journal of the mechanical behavior of biomedical materials 41 (2015) 136 –148

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Research Paper

Monotonic and cyclic loading behavior of porous scaffolds made from poly(para-phenylene) for orthopedic applications Anthony J. Hoyta, Christopher M. Yakackib, Ray S. Fertig IIIa, R. Dana Carpenterb, Carl P. Fricka,n a

University of Wyoming, Department of Mechanical Engineering, Laramie, WY, USA University of Colorado Denver, Department of Mechanical Engineering, Denver, CO, USA

b

ar t ic l e in f o

abs tra ct

Article history:

Porous poly(para-phenylene) (PPP) scaffolds have tremendous potential as an orthopedic

Received 20 June 2014

biomaterial; however, the underlying mechanisms controlling the monotonic and cyclic

Received in revised form

behavior are poorly understood. The purpose of this study was to develop a method to

2 October 2014

integrate micro-computed tomography (μCT), finite-element analysis (FEA), and experi-

Accepted 6 October 2014

mental results to uncover the relationships between the porous structure and mechanical

Available online 16 October 2014

behavior. The μCT images were taken from porous PPP scaffolds with a porosity of 75 vol%

Keywords:

and pore size distribution between 420 and 500 mm. Representative sections of the image

Aromatic polymers

were segmented and converted into finite-element meshes. It was shown through FEA that

Porous

localized stresses within the microstructure were approximately 100 times higher than the

Fatigue

applied global stress during the linear loading regime. Experimental analysis revealed the

Orthopedics

S–N fatigue curves for fully dense and porous PPP samples were parallel on log–log plots,

Poly(para-phenylene)

with the endurance limit for porous samples in tension being approximately 100 times

Mechanical properties

lower than their solid PPP counterparts (0.3–35 MPa) due to the extreme stress concentrations caused by the porous microarchitecture. The endurance limit for porous samples in compression was much higher than in tension (1.60 MPa). Through optical, laser-scanning, and scanning-electron microscopy it was found that porous tensile samples failed under Mode I fracture in both monotonic and cyclic loading. By comparison, porous compressive samples failed via strut buckling/pore collapse monotonically and by shearing fracture during cyclic loading. Monotonic loading showed that deformation behavior was strongly correlated with pore volume fraction, matching foam theory well; however, fatigue behavior was much more sensitive to local stresses believed to cause crack nucleation. & 2014 Elsevier Ltd. All rights reserved.

n

Corresponding author. Tel.: þ1 303 766 4068. E-mail address: [email protected] (C.P. Frick).

http://dx.doi.org/10.1016/j.jmbbm.2014.10.004 1751-6161/& 2014 Elsevier Ltd. All rights reserved.

journal of the mechanical behavior of biomedical materials 41 (2015) 136 –148

1.

Introduction

Poly(para-phenylenes) (PPPs) consist of directly linked repeating phenyl units (benzene rings) resulting in strength and stiffness values much greater than other traditional polymeric biomaterials (Morgan et al., 2006; Pei and Friedrich, 2012; Vuorinen et al., 2008). A recent approach in the polymerization of PPPs has been to add side groups to the aromatic backbone, which allows for increased degree of polymerization (Taylor and Samulski, 2000; Percec et al., 1999; Cianga et al., 2002). Therefore, PPPs can now be manufactured in bulk, which has allowed them to be used as a structural engineering material with excellent chemical stability. They are widely considered the stiffest and strongest commercially available thermoplastics, even though their material properties can vary based on the specific side groups present. To date only a handful of studies have investigated the potential use of PPPs as a biomaterial. A study by Vuorinen et al. (2008) investigated the effect of water absorption on the mechanical properties of PPP. They showed that water absorption was less than 1% after 44 days of soaking and a little-to-no effect was observed on the mechanical properties. Further testing by some of the current authors revealed that the mechanical properties stayed within one standard deviation of dry conditions after soaking in an aqueous environment for over 1 year (Frick et al., 2014). The bulky side groups within the structure of PPPs act as diffusional barriers that prevent water molecules from swelling the polymer (Barnes et al., 1988; Corkhill et al., 1987), resulting in negligible effects on the mechanical properties. In addition to absorption testing, initial cytotoxicity testing of PPP (Frick et al., 2014) shows that it is non-toxic, which was expected due to its chemical inertness. The mechanical characteristics of the PPP used in this study (PrimoSpire PR-250) were determined in comparison to other common biomedical grade polymers (Frick et al., 2014); it was found that PPP has strength and stiffness much greater than these materials. It was shown that PPP has an average tensile strength of 141 MPa, exceeding that of polyetheretherketone (PEEK) (96 MPa) and high density polyethelene (HDPE) (30 MPa). It was also shown that the average elastic modulus of PPP is approximately 5.0 GPa, far greater than that of PEEK, which ranges from 2.2 to 3.4 GPa (Yakacki, 2013), and HDPE, which is approximately 1.10 GPa (Callister and Rethwisch, 2010). The direct linkage of repeating phenyl units inherent in the microstructure of PPP provides strong anti-rotational biaryl bonds which lead to its exceptional mechanical strength and stiffness. Moreover, the addition of side groups along its backbone causes steric hindrance which further limit chain mobility. Despite its outstanding mechanical behavior, the viability of PPP as a loadbearing biomaterial has been largely uninvestigated. Porous scaffolds are commonly proposed for orthopedic applications to overcome the failures associated with the loosening of the implant–bone interface (Agrawal and Ray, 2001; Hench, 1991; Rezwan et al., 2006; Converse et al., 2010, 2009; Karageorgiou and Kaplan, 2005; Causa et al., 2006; Kretlow and Mikos, 2007). A porous scaffold could alleviate these problems by allowing for osteointegration, i.e. the physical intermix of bone and implant. The fundamental premise is that during healing the osteoblast cells will penetrate and proliferate into the

