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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Transactions of the Korean Society of Mechanical Engineers A
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Journal DOI :
The Korean Society of Mechanical Engineers
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Volume & Issues
Volume 25, Issue 12 - Dec 2001
Volume 25, Issue 11 - Nov 2001
Volume 25, Issue 10 - Oct 2001
Volume 25, Issue 9 - Sep 2001
Volume 25, Issue 8 - Aug 2001
Volume 25, Issue 7 - Jul 2001
Volume 25, Issue 6 - Jun 2001
Volume 25, Issue 5 - May 2001
Volume 25, Issue 4 - Apr 2001
Volume 25, Issue 3 - Mar 2001
Volume 25, Issue 2 - Feb 2001
Volume 25, Issue 1 - Jan 2001
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An Indentation Theory Based on FEA Solutions for Property Evaluation
Lee, Hyeong-Il ; Lee, Jin-Haeng ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1685~1696
DOI : 10.22634/KSME-A.2001.25.11.1685
A novel indentation theory is proposed by examining the data from the incremental plasticity theory based finite element analyses. First the optimal data acquisition location is selected, where the strain gradient is the least and the effect of friction is negligible. This data acquisition point increases the strain range by a factor of five. Numerical regressions of obtained data exhibit that strain hardening exponent and yield strain are the two main parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides the stress-strain curve with an average error less than 5%.
Finite Element Modeling of Polarization Switching in Electro-Mechanically Coupled Materials
Kim, Sang-Ju ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1697~1704
DOI : 10.22634/KSME-A.2001.25.11.1697
A finite element model for polarization switching in electro-mechanically coupled materials is proposed and applied to predict the switching behavior of a two-dimensional ferroelectric ceramic. A complicated micro-structure existing in the material is modeled as il continuum body and a simple 3 node triangle finite element with nodal displacement and voltage degrees of freedom is used for a finite element analysis. The elements use nonlinear constitutive equations, switching criterion and kinetic relation, fur representation of material response at strong electric and stress fields. The polarization state of the material is represented by internal variables in each element, which are updated at each simulation step based on the proposed constitutive equations. The model reproduces strain and electric displacement hysteresis loops observed in the material.
A Study on Failure Analysis of Low Pressure Trubine Blade Using AFM and FEM
Hong, Soon-Hyeok ; Cho, Seok-Swoo ; Joo, Won-Sik ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1705~1712
DOI : 10.22634/KSME-A.2001.25.11.1705
Mechanical component has striation with constant width and SEM can estimate fracture type and loading condition. SEM has benefit to fatigue fracture analysis but striation can be observed according to the kind of material and range of crack growth rate and can't. In this case, it needs AFM that can measure 3-dimensional surface profile with resolution of atomic size. In this study. to find fracture reason of torsion-mounted blade in nuclear plant, we estimate the relation between stress intensity factor range and root mean square roughness in 12% Cr steel by AFM and predict in-service loading condition of turbine blade. failure analysis is performed by finite element method and Goodman diagram on torsion-mounted blade.
Effect of Residual Stress on Fatigue Strength in Resistance Spot Weldment
Yang, Yeong-Su ; Son, Gwang-Jae ; Jo, Seong-Gyu ; Hong, Seok-Gil ; Kim, Seon-Gyun ; Mo, Gyeong-Hwan ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1713~1719
DOI : 10.22634/KSME-A.2001.25.11.1713
Estimation of fatigue strength on the spot welded joint is very Important for strength design of spot welded steed sheet structures. In this paper, the effect of residual stress on the fatigue life of resistance spot weldment was studied. Residual stress fields of weldment were calculated by using thermo elastic plastic finite element analysis and equivalent fatigue stress considering residual stress effect was obtained. And then we predicted fatigue life, which included the effect of the residual stresses and the actual loading stresses. The calculation and experimental results were in good agreement. Therefore, the proposed calculated model can be considered to be sufficiently powerful for the prediction of fatigue life.
