Available online at www.sciencedirect.com

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http://dx.doi.org/10.1751-6161/& 2014 El

nCorresponding autE-mail address: c

Research Paper

Monotonic and cyclic loading behavior of porousscaffolds 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

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

a r t i c l e i n f o

Article history:

Received 20 June 2014

Received in revised form

2 October 2014

Accepted 6 October 2014

Available online 16 October 2014

Keywords:

Aromatic polymers

Porous

Fatigue

Orthopedics

Poly(para-phenylene)

Mechanical properties

1016/j.jmbbm.2014.10.004sevier Ltd. All rights rese

hor. Tel.: þ1 303 766 4068frick@uwyo.edu (C.P. Fric

a b s t r a c t

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

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

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

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

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

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

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

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

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

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

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

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

lower than their solid PPP counterparts (0.3–35 MPa) due to the extreme stress concentra-

tions 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.

rved.

.k).

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1. Introduction

Poly(para-phenylenes) (PPPs) consist of directly linked repeat-ing phenyl units (benzene rings) resulting in strength andstiffness values much greater than other traditional polymericbiomaterials (Morgan et al., 2006; Pei and Friedrich, 2012;Vuorinen et al., 2008). A recent approach in the polymerizationof PPPs has been to add side groups to the aromatic backbone,which allows for increased degree of polymerization (Taylorand Samulski, 2000; Percec et al., 1999; Cianga et al., 2002).Therefore, PPPs can now be manufactured in bulk, which hasallowed them to be used as a structural engineering materialwith excellent chemical stability. They are widely consideredthe stiffest and strongest commercially available thermoplas-tics, even though their material properties can vary based onthe specific side groups present.

To date only a handful of studies have investigated thepotential use of PPPs as a biomaterial. A study by Vuorinenet al. (2008) investigated the effect of water absorption on themechanical properties of PPP. They showed that water absorp-tion was less than 1% after 44 days of soaking and a little-to-noeffect was observed on the mechanical properties. Furthertesting by some of the current authors revealed that themechanical properties stayed within one standard deviationof dry conditions after soaking in an aqueous environment forover 1 year (Frick et al., 2014). The bulky side groups within thestructure of PPPs act as diffusional barriers that prevent watermolecules from swelling the polymer (Barnes et al., 1988;Corkhill et al., 1987), resulting in negligible effects on themechanical properties. In addition to absorption testing, initialcytotoxicity testing of PPP (Frick et al., 2014) shows that it isnon-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 othercommon biomedical grade polymers (Frick et al., 2014); it wasfound that PPP has strength and stiffness much greater thanthese materials. It was shown that PPP has an average tensilestrength 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 isapproximately 5.0 GPa, far greater than that of PEEK, whichranges from 2.2 to 3.4 GPa (Yakacki, 2013), and HDPE, which isapproximately 1.10 GPa (Callister and Rethwisch, 2010). Thedirect linkage of repeating phenyl units inherent in the micro-structure of PPP provides strong anti-rotational biaryl bondswhich lead to its exceptional mechanical strength and stiffness.Moreover, the addition of side groups along its backbone causessteric hindrance which further limit chain mobility. Despite itsoutstanding mechanical behavior, the viability of PPP as a load-bearing biomaterial has been largely uninvestigated.

Porous scaffolds are commonly proposed for orthopedic

applications to overcome the failures associated with the loosen-

ing 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 heal-

ing the osteoblast cells will penetrate and proliferate into the

open-cell porous scaffold. A critical challenge facing orthopedicimplants is matching the mechanical properties of trabecularbone. Metal implants tend to have far greater mechanicalproperties than bone, leading to stress shielding which preventsfull healing of the injured site (Bobyn et al., 1992; Bugbee et al.,1997; Nagels et al., 2003; Lewis, 2013). Along with this, boneresorption is common due to the disuse and lack of stimulus forbone maintenance. Porous scaffolds made from traditionalpolymeric biomaterials lack the strength and stiffness requiredto match those of trabecular bone. But due to the high bulkmodulus of PPP, it can be manufactured at a relatively highporosity, which is necessary for successful osteointegrationin vivo (Karageorgiou and Kaplan, 2005), while still matchingthe mechanical properties of trabecular bone. For example, arecent study found that the elastic modulus of 80 vol% porousPPP was over 120 MPa, while for 70 vol% porous PPP it wasapproximately 300 MPa (DiRienzo et al., 2014).

