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Composites: Part A 39 (2008) 579–587 www.elsevier.com/locate/compositesa
Effect of specimen thickness on fracture toughness and adhesive properties of hydroxyapatite-filled polycaprolactone Shing-Chung Wong a
a,*
, Avinash Baji a, Alan N. Gent
b
Department of Mechanical Engineering, The University of Akron, Akron, OH 44325-3903, USA b Institute of Polymer Science, The University of Akron, Akron, OH 44325-3903, USA
Received 12 March 2007; received in revised form 28 August 2007; accepted 10 September 2007
Abstract The fracture toughness of hydroxyapatite (HAP)-filled polycaprolactone (PCL) biocomposites was investigated using the technique of essential work of fracture (EWF). The influence of specimen thickness on the toughness parameters was investigated. The specific essential work of fracture (we) was found to decrease with the increase in filler loading and with the thickness of the specimen. The testing procedure used for the EWF measurement obeyed the validity criteria of the concept and we determined can be considered to be a good measure of the plane-stress toughness of the composite. The adhesive strength between the HAP and the PCL phase was determined using T-peel tests. The layer of the laminates in the PCL–HAP–PCL peel test specimens was varied to study the influence of laminate thickness on the interfacial work of fracture. The effect of temperature on the interfacial work of fracture was also evaluated. The parameters were varied to determine the effect of the plastic deformation on the peel strength. The interfacial work of fracture between HAP and PCL was found to be relatively strong; however, the effect of temperature and PCL laminate thickness did not significantly vary the adhesion strength. 2007 Elsevier Ltd. All rights reserved. Keywords: A. Polymer-matrix composites (PMCs); B. Interface/interphase; D. Mechanical testing
1. Introduction Much attention is given to the fracture toughness characterization of bones [1–3]. Little is understood on the fracture behavior of biodegradable polymers and biocomposites, which offer potential bone analogue materials [4,5]. The objective of this paper is to examine the toughness of hydroxyapatite (HAP)-filled biodegradable polycaprolactone (PCL) and their interfacial adhesive strength. Such a study would provide useful information concerning how one can integrate various deformation mechanisms in anatomically shaped bone-analogue systems such that the fracture properties of biomineralized natural system, that is, bone, can be emulated. Bones consist of collagen and apatite as the major components and could be used as a template *
Corresponding author. Tel.: +1 330 972 8275; fax: +1 330 972 6027. E-mail address:
[email protected] (S.-C. Wong).
1359-835X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2007.09.004
for the design of HAP-polymer analogues [6–9]. The superior mechanical properties in terms of toughness and strength of the natural composites results from the complex hierarchical architecture of collageneous fibers and mineralized apatite nanocrystals [10]. Each collagen fibril consists of many tropocollagen molecules that are linked together by strong intramolecular bonds (hydroxypyridinium bonds). These strong intramolecular bonds enhance the reinforcing nature of the collagen fibrils and are the basis of increased toughness in the bone composites. The strength and stiffness of the calcified bones are obtained from the mineral content where the toughness is conceived to be derived from the quality of the polymer (collagen) matrix [11,12]. This notion has not yet been rigorously tested. In this study, we apply the fracture work concept [13] in assessing both the essential and non-essential components of fracture work that gives rise to the overall deformation toughness of a composite system. The essential component
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is a material property at a given thickness [14]. Furthermore, we also assess the interfacial adhesive strength using T-peel tests. The measurement is done with the bulk specimens but the data are indicative of the microscopic adhesion properties under the circumstances that there is no change in chemical interactions in the bulk and microscopic interfaces. Mechanical properties of cortical bone have been well documented in literature and served as the standard for the evaluation of biomimetic equivalent materials. The cortical bone has the following properties: 7–30 GPa in elastic modulus,p 50–150 MPa in tensile strength and 4.3– 5.4 MPa m for toughness of femur bone in transverse direction [8,15,16]. Most bones are characterized by their linear elastic toughness but there is no evidence this must be so, particularly for soft components such as cartilage. Connective tissues found in ligaments, bones and dermis are characterized by high content of wide, aligned collagen fibers. These natural tissues in general exhibit non-linear, anisotropic and viscoelastic behaviors. The typical tensile curve of a ligament exhibits a low modulus at a low strain associated with stretching of collagen bundles, linear region at intermediate strain associated