Measuring the adherence energy of the resin–metal interface with two fracture mechanics methods: The DCB and NTP tests

Abstract

OBJECTIVE:

To evaluate the abilities of the DCB and the NTP test for measuring adherence of an adhesive joint between a resin and a metal interface.

METHODS:

Two-hundred stainless steel metal beams (diam. $50 \times 5 \times 2 mm$ ) were cast and treated by the following methods: (1) sandblasting with aluminum oxide, followed by treatment with (2) the Rocatec system or (3) the Alloy primer. Superbond and Panavia F 2.0 were used as adhesives. The fracture energy ( $G_{1 C}$ ) and fracture toughness ( $K_{1 C}$ ) of two adhesives were compared by two-way analysis of variance.

RESULTS:

With the DCB test, Superbond was more effective than Panavia, regardless of the surface treatment and conditions of crack propagation. The overall effectiveness of the treatments was in the following order: sandblasting + Rocatec > sandblasting alone > sandblasting + Alloy primer. The adherence energy in an aqueous medium was lower than that in air. With the NTP test, similar performances were obtained with three surface treatments. However, the potential of Rocatec seemed slightly higher.

CONCLUSIONS:

The DCB and NTP tests provide independent measures of the inherent value of an adhesive. Rocatec appeared to provide greater resistance of the bonded joints in an aqueous environment.

Keywords

Adherence energy adhesive DCB NTP

1. Introduction

The main cause of failure for resin-bonded fixed partial dentures is joint debonding between the resin and the metal interface. Factors contributing to this failure include the type of adhesive, nature of the alloy, treatment of the metal surface [1,2], and stresses experienced by the prosthesis [3]. To improve the bonding potential of materials to the tooth structure, the prosthesis surface may be treated by mechanical methods (e.g., sandblasting), chemical methods (e.g., metal-primer), or a combination of these two methods [4,5].

Among the various methods used to test the bond strength of a joint, the shear and tensile tests are common. Regardless of the test used, many variable parameters influence the bond strength, including the interface geometry [6–8], force loading [9], and speed of the test [10]. This variability, which makes comparison among studies virtually impossible, may be due to sensitivity to the geometry of the interface [6–8], the loading of the force [9], and the solicitation speed of the test [10]. Additionally, the clinical and laboratory performances of dental adhesives rarely coincide, because dental adhesion tests are unable to separate the effects of adhesive composition, substrate properties, joint geometry, and loading type on the measured bond strength [11]. Therefore, to evaluate the inherent material properties of an adhesive joint, tests measuring the adherence energy have been proposed. The concept behind these tests is to initiate and propagate a crack through the bonded interface in a stable manner which provides a real characteristic value of the bonding joint and is independent of the specimen geometry [12–15].

The double cantilever beam (DCB) test and the notchless triangular prism (NTP) are two approaches that may be used to evaluate the adherence energy of a bonded joint. The mechanics and principles of the DCB test have been described in detail [12,13]. The DCB test is a cleavage test that measures the value of $G_{C}$ , which is an energy value that reflects the durability of the metal/resin interface. The DCB method provides valuable insights into how the microstructure enhances the toughness of the dental composite [16]. The DCB test was recently successfully applied to evaluate the mode I fracture energy of hydrated and thermally dehydrated cortical bone tissues of the young bovine femur, which has a composition similar to that of human dentine [17]. Moreover, results from the DCB test have shown a good correlation with clinical findings [18].

