The forming limits of austenitic stainless steel sheets were studied. It was found that the observed limit of straining in stretch forming, when both of the principal stresses are positive, is not set by localized necking, but instead by shearing fracture in the through thickness direction. Thus, the Marciniak-Kuczynski type of analysis, which has recently been successfully applied to both low-carbon steels and aluminum, may not apply to austenitic stainless steels. It appears that the forming limits of austenitic stainless steels may be predicted fairly well by using the classical localized and diffuse necking criteria developed by Hill. The fracture criterion of Ritchie and Thompson seems to overestimate the fracture limit. Better models are needed for the work hardening and to develop better limit strain criteria, since the work hardening seems to depend strongly on both strain rate and temperature. The formability of austenitic stainless steels appears to remain good even when coated with hard TiN, although unavoidable cracks will appear with continuing straining.
PL
Przedmiotem pracy jest odkształcalność graniczna stali austenitycznych. Zaobserwowano, że odkształcalność przy dwuosiowym rozciąganiu, gdy dwa naprężenia główne są dodatnie, nie jest wyznaczana przez lokalne tworzenie się szyjki, ale przez pękanie wywołane przez ścinanie w kierunku grubości blachy. Dlatego metoda Marciniaka-Kuczynskiego, która jest z powodzeniem stosowana do stali nisko-węglowych i aluminium, może nie stosować się do stali austenitycznych. Okazuje się, że odkształcenia graniczne stali austenitycznych mogą być poprawnie przewidywane przez zastosowanie opracowanego przez Hilla klasycznego kryterium lokalizacji i rozprzestrzeniania się szyjki. Kryterium pękania Ritchie-Thompsona wydaje się przeszacowywać granicę pękania. Ponieważ umocnienie zależy mocno od prędkości odkształcenia i temperatury, lepsze modele są potrzebne do opisu umocnienia i opracowania poprawnego kryterium granicznych odkształceń. Odkształcalność graniczna stali austenitycznej utrzymuje się na dobrym poziomie nawet wtedy, gdy stal jest pokryta TiN, chociaż nieuniknione pęknięcia pojawią się w czasie odkształcenia.
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W artykule zanalizowano wpływ doboru funkcji opisującej umacnianie plastyczne materiału na ocenę wielkości odkształceń granicznych przy wyznaczaniu granicznej krzywej tłoczności blach. Oprócz znanych w analizach obróbki plastycznej funkcji umacniania wprowadzono - na podstawie wyników prób doświadczalnych rozciągania cienkich blach - opis uwzględniający obszar występowania stałej siły. Dla zaproponowanego modelu przedstawiono wzory do obliczeń i przykłady wykresów parametrycznych granicznych odkształceń.
EN
In this study there was performed the analysis of choice of the function describing strain hardening of raw materials on limit deformation size evaluation, during drawability limit curve tracing for metal sheets. Besides of strengthening functions analysis that are well known in plastic forming (Nadaj, Swift, Ludwik) influencing the thin steel sheets bumping test results, the descrip-tion of the occurrance of the constant force up to bittle state, has been also given. For proposed model the calculation formulas and examples of parameter diagrams of limit deformation with strain paths are presented.
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This paper highlights the basic characteristics of magnesium related to forming at elevated temperatures. The paper is divided into three sections. In the first section basic characteristics and applications of magnesium alloys are discussed, after then the focus is diverted to pre-processing and post-processing parameters including punch force, blank holder force, texture conditions, thickness and temperature distributions during forming, and springback effects. In the last section improvements in formability are highlighted by referring to forming limit diagrams to compare magnesium’s performances with other alloys. By summarizing all these pre-processing and post-processing parameters directions are established to improve the formability of magnesium and guidance is provided for future research in this area.
W artykule przedstawiono wyniki badań właściwości wytrzymałościowych dla stopu aluminium AA 6061 wraz z symulacją numeryczną cienkiej struktury użebrowanej. Wyznaczono doświadczalnie podstawowe parametry wytrzymałościowe (E, Rm, Rp02, Agt), stałą materiałową K, wykładnik umocnienia n oraz krzywą odkształcalności granicznej. Wyznaczone właściwości zostały użyte do budowy modelu materiałowego w symulacjach numerycznych. Analizowano proces tłoczenia cienkiej struktury z dwoma żebrami, uwzględniając różne parametry technologiczne. Wyznaczono rozkłady odkształceń plastycznych na powierzchni struktury oraz grubości ścianek. Rozważano wpływ współ- czynnika tarcia oraz zastosowanej siły docisku na rezultaty tłoczenia.