with alignment of collagen fibers in the direction of stretch and finally failure at a high strain value. The ideal replacement scaffold should be composed of multi-phase materials with multi-scale composite structure such that it possesses strength higher than that of collagen and apatite constituents and capable of avoiding brittle fracture [17]. PCL–HAP biocomposite displays a similar trend upon tensile loading with HAP providing the stiffness to the ductile PCL matrix. The modulus and tensile strength of these biocomposites are found to be in the range of 200–320 MPa and 17–22 MPa, respectively [18]. The capacity of the bone to resist mechanical stresses and fractures depends on the quality and quantity of the bone tissues evaluated by bone mineral density (BMD). The design and development of the bone-analogue materials should be guided by the design mechanisms of the natural composites to obtain tough and mechanically strong tissue scaffolds. HAP, which is a form of calcium phosphate and is similar to the bone apatite, helps promote cell growth within the implant and forms a strong bond between the tissues and implant [19,20]. The polymer provides the matrix for the tissue scaffold and provides ductility to the composite. A composite of biodegradable polymer and bioactive ceramic is found to have good osteoconductive properties and can be used as a substitute for the natural collagen–apatite composite structure [21– 23]. Studies on potential scaffold materials comprising biodegradable polymer and bioactive ceramics were extensively performed for establishing solid freeform fabrication techniques with very little reference to the fracture properties of the anatomically shaped composite analogue systems [22,24,25]. The aim of this study is to examine the fracture toughness of HAP-filled PCL composites by analyzing the dependence of specific essential work of fracture on the
thickness of the specimen. The toughness of the composite is determined for a wide thickness range in which the stress mode for a specimen evolves from plane-stress to mixedmode (plane-stress and plane-strain) as the thickness increases. The fracture toughness for each specimen thickness is evaluated with increasing concentration of HAP. This study also addresses the interfacial work of fracture between PCL and HAP using peel laminates. The interfacial work of fracture between HAP and PCL has not been investigated in detail and can be used to analyze the strength of the ceramic–polymer interface. The effects of peel laminates and temperature on the interfacial work of fracture will be discussed. 2. Experimental work 2.1. Work of fracture measurements The technique of essential work of fracture (EWF) was developed to address mostly plane-stress fracture and tearing work for plastic films or metal sheets [13,14,26–28]. Prior to this work the EWF technique was mainly applied to characterizing polymer films and engineering plastics, with little application to tissue scaffold materials, which needs to be quantified for their tearing toughness and mechanical robustness as well. According to the concept, the fracture toughness for a material can be characterized as the work spent in the fracture process zone (FPZ) per unit cracked length and is defined as specific essential work of fracture (we). When a ductile notched specimen is loaded, the total fracture work, Wf, can be partitioned into two components: the essential work of fracture, We and the geometry-dependent non-essential or plastic work of fracture, Wp. We is associated with the work performed in the FPZ. If a characteristic FPZ exists, the essential work is a material property and proportional to the ligament length (l). Wp is the work performed in the outer plastic zone (OPZ), which varies with specimen and loading geometries, and is proportional to the ligament squared (l2): W f ¼ W e þ W p ¼ we lt þ bwp l2 t
ð1Þ
where t is the specimen thickness. By dividing both sides by lt, Eq. (1) can be converted to the following: wf ¼
Wf ¼ we þ bwp l lt
ð2Þ
where wf is the specific total fracture work and wp is the specific non-essential work of fracture. According to Eq. (2), a linear relationship is obtained on plotting wf vs. the ligament length (l). we and bwp can be obtained from the y-axis intercept and the slope respectively as shown in Fig. 1. 2.2. Interfacial fracture toughness using T-peel tests Peel testing [29–32] has been used as a popular test method to assess the peeling energy between flexible lami-
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The specimens for the peel tests were prepared independently using hot press. PCL-HAP-PCL flexible laminates were compression molded with a Teflon sheet separating part of the surfaces. The thickness of the HAP interface layer was kept constant using 0.5 mm thick compression molding plate for all the peel test samples. PCL–HAP– PCL laminates were cut from the compression molded piece to perform T-peel test as shown in Fig. 3. To reduce
Clamped Zone Fig. 1. Plot of specific total fracture work vs. ligament length. The specific essential work of fracture (we) is obtained from the y-axis intercept and the slope gives the specific plastic work (bwp).
