- Email: [email protected]
Fracture behaviour of thermosetting polymers for ophthalmic lenses
Engineering Failure Analysis 17 (2010) 4–10
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Fracture behaviour of thermosetting polymers for ophthalmic lenses A.B. Martínez a, P. Artús b,1, J.C. Dürsteter b,1, D. Arencón a,* a b
Centre Català del Plàstic, Universitat Politècnica de Catalunya, Colom 114, 08222 Terrassa, Spain Departamento I+D+i, División Gafas y Lentes, Industrias de Optica S.A.U., Alcalde Barnils 72, 08174 Sant Cugat del Vallès, Spain
a r t i c l e
i n f o
Available online 6 December 2008 Keywords: LEFM Thermosetting polymers Ophthalmic lenses Double torsion SENB
a b s t r a c t In the worldwide market we found strongly positioned two thermosetting materials for ophthalmic lenses: CR-39 and Superfin. In this work, the fracture behaviour of both materials is studied through the application of Linear Elastic Fracture Mechanics (LEFM) using two geometries: double torsion and three point bending. The fracture toughness has been determined by the double torsion technique. CR-39 showed a continuous and stable crack propagation, whereas Superfin exhibited a stick-slip behaviour whose instability decreased when the strain rate increased. The values at crack initiation agreed with the fracture toughness results of single edge notched tests in bending geometry. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction In 1947 Armorlite Company introduced in the ophthalmic market what has been the most successful resin for the production of organic lenses: PPG’s CR-39 resin. Since then, this material has dominated the world market of polymeric lenses and has spread all over the world gradually replacing inorganic glass as the main ophthalmic lens material. Organic materials were greatly appreciated from the beginning because of their lower density, which translates into lighter glasses, and because they are less brittle than their mineral alternatives, which are more prone to break when they suffer small impacts. Depending on which geographical area of the market is analyzed, a different picture of organic lens sales can be observed. For instance, in developed Asian markets, such as Japan, CR-39 resin has clearly dominated the market but a specific family of thiourethane-based high index materials is increasingly taking over and almost displacing PPG’s product. However, in the American market, although CR-39 also leads, this material shares its dominant position with a thermoplastic polymer such as polycarbonate. European markets are also strongly based on CR-39 but higher index materials increase their sales year by year. For instance, in 1992 Industrias de Optica S.A. introduced what has become a new reference in Spain: Superfin. This material belongs to the same chemical family as CR-39, i.e. allylic, but 50% of its composition is an aromatic polyester oligomer that raises its refractive index from 1.49 (CR-39) to 1.523 and modifies its mechanical properties. This wide variety of new materials that has been appearing during the last few years, usually have higher refractive index and, in some cases, are also claimed to show better mechanical properties. This situation has increased the demand for new testing methods that allow rigorous and thorough comparison of the mechanical properties while allowing some kind of estimation of their behaviour under different situations. While fracture behaviour of inorganic glasses for ophthalmic lenses has been thoroughly studied, seldom references can be found for organic materials [1,2], which are mainly thermosetting polymers.
* Corresponding author. Tel.: +34 93 783 7022. E-mail addresses: [email protected] (A.B. Martínez), [email protected] (P. Artús), [email protected] (J.C. Dürsteter), [email protected] (D. Arencón). 1 Tel.: +34 93 298 2664. 1350-6307/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2008.11.002
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
5
Thermosetting polymers are usually brittle and show a linear elastic behaviour with very little plastic deformation therefore, they fulfil the basic requirements of linear elastic fracture mechanics (LEFM). Different testing methods are available to study the fracture behaviour of these materials. A common technique for fracture toughness determination uses the single edge notched in bending (SENB) geometry. This technique is standardized by ISO 13586 and ASTM D-5049 with the specimen dimensions as shown in Fig. 1. However, the crack propagation can be studied by the double torsion technique whose geometry is shown in Fig. 2. Although not standardized, a distinguishing feature of this loading configuration is that the stress intensity factor, KI, is independent on the crack length for a range of crack lengths in the test specimen [3]. Some studies on the fracture behaviour of thermosetting polymers using double torsion techniques indicate that they usually exhibit an unstable non-continuous type of fracture called stick-slip, as opposed to thermoplastic polymers that show continuous and stable crack propagation. These two types of behaviour can be easily distinguished in the plot of the load versus displacement, as shown in Figs. 3 and 4, which are related to stable and unstable crack propagations, respectively. In the case of continuous propagation, the load on the specimen increases until the propagation starts and the crack grows at a constant load. This load corresponds to the critical stress intensity factor, KIC. When the propagation is unstable, the plot shows a characteristic saw-like profile. The propagation starts at maximum initiation load Pi and stops at a minimum arrest load Pa. These loads are directly related to the critical stress intensity factors for initiation and arrest KICi and KICa, respectively.
