# Bond Behavior of Epoxy Resin-Polydicyclopentadiene Phase Separated Interpenetrating Networks for Adhering Carbon Fiber Reinforced Polymer to Steel.

INTRODUCTIONStrengthening steel structures with carbon fiber reinforced polymer (CFRP) materials has been widely researched in the past 15 years [1-8]. The high strength-to-weight ratio of composite materials provides a promising strengthening strategy compared to conventional methods. However, premature debonding failures of CFRP-strengthened steel structures have been observed experimentally [2, 9-12], This is attributed to the formation of stress concentrations at the ends of the joints that negatively impact the performance of the strong but brittle adhesive joints. In order to prevent unfavorable debonding failures, a material with increased fracture toughness and ductility while retaining high tensile strength and moderate modulus is desirable. Unfortunately, these properties are seemingly mutually exclusive for most adhesives [13-15]. In order to combine the advantages of different adhesives, for example, one which exhibits high strength and another which exhibits high toughness, repairs have been conducted applying tougher, yet lower strength and stiffness adhesives near the plate ends, and stiffer, stronger, yet brittle adhesives elsewhere [16, 17]. In this configuration, the tougher, less stiff adhesive reduces stress concentrations near the plate ends, while the stiffer adhesive provides adequate stress transfer across the rest of the bonded joint. However, this technique requires good craftsmanship to ensure the bond integrity and is not applicable to the wet lay-up process.

An alternative approach is to use a single adhesive that exhibits the required high modulus, strength, and toughness. The design of multicomponent materials is an established method to simultaneously optimize multiple material properties. Epoxy resins are dominant materials used in adhesive applications due to their high strength and modulus, yet they are brittle materials. Increasing the toughness of an epoxy resin, through incorporation of a second, more ductile component, provides a route to tough and strong adhesive materials.

Toughening strategies for epoxy resins have been studied for decades, and tougher and stronger resins have broad potential applications not only as adhesives, but also as composite matrices used in the energy, automobile, and aerospace industries, among others. The majority of efforts to toughen thermoset polymers have focused on the addition of a soft phase to the matrix, such as rubber [18-20] or microvoids [21]. This approach usually comes at the cost of loss of modulus and strength with the addition of the soft phase. In order to overcome these drawbacks, hard fillers such as carbon nanofibers/tubes were added to the matrix to enhance the fracture toughness and other mechanical properties of the resin matrix thereby improving the performance of the composites [22-25] and adhesively bonded joints [26], The success of these approaches relies on properly dispersing and controlling the interface between the matrix and carbon nanotubes, which can be challenging [22, 25, 27].

The formation of interpenetrating polymer networks (IPNs) may provide a strategy to overcome these limitations [28-30]. IPNs are composed of two or more thermosetting networks; in sequential IPNs, one network is synthesized and/or crosslinked in the immediate presence of the other, whereas in simultaneous IPNs they are synthesized and/or crosslinked concurrently. Through the construction of either true IPNs (in which the components are molecularly mixed) or phase separated IPNs, the blended network system can possess a unique combination of the neat component mechanical properties, either following the rule of mixtures or, at particular compositions, expressing a synergistic effect that is greater than the rule of mixtures [31, 32]. The phase separated IPNs used in this study are comprised of diglycidyl ether of bisphenol A (DGEBA)-based epoxy resin and polydicyclopentadiene (PDCPD), which form micrometer-scale phase separated structures, and whose curing kinetics [33], morphology, tensile, and Mode I fracture properties [34] were studied previously, see Fig. 1 for illustration of the formation of this IPN system. Due to the well-behaved mechanical properties and established curing kinetics, these materials offer an opportunity to study how the underlying mechanical properties influence the bond behavior between CFRP and steel.

The epoxy-PDCPD phase separated IPNs have significant potential for structural applications due to the fact they combine the mechanical properties of two complementary polymers. This study investigates this hypothesis by studying the bond behavior of CFRP-steel bonded joints using this IPN system as the adhesive. These IPN adhesives provide a convenient model system with tunable properties for investigating the effects of various mechanical properties (modulus, tensile strength, fracture toughness) on the bond strength. To this end, the bond strength and failure modes were determined from double-lap shear (DLS) joint tests. To expand on the experimental testing results, a theoretical calculation of the bond strength is provided to predict the shear properties of the resins, and the stress and strain distributions within the joint using different IPN compositions. By correlating bond strength to bulk material properties, optimized blend ratios and dominant mechanical properties can be identified, providing guidance for engineering practice and material scientists in developing new adhesives.