Fracture Process Zone
nates. The quality of the adhesive bonded joints is of significant importance and can be measured by peel strength, which is defined as the force per unit width required in peeling the laminates apart. In this study, the influence of interfacial work of fracture on mechanical properties was assessed by peel strength between HAP and PCL. When only elastic deformation takes place in the flexible laminates, the fracture energy of the HAP–PCL interface can be determined from the constant peeling force using the equation G ¼ 2F =B
ð3Þ
where B is the width of the specimen laminates. The obtained value of G is assumed to be representative property of the interface and dependent on temperature and test angle. This paper discusses the dependence of peel arm thickness and temperature on the adhesive fracture energy.
h l Outer Plastic Zone Clamped Zone
t B Fig. 2. Schematic of a double-edge notched tension (DENT) specimen used for essential work of fracture (EWF) tests. The figure shows the energy dissipation zones involved in a quasi-static crack growth, viz., the fracture process zone (FPZ) and the outer plastic zone (OPZ). The essential work refers to both elastic and plastic work consumed in the FPZ and the non-essential plastic work is localized in the OPZ. The thickness, ‘t’, of the DENT specimens is varied to determine the effect of specimen thickness on the essential work of fracture technique.
2.3. Materials The biodegradable polymer, polycaprolactone (PCL) (MW = 80,000 g/mol) was obtained from Dow Chemical Company (Freeport, TX) and sintered hydroxyapatite (HAP) of particle size 53–124 lm was purchased from Clarkson Chromatography Products Inc. (South Williamsport, PA). The PCL pellets were vacuum dried at 40 C for 36–48 h prior to use. HAP was dry blended followed by extrusion using Haake mini-lab twin screw extruder (Thermo Electron Corp., Hamburg, Germany) at 130 C. The screw speed was 80 rpm and the residence time was on average 6 min for preparing composites with 0, 10, 20, and 30 wt% HAP. The specimens were compression molded at 115 C and 275 bar in pressure. The thickness of the compression molded sheet was controlled by using compression molding plates of 0.2, 0.5, 1.25, 2.5, and 3.5 mm in thickness. Rectangular bar specimens (25 mm · 75 mm · thickness) were cut from the extruded and compression molded sheet for the EWF tests. Double-edge notched tension (DENT) specimens, as shown in Fig. 2, were used for the EWF tests.
H
Metal Reinforcements 90˚
90˚
F Pp
Pp
F
HAP Layer
Polycaprolactone Laminates
l
hp Fig. 3. Schematic of a T-peel test specimen. The legs of the PCL laminates are reinforced with metal plates to reduce the effect of plastic deformation on the adhesive strength between HAP and PCL. The thickness and the test temperature are varied to study their effect on adhesive strength. ‘F’ represents the constant peeling force which is used to determine the adhesive strength.
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the plastic deformation in the peel arms, the laminates were reinforced with metal strips. The peel tests were performed at 90 angle as shown in Fig. 3.
Ultracut UCT ultramicrotome. The sections for TOM analysis were cut from the necked region of the DENT samples. Sections from 200 to 300 lm deep were also microtomed for comparison.
2.4. Mechanical properties 3. Results and discussion Rectangular double-edge notched tension (DENT) specimens were used for the EWF test. Sharp notches were created on the specimens using fresh razor blades. The notches were created for equal lengths and directly opposite each other on the DENT specimens. The actual thickness and ligament length of the specimen torn through were measured independently. The thickness of all the DENT specimens obtained from the 0.2 mm compression molded sheet was verified using optical methods. A small cross-section of the specimen was cut and imaged under optical microscope. Calibration of the optical image was performed using Image processing software (ImageJ 1.34s) and the thickness for all specimens was independently measured. 2.5. Microscopy Specimens obtained from the EWF tests were used for scanning electron microscopy (SEM) and transmission optical microscopy (TOM). Samples were cut from the fractured region of the DENT test specimen and the surface morphology examined. Samples for the SEM analysis were mounted on the aluminum stub using carbon coated double sided adhesive tape. The samples were coated with silver using sputter coater in an argon-purged chamber evacuated to 500 mTorr and examined using SEM with an accelerating voltage of 20 kV. Fifty micrometers thick sections were microtomed from DENT fractured region as described in Fig. 4 for the TOM analysis using a Leica
SEM
Microtoming Direction
Tested DENT Specimen
Optical Microscopy
Fig. 4. A schematic that shows the DENT specimen for microscopic analyses. The dotted line represents the section that is used for fracture morphology analysis. The necked region is used for SEM analysis and the remainder section is for optical microscopy. Fifty micrometers thick sections are microtomed for optical microscopy. The arrow indicates the microtomy direction. Sections are obtained from the necked region and the subsurface region.