The manner in which PPP scaffolds can be manufacturedalso makes it a viable candidate for orthopedic applications.PPP can be solution cast, hot injection molded, or hot-presssintered into a desired geometry. A manufacturing techniquefor fabricating porous PPP was established in a previous study(DiRienzo et al., 2014). It was shown that for a large array ofporosities and pore sizes, monotonic properties roughlymatched those predicted by foam theory (Gibson andAshby, 1988). Although a range of porous samples havealready been monotonically tested, the fatigue characteriza-tion of the porous scaffolds was not conducted. Other studieshave investigated the mechanical properties of biomedicalporous structures and have taken into account the fatiguecharacteristics (Lewis, 2013; Banhart, 2001; Landy et al., 2013;Lipinski et al., 2013; Yavari et al., 2013). For example, Banhartlisted fatigue testing of porous scaffolds as a necessarydestructive test in the characterization of potential biomedi-cal materials. Furthermore, the study by Landy et al. empha-sized that porous PEEK met the fatigue criteria necessary forits development as a cervical interbody fusion cage. Under-standing the fatigue resistance of potential biomaterials fororthopedic applications is of utmost importance due to thecyclic nature of physiological loading (Pruitt, 2005).

While the fatigue behavior of fully dense PPP has beeninvestigated in a previous study (Frick et al., 2014), the fatiguebehavior of porous PPP is completely unexplored. Cyclic load-ing is a common source of failure in polymeric orthopedicdevices due to the nature of humanmotion (Simske et al., 1997;Ganguly et al., 2004; Hartwig and Knaak, 1991; Brillhart andBotsis, 1994; Brillhart et al., 1991; Sobieraj et al., 2010), as such,it has been well documented that this effect must be taken intoaccount when developing a new polymer based biomaterial.The purpose of this study is to further investigate the porousPPP that most closely matches trabecular bone: 75 vol% porousscaffolds with large pore size distribution between 420 and500 mm (DiRienzo et al., 2014). The large pore size generallyagrees with the principles of osteointegration in which poresthat are greater than 300 mm are recommended (Karageorgiouand Kaplan, 2005).

The focus of this study was to develop amethod that utilizesa combination of micro-computed tomography (mCT) analysis,finite-element analysis (FEA), and experimental testing tounderstand both monotonic and cyclic behavior as well as

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how the local stresses affect the overall porous behavior. ThemCT results were used to quantitatively characterize the porousstructure, and were subsequently used as input into the finite-element model. The inherent advantage of this technique isthat it is possible to quantitatively develop a 3D model of acomplex microstructure. FEA was then used to identify stressesin discrete spatial locations throughout the porous microstruc-ture induced by global loading. By comparing experimentalresults to the finite-element model, an understanding of theunderlying mechanisms for fatigue and monotonic failure wasestablished. The technique used in this work is similar to thatused in other porous scaffold research (Elliott et al., 2002;Youssef et al., 2005; Kashef et al., 2013); however, these studiesdid not explicitly link the FEA to the cyclic behavior. Themethod of analysis presented here represents a potentialtechnique for understanding and predicting monotonic andfatigue behavior for any novel micron-scale structure, and toeffectively relate the structure to the mechanical properties.

2. Experimental methods

2.1. Materials

The PPP used in this study was PrimoSpire PR-250, provided inpowder form by Solvay Specialty Polymers, Inc. (Alpharetta,GA). Previous work has shown that PrimoSpire PR-250 consistsof an aromatic backbone with aromatic side groups (Fricket al., 2014). Sodium chloride (NaCl) was purchased fromSigma-Aldrich Co. LLC (St. Louis, MO) and was separated bya sifting process to attain the desired crystal size appropriatefor this study (420–500 mm).

2.2. Compression molding

Open-cell porous PPP scaffolds were fabricated by a sinteringtechnique developed from past research (DiRienzo et al., 2014).Briefly, this technique involved thoroughly mixing appropriateratios of NaCl to PPP powder for a desired porosity based on finalvolume and the density of each constituent. Once the PPP powderand NaCl were mixed for the desired porosity of 75 vol%, sampleswere hot-press powder sintered using a hydraulic high-tem-perature press (Model DV-62-422, Pasadena Hydraulics, Inc.).Tensile samples were made from pressed plaques, from whichthe samples were cut to dogbone shapes of dimensions recom-mended in ASTM standard D638. Cylindrical compression sam-ples of dimensions approximately 8�15mm2 were fabricated incustom made cylindrical aluminum molds. Both tensile andcompressive porous samples were then submerged in distilledwater and agitated on a shaker plate heated to 90 1C at 60 rpm for7–10 days, changing water daily, to ensure that all of the NaClwas leached. Samples were then dried in a vacuum oven at 90 1Cfor 24 h. Density measurements were then performed to validatethat the desired porosity was reached. In all cases the actualporosity was within 1.5 vol% of the desired value.