B = 6 mm
a S = 58 mm 63 mm Fig. 1. SENB geometry.
Fig. 2. Double torsion geometry.
W = 12 mm
6
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
Load, P
stable
Displacement Fig. 3. Stable crack propagation.
Pi
Load, P
slip-stick
Pa
Displacement Fig. 4. Unstable crack propagation.
The present work has studied the fracture behaviour of two thermosetting polymers, CR-39 and Superfin, very widely used for ophthalmic lenses. In addition, it has been possible to determine the method that more easily evaluates the fracture performance of the manufactured preforms. 2. Experimental details 2.1. Materials The disc-shaped preforms of Superfin and CR-39 were 6 mm thick and had a diameter of 70 mm, and were manufactured through an industrial process analogous to the one used for standard stock lenses for ophthalmic applications. CR-39 discs were polymerized through a mass radical reaction of diethyleneglycol bis-allylcarbonate (ADC) and isopropyl peroxycarbonate (IPP) as an initiator in a 97:3 ratio (wt.). The mixture was stirred for 30 min, filtered and poured into disc shaped moulds formed by two flat round glasses hold together by an adhesive tape. A thermal cycle from 40 to 90 °C in 22 h was applied to the filled moulds. After demoulding, the polymerized discs (preforms) were annealed for an extra hour at 90 °C in an oven. Superfin discs were polymerized through a process similar to CR-39. Superfin corresponds to the commercial name of a copolymer obtained from a monomer mixture of 50% ADC and 50% of an aromatic polyester oligomer of high molecular weight, terminated by allyl groups that copolymerized with ADC through a radical reaction. 2.2. Double torsion tests The double torsion test configuration consists of symmetric four-point loading around a crack or a notch on one end of a rectangular plate. This produces torsional deformation in the two plate halves.
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
7
Rectangular plates of 63 33 6 mm were mechanized from the polymer preforms. Test specimen, as shown in Fig. 2, included a 2 mm longitudinal groove along the length of the plate, in order to guide the crack growth. Notch depth was 8 mm and both the roots of the notch and the groove were sharpened using a razor blade. Wn, the moment arm (the separation between the loading and support points of each arm), was 12.5 mm. All mechanical test were performed at room temperature in a Galdabini universal testing machine using a 1 kN load cell, unless noted. In double torsion test, plain strain KIC can be calculated [4] using
K IC ¼ Pc W m
1
!1=2
3
d dn Wð1 mÞW
ð1Þ
where Pc is the applied load, W the width of the sample, Wm the arm of the torsion par, d the sample thickness, dn the thickness on the crack propagation area, m the Poisson coefficient and w a geometrical factor that can be calculated with
W ¼ 1 0:6302s þ 1:20s expðp=dÞ
ð2Þ
where s = 2d/W. As it can be observed, KIC is independent on the crack length. 2.3. SENB tests After carrying out the double torsion tests, two plate halves were obtained that were mechanized again to obtain 63 12 6 mm rectangular specimens, as show in Fig. 1, compatible with the ISO-13586 or ASTM D-5049. The span, S, was set to 48 mm and the specimens were tested in the universal testing machine at room temperature with a cross-head velocity of 1 mm/min. All the samples were notched at different depths and sharpened using a razor blade. KIC values can be calculated [5] with
K IC ¼ f
P BW 1=2
ð3Þ
where P is the load, B the thickness and f a geometrical factor that can be calculated [4] using the expression
f ¼
pffiffiffi 3 S a G 2 W ð1 þ 2aÞð1 aÞ3=2
ð4Þ
where G=[1.99 a(1 a)(15 3.93a + 2.7a3)], and a = a/W, being a the notch length. Values of KIC under plane strain are valid if the following criteria are fulfilled
B; a; ðW aÞ < 2:5ðK IC =ry Þ2
ð5Þ
being ry the material yield stress. 2.4. Three-point bending tests Unnotched prismatic samples with the same geometry used for SENB tests were flatwise tested at a 1 mm/min and a span of 58 mm. The yield stress can be calculated from the maximum load with expression