Wear Characteristics of Plastic Pinion Against Steel Gear for Different Pitch Line Velocities
Kim, Chung-Hyeon ; An, Hyo-Seok ; Jeong, Tae-Hyeong ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1720~1729
DOI : 10.22634/KSME-A.2001.25.11.1720
Wear characteristics of Nylon and acetal pinions against steel gears for different pitch line velocities was studied with a power circulating gear test rig under unlubricated condition. Specific wear rate was measured as a function of tooth number, module, tooth width and total revolution. The worn tooth surfaces were examined with a profile projector. The Nylon pinion showed lower specific wear rate than the acetal pinion. However, the Nylon pinion was fractured at high tooth loads, whereas the acetal pinion exhibited a steady wear behavior. The wear characteristics of Nylon pinion varied significantly with the Pitch line velocity. Wear occurred most severely at the tooth tip and the region immediately below the pitch line of pinion. The dominant wear mechanisms were adhesion and abrasion.
A Finite Element Analysis for a Rotating Cantilever Beam
Jeong, Jin-Tae ; Yu, Hong-Hui ; Kim, Gang-Seong ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1730~1736
DOI : 10.22634/KSME-A.2001.25.11.1730
A finite element analysis for a rotating cantilever beam is presented in this study. Based on a dynamic modeling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are (derived from Hamilton's principle. Two of the linear differential equations show the coupling effect between stretch and chordwise deformations. The other equation is an uncoupled one for the flapwise deformation. From these partial differential equations and the associated boundary conditions, two weak forms are derived: one is for the chordwise motion and the other is fur the flptwise motion. The weak farms are spatially discretized with newly defined two-node beam elements. With the discretized equations or the matrix-vector equations, the behaviors of the natural frequencies are investigated for the variation of the rotating speed.
Topographical Analysis of the Rubbed Surface using Fractal Dimension
Park, Heung-Sik ; Kim, Yeong-Hui ; Jeon, Tae-Ok ; Jo, Yeon-Sang ; Mun, Byeong-Ju ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1737~1742
DOI : 10.22634/KSME-A.2001.25.11.1737
The fractal-based method for describing rubbed surface texture has aroused great interest. The determination of rubbed surface topography is believed to be extremely important in the areas of contact mechanics, adhesion and friction. In order to describe topography of the rubbed surface, the wear test was carried out with annular surfaces of wear testing specimens in dry friction. furthermore, the relation between the fractal dimensions and the frictional conditions are also investigated and fractal descriptors was applied to rubbed surface with image processing. Fractal dimension can be determined by sum of intensity difference of image surface pixel. Fractal dimension increased according as the applied load and sliding distance increase. Topography of the rubbed surface can be effectively obtained by fractal dimensions.
Dynamic Stability Analysis of Base-Isolated Low-level Nonlinear Structure Under Earthquake Excitation
Mun, Byeong-Yeong ; Gang, Gyeong-Ju ; Gang, Beom-Su ; Kim, Gye-Su ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1743~1750
DOI : 10.22634/KSME-A.2001.25.11.1743
This paper presents an analysis of nonlinear response of the seismically isolated structure against earthquake excitation to evaluate isolation performances of a rubber bearing. In the analysis of the vibration of building, the building is modeled by lumped mass system where the restoring force is considered as linear, bilinear and trilinear. Fundamental equations of motion are derived for the base isolated structure, and hysteretic and nonlinear-elastic characteristics are considered for a numerical calculation. The excitation levels are magnified fur the recorded strong earthquake motions in order to examine dynamic stability of the structure. Seismic responses (of the building are compared fur the each restoring force type. As a result, it is shown that the effect of the motion by the nonlinear response of the building is comparatively not so large from a seismic design standpoint. The responses of the isolated structures reduce sufficiently and controled the motion of the building well in a practical range. By increasing the acceleration of the earthquake, the yielding of the farce was occurred in the concrete and steel frame, which shows the necessity of the exact nonlinear dynamic analysis.
