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BRIDGING MICROSTRUCTURE, PROPERTIES, AND PROCESSING OF POLYMER-BASED ADVANCED MATERIALS

Micromechanical Model for the Orthotropic Elastic Constants of Polyetheretherketone Composites Considering the Orientation Distribution of the Hydroxyapatite Whisker Reinforcements

[+] Author and Article Information
Justin M. Deuerling1

Department of Aerospace and Mechanical Engineering, Bioengineering Graduate Program, 148 Multidisciplinary Research Building,  University of Notre Dame, Notre Dame, IN 46556

J. Scott Vitter2

Department of Aerospace and Mechanical Engineering, Bioengineering Graduate Program, 148 Multidisciplinary Research Building,  University of Notre Dame, Notre Dame, IN 46556

Gabriel L. Converse3

Department of Aerospace and Mechanical Engineering, Bioengineering Graduate Program, 148 Multidisciplinary Research Building,  University of Notre Dame, Notre Dame, IN 46556

Ryan K. Roeder4

Department of Aerospace and Mechanical Engineering, Bioengineering Graduate Program, 148 Multidisciplinary Research Building,  University of Notre Dame, Notre Dame, IN 46556rroeder@nd.edu

1

Engineer II, Sports Medicine, R&D, RTI Biologics, 11621 Research Circle, Alachua, FL 32615.

2

Engineer Platoon Leader, United States Army, 2003 Palmer Court, Lawrence, KS 66047.

3

Director of Bioengineering, Cardiac Surgical Research Laboratories, Children’s Mercy Hospital, Kansas City, MO 64108.

4

Corresponding author.

J. Eng. Mater. Technol 134(1), 010906 (Dec 12, 2011) (8 pages) doi:10.1115/1.4005421 History: Received August 11, 2011; Revised October 10, 2011; Accepted October 25, 2011; Published December 12, 2011; Online December 12, 2011

Hydroxyapatite (HA) whisker reinforced polyetheretherketone (PEEK) composites have been investigated as bioactive materials for load-bearing orthopedic implants with tailored mechanical properties governed by the volume fraction, morphology, and preferred orientation of the HA whisker reinforcements. Therefore, the objective of this study was to establish key structure-property relationships and predictive capabilities for the design of HA whisker reinforced PEEK composites and, more generally, discontinuous short fiber-reinforced composite materials. HA whisker reinforced PEEK composites exhibited anisotropic elastic constants due to a preferred orientation of the HA whiskers induced during compression molding. Experimental measurements for both the preferred orientation of HA whiskers and composite elastic constants were greatest in the flow direction during molding (3-axis, C33 ), followed by the transverse (2-axis, C22 ) and pressing (1-axis, C11 ) directions. Moreover, experimental measurements for the elastic anisotropy and degree of preferred orientation in the same specimen plane were correlated. A micromechanical model accounted for the preferred orientation of HA whiskers using two-dimensional implementations of the measured orientation distribution function (ODF) and was able to more accurately predict the orthotropic elastic constants compared to common, idealized assumptions of randomly oriented or perfectly aligned reinforcements. Model predictions using the 3-2 plane ODF, and the average of the 3-1 and 3-2 plane ODFs, were in close agreement with the corresponding measured elastic constants, exhibiting less than 5% average absolute error. Model predictions for C11 using the 3-1 plane ODF were less accurate, with greater than 10% error. This study demonstrated the ability to accurately predict differences in orthotropic elastic constants due to changes in the reinforcement orientation distribution, which will aid in the design of HA whisker reinforced PEEK composites and, more generally, discontinuous short fiber-reinforced composites.

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Figures

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Figure 1

(a) HA whisker reinforced PEEK specimens were sectioned from the center of compression molded composite bars with the 1, 2, and 3 specimen axes coincident with the press, transverse, and flow directions, respectively, during compression molding. (b) For pole figure measurements using XRD, the specimen was positioned using a ¼-circle Eulerian cradle goniometer with the 1, 2, and 3 specimen axes initially aligned with the x-, y-, and z-axes of the goniometer, respectively. The Bragg angles, 2θ (2θ = θ1  + θ2 ), tilt angle, χ, and rotation angle, φ, correspond to rotations about the goniometer axes. (c) Stereographic projection showing the showing specimen axes and Euler angles. Dashed lines show 2D implementations of the ODF in the 3-1 and 3-2 specimen planes for use in the micromechanical model. The 3-T ODF was averaged about φ. A scalar measure of the degree of preferred orientation was taken as the volume fraction of HA whiskers with c-axes oriented within 30 deg of the 1, 2, and 3 specimen axes, as shown.

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Figure 2

Schematic diagram of the micromechanical model used to predict the anisotropic elastic constants of HA whisker reinforced PEEK composites. Structural parameters in italics were experimentally measured

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Figure 3

Elastic constants measured in each of the three principal specimen axes (C11 , C22 , and C33 ) of PEEK composites increased with increased HA whisker volume fraction (p < 0.0001, ANOVA) and exhibited orthotropic symmetry at reinforcement levels greater than 20 vol. %, with C33  > C22  > C11 (*p < 0.05, Tukey–Kramer). Error bars show one standard deviation. Experimental data are given in Table 2.

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Figure 4

Representative recalculated pole figures for a PEEK composite reinforced with 50 vol. % HA whiskers showing a c-axis (001) preferred orientation in the specimen 3-axis. There was also a weaker c-axis (001) preferred orientation in the specimen 2-axis relative to the 1-axis. The orientation distribution is shown in units of multiples of a random distribution (MRD), where MRD = 1 corresponds to a random distribution

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Figure 5

The volume fraction of HA whisker crystals in the PEEK matrix oriented within 30 deg of each specimen axis was greatest in the 3-axis, followed by the 2-axis and 1-axis. Data was pooled across all reinforcement levels. Error bars show one standard deviation. Asterisks indicate a statistically significant difference from all other axes (p < 0.05, Tukey–Kramer)

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Figure 6

The measured elastic anisotropy ratio of PEEK composites increased with an increased preferred orientation of HA whiskers, as measured by the oriented crystal ratio

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Figure 7

Linear least squares regression revealed a strong correlation between micromechanical model predictions using 2D implementations of the measured ODF (3-1 plane, 3-2 plane, and average 3-T) and the corresponding experimental data (p < 0.0001, R2  > 0.98). Model predictions of C33 using the 3-1 plane ODF (p = 0.09, paired t-test) and C22 using the 3-2 plane ODF (p = 0.79, paired t-test) were not statistically different from experimental data. All other predictions exhibited statistically significant differences from experimental data (p < 0.05, paired t-test) though the average error may have been less than 5%

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Figure 8

Comparison of experimental data and micromechanical model predictions for the longitudinal and transverse elastic constants using 2D implementations of the measured ODF (3-1 plane, 3-2 plane, and average 3-T), as well as common idealized assumptions of randomly oriented or perfectly aligned whiskers. Error bars show one standard deviation. Asterisks indicate differences between model predictions and experimental data that are not statistically significant (p > 0.05, ANOVA). Model predictions using the 3-2 plane ODF and the average 3-T ODF were in close agreement with the corresponding measured elastic constants, exhibiting less than 5% average absolute error (Table 3). Model predictions for C11 using the 3-1 plane ODF were less accurate, with greater than 10% error (Table 3)

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