rf ¼
3PS 2BW 2
ð6Þ
This equation takes in account neither the influence of the indentation in the load points nor the shear stresses. 3. Results and discussion The double torsion tests were performed at several cross-head velocities. Figs. 5 and 6 show obtained values of KIC for CR39 and Superfin, respectively. A continuous and stable propagation was found for CR-39 material with a constant fracture toughness of 0.25 MPa m1/2, independent on the cross-head velocity, as shown in Fig. 5. In the case of Superfin, Fig. 6, a stick-slip behaviour was observed. As the cross-head velocity was increased, the fracture toughness at initiation KICi decreased whereas the fracture toughness at arrest stayed almost constant. The fracture toughness at arrest was 0.25 MPa m1/2 and equal to the CR-39 fracture toughness value for continuous propagation. The decrease of the initiation values as the cross-head velocity increases could be explained by a loss of crack sharpness [4–7]. When the stress in the crack front is larger than the value of the elastic limit, the material deforms plastically, causing a loss of sharpness at the tip of the crack front known as crack tip blunting, which stops its propagation. A further load increase leads to a rise in the stored deformation energy of the sample, because the crack is not propagating. At a certain mo-
8
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
0.35
KIC (MPa m1/2)
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0
1
2
3
4
5
6
7
8
9
10 11
v (mm/min) Fig. 5. Double torsion CR-39.
0.35
KIC (MPa m1/2)
0.30 0.25 0.20 0.15 0.10 K ICi KICI
0.05 0.00
KICa K ICa 0
1
2
3
4
5
6
7
8
9 10 11
v (mm/min) Fig. 6. Double torsion Superfin.
ment, the load level is enough to reinitiate the propagation. The amount of stored energy with release capability exceeds the quantity of energy needed for a continuous or quasi-stable propagation. This causes the crack to propagate in an unstable pattern until the stored deformation energy equals the amount the sample can withstand. The resulting saw-like profile (Fig. 4) is the consequence of this repetitive process. As a consequence of the viscoelastic nature of these materials, the elastic limit increases as the strain rate does. For this reason, as the velocity rises, the instability of the crack propagation diminishes until a stable propagation is reached. The transition from unstable to stable crack propagation is achieved at velocities larger than 10 mm/min, as can be observed in Fig. 6. A Poisson coefficient of 0.31 was used for both materials. This value was estimated from previous obtained results [8]. A variation of this value would slightly change the results but it would affect neither the general trend nor the behaviour. Fracture toughness values are obtained in SENB geometry through Eq. (3) rearranged in the following form:
P BW
1=2
¼ K IC
1 f
ð7Þ
Since the geometrical factor f is a function of the notch depth (Eq. (4)), each material was tested at different notch depths. A linear fitting of the plot of P/BW1/2 versus 1/f for different notch depths allowed us to calculate the slope, KIC. Figs. 7 and 8 show the curves and results obtained in SENB geometry for Superfin and CR-39. The fracture toughness values were 0.31 and 0.25 MPa m1/2, respectively. As it can be observed, both test methods, SENB and double torsion, gave the same KIC values for CR-39, whereas the obtained values for Superfin corresponded to the initiation ones when compared at equal deformation strain rates. Critical stress intensity factors for both materials are smaller than the values obtained for other thermosetting materials, such as epoxy resins or unsaturated polyesters [4].
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
9
1.8
PQ / BW1/2 (MPa m1/2)
1.6 1.4 1.2 1.0 0.8 0.6 0.4 K IC = 0.245 MPa m1/2
0.2 0.0
0
0.04
0.08
0.12
0.16
1/f Fig. 7. SENB CR-39.
1.8
PQ / BW1/2 (MPam1/2)
1.6 1.4 1.2 1.0 0.8 0.6 0.4 K IC = 0.310 MPa m1/2
0.2 0.0 0
0.04
0.08
0.12
0.16
1/f Fig. 8. SENB Superfin.