In 1964, Irwin [19] reported that the stress field around a sharp crack in a linear-elastic material could be uniquely defined by the stress intensity factor K, and that fracture occurs when the value of K exceeds some critical value of the fracture toughness, $K_{C}$ . Thus, K is a stress field parameter that is material-independent, whereas $K_{C}$ reflects an inherent material property. $K_{1 C}$ is the critical stress intensity fracture value for crack growth in the material during mode I. The NTP was derived from the chevron-notched short rod (CNSR, ASTM E1304-89) to develop a new method for evaluating the fracture property of materials. Bubsey et al. detailed the mechanics of the NTP test in 1982 [14], and the test was first applied to dental biomaterials by Ruse et al. in 1996 [15]. This is a test where two metal prisms are assembled by an adhesive (Fig. 2). In order that the stress in the head of the crack is limited and the crack propagation is flat, metal thickness should considerably higher than that of the adhesive. A previous study showed that all bulk specimens and most of the adhesive specimens showed crack arrest, which suggested a well-controlled testing procedure [15]. The NTP test measures the toughness of the interface in bond joints ( $K_{1 C}$ ). According to finite element analysis, the $K_{1 C}$ values of poly (methyl methacrylate) obtained by the NTP correlate well with values obtained by the CNSR [14]. These results suggest that the NTP test may be used to determine the fracture mechanics of bulk materials and adhesive interfaces. Moreover the samples of NTP test can be machined easily and reproducibly without cutting an initial notch. The sample size is small, representing the natural tissues’ size and dental materials. By using this test, Ruse et al., studied the toughness of enamel-dentin joint [20] and the influence of bleaching techniques of dentin [21].

The aim of the present study was to evaluate the adherence energy of the metal/resin interface by using the DCB and NTP tests. The results obtained with two resin cements, Superbond and Panavia 21, were compared. The metal surface was sandblasted and coated with silica (by the Rocatec system) or painted with a primer (i.e., Alloy primer). A single metal was used (stainless steel AISI 304) to facilitate the comparison. Using the corresponding stress intensity factor for plane strain given by Broek [22], we determined that the fracture energies ( $G_{1 C}$ ) measured by the DCB test and the critical stresses ( $K_{1 C}$ ) obtained by the NTP test should be related by the following equation: $K_{1 C} = \sqrt{G_{1 C} E}$ , where E is the elastic modulus of the substrate.

Three hypotheses were tested in this study. (1) In terms of methodology, data from the two tests show a good correlation with the adhesive under the same treatment. (2) In experimental terms, the potential adhesion provided by the two adhesives and the three surface treatments are equivalent. (3) For the DCB test, the value of adhesion does not change when the crack propagates in an aggressive environment.

2. Materials and methods

2.1. Materials

The metal beam used in this study was stainless steel AISI 304, comprised of Fe Ni (10%), and Cr (18%). This metal has an elastic modulus (E) of 210 GPa and is similar to the prosthesis metal base in terms of Ni and Co. It was used because of its facility of machining: it can be cast, ground, or machined easily and reproducibly. Two bonding materials were used: Superbond and Panavia F 2.0. The compositions of the luting cements are listed in Table 1.

Table 1
Chemical compositions of the two adhesive monomers

Monomer Manufacturer Composition

Superbond Sun Medical Co., Japan Liquid: 4-methacryloyloxyethyl trimellitate anhydride (4-META)

Powder: poly-methyl methacrylate (PMMA)

Catalyst: tri-n-butylborane (TBB)

Panavia F 2.0 Kuraray Co., Japan Mixture A: 10-methacryloyloxydecyl dihydrogen phosphate (MDP), 2,2-bis (4-(2-hydroxy-3-methacryloyloxypropyl) phenyl) propane (Bis-GMA), hydrophobic and hydrophilic dimethacylate, colloidal silica, benxoyl peroxide (BPO)

Mixture B: Bis-GMA, hydrophobic and hydrophilic dimethacylate, N,N-diethanol-p-toluidine, colloidal silica, titanium oxide, silanized barium glass, sodium fluoride

Oxyguard: glycol polyethylene glycerine N,N-diethanol-p-toluidine

Alloy Primer: 6-n-4-vinylbenzyl propylamino di-thione triazine (VBATDT), 10-MDP

Monomer	Manufacturer	Composition
Superbond	Sun Medical Co., Japan	Liquid: 4-methacryloyloxyethyl trimellitate anhydride (4-META)
Powder: poly-methyl methacrylate (PMMA)
Catalyst: tri-n-butylborane (TBB)
Panavia F 2.0	Kuraray Co., Japan	Mixture A: 10-methacryloyloxydecyl dihydrogen phosphate (MDP), 2,2-bis (4-(2-hydroxy-3-methacryloyloxypropyl) phenyl) propane (Bis-GMA), hydrophobic and hydrophilic dimethacylate, colloidal silica, benxoyl peroxide (BPO)
Mixture B: Bis-GMA, hydrophobic and hydrophilic dimethacylate, N,N-diethanol-p-toluidine, colloidal silica, titanium oxide, silanized barium glass, sodium fluoride
Oxyguard: glycol polyethylene glycerine N,N-diethanol-p-toluidine
Alloy Primer: 6-n-4-vinylbenzyl propylamino di-thione triazine (VBATDT), 10-MDP

2.2. Surface treatments

Three types of surface treatments were performed.