2.3. lCT imaging

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

Solutions USA, Inc., Malvern, PA) with an isometric voxel sizeof 31 μm. The images were imported into ScanIP (Simpleware,Ltd., Exeter, UK) software for image processing and finite-element mesh generation. Voxels containing PPP were seg-mented from the surrounding air using a threshold-drivenregion growing algorithm. The lower threshold was adjustedso that the porosity of the model matched the known porosityof 75 vol%. In order to accurately represent the overall beha-vior of the porous structure, the sample size must be at leastfive 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 cylindricalsample. An island removal filter was used to remove anyfragments that were unconnected to the material structure,and a cavity fill process was used to remove any small voids inthe material. The voxels in the image were then converted totetrahedral elements for subsequent finite-element analysis.

2.4. Monotonic testing

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

2.5. FEA

To study the local stresses induced within the 75 vol% porousPPP scaffold, a finite-element mesh composed of 1.2 million3D tetrahedral elements was constructed from the mCTimages using the ScanIP software described previously. Thismesh was imported into Abaqus (SIMULIA, 2011) for analysisand a C3D10 (fully integrated quadratic tetragonal element)was selected. A cube of material 3 mm on each edge wasselected for analysis. Because this section represented aninternal section of the tested material, boundary conditionswere imposed on the cube surface to ensure that surfaceplanes remained planar and did not rotate out of their initialplanes. Normal displacements on all negative cube faceswere constrained to be zero. Reference points were createdon each of the positive cube surfaces and equation con-straints were used to tie normal degrees of freedom for allpositive cube faces to corresponding degrees of freedom onthe corresponding surface reference point. Displacementcontrolled loading was prescribed on the top surface refer-ence node such that the global strain was ramped up to 10%.The material was assumed to behave as an isotropic elasto-plastic material with initial elastic modulus of 4.9 GPa and aPoisson ratio of 0.38; this corresponded with the average bulk

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behavior measured for PPP. An isotropic plasticity model wasused in which yielding occurred at 204 MPa with linearhardening to a plastic strain of 200% at 215 MPa (nearlyperectly plastic).

2.6. Fatigue testing

Tensile and compressive samples were fatigued using a BoseElectroForce 3200 DMA (Eden Prairie, MN) at frequencies of1 Hz and 10 Hz under load control. It was shown throughprevious research that frequency had no effect on the fatiguebehavior of fully dense PPP resulting in the scatter of datafalling in line with one another (Frick et al., 2014). Due to thehigh glass transition temperature of PPP (�177 1C) there islittle concern of localized heating that would diminish thefatigue properties. Samples pertinent to this report weresubjected to cyclic loading (RE0) until failure and the numberof cycles for each stress was recorded to populate an S–Ncurve (i.e. stress vs. number of cycles-to-failure). The numberof cycles-to-failure for tensile samples was defined at frac-ture. For these samples, the Bose system took approximately100–300 cycles to reach the maximum cyclic stress; samplesthat retained this stress for at least two decades of log cycleswere kept for analysis. The cycles-to-failure for compressionwas defined as a sudden increase in accumulated strain asevident from a plot of strain vs. number of cycles. Some plotsshowed a gradual accumulation in strain as cycles increased;for these, a strain of 5% was defined as failure, whichcorrelates with the yield strain from the monotonically testedcompression results. The results from the fatigue analysis inboth compression and tension were assembled into an S–Ncurve to show the general fatigue behavior of the material.The endurance limit (i.e. fatigue strength) for both tensionand compression was defined as the stress associated withthe survival of 106 cycles. In total, 15 samples were tested intension, and 14 samples were tested in compression.

Fig. 1 – μCT image of 75 vol% porous PPP compressive scaffold whad been fully leached from the structure. Also illustrated are tfluctuations of relative density. The cutout is the RVE used as th

2.7. Dynamic mechanical analysis (DMA)

The modulus of 75 vol% porous PPP was determined using thinstrips with approximate dimensions of 1.25�4.5�35mm3.Tension and compression modulus testing was performed ona DMA (TA Instruments DMA Q800, Newcastle, DE) at approxi-mately room temperature (25 1C). Samples were preloaded witha force associated with a stress well within the linear elasticregion and then cyclically strained from 0% to 0.10% in eithercompression (n¼4) or tension (n¼3).

2.8. Imaging

Optical images were taken of representative porous tensileand compressive samples to analyze the fracture surface usingan 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 2.2imaging acquisition software, also by Imaging Source.

Laser-scanning microscopy (LSM) images were taken usingan Olympus LEXT OLS4100 laser scanning microscope (CenterValley, PA) at an optical zoom of 5� . Because the field of viewwas approximately 5 mm2 at this magnification, a stitchfunction within the LEXT software was utilized to buildimages of the entire fracture surface for tensile and com-pressive samples.

High magnification images were taken using an FEI Quanta450 (Hillsboro, OR) field emission scanning-electron microscope(SEM). Images were taken using the secondary electron detectorat a voltage of 5 kV and a working distance of approximately10mm. Samples were coated in carbon before imaging.