In the three-point bending test, the available length of the specimens was shorter than the standardized span. As indentation and shear stresses were not taken in account in Eq. (6), the obtained values rf = 82 MPa for Superfin, and rf = 68 MPa for CR-39, are supposed to be underestimated. It should be noticed that the tests were performed using a 10 kN load cell. Regardless, when these values were applied to check the geometrical criteria (Eq. (5)), all of them fulfilled the plane strain requirements for both tests. 4. Conclusions Double torsion method was found to be suitable to study the fracture behaviour of thermosetting materials for ophthalmic lenses. The tested polymers showed different patterns of crack propagation. Superfin material showed a stick-slip type of crack propagation (saw-like profile) caused by a crack tip blunting mechanism. On the other hand, CR-39 showed a continuous type of crack propagation. The chemical composition of Superfin has a 50% of an oligomer compared to CR-39, thus, the cross-linking density of the former is lower. In this sense, the stick-slip behaviour of Superfin could be explained on the basis of a smaller elastic limit produced by its lower cross-linking density. Critical stress intensity factor at initiation of Superfin is larger than CR-39 at low deformation velocities, but when 10 mm/min was reached both materials behaved similarly. This fact explains the better performance of Superfin when mounted on rimless frames. However, both materials showed values below what is usually obtained from mineral glasses. References [1] McAuliffe PI, Truss RW. A modified double torsion method for measuring the fracture toughness of polymeric ophthalmic lenses. J Mater Sci Mater Med 1994;5:138–43.
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A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
[2] McAuliffe PJ, Truss RW. Double torsion testing of prescription lenses. J Mater Sci Mater Med 1995;6:630–4. [3] Shyan A, Lara-Curzio E. The double torsion testing technique for determination of fracture toughness and show crack growth behaviour of materials a review. J Mater Sci 2006;41:4093–104. [4] Heredia A. Estudio de la fractura materiales compuestos por resinas de poliéster y microesferas rígidas. PhD thesis, Polytechnical University of Catalunya, 1987. [5] Williams JG. Fracture mechanics testing methods for polymer adhesives and composites. ESIS publication 28: Elsevier; 2001. [6] Bakker A. Compatible compliance and stress intensity expressions for the standard three point bending specimen. Int J Fatigue Fract Eng Mater Struct 1990;13:145. [7] Kinloch AJ, Williams JG. Crack blunting mechanism in polymers. J Mater Sci 1980;15:987–96. [8] Artús P, Dürsteler JC, Martínez AB. Low-energy dynamic indentation method for analysis of ophthalmic materials. Opt Vis Sci 2008;85:49–53.
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Fracture behaviour of thermosetting polymers for ophthalmic lenses A.B. Martínez a, P. Artús b,1, J.C. Dürsteter b,1, D. Arencón a,* a b
Centre Català del Plàstic, Universitat Politècnica de Catalunya, Colom 114, 08222 Terrassa, Spain Departamento I+D+i, División Gafas y Lentes, Industrias de Optica S.A.U., Alcalde Barnils 72, 08174 Sant Cugat del Vallès, Spain
a r t i c l e
i n f o
Available online 6 December 2008 Keywords: LEFM Thermosetting polymers Ophthalmic lenses Double torsion SENB
a b s t r a c t In the worldwide market we found strongly positioned two thermosetting materials for ophthalmic lenses: CR-39 and Superfin. In this work, the fracture behaviour of both materials is studied through the application of Linear Elastic Fracture Mechanics (LEFM) using two geometries: double torsion and three point bending. The fracture toughness has been determined by the double torsion technique. CR-39 showed a continuous and stable crack propagation, whereas Superfin exhibited a stick-slip behaviour whose instability decreased when the strain rate increased. The values at crack initiation agreed with the fracture toughness results of single edge notched tests in bending geometry. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction In 1947 Armorlite Company introduced in the ophthalmic market what has been the most successful resin for the production of organic lenses: PPG’s CR-39 resin. Since then, this material has dominated the world market of polymeric lenses and has spread all over the world gradually replacing inorganic glass as the main ophthalmic lens material. Organic materials were greatly appreciated from the beginning because of their lower density, which translates into lighter glasses, and because they are less brittle than their mineral alternatives, which are more prone to break when they suffer small impacts. Depending on which geographical area of the market is analyzed, a different picture of organic lens sales can be observed. For instance, in developed Asian markets, such as Japan, CR-39 resin has clearly dominated the market but a specific family of thiourethane-based high index materials is increasingly taking over and almost displacing PPG’s product. However, in the American market, although CR-39 also leads, this material shares its dominant position with a thermoplastic polymer such as polycarbonate. European markets are also strongly based on CR-39 but higher index materials increase their sales year by year. For instance, in 1992 Industrias de Optica S.A. introduced what has become a new reference in Spain: Superfin. This material belongs to the same chemical family as CR-39, i.e. allylic, but 50% of its composition is an aromatic polyester oligomer that raises its refractive index from 1.49 (CR-39) to 1.523 and modifies its mechanical properties. This wide variety of new materials that has been appearing during the last few years, usually have higher refractive index and, in some cases, are also claimed to show better mechanical properties. This situation has increased the demand for new testing methods that allow rigorous and thorough comparison of the mechanical properties while allowing some kind of estimation of their behaviour under different situations. While fracture behaviour of inorganic glasses for ophthalmic lenses has been thoroughly studied, seldom references can be found for organic materials [1,2], which are mainly thermosetting polymers.
