ray diffraction (for A = Pr, Sm, Eu, and Dy). In all cases, a structural and insulator-to-metal transition was evidenced, with a critical pressure that depends on the A-cation size. We analyze the compression mechanisms at work in the different manganites via the pressure dependence of the lattice parameters, the shear strain in the a-c plane, and the Raman bands associated with out-of-phase MnO6 rotations and in-plane O2 symmetric stretching modes. Our data show a crossover across the rare-earth series between two different kinds of behavior. For the smallest A-cations, the compression is nearly isotropic in the ac plane, with presumably only very slight changes of tilt angles and Jahn-Teller distortion. As the radius of the A-cation increases, the pressure-induced reduction of Jahn-Teller distortion becomes more pronounced and increasingly significant as a compression mechanism, while the pressure-induced bending of octahedra chains becomes conversely less pronounced. We finally discuss our results in the light of the notion of chemical pressure, and show that the analogy with hydrostatic pressure works quite well for manganites with small A-cations but can be misleading with large A-cations.

A practical application of an evaluation model for the restraint effect of pressure-induced bending on a plastic crack opening

This paper presents an evaluation model for the restraint effect of pressure-induced bending (PIB) on the opening of a circumferential through-wall crack (TWC) and a result of its application to the calculation of crack-opening displacement (COD) of postulated cracks for a practical leak-before-break (LBB) analysis. Three-dimensional finite element analyses with different crack lengths, restraint conditions, pipe geometries, magnitudes of internal pressure, and material tensile properties were used to investigate the influence of each parameter on the PIB restraint for the plastic COD. From these investigations, we proposed an evaluation model based on elastic–perfectly plastic behavior. Comparison with finite element analysis results demonstrated that the proposed model reliably estimated the PIB restraint effect on the plastic crack opening of a circumferential TWC and properly reflected the effect of each parameter within the range over which the analytical expression was derived. The model was then used to calculate restrained CODs of postulated cracks for a practical LBB analysis. When plastic crack behavior was considered, the PIB restraint effect was considerable for some LBB analysis cases of the primary piping systems in a typical nuclear power plant. This effect was estimated to be negligible by existing linear elastic-based models.

EVALUATION MODEL FOR RESTRAINT EFFECT OF PRESSURE INDUCED BENDING ON THE PLASTIC CRACK OPENING OF A CIRCUMFERENTIAL THROUGH-WALL CRACK

This paper presents a closed-form model for evaluating the restraint effect of pressure induced bending on the opening of a circumferential through-wall crack, which is considered plastic deformation behavior. Three-dimensional finite element analyses with different crack lengths, restraint conditions, pipe geometries, magnitudes of internal pressure, and tensile properties were used to investigate the influence of each parameter on the pressure-induced bending restraint on the crack opening displacement. From these investigations, an analytical model based on elastic-perfectly plastic material was developed in terms of the crack length, symmetric restraint length, mean radius to thickness ratio, axial stress corresponding to the internal pressure, and normalized crack opening displacement evaluated from a linear-elastic crack opening condition. Finite element analyses results demonstrate that the proposed analytical model reliably estimated the restraint effect of pressure-induced bending on the plastic crack opening of a circumferential through-wall crack and properly reflected the dependence on each parameter within the range over which the analytical expression was derived.

소성거동을 고려한 원주방향 관통균열 열림에 미치는 압력유기굽힘의 구속효과 평가 모델

This paper presents the model for evaluating restraint effect of pressure induced bending (PIB) on the circumferential through-wall crack opening displacement (COD), which considers plastic behavior of crack. This study performed three-dimensional elastic-plastic finite element (FE) analyses for different crack angle, restraint length, pipe geometry, stress level, and material conditions, and evaluated the influence of each parameter on the PIB restraint effect on COD. Based on these evaluations and additional perfectly-plastic FE analyses, a closed-form model to evaluate the restraint effect of PIB on the plastic crack opening of circumferential through-wall crack, was proposed as functions of crack angle, restraint length, radius to thickness ratio, axial stress corresponding to an internal pressure, and normalized COD evaluated from linear-elastic crack opening condition.

Analysis of surface acoustic wave pressure sensors

The authors perform sensitivity analysis theoretically on three surface acoustic wave (SAW) pressure sensor structures and two material selections. The analyses take into consideration the effects of mounting structures, ways of transferring pressure to the sensing element, and various physical and geometrical parameters. It is shown that pressure-induced bending produces a larger change of wave speed than pressure-induced extension. A proposed shallow shell structure is demonstrated to increase the sensitivity of SAW pressure sensors, and for this structure, Si SAW exhibits a slightly higher sensitivity than Ge SAW.

Evaluation of restraint effect of pressure induced bending on the elastic–plastic crack opening behaviour

The present study investigated the effect of restraint of pressure induced bending (PIB) on the elastic–plastic crack opening behaviour of a circumferential through-wall crack in a pipe. Elastic and elastic–plastic finite element analyses were performed to estimate the crack opening displacement (COD) for various restraint conditions and circumferential crack angles. The results showed that the restraint of PIB decreased the crack opening at a specific crack angle and magnitude of internal pressure, and the decrease in crack opening was considerable for larger crack angles with short restraint length. Also, the restraint effect was more significant in elastic–plastic analysis than linear elastic analysis. In the elastic–plastic analysis, the increasing internal pressure enhanced the restraint effect of PIB, and its effect was dependent on the circumferential crack angle. Additionally, it was observed that the restraint effect on COD is governed by the shorter restraint length rather than the overall restraint length when a cracked pipe is restrained non-symmetrically.

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part III: off-center cracks, restraint of bending, thickness transition and weld residual stresses

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers [1, 2][Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.

Surface small crack growth behaviour in low-cycle fatigue at elevated temperature and application limit of macroscopic crack growth law: Okazaki, M., Yada, T. and Endoh, T. Nucl. Eng. Des. Jan. (II) 1989 111, (1), 123–134

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers1, 2[Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.

Evaluation of leak flow rate and jet impingement related to leak before break: Yano, T., Matsushima, E. and Okamoto, A. Nucl. Eng. Des. Jan. (II), 1989 111, (1), 197–205

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers1, 2[Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.