Sandblasting. The metal beams were sandblasted with aluminum sand (<99.5% Al₂O₃, <0.6% SiO₂; Renfert Strahlmittel, Germany) with a grain size of 50 µm at a pressure of 0.4 MPa. The width and length of the beam were each sanded three times.

Rocatec system. After sandblasting, some metal beams were treated with the Rocatec system (silica [SiO₂] grain size 110 µm; Rocatec, 3M ESPE, Germany) at a distance of 1 cm perpendicular to the surface. Each surface was divided into thirds, and each third was scanned three times in its width and three times in its length. After treatment, silane (Ivoclar Vivadent, Liechtenstein) was used as a coupling agent.

Alloy primer. For the Panavia F 2.0 adhesive, Alloy primer (Kuraray Co., Japan) was applied after sandblasting. This primer contains 6-(4-vinylbenzyl-n-propyl) amino-1,3,5-triazine-2,4-dithiol (VBATDT) and methacryloxydecyl dihydrogene phosphate (10-MDP).

2.3. Test setup

In total, 10 groups of 10 samples each were tested according to the nature of the test (DCB vs. NTP), surface treatment (sandblasting [Sand], sandblasting with Rocatec treatment [Sand+Rocatec], or sandblasting with Alloy primer [Sand+Primer]), and the choice of luting cement (Superbond vs. Panavia F 2.0). The groups are listed in Table 2.

Table 2
Experimental plan

DCB NTP

Group Adhesive Treat Group Adhesive Treat

Group 1 SB Sand Group 6 SB Sand

Group 2 SB Sand+Roc Group 7 SB Sand+Roc

Group 3 PNV Sand Group 8 PNV Sand

Group 4 PNV Sand+Roc Group 9 PNV Sand+Roc

Group 5 PNV Sand+AP Group 10 PNV Sand+AP

DCB	NTP
Group 1	SB	Sand	Group 6	SB	Sand
Group 2	SB	Sand+Roc	Group 7	SB	Sand+Roc
Group 3	PNV	Sand	Group 8	PNV	Sand
Group 4	PNV	Sand+Roc	Group 9	PNV	Sand+Roc
Group 5	PNV	Sand+AP	Group 10	PNV	Sand+AP

Notes: Abbreviations: DCB – double cantilever beam; NTP – notchless triangular prism; Treat – surface treatment; SB – Superbond; PNV – Panavia F 2.0; Sand – sandblasting; Roc – Rocatec; AP – Alloy primer.

2.4. DCB test

In the DCB test, precracking is performed by introducing a wedge between two identical beams that are joined together with an adhesive. These beams deform and store elastic energy. The release of this energy in the adhesive joint creates and propagates a fissure. As the fissure extends and elastic energy stored in the beams is released, two new surfaces are created. In air, the fissure propagation stops after 1 day, when the release rate of the elastic energy (G) equals the energy needed to create a surface of unit dimension (Wr). For fissure propagation in water, which simulates fracture propagation under intraoral conditions, the fissure reaches its maximum length after approximately 24 h at 37°C [21]. By measuring the length of the fissure, the adherence energy (Wr) may be calculated.

In the present study, the dimensions of the specimens for the DCB test were $50 \times 5 \times 2 mm$ , with a precision of 0.05 mm. To facilitate insertion of the wedge, pairs of beams were affixed in a parallel and aligned manner to the jaw of a small vice. One end of the beam surface to be bonded was chamfered (Fig. 1). The luting materials were mixed in accordance with manufacturers’ instructions and applied to the free side of both beams. Immediately after each treatment, pairs of identical beams were fixed in parallel on a device and assembled. The specimen was separated from the vice and placed at 37°C in a thermostatic oven. After 24 h, the excess luting material was removed by wet polishing of the beam.

