Proceedings of the SEM Annual Conference June 1-4, 2009 Albuquerque New Mexico USA ©2009 Society for Experimental Mechanics Inc.
Geometric Effects in DCDC Fracture Experiments
Christian Nielsen1, Alireza V. Amirkhizi1,* and Sia Nemat-Nasser1 Center of Excellence for Advanced Materials, Department of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 920930416, USA *
[email protected] 1
ABSTRACT The effect of sample geometry on the double cleavage drilled compression (DCDC) test of PMMA is experimentally and numerically studied. The test uses axial compression to propagate cracks in a rectangular column of material containing a central circular hole. Initiated by notches, the cracks grow slowly at first with increasing load then more rapidly before being arrested due to the confined end conditions. Specific geometric parameters considered in this study are the sample thickness and hole size. Tested thicknesses include 3, 4, 5, 8, and 11 mm (all at 50 mm height and 12 mm width). The thin samples (3, 4 and 5 mm) are tested in a brace to prevent out-of-plane buckling. Width-to-hole-diameter ratios of 4 and 6 are investigated. The results of these experiments are incorporated in numerical simulations to estimate the fracture toughness of the material. Measured loads are matched with numerical models of different crack lengths to estimate energy release rates and critical stress intensity factors. The simulations consider nonlinear geometric effects as well as nonlinear material properties. The knowledge from this work will be applied to future DCDC tests of re-mendable polymers, where repeated cycles of fracture and healing will determine healing efficiency. Keywords: double cleavage drilled compression, DCDC, fracture, toughness, PMMA EXTENDED ABSTRACT The double cleavage drilled compression (DCDC) test [1] is used to study the fracture behavior of polymethyl methacrylate (PMMA). A rectangular column of PMMA with a central hole is subjected to uniaxial compression (Figure 1 right). Due to the geometry of the sample tension regions develop at the apex and base of the hole, leading to the formation and propagation of symmetric cracks. These cracks grow slowly at first with increasing applied compression, before growing more quickly at a nearly constant critical stress. The cracks are finally arrested near the ends of the specimen by flat boundary conditions (Figure 1 above). DCDC experiments are conducted on PMMA to investigate the effect of specimen thickness on fracture behavior. If the thickness of each specimen can be reduced, less material will be required for each DCDC test. Specimens measuring 50 mm tall and 12 mm wide with a central hole 3 mm in diameter are machined to 3, 4, 5, 8 or 11 mm thicknesses. To prevent out-of-plane buckling, the 3, 4 and 5 mm thick specimens are tested in a brace consisting of two plates of acrylic loosely bolted around the specimen. Vacuum grease is used to lubricate the interface. Triangular pre-cracks are pressed into the apex and base of the hole on the front and back of each specimen [2]. These pre-cracks are grown together with sinusoidal load cycling prior to the start of DCDC testing. DCDC tests are conducted using a 0.5 μm/sec displacement rate with pictures of the cracks taken every 30 seconds. The flash of camera is recorded in the data, allowing for the correlation of crack length and applied load. Reducing thickness is found to reduce the critical plateau stress at which the cracks grow quickly. This effect is no more than 10%, but the results are repeatable, with a clear trend. The initial period of slow crack growth shows no changes in behavior with changes in thickness. Several of the braced specimens have jumps in the stress attributable to their confinement and locking within the brace. Through visual inspection of the crack surfaces, two regimes are readily identifiable: (1) small pits and peaks transitioning to (2) smooth ridges and valleys oriented in the direction of crack growth like rays. In all specimens, these surface profiles correlate with
