Research Papers

Dynamic Fracture Characterization of Small Specimens: A Study of Loading Rate Effects on Acrylic and Acrylic Bone Cement

[+] Author and Article Information
Hareesh V. Tippur

e-mail: tippuhv@auburn.edu
Department of Mechanical Engineering,
Auburn University,
Auburn, AL 36849

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received April 30, 2012; final manuscript received January 8, 2013; published online April 2, 2013. Assoc. Editor: Jefferey Kysar.

J. Eng. Mater. Technol 135(3), 031001 (Apr 02, 2013) (11 pages) Paper No: MATS-12-1082; doi: 10.1115/1.4023405 History: Received April 30, 2012; Revised January 08, 2013

A long-bar apparatus for subjecting relatively small samples to stress-wave loading has been devised for failure characterization. A methodology based on digital image correlation (DIC) used in conjunction with ultra high-speed photography and a long-bar impactor has been developed for determining dynamic crack initiation stress intensity factor (SIF) (KI-inid), as well as SIFs for a rapidly growing crack (KId) during high-strain rate events. By altering the material of the pulse shaper, a range of strain rates has been attained. Commercial grade PMMA was first used to calibrate the device, and then dynamic fracture characterization was performed for the first time on PMMA-based bone cement (BC). Despite several key differences, the two materials performed similarly during quasi-static fracture tests; however, under dynamic loading conditions, bone cement exhibited significantly lower crack initiation SIF (KI-inid), lower dynamic SIFs (KId), and higher crack tip velocities for three different dynamic loading rates (K·=6.5-24×104MPams-1).

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Fig. 1

Bone cement sheet cures between two plates using spacers for desired thickness

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Fig. 2

Static (a) and dynamic and (b) specimen geometry

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Fig. 3

Schematic of long-bar impactor setup for studying crack initiation and propagation of relatively small size specimens

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Fig. 4

Close-up of the impact loading setup. Specimen with prenotch is placed in contact with the semicircular impactor head of the long-bar prior to testing. Putty is used to ensure symmetry of reflected waves from the top and bottom specimen edges.

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Fig. 5

(a) Strain histories recorded on the long-bar corresponding to three different pulse shapers. X marks the portion of the strain history coinciding with crack initiation. (b) The first 80 μs of Fig. 5(a) are shown.

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Fig. 6

(a) A pair of images recorded from the same CCD sensor of the high-speed camera. (b) Point O in the undeformed subimage displaces to a location O’ in the deformed subimage. The difference in these coordinates gives the sliding (u) and opening (v) displacements for the subimage.

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Fig. 7

Images recorded of a crack growing in bone cement using an Al pulse shaper at 2.5, 5, and 7.5 μs after initiation. Corresponding crack opening (b) and sliding (c) displacement fields are shown. Contour interval is 10 μm. Symmetry of sliding displacements indicates Mode I dominant fracture. Arrows indicate crack tip location.

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Fig. 8

Finite element model with corresponding crack opening displacement contours are shown on the specimen, along with the far left end of the long-bar. A fine mesh is used near the impact site to ensure that contact and crack tip deformation responses are captured accurately. The field corresponds to a time instant 35 μs after impact.

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Fig. 9

Quasi-static load versus displacement curves for PMMA and bone cement. Loads have been normalized by specimen thickness. Peak loads are similar, but BC fracture is relatively less catastrophic than PMMA.

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Fig. 10

SIF histories for (a) PMMA with no pulse shaper, (b) PMMA with Al pulse shaper, (c) PMMA with Al/PC sandwich pulse shaper, (d) BC with no pulse shaper, (e) BC with Al pulse shaper, (f) BC with Al/PC sandwich pulse shaper. Curves have been aligned according to time of crack initiation (ti). (Note: The scale used is consistent for a material type but different for PMMA and BC.)

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Fig. 11

Representative SIF histories from each of six testing groups from Fig. 10. Curves have been aligned according to time of impact.

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Fig. 12

The effect of material type on crack velocity is shown for (a) no pulse shaper (high loading rate: 42.0 s−1), (b) Al pulse shaper (medium loading rate: 10.7 s−1), and (c) Al/PC pulse shaper (low loading rate: 3.7 s−1). t=0 corresponds to crack initiation. Error bars indicate one standard deviation relative to the average value.

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Fig. 13

The effect of material type on dynamic SIF is shown for (a) no pulse shaper (high loading rate: 42.0 s−1), (b) Al pulse shaper (medium loading rate: 10.7 s−1), and (c) Al/PC pulse shaper (low loading rate: 3.7 s−1). t=0 corresponds to crack initiation. Error bars indicate one standard deviation relative to the average value.

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Fig. 14

Micrographs of PMMA fracture surfaces: (a) no pulse shaper and (b) Al/PC pulse shaper. Arrows indicate the beginning of common fracture surface regions. Increasing distance r is related to decreased resistance to crack growth.

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Fig. 15

Micrographs of fractured BC samples: (a) no pulse shaper (×100 and ×500) and (b) Al/PC pulse shaper (×100 and ×500). Higher roughness is shown for the higher loading rate in (a), and both images exhibit more roughness than PMMA (Fig. 13). Images were captured at a distance of ∼5 mm from crack front.



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