137

open-cell porous scaffold. A critical challenge facing orthopedic implants is matching the mechanical properties of trabecular bone. Metal implants tend to have far greater mechanical properties than bone, leading to stress shielding which prevents full healing of the injured site (Bobyn et al., 1992; Bugbee et al., 1997; Nagels et al., 2003; Lewis, 2013). Along with this, bone resorption is common due to the disuse and lack of stimulus for bone maintenance. Porous scaffolds made from traditional polymeric biomaterials lack the strength and stiffness required to match those of trabecular bone. But due to the high bulk modulus of PPP, it can be manufactured at a relatively high porosity, which is necessary for successful osteointegration in vivo (Karageorgiou and Kaplan, 2005), while still matching the mechanical properties of trabecular bone. For example, a recent study found that the elastic modulus of 80 vol% porous PPP was over 120 MPa, while for 70 vol% porous PPP it was approximately 300 MPa (DiRienzo et al., 2014). The manner in which PPP scaffolds can be manufactured also makes it a viable candidate for orthopedic applications. PPP can be solution cast, hot injection molded, or hot-press sintered into a desired geometry. A manufacturing technique for fabricating porous PPP was established in a previous study (DiRienzo et al., 2014). It was shown that for a large array of porosities and pore sizes, monotonic properties roughly matched those predicted by foam theory (Gibson and Ashby, 1988). Although a range of porous samples have already been monotonically tested, the fatigue characterization of the porous scaffolds was not conducted. Other studies have investigated the mechanical properties of biomedical porous structures and have taken into account the fatigue characteristics (Lewis, 2013; Banhart, 2001; Landy et al., 2013; Lipinski et al., 2013; Yavari et al., 2013). For example, Banhart listed fatigue testing of porous scaffolds as a necessary destructive test in the characterization of potential biomedical materials. Furthermore, the study by Landy et al. emphasized that porous PEEK met the fatigue criteria necessary for its development as a cervical interbody fusion cage. Understanding the fatigue resistance of potential biomaterials for orthopedic applications is of utmost importance due to the cyclic nature of physiological loading (Pruitt, 2005). While the fatigue behavior of fully dense PPP has been investigated in a previous study (Frick et al., 2014), the fatigue behavior of porous PPP is completely unexplored. Cyclic loading is a common source of failure in polymeric orthopedic devices due to the nature of human motion (Simske et al., 1997; Ganguly et al., 2004; Hartwig and Knaak, 1991; Brillhart and Botsis, 1994; Brillhart et al., 1991; Sobieraj et al., 2010), as such, it has been well documented that this effect must be taken into account when developing a new polymer based biomaterial. The purpose of this study is to further investigate the porous PPP that most closely matches trabecular bone: 75 vol% porous scaffolds with large pore size distribution between 420 and 500 mm (DiRienzo et al., 2014). The large pore size generally agrees with the principles of osteointegration in which pores that are greater than 300 mm are recommended (Karageorgiou and Kaplan, 2005). The focus of this study was to develop a method that utilizes a combination of micro-computed tomography (mCT) analysis, finite-element analysis (FEA), and experimental testing to understand both monotonic and cyclic behavior as well as

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journal of the mechanical behavior of biomedical materials 41 (2015) 136 –148

how the local stresses affect the overall porous behavior. The mCT results were used to quantitatively characterize the porous structure, and were subsequently used as input into the finiteelement model. The inherent advantage of this technique is that it is possible to quantitatively develop a 3D model of a complex microstructure. FEA was then used to identify stresses in discrete spatial locations throughout the porous microstructure induced by global loading. By comparing experimental results to the finite-element model, an understanding of the underlying mechanisms for fatigue and monotonic failure was established. The technique used in this work is similar to that used in other porous scaffold research (Elliott et al., 2002; Youssef et al., 2005; Kashef et al., 2013); however, these studies did not explicitly link the FEA to the cyclic behavior. The method of analysis presented here represents a potential technique for understanding and predicting monotonic and fatigue behavior for any novel micron-scale structure, and to effectively relate the structure to the mechanical properties.

Solutions USA, Inc., Malvern, PA) with an isometric voxel size of 31 μm. The images were imported into ScanIP (Simpleware, Ltd., Exeter, UK) software for image processing and finiteelement mesh generation. Voxels containing PPP were segmented from the surrounding air using a threshold-driven region growing algorithm. The lower threshold was adjusted so that the porosity of the model matched the known porosity of 75 vol%. In order to accurately represent the overall behavior of the porous structure, the sample size must be at least five times the mean pore size (Roberts and Garboczi, 2002). Accordingly, a 3-mm cube of the material (also with 75 vol% porosity) was then selected from the center of the cylindrical sample. An island removal filter was used to remove any fragments that were unconnected to the material structure, and a cavity fill process was used to remove any small voids in the material. The voxels in the image were then converted to tetrahedral elements for subsequent finite-element analysis.

2.4.

2.

Experimental methods

2.1.

Materials

The PPP used in this study was PrimoSpire PR-250, provided in powder form by Solvay Specialty Polymers, Inc. (Alpharetta, GA). Previous work has shown that PrimoSpire PR-250 consists of an aromatic backbone with aromatic side groups (Frick et al., 2014). Sodium chloride (NaCl) was purchased from Sigma-Aldrich Co. LLC (St. Louis, MO) and was separated by a sifting process to attain the desired crystal size appropriate for this study (420–500 mm).