EXPERIMENTAL

Materials

Adhesive Components. The DGEBA was supplied by Dow Chemical (Lake Jackson, TX) in the form of Dow Epoxy Resin (D.E.R.) 331 (the fraction of DGEBA molecules that are prepolymerized and possess an extra hydroxyl-containing midgroup, n, = 0.15). The hardener of this epoxy, nadie methyl anhydride (NMA, >95% purity), was purchased from SigmaAldrich (St. Louis, MO) and used as received. An epoxy resin catalyst, 2,4,6-tri(dimethylaminomethyl)phenol, was supplied by Air Products & Chemicals (Allentown, PA) as Ancamine K54 (referred to as K54 in this article) and used as received. Dicyclopentadiene (DCPD) with butylated hydroxytoluene as a stabilizer (>96% purity) was purchased from Sigma-Aldrich and used as received. The second-generation Grubbs' catalyst (G2, used in the ring-opening metathesis polymerization of DCPD) was purchased from Sigma-Aldrich and stored under an ultrapure nitrogen environment.

Phase separated IPNs, created from the sequential curing of the DGEBA/NMA/K54 epoxy resin and PDCPD, are labeled as blend xxE, where xx corresponds to the volume % of epoxy resin (consisting of DGEBA, NMA, and K54). The remaining volume corresponds to PDCPD. For example, blend 30E is 30% epoxy resin and 70% PDCPD, by volume.

For comparison purposes, specimens were also fabricated from a commercial epoxy adhesive that is widely used in aerospace industry. A low viscosity epoxy resin, Araldite LY 5052, and the hardener, Aradur 5052 (a mixture of polyamines) were purchased from Huntsman (The Woodlands, TX) [35].

Materials for DLS Testing. The steel used in DLS specimens was low carbon ASTM A108 steel plates as the inner adherends, with dimensions of 6.2 mm thick, 38.1 mm wide, and 200 mm long. The yield strength of the steel is reported as 372 MPa, and its Rockwell hardness is B70 [36].

The carbon fiber fabrics used in this study were DIALEAD F637400 manufactured by Mitsubishi Plastics Composites America (New York, NY). The reported Young's modulus of the dry fiber is 640 GPa, and the tensile strength is 2,600 MPa [37].

Specimen Preparation and DLS Test Setup

Specimens for measurement of the bond strength of CFRP-steel bonded DLS joints were fabricated using a hand lay-up technique [38].

Specimen Preparation. Prior to bonding, the steel surface was sand blasted using medium coarse sand (No. 4), with a fineness modulus of 4.46, using air pressure no less than 552 kPa. The steel surface was then cleaned with acetone and lint-free cloth to remove the dust and contaminants left on the surface. Nine layers of unidirectional carbon fiber fabrics were applied to ensure debonding instead of rupture failure, with a total of three DLS specimens per adhesive blend. The fiber fabrics were cut and stacked properly to minimize the gap between fiber tows of two adjacent layers (staggering the fiber tows), and then they were stitched together carefully for easier handling (stitched at four points only, between the fiber tows and away from the midpoint and two ends, to minimize the disturbance to the bonded interface).

