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Tensile fracture behavior of a biodegradable polymer, poly(lactic acid)
ARTICLE IN PRESS
POLYMER TESTING Polymer Testing 25 (2006) 628–634 www.elsevier.com/locate/polytest
Test Method
Tensile fracture behavior of a biodegradable polymer, poly(lactic acid) Kazuo Arakawa, Toshio Mada, Sang-Dae Park, Mitsugu Todo Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga 816-8580, Fukuoka, Japan Received 15 March 2006; accepted 19 April 2006
Abstract The stable and dynamic fracture behavior of a biodegradable polymer, poly(lactic acid) (PLA), was investigated using single-edge-cracked tensile specimens. To study the dynamic effect of brittle facture, the specimens were pin-loaded using a special jig that allowed them to split and fly off in the loaded direction after fracture. The non-elastic effect of viscoelastic and plastic deformations was also measured using an optical high-speed extensometer, which consisted of an optical fiber and a position-sensing detector (PSD). For the stable and dynamic fracture process, external work applied to the specimen and its fracture surface was partitioned into Us and Ud, and As and Ad, respectively. The energy release rate, Gs, for stable crack growth was determined using Us/As. The kinetic and non-elastic energies were measured and subtracted from Ud to evaluate the fracture energy for the dynamic process, Ef. The dynamic energy release rate, Gf, was then determined as Ef/ Ad. Gd was also obtained as Ud/Ad to correlate with Gs and Gf, and the results are discussed. r 2006 Elsevier Ltd. All rights reserved. Keywords: Material testing; Biodegradable polymer; PLA; Fracture; Crack growth; Elastic energy
1. Introduction Biodegradable polymers have recently been introduced to various fields as alternatives to traditional materials. For example, poly(lactic acid) (PLA) is attracting attention as a medical biomaterial owing to its biocompatibility and absorbability in human bodies [1]. In orthopedic and oral surgeries, PLA is often used for bone fixation devices at fracture sites. PLA devices have an important advantage over traditional metal devices; Corresponding author. Tel.: +81 92 583 7761;
fax: +81 92 593 3947. E-mail address: [email protected] (K. Arakawa). 0142-9418/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2006.04.004
there is no need for a second operation to remove the devices after recovery, relieving the physical and mental burdens on patients [2,3]. However, there is a problem; PLA devices can crack during treatment since they are not as resilient as metal devices. Therefore, it is necessary to develop more reliable PLA devices in terms of their mechanical properties, such as their strength and fracture toughness. In addition, the precise evaluation of their mechanical properties is required to assure the safety of PLA devices. Conventionally, PLA specimens with flat, smooth surfaces have been subject to tensile and bending tests. However, PLA devices in the human body can develop flaws and surface defects during the degradation process. Therefore, it is important to examine the fracture behavior using
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
Three-mm-thick PLA plates were fabricated using a hot press with an attached water-cooling system. The pellets were melted at 180 1C, pressed under 30 MPa for 1 h, and then quenched with iced water for 10 min to prevent crystallization of the material. Experiments were performed on single-edgecracked tensile specimens, as shown in Fig. 1. The specimens measured 190 mm in length and 20 mm in width. To change the fracture initiation load of the specimens, sharp pre-cracks with lengths between 2 and 5 mm were generated by tapping a fresh razor blade into a pre-machined saw cut on the specimen edge. As illustrated in the figure, the specimen was clamped rigidly at its lower part and loaded on the upper part using a steel pin and grip. A load was introduced using a special jig consisting of four steel bars, as shown in Fig. 2. The shape of the jig allowed the specimen to split and fly off in the load direction after fracture. The height the specimen attained was recorded with a thin paper pipe (0.3 g) inserted between the bars, which stopped at the highest position reached by the upper part of the split specimen (30 g). This was used to estimate the elastic energy in the specimen. In this study, the elastic energy in the jig was disregarded since it was much stiffer than the specimen. All the specimens were tested under displacement-controlled conditions using a tensiletesting machine. Tests were performed at room temperature and at a constant crosshead rate of 1 mm/min. Fig. 1 also shows the configuration used for the displacement measurements of the loading point and the region underneath the pre-cracked position, i.e. the center of the specimen. The loading-point displacement was determined with the tensile-testing
O
75
Grip d=3
Crack 190
Crack
20
20
2. Specimen material and experimental methods PLA pellets (Lacty#9030; Shimadzu) were used as specimen material. The average molecular weight was about 2 105, and the glass transition and melting temperatures were 61 and 175 1C, respectively.