2.2.

Compression molding

Open-cell porous PPP scaffolds were fabricated by a sintering technique developed from past research (DiRienzo et al., 2014). Briefly, this technique involved thoroughly mixing appropriate ratios of NaCl to PPP powder for a desired porosity based on final volume and the density of each constituent. Once the PPP powder and NaCl were mixed for the desired porosity of 75 vol%, samples were hot-press powder sintered using a hydraulic high-temperature press (Model DV-62-422, Pasadena Hydraulics, Inc.). Tensile samples were made from pressed plaques, from which the samples were cut to dogbone shapes of dimensions recommended in ASTM standard D638. Cylindrical compression samples of dimensions approximately 8  15 mm2 were fabricated in custom made cylindrical aluminum molds. Both tensile and compressive porous samples were then submerged in distilled water and agitated on a shaker plate heated to 90 1C at 60 rpm for 7–10 days, changing water daily, to ensure that all of the NaCl was leached. Samples were then dried in a vacuum oven at 90 1C for 24 h. Density measurements were then performed to validate that the desired porosity was reached. In all cases the actual porosity was within 1.5 vol% of the desired value.

2.3.

lCT imaging

Images of a representative cylindrical sample were obtained using a μCT system (Inveon micro PET/CT, Siemens Medical

Monotonic testing

Uniaxial monotonic tensile and compression testing was conducted on a hydraulic load frame (858 Mini Bionix II, MTS Systems Corporation, Eden Prairie, MN) equipped with a laser extensometer (LX 500, MTS Systems Corporation, Eden Prairie, MN) at a displacement rate of 0.01 mm/s. Reflective tape was placed directly on the sample for tensile testing and on the load frame platens for compression tests. Tensile samples were strained until fracture and compression tests were strained well into the third regime of compression behavior (densification). Tensile yield was defined as the maximum stress on the stress–strain plot. Compression yield was defined as the stress associated with the intersection of a linear fit to the elastic region and a linear fit to the plateau region.

2.5.

FEA

To study the local stresses induced within the 75 vol% porous PPP scaffold, a finite-element mesh composed of 1.2 million 3D tetrahedral elements was constructed from the mCT images using the ScanIP software described previously. This mesh was imported into Abaqus (SIMULIA, 2011) for analysis and a C3D10 (fully integrated quadratic tetragonal element) was selected. A cube of material 3 mm on each edge was selected for analysis. Because this section represented an internal section of the tested material, boundary conditions were imposed on the cube surface to ensure that surface planes remained planar and did not rotate out of their initial planes. Normal displacements on all negative cube faces were constrained to be zero. Reference points were created on each of the positive cube surfaces and equation constraints were used to tie normal degrees of freedom for all positive cube faces to corresponding degrees of freedom on the corresponding surface reference point. Displacement controlled loading was prescribed on the top surface reference node such that the global strain was ramped up to 10%. The material was assumed to behave as an isotropic elastoplastic material with initial elastic modulus of 4.9 GPa and a Poisson ratio of 0.38; this corresponded with the average bulk

journal of the mechanical behavior of biomedical materials 41 (2015) 136 –148

behavior measured for PPP. An isotropic plasticity model was used in which yielding occurred at 204 MPa with linear hardening to a plastic strain of 200% at 215 MPa (nearly perectly plastic).

2.6.

Fatigue testing

Tensile and compressive samples were fatigued using a Bose ElectroForce 3200 DMA (Eden Prairie, MN) at frequencies of 1 Hz and 10 Hz under load control. It was shown through previous research that frequency had no effect on the fatigue behavior of fully dense PPP resulting in the scatter of data falling in line with one another (Frick et al., 2014). Due to the high glass transition temperature of PPP ( 177 1C) there is little concern of localized heating that would diminish the fatigue properties. Samples pertinent to this report were subjected to cyclic loading (R E0) until failure and the number of cycles for each stress was recorded to populate an S–N curve (i.e. stress vs. number of cycles-to-failure). The number of cycles-to-failure for tensile samples was defined at fracture. For these samples, the Bose system took approximately 100–300 cycles to reach the maximum cyclic stress; samples that retained this stress for at least two decades of log cycles were kept for analysis. The cycles-to-failure for compression was defined as a sudden increase in accumulated strain as evident from a plot of strain vs. number of cycles. Some plots showed a gradual accumulation in strain as cycles increased; for these, a strain of 5% was defined as failure, which correlates with the yield strain from the monotonically tested compression results. The results from the fatigue analysis in both compression and tension were assembled into an S–N curve to show the general fatigue behavior of the material. The endurance limit (i.e. fatigue strength) for both tension and compression was defined as the stress associated with the survival of 106 cycles. In total, 15 samples were tested in tension, and 14 samples were tested in compression.

2.7.

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Dynamic mechanical analysis (DMA)

The modulus of 75 vol% porous PPP was determined using thin strips with approximate dimensions of 1.25  4.5  35 mm3. Tension and compression modulus testing was performed on a DMA (TA Instruments DMA Q800, Newcastle, DE) at approximately room temperature (25 1C). Samples were preloaded with a force associated with a stress well within the linear elastic region and then cyclically strained from 0% to 0.10% in either compression (n¼4) or tension (n¼ 3).

2.8.