The field of tissue engineering using biodegradable polymers such as PCL is a rapidly growing field and as such the thorough evaluation of the fracture properties is of critical importance. Dispersion of particle HAP into the polymer matrix acts as hardening filler and enhances the mechanical property of ductile PCL. It was shown by us [33] that incorporation of HAP into PCL matrix improves the modulus of the scaffold and results in reduction of tensile strength, thus embrittling the ductile matrix. This is usually observed for HAP-filled PCL composites if the interface between the polymer-filler is not optimized. And often the agglomeration of HAP complicates the matter. The filler–matrix interaction can be further improved by using nanometer length scale particles and better dispersion techniques. This study was conducted in an attempt to address the fracture properties of HAP interfacing with PCL and to understand the effect of specimen geometry on the fracture and adhesion parameters. Representative load–displacement curves for 0, 10, 20, and 30 wt% HAP-filled PCL with different ligament lengths obtained from 3.5 mm thick DENT specimens are shown in Fig. 5. Geometric similarity in loading can be observed. Seven different ligament lengths were tested for each composite and thickness. In all the specimens tested, the area under the load–displacement curve increases with the ligament length. The fracture parameter, we, can be deduced from the extrapolation to zero ligament length as the crack propagates in consistent fashion for all the ligament lengths. The trend followed by all load–displacement curves can be illustrated by several stages. The load increases as displacement increases. After the maximum load is reached, necking starts at the crack tip, resulting in the load drop. The entire ligament yields and is followed by crack growth across the necked region until the specimen completely fractures. The complete yielding of the ligament was characterized by the occurrence of stress whitening in the DENT specimen. At the end of linear-elastic region, the outer plastic zone develops and the crack propagation takes place once the maximum load has been reached [34]. The EWF was derived from the ‘best fit’ linear regression analysis evaluated on the plot of wf vs. ligament length (l), as shown in Fig. 6. The slope of the plot gives the bwp whereas we were obtained from the y-intercept of the extrapolated data. The values of bwp and we were obtained using Eq. (2) for all the composites tested and are summarized in Table 1. we decreases with HAP content for each thickness of DENT samples used. Based on our earlier work using wide angle X-ray diffraction (WAXD), the introduction of HAP induces the formation of PCL crys-
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Fig. 5. DENT load–extension curves for HAP reinforced PCL. (a) 0, (b) 10, (c) 20 and, (d) 30 wt% HAP.
Fig. 6. Specific work of fracture vs. ligament length for HAP-filled PCL. The slope of the plot represents the specific non-essential work of fracture (bwp) and the y-intercept of the extrapolated data yields the essential fracture work (we).
tals and thus results in the reduction of toughness values for the composites [33]. The decrease in the we values is attributed to the change in the degree of crystallinity upon introduction of the HAP content. The degree of crystallinity increases consistently with the filler loading, thus embrittling the ductile PCL. Simultaneously, the nonessential plastic work is found to decrease with increase in the concentration of HAP suggesting the reduction in the energy absorbed during plastic deformation. The extent of plastic deformation undergone by the material during the fracture process is represented by bwp. The slopes of the regression lines are found to vary with the thickness of the specimen because the plastic constraint varies with specimen geometry and thickness. Fig. 7 shows the Hill’s criterion used for 3.5 mm thick unfilled PCL. Hill’s criterion [24] was used to verify that the tests were under the plane-stress conditions. The yield stress values for the composites were obtained from an average of five specimens tested for each composite. The
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Table 1 Effect of DENT specimen thickness on the essential work and non-essential work of fracture Specimen thickness (mm)
0 wt% HAP 2
0.2 0.5 1.25 2.5 3.5
10 wt% HAP 3
2
20 wt% HAP 3
2
30 wt% HAP 3
we (kJ/m )
bwp (MJ/m )
we (kJ/m )
bwp (MJ/m )
we (kJ/m )
bwp (MJ/m )
we (kJ/m2)
bwp (MJ/m3)
64.13 62.98 59.02 55.25 53.86
6.55 12.73 16.33 15.60 15.11
58.79 54.56 51.09 47.28 45.58
7.43 13.06 14.22 13.86 14.61
51.39 50.86 46.38 42.26 40.79
7.62 13.12 13.37 11.79 12.70
41.39 40.36 37.64 33.47 32.11
6.36 12.35 12.20 11.33 11.67
tested, from our observation it can be concluded that the tearing region corresponds approximately to a mixed-mode stress state. As the thickness of the specimen increases, the stress state becomes more plane-strain and hence toughness decreases. Fig. 9a shows the transmitted optical micrograph (TOM) of the fractured surface of unreinforced PCL obtained from the tested DENT samples. Fig. 9b shows the TOM of the section obtained from 200 to 300 lm below the fractured surface to compare the degree of deformation. Representative SEM photomicrographs of 0 wt% HAP-filled PCL sample is shown in Fig. 10. The surface for the SEM analysis was acquired from the fractured tip
Fig. 7. A schematic indicating the Hill’s criterion on 3.5 mm thick PCL. The horizontal dotted line represents the value of 1.15ry.