Fig. 1.

Length of the fissure at equilibrium. E – Young’s modulus of the substratum; △ – beam thickness; h – wedge height; and l – fissure length at equilibrium. For a given geometry, the adherence energy depends only on E and l. $G_{1 C}$ is expressed in terms of J/m².

A 410 µm steel wedge was introduced into the joint with a specially designed bench into two perpendicular micrometer screws to direct the movements of the wedge and beams. The release of elastic energy from the beams provoked a fissure that propagated for 1 day in air. The length of the fissure was measured three times under a microscope at a magnification of ×80 on both sides of the beam, and the measurements of the two sides were averaged. The samples were stored in water at 37°C for another 24 h, and the lengths were remeasured. The adherence energy (Wr) was calculated from the length of the fissure measured after storage in water, according to the theory proposed by Maugis and Barquin [23].

2.5. NTP test

When placed in the testing holder, the specimens for the NTP test achieved a configuration similar to that of the standard CNSR specimen. After cleaning, the surfaces of specimens for the NTP test were treated identically to those for the DCB test (see above). Two stainless steel prismatic specimens ( $6 \times 6 \times 6 mm$ ) were bonded with the testing materials and inserted into a device at a distance of 100 µm (Fig. 2). After the resin cements were hardened for 30 min, the assembly was removed and placed in a thermostatic oven at 100% humidity and 37°C for at least 24 h. Excess resin cements were carefully removed with a semi-automatic polisher under water with sandpaper (SiC; grain sizes of 800, 1200, and 2400). The notch size (0.1 mm) may be controlled by inserting a blade of specific thickness during sample clamping.

Fig. 2.

(A) Two stainless steel prismatic specimens, measuring $6 \times 6 \times 6 mm$ . (B) Specimens fixed in the NTP test device. (C) NTP test device attached to the traction machine (Lloyd Instruments). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151562.)

The sample was placed on a tensile testing machine (JJ Lloyd T 30K, Lloyd Instruments, UK) to measure the maximum stress ( $P_{max}$ ) at the time of rupture at a speed of 0.1 mm/min. The tenacity of the glue ( $K_{1 C}$ ) was calculated from the formula described by Bubsey et al. [14]: $\begin{matrix} (1) & K_{1 C} = \frac{P_{max}}{D \sqrt{W}} Y_{min}^{*}, \end{matrix}$ where $K_{1 C}$ is expressed in $MPa \times \sqrt{m}$ ; D is the diameter of the sample; W is the height of the sample and the sample holder; and $Y_{min}^{*}$ is a dimensionless stress intensity coefficient. The parameter $Y_{min}^{*}$ is a parameter calibration whose value was measured by Ruse to be 28 by linear extrapolation of the data of Bubsey et al. [14] and Ruse et al. [15].

3. Results

3.1. DCB test

Figure 3 shows a representative specimen after the DCB test. Table 2 reports the mean, standard deviation (SD), and coefficient of variation (CV) results for the adherence energy (Wr) in air and after storage in water for 1 day. The energy data were analyzed by two-way analysis of variance (ANOVA), according to three parameters: the bonding materials, surface treatment, and condition (air and water). ANOVA revealed significant differences ( $p < 0.05$ ) among these parameters, as shown in Table 3, Fig. 4. Superbond was more effective than Panavia F 2.0, regardless of the surface treatment or conditions of crack propagation. The overall effectiveness of the treatments went in the order of sandblasting + Rocatec > sandblasting alone > sandblasting + Alloy primer. The Wr value in the aqueous medium was lower than the value in air.

Fig. 3.

Demonstration of the DCB test. After the relatively fast unloading of the specimen, the toughening was almost completely lost. Fast unstable crack growth occurred after a crack had initiated from the notch. Thus, loss of toughening was probably due to fast crack growth, potentially because of viscoelastic effects. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151562.)

