Modeling the axially symmetric crack growth under blasting and hydrofracturing near free surface

2008 ◽  
Vol 44 (5) ◽  
pp. 473-481 ◽  
Author(s):  
E. N. Sher ◽  
A. M. Mikhailov
Keyword(s):  
Free Surface ◽  
Crack Growth ◽  
Axially Symmetric ◽  
Symmetric Crack

Effects of Loading Spectra on High pH Crack Growth Behavior of X65 Pipeline Steel

CORROSION ◽  
10.5006/3472 ◽  
2020 ◽  
Vol 76 (6) ◽  
pp. 601-615 ◽  
Author(s):  
Hamid Niazi ◽  
Karina Chevil ◽  
Erwin Gamboa ◽  
Lyndon Lamborn ◽  
Weixing Chen ◽  
...  
Keyword(s):  
Free Surface ◽  
Crack Initiation ◽  
Crack Propagation ◽  
Strain Rate ◽  
Crack Growth ◽  
Pipeline Steel ◽  
Crack Tip ◽  
Growth Behavior ◽  
Crack Growth Behavior ◽  
Secondary Crack

The effects of mechanical factors on crack growth behavior during the second stage of high pH stress corrosion cracking in pipeline steel were investigated by applying several loading scenarios on compact tension (CT) specimens. The main mechanism for stage 2 of intergranular crack propagation is anodic dissolution ahead of the crack tip which is highly dependent on crack-tip strain rate. The maximum and minimum crack growth rates were 3 × 10−7 mm/s and 1 × 10−7 mm/s, respectively. It was observed that several factors such as mean stress intensity factor, amplitude, and frequency of loading cycles determine the crack-tip strain rate. Low R-ratio cycles, particularly high-frequency ones, enhance secondary crack initiation, and crack coalescence on the free surface. This mechanism accelerates crack advance on the free surface which is accompanied with an increase in mechanical driving force for crack propagation in the thickness direction. These findings have implications for pipeline operators and could be used to increase the lifespan of the cracked pipelines at stage 2. For those pipelines, any loading condition that increases the strain rate ahead of the crack tip enhances anodic dissolution and is detrimental. Additionally, secondary crack initiation and coalescence could be minimized by avoiding internal pressure fluctuation, particularly rapid large pressure fluctuations.

Subharmonic resonant interaction of a gravity–capillary progressive axially symmetric wave with a radial cross-wave

2019 ◽  
Vol 869 ◽  
pp. 439-467 ◽  
Author(s):  
Meng Shen ◽  
Yuming Liu
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Threshold Value ◽  
Resonant Interaction ◽  
The Body ◽  
Wave Radiation ◽  
Axially Symmetric ◽  
Damping Term ◽  
The Cross ◽  
Cross Waves

We theoretically investigate the problem of subharmonic resonant interaction of a progressive (axially symmetric) ring wave with a radial cross-wave in the context of the potential-flow formulation for gravity-capillary waves. The objective is to understand the nonlinear mechanism governing energy transfer from a progressive ring wave to its subharmonic cross-waves through triadic resonant interactions. We first show that for an arbitrary three-dimensional body floating in an unbounded free surface, there exists a set of homogeneous solutions at any frequency in the gravity-capillary wave context. The homogeneous solution depends solely on the mean free-surface slope at the waterline of the body and physically represents a progressive radial cross-wave. Unlike standing cross-waves, a progressive cross-wave loses energy during propagation by overcoming the work done by surface tension at the waterline and through wave radiation. We then consider the subharmonic interaction of a progressive ring wave, which is forced by a radial swelling–contraction deformation of a vertical circular cylinder, with subharmonic cross-waves. We derive the nonlinear spatial–temporal evolution equation governing the motion of the cross-wave by use of the average Lagrangian method. In addition to energy-input terms from the interaction with the forced ring wave, the evolution equation contains a damping term associated with energy loss in cross-wave propagation. We show that the presence of the damping term leads to a non-trivial threshold value of the ring wave steepness (or amplitude) beyond which the cross-wave becomes unstable and grows with time by taking energy from the ring wave. Finally, we extend this analysis to the experimental case of Tatsuno et al. (Rep. Res. Inst. Appl. Mech. Kyushu University, vol. 17, 1969, pp. 195–215) in which asymmetric wave patterns are observed during high-frequency vertical oscillations of a surface-piercing sphere. The theoretical prediction of the threshold value of oscillation amplitude and characteristic features of generated radial cross-waves agrees reasonably well with experimental observations.