sectional maximum stress vs. ligament length is plotted for 0 wt% HAP specimens (3.5 mm thickness) as shown in Fig. 7. The maximum sectional stress for all the samples tested is found to be less than 1.15ry, satisfying the Hill’s criterion. A plot of we vs. specimen thickness for the composites is shown in Fig. 8. Increase in specimen thickness reduces the toughness values of the composite. Even though, the Hill’s criterion is met for all the specimens
Fig. 8. Plot of specific essential work of fracture vs. specimen thickness. The toughness value slightly decreases with an increase in specimen thickness.
Fig. 9. Transmitted optical micrograph (TOM) of the microtomed sections. (a) The section obtained from the necked region of the DENT specimen and (b) section obtained from 200 to 300 lm below the fractured surface.
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Fig. 10. A representative SEM photomicrograph of fractured DENT specimen of PCL.
surface of the EWF samples. Both TOM and SEM photomicrographs demonstrate a high degree of deformation in the fractured region. The TOM micrograph of the section obtained from the 200 to 300 lm below surface shows little deformation and it can be deduced that a substantial portion of plastic deformation is localized in the FPZ of the DENT samples. From the TOM and SEM studies, the composites undergo clearly ductile tearing and the EWF method can be used to characterize the ductile fracture behavior of HAP-containing PCL. Interfacial work of fracture was assessed by measuring the peel strengths between the adhering layers of HAP and PCL laminates. The peel test is an established technique to assess interfacial strength of polymer adhesives, composite laminates, but it is the first time we employ peel-testing on HAP and PCL components. Note than only mechanical interlocking rather than chemical bonding exists between HAP and PCL and therefore this technique can be deemed appropriate for measuring the adhesion strength. The effect of plastic work in the peel tests is significantly reduced by reinforcing the legs of the PCL laminates using metallic strips. Fig. 11 displays the typical load extension curves under peeling and the comparative studies performed on the samples with and without reinforced peel arms to quantify the effect of reinforcement. The value of the peel energy determined may include adhesive fracture energy and the energy associated in bending the peeling arms. The adhesive fracture energy is the characteristic of the interface and is a measure of the interfacial adhesion [35,36]. The thickness of the PCL laminates is varied to study the effect of plastic deformation on the peel strength. Theoretically, as the thickness of the laminates
Fig. 11. T-peel load–extension curves of PCL–HAP–PCL with and without reinforced peel arms. The slight reduction in peel strength with arm reinforcement suggests reduction of plastic work in bending the peel arms. The rather constant but complex peeling force–extension is curve is characteristic of peeling tests of adhesives [37,38].
increases, more energy arising from plastic deformation is dissipated. This increases the measured peel force. On exceeding the critical laminate thickness, no plastic yielding of the laminates takes place and the measured peel force represents a direct measure of the adhesive fracture energy. The fracture energy for all three laminate thicknesses at a constant peeling force was calculated using Eq. (3). The peel samples were treated at temperatures (20, 0, 25, and 40 C) prior to the test. There is no significant difference in the peel strength measured for the temperature effects. Table 2 summarizes the measured peel strength for PCL laminate thickness and temperature effects.
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Table 2a Effect of PCL laminate thickness on the peel strength PCL layer thickness h (mm)
Test speed (mm/min)
Average specimen dimensions L (mm)
B (mm)
1.25 2.5 3.5
10 10 10
90 90 90
14.30 13.86 13.99
Average peel force (N)
Peel strength (kJ/m2)
42.50 50.00 66.00
6.72 7.23 9.34
Average peel force (N)
Peel strength (kJ/m2)
46.00 38.00 44.00 39.00
7.36 6.08 7.01 6.24
Table 2b Effect of temperature on the peel strength Temperature (C)
20 0 25 40
Test speed (mm/min)
10 10 10 10
Average specimen dimensions L (mm)
B (mm)
90 90 90 90
12.50 12.50 12.50 12.50
The PCL laminate thickness was kept constant at 2.5 mm.
