An efficient numerical method for predicting the evolution of internal variables and springback in bending under tension at large strains

2013 ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeau-Ren Jeng
2012 ◽  
Vol 586 ◽  
pp. 302-305
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Li Hui Lang

The paper concerns with three-dimensional analysis of the process of bending under tension for incompressible, rigid viscoplastic material at large strains. The constitutive equations consist of the Mises-type yield criterion and its associated flow rule. No restriction is imposed on the dependence of the equivalent stress on the equivalent strain rate. The problem is reduced to evaluating ordinary integrals and solving transcendental equations.


2020 ◽  
Vol 321 ◽  
pp. 12028
Author(s):  
HOGREFE Katharina ◽  
BUZOLIN Ricardo ◽  
POLETTI María Cecilia

This work uses flow stresses obtained experimentally at different strain rates and temperatures to validate flow modelling results. Flow curves of Ti6Al4V are measured via torsion experiments with a Gleeble® 3800 up to effective strains of 8. A physically based model that describes the evolutions of microstructure and the flow stress in the β-phase field was developed. A model of continuous dynamic recrystallization (CDRX) based on the work of Gourdet and Montheillet [1] for aluminium alloys is combined in this work with elements taken from Kocks and Mecking [2]. The model consists of a detailed description of the microstructure, based on different dislocation density populations and grain boundaries. All these internal variables evolve according to a production and a recovery term correlated mathematically with the temperature and the strain rate. The modelled output variables besides the flow stress are the total, the interior and the wall dislocation densities as well as the subgrain and grain sizes developed by continuous dynamic recrystallization. The model describes the softening occurring during large strain deformations, which is partly produced by the formation of new high angle grain boundaries (HAGB). The fraction of HAGB was used to determine the recrystallization grade, validated with microstructural characterization.


Author(s):  
W.M. Stobbs

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.


Author(s):  
R.W. Carpenter ◽  
Changhai Li ◽  
David J. Smith

Binary Nb-Hf alloys exhibit a wide bcc solid solution phase field at temperatures above the Hfα→ß transition (2023K) and a two phase bcc+hcp field at lower temperatures. The β solvus exhibits a small slope above about 1500K, suggesting the possible existence of a miscibility gap. An earlier investigation showed that two morphological forms of precipitate occur during the bcc→hcp transformation. The equilibrium morphology is rod-type with axes along <113> bcc. The crystallographic habit of the rod precipitate follows the Burgers relations: {110}||{0001}, <112> || <1010>. The earlier metastable form, transition α, occurs as thin discs with {100} habit. The {100} discs induce large strains in the matrix. Selected area diffraction examination of regions ∼2 microns in diameter containing many disc precipitates showed that, a diffuse intensity distribution whose symmetry resembled the distribution of equilibrium α Bragg spots was associated with the disc precipitate.


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