* Corresponding author. Tel.: +34 93 783 7022. E-mail addresses: [email protected] (A.B. Martínez), [email protected] (P. Artús), [email protected] (J.C. Dürsteter), [email protected] (D. Arencón). 1 Tel.: +34 93 298 2664. 1350-6307/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2008.11.002
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
5
Thermosetting polymers are usually brittle and show a linear elastic behaviour with very little plastic deformation therefore, they fulfil the basic requirements of linear elastic fracture mechanics (LEFM). Different testing methods are available to study the fracture behaviour of these materials. A common technique for fracture toughness determination uses the single edge notched in bending (SENB) geometry. This technique is standardized by ISO 13586 and ASTM D-5049 with the specimen dimensions as shown in Fig. 1. However, the crack propagation can be studied by the double torsion technique whose geometry is shown in Fig. 2. Although not standardized, a distinguishing feature of this loading configuration is that the stress intensity factor, KI, is independent on the crack length for a range of crack lengths in the test specimen [3]. Some studies on the fracture behaviour of thermosetting polymers using double torsion techniques indicate that they usually exhibit an unstable non-continuous type of fracture called stick-slip, as opposed to thermoplastic polymers that show continuous and stable crack propagation. These two types of behaviour can be easily distinguished in the plot of the load versus displacement, as shown in Figs. 3 and 4, which are related to stable and unstable crack propagations, respectively. In the case of continuous propagation, the load on the specimen increases until the propagation starts and the crack grows at a constant load. This load corresponds to the critical stress intensity factor, KIC. When the propagation is unstable, the plot shows a characteristic saw-like profile. The propagation starts at maximum initiation load Pi and stops at a minimum arrest load Pa. These loads are directly related to the critical stress intensity factors for initiation and arrest KICi and KICa, respectively.
B = 6 mm
a S = 58 mm 63 mm Fig. 1. SENB geometry.
Fig. 2. Double torsion geometry.
W = 12 mm
6
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
Load, P
stable
Displacement Fig. 3. Stable crack propagation.
Pi
Load, P
slip-stick
Pa
Displacement Fig. 4. Unstable crack propagation.
The present work has studied the fracture behaviour of two thermosetting polymers, CR-39 and Superfin, very widely used for ophthalmic lenses. In addition, it has been possible to determine the method that more easily evaluates the fracture performance of the manufactured preforms. 2. Experimental details 2.1. Materials The disc-shaped preforms of Superfin and CR-39 were 6 mm thick and had a diameter of 70 mm, and were manufactured through an industrial process analogous to the one used for standard stock lenses for ophthalmic applications. CR-39 discs were polymerized through a mass radical reaction of diethyleneglycol bis-allylcarbonate (ADC) and isopropyl peroxycarbonate (IPP) as an initiator in a 97:3 ratio (wt.). The mixture was stirred for 30 min, filtered and poured into disc shaped moulds formed by two flat round glasses hold together by an adhesive tape. A thermal cycle from 40 to 90 °C in 22 h was applied to the filled moulds. After demoulding, the polymerized discs (preforms) were annealed for an extra hour at 90 °C in an oven. Superfin discs were polymerized through a process similar to CR-39. Superfin corresponds to the commercial name of a copolymer obtained from a monomer mixture of 50% ADC and 50% of an aromatic polyester oligomer of high molecular weight, terminated by allyl groups that copolymerized with ADC through a radical reaction. 2.2. Double torsion tests The double torsion test configuration consists of symmetric four-point loading around a crack or a notch on one end of a rectangular plate. This produces torsional deformation in the two plate halves.