Imaging

Optical images were taken of representative porous tensile and compressive samples to analyze the fracture surface using an Imaging Source camera (model DBK31BU03.H, Bremen, Germany) equipped with a Navitar Zoom 7000 lens (Rochester, New York). Images were uploaded into IC Capture Version 2.2 imaging acquisition software, also by Imaging Source. Laser-scanning microscopy (LSM) images were taken using an Olympus LEXT OLS4100 laser scanning microscope (Center Valley, PA) at an optical zoom of 5  . Because the field of view was approximately 5 mm2 at this magnification, a stitch function within the LEXT software was utilized to build images of the entire fracture surface for tensile and compressive samples. High magnification images were taken using an FEI Quanta 450 (Hillsboro, OR) field emission scanning-electron microscope (SEM). Images were taken using the secondary electron detector at a voltage of 5 kV and a working distance of approximately 10 mm. Samples were coated in carbon before imaging.

3.

Results

The mCT image of a representative 75 vol% porous PPP scaffold is shown in Fig. 1. Analysis of the image verified that all

Fig. 1 – μCT image of 75 vol% porous PPP compressive scaffold with an enlarged cutout view. This image shows that all NaCl had been fully leached from the structure. Also illustrated are the irregular strut patterns, peculiar cell shapes, and local fluctuations of relative density. The cutout is the RVE used as the input into the FEA model.

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the NaCl particles had been successfully leached, leaving behind an open-cell porous structure. In addition, the μCT image illustrates the irregular strut patterns, peculiar cell shapes, and local fluctuations of relative density. It is apparent that the actual structure of the porous scaffold differs drastically from the simple geometry defined by foam theory (Gibson and Ashby, 1988). The results from this analysis were subsequently used as the input for the FEA model; a 3 mm by 3 mm cube of material within the scaffold was selected such that the internal behavior of the structure could be modeled without the external effects associated with a free edge. The monotonic strain-to-failure plots of 75 vol% porous PPP shown in Fig. 2A and B illustrate the general behavior of porous PPP in tension and compression, respectively. In tension, the porous scaffold shows a linear region followed by a short plateau and fracture. Failure is brittle in nature with an average elastic modulus of 143 MPa followed by an average strength of 3.5 MPa. The compression testing of porous PPP shows the three regimes typical of porous elastomeric compressive behavior similar to that described by Gibson and Ashby (1988), whose model consisted of interconnected beams. During loading there was first an elastic portion where stress increases linearly with deformation; in this regime the struts of the porous scaffold elastically bend. Upon subsequent loading there is a deviation from linearity in which the stress approaches a plateau regime; here individual struts bend and buckle at discrete locations. Finally, a densification regime in

which the struts plastically deform and collapse, ultimately crushing the porous structure. In this regime, the stress rises steeply and the porous structure begins to behave as a compacted solid. The average elastic modulus and strength in compression of the porous scaffold were 167 MPa and 6.6 MPa, respectively. Table 1 summarizes averaged porous mechanical properties and one standard deviation alongside

Fig. 2 – Monotonic strain-to-failure behavior of representative 75 vol% porous PPP. (A) Tensile results show brittle behavior and premature failure. (B) Compressive results show the 3 stages typical of porous compressive behavior: linear elastic, plateau, and densification.

Fig. 3 – (A) Maximum principal stresses (in MPa) shown for a 75 vol% RVE under an applied tensile stress of 0.14 MPa. All deformation under this applied load is elastic. (B) Tensile results from FEA model compared with representative experimental data.

Table 1 – Mechanical properties of 75 vol% porous PPP in comparison to fully dense PPP. The listed values represent the average and one standard deviation. Fully dense PPP

(MPa)

Elastic modulus Tensile strength Compressive strength

50087562 141.1710.0 167.877.1

Porous PPP Tensile modulus Tensile strength Compressive modulus Compressive strength

(MPa) 142.9713.9 3.570.2 167.4718.5 6.670.3

journal of the mechanical behavior of biomedical materials 41 (2015) 136 –148

the yield strength and modulus of fully dense PPP in both tension and compression. Fig. 3A shows the local maximum principal stresses in the porous scaffold computed using the FEA under purely elastic loading of a globally applied stress of 0.14 MPa. Note that localized strut regions in the porous material are under stresses two orders of magnitude larger than the applied stress. A predicted FEA tensile stress–strain curve was computed and

Table 2 – Constants A and b associated with Eq. (1), determined through power law curve fit to experimental results, for fully dense PPP and 75 vol% porous PPP in both compression and tension. Note the similarity in values for the exponential (b). Also listed are the endurance limits reached for fully dense and both porous samples. The porous compressive samples had a higher endurance limit than the porous tensile samples. PPP sample

A

b

Endurance limit (MPa)

Fully dense Porous— compression Porous—tension

329.0 39.4

 0.18  0.23

35 1.60

6.4

 0.21

0.30

compared with the experimental results of Fig. 2A. This comparison is shown in Fig. 3B, where good agreement is observed up to failure of the experimental sample. The discrepancy immediately prior to failure is due to the fact that fracture is not explicitly modeled in the FEA simulation,

141

whereas fracture is the final failure associated with the experimental data. Nevertheless, the local stresses in the elastic loading regime prior to failure are assumed to be accurate. Fatigue testing was conducted on 75 vol% porous PPP in tension and compression, and compared to tensile fatigue of fully dense PPP (Frick et al., 2014). Fig. 4A shows the number of cycles to failure as a function of applied stress (so-called S–N curves). Fig. 4B displays just the porous samples in semi-log plot format for clarity. As can be seen, the general characteristic of both curves follows a typical power law curve fit of the form