Crosshead δ (1 mm/min)
Pin
20
φ6
δ'
Lens PSD
Fiber
75
PLA specimens that are notched or cracked. To date, only a few experimental studies examining the fracture behavior of PLA have been published. To study this problem, we fabricated PLA plates from pellets using a hot press, and measured the fracture behavior of single-edge-notch-bend specimens under static and impact loading [4–7]. As a fracture parameter that controls crack growth, the stress intensity factor K or the J-integral was determined using a load–displacement diagram, i.e. the external work applied to the specimen. Essentially, PLA undergoes brittle fracture, and K and J depend on the loading rate. The concept of K or the J-integral plays an important role in understanding fracture behavior. However, more detailed investigation of the effects of inertia or the kinetic energy of the specimen during dynamic crack propagation is required [8–21]. It has also been suggested that the non-elastic effect of the viscoelastic and plastic deformations of the specimen should be determined and considered in the fracture analysis [20]. This study examined these two effects in PLA specimens. To examine the kinetic effect, singleedge-cracked tensile specimens were pin-loaded using a special jig, so that they could split and fly off after fracture. The non-elastic effect of viscoelastic and plastic deformation was also measured using an optical high-speed extensometer [22]. The tensile specimens exhibited stable crack growth in the early stage of fracture and dynamic crack propagation in the later stage. Therefore, fracture was divided into two processes: the external work applied to the specimen and the corresponding fracture surface was partitioned into Us and Ud, and As and Ad, for the stable and dynamic processes, respectively. The energy release rate for stable crack growth, Gs, was then determined as Us/As. The energy release rate for dynamic crack propagation, Gf, was evaluated by first quantifying the kinetic and non-elastic energies. Then, these energies were subtracted from the external work, Ud, to give the fracture energy, Ef. Finally, Gf was determined as Ef/Ad. The values of Gd ( ¼ Ud/Ad) were also obtained for comparison with Gs and Gf.
629
Amp Laser Diode
Clamp
Memory
Fig. 1. Specimen geometry and the experimental setup used for loading and displacement measurement using an optical fiber and position-sensing detector (PSD).
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
where S1 and S2 are the distances between the fiber and the lens, and between the lens and the PSD, respectively.
Load
Load φ20
Paper pipe Pin
3. Definition of fracture energy
Grip Specimen Crack Fig. 2. Loading jig and the method used to measure the flying height of a split specimen.
Y1
PSD
Lens
U ex ¼ U s þ U d ,
Fiber
L q
p
y
S1
S2
L
Y2
machine, while the displacement near the pre-crack was measured using an optical fiber and a positionsensing detector (PSD). A laser diode was used as the light source, and an amplifier and a digital wave memory were used to record the output signals from the PSD. Since the PSD had a frequency response of 100 kHz, it permitted both static and dynamic measurements [22]. Fig. 3 illustrates the optical setup for the displacement measurement using the fiber and PSD. The output light from the fiber attached to the specimen was collected with a lens and focused on the PSD. The light position on the PSD, y, is given as (1)
where L is the half-length of the sensor, and Y1 and Y2 are the output signals from the terminals (see Fig. 3). The fiber position was shifted according to the load applied to the specimen. The relationship between the fiber shift, p, and the light shift, q, on the PSD is given as p ¼ qS 1 =S 2 ,
(3)
where Us and Ud are the energies related to stable and dynamic crack propagations, respectively. We assumed that Us is the fracture energy created for new surfaces during stable crack growth. We also assumed that Ud could be partitioned into three regions, as shown in Fig. 4: U d ¼ Ef þ Ee þ En,
Fig. 3. Principle of displacement measurement using an optical fiber and PSD.
y=L ¼ ðY 1 Y 2 Þ=ðY 1 þ Y 2 Þ,
Fig. 4 shows a typical load, P, versus displacement, d, diagram for a PLA specimen determined using the tensile testing machine. As indicated in the figure, P increased almost linearly with d, and then decreased after the maximum load, Pm, due to the initiation of stable crack growth, and dropped abruptly at Pc and dc, the critical values related to dynamic fracture initiation in the specimen. The P–d diagram in Fig. 4 is divided into two regions:
(2)
(4)
where Ef is the dynamic fracture energy created for new surfaces, Ee is the elastic energy in the specimen and En is the non-elastic energy due to viscoelastic and plastic deformations of the specimen. Ee and En were determined in the following manner. First, Ee was converted into the flying energy of the split specimen after fracture. The viscosity of the material could be neglected during dynamic crack propagation, so that the change from PLA
Pm
0.8
Load P , kN
630
0.6
Us
Pc
0.4
0.2
En + Ee + Ef = Ud δn
0
0
0.2
δe+δn 0.4 0.6 Displacement δ, mm
δc 0.8
Fig. 4. Load P versus displacement d diagram for a PLA specimen under displacement-controlled conditions.
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
Pc to dn was elastic (see Fig. 4) [20]. Finally, the following relation held:
0.7 PLA
0.6
150 1.5
100
1.0
50
0.5
0 0
0.2
External Work Ud, J
0.4 0.3 0.2 0.1 0
0
0.2
0.4
0.6 0.8 Load Pc, kN
1
1.2
Fig. 5. Relationship between the external work applied to specimens, Ud, and the critical fracture load, Pc.
0.4
0.6
0.8
1
1.2
Load Pc , kN Fig. 6. Relationship between the flying height of a split specimen, He, and the critical fracture load, Pc.
