scholarly journals Incubation Time and Cavitation Erosion Rate of Work-Hardening Materials

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Jean-Pierre Franc
Keyword(s):  
Steady State ◽  
Incubation Time ◽  
Erosion Rate ◽  
Cavitation Erosion ◽  
Mean Amplitude ◽  
Hardened Layer ◽  
Impact Loads ◽  
Hydrodynamic Impact ◽  
Ductile Materials ◽  
The Mean

A phenomenological analysis of the cavitation erosion process of ductile materials is proposed. On the material side, the main parameters are the thickness of the hardened layer together with the conventional yield strength and ultimate strength. On the fluid side, the erosive potential of the cavitating flow is described in a simplified way using three integral parameters: rate, mean amplitude, and mean size of hydrodynamic impact loads. Explicit equations are derived for the computation of the incubation time and the steady-state erosion rate. They point out two characteristic scales. The time scale, which is relevant to the erosion phenomenon, is the covering time—the time necessary for the impacts to cover the material surface—whereas the pertinent length scale for ductile materials is the thickness of the hardened layer. The incubation time is proportional to the covering time with a multiplicative factor, which strongly depends on flow aggressiveness in terms of the mean amplitude of impact loads. As for the erosion rate under steady-state conditions, it is scaled by the ratio of the thickness of hardened layers to the covering time with an additional dependence on flow aggressiveness, too. The approach is supported by erosion tests conducted in a cavitation tunnel at a velocity of 65 m/s on stainless steel 316 L. Flow aggressiveness is inferred from pitting tests. The same model of material response that was used for mass loss prediction is applied to derive the original hydrodynamic impact loads due to bubble collapses from the geometric features of the pits. Long duration tests are performed in order to determine experimentally the incubation time and the mean depth of penetration rate and to validate the theoretical approach.

Assessment of Cavitation Erosion of Gas-Nitrided Cr-Ni-Mo Steels

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Ion Mitelea ◽  
Cristian Ghera ◽  
Ilare Bordeaşu ◽  
Corneliu Crăciunescu
Keyword(s):  
Electron Microscopy ◽  
Erosion Rate ◽  
Structural Changes ◽  
Cavitation Erosion ◽  
Erosion Resistance ◽  
Thermochemical Treatment ◽  
Gas Nitriding ◽  
The Mean ◽  
Cavitation Erosion Resistance ◽  
Scanning Electron

The effect of the gas-nitriding thermochemical treatment on the cavitation erosion resistance of a Cr-Ni-Mo alloy is analyzed using a piezoceramic vibrating equipment and following the ASTM G32-2010 standard. The evaluation of the cavitation erosion behavior was made based on the analysis of the mean depth of erosion (MDE) and mean depth of erosion rate (MDER), for samples subjected to the cavitation erosion for different times. The surface topography and the structural changes in the marginal layer were analyzed through optical and scanning electron microscopy. Following nitriding the cavitation erosion resistance was about 9.6 times higher compared to the annealed state and about 8.2 times higher compared to the hardened and tempered state.

A New Model for the Equation Describing the Cavitation Mean Depth Erosion Rate Curve

2017 ◽  
Vol 68 (4) ◽  
pp. 894-898 ◽  
Author(s):  
Lavinia Madalina Micu ◽  
Ilare Bordeasu ◽  
Mircea Octavian Popoviciu
Keyword(s):  
Mechanical Properties ◽  
Chemical Composition ◽  
Stainless Steels ◽  
Erosion Rate ◽  
Cavitation Erosion ◽  
Linear Variation ◽  
Erosion Rates ◽  
Supplementary Term ◽  
The Mean ◽  
Experimental Values

Paper present a new relation describing the curve MDER(t) which mediates the experimentally obtained values of the mean depth erosion rates. These curves are used to characterize the cavitation erosion behavioor of materials tested in the Cavitation Laboratory of Timisoara Polytechnic University. Practically the new relation is an improvement of the analytical model established in 2004 by Bordeasu and coworkers, by introducing a supplementary element, which take into consideration the shape of the zone in where the cavitation erosion rate became stable and has linear variation. These addition allow increasing the approximation of the experimental values and also putting into evidence the tiny differences between different materials (various types of stainless steels, highly alloyed bronzes etc.) which till now were considered with similar resistance. Thus, the supplementary term allow a better differentiation resulting from the chemical composition, the structure and the mechanical properties.

