Mixed-Mode Dynamic Fracture of Nanolayered Metal Ceramics
Logan Shannahan1, Leslie Lamberson1a, Michel Barsoum1
1Drexel University, 3141 Chestnut Street, Philadelphia, PA, USA
Abstract. The classical calculation of stress intensity factors in dynamic fracture mechanics assumes material isotropy. In this work, an over deterministic least-squares approach is presented and used to evaluate mode I (opening) and mode II (shear) stress intensity factors (SIF) for fracture considering orthotropic material symmetry; and is compared to isotropic calculations. This method is used to examine the fracture behavior of a metal-ceramic nanolayered material, or MAX phase, titanium silicon carbide (Ti3SiC2) in the parallel and perpendicular die-press directions under dynamic transient loading. Digital image correlation (DIC) is used to extract displacement fields for fracture analysis, a sensitivity analysis is conducted to converge on a K-dominant region at a determined distance from the crack tip, and a Newton-Raphson method is used to solve for the location of the crack tip during propagation. Preliminary results reveal directionally dependent mixed-mode fracture behavior, with fracture toughness values at initiation quantitatively between the conventional engineering metal and structural ceramic constituents of the MAX phase.
Introduction
Next generation materials such as polymer matrix composites, and MX and MAX metal-ceramic materials have directionally dependent mechanical properties due to manufacturing and microstructural characteristics. To this end, their fracture properties, particularly under complex transient loading conditions, are fundamentally important to correctly characterize and predict failure. Similar to binary metal carbides and nitrides (MX) with nominally the same thermal, elastic and electric properties, MAX phases have a potentially advantageous difference from MX materials in that they are readily machinable [1]. Typically made by hot-pressing powders in a die, Ti3SiC2 used for testing has better electrical and thermal conductivity than either Ti or TiC, a Young’s modulus roughly three times Ti of 320 GPa, and due to the ceramic layers a resistance to oxidation at temperatures greater than 14000C in air [1]; yet despite these established properties, relatively little is known about their dynamic fracture behavior.
Experimental Procedure
Mode I (opening) and mode II (shear) stress intensity factors (SIF) of titanium silicon carbide were examined in the die-press direction and perpendicular to the die-press on 100 x 30 x 3 mm samples. A projectile is fired at the Ti3SiC2 samples at rates between 1 and 30 m/s with a pre-notch and pre-crack on the opposite side of the impact surface. When the compression wave reaches the far free end of the sample, it returns the other direction as a tensile wave and opens up the crack; and when the projectile purposefully not aligned horizontally with the notch, mixed-mode (I and II) loading conditions are achieved. High-speed imaging from a Photron SA-5 camera is used to capture the resulting crack initiation and propagation images, speckled for DIC analylsis.
Figure1. Crack initiation and propagation from a 25 meter per second (85 mph) impact on Ti3SiC2 instigating nominally pure crack opening.
SIF Methodology
An over-deterministic linear least squares regression was used to extract SIF histories from the beginning of loading until the initiation of crack growth at an established region ahead of the crack [2,3]. The asymptotic expressions for crack tip displacement fields ux and uy in terms of mode I (opening) and mode II (shear) SIF’s KI and KII for an orthotropic material, are a function of the elastic compliance terms. The data is transformed to polar coordinates to increase accuracy [2] and the SIFs are extracted using a least squares fit to the data. Before calculating the SIFs, a sensitivity analysis is used to choose the range of data points from the full-field data for analysis. In order to maintain consistency between the tests, the same range was used in every case. This range was chosen so that the region under consideration is in the region of K-dominance, as this allows the omission of higher order terms in the asymptotic expression in a linear elastic mechanics framework. For these tests a region 0.2 < r / Sample Thickness (2-6 mm in this case) < 0.3 and -1350 < θ < 1350 to avoid both the process zone and edge effects.
Figure2. Rotation of coordinate system to increase accuracy in calculating mixed-mode fracture parameters from displacement fields.
Conclusions
Preliminary results have established that titanium silicon carbide behaves in a surprisingly brittle under the dynamic transient loading conditions, lending itself well to the analysis methodology assuming K-dominance. While pseudo-plastic failure mechanisms of kink bands and delaminations were seen under the scanning electron microscope at smaller length scales of these materials under deformation, Ti3SiC2 appeared to have a small plastic zone and strong Mode I dominance at the continuum level. The direction perpendicular to the die proved weaker as cracks were able to grow between nanolayers with less resistance to the crack path, and this appeared more evident in the orthotropic SIF analysis. For crack initiation, the fracture toughness values appeared to be approximately an order of magnitude higher than silicon carbide at between 20 to 60 MPa√m.
References
[1] M.W. Barsoum, T. El‐Raghy, Synthesis and characterization of a remarkable ceramic: Ti3SiC2, Journal of the American Ceramic Society, 79 (1996) 1953-1956.
[2] M.S. Kirugulige and H.V. Tippur. Measurement of fracture param- eters for a mixed-mode crack driven by stress waves using image correlation technique and high-speed digital photography. Strain, 45(2):108–122, 2009.
[3] L. Shannahan, et al., Rate-dependent mixed-mode fracture of human femoral bone, International Journal of Fracture, in review, (2015). 1-10.