Effects of Die Deformation and Channel Angle on Deformation Behavior of Materials During Equal Channel Angular Pressing with Pure-Zr
Gwon, Gi-Hwan ; Chae, Su-Won ; Gwon, Suk-In ; Kim, Myeong-Ho ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1751~1758
DOI : 10.22634/KSME-A.2001.25.11.1751
Among severe plastic deformation processes, ECAP has drawn much attention due to its advantages including ultra-fine grain size material production. In this paper, ECAP process with pure -Zirconium is investigated due to its applicability to nuclear reactors. The finite element method is employed to investigate the deformation behavior of materials during ECAP process. In particular, effects of process parameters such as die deformation and channel angles on the material behaviors have been investigated. Experimental studies have also been performed to verify the numerical results.
Fault Detection of a Gear with Initial Pitting using the Boomed Phase Map of Continuous Wavelet Transform
Lee, Sang-Gwon ; Sim, Jang-Seon ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1759~1766
DOI : 10.22634/KSME-A.2001.25.11.1759
Vibration transient generated by developing localized fault in gear can be used as indicators in gear fault detection. In this paper, we propose the zoomed phase map for a fault signal using continuous wavelet transfers to detect this vibration transient. Local fault induces the abrupt fluctuation of load exciting tooth and phase lag in the vibration signal measured on the gearbox. The relatively large fault like "tip breakage" easily can be detected by the clear fluctuation of exciting load. However, minor fault like "initial pitting"cannot be detected using the load fluctuation. To defect this kind of minor fault, the phase map for a fault signal is taken into account. The phase lag by minor fault is observed well in the zoomed phase map.
Optimal Design of a High Speed Carbon Composite Air Spindle
Bang, Gyeong-Geun ; Lee, Dae-Gil ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1767~1776
DOI : 10.22634/KSME-A.2001.25.11.1767
For the stable operation of high speed air spindle, the low rotational inertia and high damping ratio of spindle shafts as well as high fundamental natural frequency are indispensable. Conventional steel spindles are net appropriate for very high speed operation because of their high rotational inertia and low damping ratio. In this study, a high speed spindle composed of carbon fiber epoxy composite shaft and steel flange was designed for maximum critical speed considering minimum static deflection and radial expansion due to bending load and centrifugal force during high speed relation. The stacking angle and the stacking thickness of the composite shaft and the adhesive bonding length of the 7teel flange were selected through vibrational analysis considering static and thermal loads due to temperature rise.
Engineering J-Integral Estimation for Semi-Elliptical Surface Cracked Plates in Tension
Sim, Do-Jun ; Kim, Yun-Jae ; Choe, Jae-Bung ; Kim, Yeong-Jin ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1777~1784
DOI : 10.22634/KSME-A.2001.25.11.1777
This paper provides d simplified engineering J estimation method fur semi-e1liptical surface cracked plates in tension, based on the reference stress approach. Note that the essential element of the reference stress approach is the plastic limit lead in the definition of the reference stress. However, for surface cracks, the definition of the limit load is ambiguous ("local" or "global"limit lead), and thus the most relevant limit load (and thus reference stress) for the J estimation should be determined. In the present work, such limit load solution is found by comparing reference stress bated J results with those from extensive 3-D finite element analyses. Validation of the proposed equation against FF J results based on tactual experimental tensile data of a 304 stainless steel shows excellent agreements not only far the J values at the deepest point but also for those at an arbitrary paint along the crack front, including at the surface point. Thus the present results provide a good engineering tool for elastic-plastic fracture analyses of surface cracked plates in tension.