Fig. 4 – (A) An S–N curve comparing fully dense PPP to 75 vol% porous PPP in tension and compression. This shows the tensile fatigue strength (σe) of fully dense PPP and also the near parallel relationship between fully dense, porous compression, and porous tension. Note: Log–log scale. (B) Zoomed in view of S–N curve to include just 75 vol% porous PPP samples on a semi-log plot for clarity. This shows the porous fatigue strength for both compressive and tensile samples (σe).

originally proposed by Basquin (1910) σ ¼ ANbf

ð1Þ

where Nf is the number of cycles to failure associated with an induced cyclic stress amplitude, σ, while A and b are constants that are determined through a least squares approach used to fit a line to the data points. From these relationships, the constants from Eq. (1) were determined for each fatigue test and are presented in Table 2. It is important to note that the values for b are relatively close for all three fatigue tests, indicating that the general behavior is similar. In fact, they all show values close to  0.2, resulting in three nearly parallel curves, as is evident in Fig. 4A. For this study the endurance limit was defined as the stress associated with a sample that did not fail while surpassing 106 cycles. Table 2 also summarizes the experimental endurance limits achieved during this study, which are also shown on the S–N curves in Fig. 4 denoted as σe. As suggested by the large differences in strengths between compression and tension in the monotonic tests, the porous scaffold had a significantly higher endurance limit (approximately a factor of 5) in compression than in tension. There is also a noticeably large difference between the endurance limit of fully dense and porous PPP samples. In fact, the ratio of fully dense tensile to porous tensile endurance limits is nearly a factor of 117. A large difference is expected since the introduction of voids into the bulk structure also introduces a large amount of stress concentration as well as a significant reduction in cross-sectional area. To further explore the behavior of 75 vol% porous PPP in fatigue, data was extrapolated on a per cycle basis. The results of this are shown in Figs. 5 and 6 for tension and compression, respectively. Fig. 5A displays the stress–strain relationship for selected cycles throughout the lifetime of a representative porous tensile sample. The behavior remained linear-elastic throughout the lifetime of the sample with little-to-no evidence of a hysteresis. With increasing number of cycles, the slope of the curve begins to decrease. Fig. 5B shows the modulus and accumulation of strain as a function of cycles for the same porous tensile sample. The modulus remained relatively constant up until a critical point at around half its fatigue lifetime. This effect is somewhat mirrored by the constant strain associated with each cycle shown on the same plot up to the onset of fracture where strain increased rapidly to failure. Furthermore, there is a small change in the rate of strain

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journal of the mechanical behavior of biomedical materials 41 (2015) 136 –148

Fig. 5 – (A) Stress–strain relationship for selected fatigue cycles throughout the lifetime of a representative 75 vol% porous PPP tensile sample (failure at 83,448 cycles). The curves remain nearly parallel to one another for most of the fatigue life, with little-to-no hysteresis and a small decrease in modulus as the onset of fracture approached. (B) Modulus and strain accumulation as a function of log cycles for the same tensile sample. Modulus remains constant throughout most of the sample lifetime, with a gradual decrease in modulus towards the onset of fracture. The strain remains constant as well, with a gradual change in strain rate before a sharp change at the onset of fracture. Failure occurs through brittle Mode I fracture.

accumulation at approximately the same point where the modulus is seen to diminish, suggesting a deviation from linear-elastic behavior. Similar results are seen for a representative porous sample in compression, as presented in Fig. 6. The stress–strain relationship illustrated in Fig. 6A shows that most of the lifetime of the compression sample remained elastic with no evidence of a hysteresis. Upon further cyclic loading there is a noticeable shift in the curve denoting plastic deformation within the region associated with fracture. Fig. 6B shows that the modulus remained constant throughout the lifetime of the sample up until the onset of fracture where the modulus decreased rapidly. This effect is a reflection of the accumulation of strain shown on the same plot for the porous compression sample. Strain remained constant throughout the lifetime of the sample with a drastic increase with the onset of fracture, which was also captured in the stress–strain plot in Fig. 6A. Fig. 7A illustrates a tensile fatigue fracture surface of a representative porous sample through optical, LSM, and SEM imaging alongside Fig. 7B which shows analogous results for a monotonic tensile fracture surface. As is evident from the

Fig. 6 – (A) Stress–strain relationship for selected fatigue cycles throughout the lifetime of a representative 75 vol% porous PPP compressive sample (failed at 18,320 cycles). The curves remain nearly in line with one another with no hysteresis up until the onset of fracture where plastic strain is seen to occur. (B) Modulus and strain accumulation as a function of log cycles for the same compressive sample. Modulus remains constant throughout the majority of the sample lifetime, with a sudden decrease in modulus at the onset of fracture. The accumulated strain remains constant as well, with a sharp increase at the onset of fracture. Failure is brought on by shearing mechanisms.

optical image in column A, the porous tensile fatigue sample fractured nearly perpendicular to the direction of loading, indicating brittle Mode I fracture, similar to that of the monotonically tested sample in column B. The LSM images show the height contours of the fatigue fracture surfaces. The color scale included with each image illustrates the height associated with each color; red being the highest and purple/black being the lowest. Thus, the red on the tensile samples indicate a smooth surface and the yellow/green openings throughout the sample indicate the presence of pores. If there were cracks formed away from the fracture surface they would be visible by yellow or green cracks throughout the red surface. The LSM images also show surface artifacts formed by imperfections in the aluminum molding plates. This was verified through LSM imaging of an untested sample, which showed these same surface artifacts. Further investigation near the fracture surface with the SEM for both the fatigue and monotonically loaded specimens showed no evidence of global damage away from the fracture surface. These collections of images indicate that nucleation and propagation of a single crack lead to ultimate failure of the sample.

journal of the mechanical behavior of biomedical materials 41 (2015) 136 –148

143

Fig. 7 – Tensile samples of 75 vol% porous PPP showing fracture surface through optical, LSM, and SEM imaging techniques. Successive images shown in columns A and B are of a tensile fatigue sample and a monotonically tested tensile sample, respectively. As is evident from the images, there are no signs of cracking away from the fracture surface for both fatigued and monotonically failed samples. Both exhibit Mode I fracture in which a strut fails and the crack coelesced until ultimate failure of the sample.