3. Results

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

ith an enlarged cutout view. This image shows that all NaClhe irregular strut patterns, peculiar cell shapes, and locale input into the FEA model.

Table 1 – Mechanical properties of 75 vol% porous PPP incomparison to fully dense PPP. The listed values repre-sent the average and one standard deviation.

Fully dense PPP (MPa)

Elastic modulus 50087562Tensile strength 141.1710.0Compressive strength 167.877.1

Porous PPP (MPa)Tensile modulus 142.9713.9Tensile strength 3.570.2Compressive modulus 167.4718.5Compressive strength 6.670.3

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the NaCl particles had been successfully leached, leavingbehind an open-cell porous structure. In addition, the μCTimage illustrates the irregular strut patterns, peculiar cellshapes, and local fluctuations of relative density. It is appar-ent that the actual structure of the porous scaffold differsdrastically from the simple geometry defined by foam theory(Gibson and Ashby, 1988). The results from this analysis weresubsequently used as the input for the FEA model; a 3 mm by3 mm cube of material within the scaffold was selected suchthat the internal behavior of the structure could be modeledwithout the external effects associated with a free edge.

The monotonic strain-to-failure plots of 75 vol% porous PPPshown in Fig. 2A and B illustrate the general behavior of porousPPP in tension and compression, respectively. In tension, theporous scaffold shows a linear region followed by a shortplateau and fracture. Failure is brittle in nature with an averageelastic modulus of 143 MPa followed by an average strength of3.5 MPa. The compression testing of porous PPP shows thethree regimes typical of porous elastomeric compressive beha-vior similar to that described by Gibson and Ashby (1988),whose model consisted of interconnected beams. During load-ing there was first an elastic portion where stress increaseslinearly with deformation; in this regime the struts of theporous scaffold elastically bend. Upon subsequent loadingthere is a deviation from linearity in which the stress app-roaches a plateau regime; here individual struts bend andbuckle at discrete locations. Finally, a densification regime in

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

which the struts plastically deform and collapse, ultimatelycrushing the porous structure. In this regime, the stress risessteeply and the porous structure begins to behave as acompacted solid. The average elastic modulus and strengthin compression of the porous scaffold were 167 MPa and6.6 MPa, respectively. Table 1 summarizes averaged porousmechanical properties and one standard deviation alongside

Fig. 3 – (A) Maximum principal stresses (in MPa) shown for a75 vol% RVE under an applied tensile stress of 0.14 MPa. Alldeformation under this applied load is elastic. (B) Tensileresults from FEA model compared with representativeexperimental data.

Table 2 – Constants A and b associated with Eq. (1),determined through power law curve fit to experimentalresults, for fully dense PPP and 75 vol% porous PPP inboth compression and tension. Note the similarity invalues for the exponential (b). Also listed are the endur-ance limits reached for fully dense and both poroussamples. The porous compressive samples had a higherendurance limit than the porous tensile samples.

PPP sample A b Endurance limit(MPa)

Fully dense 329.0 �0.18 35Porous—compression

39.4 �0.23 1.60

Porous—tension 6.4 �0.21 0.30

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the yield strength and modulus of fully dense PPP in bothtension 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

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 dis-

crepancy immediately prior to failure is due to the fact that

fracture is not explicitly modeled in the FEA simulation,

whereas fracture is the final failure associated with the experi-

mental 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 offully dense PPP (Frick et al., 2014). Fig. 4A shows the numberof cycles to failure as a function of applied stress (so-calledS–N curves). Fig. 4B displays just the porous samples in semi-logplot format for clarity. As can be seen, the general characteristicof 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 thetensile fatigue strength (σe) of fully dense PPP and also thenear parallel relationship between fully dense, porouscompression, 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 showsthe porous fatigue strength for both compressive and tensilesamples (σe).

originally proposed by Basquin (1910)

σ ¼ANbf ð1Þ

where Nf is the number of cycles to failure associated with aninduced cyclic stress amplitude, σ, while A and b are constantsthat are determined through a least squares approach used tofit a line to the data points. From these relationships, theconstants from Eq. (1) were determined for each fatigue testand are presented in Table 2. It is important to note that thevalues for b are relatively close for all three fatigue tests,indicating that the general behavior is similar. In fact, they allshow values close to �0.2, resulting in three nearly parallelcurves, as is evident in Fig. 4A.

