Investigation of mixed-mode dynamic fracture in syntactic foams using digital image correlation method and high-speed photography

In this work, a combination of digital image correlation and high-speed photography is used to study mixed-mode dynamic fracture in syntactic foams under stress wave loading conditions. Edge cracked foam samples are subjected to mixed mode loading by impacting eccentrically relative to the initial crack plane in three point bend configuration. Ultra high-speed CCD digital camera is used to record the spray painted random speckle patters on the specimen surface around the crack tip at framing rates of 200,000 frames per second. Two sets of images are recorded, one set before impact and another set after impact. Entire crack tip deformation history, from the time of impact up to complete fracture is mapped. A regularized restoration smoothing technique, which smoothes the displacements while allowing for discontinuity of displacements across the crack faces is developed. Overdeterministic least-squares analyses of crack opening and sliding displacement fields are used to obtain mixedmode dynamic stress intensity factor histories for both preand post-crack initiation periods. The stress intensity factor histories obtained from the image correlation method are compared with the ones from computations. Introduction The focus of the current work is fracture behavior of syntactic foams. These are light-weight particulate composites manufactured by dispersing prefabricated hollow microballoons in a matrix material. The porosity in these materials results in lower density and superior thermal, dielectric, fire resistant, hygroscopic properties and sometimes radar or sonar transparency. They can also be tailored to suit a particular application by selecting microballoons from a wide range of materials (glass, carbon or polymer microballoons) to be used with different matrix materials (metal, polymer or ceramic). The measurement of real-time surface deformations during a dynamic failure event such as fracture initiation and propagation is quite challenging due to a combination of spatial and temporal resolution demands involved. One of the very early efforts in this regard dates back to the work of de Graaf [1]. In this paper, photoelastic measurement was attempted to witness stress waves around a dynamically growing crack in steel. This method continues to be a popular choice when dealing with opaque solids [2, 3]. In recent years, Coherent Gradient Sensing (CGS) has become a powerful interferometric tool for studying mode-I as well as mixed-mode dynamic fracture of opaque solids because of its robustness and insensitivity to rigid body motion and vibrations [4-7]. Moiré interferometry has also been used to measure in-plane crack tip displacement fields in dynamic fracture experiments [8]. The interferometric techniques, however, generally involve elaborate surface preparation (transferring of gratings in case of moiré interferometry and preparing a specularly reflective surface in case of CGS, birefringent coatings in reflection photoelasticity, etc.). For cellular materials (syntactic foams, polymer metal foams, cellulosic materials, etc.) such surface preparations are rather challenging and in some cases may not be feasible. In such instances, digital image correlation could be a very useful tool due to the relative simplicity of surface preparation. It involves decorating a surface with black and white paint mists alternatively. Recent advances in image processing methodologies and ubiquitous computational capabilities have made it possible to apply this technique to a variety of applications bio-mechanics, metal forming, characterization of C/C composites, to name a few. With the advent of digital high-speed cameras in recent years, recording rates as high as several millions frames per second at a relatively high spatial resolution are possible. This has opened the possibility of using DIC to estimate surface displacements and strains for estimating fracture/damage parameters. In the current work, the DIC technique is extended to mixed-mode dynamic fracture studies by estimating stress intensity factors for a stationary and a propagating crack tip in edge cracked syntactic foam sheets subjected to stress wave loading. A rotating mirror type high-speed digital camera is used to record random speckle pattern in the crack tip vicinity. The entire crack tip deformation and dominant strain history from the time of impact to complete fracture is mapped. Over-deterministic least-squares analyses of crack tip displacement fields are used to obtain dynamic * Graduate student † Alumni Professor, Department of Mechanical Engineering, Auburn University, AL 36849, USA (E-mail: tippuhv@auburn.edu, Tel: +1-334-844-3327) ‡ Professor, Department of Electrical and Computer Engineering, Auburn University, AL 36849, USA stress intensity factor (SIF) histories for both preand post-crack initiation periods. The SIF histories obtained from the image correlation method are compared with the ones from finite element computations. The DIC approach In the digital image correlation technique, random speckle patterns on specimen surface are monitored during a fracture event. These patterns, one before and one after the deformation are acquired, digitized, and stored. Then a sub-image in the undeformed image is chosen and its location in the deformed image is sought. Once the location of a sub-image in the deformed image is found, the local displacements can be readily quantified. In the current work, a three-step approach is developed in a MATLAB [9] environment to estimate 2D displacements and strains. In the first step, 2D cross-correlation [10] is performed between two selected sub-images. The peak of the correlation function was detected to sub-pixel accuracy (1/16 of a pixel) by bicubic interpolation. This process is repeated for the entire image to get full-field in-plane displacements. In the second step, an iterative approach is used to minimize the 2D correlation coefficient by using nonlinear optimization technique. In the current work, the Newton-Raphson method [11] which uses line search and BFGS algorithm to update an inverse Hessian matrix is employed. In the third step, a regularized restoration filter [12] with a second order fit was employed for smoothing of displacements. This method uses an unbiased optimum smoothing parameter based on the noise level present in the displacement field and same time allows for discontinuity of displacements across the crack faces, thus preserving the strain concentration near the crack tip. Experimental set-up A schematic of the experimental set-up used in this study is shown in Fig. 1. It consisted of Instron-Dynatup 9250-HV drop-tower for impacting the specimen and a Cordin 550 ultra-high-speed digital camera for capturing the images in real-time. The drop-tower had an instrumented tup for recording the impact force history and a pair of anvils for recording support reaction histories. The set-up also consisted of a delay/pulse generator to generate a trigger pulse when the tup contacts the specimen. Since all the images were recorded during the dynamic event lasting over a hundred micro seconds, the set-up used two high-energy flash lamps, triggered by the camera, to illuminate the specimen. The set-up also utilized two computers, one to record the tup force and anvil reaction histories (5 MHz acquisition rate) and the other to record the images.