0.15
50
PLA
0.12
40 Ee
0.09
30
0.06
Ee / Ud
0.03 0
20 10 0
0
0.1
0.2 0.3 0.4 0.5 External Work Ud , J
0.6
Fig. 7. Relationship between the elastic energy, Ee, and external work applied to a specimen, Ud.
produced elastic energy in the specimen, which increased the flying height. The elastic energy, Ee, in the specimen was evaluated using E e ¼ mgH e ,
0.5
Flying Velocity Ve, m/s
The external work for the stable fracture process, Us, was determined using the area (D0PmPc) on the P–d diagram (see Fig. 4). To simplify the analysis, the area was assumed to be a triangle. The values of Us obtained from seven specimens were examined as a function of the maximum load Pm. No intimate correlation was found between Us and Pm since there was large scatter in the data. This suggests that the initiation of stable crack growth in the tensile specimens of PLA was strongly associated with a pre-crack condition, such as its flatness or sharpness, rather than the loading condition of the specimen. Fig. 5 shows the external work for the dynamic fracture process, Ud, determined from the area (D0Pcdc) on the P– d diagram. As seen in the figure, there was a good correlation between Ud and the critical load Pc. This implies that dynamic fracture initiation was strongly related to the loading conditions of the specimens. The flying height of the split specimen, He, was determined as a function of the critical load, Pc. Fig. 6 shows the variation in He versus Pc, plotted using the experimental results obtained from seven specimens. As illustrated in the figure, He increased with Pc. This suggests that the fracture load
2.0
200
Ee /Ud , %
4. Evaluation of fracture energies
PLA Flying Height He, mm
(5)
250
Elastic Energy Ee , J
E n =U d ¼ dn =dc .
631
(6)
where m is the total mass of the specimen, loading pin, grip and paper pipe, and g is the gravitational acceleration. Fig. 7 shows Ee as a function of Ud, where the ratio Ee/Ud is also indicated. Ee increased almost linearly with Ud, while Ee/Ud decreased slightly. Ee/Ud was about 25% in the region of small Ud, and about 23% in the region of large Ud. In this analysis, the energy loss caused by elastic-wave generation from the crack tip, and the friction between the loading jig and paper pipe or split specimen, was disregarded, because we were unable to quantify it. Hence, the elastic energy determined from Eq. (6) might have been underestimated.
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
0.6 PLA
0.5 Displacement δn, mm
0.4 0.3 0.2 0.1 0
0
0.2
0.4
1 0.6 0.8 Displacement δc , mm
1.2
1.4
Fig. 9. Relationship between the residual displacement, dn, and the critical displacement, dc.
100 0.2
PLA
0.15
80 En
60
0.1
40 En / Ud
0.05
0
En / Ud , %
To evaluate the non-elastic energy of the specimen, En, the residual displacement dn must be determined (see Fig. 4). This was done by measuring the displacement d0 beside the crack position before and after fracture (see Fig. 1). Fig. 8 shows d0 as a function of time t. As shown in the figure, d0 dropped abruptly as the fracture initiated dynamically at the critical value d0c , and then exhibited damping oscillation after fracture. Note that there was residual displacement during the oscillation owing to the non-elastic deformation of the material. dn was determined as follows. First, the midpoints of the initial two oscillations were determined, since the baseline changed. Then, a straight line passing through the two points was obtained. The intersection of the line with the curve falling from d0c was used as the residual displacement, d0n , for the split specimen. Finally, the values of dn for the entire specimen were determined by assuming that dn ¼ 2d0n . Fig. 9 shows dn as a function of the critical displacement, dc. Since dn increased with dc, this implies that the dn of the specimen increased with the critical displacement of the specimen. The non-elastic energy, En, was evaluated from Eq. (5). The results are indicated in Fig. 10, which shows En and the ratio En/Ud as a function of Ud. As seen in the figure, En increased with Ud, while En/Ud remained nearly constant at 38%. Fig. 11 shows the fracture energy, Ef, evaluated using Eq. (4) and the ratio Ef/Ud. Ef increased almost proportionally with Ud. Although there was a slight change in Ef/Ud, it remained nearly constant
Nonelastic Energy En , J
632
20 0 0
0.1
0.2 0.3 0.4 0.5 External Work Ud , J
0.6
Fig. 10. Relationship between the non-elastic energy, En, and the external work applied to the specimen, Ud.
0.4 PLA
0.2 δc' 0.1
100
0.3 Fracture Energy Ef , J
Displacement δ', mm
0.3
Sampling ∆t =1µs
0
PLA
0.25
80
0.2 60
Ef
0.15
40
Ef /Ud
0.1
20
0.05 0
0.5
1
1.5
2
Time t, msec Fig. 8. Displacement d0 beside the crack before and after fracture, measured with an optical fiber and PSD (sampling time Dt ¼ 1 ms).
0
Ef /Ud , %
δc'
0
0.1
0.2 0.3 0.4 0.5 External Work Ud , J
0.6
0
Fig. 11. Relationship between the fracture energy, Ef, and the external work applied to the specimen, Ud.