For this study the endurance limit was defined as the stressassociated with a sample that did not fail while surpassing 106

cycles. Table 2 also summarizes the experimental endurancelimits achieved during this study, which are also shown on theS–N curves in Fig. 4 denoted as σe. As suggested by the largedifferences in strengths between compression and tension in themonotonic tests, the porous scaffold had a significantly higherendurance limit (approximately a factor of 5) in compressionthan in tension. There is also a noticeably large differencebetween the endurance limit of fully dense and porous PPPsamples. In fact, the ratio of fully dense tensile to porous tensileendurance limits is nearly a factor of 117. A large difference isexpected since the introduction of voids into the bulk structurealso introduces a large amount of stress concentration as well asa significant reduction in cross-sectional area.

To further explore the behavior of 75 vol% porous PPP infatigue, data was extrapolated on a per cycle basis. The resultsof this are shown in Figs. 5 and 6 for tension and compres-sion, respectively. Fig. 5A displays the stress–strain relationshipfor selected cycles throughout the lifetime of a representativeporous tensile sample. The behavior remained linear-elasticthroughout the lifetime of the sample with little-to-no evidenceof a hysteresis. With increasing number of cycles, the slope ofthe curve begins to decrease. Fig. 5B shows the modulus andaccumulation of strain as a function of cycles for the sameporous tensile sample. The modulus remained relatively con-stant up until a critical point at around half its fatigue lifetime.This effect is somewhat mirrored by the constant strainassociated with each cycle shown on the same plot up to theonset of fracture where strain increased rapidly to failure.Furthermore, there is a small change in the rate of strain

Fig. 6 – (A) Stress–strain relationship for selected fatiguecycles throughout the lifetime of a representative 75 vol%porous PPP compressive sample (failed at 18,320 cycles). Thecurves remain nearly in line with one another with nohysteresis up until the onset of fracture where plastic strainis seen to occur. (B) Modulus and strain accumulation as afunction of log cycles for the same compressive sample.Modulus remains constant throughout the majority of thesample lifetime, with a sudden decrease in modulus at theonset of fracture. The accumulated strain remains constantas well, with a sharp increase at the onset of fracture. Failureis brought on by shearing mechanisms.

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

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accumulation at approximately the same point where themodulus is seen to diminish, suggesting a deviation fromlinear-elastic behavior. Similar results are seen for a represen-tative porous sample in compression, as presented in Fig. 6. Thestress–strain relationship illustrated in Fig. 6A shows that mostof the lifetime of the compression sample remained elastic withno evidence of a hysteresis. Upon further cyclic loading there isa noticeable shift in the curve denoting plastic deformationwithin the region associated with fracture. Fig. 6B shows thatthe modulus remained constant throughout the lifetime of thesample up until the onset of fracture where the modulusdecreased rapidly. This effect is a reflection of the accumulationof strain shown on the same plot for the porous compressionsample. Strain remained constant throughout the lifetime ofthe 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 arepresentative porous sample through optical, LSM, and SEMimaging alongside Fig. 7B which shows analogous results for amonotonic tensile fracture surface. As is evident from the

optical image in column A, the porous tensile fatigue samplefractured nearly perpendicular to the direction of loading,indicating brittle Mode I fracture, similar to that of the mono-tonically tested sample in column B. The LSM images show theheight contours of the fatigue fracture surfaces. The color scaleincluded with each image illustrates the height associated witheach color; red being the highest and purple/black being thelowest. Thus, the red on the tensile samples indicate a smoothsurface and the yellow/green openings throughout the sampleindicate the presence of pores. If there were cracks formedaway from the fracture surface they would be visible by yellowor green cracks throughout the red surface. The LSM imagesalso show surface artifacts formed by imperfections in thealuminum molding plates. This was verified through LSMimaging of an untested sample, which showed these samesurface artifacts. Further investigation near the fracture surfacewith the SEM for both the fatigue and monotonically loadedspecimens showed no evidence of global damage away fromthe fracture surface. These collections of images indicate thatnucleation and propagation of a single crack lead to ultimatefailure of the sample.

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 andmonotonically failed samples. Both exhibit Mode I fracture in which a strut fails and the crack coelesced until ultimate failureof the sample.

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The image collections in Fig. 8 show the fracture surface of arepresentative fatigued compressive sample (Fig. 8A) alongsidea monotonically failed sample (Fig. 8B), in the same manner asthat of Fig. 7. These images clearly show the differences infailure of the fatigue sample and the monotonic sample. Thefatigue failure illustrates a crack which formed in the directionof maximum shear stress, while the monotonic sample experi-enced pore collapse and ultimate densification. The fatiguefracture surface in column A showed no evidence of cracksforming away from the failure crack, indicating strut failure ina localized area and crack propagation in the direction ofmaximum shear stress. However, it is important to note thatheavymaterial damage occurred in the shear band area aroundthe crack. The monotonically failed sample shows that porescollapsed which escalated into densification throughout thestructure.