Development of Three-Dimensional Layered Finite Element for Thermo-Mechanical Analysis
Jo, Seong-Su ; Ha, Seong-Gyu ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1785~1795
DOI : 10.22634/KSME-A.2001.25.11.1785
A multi-layered brick element fur the finite element method is developed for analyzing the three-dim-ensionally layered composite structures subjected to both thermal and mechanical boundary conditions. The element has eight nodes with one degree of freedom for the temperature and three for the display-ements at each node, and can contain arbitrary number of layers with different material properties with-in the element; the conventional element should contain one material within an element. Thus the total number of nodes and elements, which are needed to analyze the multi-layered composite structures, can be tremendously reduced. In solving the global equation, a partitioning technique is used to obtain the temperature and the displacements which are caused by both the mechanical boundary conditions and temperature distributions. The results by using the developed element are compared wish the commercial package, ANSYS and the conventional finite element methods, and they are in good agreement. It is also shown that the Number of nodes and elements can be tremendously reduced using the element without losing the numerical accuracies.
Shape Design of Micro Electrostatic Actuator using Multidimensional Design Windows
Jeong, Min-Jung ; Kim, Yeong-Jin ; Daisuke Ishihara ; Yoshimura, Shinobu ; Yagawa, Genki ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1796~1801
DOI : 10.22634/KSME-A.2001.25.11.1796
For micro-machines, very few design methodologies based on optimization hale been developed so far. To overcome the difficulties of design optimization of micro-machines, the search method for multi-dimensional design window (DW)s is proposed. The proposed method is defined as areas of satisfactory design solutions in a design parameter space, using both continuous evolutionary algorithms (CEA) and the modified K-means clustering algorithm . To demonstrate practical performance of the proposed method, it was applied to an optimal shape design of micro electrostatic actuator of optical memory. The shape design problem has 5 design parameters and 5 objective functions, and finally shows 4 specific design shapes and design characters based on the proposed DWs.
Transient Analysis of Composite Cylindrical Shells with Ring Stiffeners
Kim, Yeong-Wan ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1802~1812
DOI : 10.22634/KSME-A.2001.25.11.1802
The theoretical method is developed to investigate the effects of ring stiffeners on free vibration characteristics and transient response for the ring stiffened composite cylindrical shells subjected to the impulse pressure Loading. In the theoretical procedure, the Love's thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect is adopted to formulate the theoretical model. The concentric or eccentric ring stiffeners are laminated with composite and have the uniform rectangular cross section. The modal analysis technique is used to develop the analytical solutions of the transient problem. The analysis is based on an expansion of the loads, displacements in the double Fourier series that satisfy the boundary conditions. The effect of stiffener's eccentricity, number, size, and position on transient response of the shells is examined. The results are verified by comparison with FEM results.
Residual Stress and Displacement Analysis of Thick Plate for Partial Penetration Multi-Pass Weldment
Kim, Seok ; Bae, Seong-In ; Song, Jeong-Il ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1813~1819
DOI : 10.22634/KSME-A.2001.25.11.1813
Partial penetration welding Joint defines that groove welds without steel backing, welded from on side, and groove weeds welded from both sides but without back gouging, that is. it has an unwelded portion at the root of the weld. In this study we analysed fur residual stress and displacement distribution on partial penetration welding condition of thick plate metal. For 25.4mm thick plate, theoretical residual stress and displacement analysis by finite element method using ABAQUS was carried out and compared with the experimental result using hole-drilling method. In results of the condition of partial penetration, it appeared that longitudinal stress at welding area was a little difference and transverse stress did not have any effect by partial penetration multi-pass welding. From a point of welding distortion in partial penetration multi-pass welding, it seemed to be better to control root face smaller than 6.35mm.