All the tested samples were inspected visually to determine the type of fracture. For all the samples, debonding was observed between the HAP layer (adhesive) and the PCL layer (adherent) verifying the occurrence of polymer–ceramic interfacial fracture. The peel strength reported herein is thus indicative of the adhesive strength of bulk HAP and PCL interfaces. The load–extension curves as shown in Fig. 11 are highly characteristic of the typical peel testing of adhesives [37,38]. Tissue scaffolds are three dimensional structures that provide a site for cell attachment, proliferation and differentiation. For a scaffold to function effectively, it must possess desired in vivo mechanical properties. The dependence of the scaffold material used on the temperature and geometry needs to be critically addressed and established prior to design and materials selection. Tissue engineering using biodegradable and bioresorbable scaffolds provides an alternative approach to treat or reconstruct tissues. This study addresses the geometric (thickness) and temperature effects on the toughness and adhesive strength of the HAP reinforced PCL. The value of this work is derived from the ability to quantify scaffold toughness and the interfacial adhesion strength between components. With more understanding of how the toughness and interfacial adhesion depend on the geometry of the bioactive components used, the properties of the anatomically shaped scaffold can be tailored to different processing routes such as fused deposition, laser sintering and other forms of solid freeform fabrication. The effects of body temperature and ageing on the in vivo mechanical and degradation properties of the HAPfilled PCL need to be evaluated as well. 4. Conclusions Fracture toughness of the composites was successfully evaluated using the EWF theory. we was found to decrease
with HAP content. The decrease in ductility or toughness can be attributed to the change in crystallinity of the PCL upon introduction of HAP. The influence of specimen thickness on the fracture parameters was studied, and from the results obtained, it can be concluded that we and bwp depend on the specimen thickness. The load–displacement curves obtained for various ligaments lengths and thicknesses were geometrically similar to each other. All the specimens were fractured by ductile tearing of the ligament region and fully yielded. The ductile behavior can also be noticed from the SEM and TOM micrographs. Hence, the EWF method could provide a reliable toughness assessment for analysis and modeling. The interfacial work of fracture obtained for PCL–HAP laminate thicknesses and temperature treatments was obtained from T-peel tests. The peel strength was little influenced by the temperature and laminate thickness. The high values of the peel strength indicate reasonably strong mechanical bonding between HAP and PCL, even by simple mechanical mixing as prevalent in bone-analogue composite scaffold fabrication. Acknowledgement S.C.W. also acknowledges the support of NSF MRI Grant# DMI 0520967 administered by the Design, Manufacturing and Innovation Division. References [1] Zioupos P, Currey JD. Changes in the stiffness, strength, and toughness of human cortical bone with age. Bone 1998;22:57–66. [2] Lucksanambool P, Higgs WAJ, Higgs RJED, Swain MW. Fracture toughness of bovine bone, influence of orientation and storage media. Biomaterials 2001;22:3127–32. [3] Yang QD, Cox BN, Nalla RK, Ritchie RO. Re-evaluating the toughness of human cortical bone. Bone 2006;38:878–87. [4] Wang M. Developing bioactive composite materials for tissue replacement. Biomaterials 2003;24:2133–51. [5] Nazhat SN, Kellomaki M, Tormala P, Tanner KE, Bonfield W. Dynamic mechanical characterization of biodegradable composites of hydroxyapatite and polylactides. J Biomed Mater Res 2001;58:335–43. [6] Ji B, Gao H. A study of fracture mechanisms in biological nanocomposites via the virtual internal bond model. Mater Sci Eng A (Struct) 2004;366:96–103. [7] Landis WJ. The strength of a calcified tissue depends in part on the molecular-structure and organization of its constituent mineral crystals in the organic matrix. Bone 1995;16:533–44. [8] Bonfield W. Materials for the replacement of osteoarthritic hip joints. Met Mater 1987;3:712–6; Bonfield W. Materials for the replacement of osteoarthritic hip joints. J Mater Sci (Mater Med) 1997;8:775–9. [9] Fung YC. Biomechanics: mechanical properties of living tissues. 2nd ed. New York: Springer; 1993. [10] Landis WJ. The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix. Bone 1995;16:533–44. [11] Zioupos P, Currey JD, Hamer AJ. The role of collagen in the declining mechanical properties of aging human cortical bone. J Biomed Mater Res 1999;45:108–16. [12] Zioupos P. Ageing human bone: factors affecting its biomechanical properties and the role of collagen. J Biomater Appl 2001;15:187–229.
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