Numerical study of the square cup stamping process: a stochastic analysis

The industrial demand for products with better quality and lower production costs have encouraged the widespread application of the finite element analysis (FEA) in the development and optimization of sheet metal forming processes. To ensure that the FEA solutions are reliable and robust it is important to take into account the uncertainties that inevitably arise in a real industrial environment. In this context, a numerical study on the influence of the material and process uncertainty in the stamping results of a square cup is presented. In this analysis, it is assumed uncertainty in the elasticity properties, hardening law parameters, anisotropy coefficients, blank thickness, friction coefficient and in the blank holder force. The effect of the uncertainty in these input parameters is evaluated in the punch force, equivalent plastic strain, thickness and cup geometry. Firstly, quasi-Monte Carlo method was used to evaluate the variability in the simulation outputs, considering the uncertainty of the input parameters. This analysis shows that the geometry is the output most sensitive to the uncertainty of the input parameters. Afterwards, a variance-based sensitivity analysis was carried out to identify the input parameters that most influence the output variability. It was concluded that the hardening law parameters and the anisotropy coefficients have the most influence in the stamping results variability of a square cup.

Prediction of Strain Limits via the Marciniak-Kuczynski Model and a Novel Semi-Empirical Forming Limit Diagram Model for Dual-Phase DP600 Advanced High Strength Steel

The prediction capability of a forming limiting diagram (FLD) depends on how the yield strength and anisotropy coefficients evolve during the plastic deformation of sheet metals. The FLD predictions are carried out via the Marciniak-Kuczynski (M-K) criterion with anisotropic yield functions for DP600 steel of various thicknesses. Then, a novel semi-empirical FLD criterion is proposed, and prediction capabilities of the criterion are tested with different yield criteria. The results show that the yield functions are very sensitive to anisotropic evolution. Thus, while the FLD curves from the M-K model and the proposed model are not the same for each thickness, the proposed model has better prediction than the M-K model.

Analysis of anisotropy in the upsetting process of AA2014 cast alloy embedded with fly ash

Developing new metal matrix composites for a wide variety of applications and analyzing the formability aspects are challenging in the area of manufacturing. In the current study, solid cylindrical samples with AA2014 as matrix material and fly ash as reinforcement were used for the investigation. AA2014 was heated to a pouring temperature of 750 ℃ and the preheated fly ash was added to the molten AA2014 in different compositions. The whole mixture was stirred to prepare composite rods of AA2014, AA2014 + 3% fly ash and AA2014 + 6% fly ash. Each set of cylindrical samples were compressed between a set of dies till fracture by employing grease, white grease and no lubrication conditions. The varying friction conditions and composition influence the anisotropy of the billets at fracture. Empirical equations were modeled to investigate the effect of anisotropy on the stress trixiality and fracture strain at the onset of fracture. The developed equation is useful in estimating critical damage constants for any material and for any lubrication condition. A correlation between damage anisotropy factor, damage constant and fracture strain was established to understand the formability limits for different anisotropy coefficients.

Moment tensors of double-couple microseismic sources in anisotropic formations

Moment tensors of kinematically double-couple microseismic events triggered in anisotropic formations are known to exhibit non-double-couple focal mechanisms. The weak anisotropy approximation of these mechanisms reveals the combinations of anisotropy coefficients of vertically transversely isotropic and orthorhombic focal regions responsible for the deviations of moment tensors from double couples. Numerical examples for models of typical unconventional shales indicate the non-double-couple components of moment tensors to be sufficiently large to cause misinterpretation of the nature of ruptures associated with hydraulic fracturing.

Генерация второй гармоники от тонкого цилиндрического слоя. III. Условия отсутствия генерации

More than 50 different combinations are given for parameters of the problem of second harmonic generation by a plane electromagnetic elliptically polarized wave from a thin optical layer on the surface of cylindrical particle, in which the generation from the lateral surface cannot be observed. Also, 18 combinations of parameters are found, in which generation from the end surfaces of the cylindrical particle is not observed. More than 30 problem parameter combinations are given, in which linearly polarized second harmonic radiation is generated from the side surface (or from the end surfaces). The combinations of problem parameters are indicated, at which generation from the entire surface of the cylindrical particle cannot be observed, and also parameter combinations at which the generation has linear polarization. A method is proposed for determining the anisotropy coefficients on the base of the properties above.

Механическая и динамическая стабильность комплектного и нестехиометрического 3C-Si-=SUB=-x-=/SUB=-C-=SUB=-y-=/SUB=- из ab initio расчетов

The energies of formation of vacancies in the carbon and silicon sublattices, the independent elastic constants, the all-round compression, shear and Young’s moduli, and the anisotropy coefficients are determined for the complete and nonstoichiometric cubic phases of 3 C -Si_ x C_ y ( x , y = 1.0–0.75) by ab initio methods of the band theory. In the formalism of the density functional perturbation theory (DFPT), the phonon dispersion dependences are obtained for these phases (the comparison with the experiment is given for the complete phase). It is shown that the mechanical characteristics of the phases become strongly anisotropic upon the transition from 3 C -SiC_0.875 to 3 C -SiC_0.75. It is established from the analysis of the phonon dispersion curves that the 3 C -SiC_0.875 and 3 C -SiC_0.75 phases, in contrast to the complete 3 C -SiC phase, are dynamically unstable at T = 0 K.

Application of Barlat Yld-96 Yield Criterion for Predicting Formability of Pre-Strained Dual Phase Steel Sheets

The selection of advanced material model considering the anisotropy mechanical properties of the thin sheet is vital in order to estimate stress based forming limit diagram (σ-FLD). In present study associative plasticity theory was applied indulging Barlat Yld-96 anisotropy yield function and the Swift hardening law was implemented for estimating the limiting stresses from the conventional strain FLD (ε-FLD) of an automotive grade dual phase steel DP600. Three different approaches were made to evaluate Yld-96 anisotropy coefficients using experimental results of stack compression and tensile tests. To impose complex strain path, two stage stretch forming processes were simulated in finite element solver LS-DYNA. After biaxial pre-straining, the sample geometries were varied to achieve different strain paths during the second stage of deformation. The results indicated that there was negligible difference in limiting stress estimated by Yld-96 plasticity theory when the anisotropy coefficients were calculated based on plastic strain at ultimate tensile strength compare to that by minimum plastic work method. It was concluded that the dynamic shift of ε-FLD could be restricted by σ-FLD estimated using Yld 96 plasticity theory, and hence it was proposed to be a suitable damage model to evaluate formability of pre-strained DP600 steels.

Effect of Strain on the Anisotropy Coefficient of Sheet Alloys AA2024, Ti-2Al-1Mn, Titanium Grade 2, STEEL X10CrNiTi18-9

Anisotropy of the plastic properties is an index of sheet’s ability to stamping. In this work the transverse deformation coefficient and r-value were used. Uniaxial test was made for annealed pieces of 1 mm thickness from aluminum alloy AA2024, steel X10CrNiTi18-9, Titanium Grade 2 and titanium alloy Ti-2Al-1Mn. Pieces were cut at angle of 0, 22.5, 45, 67.5 and 90O to the rolling direction. Steel pieces have anisotropy coefficients practically independent from angle between it’s’ axis and the rolling direction. Pieces made of AA2024 cut at angle 45О to the rolling direction have largest anisotropy coefficients. Titanium alloys have the largest coefficients for angle 67,5О between axis of piece and the rolling direction. Both indexes of anisotropy are higher for titanium alloys, which is property of HCP-metals.