Supplemental videos showing the failure of representativesamples of porous fatigue fracture in tension and compressionare available for viewing online. Reflective of the behaviorshown in Figs. 5 and 7; the tensile sample showed brittle ModeI fracture. The supplemental video showing fatigue failure

of a representative compression sample is reflective of thebehavior shown in Figs. 6 and 8. This video shows thepropagation of a shear crack in the direction of maximumshear stress. At this point particles begin to fall from the crackas the two surfaces of the nucleated crack rub against oneanother. Ultimately, this is of no concern since failure waseminent at this point. At low cycles there were no particlesexpelled from the structure since the shear crack had notformed and the behavior remained elastic. The final stage offailure is shown at the end of the video, which reveals a shearcrack similar to that shown in Fig. 8A.

4. Discussion

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

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

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biomaterials due to the cyclic nature of loading in the humanbody as a result of daily activity. For example, soft-tissuefixation procedures generally require 8–12 weeks for healingto take place (Rodeo et al., 1993) and need to be fully supportedby the implanted device for the duration of this process. Inaddition, the implant must have mechanical properties similarto trabecular bone to avoid stress shielding and bone resorption.Thus it is imperative to ensure that a fixation device does notfail, by any mechanism, prior to full bone ingrowth. Typicalfatigue failures occur at a fraction of the macroscopic yieldstrength of a particular material and defining the stressesassociated with a certain number of cycles is critical in ensuringthat 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 tomassive pore collapse and densification. Monotonically, theresults matched well with foam theory provided by Gibsonand Ashby (1988) literature. This theory is based on theassumption that open-cell foams can be modeled as a cubicarray 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 celledge from which the modulus and yield strength are calcu-lated using linear-elastic deflection by standard beam theory.Under this theoretical model, the modulus and yield strengthof foam can be expressed as follows:

En ¼ Es 1�Vf� �2 ð2Þ

σn ¼ 0:23σys 1�Vf� �3

2 1þ 1�Vf� �1

2

� �ð3Þ

where values with an asterisk denote the property of theporous structure and values subscripted with an s are theproperty of the solid. The value Vf is the porosity of thescaffold, and in this case is 0.75. While the results presentedin Fig. 2 matched well with theory, it is important to under-stand that the geometry of a single pore is significantlydifferent than the simplified regular cell packing of the Ashbyand Gibson model. The mCT image shown in Fig. 1 visiblydemonstrates that the open-cell pores do not take on thesimplified cubic array of beams as the theory assumes, but

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instead showed an irregular strut pattern with peculiar cellshapes and local fluctuations in relative density.

The FEA results displayed in Fig. 3 showed that tensilestresses in discrete spatial locations during initial elasticloading are about 100 times more than the global appliedstress. However, stress throughout most of the porous speci-men is only about 10 times greater than the global appliedstress. During global loading, over what appears to be linearloading, the local stresses begin to exceed the yield strength ofthe bulk material. Given the assumption of perfect plasticity,the local regions under stresses above yielding deform readilyand consequently, other spatial locations begin to support theapplied tensile load. Therefore, the ratio of the highest localstress to the global applied tensile stress begins to decrease,and becomes more evenly distributed. Even though the mono-tonic results predicted by foam theory match well withexperimental results, the associated microstructural mechan-isms are much different. Foam theory predicts bending ofidealized beams within the structure, while experimentalresults in tension suggest localized plasticity during initialloading that result in premature brittle fracture.

Upon initial loading in compression, the struts bend andplastically deform, restricting deformation of the other sur-rounding struts. Further loading leads to strut buckling andpore collapse. While the local stresses of the porous scaffoldare directly dependent upon pore morphology, the globalstress–strain behavior is primarily dependent on pore volumefraction only. High local stresses have a small effect on theglobal behavior because they quickly relax due to plasticdeformation and, consequently, the stress becomes moreevenly distributed, similar to tension. Therefore, monotonicloading is relatively insensitive to pore size and shape; this isconsistent with the findings from past research where themechanical properties of different pore size distributions for agiven volume fraction porosity were within one standarddeviation of one another (DiRienzo et al., 2014). The monotoniccompression results shown here are similar to those foraluminum foams (Zhou et al., 2004), in which plastic collapsein compression was caused by the formation of plastic hingesdue to bending of members within the initial loading regime.Although the microstructural mechanisms are different (foraluminum, the formation of fine dislocation shear bands),the progression of plasticity is similar. The introduction ofplasticity in the apparent linear domain was also observed byYoussef et al. (2005) in polyurethane foams with relativedensities of 33% (i.e. Vf¼0.67). They concluded through FEAmodeling that local micro-plastic deformation was the keymechanism for failure of porous materials.

