A study of mixed-mode dynamic fracture in advanced particulate composites by optical interferometry, digital image correlation and finite element methods

Abstract

Understanding the fracture mechanics of materials under stress wave loading is essential for impact resistant design of structures. In this context, mixed-mode dynamic fracture behavior of two-phase composites - a functionally graded material (FGM) and a syntactic structural foam – are investigated experimentally and numerically. FGMs are macroscopically nonhomogeneous engineered materials with spatially varying volume fraction of the constituents. Syntactic foams are homogeneous buoyant materials used in naval/marine applications as well as for energy dissipation in military and industrial environments. Catastrophic failure in these materials is often observed to occur in a mixed-mode fashion involving a combination of tensile and shear fractures. Real-time and full-field measurement of crack tip deformations in these circumstances is rather challenging because the events typically last only a couple of hundred microseconds, and need optical tools coupled with ultra-high speed imaging devices to understand the associated failure mechanisms. To date very few methods are available for performing direct measurements of crack tip fields. This dissertation aims to address these by studying the dynamic fracture behavior of such novel materials by developing suitable measurement and modeling tools.

The first part of this research extends the optical method of Coherent Gradient Sensing (CGS) to the study of mixed-mode dynamic fracture behavior of functionally graded materials. The mixed-mode loading is generated by loading samples eccentrically relative to the initial crack plane. CGS and high-speed photography are used to map transient crack tip deformations. Two configurations, one with a crack on the stiffer side of a graded sheet and the second with a crack on the compliant side, are examined experimentally. Differences in both pre- and post-crack initiation behaviors are observed in terms of crack initiation time, crack path, crack speed and stress intensity factor histories. A crack kinks by a much larger angle when it originates from the stiffer side of the FGM compared to the compliant side.

In the second part of this work, the method of digital image correlation is developed to study transient deformations associated with rapid mixed-mode crack growth in materials. Edge cracked polymer beams and syntactic foam samples are studied under low-velocity impact loading conditions. Decorated random speckle patterns in the crack tip vicinity are recorded using an ultra high-speed CCD camera at framing rates of 200,000 frames per second. A three-step digital image correlation technique is developed and implemented in a MATLAB environment for evaluating crack opening/sliding displacements and the associated strains. Using this approach, the entire crack tip deformation history, from the time of impact to complete fracture, is mapped successfully. The current work being the first of its kind using a rotating mirror type multi-channel high-speed digital camera system, calibration tests and procedures are established by carrying out a series of benchmark experiments. The accuracy of measured displacements is in the range 2 to 6% of a pixel (0.6 to 1.8 micro meter) and that of the dominant strain is about 150-300 micro strains.

In the last part, finite element modeling of mixed-mode dynamic crack growth in FGM using cohesive element formulations is performed. A user-defined subroutine is developed and linked with ABAQUS implicit procedure. The simulated crack paths are in agreement with the experimental ones. The computed results prior to crack initiation show the presence of larger negative constraining stresses (T-stresses) near the crack tip when the crack is situated on the compliant side of the FGM. The simulations reveal that more energy is dissipated when the crack is situated on the compliant side of the