Jérôme Molimard

Thin Film Colorimetric Interferometry

Measurement technique for the study of very thin lubrication films down to one nanometer in a point contact between a steel ball and a transparent disc is used to explore the relationship between central and minimum film thickness and rolling speed at the interface between elastohydrodynamic and boundary lubrication for a series of lubricating fluids. This technique based on the colorimetric interferometry combines powerful film thickness mapping capabilities with high accuracy. It was confirmed that both hexadecane and mineral base oil obey the linear relationship between log central and minimum film thickness and log rolling speed predicted by elastohydrodynamic theory down to approximately one nanometer. Conversely, squalane and additive-treated mineral base oil showed film thickness enhancement at slow speeds caused by boundary layers formation within the lubricant film. Obtained experimental data was used for the determination of pressure-viscosity coefficients of test fluids. The measurement technique also enabled us to produce information about the influence of boundary layers on film thickness shape. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Seattle, Washington, October 1–4, 2000

Identification of the four orthotropic plate stiffnesses using a single open-hole tensile test

The identification of mechanical parameters for real structures is still a challenge. With the improvement of optical full-field measurement techniques, it has become easier, but in spite of many publications showing the feasibility of such methods, experimental results are still scarce. In this paper we present a first step towards a global approach of mechanical identification for composite materials. The chosen mechanical test is an open-hole tensile test according to standard recommendations. For the moment, experimental data are provided by a moiré interferometry setup. The global principle of the identification developed in this paper is to minimize a discrepancy between experimental and theoretical results, expressed as a cost function, using a Levenberg-Marquardt algorithm. This approach has the advantage of having high adaptability, largely because the optical system, the signal processing as well as the mechanical aspects, can be taken into consideration by the model. In this paper we consider different types of cost functions, which are tested using an identifiability criterion. Although mechanically based cost functions have been studied, a simpler mathematical form is finally more efficient. Two different models were tested. The first is an analytical model based on the Lekhnitskii approach. This approach has the advantage of being a meshless solution; however, the results appeared to be partially false due to boundary effects, leading to a second approach, a classical finite element analysis. The resulting identified values are similar to values from classical mechanical tests (within 6%). which, in practice, validates our approach.

New tools for the experimental study of EDH and limit lubrications

Abstract Interferometry is a widely used technique in EHL. The classical processing on interferograms (see Gohar [1]) is, however no longer adequate for modern tribological conditions (for example tests on additives). A new image analysis technique has been developed for this purpose. This technique is based on white light interferometry and RGB description of colours, and it is described and validated below. The typical result is a 3D thickness map of the contact, established without any assumption on the fringe order. Tests are carried out thanks to a new device on a synthetic reference fluid for a thickness range from 20 to 600 nm. This overall approach shows that the image analysis technique is accurate to study very low film thickness. Such experimental tools could lead to studies on starvation, roughness or additive in the future.

Introduction to the Bayesian Approach Applied to Elastic Constants Identification

The basic formulation of the least-squares method, based on the L2 norm of the residuals, is still widely used today for identifying elastic constants of aerospace materials from experimental data. While this method often works well, methods that can benefit from statistical information, such as the Bayesian method, may sometimes be more accurate. We seek situations with significant difference between the material properties identified by the two methods. For a simple three-bar truss example we illustrate three situations in which the Bayesian approach systematically leads to more accurate results: different sensitivity of the measured response to the parameters to be identified, different uncertainty in the measurements, and correlation among response components. When all three effects add up, the Bayesian approach can be much more accurate. Furthermore, the Bayesian approach has the additional advantage of providing the uncertainty in the identified parameters.We also compare the two methods for a more realistic problem of identification of elastic constants from natural frequencies of a composite plate.

Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields

The ply elastic constants needed for classical lamination theory analysis of multi-directional laminates may differ from those obtained from unidirectional laminates because of three dimensional effects. In addition, the unidirectional laminates may not be available for testing. In such cases, full-field displacement measurements offer the potential of identifying several material properties simultaneously. For that, it is desirable to create complex displacement fields that are strongly influenced by all the elastic constants. In this work, we explore the potential of using a laminated plate with an open-hole under traction loading to achieve that and identify all four ply elastic constants (E1, E2, ν12, G12) at once. However, the accuracy of the identified properties may not be as good as properties measured from individual tests due to the complexity of the experiment, the relative insensitivity of the measured quantities to some of the properties and the various possible sources of uncertainty. It is thus important to quantify the uncertainty (or confidence) with which these properties are identified. Here, Bayesian identification is used for this purpose, because it can readily model all the uncertainties in the analysis and measurements, and because it provides the full coupled probability distribution of the identified material properties. In addition, it offers the potential to combine properties identified based on substantially different experiments. The full-field measurement is obtained by moiré interferometry. For computational efficiency the Bayesian approach was applied to a proper orthogonal decomposition (POD) of the displacement fields. The analysis showed that the four orthotropic elastic constants are determined with quite different confidence levels as well as with significant correlation. Comparison with manufacturing specifications showed substantial difference in one constant, and this conclusion agreed with earlier measurement of that constant by a traditional four-point bending test. It is possible that the POD approach did not take full advantage of the copious data provided by the full field measurements, and for that reason that data is provided for others to use (as on line material attached to the article).

