The manufacturing process of forging of large crankshafts is affected by bending of the shaft during heat treatment, as well as at the forging step. For this reason, analysis of the curvature of the shaft at various stages of the technology is needed. This paper deals with the modeling of elastic-plastic bending of crankshafts during heat treatment after forging. Present work is dedicated to heat treatment after forging. The aim of the paper is to develop a model and finite element (FE) software to simulate the elastic-plastic deformation of the shaft due to thermal expansion and dilatometric effect caused by phase transformations. Shaft material model is developed and the elastic-plastic characteristics are implemented in the FE code. Heat exchange with the cooling medium, dependence of thermal properties on temperature, and heat of phase transformations are accounted for in a solution of the thermal problem. Dilatometric tests are performed to supply data for identification of the phase transformation model. The method of estimation of the curvature of the shaft with one design variable is proposed. This allows to perform optimization of heat treatment in order to reduce the curvature of the shaft. The calculations are performed for several modes of the heat treatment. It is shown that in the presence of phase transformations, cooling process is accompanied by a three-time changing of stress sign and the direction of bending of the crankshaft, which is due to the nonlinearity of thermal deformation during the phase transformations.
Mathematical model of small-diameter wires extrusion from biocompatible MgCa08 (Mg -0.8% Ca) magnesium alloy was developed in the current paper in order to determine window of allowable technological parameters. Compression and tensile tests were carried out within temperature range 250-400• C and with different strain rates to determine the fracture conditions for the studied alloy. Finite element (FE) analysis was used to predict the billet temperature evolution and material damage during processing. The extrusion model takes into account two independent fracture mechanisms: a) surface cracking due to exceeding of the incipient melting temperature and b) utilization of material formability. FE simulations with different initial billet temperatures and pressing speeds were performed in order to determine the extrusion limit diagram (ELD) for MgCa08 magnesium alloy. The developed ELD was used to select the parameters for the direct extrusion of wires with diameter of 1 mm. Then, the extrusion of twelve wires was conducted at 400• C with pressing speed 0.25 mm/s. It was reported that the obtained wires were free from defects, which confirmed the good agreement between numerical and experimental results.Keywords: magnesium alloys, extrusion, ductile fracture, FE analysis W pracy zaproponowano model matematyczny procesu wyciskania prętów o małych średnicach z biokompatybilnego stopu magnezu MgCa08 (Mg -0.8% Ca). Na podstawie opracowanego modelu możliwy jest dobór parametrów technologicznych rozpatrywanego procesu. Model procesu wyciskania zawiera model do prognozowania utraty spójności materiału, który został opracowany w oparciu o próby spęczania oraz jednoosiowego rozciągania w zakresie temperatur 250-400• C dla różnych pręd-kości odkształcenia. W oparciu o metodę elementów skończonych (MES) przeprowadzona została analiza numeryczna rozkładu temperatury oraz wskaźnika wykorzystania odkształcalności materiału w procesie wyciskania. Zaproponowany model zawiera dwa możliwe mechanizmy utraty spójności: a) wynikający z lokalnego przekroczenia temperatury topnienia, b) wynikający z wyczerpania zapasu plastyczności. W oparciu o przeprowadzoną analizę MES procesu wyciskania dla różnych temperatur oraz prędkości wyciskania opracowano diagram ELM (extrusion limit diagram) dla stopu MgCa08. Na podstawie opracowanego diagramu ELM dobrano parametry procesu wyciskania prętów o średnicy 1 mm. Weryfikację modelu procesu wyciskania dla stopu MgCa08 wykonano w warunkach laboratoryjnych, gdzie przeprowadzono dwunasto żyłowy proces wyciskania prętów w temperaturze 400• C i prędkości 0.25 mm/s. Otrzymane pręty były wolne od wad, co potwierdziło dobrą zgodność pomiędzy wynikami numerycznymi i eksperymentalnymi.
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