By Wiktor Gambin (auth.)
The classical, phenomenological idea of plastically anisotropic fabrics has handed some distance: from the paintings of von Mises offered in 1928, and the HilI formula given in 1948, to the newest papers on huge elastic-plastic deformations of anisotropic steel sheets. A attribute function of this process is a linear circulate rule and a quadratic yield criterion. Mathematical simplicity of the speculation is a cause of its a variety of functions to the research of engineering buildings in the course of the onset of plastic deformations. even though, such an method isn't really enough for description of the steel forming procedures, while a steel point undergoes very huge plastic traces. If we take an before everything isotropic piece of steel, it turns into plastically anisotropic through the forming method, and the prompted anisotropy gradually raises. This truth strongly determines instructions of plastic stream, and it results in an unforeseen pressure localization in sheet components. to give an explanation for the above, it is crucial take into consideration a polycrystalline constitution of the steel, plastic slips on slip platforms of grains, crystallographic lattice rotations, and eventually, a formation of textures and their evolution throughout the complete deformation procedure. briefly, it is crucial to introduce the plasticity of crystals and polycrystals. The polycrystal research exhibits that, whilst the complex plastic lines ensue, a few privileged crystallographic instructions, referred to as a crystallographic texture, ensue within the fabric. the feel formation and evolution are a major cause of the brought about plastic anisotropy in natural metals.
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Sample text
The seeond case of hardening is the kinematie hardening. The shift of the yield surface during the plastic yielding process is known as the Bausehinger effeet. To 39 ANISOTROPIC PLASTICITY deseribe it, we must introduee a shift tensor aij' and to use as the argument deseribing the surfaee, the quantity (Tij - a i j instead of aij' Evolution laws for Uij assume that its inerement is proportional to a ij as it was proposed by MELAN [65], or to aeeording to Prager's suggestion [66], or to a ij - a i j due to ZIEGLER'S [67] proposition.
10). Notiee that an arbitrary process of plastie deformation may be eonsidered as a eertain trajectory in the plastie strain space. 10), is proportional to the length of the eorresponding trajectory in the plastie strain space. 29) '0 is the ODQVIST parameter [71]. The above parameter is very eonvenient for deseription of the isotropie strain-hardening for plastieally isotropie materials. 27). 31) Then, in the ease of plastieally anisotropie materials, we have always to do with the work-hardening.
The multiplier Al must be non-negative. The restriction Al ~ O. 67) that the dissipation of plastic energy is non-negative, and from the condition - that CT/lH/lIrICTIrI is always positive. 73). namely (2,74) */ The approach suggested by 1. Rychlewski. 75) and it is weIl known as the plastic anisotropy tensor. In a general case, the tensor M /jld has 15 independent components. The structure and properties of this tensor have been investigated in many papers, starting from the fundamental work of VON MISES [6], through the works of OLSZAK and URBANOWSKI [7], SAWCZUK and BOEHLER [8], up to the recent papers by RYCHLEWSKI and co-workers [9].