The image collections in Fig. 8 show the fracture surface of a representative fatigued compressive sample (Fig. 8A) alongside a monotonically failed sample (Fig. 8B), in the same manner as that of Fig. 7. These images clearly show the differences in failure of the fatigue sample and the monotonic sample. The fatigue failure illustrates a crack which formed in the direction of maximum shear stress, while the monotonic sample experienced pore collapse and ultimate densification. The fatigue fracture surface in column A showed no evidence of cracks forming away from the failure crack, indicating strut failure in a localized area and crack propagation in the direction of maximum shear stress. However, it is important to note that heavy material damage occurred in the shear band area around the crack. The monotonically failed sample shows that pores collapsed which escalated into densification throughout the structure. Supplemental videos showing the failure of representative samples of porous fatigue fracture in tension and compression are available for viewing online. Reflective of the behavior shown in Figs. 5 and 7; the tensile sample showed brittle Mode I fracture. The supplemental video showing fatigue failure

of a representative compression sample is reflective of the behavior shown in Figs. 6 and 8. This video shows the propagation of a shear crack in the direction of maximum shear stress. At this point particles begin to fall from the crack as the two surfaces of the nucleated crack rub against one another. Ultimately, this is of no concern since failure was eminent at this point. At low cycles there were no particles expelled from the structure since the shear crack had not formed and the behavior remained elastic. The final stage of failure is shown at the end of the video, which reveals a shear crack similar to that shown in Fig. 8A.

4.

Discussion

The purpose of this study was to characterize the monotonic and fatigue behavior of 75 vol% porous PPP and to investigate the associated failure mechanisms. As porous PPP has been suggested as an orthopedic biomaterial, a basic characterization of its material properties is an important first step. It is important to understand the fatigue characteristics of potential

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Fig. 8 – Compressive samples of 75 vol% porous PPP showing fracture surface through optical, LSM, and SEM imaging techniques. Successive images in column A is of fatigued sample; images in column B is of monotonic sample. The fatigue sample shows evidence of a shear crack in the direction of maximum shear stress, and no signs of global cracks away from the fracture surface. The monotonically failed sample shows evidence of pore collapse and global cracking, and also compressed into the third regime of compressive failure, common with monotonic compressive failure.

biomaterials due to the cyclic nature of loading in the human body as a result of daily activity. For example, soft-tissue fixation procedures generally require 8–12 weeks for healing to take place (Rodeo et al., 1993) and need to be fully supported by the implanted device for the duration of this process. In addition, the implant must have mechanical properties similar to trabecular bone to avoid stress shielding and bone resorption. Thus it is imperative to ensure that a fixation device does not fail, by any mechanism, prior to full bone ingrowth. Typical fatigue failures occur at a fraction of the macroscopic yield strength of a particular material and defining the stresses associated with a certain number of cycles is critical in ensuring that the device will not succumb to fatigue failure. PPP with a porosity of 75 vol% was tested monotonically, and it was found that in tension failure was brittle in nature; while in compression there was strut buckling leading to massive pore collapse and densification. Monotonically, the results matched well with foam theory provided by Gibson and Ashby (1988) literature. This theory is based on the assumption that open-cell foams can be modeled as a cubic array of members with adjacent cells staggered such that

their struts invoke a force on the other member at mid-span. This force exerts a moment on the square cross-section cell edge from which the modulus and yield strength are calculated using linear-elastic deflection by standard beam theory. Under this theoretical model, the modulus and yield strength of foam can be expressed as follows: En ¼ Es 1 Vf


2

σ n ¼ 0:23σ ys 1 Vf

ð2Þ
32 
1  1 þ 1 Vf 2

ð3Þ

where values with an asterisk denote the property of the porous structure and values subscripted with an s are the property of the solid. The value Vf is the porosity of the scaffold, and in this case is 0.75. While the results presented in Fig. 2 matched well with theory, it is important to understand that the geometry of a single pore is significantly different than the simplified regular cell packing of the Ashby and Gibson model. The mCT image shown in Fig. 1 visibly demonstrates that the open-cell pores do not take on the simplified cubic array of beams as the theory assumes, but

