Hareesh V. Tippur

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.

A functionally graded particulate composite: Preparation, measurements and failure analysis

Abstract A functionally graded composite is prepared and the spatial gradation of Youngs modulus in the functionally graded material (FGM) is measured. Elastic modulus gradients occur over length scales suitable for experimental mechanics investigations using optical interferometry. Crack tip fields are mapped in the FGM under quasi-static loading conditions with cracks oriented perpendicular to the direction of the elastic gradient and near the interface of the graded and the homogeneous portions of three-point-bending specimens. The optical measurements are used to extract fracture parameters based on the prevailing understanding of the crack tip behavior in FGMs. The results are also compared with finite element computations which incorporate measured elastic properties of the FGM. The advantage of using FGM interlayer as opposed to piecewise homogeneous joints is demonstrated through crack initiation tests.

Compositionally graded materials with cracks normal to the elastic gradient

Mixed-mode crack tip deformations and fracture parameters in glass-filled epoxy beams with cracks normal to the elastic gradient are studied. Crack tip fields are optically measured for different crack locations in the elastic gradient when subjected to symmetric pure bending. A companion finite element model is developed and validated by the measurements. The numerical model is then used to examine the influence of the elastic gradient on crack location by evaluating stress intensity factor, mode-mixity and energy release rate. For certain crack locations, computed stress intensity factors and energy release rates in the graded material exceed that of the bimaterial counterpart. However, when reconciled with measured critical values of the fracture parameters, graded beams show consistently better performance for all crack locations in the graded region. Crack kinking due to compositional gradients are examined and are successfully compared with the vanishing KII criterion based on a locally homogeneous material behavior.

Quasi-static and dynamic crack growth along bimaterial interfaces: A note on crack-tip field measurements using coherent gradient sensing

The paper presents a preliminary experimental investigation of crack-tip deformation fields near quasistatically and dynamically growing cracks in bimaterial interfaces. A three-point-bend bimaterial specimen with a relatively large stiffness mismatch between the two materials is studied. A recently developed optical method of coherent gradient sensing (CGS) is used to map crack-tip deformation fields.The quasi-static measurements are interpreted using plane-stress, singular-field solution for the interface crack tip. Results are compared with two-dimensional finite-element computations performed on identical specimen geometries and material mismatch.32 Impact studies conducted with bimaterial specimens provide the first experimental results of deformation fields near dynamically growing cracks along interfaces. Very high crack velocities, up to 80 percent of the Rayleigh wave speed for the less stiffer material of the two, are observed.

Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient

The nature of the singular field around the crack in functionally graded material (FGM) is analyzed parametrically using finite element method. The numerical simulations are carried out by varying the location of the crack in the graded region for different material gradients. Using linear material property variation in the gradient zone, the influence of material gradient and the crack position on the fracture parameters such as complex stress intensity factor (SIF) and energy release rate are studied. The crack opening displacement profiles of FGM are compared with the homogeneous and bimaterial counterparts. The analysis shows that the fracture parameters of FGM approach that of the bimaterial as the material gradient is increased, regardless of the position of the crack in the graded region. The extent of applicability of the homogenous crack tip fields around the crack in FGM is analyzed, and the results show that the size of the homogeneous field reduces with the increase in material gradient. Static fracture experiments are conducted on epoxy based FGM to determine complex SIF with electrical strain gages, using the homogeneous field equations to convert the strains to SIF. The measured SIF values compare favorably with the numerical results providing a limited experimental validation of the computations and the use of homogeneous field for FGM.

Measurement of transient deformations using digital image correlation method and high-speed photography: application to dynamic fracture

The digital image correlation method is extended to the study of transient deformations such as the one associated with a rapid growth of cracks in materials. A newly introduced rotating mirror type, multichannel digital high-speed camera is used in the investigation. Details of calibrating the imaging system are first described, and the methodology to estimate and correct inherent misalignments in the optical channels are outlined. A series of benchmark experiments are used to determined the accuracy of the measured displacements. A 2%-6% pixel accuracy in displacement measurements is achieved. Subsequently, the method is used to study crack growth in edge cracked beams subjected to impact loading. Decorated speckle patterns in the crack tip vicinity at rates of 225,000 frames per second are registered. Two sets of images are recorded, one before the impact and another after the impact. Using the image correlation algorithms developed for this work, the entire crack tip deformation history, from the time of impact to complete fracture, is mapped. The crack opening displacements are then analyzed to obtain the history of failure characterization parameter, namely, the dynamic stress intensity factor. The measurements are independently verified successfully by a complementary numerical analysis of the problem.