Table 3

Average fracture energy values in air or water

Group	No.	Adhesive + Tx	Wr air (J/m²)			Wr H₂O (J/m²)

			Mean	SD	CV (%)	Mean	SD	CV (%)
1	10	SB+Sand	541.9	138	25.5	154.5	40	25.9
2	10	SB+Roc	605.9	71	11.7	471.3	63	13.3
3	10	PNV+Sand	81.2	17	20.5	80.1	18	22
4	10	PNV+Roc	77.6	10	12.5	73.4	10	13
5	10	PNV+AP	56.6	13	23	55.6	14	24.6

Notes: Abbreviations: Tx – treatment; Wr air – fracture energy measured in air; Wr water – fracture energy measured in water after 24 h; SD – standard deviation; CV – coefficient of variation; SB – Superbond; PNV – Panavia F 2.0; Sand – sandblasting; Roc – Rocatec; AP – Alloy Primer.

Fig. 4.

Fracture energy value of adhesives measured by DCB test in air or water. SB – Superbond; PNV – Panavia F 2.0; Sand – sandblasting; Roc – Rocatec; AP – Alloy Primer. Statistically significant difference ( $p < 0.05$ ), NS – No significant difference. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151562.)

3.2. NTP test

Figure 5 shows a representative specimen before and after the NTP test. Table 4, Fig. 6 reports the mean, SD, and CV results for the $K_{1 C}$ values determined with the NTP test. The performances obtained by NTP with sandblasting with or without Rocatec or Alloy primer were very similar, and it was not possible to discern differences between them. However, the potential of Rocatec for improved adherence seemed to be slightly higher.

Fig. 5.

Light microscopy ( $G \times 7$ ) with the NTP test for the Superbond adhesive + sandblasting. Images show the two parts of a sample that was initially bonded together and then was separated by the NTP test device. The interfacial failure is a mixed-type failure. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151562.)

Table 4

Average toughness of the bonded joints under different surface treatments

1	No.	Adhesive + Tx	Mean ( $MPa \cdot M^{1 / 2}$ )	SD	CV (%)
6	10	SB+Sand	1.56	0.2	14.4
7	10	SB+Roc	1.68	0.1	6.8
8	10	PNV+Sand	1.72	0.2	12.1
9	10	PNV+Roc	1.84	0.2	9.1
10	10	PNV+AP	1.70	0.2	9.9

Notes: Abbreviations: Tx – treatment; SD – standard variation; CV – coefficient of variation; SB – Superbond; PNV – Panavia F 2.0; Sand – sandblasting; Roc – Rocatec; AP – Alloy primer.

Fig. 6.

Toughness of the bonded joints measured by NTP test in air. SB – Superbond; PNV – Panavia F 2.0; Sand – sandblasting; Roc – Rocatec; AP – Alloy primer. Statistically significant difference ( $p < 0.05$ ), NS – No significant difference. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/BME-151562.)

4. Discussion

The precracking of the specimens was necessary, because a sharp crack is essential for the accurate evaluation of the $G_{1 C}$ . Usually, the applied $G_{1 C}$ needed to initiate fracture from a notch is much higher than that needed from a truly sharp crack [24]. Once a sharp crack had been initiated, it was relatively easy to control the crack extension during subsequent crack growth experiments.

4.1. Elastic modulus

It is well established that the adhesive strength in terms of E influences the adhesion of an assembly tested at a constant speed in shear and tensile tests [25,26]. In our study, the metal beam (stainless steel AISI 304) had an E of 210 GPa, which is similar to that of a prosthesis metal base of Ni and Co. The E value for the metal beam was nearly 70 times higher than that of bonding materials (E of 0.8–1.0 GPa for Superbond and 3 GPa for Panavia) [25]. Because of the high difference in E between the beam and the bonding material, the adherence energy created by the bond was mainly stored in the metal beams. Two previous studies found no differences between a Ni–Co–Mo substrate and a stainless steel 304 substrate when evaluating the metallic bonding joint [27,28].

For the measured values with the NTP test, the effect of the E of Panavia may partially explain the values of $K_{1 C}$ , which were higher than those of Superbond. In fact, when the system is out of balance (i.e., when the strain rate is not negligible), the macromolecules rearrange to a solid form. As the network becomes more interrelated, the strength needed to break the chains increases, because the chains do not have time to rearrange in response to the rapidly changing stress.