A New Dynamic Analysis of 6-3 Stewart Platform Manipulator
Kim, Nak-In ; Lee, Chong-Won ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1820~1828
DOI : 10.22634/KSME-A.2001.25.11.1820
The dynamics of the 6-3 Stewart platform manipulator (SPM) is newly derived based on the kinematic relations particularly developed fur the SPM. The essence of the analysis is to deal with three subsystems of the SPM, each consisting of the command and feedback line links associated with two joined neighboring actuators. The dynamics of the command and feedback line links are first formulated using Lagrange and Newton-Euler method and then combined to derive the dynamic equations of motion fur the SPM. The derived nonlinear equations of motion are so computationally effective that it can be easily applied to real-time high-speed tracking control of 6-3 SPM.
Ductile Fracture Behaviour of SA 533B Pressure Vessel Steel Under Mixed Mode (I/II) Loading
O, Dong-Jun ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1829~1834
DOI : 10.22634/KSME-A.2001.25.11.1829
The aim of this study is to investigate the ductile fracture behavior under mixed mode (I/II) loading using SA533B pressure vessel steel. Anti-symmetric 4-point (AS4P) bonding tests were performed to obtain the J-R curves under two different mixed mode (I/II) loadings. In addition, the fractographic examination of fracture surfaces was carried out to compare with those of pure Mode I and Mode II. In conclusions, the J-R curves under Mixed Mode (I/II) loading were located between those of Mode I and Mode II loadings. When the mixture ratio of mixed mode (I/II) loading was high, the J-R currie of mixed mode (I/II) loading approached that of pure mode I loading after some amount of crack propagation. In contrast with the above fact, if the mixture ratio was low, the J-R curve looked after that of pure mode II loading. The fractographic evidences such as the shape of dimples under different loading conditions supported these conclusions.
A Study on Energy Release Rate for Interface Cracks in Anisotropic Dissimilar Materials
Kim, Jin-Gwang ; Jo, Sang-Bong ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1835~1843
DOI : 10.22634/KSME-A.2001.25.11.1835
The energy release rate for an interface crack in anisotropic dissimilar materials was obtained by the eigenfunction expansion method and also was analyzed numerically by the reciprocal work contour integral method. It was shown that the results for orthotropic dissimilar materials are consistent with the other worker's results.
Design of Rolling Path Schedule for Refinement of Austenite Grain
Hong, Chang-Pyo ; Park, Jong-Jin ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1844~1853
DOI : 10.22634/KSME-A.2001.25.11.1844
In the present investigation, it was attempted to design the rolling pass schedule fur a clean steel of 0.1C-1.5Mn-0.25Si with the objective of the austenite grain refinement. As the method of approach, a coupled mathematical modeling technique was proposed which consists of a recrystallization model and a flow stress modes. The validity of the coupled model was examined through comparison with results of continuous and discontinuous compression tests at various temperatures, strains and strain rates. The coupled model was incorporated with the finite element method to set up a systematic design methodology far the rolling path schedule for austenite grain refinement. Two path schedules were obtained and discussed in the paper with regard to rolling path time, average grain size, grain size deviation in thickness, etc.
Power Transmission Characteristics of a Hydro-Mechanical Transmission
Seong, Deok-Hwan ; Kim, Hyeong-Ui ; Lee, Geun-Ho ; Kim, Hyeon-Su ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1854~1862
DOI : 10.22634/KSME-A.2001.25.11.1854
In this paper, power flow characteristics of a hydromechanical transmission(HMT) are investigated using network analysis. The HMT used in this study consist of a hydrostatic unit(HSU), planetary gear sets, clutches and brakes providing forward 4 speeds and backward 2 speeds. Since the HMT power flows showing a closed loop and the HSU efficiency varies depending on the pressure and speed, a systematic approach is required to analyze the power transmission characteristics of the HMT. In order to analyze the closed loop power flow and the HSU power loss which changes depending on the pressure and speed, network model is constructed fur each speed range. In addition, an algorithm is proposed to calculate an accurate HSU loss corresponding to the experimental results. It is found from the network analysis that the torque and speed of each transmission element including the HSU can be obtained as well as direction of the power flow by the proposed algorithm. It is expected that the network analysis can be used in the design of relatively complicated transmission system such as HMT.