The monotonic results shown in Fig. 2 and Table 1 exem-plify the significant difference between porous compressionand porous tension; this effect has also been observed in open-cell aluminum foams (Harte et al., 1999). During tensile loading,local areas experience a progression of plasticity that causes adeviation from linear elasticity. The pores inherently inducelarge stress concentrations, as was observed through the FEAmodel in Fig. 3, that initiate a single Mode I crack. Thismechanism has also been observed in polyvinyl chloride foamsin which brittle tensile fracture was initiated at a crack tip thatthen propagated through the cross-section until failure (Kabiret al., 2006). In compression, the initial loading scheme is

similar to that of tensile since their elastic moduli are statis-tically similar. But once local struts begin to plastically bendand buckle, they inherently restrict the motion of neighboringstruts, resulting in higher effective compressive yield strengththan in tension. This local densification has been studied inpolyurethane foam where bands of locally collapsed cellsimpinged on neighboring cells, effectively restricting theirmotion (Elliott et al., 2002). Subsequently, once yielding hasoccurred, local pockets of plasticity within the PPP compressivescaffold lead to the structure experiencing massive bendingand buckling as it approaches the plateau regime; here, porescollapse and densification of the whole structure ensues. Bothmonotonic tensile and compressive failures are brought on byearly plastic deformation within the initial loading regime, asverified by the FEA results shown in Fig. 3. This model showsthat individual struts in the scaffold experience stresses on theorder of or above the yield strength within the initial loadingregime, resulting in premature failure for both loading types.

The tensile fatigue fracture surface shown in Fig. 7A looksvery similar to the monotonic fracture surface shown in Fig. 7B.The general behavior of a tensile sample under fatigue loadingremains macroscopically elastic throughout the majority of itslifetime as shown in Fig. 5A, with a change in modulus as thesample approached fracture. It is observed through Fig. 5B thatthe modulus remains constant up to a critical point thatcoincides with the accumulation of permanent strain. Fromthe S–N curves of Fig. 4 it is seen that the endurance limitachieved in fully dense tension (35 MPa) is approximately twoorders of magnitude greater than the endurance limit achievedfor porous tension (0.3 MPa), and the two curves are nearlyparallel. The initial loading of the porous sample, as discussedpreviously, experiences stresses that are over 100 times greaterthan the nominal applied stress and therefore, the initialloading regime shows that local stresses are on the order ofthe fully dense endurance limit, even though the applied loadis two orders of magnitude less. Thus, local struts experiencestress on the order of the fully dense endurance limit, whichelucidates why cracks initiate in fatigue at a lower stress. Thisphenomenon can be seen in the supplemental video for tensilefatigue, where a single strut experienced stresses on the orderof the fully dense endurance limit resulting in nucleation of asingle crack. The crack then propagated through the remainingcross-section resulting in brittle Mode I fracture. This behavioris 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 tensionfailures is associated with the same failure mechanisms andlook similar, as shown in Fig. 7. Both monotonic and fatigueloaded struts experienced localized plasticity that was thendistributed over the cross-section resulting in brittle failurecaused by the inherent stress concentrations introduced by theNaCl crystals.

In contrast to the tension samples, the fracture images ofthe compression samples shown in Fig. 8 indicate that therewere very different modes of failure associated with monotonicloading relative to fatigue loading. The monotonic sampleshown in Fig. 8B indicates the typical results from densificationafter massive bending and buckling of the struts associatedwith the early onset of plasticity that was distributed over thecross-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 atstresses higher than tensile fatigue. The fatigue fracture resultsin compression of porous PPP are similar to those of trabecularbone (Choi and Goldstein, 1992), in which fracture was observedat an oblique angle of approximately 451, relative to the loadingdirection.

A study by Zhou et al. (2005) showed that the fracturemechanics for an open-cell aluminum foam in compressivefatigue were similar to those of porous PPP. They showed thatsurface cracks were initiated in selected individual struts andupon growth caused an accumulation of damage, which wouldreach a certain critical level in which the un-failed struts couldnot sustain the maximum stress. At low-cycle/high-stress, thefatigue strength of PPP was on the order of the monotonic yieldstrength; however, at high-cycle/low-stress, the fatigue strengthwas a fraction of the yield strength, suggesting that strutbuckling and pore collapse were not a governing mechanism,but instead surface cracks initiating from the large local stresseson the order of the bulk endurance limit. It is apparent from thestress–strain behavior shown in Fig. 6A that the compressivesample remained macroscopically elastic throughout most ofthe fatigue life, up until the onset of fracture, suggesting a lackof macroscopic plasticity that was observed during monotonicloading. Modulus decrease began to occur prior to ultimatefailure and slightly before significant strain accumulation wasobserved, as shown in Fig. 6B. The supplemental video showingthe fatigue failure of a representative PPP compression sampleillustrates the propagation of the crack in the direction ofmaximum shear stress. Subsequently, this video also demon-strates the interaction of the crack surfaces once a shear crackhad formed. Particles fall from the sample suggesting that thesurfaces rub against one another as more struts take on theload before succumbing to the propagation of the shear crack.This fracture is fundamentally different than monotonic load-ing where buckling is observed over the cross-section resultingin ultimate densification. Furthermore, because of this interac-tion, the endurance limit is significantly higher for compressionwhen compared to the tensile results.