Monitoring the resin infusion manufacturing process under industrial environment using distributed sensors

A novel direct approach to detect the resin flow front during the Liquid Resin Infusion process under industrial environment is proposed. To detect the resin front accurately and verify the results, which are deduced from indirect micro-thermocouples measurements, optical fiber sensors based on Fresnel reflection are utilized. It is expected that the results derived from both techniques will lead to an improvement of our understanding of the resin flow and in particular prove that micro-thermocouples can be used as sensors as routine technique under our experimental conditions. Moreover, comparisons with numerical simulations are carried out and experimental and simulated mold filling times are successfully compared.

Demodulation of spatial carrier images: Performance analysis of several algorithms using a single image

Optical full-field techniques have a great importance in modern experimental mechanics. Even if they are reasonably spread among the university laboratories, their diffusion in industrial companies remains very narrow for several reasons, especially a lack of metrological performance assessment. A full-field measurement can be characterized by its resolution, bias, measuring range, and by a specific quantity, the spatial resolution. The present paper proposes an original procedure to estimate in one single step the resolution, bias and spatial resolution for a given operator (decoding algorithms such as image correlation, low-pass filters, derivation tools …). This procedure is based on the construction of a particular multi-frequential field, and a Bode diagram representation of the results. This analysis is applied to various phase demodulating algorithms suited to estimate in-plane displacements.

Characterisation of in-vivo mechanical action of knee braces regarding their anti-drawer effect

BACKGROUND The knee joint is vulnerable to various injuries and degenerative conditions, potentially leading to functional instability. Usual treatments involve knee orthoses to support the joint. However, the level of mechanical action of these devices remains controversial despite high prescription and demand. METHODS The mechanical ability of three commercial hinged knee braces and one sleeve to prevent a static drawer was evaluated using a GNRB arthrometer. The testing of both pathological and healthy joints was performed on 16 patients with documented injuries involving the ACL, and an original method allowed decoupling the contribution of the brace. RESULTS The mean stiffness of the three hinged braces ranged between 2.0 and 7.1 N/mm. The most efficient brace was able to exert a restraining force on the joint equivalent to the one exerted by a healthy ACL, up to a 2.8 mm anterior displacement of the tibia. For higher anterior displacements, the restraining force of the brace dropped below the level of action of the intact ACL because of the particular non-linear behaviour of this structure. Finally, the most efficient brace was found to vary from subject to subject. CONCLUSIONS This study confirmed that fabric-based knee braces may effectively replace the passive mechanical role of the ACL within the low stiffness region of this structure. Although bracing may have other benefits (e.g., proprioception), this shows that they act as an effective passive restraint to low grade anterior laxities. Besides, a high patient-specificity of their effects highlighted the need of personalised objective testing for brace selection.

Numerical and experimental analyses of resin infusion manufacturing processes of composite materials

Liquid resin infusion (LRI) processes are promising manufacturing routes to produce large, thick, or complex structural parts. They are based on the resin flow induced, across its thickness, by a pressure applied onto a preform/resin stacking. However, both thickness and fiber volume fraction of the final piece are not well controlled since they result from complex mechanisms which drive the transient mechanical equilibrium leading to the final geometrical configuration. In order to optimize both design and manufacturing parameters, but also to monitor the LRI process, an isothermal numerical model has been developed which describes the mechanical interaction between the deformations of the porous medium and the resin flow during infusion. 1 , 2 With this numerical model, it is possible to investigate the LRI process of classical industrial part shapes. To validate the numerical model, first in 2D, and to improve the knowledge of the LRI process, this study details a comparison between numerical simulations and an experimental study of a plate infusion test carried out by LRI process under industrial conditions. From the numerical prediction, the filling time, the resin mass and the thickness of the preform can be determined. On another hand, the resin flow and the preform response can be monitored by experimental methods during the filling stage. One key issue of this research study is to highlight the changes in major process parameters during the resin infusion stage, such as the temperature of the preform and resin, and the variations of both thickness and fiber volume fraction of the preform. Moreover, this numerical/experimental approach is the best way to improve our knowledge on the resin infusion processes, and finally, to develop simulation tools for the design of advanced composite parts.

Bayesian Statistical Identification of Orthotropic Elastic Constants Accounting for Measurement and Modeling Errors

Bayesian identification provides a framework that can handle both measurement and modeling errors. Furthermore it identifies a probability distribution function thus providing information on both variance and correlation of the identified properties. However, the procedure can be very costly computationally. In order to address the computational cost issue a Bayesian identification procedure based on response surface methodology is proposed. The procedure is illustrated on the problem of identifying orthotropic elastic constants from natural frequencies of a free composite plate. The procedure accounts for measurement noise, uncertainty in other input parameters to the vibration model (plate dimensions, density) as well as systematic error effects. The joint probability distribution of the four elastic ply constants is identified and characterized by mean value and variancecovariance matrix. We find that some properties, such as Poissons ratio, are identified with much higher uncertainty than other and that significant correlation between the identified properties is present. The developed procedure allowed substantial reduction in computational cost. However, in spite of the cost reduction techniques, it remains at the edge of what is presently reasonable computation time.