Evaluation of stresses in a combined plane strain-simple shear test

A biaxial testing device for sheet metal has been developed that can impose a combination of\ud plane strain and simple shear deformation. The specimen has a large width to height ratio and a small height\ud to thickness ratio. The forces in tensile and shear direction are easily measured and the tensile stress and shear\ud stress can easily be derived. For a full description of stresses, however, the stress in lateral direction should also\ud be known. This stress is a result of the constraint, imposed by the large width to height ratio and cannot be\ud measured directly. The strain in the specimen is measured on the surface. By imposing the Drucker normality\ud principle, the direction of the tangent to the yield surface is known and the unknown stress increment in lateral\ud direction can be obtained. Computer simulations are performed to test whether the intended approach can\ud recalculate all stress components from measurement of 3 in-plane strains and just 2 stresses. Without hardening,\ud good results are obtained for a complete interval between the pure shear point up to a point between uniaxial\ud stress and the plane strain point on the yield locus. With hardening, the algorithm requires a lot of data points\ud to avoid drifting from the exact solution. It is noted that, although the normality rule is used, it is not necessary\ud to have an a-priori knowledge of the yield functio

The construction of confidence intervals for frequency analysis using resampling techniques: a supplementary note

International audienceIn a recent contribution, Hall et al. (2004) examined the use of the Bootstrap resampling technique as a means of constructing confidence limits for the quantiles of the (two-parameter) Gumbel and the (three-parameter) Weibull distributions. Particular emphasis was placed on the behaviour of sample sizes of the order of 30, which are typical of those encountered in hydrological frequency analysis. The resampled confidence limits obtained for the Gumbel distribution were found to be comparable with those based upon a well-known theoretical approximation. However, those for samples of size 30 from the Weibull distribution were shown to be more problematical, with the results dependent upon the skewnesses of the resampled distributional parameters. For a further and more quantitative assessment of the suitability of Bootstrap resampling for constructing confidence intervals, so-called coverage rates were evaluated for the Weibull distribution in a supplementary study. The results show a satisfactory performance when using the percentile method but do not really mitigate the conclusion of the original study that resampled confidence limits should be employed with caution when sample sizes are of the order of 30. Keywords: Bootstrap, Jack-knife, frequency analysis, maximum likelihood method, maximum product of spacings method, confidence intervals, coverage rate

Improvements in FE-analysis of real-life sheet metal forming

An overview will be presented of recent developments concerning the application\ud and development of computer codes for numerical simulation of sheet metal forming\ud processes. In this paper attention is paid to some strategies which are followed to improve the\ud accuracy and to reduce the computation time of a finite element simulation. Special attention\ud will be paid to the mathematical modeling of the material deformation and friction, and the\ud effect of these models on the results of simulations. An equivalent drawbead model is\ud developed which avoids a drastic increase of computation time without significant loss of\ud accuracy. The real geometry of the drawbead is replaced by a line on the tool surface. When\ud an element of the sheet metal passes this drawbead line an additional drawbead restraining\ud force, lift force and a plastic strain are added to that element. A commonly used yield\ud criterion for anisotropic plastic deformation is the Hill yield criterion. This description is not\ud always sufficient to accurately describe the material behavior. This is due to the\ud determination of material parameters by uni-axial tests only. A new yield criterion is\ud proposed, which directly uses the experimental results at multi-axial stress states. The yield\ud criterion is based on the pure shear point, the uni-axial point, the plane strain point and the\ud equi-biaxial point

The construction of confidence intervals for frequency analysis using resampling techniques

International audienceResampling techniques such as the Bootstrap and the Jack-knife are generic methods for the estimation of uncertainties in statistics. When applied in frequency analysis, resampling techniques can provide estimates of the uncertainties in both distribution parameters and quantile estimates in circumstances in which confidence limits cannot be obtained theoretically. Test experiments using two different parameter estimation methods on two types of distributions with different initial sample sizes and numbers of resamples has confirmed the utility of such methods. However, care is necessary in evaluating the skewness of the resampled quantiles, especially with small initial sample sizes. Keywords: Bootstrap, Jack-knife, frequency analysis, maximum likelihood method, maximum product of spacings metho