François Hild

Multiscale displacement field measurements of compressed mineral-wool samples by digital image correlation.

We propose a multiscale approach to determine the displacement field by digital image correlation. The displacement field is first estimated on a coarse resolution image and progressively finer details are introduced in the analysis as the displacement is more and more securely and accurately determined. Such a scheme has been developed to increase the robustness, accuracy, and reliability of the image-matching algorithm. The procedure is used on two different types of examples. The first one deals with a representative image that is deformed precisely and purposefully to assess the intrinsic performances. In particular, the maximum measurable strain is determined. The second case deals with a series of pictures taken during compression experiments on mineral-wool samples. The different steps ofthe procedure are analyzed and their respective role is assessed. Both reflection and transmission images are tested.

Digital image correlation used to analyze the multiaxial behavior of rubber-like materials

We present an experimental approach to discriminate models describing the mechanical behavior of polymeric materials. A biaxial loading condition is obtained in a multiaxial testing machine. An evaluation of the displacement field obtained by digital image correlation allows us to evaluate the heterogeneous strain field observed during these tests. We focus on the particular case of hyper-elastic models to simulate the behavior of a rubber-like material. Different expressions of hyper-elastic potential are used to model experiments under uniaxial and biaxial loading conditions.

Analysis of a Multiaxial Test on a C/C Composite by Using Digital Image Correlation and a Damage Model

The “planar” digital image correlation technique needs a single CCD camera to acquire the surface patterns of a zone of a specimen in the underformed and deformed states. With these two images, one can determine in-plane displacement and strain fields. The digital image correlation technique used herein is based on Fast Fourier Transforms, which are very effective in reducing the computation cost. Its performance is assessed and discussed on artificial signals and in a real experimental situation. The technique is utilized to analyze experimental results of a plane shear experiment and validate a damage meso-model describing different degradations in a C/C composite material.

A damage model for the dynamic fragmentation of brittle solids

Impact produces high stress waves leading to the degradation of brittle materials such as ceramics. Based on a probabilistic approach, single and multiple fragmentation regimes are exhibited. The deterministic nature of the numerical simulation is discussed with respect to stress rate and volume. A damage model is proposed to account for dynamic loadings. Characteristic parameters are proposed and used to choose the mesh size. The mesh sensitivity is studied on a spalling configuration. Numerical predictions are compared with experimental data obtained on Edge-On Impact configurations.

Integrated Digital Image Correlation for the Identification of Mechanical Properties

Digital Image Correlation (DIC) is a powerful technique to provide full-field displacement measurements for mechanical tests of materials and structures. The displacement fields may be further processed as an entry for identification procedures giving access to parameters of constitutive laws. A new implementation of a Finite Element based Integrated Digital Image Correlation (I-DIC) method is presented, where the two stages (image correlation and mechanical identification) are coupled. This coupling allows one to minimize information losses, even in case of low signal-to-noise ratios. A case study for elastic properties of a composite material illustrates the approach, and highlights the accuracy of the results. Implementations on GPUs (using CUDA) leads to high speed performance while preserving the versatility of the methodology.

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

Abstract 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 10 0 /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.

On the probabilistic–deterministic transition involved in a fragmentation process of brittle materials

Dynamic loadings produce high stress waves leading to the fragmentation of brittle materials such as ceramics, concrete, glass and rocks. The main mechanism used to explain the change of the number of fragments with stress rate is a shielding phenomenon. However, under quasi-static loading conditions, a weakest link hypothesis may be applicable. Therefore, depending on the local strain or stress rate, different fragmentation regimes are observed. One regime corresponds to single fragmentation for which a probabilistic approach is needed. Conversely, the multiple fragmentation regime may be described by a deterministic approach. The transition between the two fragmentation regimes is discussed for high performance concrete, glass and SiC ceramics.

Dynamic Fragmentation of Brittle Solids: A Multi-Scale Model

Modeling dynamic fragmentation of brittle materials usually implies to choose between a discrete description of the number of fragments and a continuum approach with damage variables. A damage model that can be used in the whole range of loadings (from quasi-static to dynamic ones) is developed. The deterministic or probabilistic nature of fragmentation is discussed. Qualitative and quantitative validations are given by using a real-time visualization configuration for analyzing the degradation kinetics during impact and a moire technique to measure the strains in a ceramic tile during impact. Finally, a closed-form solution of the change of the number of broken defects with the applied stress gives a way of optimizing the microstructure of ceramics for armor applications.

A Probabilistic Damage Model of the Dynamic Fragmentation Process in Brittle Materials

Abstract Dynamic fragmentation is observed in brittle materials such as ceramics, concrete, glass, or rocks submitted to impact or blast loadings. Under such loadings, high-stress-rate tensile fields develop within the target and produce fragmentations characterized by a high density of oriented cracks. To improve industrial processes such as blast loadings in open quarry or ballistic efficiencies of armors or concrete structures against impact loadings, it is essential to understand the main properties of such damage processes (namely, characteristic time of fragmentation, characteristic density, orientation and extension of cracking, ultimate strength) as functions of the loading rate, the size of the structure (or the examination volume), and the failure properties of the brittle material concerned. In the present contribution, the concept of probability of nonobscuration is developed and extended to predict the crack density for any size, shape of the loaded volume, stress gradients, and stress rates. A closed-form solution is used to show how a brittle and random behavior under quasi-static loading becomes deterministic and stress rate dependent with increasing loading rates. Two definitions of the tensile strength of brittle materials are proposed. As shown by Monte Carlo simulations, for brittle materials, the “ultimate macroscopic strength” applies under high loading rate or in a large domain, whereas the “mean obscuration stress” applies under low stress rate or in a small domain. Next, a multiscale model is presented and used to simulate damage processes observed during edge-on impact tests performed on an ultra-high-strength concrete. Finally, the fragmentation properties predicted by modeling of six brittle materials (dense and porous SiC ceramics, a microconcrete, an ultra-high-strength concrete, a limestone rock, and a soda-lime silicate glass) are compared.

An extended and integrated digital image correlation technique applied to the analysis of fractured samples The equilibrium gap method as a mechanical filter

To reduce the measurement uncertainty, a measurement technique is proposed for estimating full displacement fields by complementing digital image correlation with an additional penalization on the distance between the estimated displacement field and its projection onto the space of elastic solutions. The extended finite element method is used for inserting discontinuities independently of the underlying mesh. An application to the brittle fracture of a silicon carbide specimen is used to illustrate the application. To complete the analysis, the crack tip location and the stress intensity factors are estimated. This allows for a characterization of the measurement and identification procedure in terms of uncertainty.