Mario Cottron

Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I

A Michelson interferometer is applied to a mode I fracture mechanic problem to investigate the out-of-plane displacement near the crack tip. For an elastic cracked plate, it appears that the two-dimensional theory predicts correctly the free-stress surface displacement only in a region greater than half the specimen thickness. Combining this two-dimensional solution and the measurements provided by the interferometer, the out-of-plane displacement is likewise accessible inside the previous region where the state of stress is three-dimensional. A mathematical formulation, using an exponential integral function is then proposed to describe the out-of-plane surface displacement in the measurement area around the crack tip.

Grating interrogations: from small to large strain measurement

Our purpose is the direct strain measurement from the interrogation of a crossed grating marked on the surface of a specimen. The observation of the object through a master grid (as in moiré method) is replaced by a direct characterization of the pattern using a Fourier transform. This gives direct access to the modification of the pitches which leads to quantification of the strain without the intermediary of a fringe pattern. The comparison between the undeformed and deformed states allows the determination of the magnitude and orientation of principal strains and of the local rigid-body rotation. We describe three analysis techniques, one using the diffraction phenomenon, another utilizing a numerical spectral evaluation and third combining diffraction and phase-shifting procedure. These grid interrogations have different domains of application and a suitable choice of these analysis techniques allows a very large measurement range (10−5 to high strain according to the grating resistance).

Optical methods applied to the investigation of fracture mechanics

Because of the increase of catastrophic crack propagations at the middle of this century, it became necessary to develop a fracture theory in order to extend the life of structures and for evident reasons of security. These first search works have given a better understanding of the fracture in a linear medium by defining the stress distribution around a crack-tip. The stress singularity is then characterized for each fracture mode by a factor independent of the mechanical properties of the material, the stress intensity factor. This linear theory is always useful because of the common employment of brittle materials. A few decades after, the progress in the study of non-linear behaviors has induced a theory of ductile fracture. For this kind of material, the singularity amplitude is then characterized by the energy release rate. These theoretical works have required the development of experimental methods to test some results to understand special fracture phenomena. Among the experimental methods, the optical ones, which allow non-contact and so non-disturbing measurements, are every powerful. The advent of the laser, the use of image processing and numerical procedure to analyze the experimental data allows by optical methods the determination of stresses or kinematic values with a high precision. Our purpose is to present a few optical methods and the associated analysis techniques developed in our laboratory which seem to be well adapted to measure characteristic parameters of brittle or ductile fracture.

Improvement of local strain measurement by grid method: new optical device and quasi-heterodyne technique

Among optical strain measurement methods, the grid method is a powerful one. Progresses in the technique of information processing have contributed to develop classical analysis (optical and numerical Fourier transform). We propose a new optical device that allows the interference of diffracted beams from two crossed gratings of parallel lines marked on the specimen surface. The analysis of the interference fringes during loading provides the geometry of the gratings and so leads to the strain determination. The proposed method is insensitive to the specimen translations and presents a range from 105, with the use of a phase-shifting technique, to a few 102. Using experimental traction tests, we compare this method with the classical ones and we develop the performances of the proposed method (sensitivity and large measurement range).

High Speed Local Strain Determination from Grating Diffraction

The spectral analysis of grating allows, for static loading, the direct measurement of local strains at the surface of a body. This grating analysis is achieved by two ways (optical diffraction phenomenon or numerical Fourier transform) in order to determine at each step of load pitches and orientations of crossed grating. Our purpose is to extend this strain measurement method to investigate dynamic problems. The grating interrogation is performed using optical diffraction of a laser beam with an oblique incidence. In order to separate the diffracted beams during the dynamic event, we associate with each strain state a specific angle of the incident laser beam. This procedure allows to record 23 strain states at a maximum frequency equal to 1 MHz. The diffracted spots can be stored by two ways (film and CCD camera) and their analysis gives a strain sensitivity of 2.10−4.

Experimental Study of the Out-Of-Plane Displacement Fields for Different Crack Propagation Velocities

The fundamental aim of this study is to determine the influence of crack propagation speed on the out-of-plane displacement fields in the neighbourhood of a crack tip (i.e. on the size of the 3D effects zone). As the crack propagation is a complex process that involves the deformation mechanisms, the out-of-plane displacement measurement gives pertinent information about the 3D effects. We propose in this paper, to analyse the out-of-plane displacements fields for different crack velocities in brittle materials.

Holographic Recording of Gratings for Dynamic Strain Field Measurement

A new development of holographic recording for strain field evaluation during a transient event is proposed. The suggested metrology is a method associating holographic recording with numerical analysis of grating deposed on the specimen surface. An holographic camera allowing the storage of 6 grating images is presented. This process is based on the temporal coding of each hologram, which is realised by fast variation of the reference beam orientation. Characteristics of this dynamic holographic recording technique are exposed, and the experimental prototype and its characteristics are reported.

Identification of Three-dimensional Effects in Cracked Plates from Quasi-heterodyne Interferometry

A Michelson interferometer is applied to a mode I fracture mechanics problem to investigate the out-of-plane displacement around the crack tip. A series of experiments are performed with single edge-notched specimens, made of PMMA and Araldite. For such elastic plates, strong three-dimensional (3D) effects occur in fact in the vicinity of the crack tip up to a radial distance of about half the specimen thickness. Outside this region the state of plane stress dominates (K-field) and provides a classical mathematical expression for the out-of-plane displacement associated. Combining this two-dimensional (2D) solution and the measurements provided by the interferometer, the out-of-plane displacement is likewise accessible inside the region where the state of stress is fully three-dimensional. We propose then a new mathematical expression, including an exponential integral function, to describe the out-of-plane displacement surface both in the 2D and 3D region near the crack tip. A numerical study, using a finite element code, is finally achieved and supports the present investigation.

Dynamic photoelasticity applied to crack-branching investigations

Experimental investigations of crack-branching on central-notched plates in polymer are presented using dynamic photoelasticity. From a multiparameter representation of the stresses around the crack-tip, the stress-intensity factor is determined by a multiple-point method which couples iterative process and minimization procedure. The experimental device (high-speed camera, loading system) is described and the results are discussed. The polymer tested seems to correlate with the macroscopic branching criteria commonly found in dynamic fracture analysis.