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
7
Rectangular plates of 63 33 6 mm were mechanized from the polymer preforms. Test specimen, as shown in Fig. 2, included a 2 mm longitudinal groove along the length of the plate, in order to guide the crack growth. Notch depth was 8 mm and both the roots of the notch and the groove were sharpened using a razor blade. Wn, the moment arm (the separation between the loading and support points of each arm), was 12.5 mm. All mechanical test were performed at room temperature in a Galdabini universal testing machine using a 1 kN load cell, unless noted. In double torsion test, plain strain KIC can be calculated [4] using
K IC ¼ Pc W m
1
!1=2
3
d dn Wð1 mÞW
ð1Þ
where Pc is the applied load, W the width of the sample, Wm the arm of the torsion par, d the sample thickness, dn the thickness on the crack propagation area, m the Poisson coefficient and w a geometrical factor that can be calculated with
W ¼ 1 0:6302s þ 1:20s expðp=dÞ
ð2Þ
where s = 2d/W. As it can be observed, KIC is independent on the crack length. 2.3. SENB tests After carrying out the double torsion tests, two plate halves were obtained that were mechanized again to obtain 63 12 6 mm rectangular specimens, as show in Fig. 1, compatible with the ISO-13586 or ASTM D-5049. The span, S, was set to 48 mm and the specimens were tested in the universal testing machine at room temperature with a cross-head velocity of 1 mm/min. All the samples were notched at different depths and sharpened using a razor blade. KIC values can be calculated [5] with
K IC ¼ f
P BW 1=2
ð3Þ
where P is the load, B the thickness and f a geometrical factor that can be calculated [4] using the expression
f ¼
pffiffiffi 3 S a G 2 W ð1 þ 2aÞð1 aÞ3=2
ð4Þ
where G=[1.99 a(1 a)(15 3.93a + 2.7a3)], and a = a/W, being a the notch length. Values of KIC under plane strain are valid if the following criteria are fulfilled
B; a; ðW aÞ < 2:5ðK IC =ry Þ2
ð5Þ
being ry the material yield stress. 2.4. Three-point bending tests Unnotched prismatic samples with the same geometry used for SENB tests were flatwise tested at a 1 mm/min and a span of 58 mm. The yield stress can be calculated from the maximum load with expression
rf ¼
3PS 2BW 2
ð6Þ
This equation takes in account neither the influence of the indentation in the load points nor the shear stresses. 3. Results and discussion The double torsion tests were performed at several cross-head velocities. Figs. 5 and 6 show obtained values of KIC for CR39 and Superfin, respectively. A continuous and stable propagation was found for CR-39 material with a constant fracture toughness of 0.25 MPa m1/2, independent on the cross-head velocity, as shown in Fig. 5. In the case of Superfin, Fig. 6, a stick-slip behaviour was observed. As the cross-head velocity was increased, the fracture toughness at initiation KICi decreased whereas the fracture toughness at arrest stayed almost constant. The fracture toughness at arrest was 0.25 MPa m1/2 and equal to the CR-39 fracture toughness value for continuous propagation. The decrease of the initiation values as the cross-head velocity increases could be explained by a loss of crack sharpness [4–7]. When the stress in the crack front is larger than the value of the elastic limit, the material deforms plastically, causing a loss of sharpness at the tip of the crack front known as crack tip blunting, which stops its propagation. A further load increase leads to a rise in the stored deformation energy of the sample, because the crack is not propagating. At a certain mo-
8
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
0.35
KIC (MPa m1/2)
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0
1
2
3
4
5
6
7
8
9
10 11
v (mm/min) Fig. 5. Double torsion CR-39.
0.35
KIC (MPa m1/2)
0.30 0.25 0.20 0.15 0.10 K ICi KICI
0.05 0.00
KICa K ICa 0
1
2
3
4
5
6
7
8
9 10 11
v (mm/min) Fig. 6. Double torsion Superfin.