R-Curves in Al2O3 - Al2O3/ZrO2 Laminates

2005 ◽  
Vol 290 ◽  
pp. 214-221 ◽  
Author(s):  
Javier Pascual ◽  
Francis Chalvet ◽  
Tanja Lube ◽  
Goffredo de Portu
Keyword(s):  
Free Surface ◽  
Crack Growth ◽  
Function Method ◽  
Fracture Behavior ◽  
Sandwich Beam ◽  
Stable Crack Growth ◽  
Fracture Pattern ◽  
Bending Test ◽  
Notched Specimen ◽  
Growth Experiments

In order to better understand the fracture behavior of Al2O3-Al2O3/ZrO2 laminates, controlled crack growth experiments were carried out. The method proposed consists of a threepoint bending test of a sandwich beam in which a notched specimen is located in between two metallic bars. Under certain conditions that will be commented, stable crack growth can be obtained. The fracture pattern is related to the residual stresses present in the laminate. R-curves for the laminate were also calculated using the weight function method, including the influence of the free surface. Toughness values are presented in the R-curve after friction considerations.

Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface

1983 ◽  
Vol 126 ◽  
pp. 545-567 ◽  
Author(s):  
F. Preisser ◽  
D. Schwabe ◽  
A. Scharmann
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Cylindrical Surface ◽  
Thermocapillary Convection ◽  
Cylinder Surface ◽  
Axially Symmetric ◽  
Zone Length ◽  
Aspect Ratios ◽  
Temperature Oscillations ◽  
Free Cylindrical Surface

In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a < 1 the radial extension of the roll equals the zone length. The stream velocities and the temperature distribution were measured.The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface.The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Mac is exceeded. A unique Mac = 7 × 103 has been found for zones with lengths l < 3·5 mm. The oscillatory state of thermocapillary convection has experimentally been proved to be a distortion of the laminar state in form of a wave travelling in the azimuthal direction. A unique non-dimensional wavenumber ≈ 2·2 (near Mac) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.

scholarly journals Free Surface Axially Symmetric Flows and Radial Hydraulic Jumps

2016 ◽  
Vol 142 (4) ◽  
pp. 06015025 ◽  
Author(s):  
Alessandro Valiani ◽  
Valerio Caleffi
Keyword(s):  
Free Surface ◽  
Hydraulic Jumps ◽  
Axially Symmetric

Magnetic Fluid Bridge between Coaxial Cylinders with a Line Conductor in Case of Wetting

2015 ◽  
Vol 233-234 ◽  
pp. 335-338 ◽  
Author(s):  
Alexandra Vinogradova ◽  
Vera Naletova ◽  
Vladimir Turkov
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Analytical Solution ◽  
Magnetic Fluid ◽  
Axially Symmetric ◽  
Magnetic Liquid ◽  
Coaxial Cylinders ◽  
Straight Wire ◽  
A Current ◽  
Symmetric Shape

We consider a heavy, incompressible, homogenous, isothermal magnetic fluid between two coaxial cylinders in case of wetting. There is a current-carrying straight wire on the axis of these cylinders. The magnetic fluid is immersed in a non-magnetic liquid with the same density (the case of hydroimponderability). We apply the Langevin law to describe a magnetic fluid magnetization. Using the general analytical solution for any axially symmetric shape of the magnetic fluid free surface in any axisymmetric magnetic field, we investigate the break-up and the rebuilding of the magnetic fluid bridge in case of wetting.