Resin Formulation and Lay-Up Procedure. For the preparation of phase separated IPNs DLS specimens, the epoxy resin components (DGEBA, 95.3 phr NMA, and 1 phr K54) and DCPD (without Grubbs catalyst) were mixed at various volume ratios using a Cole-Parmer (Vernon Hills, IL) Stir-Pak heavy duty mixer (Model 50007-40), with an impeller blade. When the samples were ready for saturating the fibers, G2 was added to the mixture of DCPD and epoxy resin components while the sample was under impeller mixing. The G2 concentration was held constant at 1.5 * [10.sup.-3] M. The blends with G2 were vigorously mixed using the impeller mixer and then briefly placed under light vacuum from a diaphragm pump (purchased from Marathon Electric, Wausau, WI; Model JQK 56C17F15524B P) for about 30 s to remove bubbles induced during mixing. Lay-up procedures were consistent for the neat resins and blends and involved formulation of the resin systems as described above and in Ref. 34, and then saturating the carbon fibers with resin (approximately 1 mL of resin was made per 6.5 [cm.sup.2] of fiber). After saturation with the resin, the fiber lay-up was then applied to the steel surface and aligned properly to realize a 25 mm overlap length on either side of the DLS joint. Excessive resin was squeezed out by applying two ceramic magnets (75 mm long, 50 mm wide, 12.5 mm thick, purchased from McMaster-Carr) on the lay-up, maintaining a uniform and constant pressure throughout the curing process. The maximum pull force rating of the magnet is 58 N, based on direct contact with a rust-free and unpainted iron plate.

The entire fabrication process was completed within 4 h after sand blasting to minimize the effects of oxidization of the steel surface. The fabricated specimens were then placed in an oven (Skutt Automatic Kiln, Portland, OR; Model KM-818) and cured with an optimized staged curing schedule involving 1 h at 30[degrees]C, 2 h at 70[degrees]C, 5 h at 100[degrees]C, 4 h at 160[degrees]C, and 2 h at 200[degrees]C. The kinetics of the system dictate that, in a two-step curing process, PDCPD cures first at 30[degrees]C and 70[degrees]C, while the epoxy resin cures at the elevated temperatures [33], thus the epoxy-PDCPD IPNs fall into the category of in situ sequential IPNs [30]. After curing, the magnets were removed and the excessive cured resin was ground off carefully with a Treadmill grinder. Great care was taken to remove the cured resin close to the steel surface, to avoid any resin-rich areas and chamfer or fillet effects, which may artificially decrease or increase the bond strength. The final product is shown in Fig. 2.

For comparison purposes, DLS specimens were also prepared containing the commercial epoxy adhesive composed of Araldite LY 5052 cured with Aradur 5052. Similar procedures were employed as outlined above, with the exception of the curing temperature. In the case of Araldite LY 5052 cured with Aradur 5052, select specimens were cured at room temperature, whereas other specimens were cured at 80[degrees]C.

Test Setup. The fabricated specimens were tested in a servohydraulic testing frame (Shore Western 306 series, 4-column frame, 2,000 kN loading capacity, Monrovia, CA), under monotonic tensile loading with a loading rate of 0.25 mm/min. The applied tensile force and the displacement of the actuator stroke were recorded by a data acquisition system integrated in the controller with a time interval of 0.2 s per data point. Due to the limited overlap length of the DLS joint (~25 mm), there was not sufficient space to mount a series of strain gauges to capture the gradient of axial strain of the outer adherend, thereby calculating the shear stresses along the bondline [39, 40]; therefore, strain gauges were not used in this study.

Tensile and Fracture Properties of Neat Epoxy, Neat PDCPD, and Phase Separated IPNs. To develop the experimental and theoretical relationships between the bond strength of the DLS specimen and the resin mechanical properties, the tensile and fracture properties of the neat epoxy resin, neat PDCPD, Araldite 5052, and the phase separated IPNs are tabulated in Table 1 as reported in prior publications [33-35]. In general, the mechanical properties of the neat resins and blended systems are well behaved and follow the rule of mixtures, allowing for an ideal system to explore the impact of resin properties on the bond strength.

THEORY

The bond strength and stress-strain distribution for DLS joints can be analyzed using the Hart-Smith model [16]. Shear properties are required to calculate the theoretical bond strength. However, only bulk tensile properties are typically available in the literature. The IPN System, that is, consisting of an epoxy resin and PDCPD, interpenetrate one another on the microscopic level (the phase separation length scale is in micrometer, see in Fig. 1 and Ref. 34, which describes in great detail the characteristics of the phase separated IPN structure). Macroscopically, the microphase separated INPs behave as homogeneous and isotropic materials (similar to that of a copolymer). It is therefore assumed that the bulk materials are isotropic, homogeneous and follow von Mises yield criterion, so the shear modulus is calculated as:

[G.sub.a] = [E.sub.a]/2(1 + [v.sub.a]) (1)

where [E.sub.a] and [v.sub.a] are the Young's modulus and Poisson's ratio of the resin, respectively. The shear yield strength, [[tau].sub.p], can be related to the tensile yield strength, [f.sub.t], by:

[[tau].sub.p] = [f.sub.t]/[square root of (3)] (2)

For a balanced joint, 2[E.sub.o][t.sub.o] = [E.sub.i]/[t.sub.i], where [E.sub.o] and [E.sub.i] are the longitudinal modulus of the outer and inner adherends, and [t.sub.o] and [t.sub.i] are the thickness of the outer and inner adherends, respectively. For given adherends, the maximum attainable bond strength, [P.sub.u_max], is a function of the shear toughness of the adhesive, [U.sub.shear]:

[P.sub.u_max] = b[square root of (8[E.sub.i][t.sub.i][t.sub.a])] [square root of ([U.sub.shear])] (3)

where [U.sub.shear] = [[tau].sub.p]([[gamma].sub.e]/2 + [[gamma].sub.p]) is the shear toughness of the adhesive, [[gamma].sub.e] = [[tau].sub.p]/[G.sub.a] is the adhesive shear yield strain, [[gamma].sub.p] is the adhesive plastic shear strain capacity, b is the width of the joint, and [t.sub.a] is the adhesive layer thickness. A similar equation is also found based on a bond-slip approach [41]. When the joint is unbalanced, 2[E.sub.o][t.sub.o] > [E.sub.i][t.sub.i], as for the DLS specimens tested in this article, the maximum attainable bond strength is reduced by multiplying by a factor of [square root of ((1 + ETR(2)/2ETR(2)))], where

ETR(2) = 2[E.sub.o][t.sub.o]/[E.sub.i][t.sub.i] (4)

Therefore, the maximum attainable bond strength becomes

[P.sub.u_max] = [square root of (1 + ETR(2)/2ETR(2))]b[square root of (8[E.sub.i][t.sub.i][t.sub.i][t.sub.a])] [square root of ([U.sub.shear])] (5)

This strength can be obtained with sufficiently long overlap length (longer than the critical overlap length, defined in Ref. 16, eq. 112). For overlap lengths shorter than the critical overlap length, a closed-form solution is not available and the solution can be found numerically.

The stress and strain distributions along the bonded overlap can also be solved by using the Hart-Smith model [16]. In the elastic region, the shear stress r solution is

[tau]=Acosh([lambda][chi]) + Bsinh([lambda][chi]) (6)

where constants A and B are to be determined by boundary conditions, and [lambda] is the characteristic value of the governing differential equation

[lambda] [square root of ([G.sub.a]/[t.sub.a](1/[E.sub.o][t.sub.o] + 2/[E.sub.i][t.sub.i]))] (7)

The shear strain can be calculated based on linear elasticity [gamma] = [tau]/[G.sub.a], after the shear stress solution is obtained.

When the peak shear stress at the joint ends increases to the shear yield strength [[tau].sub.p], plastic shear deformation occurs. As the tensile loading further increases, the plastic shear strain increases and the yielded zone propagates towards the center of the overlap. The length of the yielded section of the overlap is defined as the plastic zone size. This stress redistribution process depends highly on the deformation capacity of the adhesive layer, which is affected by the magnitude of adhesive plastic shear strain [[gamma].sub.p], and hence the shear toughness [U.sub.shear] of the adhesive. The shear strain and stress in this elastoplastic regime can be solved by including additional equations of compatibility, which requires the continuity of shear strain and smoothness at the transition of elastic and plastic regions. For an unbalanced joint, shear yielding first occurs at either end (at the location where the magnitude of shear stress is higher). Determining the plastic zone size and the corresponding stress and strain requires numerical iteration as described in detail in Ref. 16, appendix A1.2.