scholarly journals A Cavitation Erosion Model for Ductile Materials

2002 ◽  
Vol 124 (3) ◽  
pp. 601-606 ◽  
Author(s):  
N. Berchiche ◽  
J. P. Franc ◽  
J. M. Michel
Keyword(s):  
Cross Sections ◽  
Cavitation Erosion ◽  
Experimental Tests ◽  
Material Surface ◽  
Impact Loads ◽  
Physical Analysis ◽  
Ductile Materials ◽  
Hardening Process ◽  
Strain Relationship ◽  
The Impact

An analytical model is proposed for the prediction of cavitation erosion of ductile materials. It is based upon a physical analysis of the work-hardening process due to the successive bubble collapses. The material is characterized by its classical stress-strain relationship and its metallurgical behavior is analyzed from microhardness measurements on cross sections of eroded samples. The flow aggressiveness is determined from pitting tests, using the material properties to go back to the impact loads. The histogram of impact loads is applied numerically a large number of times on the material surface and the evolution of the mass loss with the exposure time is computed. The approach is supported by experimental tests.

Analysis on Fatigue Fracture of the Flame-Quenched 8.8Al-Bronze by Ultrasonic Vibratory Cavitation Erosion

2006 ◽  
Vol 118 ◽  
pp. 463-468
Author(s):  
Sung Mo Hong ◽  
Min Ku Lee ◽  
G.H. Kim ◽  
Chang Kyu Rhee ◽  
K.H. Kim ◽  
...  
Keyword(s):  
Steady State ◽  
Incubation Period ◽  
Load Distribution ◽  
Cavitation Erosion ◽  
Impact Load ◽  
Fatigue Properties ◽  
Impact Loads ◽  
Cavitation Damage ◽  
Number Of Cycles ◽  
The Impact

In this study the fatigue properties due to cavitation damage of flame-quenched 8.8Al-bronze (8.8Al-4.5Ni-4.5Fe-Cu) as well as current nuclear pump materials (8.8Al-bronze, SUS316 and SR50A) have been investigated by using an ultrasonic vibratory cavitation test. For this the impact loads of cavitation bubbles generated by ultrasonic vibratory device quantitatively evaluated and simultaneously the cavitation erosion experiments have been carried out. The fatigue analysis on the cavitation damage of the materials has been made from the determined impact load distribution (e.g. impact load, bubble count) and erosion parameters (e.g. incubation period, MDPR). According to Miner’s law, the exponents b of the F-N relation (Fb N = Constant) at the incubation stage (N: the number of fracture cycle) were 5.62, 4.16, 6.25 and 8.1 for the 8.8Al-bronze, flame-quenched sample, SUS316 and SR50A alloys, respectively. At steady-state, the exponents b of the F-N curve (N: the number of cycles required for a 1μm increment of MDP) were determined as 6.32, 5, 7.14 and 7.76 for the 8.8Al-bronze, flame-quenched sample, SUS316 and SR50A alloys, respectively.

scholarly journals Effect of Nitrogen Ion Implantation on the Cavitation Erosion Resistance and Cobalt-Based Solid Solution Phase Transformations of HIPed Stellite 6

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2324
Author(s):  
Mirosław Szala ◽  
Dariusz Chocyk ◽  
Anna Skic ◽  
Mariusz Kamiński ◽  
Wojciech Macek ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Stainless Steel ◽  
Ion Implantation ◽  
Phase Transformations ◽  
Erosion Rate ◽  
Cavitation Erosion ◽  
Matrix Phase ◽  
Nitrogen Ion Implantation ◽  
Stellite 6 ◽  
Nitrogen Ion

From the wide range of engineering materials traditional Stellite 6 (cobalt alloy) exhibits excellent resistance to cavitation erosion (CE). Nonetheless, the influence of ion implantation of cobalt alloys on the CE behaviour has not been completely clarified by the literature. Thus, this work investigates the effect of nitrogen ion implantation (NII) of HIPed Stellite 6 on the improvement of resistance to CE. Finally, the cobalt-rich matrix phase transformations due to both NII and cavitation load were studied. The CE resistance of stellites ion-implanted by 120 keV N+ ions two fluences: 5 × 1016 cm−2 and 1 × 1017 cm−2 were comparatively analysed with the unimplanted stellite and AISI 304 stainless steel. CE tests were conducted according to ASTM G32 with stationary specimen method. Erosion rate curves and mean depth of erosion confirm that the nitrogen-implanted HIPed Stellite 6 two times exceeds the resistance to CE than unimplanted stellite, and has almost ten times higher CE reference than stainless steel. The X-ray diffraction (XRD) confirms that NII of HIPed Stellite 6 favours transformation of the ε(hcp) to γ(fcc) structure. Unimplanted stellite ε-rich matrix is less prone to plastic deformation than γ and consequently, increase of γ phase effectively holds carbides in cobalt matrix and prevents Cr7C3 debonding. This phenomenon elongates three times the CE incubation stage, slows erosion rate and mitigates the material loss. Metastable γ structure formed by ion implantation consumes the cavitation load for work-hardening and γ → ε martensitic transformation. In further CE stages, phases transform as for unimplanted alloy namely, the cavitation-inducted recovery process, removal of strain, dislocations resulting in increase of γ phase. The CE mechanism was investigated using a surface profilometer, atomic force microscopy, SEM-EDS and XRD. HIPed Stellite 6 wear behaviour relies on the plastic deformation of cobalt matrix, starting at Cr7C3/matrix interfaces. Once the Cr7C3 particles lose from the matrix restrain, they debond from matrix and are removed from the material. Carbides detachment creates cavitation pits which initiate cracks propagation through cobalt matrix, that leads to loss of matrix phase and as a result the CE proceeds with a detachment of massive chunk of materials.