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instead showed an irregular strut pattern with peculiar cell shapes and local fluctuations in relative density. The FEA results displayed in Fig. 3 showed that tensile stresses in discrete spatial locations during initial elastic loading are about 100 times more than the global applied stress. However, stress throughout most of the porous specimen is only about 10 times greater than the global applied stress. During global loading, over what appears to be linear loading, the local stresses begin to exceed the yield strength of the bulk material. Given the assumption of perfect plasticity, the local regions under stresses above yielding deform readily and consequently, other spatial locations begin to support the applied tensile load. Therefore, the ratio of the highest local stress to the global applied tensile stress begins to decrease, and becomes more evenly distributed. Even though the monotonic results predicted by foam theory match well with experimental results, the associated microstructural mechanisms are much different. Foam theory predicts bending of idealized beams within the structure, while experimental results in tension suggest localized plasticity during initial loading that result in premature brittle fracture. Upon initial loading in compression, the struts bend and plastically deform, restricting deformation of the other surrounding struts. Further loading leads to strut buckling and pore collapse. While the local stresses of the porous scaffold are directly dependent upon pore morphology, the global stress–strain behavior is primarily dependent on pore volume fraction only. High local stresses have a small effect on the global behavior because they quickly relax due to plastic deformation and, consequently, the stress becomes more evenly distributed, similar to tension. Therefore, monotonic loading is relatively insensitive to pore size and shape; this is consistent with the findings from past research where the mechanical properties of different pore size distributions for a given volume fraction porosity were within one standard deviation of one another (DiRienzo et al., 2014). The monotonic compression results shown here are similar to those for aluminum foams (Zhou et al., 2004), in which plastic collapse in compression was caused by the formation of plastic hinges due to bending of members within the initial loading regime. Although the microstructural mechanisms are different (for aluminum, the formation of fine dislocation shear bands), the progression of plasticity is similar. The introduction of plasticity in the apparent linear domain was also observed by Youssef et al. (2005) in polyurethane foams with relative densities of 33% (i.e. Vf ¼ 0.67). They concluded through FEA modeling that local micro-plastic deformation was the key mechanism for failure of porous materials. The monotonic results shown in Fig. 2 and Table 1 exemplify the significant difference between porous compression and porous tension; this effect has also been observed in opencell aluminum foams (Harte et al., 1999). During tensile loading, local areas experience a progression of plasticity that causes a deviation from linear elasticity. The pores inherently induce large stress concentrations, as was observed through the FEA model in Fig. 3, that initiate a single Mode I crack. This mechanism has also been observed in polyvinyl chloride foams in which brittle tensile fracture was initiated at a crack tip that then propagated through the cross-section until failure (Kabir et al., 2006). In compression, the initial loading scheme is

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similar to that of tensile since their elastic moduli are statistically similar. But once local struts begin to plastically bend and buckle, they inherently restrict the motion of neighboring struts, resulting in higher effective compressive yield strength than in tension. This local densification has been studied in polyurethane foam where bands of locally collapsed cells impinged on neighboring cells, effectively restricting their motion (Elliott et al., 2002). Subsequently, once yielding has occurred, local pockets of plasticity within the PPP compressive scaffold lead to the structure experiencing massive bending and buckling as it approaches the plateau regime; here, pores collapse and densification of the whole structure ensues. Both monotonic tensile and compressive failures are brought on by early plastic deformation within the initial loading regime, as verified by the FEA results shown in Fig. 3. This model shows that individual struts in the scaffold experience stresses on the order of or above the yield strength within the initial loading regime, resulting in premature failure for both loading types. The tensile fatigue fracture surface shown in Fig. 7A looks very similar to the monotonic fracture surface shown in Fig. 7B. The general behavior of a tensile sample under fatigue loading remains macroscopically elastic throughout the majority of its lifetime as shown in Fig. 5A, with a change in modulus as the sample approached fracture. It is observed through Fig. 5B that the modulus remains constant up to a critical point that coincides with the accumulation of permanent strain. From the S–N curves of Fig. 4 it is seen that the endurance limit achieved in fully dense tension (35 MPa) is approximately two orders of magnitude greater than the endurance limit achieved for porous tension (0.3 MPa), and the two curves are nearly parallel. The initial loading of the porous sample, as discussed previously, experiences stresses that are over 100 times greater than the nominal applied stress and therefore, the initial loading regime shows that local stresses are on the order of the fully dense endurance limit, even though the applied load is two orders of magnitude less. Thus, local struts experience stress on the order of the fully dense endurance limit, which elucidates why cracks initiate in fatigue at a lower stress. This phenomenon can be seen in the supplemental video for tensile fatigue, where a single strut experienced stresses on the order of the fully dense endurance limit resulting in nucleation of a single crack. The crack then propagated through the remaining cross-section resulting in brittle Mode I fracture. This behavior is in agreement with porous sintered steels (Chawla and Deng, 2005) as well as stainless steel foams (Kashef et al., 2013). Thus, the fracture surface of both monotonic and fatigue tension failures is associated with the same failure mechanisms and look similar, as shown in Fig. 7. Both monotonic and fatigue loaded struts experienced localized plasticity that was then distributed over the cross-section resulting in brittle failure caused by the inherent stress concentrations introduced by the NaCl crystals. In contrast to the tension samples, the fracture images of the compression samples shown in Fig. 8 indicate that there were very different modes of failure associated with monotonic loading relative to fatigue loading. The monotonic sample shown in Fig. 8B indicates the typical results from densification after massive bending and buckling of the struts associated with the early onset of plasticity that was distributed over the cross-section. The fatigue fracture surface, on the other hand,