Figure 1 Left: DCDC specimen geometry Above: Typical crack progression in a DCDC specimen: a) virgin sample; b) after load cycling; c) slow crack growth during DCDC test; d) fast crack growth during DCDC test; e) cracks arrested by end conditions Right: Two dimensional finite element model of the DCDC test the observed slow and fast crack growth rates. The effect of specimen hole size on the DCDC test is also experimentally investigated. Previous work has looked at width-to-hole-diameter ratios of 2, 3, 4 or 5 [2, 3]. The present work regarding the effect of thickness uses specimens with a ratio of 4. A specimen with a ratio of 6 is tested for comparison. Measuring 50 mm tall, 12 mm wide and 3 mm thick with a 2 mm diameter hole, the sample is load cycled in liquid nitrogen to initiate the cracks without causing inelastic deformation. DCDC testing is conducted at room temperature following the same procedure as the specimens with a ratio of 4. Reducing the hole size leads to significant inelastic deformation during DCDC testing. Regions around the hole approximately 45 degrees from the midplane show the most deformation. The crack surfaces appear smooth, with no differentiation between the slow and fast crack growth regimes as previously observed. Based on the experimentally obtained relationship between applied stress and crack length, the critical stress intensity of the material is estimated. Several models have been proposed for making such an estimation [2, 4-6]. In the present work, a new model is used that correlates experimental results with a finite element model to estimate stored internal energy, energy release rate, and critical stress intensity. Due to symmetry, the finite element model considers one quarter of the total DCDC geometry (Figure 1 right), with the crack length set by the boundary conditions. The two-dimensional model uses 2232 plane strain shell elements. Nonlinear geometric effects are considered, but the PMMA is approximated using a linear isotropic material model (E = 3100 MPa, ν = 0.40). Displacement steps are applied to the top nodes and the model is solved using LS-DYNA’s implicit solver. For the prescribed crack length, the total applied force is used to correlate the model with the experimental results. Growing the crack by one element, ∆l, and comparing the internal energy, U, yields the strain energy release rate: 2 The critical stress intensity is then:
∆ ∆
.
(1)
ν
.
(2)
A Python computer script controls this procedure, growing the crack through a series of models and calculating the fracture properties. Based on the observed experimental results, reducing DCDC specimen thickness is a viable option to reducing volume. The use of a brace for stability, however, frequently affects the results and generally complicates the setup. Scaling down the specimens is another approach to reduce specimen volume, although larger camera lenses or higher resolution pictures will be required for precise crack length measurements. The experimental results can be used to estimate critical stress intensity factors using a collection of sequential finite element models. The results of this work will be applied to future studies of healable polymers (healomers). The DCDC test is ideally suited for characterizing healing efficiency, since crack length can be controlled and the sample remains intact [7]. Reducing the volume of material necessary for an effective DCDC test will preserve limited quantities of polymer for other characterization tests. The critical stress intensities estimated by the proposed model will serve as a basis for determining the healing efficiency of the polymer over multiple cycles of fracture and repair. ACKNOWLEDGEMENTS This work was conducted partially with the support of Air Force Office of Scientific Research grant FA9550-08-10314 to UC San Diego. REFERENCES [1] Janssen C, ‘Specimen for fracture mechanics studies on glass’, 10th International Congress on Glass, Kyoto Japan, Ceramic Society of Japan, 1974. [2] Plaisted T et al, ‘Compression-induced axial crack propagation in DCDC polymer samples: experiments and modeling’, Int J Fract, 141, 447-457, 2006. [3] Indonji K et al, ‘Evaluation of the stress intensity factor of brittle polymers based on the crack arrest concept’, J Reinforced Plastics Composites, 12(7), 778-786, 1993. [4] Marshall G et al, ‘The correlation of fracture data for PMMA’, J Mater Sci, 8(1), 138-140, 1973. [5] Michalske T et al, ‘Stress intensity calibration for the double cleavage drilled compression specimen‘, Eng Fracture Mech, 45(5), 637-642, 1993. [6] He M et al, ‘Analysis of the double cleavage drilled compression specimen for interface fracture energy measurements over a range of mode mixities’, Acta Metallurgica Materialia, 43(9), 3453-3458, 1995. [7] Plaisted T et al, ‘Quantitative evaluation of fracture, healing and re-healing of a reversibly cross-linked polymer’, 55, 5684-5696, 2007.