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

Quantitative analysis of static equilibrium in women after mastectomy

2014 ◽  
Vol 14 (1) ◽  
pp. 81-87
Author(s):  
Maciej Rachwał ◽  
Justyna Drzał-Grabiec ◽  
Katarzyna Walicka-Cupryś ◽  
Aleksandra Truszczyńska
Keyword(s):  
Mean Amplitude ◽  
Control Group ◽  
Foot Pressure ◽  
Locomotor System ◽  
Center Of Foot Pressure ◽  
The Mean ◽  
Almost All ◽  
Posture Stability ◽  
Mastectomy Group ◽  
Better Than

Abstract Background: The post-mastectomy changes to the locomotor system are related to the scar and adhesion or to the lymphatic edema after amputation which, in turn, lead to local and global distraction of the work of the muscles. These changes lead to body statics disturbance that changes the projection of the center of gravity and worsens motor response due to changing of the muscle sensitivity. Objective: The aim of the study was to evaluate the static balance of women after undergoing mastectomy. Methods: The study included 150 women, including 75 who underwent mastectomy (mean age: 60±7.6) years, mean body mass index (BMI): 26 (±3.6) kg/m2) and 75 who were placed in the control group with matched age and BMI. The study was conducted using a tensometric platform. Results: Statistically significant differences were found for almost all parameters between the post-mastectomy group and group of healthy women, regarding center of foot pressure (COP) path length in the Y and X axes and the mean amplitude of COP. Conclusions: First, the findings revealed that balance in post-mastectomy women is significantly better than in the control group. Second, physiotherapeutic treatment of post-mastectomy women may have improved their posture stability compared with their peers.

Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell

1969 ◽  
Vol 39 (3) ◽  
pp. 477-495 ◽  
Author(s):  
R. A. Wooding
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Saturated Porous Medium ◽  
Mean Amplitude ◽  
Wave Number ◽  
Two Fluids ◽  
Averaged Equations ◽  
The Mean ◽  
Hele Shaw Cell

Waves at an unstable horizontal interface between two fluids moving vertically through a saturated porous medium are observed to grow rapidly to become fingers (i.e. the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approximately as (time)2, followed by a transition to a growth proportional to time. Correspondingly, the mean wave-number decreases approximately as (time)−½. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an unclosed set, but closure is achieved by assuming a law for the mean wave-number based on similarity. It is found that the mean amplitude is fairly insensitive to changes in wave-number. Numerical solutions of the averaged equations give more detailed information about the growth behaviour, in excellent agreement with the similarity results and with the Hele-Shaw experiments.

Evaluation of Single-Hole Hydraulic Tests in Fractured Crystalline Rock by Steady-State and Transient Methods: A Comparison

1985 ◽  
Vol 50 ◽  
Author(s):  
J-E. Andersson ◽  
O. Persson
Keyword(s):  
Steady State ◽  
Hydraulic Conductivity ◽  
Flow Pattern ◽  
Transient Analysis ◽  
Crystalline Rock ◽  
Steady State Analysis ◽  
Single Hole ◽  
The Mean ◽  
Transient Methods ◽  
State Analysis

AbstractThe results from a large number of single-hole packer tests in crystalline rock from three test sites in Sweden have been analysed statistically. Average hydraulic conductivity values for 25 m long test intervals along boreholes with a maximal length of about 700 m are used in this study. A comparison between steady state and transient analysis of the same test data has been performed.The mean vaule of the hydraulic conductivity determined from steady state analysis was found to be about two to three times higher compared to transient analysis. However, in some cases the steady state analysis resulted in 10 to 20 times higher values compared to the transient analysis. Such divergence between the two analysis methods may be caused by deviations from the assumed flow pattern, borehole skin effects and influence of hydraulic boundaries.

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