The maximum peeling stress of DLS joints is a function of the maximum shear stress, mechanical and geometrical properties of the outer adherend, and the apparent modulus of the adhesive under peeling [E'.sub.c] [16]:

[[sigma].sub.max] = [[tau].sub.max] [[3[E'.sub.c](1-[v.sup.2.sub.o])[t.sub.o]/[E.sub.o][t.sub.a]].sup.1/4] (8)

where [v.sub.o] is the Poisson's ratio of the outer adherend. It is noted that the maximum peeling stress becomes constant once shear yielding occurs, since [[tau].sub.max] = [[tau].sub.p] and the rest of the parameters remain unchanged.

RESULTS AND DISCUSSION

Bond Strength and Failure Modes of DLS Specimens of Varying Composition

The bond strengths (debonding failure loads) of the tested DLS specimens are summarized in Table 3 and represented in Fig. 3. All epoxy-PDCPD blend specimens exhibited higher bond strengths than specimens composed of either neat component. For example, blend 30E (containing 30 vol % epoxy) exhibited the highest bond strength (69.1 [+ or -] 2.1 kN), which is ~35% higher than that of the neat epoxy (50.5 [+ or -] 3.8 kN), and ~125% higher than that of neat PDCPD (30.9 [+ or -] 0.3 kN). The average bond strength of the neat epoxy component of the blends was fairly close to that of commercially available Araldite 5052 cured under elevated temperature (Araldite-80C), whose average bond strength increased by around 16% compared to the room temperature cured specimens (Araldite-RT).

Failure Modes

For specimens containing neat PDCPD as the adhesive, as shown in Fig. 4a, the failure surface was dominated by steel-adhesive interfacial debonding with a small amount of carbon fiber and resin left on the steel surface, which indicates that the steel-adhesive interface is the weakest link. By contrast, a mixed failure mode is observed for neat epoxy specimens, in which CFRP delamination is dominant, as shown in Fig. 4f. As the volume fraction of the epoxy decreased, the failure mode gradually transitioned from mixed failure mode to pure CFRP delamination, as shown in Fig. 4b and c, indicating that the steel-adhesive interfacial bond strength is greater than the CFRP interlaminar strength for this joint configuration.

Relationship of Bond Strength to Bulk Material Properties

The bond strength of DLS joints depends on the geometrical, mechanical, and chemical properties of the constituent materials. In this study, the geometry and preparation method were kept consistent, and only the resin varied. Bond strength as a function of the mechanical properties of the resins are shown in Fig. 5. Formulations with the highest tensile strength, Young's modulus, or fracture toughness did not provide the highest bond strength. Rather, blend 30E, with moderate tensile strength, Young's modulus, and fracture toughness, exhibited the highest bond strength (Fig. 5a-c). The bond strength decreased as the tensile toughness increased (Fig. 5d).

Bond Strength as a Function of Shear Toughness

Based on the Hart-Smith model, theoretical shear toughness can be calculated based on the debonding failure load of each specimen if the other properties of the joint are known, using Eq. 5. This approach was found to have good agreement with experimental and numerical results [42].

The thickness of the outer adherend (CFRP composite) of the DLS joint, [t.sub.o], can be obtained by measuring the total thickness of the joint, [t.sub.DLS], and subtracting the thickness of the inner adherend, [t.sub.i], which is simply [t.sub.o] = ([t.sub.DLS] - [t.sub.i])/2. The manufacturing method of the DLS joint, which was described in the experimental details, leads to an average thickness of the outer adherend of 4.45 mm (standard deviation is 0.17 mm). Note that if the thin film of resin between steel surface and the adjacent carbon fiber is considered as the adhesive layer, this outer adherend thickness includes the thickness of adhesive layer [t.sub.a], which can be approximated as [t.sub.a]~[t.sub.o]/n --[t.sub.fiber], where n is the number of carbon fiber layers [38]. The areal weight of fiber fabric is measured as 0.0464 g/[cm.sup.2] and the dry fiber unit volumetric density is reported 2.12 g/[cm.sup.3] [37], resulting an average fiber thickness (excluding the packing effect) of 0.219 mm. This gives an average adhesive thickness of 0.27 mm. Therefore, the resulted thickness of the outer adherend after subtracting the adhesive layer thickness is 4.18 mm.

