On the use of simulated experiments in designing tests for material characterization from full-field measurements

The present paper deals with the use of simulated experiments to improve the design of an actual mechanical test. The analysis focused on the identification of the orthotropic properties of composites using the unnotched Iosipescu test and a full-field optical technique, the grid method. The experimental test was reproduced numerically by finite element analysis and the recording of deformed grey level images by a CCD camera was simulated trying to take into account the most significant parameters that can play a role during an actual test, e.g. the noise, the failure of the specimen, the size of the grid printed on the surface, etc. The grid method then was applied to the generated synthetic images in order to extract the displacement and strain fields and the Virtual Fields Method was finally used to identify the material properties and a cost function was devised to evaluate the error in the identification. The developed procedure was used to study different features of the test such as the aspect ratio and the fibre orientation of the specimen, the use of smoothing functions in the strain reconstruction from noisy data, the influence of missing data on the identification. Four different composite materials were considered and, for each of them, a set of optimized design variables was found by minimization of the cost function.     

Full-Field Strain Measurement and Identification of Composites Moduli at High Strain Rate with the Virtual Fields Method

The present paper deals with full-field strain measurement on glass/epoxy composite tensile specimens submitted to high strain rate loading through a split Hopkinson pressure bar (SHPB) device and with the identification of their mechanical properties. First, the adopted methodology is presented: the device, including an Ultra-High Speed camera, and the experimental procedure to obtain relevant displacement maps are described. The different full-field results including displacement, strain and acceleration maps for two mechanical tests are then addressed. The last part of the paper deals with an original procedure to identify stiffnesses on this dynamic case only using the actual strain and acceleration maps (without the applied force) by using the Virtual Fields Method. The results provide very promising values of Young’s modulus and Poisson’s ratio on a quasi-isotropic glass-epoxy laminate. The load reconstructed from the moduli and strains compares favourably with that from the readings.     

Characterization of the post-necking strain hardening behavior using the virtual fields method

The present study aims at characterizing the post-necking strain hardening behavior of three sheet metals having different hardening behavior. Standard tensile tests were performed on sheet metal specimens up to fracture and heterogeneous logarithmic strain fields were obtained from a digital image correlation technique. Then, an appropriate elasto-plastic constitutive model was chosen. Von Mises yield criterion under plane stress and isotropic hardening law were considered to retrieve the relationship between stress and strain. The virtual fields method (VFM) was adopted as an inverse method to determine the constitutive parameters by calculating the stress fields from the heterogeneous strain fields. The results show that the choice of a hardening law which can describe the hardening behavior accurately is important to derive the true stress–strain curve. Finally, post-necking hardening behavior was successfully characterized up to the initial stage of localized necking using the VFM with Swift and modified Voce laws.     

Experimental Energy Balance During the First Cycles of Cyclically Loaded Specimens Under the Conventional Yield Stress

This paper, as an extension of Maquin and Pierron (Mech Mater 41(8):928–942, 2009), presents an experimental procedure developed to macroscopically estimate the energy balance during the very first cycles of a uniaxially loaded metallic specimen at low stress levels. This energy balance is performed by simultaneously measuring the plastic input energy using a load cell and a strain gauge, and the dissipative energy using the temperature field provided by an infrared camera. Some experimental limitations led to restrain the present procedure to positive stress ratios, and to complement this energy balance by a second measurement while the material plastic work per cycle is negligible compared to the dissipative energy. Some results obtained on a cold rolled low carbon steel specimen are presented. First, a sensitivity study is undertaken to precisely determine the detection threshold on both thermal and plastic energies. Then, after having verified the homogeneity of the dissipative source fields, energy balances have been performed at different stress levels. It was thus confirmed that the slow variations of the dissipative sources occurring during the first cycles are due to micro-plastic adaptation, and that the dissipative sources remaining after some hundreds of cycles are due to viscoelastic (internal friction) phenomena. This procedure provides a better understanding of dissipation based approaches to fatigue found in the literature and an advanced tool to study viscoelastic phenomena in uniaxial loading.     

Overview of Identification Methods of Mechanical Parameters Based on Full-field Measurements

This article reviews recently developed methods for constitutive parameter identification based on kinematic full-field measurements, namely the finite element model updating method (FEMU), the constitutive equation gap method (CEGM), the virtual fields method (VFM), the equilibrium gap method (EGM) and the reciprocity gap method (RGM). Their formulation and underlying principles are presented and discussed. These identification techniques are then applied to full-field experimental data obtained on four different experiments, namely (i) a tensile test, (ii) the Brazilian test, (iii) a shear-flexural test, and (iv) a biaxial test. Test (iv) features a non-uniform damage field, and hence non-uniform equivalent elastic properties, while tests (i), (ii) and (iii) deal with the identification of uniform anisotropic elastic properties. Tests (ii), (iii) and (iv) involve non-uniform strain fields in the region of interest. Working group “Identification” of the French CNRS research network (GDR 2519) “Mesures de champs et identification en Mécanique des Solides / Full-field Measurements and Identification in Solid Mechanics”.