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shows that the fracture mechanics are completely different, resulting in failure in the direction of maximum shear stress at stresses higher than tensile fatigue. The fatigue fracture results in compression of porous PPP are similar to those of trabecular bone (Choi and Goldstein, 1992), in which fracture was observed at an oblique angle of approximately 451, relative to the loading direction. A study by Zhou et al. (2005) showed that the fracture mechanics for an open-cell aluminum foam in compressive fatigue were similar to those of porous PPP. They showed that surface cracks were initiated in selected individual struts and upon growth caused an accumulation of damage, which would reach a certain critical level in which the un-failed struts could not sustain the maximum stress. At low-cycle/high-stress, the fatigue strength of PPP was on the order of the monotonic yield strength; however, at high-cycle/low-stress, the fatigue strength was a fraction of the yield strength, suggesting that strut buckling and pore collapse were not a governing mechanism, but instead surface cracks initiating from the large local stresses on the order of the bulk endurance limit. It is apparent from the stress–strain behavior shown in Fig. 6A that the compressive sample remained macroscopically elastic throughout most of the fatigue life, up until the onset of fracture, suggesting a lack of macroscopic plasticity that was observed during monotonic loading. Modulus decrease began to occur prior to ultimate failure and slightly before significant strain accumulation was observed, as shown in Fig. 6B. The supplemental video showing the fatigue failure of a representative PPP compression sample illustrates the propagation of the crack in the direction of maximum shear stress. Subsequently, this video also demonstrates the interaction of the crack surfaces once a shear crack had formed. Particles fall from the sample suggesting that the surfaces rub against one another as more struts take on the load before succumbing to the propagation of the shear crack. This fracture is fundamentally different than monotonic loading where buckling is observed over the cross-section resulting in ultimate densification. Furthermore, because of this interaction, the endurance limit is significantly higher for compression when compared to the tensile results. It is apparent that the fatigue-loaded samples were more susceptible to stress concentrations induced by the cubic nature of the NaCl crystals, whereas the monotonically loaded samples were not. This suggests that the fatigue life of the porous samples would be significantly improved if the stress concentration was lessened for a given volume fraction porosity. Nevertheless, the fatigue behavior of porous PPP is similar to that of trabecular bone, where crack growth and damage accumulation were the dominant mode of failure at high-cycle and low-cycle failure, respectively (Palissery et al., 2004; Michel et al., 1993). It is important to note that PPP offers a high glass transition temperature ( 177 1C) making it insensitive to testing frequency and temperature. As mentioned, this has been shown in past research where fully dense PPP was fatigued at 1 Hz and 10 Hz with both results falling within the normal scatter of data (Frick et al., 2014). This suggests that heating during cyclic loading has a negligible effect on mechanical behavior. It has been shown that when testing far from the glass transition temperature (i.e. room temperature) frequency will not have an effect on the endurance limit (Hartwig and Knaak, 1991). Furthermore, it was shown that cyclic loading of PPP resulted

in negligible hysteresis indicated by a tan delta of approximately zero. Thus, it is reasonable to compare the mechanical behavior of PPP to non-polymeric engineering materials. The results presented here reveal the underlying failure mechanisms for monotonic and cyclic loading for 75 vol% porous scaffolds made from PPP. Resistance to fatigue is a major concern for all biomaterial applications that are load bearing. For porous scaffolds, the material must not fail before bone can integrate into the matrix and provide additional biological support. Further investigation into the effect of pore geometry is needed to quantify how much the stress concentrations remnant of the NaCl crystals has on the fatigue life of porous PPP. A study by Chawla and Deng (2005) showed that plastic strain intensification began at the tip of irregular pores within the microstructure of porous sintered steel. They also revealed that steel with more rounded pores exhibited better monotonic and fatigue behavior as a result of more homogeneous deformation and decreased strain localization. One of the next steps in the evolution of PPP as a potential biomaterial is to further investigate in vitro cellular interaction in conjunction with in vivo cellular ingrowth studies in rat segmental defect models (Oest et al., 2007; Rai et al., 2007; Boerckel et al., 2009). Preliminary studies in this regard are already in progress. The culmination of this research will be the design and fabrication of biomedical devices, such as patient specific interbody fusion cages that can be tailored to better match the modulus of the surrounding bone. The cyclic and monotonic loading behavior, in conjunction with the cellular ingrowth results and a strong understanding of biomedical applications, will be further employed in the understanding and development of porous PPP as a biomedical device. In addition, an understanding of how osteointegration influences the mechanical properties of porous PPP will be gained that will effectively support the development of optimal patient specific orthopedic devices.

5.

Conclusions

An effective technique for relating microstructure to mechanical properties was established in this work. This technique applies mCT analysis, FEA, and experimental results to the understanding of monotonic and fatigue behavior of any novel microstructure. Using this technique, the following conclusions were drawn from the current research: 1. Monotonic tensile failure of 75 vol% porous PPP was found to begin with localized plasticity during initial loading, which led to brittle fracture. The FEA model predicted stresses approximately 100 times greater than the globally applied load at discrete spatial locations. 2. Monotonic compressive failure associated with porous PPP was the result of a local accumulation of plasticity resulting in strut buckling, pore collapse and densification, consistent with foam theory. 3. Fatigue failure of porous PPP was found to be the result of crack nucleation and propagation initiated by stress concentrations on the order of the bulk endurance limit. FEA revealed that these stress concentrations were somewhat dependent upon the geometry of the NaCl leachable media.

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4. Fatigue failure of porous PPP in tension resulted in Mode I fracture, similar to the monotonic tests. 5. The fatigue strength for porous PPP in compression was fundamentally different than in monotonic loading. This was the result of plastically deformed strut interaction with undeformed struts, preventing further motion in compression, and resulting in a shearing behavior that increased the endurance limit in comparison to tensile fatigue.

Acknowledgments The authors would like to thank Solvay Specialty Polymers, LLC for their support with this research. We would also like to express gratitude to Dustin Bales and Eric J. Losty for their contributions towards the initial results of this work. In addition, we would like to thank Kendra Huber for her assistance with mCT imaging and Chris Laursen, Susan Swapp, and Norbert Swoboda-Colberg for their assistance with SEM imaging.

Appendix A.

Supplementary Information

Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jmbbm. 2014.10.004.

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