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
12 PLA Gs, Gf , Gd , kJ/m2
10 Gd = Ud/Ad
8
Gf = Ef /Ad
6 4
Gs = Us/As
2 0
0.2
0.4 0.3 0.5 External Work Ud , J
0.6
Fig. 12. Energy release rates Gs, Gf and Gt as functions of the external work applied to the specimen, Ud.
at 38%. This suggests that the ratio Ef/Ud was not strongly influenced by the fracture conditions, such as Pc, dc or Ud. 5. Energy release rate (G) The energy release rate, G, was estimated using G s ¼ U s =As ;
G f ¼ E f =Ad ;
G d ¼ U d =Ad ,
633
parts: the external works for stable and dynamic fractures, Us and Ud, respectively. The energy release rate was estimated using G s ¼ U s =As and G d ¼ U d =Ad , where As and Ad are the fracture surfaces created by stable and dynamic crack growth, respectively. The flying height was measured to estimate the elastic energy, Ee, in the specimen. The non-elastic energy, En, was also estimated from the residual deformation of the specimen. The dynamic fracture energy, Ef, was then evaluated and correlated with the external work applied to the specimen, Ud. To evaluate the energy release rate during dynamic fracture, G f ¼ E f =Ad was determined, and the following findings were obtained: (1) Ee, En, and Ef increased almost linearly with Ud. (2) Ee/Ud, En/Ud and Ef/Ud were about 24%, 38% and 38%, respectively. (3) Gs remained essentially constant over a wide rage of Ud. (4) Gd and Gf increased almost linearly with Ud. (5) Gd was overestimated, since it included Ee and En. Acknowledgment
(7)
where As and Ad are the fracture-surface areas created by stable and dynamic crack growth, respectively. Gs, Gf, and Gd are shown in Fig. 12 as functions of Ud. Gs remained essentially constant over a wide rage of Ud. No large change was observed on the corresponding fracture surfaces during stable growth. The surfaces were relatively flat and smooth. This indicates that energy dissipation was constant during stable crack growth. Gf and Gd increased almost linearly with Ud, and Gd was much larger than Gf. This implies that Gd was overestimated since the Ee and En of the specimen were included. The corresponding fracture surfaces of the specimens tended to become rougher as Gf increased [21], suggesting that the dynamic effect becomes prominent as the crack velocity increases. 6. Conclusions The stable and dynamic fracture of PLA was studied using single-edge-cracked tensile specimens and an optical high-speed extensometer. The specimens were pin-loaded with a special jig so that they could split and fly away after fracture. The load–displacement diagram was divided into two
This research was supported by Grant-in-aid from Japan Society for the Promotion of Science (Grant nos.15360059 and 16560074).
References [1] L. Fambri, C. Migliaresi, K. Kesenci, E. Piskin, Biodegradable polymers, in: R. Barbucci (Ed.), Integrated Biomaterials Science, Kluwer Academic/Plenum Publishers, New York, 2002, pp. 119–187. [2] S. Higashi, T. Yamamuro, T. Nakamura, Y. Ikada, S.-H. Hyon, K. Jamshidi, Polymer–hydroxyapatite composites for biodegradable bone fillers, Biomaterials 7 (1986) 183–187. [3] Y. Shikinami, M. Okuno, Bioresorble devices made of forged composites of hydroxyapatite (HA) particles and poly L-lactide (PLLA), part I. basic characteristics,, Biomaterials 20 (1999) 859–877. [4] M. Todo, N. Shinohara, K. Arakawa, Effects of crystallization and loading rate on the mode I fracture toughness of biodegradable poly(lactic acid), J. Mater. Sci. Lett. 21 (2002) 1203–1206. [5] N. Shinohara, M. Todo, K. Arakawa, Effect of microstructure and loading rate on the mode I fracture behavior of poly(lactic acid), Trans. Jpn. Soc. Mech. Eng. Ser. A 69 (677) (2003) 95–101 (in Japanese). [6] M. Todo, N. Shinohara, K. Arakawa, H. Tsuji, Effect of hydrolysis on fracture behavior of poly(L-lactide), Kobunshi Ronbunshu 60 (11) (2003) 644–651 (in Japanese).
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[7] S.-D. Park, M. Todo, K. Arakawa, Effect of annealing on the fracture toughness of poly(lactic acid), J. Mater. Sci. Lett. 39 (2004) 1113–1116. [8] T. Kobayashi, J.W. Dally, Relation between crack velocity and the stress intensity factor in Birefringent polymers, in: G.T. Hahn, M.F. Kanninen (Eds.), Fast Fracture and Crack Arrest, ASTM STP, 1977, pp. 257–273. [9] J.W. Dally, A. Shukla, Energy loss in Homalite 100 during crack propagation and arrest, Eng. Fract. Mech. 13 (1980) 807–817. [10] A. Shukla, H. Nigam, A note on the stress intensity factor and crack velocity relationship for Homalite 100, Eng. Fract. Mech. 25 (1986) 91–102. [11] A.S. Kobayashi, M. Ramulu, M.S. Dadkhah, K.-H. Yang, B.S.J. Kang, Dynamic fracture toughness, Int. J. Fract. 30 (1986) 275–285. [12] P.S. Theocaris, G.S. Papadopoulos, Elasto-dynamic forms of caustics for running cracks under constant velocity, Eng. Fract. Mech. 13 (1980) 683–698. [13] W.G. Knauss, K. Ravi-Chandar, Some basic problems in stress wave dominated fracture, Int. J. Fract. 27 (1985) 127–143. [14] K. Takahashi, K. Arakawa, Dependence of crack acceleration on the dynamic stress intensity factor in polymers, Exp. Mech. 27 (1987) 195–200.