It is apparent that the fatigue-loaded samples were moresusceptible to stress concentrations induced by the cubic natureof the NaCl crystals, whereas the monotonically loaded sampleswere not. This suggests that the fatigue life of the poroussamples would be significantly improved if the stress concen-tration was lessened for a given volume fraction porosity.Nevertheless, the fatigue behavior of porous PPP is similar tothat of trabecular bone, where crack growth and damageaccumulation were the dominant mode of failure at high-cycleand low-cycle failure, respectively (Palissery et al., 2004; Michelet al., 1993). It is important to note that PPP offers a high glasstransition temperature (�177 1C) making it insensitive to testingfrequency and temperature. As mentioned, this has been shownin past research where fully dense PPP was fatigued at 1 Hz and10 Hz with both results falling within the normal scatter of data(Frick et al., 2014). This suggests that heating during cyclicloading has a negligible effect on mechanical behavior. It hasbeen shown that when testing far from the glass transitiontemperature (i.e. room temperature) frequency will not have aneffect 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 approximatelyzero. Thus, it is reasonable to compare the mechanical behaviorof PPP to non-polymeric engineering materials.

The results presented here reveal the underlying failuremechanisms for monotonic and cyclic loading for 75 vol%porous scaffolds made from PPP. Resistance to fatigue is a majorconcern for all biomaterial applications that are load bearing. Forporous scaffolds, the material must not fail before bone canintegrate into the matrix and provide additional biologicalsupport. Further investigation into the effect of pore geometryis needed to quantify how much the stress concentrationsremnant of the NaCl crystals has on the fatigue life of porousPPP. A study by Chawla and Deng (2005) showed that plasticstrain intensification began at the tip of irregular pores withinthe microstructure of porous sintered steel. They also revealedthat steel with more rounded pores exhibited better monotonicand fatigue behavior as a result of more homogeneous deforma-tion and decreased strain localization. One of the next stepsin the evolution of PPP as a potential biomaterial is to fur-ther investigate in vitro cellular interaction in conjunctionwith in vivo cellular ingrowth studies in rat segmental defectmodels (Oest et al., 2007; Rai et al., 2007; Boerckel et al., 2009).Preliminary studies in this regard are already in progress. Theculmination of this research will be the design and fabrication ofbiomedical devices, such as patient specific interbody fusioncages that can be tailored to better match the modulus of thesurrounding bone. The cyclic and monotonic loading behavior,in conjunction with the cellular ingrowth results and a strongunderstanding of biomedical applications, will be further emp-loyed in the understanding and development of porous PPPas a biomedical device. In addition, an understanding of howosteointegration influences the mechanical properties of porousPPP will be gained that will effectively support the developmentof optimal patient specific orthopedic devices.

5. Conclusions

An effective technique for relating microstructure to mechan-ical properties was established in this work. This techniqueapplies mCT analysis, FEA, and experimental results to theunderstanding of monotonic and fatigue behavior of anynovel microstructure. Using this technique, the followingconclusions were drawn from the current research:

1.

Monotonic tensile failure of 75 vol% porous PPP was foundto begin with localized plasticity during initial loading,which led to brittle fracture. The FEA model predictedstresses approximately 100 times greater than the globallyapplied load at discrete spatial locations.

2.

Monotonic compressive failure associated with porousPPP was the result of a local accumulation of plasticityresulting in strut buckling, pore collapse and densification,consistent with foam theory.

3.

Fatigue failure of porous PPP was found to be the res-ult of crack nucleation and propagation initiated by stressconcentrations on the order of the bulk endurancelimit. FEA revealed that these stress concentrations weresomewhat dependent upon the geometry of the NaClleachable media.

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4.

Fatigue failure of porous PPP in tension resulted in Mode Ifracture, similar to the monotonic tests.

5.

The fatigue strength for porous PPP in compression wasfundamentally different than in monotonic loading. Thiswas the result of plastically deformed strut interaction withundeformed struts, preventing further motion in compres-sion, and resulting in a shearing behavior that increasedthe 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 toexpress gratitude to Dustin Bales and Eric J. Losty for theircontributions towards the initial results of this work. Inaddition, we would like to thank Kendra Huber for herassistance with mCT imaging and Chris Laursen, SusanSwapp, and Norbert Swoboda-Colberg for their assistancewith SEM imaging.

Appendix A. Supplementary Information

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

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