EN
In the paper the strength test results for AA 6061 are presented together with numerical simulation of thin sheet panels with stiffening ribs. The basic strength parameters (E, Rm, Rp02, Agt), material constant K, strain-hardening coefficient n and forming limit curve were determined experimentally. The determined properties were used for definition of material model in numerical simulations. Forming process of thin sheet panels with two ribs taking into account different technological parameters was analysed. The plastic strain and thickness distributions were determined. The influence of friction condition and holding force on the forming process was investigated.
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This paper presents the numerical and experimental investigation of the incremental sheet forming (ISF) process with the Lemaitre damage model to incrementally form parts of conical shapes. The Lemaitre damage model was prepared as a material subroutine (VUMAT) and linked to Abaqus/Explicit. The elastic–plastic parameters for the simulation were identified through tensile testing of the ASTM E8 specimen. The digital image correlation (DIC) was performed during the tensile testing to identify the damage parameters of the Lemaitre damage model. Scanning electron microscopy (SEM)-based area method was used to identify the area fraction vis-a-vis the variation of the strain. Thereafter, the identified area fractions with respect to strains have been calibrated to obtain the damage parameters through an inverse analysis approach. The identified parameters were used to form conical objects of Al1050 H14 sheets of 2 mm thickness through finite element (FE) simulation. The results obtained through FE simulation were compared with the experimental outcomes to investigate the efficiency of the Lemaitre damage model to simulate the ISF process. The responses obtained through FE simulation and experiments have been discussed in terms of limiting wall angle and forming depth, damage evolution, deformation mechanism, forming limit diagram, geometrical accuracy, forming forces, thickness distribution, and surface roughness.
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This paper presents an investigation on the detection of strain localization in numerical simulation of sheet metal forming. Two methods to determine the onset of localized necking have been compared. The first criterion, newly implemented in this work, is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method, studied in the authors’ earlier works, is determined by the maximum of the strain acceleration. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. This has allowed to construct numerical forming limit curves (FLCs). The numerical FLCs have been compared with the experimental one. Mesh sensitivity analysis for these criteria has been performed for the selected specimens. It has been shown that the numerical FLC obtained with the new criterion predicts formability limits close to the experimental results so this method can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes.
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This paper presents the results of numerical simulations of the formability tests carried out for a pre-stretched 1 mm thick DC04 steel sheet. Simulation consisted of the subsequent stages as follows: uniaxial stretching of the sheet, unloading and stress relaxation, cutting specimens out of the pre-stretched sheet and bulging the blank with a hemispherical punch. Numerical modeling has been verified by comparison of the simulation results with the experimental ones. Good concordance of the results indicates correct performance of the numerical model and possibility to use it in further theoretical studies.
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Failure in sheet metal forming can occur by necking, fracture or wrinkling. By using a forming limit diagram (FLD) as a powerful tool to prevent sheets metal failures in the forming process, provides parameters controlling throughout forming. There are different developed methods for predicting FLDs, which estimate sheet metal forming strains limits. Assessment of FLD estimation reveals that there is a dependency between the effect of several factors containing normal stress, shear stress, sheet thickness, mechanical properties, metallurgical properties, yield function, strain path, and bending with formability. In this research, the effects of bending via two finite element models are investigated. In the first method, the out-of-plane deformation is applied by increasing punch displacement to study the effects of bending. In the second method, the effect of bending is investigated via changing punch diameter (25, 50, 70 and, 100 mm). The Marciniak–Kuczynski (M–K) theory is used to predict the time of localized necking in finite element simulations. Furthermore, a novel method for the determination of the inhomogeneity coefficient is presented in M–K model to simulate the groove width for M–K model. To verify finite element simulation results, Nakazima tests with 50 and 100 mm punch diameters were done as experimental studies. The comparison of experimental results and finite element analysis illustrates that the increasing bending or the out-of-plane loading can improve formability. At the end, the effect of bending on FLD is reported as an equation based on minor and major strains.
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