[15] F.G. Katsamanis, C.G. Delides, Fracture surface energy measurements of PMMA: a new experimental approach, J. Phys. D 21 (1988) 79–861. [16] T. Nishioka, T. Murakami, H. Uchiyama, K. Sakakura, H. Kittaka, Specimen size effects on dynamic crack propagation and arrest in DCB specimens, Eng. Fract. Mech. 39 (1991) 757–767. [17] K. Arakawa, K. Takahashi, Relationships between fracture parameters and fracture surface roughness of brittle polymers, Int. J. Fract. 48 (1991) 103–114. [18] K. Arakawa, K. Takahashi, Branching of a fast crack in polymers, Int. J. Fract. 48 (1991) 245–259. [19] K. Arakawa, D. Nagoh, K. Takahashi, Crack velocity and acceleration effects on the dynamic stress intensity factor in polymers, Int. J. Fract. 83 (1997) 305–313. [20] K. Arakawa, D. Nagoh, K. Takahashi, Dynamic crack propagation and unloading behavior of brittle polymers, Int. J. Fract. 96 (1999) 347–360. [21] K. Arakawa, T. Mada, K. Takahashi, Correlations among dynamic stress intensity factor, crack velocity and acceleration in brittle fracture, Int. J. Fract. 105 (2000) 311–320. [22] K. Arakawa, T. Mada, Measurement of brittle fracture energy in PMMA (2nd report), application of high-speed extensometer, Trans. Jpn. Soc. Mech. Eng. Ser. A 70 (695) (2004) 936–940 (in Japanese).
POLYMER TESTING Polymer Testing 25 (2006) 628–634 www.elsevier.com/locate/polytest
Test Method
Tensile fracture behavior of a biodegradable polymer, poly(lactic acid) Kazuo Arakawa, Toshio Mada, Sang-Dae Park, Mitsugu Todo Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga 816-8580, Fukuoka, Japan Received 15 March 2006; accepted 19 April 2006
Abstract The stable and dynamic fracture behavior of a biodegradable polymer, poly(lactic acid) (PLA), was investigated using single-edge-cracked tensile specimens. To study the dynamic effect of brittle facture, the specimens were pin-loaded using a special jig that allowed them to split and fly off in the loaded direction after fracture. The non-elastic effect of viscoelastic and plastic deformations was also measured using an optical high-speed extensometer, which consisted of an optical fiber and a position-sensing detector (PSD). For the stable and dynamic fracture process, external work applied to the specimen and its fracture surface was partitioned into Us and Ud, and As and Ad, respectively. The energy release rate, Gs, for stable crack growth was determined using Us/As. The kinetic and non-elastic energies were measured and subtracted from Ud to evaluate the fracture energy for the dynamic process, Ef. The dynamic energy release rate, Gf, was then determined as Ef/ Ad. Gd was also obtained as Ud/Ad to correlate with Gs and Gf, and the results are discussed. r 2006 Elsevier Ltd. All rights reserved. Keywords: Material testing; Biodegradable polymer; PLA; Fracture; Crack growth; Elastic energy
1. Introduction Biodegradable polymers have recently been introduced to various fields as alternatives to traditional materials. For example, poly(lactic acid) (PLA) is attracting attention as a medical biomaterial owing to its biocompatibility and absorbability in human bodies [1]. In orthopedic and oral surgeries, PLA is often used for bone fixation devices at fracture sites. PLA devices have an important advantage over traditional metal devices; Corresponding author. Tel.: +81 92 583 7761;
fax: +81 92 593 3947. E-mail address: [email protected] (K. Arakawa). 0142-9418/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2006.04.004
there is no need for a second operation to remove the devices after recovery, relieving the physical and mental burdens on patients [2,3]. However, there is a problem; PLA devices can crack during treatment since they are not as resilient as metal devices. Therefore, it is necessary to develop more reliable PLA devices in terms of their mechanical properties, such as their strength and fracture toughness. In addition, the precise evaluation of their mechanical properties is required to assure the safety of PLA devices. Conventionally, PLA specimens with flat, smooth surfaces have been subject to tensile and bending tests. However, PLA devices in the human body can develop flaws and surface defects during the degradation process. Therefore, it is important to examine the fracture behavior using
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
Three-mm-thick PLA plates were fabricated using a hot press with an attached water-cooling system. The pellets were melted at 180 1C, pressed under 30 MPa for 1 h, and then quenched with iced water for 10 min to prevent crystallization of the material. Experiments were performed on single-edgecracked tensile specimens, as shown in Fig. 1. The specimens measured 190 mm in length and 20 mm in width. To change the fracture initiation load of the specimens, sharp pre-cracks with lengths between 2 and 5 mm were generated by tapping a fresh razor blade into a pre-machined saw cut on the specimen edge. As illustrated in the figure, the specimen was clamped rigidly at its lower part and loaded on the upper part using a steel pin and grip. A load was introduced using a special jig consisting of four steel bars, as shown in Fig. 2. The shape of the jig allowed the specimen to split and fly off