Macro modelling and homogenization for transformation induced plasticity of a low-alloy steel

Metal forming processes are important technologies for the production of engineering structures. In order to optimize the resulting material properties, it becomes necessary to simulate the entire forming process by taking into account physical effects such as phase transformations. In this work, we concentrate on the phase change from austenite to martensite and present a macroscopic material model, which combines the effect of classical plasticity with the effect of transformation induced plasticity (TRIP). An extensive experimental database for a low-alloy steel is used for parameter identification, thus taking into account the effects of uniaxial compressive and tensile stress on the kinetics of phase transformation at different temperatures. For temperatures below the martensite start temperature with simultaneous stresses above the yield limit, it is difficult to obtain experimental data. Consequently, a numerical homogenization technique is employed for this case. In a further part of this paper, an effective integration scheme is provided, which is implemented into a commercial finite element program. In a finite element simulation, the austenite to martensite phase transformation in a shaft subjected to thermal loading is investigated.     

13C-NMR.-Substituenteninkremente der N3-Gruppe in Azido-1,4-benzochinonen

¹³C-NMR. Substituent Increments of the Azido-group in 1,4-Benzoquinones The empirical substituent increments of the azido-group in 1,4-benzoquinones have been derived from the ¹³C-NMR. chemical shifts of 2-azido-5-chloro-1,4-benzoquinone. The validity of the obtained values was tested by comparison of the empirical and computed ¹³C-NMR. chemical shifts of other azido-chloro-1,4-benzoquinones.     

13C-NMR.-Spektren von Dicyanhydrochinonen und Dicyan-p-benzochinonen

¹³C-NMR. Spectra of Dicyanohydroquinones and Dicyano-p-benzoquinones The ¹³C-NMR. spectra of 12 dicyanohydroquinones and fully substituted dicyano- and diazido-p-benzoquinones have been measured and assigned by comparison with related benzene and p-benzoquinone derivatives. For p-benzoquinones the influence of the cyano and azido substituents on the chemical shift of the CO-, α- and β-C-atoms has been investigated.     

The lagrange multiplier rule for multi-dimensional problems of optimal control

In this paper a modified form of Pontryagin's maximum principle is developed, which also holds for problems of optimal control with respect to functions of several independent variables.