4.2. Influence of adhesives

In the DCB test, the adherence energy created by Superbond was superior to that of Panavia, regardless of the surface treatment or conditions of crack propagation. However, in the NTP test, there was no significant difference between the adhesives. The acidic monomers derived from the carboxylic 4-META (e.g., in Superbond) or phosphoric MDP acids (e.g., in Panavia) are able to bond with the superficial oxide layer of metal and calcium in hydroxyapatite [29]. The high adherence energy obtained with Superbond can be explained by the fact that this energy is proportional to the number of carbon–carbon connections that exist between two points of reticulation to cause rupture. Superbond is a linear polymer whose temperature of vitreous transition (Tg) is 100°C. In contrast, Panavia is a composite with a reticular matrix [27]. Although the number of carbon connections is unknown for these two materials, a linear polymer has more connections than a reticular polymer [30]. Moreover, the main functional group of Superbond, 4-MET, is known to improve the bond strength and wetting to metals [31].

Methacrylate-based self-etching primers/adhesives have a pH value in the range of 1.5 to 2.5 [32]. Under such strongly acidic conditions, an ester such as MDP is hydrolytically degraded [33,34]. Self-etching adhesives show relatively high water uptake, resulting in the generation of water at the interface [35]. The Alloy primer contains VBATDT, which has been reported to harm the polymerization of resin-based materials that contain a benzoyl peroxide-amine initiator system, such as Panavia [36].

4.3. Influence of surface treatment

From our analysis, it appears that the Rocatec system is effective in promoting bonding adherence. These results confirm the findings of a previous study that the Rocatec system is generally more effective than simple activation by sandblasting [37]. In the Rocatec system, silica deposition is followed by the application of a coupling agent (silane), which acts as a connector between the oxide surface and the polymer, dramatically increasing the number of binding sites between the metal and the adhesive. This treatment does not always improve the strength in air, but may instead improve the strength in the presence of a liquid [38].

Our results are consistent with those of a previous study, which found that silane can be used to improve the reproducibility of adhesion in air [39] and liquid [37,40]. After storage in water, these studies found that it was difficult to divide the studied alloys into a dental base alloys group and a noble alloys group. The silica coating significantly limited the propagation of fissures in water. Higher values of adherence energy were recorded with the Rocatec system for all alloys except the palladium alloy, which was only treated with the Silicoater MD system. Samples treated with V-Primer were sensitive to hydrolytic attack.

4.4. Relationship between DCB and NTP

In linear elastic fracture mechanics, three modes of loading are considered: mode I (opening mode), mode II (shearing mode), and mode III (tearing mode). The failure of a brittle material usually occurs in mode I. In the case of an adhesive joint, the fracture criteria, such as $G_{C}$ and $K_{C}$ , may be determined as long as the crack propagates in the bulk of the adhesive or the adherents. Both $G_{C}$ and $K_{C}$ are independent of the geometry of the cracked body and, ideally, even of the test conditions. Unfortunately, the fracture mechanics of adhesive joints is quite complex, because the fractured surface may be situated in the materials that form the joint, along the interface, or between these possible paths.

Theoretically, the fracture energies measured by the DCB test ( $G_{1 C}$ ) and the critical stresses ( $K_{1 C}$ ) obtained by the NTP should be related by the following equation: $K_{1 C} = \sqrt{G_{1 C} E}$ . We chose to control the relationship such that two groups of the same nature (surface treatment and adhesive) were tested by DCB and NTP. In the comparison of sandblasting + Superbond compared with sandblasting + Panavia, the measured $K_{1 C}$ values were $1.56 MPa \cdot M^{1 / 2}$ ( $1.56 \times 10^{6} Pa \cdot M^{1 / 2}$ ) and $1.72 MPa \cdot M^{1 / 2}$ ( $1.72 \times 10^{6} Pa \cdot M^{1 / 2}$ ), respectively. The $K_{1 C}$ was calculated by substituting the fracture energy G in air into the above equation, which yielded $K_{1 C} = \sqrt{542 \times 10^{9}} = 0.74 \times 10^{6} Pa \cdot M^{1 / 2}$ for the Superbond group and $K_{1 C} = \sqrt{81.2 \times 3.0 \times 10^{9}} = 0.5 \times 10^{6} Pa \cdot M^{1 / 2}$ for the Panavia group. Therefore, the ratios of the measured to the calculated $K_{1 C}$ were about 1 to 2 and 1 to 3, respectively.