in the load direction after fracture. The height the specimen attained was recorded with a thin paper pipe (0.3 g) inserted between the bars, which stopped at the highest position reached by the upper part of the split specimen (30 g). This was used to estimate the elastic energy in the specimen. In this study, the elastic energy in the jig was disregarded since it was much stiffer than the specimen. All the specimens were tested under displacement-controlled conditions using a tensiletesting machine. Tests were performed at room temperature and at a constant crosshead rate of 1 mm/min. Fig. 1 also shows the configuration used for the displacement measurements of the loading point and the region underneath the pre-cracked position, i.e. the center of the specimen. The loading-point displacement was determined with the tensile-testing
O
75
Grip d=3
Crack 190
Crack
20
20
2. Specimen material and experimental methods PLA pellets (Lacty#9030; Shimadzu) were used as specimen material. The average molecular weight was about 2 105, and the glass transition and melting temperatures were 61 and 175 1C, respectively.
Crosshead δ (1 mm/min)
Pin
20
φ6
δ'
Lens PSD
Fiber
75
PLA specimens that are notched or cracked. To date, only a few experimental studies examining the fracture behavior of PLA have been published. To study this problem, we fabricated PLA plates from pellets using a hot press, and measured the fracture behavior of single-edge-notch-bend specimens under static and impact loading [4–7]. As a fracture parameter that controls crack growth, the stress intensity factor K or the J-integral was determined using a load–displacement diagram, i.e. the external work applied to the specimen. Essentially, PLA undergoes brittle fracture, and K and J depend on the loading rate. The concept of K or the J-integral plays an important role in understanding fracture behavior. However, more detailed investigation of the effects of inertia or the kinetic energy of the specimen during dynamic crack propagation is required [8–21]. It has also been suggested that the non-elastic effect of the viscoelastic and plastic deformations of the specimen should be determined and considered in the fracture analysis [20]. This study examined these two effects in PLA specimens. To examine the kinetic effect, singleedge-cracked tensile specimens were pin-loaded using a special jig, so that they could split and fly off after fracture. The non-elastic effect of viscoelastic and plastic deformation was also measured using an optical high-speed extensometer [22]. The tensile specimens exhibited stable crack growth in the early stage of fracture and dynamic crack propagation in the later stage. Therefore, fracture was divided into two processes: the external work applied to the specimen and the corresponding fracture surface was partitioned into Us and Ud, and As and Ad, for the stable and dynamic processes, respectively. The energy release rate for stable crack growth, Gs, was then determined as Us/As. The energy release rate for dynamic crack propagation, Gf, was evaluated by first quantifying the kinetic and non-elastic energies. Then, these energies were subtracted from the external work, Ud, to give the fracture energy, Ef. Finally, Gf was determined as Ef/Ad. The values of Gd ( ¼ Ud/Ad) were also obtained for comparison with Gs and Gf.
629
Amp Laser Diode
Clamp
Memory
Fig. 1. Specimen geometry and the experimental setup used for loading and displacement measurement using an optical fiber and position-sensing detector (PSD).
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
where S1 and S2 are the distances between the fiber and the lens, and between the lens and the PSD, respectively.
Load
Load φ20
Paper pipe Pin
3. Definition of fracture energy
Grip Specimen Crack Fig. 2. Loading jig and the method used to measure the flying height of a split specimen.
Y1
PSD
Lens
U ex ¼ U s þ U d ,
Fiber
L q
p
y
S1
S2
L
Y2
machine, while the displacement near the pre-crack was measured using an optical fiber and a positionsensing detector (PSD). A laser diode was used as the light source, and an amplifier and a digital wave memory were used to record the output signals from the PSD. Since the PSD had a frequency response of 100 kHz, it permitted both static and dynamic measurements [22]. Fig. 3 illustrates the optical setup for the displacement measurement using the fiber and PSD. The output light from the fiber attached to the specimen was collected with a lens and focused on the PSD. The light position on the PSD, y, is given as (1)
where L is the half-length of the sensor, and Y1 and Y2 are the output signals from the terminals (see Fig. 3). The fiber position was shifted according to the load applied to the specimen. The relationship between the fiber shift, p, and the light shift, q, on the PSD is given as p ¼ qS 1 =S 2 ,
(3)
where Us and Ud are the energies related to stable and dynamic crack propagations, respectively. We assumed that Us is the fracture energy created for new surfaces during stable crack growth. We also assumed that Ud could be partitioned into three regions, as shown in Fig. 4: U d ¼ Ef þ Ee þ En,
Fig. 3. Principle of displacement measurement using an optical fiber and PSD.