Precision Stage Using A Novel Contact-Free Planar Actuator Based on Combination of Electromagnetic forces
Jeong, Gwang-Seok ; Baek, Yun-Su ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1863~1872
DOI : 10.22634/KSME-A.2001.25.11.1863
In this Paper, we suggest the precision stage using a novel non-contact planar actuator that utilizes an interaction between an array type of air-core solenoids and permanent magnets. The former with axes arranged in the mutually orthogonal direction is fixed on the stator and the latter with the same polar direction is attached below the stage. The promising magnetic structure has little uncertainty such as hysteresis loss caused by ferromagnetic material, then it is simple to quantify the magnetic phenomenon. And all the magnetic forces are transmitted through narrow air-gap between the coil and the permanent magnet, therefore the structure can be highly compacted. Furthermore, the stage or plate can be perfectly isolated from the stator without any wire connection, leading to diminish the generating possibility of wear particles due to mechanical contact. Then. it is estimated that the proposed operating principle is very suitable for work requiring high accuracy and cleanness. or general-purpose nano stage. The main issues rebated to the plate driving are discussed here.
Effect of Restraint of Pressure Induced Bending on Crack Opening Evaluation for Circumferential Through-Wall Cracked Pipe
Kim, Jin-Won ; Park, Chi-Yong ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1873~1880
DOI : 10.22634/KSME-A.2001.25.11.1873
The effects of restraint of pressure induced bending(PIB) on crack opening for circumferential through-wall crack in a pipe were investigated. In this study, the elastic and elastic-plastic finite element analyses were performed to evaluate crack opening displacement(COD) for various restraint conditions and crack size. The results showed the restraint of PIB decreased crack opening for a given crack size and tensile stress, and the decrease in crack opening was considerable for large crack and short restraint length. A1so, the effect was more significant in tole results of elastic-plastic analysis compared with in the elastic analysis results. In the elastic-plastic analysis results, tole restraint effect was increased with increasing applied tensile stress corresponding to internal pressure. Additionally, the restraint effect on COD was independent on the variation in pipe diameter and decreased with increasing pipe thickness, and It depended on not total restraint length but shorter restraint length for non-symmetrically restrained.
Finite Element Analysis for Actuating Performance Evaluation of LIghtweight Piezo-composite Curved Acutator
Gu, Nam-Seo ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1881~1886
DOI : 10.22634/KSME-A.2001.25.11.1881
A numerical method for actuating performance evaluation of LIPCA proposed using a finite element method. Fully coupled formulations for piezo-electric materials were introduced and 3-dimensional eight-node incompatible element was used. After verifying the developed code with typical examples, the center deflections of LIPCA were calculated and compared with the experimental result, which were in fairly agreement.
An Experimental Study on the Change of the Material Properties and the Fatigue Life of Natural Rubber due to Carbon Black
Kim, Jae-Hun ; Kim, Yeong-Hak ; Jeong, Hyeon-Yong ;
Transactions of the Korean Society of Mechanical Engineers A, volume 25, issue 11, 2001, Pages 1887~1894
DOI : 10.22634/KSME-A.2001.25.11.1887
The effects of carbon black on the material properties and the fatigue life of the carbon-black filled natural rubbers were investigated. Different kinds of carbon blacks resulted in different fatigue lives, hysteresis, and critical J-values. It was noticed that the hysteresis was inversely proportional to the difference between DBPA and CTAB, and the critical J-value was almost the same regardless of the length of a precrack. In addition, different kinds of carbon blacks resulted in different fracture morphologies, and micro-scale and macro-scale roughnesses. The critical J-value was proportional to the micro-scale roughness. and it seemed relate to the size distribution of carbon black particles. By reviewing all the experimental data. it was finally noticed that the logarithmic value of the fatigue life could be linearly expressed by a multiplication of the critical J-value and the logarithmic value of the hysteresis.