From these findings, we conclude that we cannot directly compare the values of the fracture energy (Wr) with the values of the toughness of the joint ( $K_{1 C}$ ), because the speed of crack propagation is an important variable influencing the measurements. In fact, we do not know the speed of crack propagation in the NTP test, which was disproportionally higher than the speed of movement imposed by the tensile testing machine (0.1 mm/min).

The stress condition within a loaded adhesive joint is quite complex, due to differences in the mechanical properties of the different adhesive joint components (e.g., E, shear modulus, Poisson’s ratio, yield strength, etc.). Residual polymerization stresses further complicate the stress condition at the joint [41]. Nevertheless, it is possible to discuss the credibility of these two parameters to evaluate a dental bonding joint. $G_{C}$ uses a thermodynamic approach, relying on energetic changes, whereas $K_{C}$ uses a purely mechanical approach, relying on stress conditions. These parameters are often used under the assumption that the material is truly elastic. In the intraoral environment, the fracture is almost never abrupt, but proceeds progressively below the critical stress. The advantage of the DCB test is that it is able to monitor the crack in an aqueous environment. In clinical dentistry, the bonded joints are always in contact with the saliva that is the true medium of crack propagation. The water or aqueous solution changes the permittivity of the crack front and helps to reduce the energy of adhesion.

5. Conclusion

Fracture mechanics theory implies that the DCB and NTP tests provide adhesion values that are independent of the nature and conditions of testing. Our results highlight the influence of two factors: the speed of crack propagation and the rheology of the adhesive. Given the importance of both of these parameters, it was impossible to conclude whether the performance of Superbond or Panavia was superior in terms of adherence. However, both tests showed the value of using a promoter (Rocatec) in the surface treatments. This promoter provided greater resistance of the bonded joints in an aqueous environment.

In the future, we propose the following complementary approaches. With the NTP test, we recommend comparing the toughness values ( $K_{1 C}$ ) at different cracking speeds. In theory, if the NTP test provides a good value for $K_{1 C}$ that is characteristic of the assembly, then a variable speed imposed on the tensile machine should not influence this value. Second, we recommend comparing the $K_{1 C}$ values obtained by the NTP and other tests, to characterize the toughness (mode bending or indentation).

Conflict of interest

The authors declare that they have no conflict of interest.

Financial support

None.

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DCB			NTP

Group	Adhesive	Treat	Group	Adhesive	Treat
Group 1	SB	Sand	Group 6	SB	Sand
Group 2	SB	Sand+Roc	Group 7	SB	Sand+Roc
Group 3	PNV	Sand	Group 8	PNV	Sand
Group 4	PNV	Sand+Roc	Group 9	PNV	Sand+Roc
Group 5	PNV	Sand+AP	Group 10	PNV	Sand+AP

Measuring the adherence energy of the resin–metal interface with two fracture mechanics methods: The DCB and NTP tests

Abstract

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSIONS:

Keywords

1. Introduction

2. Materials and methods

2.1. Materials

2.3. Test setup

Table 2 Experimental plan DCB NTP Group Adhesive Treat Group Adhesive Treat Group 1 SB Sand Group 6 SB Sand Group 2 SB Sand+Roc Group 7 SB Sand+Roc Group 3 PNV Sand Group 8 PNV Sand Group 4 PNV Sand+Roc Group 9 PNV Sand+Roc Group 5 PNV Sand+AP Group 10 PNV Sand+AP

3.1. DCB test

4.1. Elastic modulus

4.2. Influence of adhesives

4.3. Influence of surface treatment

4.4. Relationship between DCB and NTP

5. Conclusion

Conflict of interest

Financial support

References

Table 2
Experimental plan

DCB NTP

Group Adhesive Treat Group Adhesive Treat

Group 1 SB Sand Group 6 SB Sand

Group 2 SB Sand+Roc Group 7 SB Sand+Roc

Group 3 PNV Sand Group 8 PNV Sand

Group 4 PNV Sand+Roc Group 9 PNV Sand+Roc

Group 5 PNV Sand+AP Group 10 PNV Sand+AP