y=L ¼ ðY 1 Y 2 Þ=ðY 1 þ Y 2 Þ,
Fig. 4 shows a typical load, P, versus displacement, d, diagram for a PLA specimen determined using the tensile testing machine. As indicated in the figure, P increased almost linearly with d, and then decreased after the maximum load, Pm, due to the initiation of stable crack growth, and dropped abruptly at Pc and dc, the critical values related to dynamic fracture initiation in the specimen. The P–d diagram in Fig. 4 is divided into two regions:
(2)
(4)
where Ef is the dynamic fracture energy created for new surfaces, Ee is the elastic energy in the specimen and En is the non-elastic energy due to viscoelastic and plastic deformations of the specimen. Ee and En were determined in the following manner. First, Ee was converted into the flying energy of the split specimen after fracture. The viscosity of the material could be neglected during dynamic crack propagation, so that the change from PLA
Pm
0.8
Load P , kN
630
0.6
Us
Pc
0.4
0.2
En + Ee + Ef = Ud δn
0
0
0.2
δe+δn 0.4 0.6 Displacement δ, mm
δc 0.8
Fig. 4. Load P versus displacement d diagram for a PLA specimen under displacement-controlled conditions.
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Pc to dn was elastic (see Fig. 4) [20]. Finally, the following relation held:
0.7 PLA
0.6
150 1.5
100
1.0
50
0.5
0 0
0.2
External Work Ud, J
0.4 0.3 0.2 0.1 0
0
0.2
0.4
0.6 0.8 Load Pc, kN
1
1.2
Fig. 5. Relationship between the external work applied to specimens, Ud, and the critical fracture load, Pc.
0.4
0.6
0.8
1
1.2
Load Pc , kN Fig. 6. Relationship between the flying height of a split specimen, He, and the critical fracture load, Pc.
0.15
50
PLA
0.12
40 Ee
0.09
30
0.06
Ee / Ud
0.03 0
20 10 0
0
0.1
0.2 0.3 0.4 0.5 External Work Ud , J
0.6
Fig. 7. Relationship between the elastic energy, Ee, and external work applied to a specimen, Ud.
produced elastic energy in the specimen, which increased the flying height. The elastic energy, Ee, in the specimen was evaluated using E e ¼ mgH e ,
0.5
Flying Velocity Ve, m/s
The external work for the stable fracture process, Us, was determined using the area (D0PmPc) on the P–d diagram (see Fig. 4). To simplify the analysis, the area was assumed to be a triangle. The values of Us obtained from seven specimens were examined as a function of the maximum load Pm. No intimate correlation was found between Us and Pm since there was large scatter in the data. This suggests that the initiation of stable crack growth in the tensile specimens of PLA was strongly associated with a pre-crack condition, such as its flatness or sharpness, rather than the loading condition of the specimen. Fig. 5 shows the external work for the dynamic fracture process, Ud, determined from the area (D0Pcdc) on the P– d diagram. As seen in the figure, there was a good correlation between Ud and the critical load Pc. This implies that dynamic fracture initiation was strongly related to the loading conditions of the specimens. The flying height of the split specimen, He, was determined as a function of the critical load, Pc. Fig. 6 shows the variation in He versus Pc, plotted using the experimental results obtained from seven specimens. As illustrated in the figure, He increased with Pc. This suggests that the fracture load
2.0
200
Ee /Ud , %
4. Evaluation of fracture energies
PLA Flying Height He, mm
(5)
250
Elastic Energy Ee , J
E n =U d ¼ dn =dc .
631
(6)
where m is the total mass of the specimen, loading pin, grip and paper pipe, and g is the gravitational acceleration. Fig. 7 shows Ee as a function of Ud, where the ratio Ee/Ud is also indicated. Ee increased almost linearly with Ud, while Ee/Ud decreased slightly. Ee/Ud was about 25% in the region of small Ud, and about 23% in the region of large Ud. In this analysis, the energy loss caused by elastic-wave generation from the crack tip, and the friction between the loading jig and paper pipe or split specimen, was disregarded, because we were unable to quantify it. Hence, the elastic energy determined from Eq. (6) might have been underestimated.
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
0.6 PLA
0.5 Displacement δn, mm
0.4 0.3 0.2 0.1 0
0
0.2
0.4
1 0.6 0.8 Displacement δc , mm
1.2
1.4
Fig. 9. Relationship between the residual displacement, dn, and the critical displacement, dc.
