Improving signal-to-noise by evaluation of correlation functions

Summary The autocorrelation function and the cross-correlation function are to be seen as valuable means for improving analytical measurements. The autocorrelation function describes the properties of noise and helps to detect errors at an early stage. By means of cross-correlation, very weak signals in a strong noise can be detected. In this way measurements below the normal limit of detection become possible. By using correlation functions strategies for carrying out analytical measurements advantageously can be derived.

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Verbesserung des Signal/Rausch-Verhältnisses durch Auswertung von Korrelationsfunktionen

Zusammenfassung Die Autokorrelationsfunktion und die Kreuzkorrelationsfunktion erweisen sich als wertvolle Werkzeuge zur Verbesserung analytischer Messungen. Die Autokorrelationsfunktion beschreibt die Eigenschaften des Rauschens und hilft, Fehler zu einem frühen Zeitpunkt zu entdecken. Mit Hilfe der Kreuzkorrelation können sehr schwache Signale in starkem Rauschen delektiert werden. Auf diese Weise werden Messungen unterhalb der normalen Nachweisgrenze möglich. Durch die Benutzung von Korrelationsfunktionen können Strategien für vorteilhafte analytische Messungen abgeleitet werden.

     

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10^?3 and 10⁰/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.     

Elastic-plastic behaviour of dual-phase, high-strength steel under strain-path changes

The elastic-plastic behaviour of dual-phase, high-strength steel sheets under two-stage strain-path changes has been investigated. Three different loading sequences, namely monotonic, 45° tensile path changes and orthogonal tensile path changes complied by sequences of simple uniaxial tensile tests, were analysed at room temperature. From the experiments, it was found that there is a considerable reduction of the initial flow stress over the strain-path changes. The transient softening phenomenon is observed to be a function of orientation, and the period of the transient behaviour following the strain-path change is lengthened with the amount of pre-strain. A constitutive model is adopted that includes combined isotropic and kinematic hardening and is capable of describing the marked transient softening behaviour after the pre-straining. The experimental stress–strain behaviour subsequent to the strain path change is predicted with reasonable accuracy, while the model fails to accurately describe the transient, deformation-induced anisotropy in the plastic flow.     

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

A Study of Large Plastic Deformations in Dual Phase Steel Using Digital Image Correlation and FE Analysis

Large plastic deformation in sheets made of dual phase steel DP800 is studied experimentally and numerically. Shear testing is applied to obtain large plastic strains in sheet metals without strain localisation. In the experiments, full-field displacement measurements are carried out by means of digital image correlation, and based on these measurements the strain field of the deformed specimen is calculated. In the numerical analyses, an elastoplastic constitutive model with isotropic hardening and the Cockcroft–Latham fracture criterion is adopted to predict the observed behaviour. The strain hardening parameters are obtained from a standard uniaxial tensile test for small and moderate strains, while the shear test is used to determine the strain hardening for large strains and to calibrate the fracture criterion. Finite Element (FE) calculations with shell and brick elements are performed using the non-linear FE code LS–DYNA. The local strains in the shear zone and the nominal shear stress-elongation characteristics obtained by experiments and FE simulations are compared, and, in general, good agreement is obtained. It is demonstrated how the strain hardening at large strains and the Cockcroft–Latham fracture criterion can be calibrated from the in-plane shear test with the aid of non-linear FE analyses. An erratum to this article can be found at