Dimitri Debruyne

Precise determination of the Poisson ratio in soft materials with 2D digital image correlation

In this article, we demonstrate the application of digital image correlation (DIC) in evaluating the strains and Poisson ratio of a range of soft materials in terms of their spatial and temporal resolutions. Homogeneous samples of polydimethylsiloxane (PDMS) elastomer were used as control substance and were measured to have Poisson ratios of 0.498, 0.503, 0.500, and 0.499, in agreement with the reported incompressible value of 0.50. Two carbon nanotube (CNT) elastomer composites of identical composition, but one of a homogeneous and the other of a highly inhomogeneous CNT distribution, were used to determine the spatial resolution with good results. The relaxation of a polydomain liquid crystal elastomer (3D-LCE), a cholesteric liquid crystal elastomer (CLCE), and a polyacrylamide gel (PAAm) in water, were used to determine the temporal resolution of the technique. A video at 25 fps was used to evaluate the time dependence of the 3D-LCE over which time an increase in the Poisson ratio was observed. The 3D-LCE relaxes from its initial state at 0.42 to 0.50, converging towards incompressibility at equilibrium. The CLCE was found to have a similar initial value of 0.44 but converged to ∼0.60, a consequence of its anisotropic elastic nature. PAAm gel relaxation in water was studied over a time period of 7 hours with digital images taken periodically every minute. Its Poisson ratio was found to decrease smoothly from 0.50 to 0.26, with an accompanying reduction in force. The equilibrium result compares well to the 0.25 value predicted by a theory of the strain-induced swelling of dilute gels. In summary, we find DIC to be a powerful and easy to implement method of accurately measuring local strains in a range of soft materials.

Full-field optical deformation measurement in biomechanics: Digital speckle pattern interferometry and 3D digital image correlation applied to bird beaks

In this paper two easy-to-use optical setups for the validation of biomechanical finite element (FE) models are presented. First, we show an easy-to-build Michelson digital speckle pattern interferometer (DSPI) setup, yielding the out-of-plane displacement. We also introduce three-dimensional digital image correlation (3D-DIC), a stereo photogrammetric technique. Both techniques are non-contact and full field, but they differ in nature and have different magnitudes of sensitivity. In this paper we successfully apply both techniques to validate a multi-layered FE model of a small bird beak, a strong but very light biological composite. DSPI can measure very small deformations, with potentially high signal-to-noise ratios. Its high sensitivity, however, results in high stability requirements and makes it hard to use it outside an optical laboratory and on living samples. In addition, large loads have to be divided into small incremental load steps to avoid phase unwrapping errors and speckle de-correlation. 3D-DIC needs much larger displacements, but automatically yields the strains. It is more flexible, does not have stability requirements, and can easily be used as an optical strain gage.

Identification of Post-Necking Hardening Behaviour of Sheet Metal: a Practical Application to Clinch Forming

Clinching is a mechanical joining technique which involves severe local plastic deformation of two or more sheet metal parts resulting in a permanent mechanical interlock or joint. The required forming load and energy can be determined with the aid of the finite element method. However, a good knowledge of the elasto-plastic properties is of utmost importance to perform a sufficiently accurate simulation. This paper presents two alternative material tests to identify the hardening behaviour of sheet metal beyond the point of maximum uniform elongation. In addition, the material tests were applied to DC05 and the identified material behaviour is evaluated through the prediction of the forming load during clinching.

Assessment of Measuring Errors in Strain Fields Obtained via DIC on Planar Sheet Metal Specimens with a Non-Perpendicular Camera Alignment

The determination of strain fields based on displacement components obtained via 2D-DIC is subject to several errors that originate from various sources. In this contribution, we study the impact of a non-perpendicular camera alignment to a planar sheet metal specimen’s surface subject to biaxial loading conditions. The errors are estimated in a numerical experiment. To this purpose, deformed images - that were obtained by imposing finite element (FE) displacement fields on an undeformed image - are numerically rotated for various Euler angles. It is shown that a 3D-DIC stereo configuration induces a substantial compensation for the introduced image-plane displacement gradients. However, higher strain accuracy and precision are obtained - up to the level of a perfect perpendicular alignment - in a proposed ”rectified” 2D-DIC setup. This compensating technique gains benefit from both 2D-DIC (single camera view, basic amount of correlation runs, no cross-camera matching nor triangulation) and 3D-DIC (oblique angle compensation).