Dynamic fracture of compositionally graded materials with cracks along the elastic gradient: experiments and analysis

Abstract Crack tip deformation and fracture parameter histories in compositionally graded glass-filled epoxy are evaluated for low velocity impact loading. The situations when the elastic gradient is unidirectional with crack orientation along the gradient are examined. The fracture behavior of graded compositions is studied relative to homogeneous counterparts made of identical constituents. Optical method of CGS and high-speed photography are used to measure crack tip deformations prior to crack initiation and during dynamic crack growth. The apparent stress intensity factors prior to crack initiation are determined using dynamic equivalent of the stationary fields for FGMs while crack tip fields for steadily growing cracks in FGMs are used for post-initiation situations. Results from finite element simulations up to crack initiation are in excellent agreement with the experimental evaluations. Post crack initiation stress intensity factor histories and crack growth resistance behaviors for FGMs with monotonically increasing and decreasing elastic gradient are strikingly different. When the crack growth occurs into material with progressively increasing filler volume fraction, continuously increasing KID(t) is seen while a decreasing trend is observed when the gradient is of the opposite sense. The fracture behaviors are explained by independent fracture tests and fractured surface micrographs.

Dynamic fracture parameters and constraint effects in functionally graded syntactic epoxy foams

Abstract Functionally graded syntactic foam sheets are developed by dispersing microballoons in epoxy for studying dynamic fracture behavior under low velocity impact loading. The volume fraction of microballoons is graded linearly over the width of the sheets. The mode-I crack initiation and growth behaviors are studied using reflection coherent gradient sensing technique and high-speed photography in samples with crack on the compliant and stiff sides and oriented along the compositional gradient. Crack growth along the gradient in each case shows sudden acceleration followed by steady state growth and deceleration during the window of observation. In both cases, the crack accelerations are similar while crack decelerations show differences. The dynamic stress intensity factor history prior to crack initiation in each case shows a rapid increase at different rates with the crack on the compliant side of the graded sheet experiencing higher rate of loading relative to the one with the crack on the stiffer side. Post-crack initiation stress intensity factor histories suggest increasing fracture toughness with crack growth in the graded sample with the crack on the compliant side while a decreasing trend is seen when the crack is on the stiffer side. Optical measurements are supplemented by finite element simulations for studying crack tip constraint effects on fracture behavior of graded foam sheets. Computed plane strain constraints in graded configurations are essentially identical to the homogeneous counterpart and the computed stress intensity factors obtained from plane stress elasto-dynamic analyses of the graded foams correlate well with the experimental measurements prior to crack initiation. The computed T-stress histories however, show an earlier loss of negative crack tip constraint in case of the graded foam sample with a crack on the compliant side. This correlates well with the higher crack tip loading rate and earlier crack initiation suggesting a possible role of in-plane constraint on fracture of graded foam. The coincidence of the time rate of change of in-plane constraint parameter becoming stationary close to experimentally observed crack initiation times are noted.

Evaluation of Mechanical Properties of Functionally Graded Materials

An experimental technique for evaluating the elastic properties of functionally graded materials (FGMs) is proposed. Ultrasonic pulse-echo measurements in conjunction with elastic impact testing permit determination of Youngs modulus, Poissons ratio, and the mass density of the material and its longitudinal variation. The details of the formulation of the technique and the implementation issues are discussed in this paper. These techniques have been applied successfully to evaluate the properties of a model functionally graded material.

Poptube approach for ultrafast carbon nanotube growth

Microwave irradiation can be used to heat conductive materials and metallocene precursors to initiate ultrafast CNT growth. It takes only 15-30 seconds to grow CNTs at room temperature in air, without the need for any inert gas protection and additional feed stock gases.