ment, the load level is enough to reinitiate the propagation. The amount of stored energy with release capability exceeds the quantity of energy needed for a continuous or quasi-stable propagation. This causes the crack to propagate in an unstable pattern until the stored deformation energy equals the amount the sample can withstand. The resulting saw-like profile (Fig. 4) is the consequence of this repetitive process. As a consequence of the viscoelastic nature of these materials, the elastic limit increases as the strain rate does. For this reason, as the velocity rises, the instability of the crack propagation diminishes until a stable propagation is reached. The transition from unstable to stable crack propagation is achieved at velocities larger than 10 mm/min, as can be observed in Fig. 6. A Poisson coefficient of 0.31 was used for both materials. This value was estimated from previous obtained results [8]. A variation of this value would slightly change the results but it would affect neither the general trend nor the behaviour. Fracture toughness values are obtained in SENB geometry through Eq. (3) rearranged in the following form:
P BW
1=2
¼ K IC
1 f
ð7Þ
Since the geometrical factor f is a function of the notch depth (Eq. (4)), each material was tested at different notch depths. A linear fitting of the plot of P/BW1/2 versus 1/f for different notch depths allowed us to calculate the slope, KIC. Figs. 7 and 8 show the curves and results obtained in SENB geometry for Superfin and CR-39. The fracture toughness values were 0.31 and 0.25 MPa m1/2, respectively. As it can be observed, both test methods, SENB and double torsion, gave the same KIC values for CR-39, whereas the obtained values for Superfin corresponded to the initiation ones when compared at equal deformation strain rates. Critical stress intensity factors for both materials are smaller than the values obtained for other thermosetting materials, such as epoxy resins or unsaturated polyesters [4].
A.B. Martínez et al. / Engineering Failure Analysis 17 (2010) 4–10
9
1.8
PQ / BW1/2 (MPa m1/2)
1.6 1.4 1.2 1.0 0.8 0.6 0.4 K IC = 0.245 MPa m1/2
0.2 0.0
0
0.04
0.08
0.12
0.16
1/f Fig. 7. SENB CR-39.
1.8
PQ / BW1/2 (MPam1/2)
1.6 1.4 1.2 1.0 0.8 0.6 0.4 K IC = 0.310 MPa m1/2
0.2 0.0 0
0.04
0.08
0.12
0.16
1/f Fig. 8. SENB Superfin.
In the three-point bending test, the available length of the specimens was shorter than the standardized span. As indentation and shear stresses were not taken in account in Eq. (6), the obtained values rf = 82 MPa for Superfin, and rf = 68 MPa for CR-39, are supposed to be underestimated. It should be noticed that the tests were performed using a 10 kN load cell. Regardless, when these values were applied to check the geometrical criteria (Eq. (5)), all of them fulfilled the plane strain requirements for both tests. 4. Conclusions Double torsion method was found to be suitable to study the fracture behaviour of thermosetting materials for ophthalmic lenses. The tested polymers showed different patterns of crack propagation. Superfin material showed a stick-slip type of crack propagation (saw-like profile) caused by a crack tip blunting mechanism. On the other hand, CR-39 showed a continuous type of crack propagation. The chemical composition of Superfin has a 50% of an oligomer compared to CR-39, thus, the cross-linking density of the former is lower. In this sense, the stick-slip behaviour of Superfin could be explained on the basis of a smaller elastic limit produced by its lower cross-linking density. Critical stress intensity factor at initiation of Superfin is larger than CR-39 at low deformation velocities, but when 10 mm/min was reached both materials behaved similarly. This fact explains the better performance of Superfin when mounted on rimless frames. However, both materials showed values below what is usually obtained from mineral glasses. References [1] McAuliffe PI, Truss RW. A modified double torsion method for measuring the fracture toughness of polymeric ophthalmic lenses. J Mater Sci Mater Med 1994;5:138–43.
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[2] McAuliffe PJ, Truss RW. Double torsion testing of prescription lenses. J Mater Sci Mater Med 1995;6:630–4. [3] Shyan A, Lara-Curzio E. The double torsion testing technique for determination of fracture toughness and show crack growth behaviour of materials a review. J Mater Sci 2006;41:4093–104. [4] Heredia A. Estudio de la fractura materiales compuestos por resinas de poliéster y microesferas rígidas. PhD thesis, Polytechnical University of Catalunya, 1987. [5] Williams JG. Fracture mechanics testing methods for polymer adhesives and composites. ESIS publication 28: Elsevier; 2001. [6] Bakker A. Compatible compliance and stress intensity expressions for the standard three point bending specimen. Int J Fatigue Fract Eng Mater Struct 1990;13:145. [7] Kinloch AJ, Williams JG. Crack blunting mechanism in polymers. J Mater Sci 1980;15:987–96. [8] Artús P, Dürsteler JC, Martínez AB. Low-energy dynamic indentation method for analysis of ophthalmic materials. Opt Vis Sci 2008;85:49–53.