Digital Image Correlation in the Classroom: Determining Stress Concentration Factors with Webcams

In this study, we introduce graduate students to an experiment with digital image correlation (DIC). From an educational point of view, the aim is to get students familiar with basic aspects of stereovision and DIC, for example, speckle pattern, subset size, focus, aperture, etc. First, a homogeneous uniaxial tensile test is conducted on a rubber dogbone, allowing the determination of the hyperelastic stress—strain relationship. Next, a nondestructive 2D deformation test on a rubber specimen with a specific geometry is performed on a small tensile setup. At various load steps, images are captured with a low-cost webcam and are processed with our in-house DIC software which is available for each individual student. Assuming a Mooney—Rivlin material model based on the determined stress—strain data, one can derive stress concentration factors for the specific holes and notches present in the specimen. A comparison is made to analytical calculations of the stress concentration factors and eventually a finite element analysis of the experiment can be performed. In this way, a synergy between experiment, simulation, and theoretical calculations is achieved. Moreover, we have accomplished all stages in the engineering process of determination of material properties, simulation, and validation. The particular experimental setup is chosen to avoid the use of special equipment, for example, sophisticated tensile devices and expensive high-tech cameras, without losing the focus of the objective.

Anisotropic yield surface identification of sheet metal through stereo finite element model updating

Finite element model updating is a powerful technique to inversely identify material behaviour. A profound understanding of plastic anisotropy of sheet metal is crucial in controlling complex sheet forming applications through finite element simulations. In this contribution, a generic stereo finite element model updating approach combining stereo digital image correlation and finite element model updating is described to identify the plastic anisotropy of sheet metal DC06 which is represented by Hill’s 1948 yield criterion. The feasibility of stereo finite element model updating is illustrated by applying the proposed method to an Erichsen bulging test. Additionally, it is found that the unknown friction coefficient between the punch and the sheet can be simultaneously identified. Finally, the reliability of the identified parameters is scrutinized.

Advanced Test Simulator to Reproduce Experiments at Small and Large Deformations

Full field measurements and inverse methods can be conveniently used to identify the constitutive properties of materials. Several methods are available in the literature which can be applied to many different types of materials and constitutive models (linear elasticity, elasto-plasticity, hyper-elasticity, etc.). The effectiveness of the identification procedure is related to the specimen geometry and the quality of the optical measurement technique. A method to improve and optimize the identification procedure is to numerically simulate the whole process. In such a way it is possible to compare different configurations and chose the one that shows the lowest identification error.

Sources of systematic errors in the determination of heterogeneous strain fields obtained via DIC

The determination of strain fields based on displacement ??elds obtained via DIC is subjected to several errors that originate from various sources. In this contribution, we focus on a triplet of these when substantial plastic deformation of the specimen is probed. First, attention is paid to errors that can be directly attributed to the derivation of the strain ??elds, e.g. the strain-window size and the strain-window interpolation order. Next, we focus on errors that arise from different implementations of the DIC technique. In particular, we investigate the in??uence of the shape function, the interpolation order and the subset size on the derived strains. A dynamic shape function criterion is developed that increases the transformation order according to the degree of heterogeneity. It is shown that the impact of the subset size on the derived strains persists, despite the fact that it is embodied in the noise of the displacement ??elds and should largely evaporate during the smoothing procedure. Finally, we study the impact of a non-perpendicular alignment of the camera on a planar specimen. To this purpose, we make a mutual comparison of 2D results obtained via a perpendicular and a non-perpendicular CCD, and a 3D evaluation of the stereo setup. In addition, we estimate the impact of a recti??cation of the images obtained via the non-perpendicular alignment.

Multi-axial Quasi-static Strength of a Clinched Sheet Metal Assembly

Conventionally, the mechanical behavior of clinched connections is investigated by a single shear lap test and/or a pull-out test. In practical applications, however, there is a strong probability that a combination of shear and pull-out components is exerted on the clinched joint. This paper deals with the development of an Arcan-like device which enables to introduce various shear/tensile ratio’s in a clinched sheet metal assembly. Since clinch forming locally results in a complex region, a good knowledge of the plastic material properties is of the utmost importance to perform a sufficiently accurate simulation. The identification of post-necking hardening behavior of sheet metal is complex and there is no general agreement on how to perform this. In this study, different methods are used to identify the post-uniform hardening behavior of DC05. The impact of these different procedures on the simulation of the multi-axial loading behavior of a so-called non-cutting single-stroke round clinched connection is investigated. The experimental results are used to check the validity of numerical models to predict the strength under multi-axial loading.

Determination of hardening behaviour and contact friction of sheet metal in a multi-layered upsetting test

This paper describes the identification of hardening parameters of DC05 sheet metal and contact friction coefficients using a multi-layered upsetting test (MLUT), the modified two specimen method (MTSM) and a finite element based inverse method. The MLUT is an alternative compression test that is based on the stacking of small circular specimens on top of one another. This test was designed in order to identify frictional and material behavior under severe local forging of sheet metal as encountered during a clinching operation. The MTSM is adopted in order to identify the friction coefficient between the tools and the stacked circular specimens which are cut from the base material by spark erosion. Next, the hardening behavior is identified inversely by combining the results of a MLUT and finite element simulations of the test setup. Finally, the results are compared with standard tensile tests and it is shown that the MLUT is a viable alternative for the identification of the local hardening behavior of sheet metal where standard test specimens cannot be prepared due to size limitations of the specimen.