Plasticité et élasticité des pâtes argileuses

Résumé Dans l'introduction, l'auteur rappelle que peu de chercheurs ont consacré leur activité à l'étude des phénomènes élastiques présentés par les pâtes argileuses.Afin de mieux connaître ces phénomènes, un appareil a été construit. Il permet l'enregistrement simultané des efforts appliqués et des déformations présentées par une éprouvette soumise à un couple de cisaillement.Des essais faits sur une pâte d'argile pure ont permis, entre autres conclusions, de constater que:la forme du cisaillement varie suivant la valeur de la contrainte.pour un cisaillement déterminé, le cisaillement élastique est indépendant de la contrainte appliquéele cisaillement permanent dépend du temps de maintien de la contrainte.Enfin, l'auteur signale que les modèles proposés jusqu'à maintenant pour représenter le comportement d'une pâte argileuse ne conviennent pas.     

Shear-strain contours from moiré interferometry

Whole-field contour maps of shear strains _xy are derived from displacement fields obtained by moiré interferometry with 2400 /mm (60,960 /in.). Cross-derivatives of displacements are obtained by mechanical differentiation. They are summed by graphical additive moiré. The high sensitivity of moiré interferometry permits quantitative analysis in the small-strain domain.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Recent Applications of Moiré Interferometry

Moiré interferometry has been a valuable experimental technique for the understanding of the mechanical behavior of materials and structures. Over the last decade less emphasis has been placed on the development of the technique and more towards applications. This paper is a review article on recent applications using moiré interferometry in the fields of microelectronics devices, material characterization, micromechanics, residual stress, composite materials, fracture mechanics, and biomechanics. The general principles of moiré interferometry and advancement of techniques will not be discussed in this text, but references will be provided.     

Painlevé paradox during oblique impact with friction

In analyses using non-smooth dynamics, oblique impact of rough bodies in an unsymmetrical configuration can result in self-locking or “jam” at the sliding contact if the coefficient of friction is sufficiently large; this has been termed, Painlevé’s paradox. In the range of configurations and coefficients of friction where Painlevé’s paradox occurs, analyses based on rigid body dynamics give results indicating that either there are multiple solutions or the solution is nonexistent. This conundrum has been resolved by considering that the contact has small normal and tangential compliance which is representative of deformability in a local region around the contact point. An analysis using a hybrid model which includes local compliance of the contact region has calculated the time-dependent changes in relative motion of colliding bodies for a range of incident angles of obliquity, tan^?1[?V₁(0)/V₃(0)] where V₁(0)and V₃(0) are the incident tangential and normal relative velocities at the contact point, respectively. The paradox is shown to result from a negative relative acceleration of the contact points during an initial period of sliding – a negative acceleration that is inconsistent with the assumption of rigid-body contact.     

Moiré interferometry at VPI & SU

A relatively easy technique for producing high-frequency gratings on specimens extends moiré techniques into the high-sensitivity domain. Whole-field patterns of inplane displacement components are obtained with grating frequencies of 1200, 2400 and 4000 l/mm (30,480, 60,960 and 101,600 l/in.). Moiré interferometry is a case of two-beam interference, characterized by extensive range, excellent fringe contrast and fringe localization on the specimen surface. It is a reflection technique, compatible with opaque specimens and live observation of deformation.     

Moiré techniques for measuring strains during welding

The present work measures dynamic strains near welds using a projected-grating moiré technique. Experimental procedures are described for producing the orthogonal submaster gratings and etched heat-resistant specimen gratings necessary for this work. A modification of the gridanalyzer method allows all strain information to be obtained from a single photograph. A mathematical procedure combines fringe patterns from small adjacent sections of a surface into a larger continuous pattern. Computerized regression techniques enable more rapid and accurate analysis of the data. Results from welds in an Al?Mg alloy show the feasibility of dynamic welding-strain analysis using this approach. Welding deformation is found to be almost entirely shear straining, which explains the nature and orientation of high-temperature cracks sometimes found near welds.     

The moiré method applied to three-dimensional elastic problems

The purpose of this paper is to develop the technique of moiré for three-dimensional strain and stress analysis. The classical problem of contact of a sphere with a semi-infinite space is studied, and experimental results are compared with those of Hertz's solution. Results show that the method is accurate and has a high sensitivity. The results prove also that the strain distribution in a very small region with a steep gradient can be detected quite precisely.Paper was presented at the 1964 SESA Spring Meeting held in Salt Lake City, Utah, on May 6–8.     

