Sridhar Krishnaswamy

A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results

A first order diffraction analysis of an optical interferometer, Coherent Gradient Sensor (CGS), for measuring surface gradients is presented. Its applicability in the field of fracture mechanics is demonstrated by quantitatively measuring the gradients of out-of-plane displacements around a crack tip in a three point bent fracture specimen under static loading. This method has potential for the study of deformation fields near a quasi-statically or dynamically growing crack.

Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance

A new full field optical technique-‘Coherent Gradient Sensing’ (CGS)-is developed and used to study crack tip deformations in transparent as well as opaque solids. A first order diffraction analysis is provided for the technique and its feasibility is demonstrated both in transmission and reflection modes. Preliminary results from the dynamic crack growth experiment clearly demonstrate the capability of CGS to be an effective experimental alternative to other optical methods used in dynamic fracture studies. Notably, it is a full field technique which works with optically isotropic materials.The static fringe patterns obtained from the experiments are analyzed in regions outside the 3-D zone. For geometries where the region outside the 3-D zone is K-dominant, the fringes provide an accurate value of 2-D stress intensity factor. For geometries where the region outside the 3-D zone is not K-dominant, Williams expansion is used in conjunction with a least squares procedure to obtain the stress intensity factors.

Measurement of transient crack-tip deformation fields using the method of coherent gradient sensing

Abstract A shearing interferometric method (CGS) is proposed as a viable alternative to currently used experimental techniques for the study of dynamic crack propagation in both transparent and opaque media. CGS is a full-field optical technique that provides real-time fringes representing crack-tip deformation or stress state. The results of the experiments are interpreted on the basis of the conventional singular asymptotic analysis as well as a newly developed transient higher-order asymptotic analysis. The excellent agreement obtained between the experimental results and the higher-order asymptotic analysis clearly indicates that the contribution of the non-singular terms to the total stress and deformation fields is too important to be ignored.

On the Extent of Dominance of Asymptotic Elastodynamic Crack-Tip Fields: Part I—An Experimental Study Using Bifocal Caustics

The question of the domain of dominance of mode I asymptotic elastodynamic crack-tip fields is investigated experimentally for the cases of dynamically loaded stationary cracks as well as dynamically propagating cracks. The experiments reported are on three-point bend specimens loaded dynamically using a drop-weight tower. An optical configuration leading to a bifocal high-speed camera is proposed. This is used in conjunction with the method of caustics to obtain apparent dynamic stress intensity factor measurements simultaneously from two different regions around the crack tip. The results of this study indicate that three-dimensional and transient effects necessarily have to be taken into account in the interpretation of dynamic fracture experiments.

On the Extent of Dominance of Asymptotic Elastodynamic Crack-tip Fields: Part II - Numerical Investigation of Three Dimensional and Transient Effects

In Part I of this paper, the question of the extent of dominance of the mode I asymptotic elastodynamic crack-tip field (the K d I -field) was studied experimentally. Here, the results of two and three-dimensional elastodynamic finite element simulations of the drop-weight experiments are reported. The load records as obtained from the impact hammer and supports of the drop-weight loading device were used as boundary tractions in the numerical simulations. For the laboratory specimen studied, the results of the simulations indicate that the asymptotic elastodynamic field is not an adequate description of the actual fields prevailing over any sizeable region around the crack tip. This confirms the experimental results of Part I which showed that three-dimensional and transient effects necessarily have to be taken into account for valid interpretation of experimental results.

Dynamic measurement of the J integral in ductile metals: Comparison of experimental and numerical techniques

Experiments and analyses designed to develop an extension of the method of caustics to applications in dynamic, elastic-plastic fracture mechanics are described. A relation between the caustic diameter, D, and the value of the J integral was obtained experimentally and numerically for a particular statically loaded specimen geometry (three point bend) and material (4340 steel). Specimens of the same geometry and material were then loaded dynamically in impact. The resulting caustics, recorded using high speed photography, were analyzed on the basis of the J versus D relation to determine the time history of the dynamic value of J, Jd(t). The history of Jdthus obtained is compared with good agreement to an independent determination of Jd(t) based on a two-dimensional, dynamic, elastic-plastic finite element analysis, which used the experimentally measured loads as traction boundary conditions.

On the application of the optical method of caustics to the investigation of transient elastodynamic crack problems: Limitations of the classical interpretation

Abstract Several possible sources of inaccuracy that occur in the classical interpretation of caustics patterns generated during transient crack growth in elastic materials are examined using a ‘Bifocal Caustics’ set-up and a new full field optical technique called ‘Coherent Gradient Sensing’. During unsteady dynamic crack growth, strict KdI-dominance is generally absent, especially at times close to crack initiation and arrest, even in regions outside the crack-tip 3-D zone where plane stress conditions persist. In such cases a truly transient higher order expansion is found to be essential for correctly describing stress fields outside the 3-D zone.

MEASUREMENT OF TRANSIENT CRACK TIP FIELDS USING THE COHERENT GRADIENT SENSOR

A shearing interferometric method (CGS) is used to study dynamic crack-tip fields in both transparent and opaque media. CGS is a full-field optical technique that provides real-time fringes representing crack-tip deformation or stress state. The results of the experiments are interpreted on the basis of a newly developed transient higher-order asymptotic analysis. The good agreement between the experimental results and the transient higher-order asymptotic analysis clearly indicates that the contribution of the non-singular terms to the total stress and deformation fields is significant.

A Bifocal Arrangement for Reflected Caustics for the Investigation of the Domain of Dominance of Asymptotic Elastic Fields in Dynamic Fracture

ABSTRACT The question of the domain of dominance of the plane-stress asymptotic elastic fields in dynamic fracture is addressed for the two cases of dynamically loaded stationary cracks as well as dynamically propagating cracks. The experiments reported in this work are on three-point bend, 4340 steel specimens loaded dynamically using a drop-weight tower. A new optical configuration is proposed which would allow for the simultaneous measurement of the apparent dynamic stress-intensity factor from two different regions around the crack-tip using the method of caustics. The results of the study indicate the importance of three-dimensional and transient effects in the interpretation of optical measurements.