Hydrodynamic jet incident on an uneven wall

2018 ◽  
Vol 28 (04) ◽  
pp. 771-827 ◽  
Author(s):  
Jianfeng Cheng ◽  
Lili Du
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Atmospheric Pressure ◽  
Free Boundary Problems ◽  
Applied Mathematics ◽  
Impinging Jet ◽  
Two Dimensions ◽  
Minimum Problem ◽  
Axially Symmetric ◽  
Optimal Decay

The axially symmetric free surface problem of an ideal incompressible jet issuing from a nozzle and impinging on an uneven wall is investigated in this paper. More precisely, we show that given a semi-infinitely long axially symmetric nozzle, a mass flux [Formula: see text] in the inlet and a constant atmospheric pressure, there exists a unique incompressible impinging jet whose free surface goes to infinity and is close to the impermeable wall at far field. Moreover, the free surface of the impinging jet initiates at the edge of the semi-infinitely long nozzle and the pressure remains the constant atmospheric pressure on the free surface. The main ingredient to show the existence and the uniqueness of the impinging jet is based on the variational method developed in a series of the celebrated works [Existence and regularity for a minimum problem with free boundary, J. Reine Angew. Math. 325 (1981) 105–144; Variational Principles and Free-Boundary Problems, Pure and Applied Mathematics (John Wiley & Sons, 1982)] by Alt, Caffarelli and Friedman. Furthermore, some important properties of the axially symmetric impinging jet, such as positivity of the radial velocity, asymptotic behavior of the impinging jet, and the optimal decay rate of the free surface and the impinging jet, are obtained. Moreover, the problem of the axially symmetric jet impinging on a hemispherical cup is also considered. Finally, we establish the well-posedness theory on the incompressible impinging jet in two dimensions.

Evaluation of Growth of Subsurface Crack by Fatigue: Simulation of Penetration of Internal Flaw to Surface of the Structure

2013 ◽  
Author(s):  
Masanori Kikuchi ◽  
Shinya Yamada ◽  
Ryousuke Serizawa ◽  
Yulong Li
Keyword(s):  
Free Surface ◽  
Power Plant ◽  
Nuclear Power Plant ◽  
Crack Growth ◽  
Surface Crack ◽  
Nuclear Power ◽  
Crack Depth ◽  
Subsurface Crack ◽  
Loading Direction ◽  
Tension Loading

In nuclear power plant, there is a proximity rule to evaluate subsurface crack, which exists near free surface of the structure. If the distance between this subsurface crack to free surface exceeds some limit, this subsurface crack is transformed to surface crack, and residual fatigue life is evaluated. Subsurface crack has many parameters, such as, crack length, crack depth, distance between crack front to free surface, and aspect ratio of subsurface crack. As a result, proximity rule is proposed by many organizations, and each rule is different from each other largely. It is necessary to verify which is more preferable, but to determine it experimentally is very difficult due to existence of many parameters. Numerical simulation is needed for this purpose. This problem is simulated using S-version FEM. Using S-FEM, subsurface is modeled independently from global structure, and crack growth is easily simulated. In maintenance code of nuclear power plant, initial defects are modeled as elliptical cracks in a normal plane to tension loading direction, and growth rate is estimated in this plane. But by using S-FEM, real defect shape is modeled realistically, and crack growth by fatigue is simulated. Usually, such small defects are subjected to multi-axial loading, and crack growth behaviors are very complicated. Finally, detect shape becomes elliptical or circular crack in a plane normal to tension loading direction in the structure. Fatigue cycles for these growing processes are calculated, and conservativeness of this maintenance code is discussed. Then subsurface crack growth is simulated. Inner subsurface crack grows toward free surface, penetrate to free surface and grows as a surface crack. These processes are simulated smoothly by S-FEM. Parametric studies are conducted for this problem, and proximity rules are verified with numerical results.

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