Bulge Testing Transparent Thin Films with Moiré Deflectometry

The problem that is addressed here is the measurement of the mechanical properties of very thin, transparent films using bulge tests. All existing techniques make use of reflection from the film surface, but they can be difficult or impossible to apply to very thin, transparent films. Consequently, a novel approach based on the formation of a lens structure and using transmitted light is developed. In this technique, the focal length of the lens structure formed by the bulged film and the pressurizing medium is determined by moiré deflectometry with a corrected governing equation. The resulting curvature of the bulge film is used in the stress analysis of the bulge-test. By combining circular and rectangular configurations, the Young’s modulus and Poisson’s ratio of a 3 μm PET film were 4.65 ± 0.11 GPa and 0.34 ± 0.01, respectively. Consistent residual stresses were obtained from both configurations.     

A connection formula for the second Painlevé transcendent

We consider the second Painlevé transcendent $$\frac{{d^2 y}}{{dx^2 }} = xy + 2y^3 .$$ It is known that if y(x) ～ k Ai (x) as x → + ∞, where ?1<k<1 and Ai (x) denotes Airy's function, then $$y(x) \sim d|x|^{ - \tfrac{1}{4}} sin\{ \tfrac{2}{3}|x|^{\tfrac{3}{2}} - \tfrac{3}{4}d^2 1n|x| - c\} ,$$ where the constants d, c depend on k. This paper shows that $$d^2 = \pi ^{ - 1} 1n(1 - k^2 )$$ , which confirms a conjecture by Ablowitz & Segur.     

A fractional gradient representation of the Poincaré equations

A gradient representation and a fractional gradient representation of the Poincaré equations are studied. Firstly, the condition presented here for the Poincaré equation can be considered as a gradient system. Then, a condition under which the Poincaré equation can be considered as a fractional gradient system is obtained. Finally, two examples are given to illustrate applications of the result.     

Comportement élastoplastique homogeneisé d'un milieu rocheux fracture

The overall behaviour of a periodic medium made up of a rock matrix crossed by one or several networks of plane parallel joints is examined from a micromechanical point of view. It is assumed that the rock matrix as well as the joints exhibit a perfect plastic behaviour. The localization within the elementary cell is shown to be of the Reuss type, the microscopic stress field being uniform. The macroscopic behaviour is therefore perfectly plastic. The macroscopic elastic stiffness, possibly nonlinear, is derived from those of the joints and matrix. The macroscopic yield criterion is obtained from the intersection of the matrix and joint criteria. If the normality rule is valid for the constituants, it applies at the macroscopic scale as well.     

An electron moiré method for a common SEM

In the electron moiré method, a high-frequency grating is used to measure microscopic deformation, which promises significant potential applications for the method in the microscopic analysis of materials. However, a special beam scanning control device is required to produce a grating and generate a moiré fringe pattern for the scanning electron microscope (SEM). Because only a few SEMs used in the material science studies are equipped with this device, the use of the electron moiré method is limited. In this study, an electron moiré method for a common SEM without the beam control device is presented. A grating based on a multi-scanning concept is fabricated in any observing mode. A real-time moiré pattern can also be generated in the SEM or an optical filtering system. Without the beam control device being a prerequisite, the electron moiré method can be more widely used. The experimental results from three different types of SEMs show that high quality gratings with uniform lines and less pitch error can be fabricated by this method, and moiré patterns can also be correctly generated.The project supported by the National Natural Science Foundation of China (10662005) and JSPS fellowship in Japan. The English text was polished by Keren Wang.     

Hole-drilling method using grating rosette and Moiré interferometry

The hole-drilling method is one of the most wellknown methods for measuring residual stresses. To identify unknown plane stresses in a specimen, a circular hole is first drilled in the infinite plate under plane stress, then the strains resulting from the hole drilling is measured. The strains may be acquired from interpreting the Moire signature around the hole. In crossed grating Moire interferometry, the horizontal and vertical displacement fields （u and v） can be obtained to determinate two strain fields and one shearing strain field. In this paper, by means of Moire interferometry and three directions grating （grating rosette） developed by the authors, three displacement fields （u, v and s） are obtained to acquire three strain fields. As a practical application, the hole-drilling method is adopted to measure the relief strains for aluminum and fiber reinforced composite. It is a step by step method; in each step a single laminate or equivalent depth is drilled to find some relationships between the drilling depth and the residual strains relieved in the fiber reinforced composite materials.     

A moiré microscope for finite deformation micro-mechanical studies

A new version of a moiré microscope is presented that embodies the theory of optical moiré interferometry. To interrogate the deformed specimen grating, the device uses a transmission diffraction grating that allows for a simple and quick change of the virtual reference grating vector without disturbing the optical alignment of the other components in the optical train. To analyze deformation from the acquired moiré interference fringe patterns, the displacement light-itensity moiré optical law introduced by Sciammarella is revisited. The analysis of deformation is consistent with the continuum principles of finite deformation and can readily be used to obtain micro-mechanical quantities of interest such as the local strains, stretches and rotations.