100 0.2
PLA
0.15
80 En
60
0.1
40 En / Ud
0.05
0
En / Ud , %
To evaluate the non-elastic energy of the specimen, En, the residual displacement dn must be determined (see Fig. 4). This was done by measuring the displacement d0 beside the crack position before and after fracture (see Fig. 1). Fig. 8 shows d0 as a function of time t. As shown in the figure, d0 dropped abruptly as the fracture initiated dynamically at the critical value d0c , and then exhibited damping oscillation after fracture. Note that there was residual displacement during the oscillation owing to the non-elastic deformation of the material. dn was determined as follows. First, the midpoints of the initial two oscillations were determined, since the baseline changed. Then, a straight line passing through the two points was obtained. The intersection of the line with the curve falling from d0c was used as the residual displacement, d0n , for the split specimen. Finally, the values of dn for the entire specimen were determined by assuming that dn ¼ 2d0n . Fig. 9 shows dn as a function of the critical displacement, dc. Since dn increased with dc, this implies that the dn of the specimen increased with the critical displacement of the specimen. The non-elastic energy, En, was evaluated from Eq. (5). The results are indicated in Fig. 10, which shows En and the ratio En/Ud as a function of Ud. As seen in the figure, En increased with Ud, while En/Ud remained nearly constant at 38%. Fig. 11 shows the fracture energy, Ef, evaluated using Eq. (4) and the ratio Ef/Ud. Ef increased almost proportionally with Ud. Although there was a slight change in Ef/Ud, it remained nearly constant
Nonelastic Energy En , J
632
20 0 0
0.1
0.2 0.3 0.4 0.5 External Work Ud , J
0.6
Fig. 10. Relationship between the non-elastic energy, En, and the external work applied to the specimen, Ud.
0.4 PLA
0.2 δc' 0.1
100
0.3 Fracture Energy Ef , J
Displacement δ', mm
0.3
Sampling ∆t =1µs
0
PLA
0.25
80
0.2 60
Ef
0.15
40
Ef /Ud
0.1
20
0.05 0
0.5
1
1.5
2
Time t, msec Fig. 8. Displacement d0 beside the crack before and after fracture, measured with an optical fiber and PSD (sampling time Dt ¼ 1 ms).
0
Ef /Ud , %
δc'
0
0.1
0.2 0.3 0.4 0.5 External Work Ud , J
0.6
0
Fig. 11. Relationship between the fracture energy, Ef, and the external work applied to the specimen, Ud.
ARTICLE IN PRESS K. Arakawa et al. / Polymer Testing 25 (2006) 628–634
12 PLA Gs, Gf , Gd , kJ/m2
10 Gd = Ud/Ad
8
Gf = Ef /Ad
6 4
Gs = Us/As
2 0
0.2
0.4 0.3 0.5 External Work Ud , J
0.6
Fig. 12. Energy release rates Gs, Gf and Gt as functions of the external work applied to the specimen, Ud.
at 38%. This suggests that the ratio Ef/Ud was not strongly influenced by the fracture conditions, such as Pc, dc or Ud. 5. Energy release rate (G) The energy release rate, G, was estimated using G s ¼ U s =As ;
G f ¼ E f =Ad ;
G d ¼ U d =Ad ,
633
parts: the external works for stable and dynamic fractures, Us and Ud, respectively. The energy release rate was estimated using G s ¼ U s =As and G d ¼ U d =Ad , where As and Ad are the fracture surfaces created by stable and dynamic crack growth, respectively. The flying height was measured to estimate the elastic energy, Ee, in the specimen. The non-elastic energy, En, was also estimated from the residual deformation of the specimen. The dynamic fracture energy, Ef, was then evaluated and correlated with the external work applied to the specimen, Ud. To evaluate the energy release rate during dynamic fracture, G f ¼ E f =Ad was determined, and the following findings were obtained: (1) Ee, En, and Ef increased almost linearly with Ud. (2) Ee/Ud, En/Ud and Ef/Ud were about 24%, 38% and 38%, respectively. (3) Gs remained essentially constant over a wide rage of Ud. (4) Gd and Gf increased almost linearly with Ud. (5) Gd was overestimated, since it included Ee and En. Acknowledgment
(7)
where As and Ad are the fracture-surface areas created by stable and dynamic crack growth, respectively. Gs, Gf, and Gd are shown in Fig. 12 as functions of Ud. Gs remained essentially constant over a wide rage of Ud. No large change was observed on the corresponding fracture surfaces during stable growth. The surfaces were relatively flat and smooth. This indicates that energy dissipation was constant during stable crack growth. Gf and Gd increased almost linearly with Ud, and Gd was much larger than Gf. This implies that Gd was overestimated since the Ee and En of the specimen were included. The corresponding fracture surfaces of the specimens tended to become rougher as Gf increased [21], suggesting that the dynamic effect becomes prominent as the crack velocity increases. 6. Conclusions The stable and dynamic fracture of PLA was studied using single-edge-cracked tensile specimens and an optical high-speed extensometer. The specimens were pin-loaded with a special jig so that they could split and fly away after fracture. The load–displacement diagram was divided into two
This research was supported by Grant-in-aid from Japan Society for the Promotion of Science (Grant nos.15360059 and 16560074).
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