103 research outputs found
The modified BenjaminBona-Mahony equation via the extended generalized Riccati equation mapping method
Abstract The generalized Riccati equation mapping is extended together with the ( ) expansion method and is a powerful mathematical tool for solving nonlinear partial differential equations. In this article, we construct twenty seven new exact traveling wave solutions including solitons and periodic solutions of the modified Benjamin-Bona-Mahony equation by applying the extended generalized Riccati equation mapping method. In this method, implemented as the auxiliary equation, where , r s and p are arbitrary constants and called the generalized Riccati equation. The obtained solutions are described in four different families including the hyperbolic functions, the trigonometric functions and the rational functions. In addition, it is worth mentioning that one of newly obtained solutions is identical for a special case with already published result which validates our other solutions. Mathematics Subject Classification: 35K99, 35P99, 35P05 Keywords: The modified Benjamin-Bona-Mahony equation, the generalized Riccati equation, the ( ) / G G ′ -expansion method, traveling wave solutions, nonlinear evolution equations
Effects of Thermal Fatigue on Laser Modified H13 Die Steel
In order to improve the wear properties of H13 die steel, the thermal fatigue properties of AISI H13 tool steel were investigated at a varied number of cycles for enhancing surface hardness. A CO2 laser system was used with a 0.09mm focused spot size on the sample surface. The peak power of 1137kW and pulse repetition frequency (PRF) of 2300Hz were the parameters controlled. The Nabertherm model of a thermal fatigue machine used consisted of the cylindrical high temperature furnace with digital control panel, controlled temperature quenching system and pneumatics control sample movement mechanism. The samples were immersed in molten aluminum and quenched in ionized water emulsion at 17oC temperature within a specific time per cycle. The quenching system was equipped with a thermocouple to control the water temperature. The testing was done on1,750 and 3,500 cycles. The treated samples was characterized for metallographic study and hardness. The metallographic study was conducted using an optical microscope for laser modified layer thickness and grain size and the hardness properties were measured using a Vickers indenter. Erosion occurred from the sample after 3500 cycles. The hardness of the laser treated layer was lowered, after a thermal fatigue test, from 650 HV0.1 to 510 HV0.1.These findings are important for designing high wear resistant surfaces through laser surface modification for applications forming semi-solid dies
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Thermal fatigue properties of laser treated steels
This paper presents the thermal fatigue resistance of laser treated steels. The C40 and AISI H13 steels were machined into a geometry which allowed thermal gradients on the inner and outer surface during testing. A CO2 laser system was used with a focused spot size of 0.09 mm on the sample surface. The laser peak power and pulse repetition frequency (PRF) range were set to 760 and 1515 W, and 2900 to 3500 Hz respectively. The thermal fatigue machine used consists of Nabertherm model cylindrical high temperature furnace with digital control panel, controlled temperature quenching system, and pneumatics control sample movement mechanism. The thermal fatigue test involved immersion of samples into molten aluminium, and quenched in ionised water emulsion at 17°C temperature. The quenching system equipped with thermocouple to control the water temperature. Testing was done at a total of 1,750 number of cycles. Internal surface cooling was controlled by water inlet and outlet tubes. Samples were cleaned using NaOH solution after thermal fatigue testing to remove oxides on the surface. The solution temperature and magnetic stirrer speed were set to 100°C and 4.5 rpm respectively. Samples were characterised using scanning electron microscope (SEM), energy discharge x-ray spectroscopy (EDXS) and 2D stylus profilometer. Presence of different phases on the sample surface were analysed from back-scattered detector micrographs. Heat checks were observed on laser glazed surface at several regions. Carbides and oxides elements were detected on the sample surface after the thermal fatigue test. The relationship between surface roughness of laser treated surface and thermal fatigue behaviour was investigated
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An Analytical Model to Predict and Minimize the Residual Stress of Laser Cladding Process
Laser Cladding is one of the advanced thermal techniques used to repair or modify the surface properties of high value components such as tools, military and aerospace parts. Tensile residual stresses are formed in the thermally treated area of this process. This work focuses on to find out key factors of formation and minimization of tensile residual stresses in dissimilar materials. In order to predict the tensile residual stress, one dimensional analytical model has been adopted. Four cladding materials (Al2O3, TiC, TiO2, ZrO2) on the H13 tool steel substrate and a range of preheating temperature of the substrate, from 300K to 1200K, have been investigated. The thermal strain and Young’s modulus are found as key factors of formation and minimization of residual stresses. Additionally, the investigation of preheating temperature of the substrate showed the reduction of residual stress with increasing the preheating temperature of the substrate
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Effect of powder metallurgy synthesis parameters for pure aluminium on resultant mechanical properties
In this work, pure aluminium powders of different average particle size were compacted, sintered into discs and tested for mechanical strength at different strain rates. The effects of average particle size (15, 19, and 35 μm), sintering rate (5 and 20 °C/min) and sample indentation test speed (0.5, 0.7, and 1.0 mm/min) were examined. A compaction pressure of 332 MPa with a holding time of six minutes was used to produce the green compacted discs. The consolidated green specimens were sintered with a holding time of 4 h, a temperature of 600 °C in an argon atmosphere. The resulting sintered samples contained higher than 85% density. The mechanical properties and microstructure were characterized using indentation strength measurement tests and SEM analysis respectively. After sintering, the aluminium grain structure was observed to be of uniform size within the fractured samples. The indentation test measurements showed that for the same sintering rate, the 35 μm powder particle size provided the highest radial and tangential strength while the 15 μm powder provided the lowest strengths. Another important finding from this work was the increase in sintered sample strength which was achieved using the lower sinter heating rate, 5 °C/min. This resulted in a tangential stress value of 365 MPa which was significantly higher than achieved, 244 MPa, using the faster sintering heating rate, 20 °C/min
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