The fiber volume fraction (FVF), can then be approximated as FVF = n[t.sub.fiber]/[t.sub.o]. This yields an estimated fiber volume faction of 47%. The corresponding longitudinal modulus of the outer adherend, E0, can be approximated using the rule of mixtures

[E.sub.o] = [E.sub.fiber]FVF + [E.sub.matrix] (1-FVF) (9)

where [E.sub.fiber] is the modulus of the dry fibers along the fiber direction and [E.sub.matrix] is the Young's modulus of the matrix resin (assumed isotropic). The results are listed in Table 2. It is noted that the longitudinal modulus is dominated by the modulus of the fibers, and the variation due to the matrix resin is small.

The inputs for the theoretical model and the calculated shear toughnesses are shown in Table 3. Blend 30E exhibited the highest shear toughness among all the specimens tested (~104% higher than neat epoxy and ~360% higher than neat PDCPD), while PDCPD with the highest bulk tensile and Mode I fracture toughness, exhibited the lowest shear toughness. The low shear toughness of PDCPD might be due to relatively weak adhesion between PDCPD and steel, resulting in adhesive-steel interfacial debonding before the shear ductility of PDCPD is fully engaged. The shear toughness calculated based on debonding failure loads is shown in Fig. 6, together with the plot of the maximum attainable bond strengths, expressed in Eq. 5. It is demonstrated that the data points align well with the maximum attainable bond strength [P.sub.u_max] (defined in Eq. 5), which serves as the upper bound of bond strength. The deviation between the two increases as the bond strength increases, which is due to the increase of the critical bonded overlap length as the bond strength increases, see Ref. 16, eq. 112. In order to achieve the maximum attainable bond strength [P.sub.u_max], an overlap longer than the critical overlap length is necessary. This figure demonstrates the potential of bond strength by increasing the overlap length. It also shows that for specimens with lower shear toughness, increasing the overlap length will not increase the bond strength much; however, as the shear toughness increases, the increase of bond strength is more significant by increasing the overlap length.

Prior studies have demonstrated the ability of the Hart-Smith model to predict the stress-strain distribution along the bondline in DLS joints [48-50]. A closer look at the distributions of shear stress and shear strain along the bonded overlap is shown in Fig. 7. Epoxy and PDCPD specimens remained elastic up to failure, while blend 30E yielded at the loaded end with development of a significant plastic zone (plateau at the joint end in Fig. 7a). This indicates that blend 30E has a greater capacity to redistribute the stress, hence increasing the bond strength. The corresponding shear strain distributions in Fig. 7b demonstrate that the maximum shear strain ymm at the joint end of blend 30E is the highest, because this is the highest debonding failure load among all specimens, which induces the highest shear deformation along the bondline. The shear strains of PDCPD and epoxy specimens are much smaller and close to each other, as they exhibited the first and second lowest debonding failure loads as well as the difference in joint stiffness. Since the epoxy is stiffer than PDCPD, it is more efficient in transferring the load from steel to CFRP; therefore, shear deformations are higher close to the joints ends and lower in the middle (stiffer adhesive can transfer the load more efficiently with a smaller bonded overlap length, but a higher stress and strain will be induced close to the joint ends). Similarly, the strain distribution curve of PDCPD is flatter than and close to that of the epoxy specimen because of the lower stiffness of PDCPD specimen despite the lower bond strength.

The maximum peeling stress was calculated using Eq. 8 to illustrate the shear toughness dominancy. The maximum peeling stress ranged from 29.5 MPa (blend 20E) to 37.8 MPa (neat epoxy) for the resins of interest, except for neat PDCPD, as shown in Table 4. It is noted that the average maximum peeling stresses of blend 70E and neat epoxy are almost identical, but the bond strength of blend 70E is 27% greater than that of the neat epoxy, indicating that it is mainly the increase of shear toughness that contributes to the increase of bond strength.

The increase of bond strength and shear toughness of these phase separated IPNs is significant not only for structural bonding applications, but also important in developing composites for energy, automobile, and aerospace industries [31]. For example, the increased interfacial bond strength can help to resist thermally induced interfacial shear stresses due to different thermal expansion coefficients of carbon fiber and metal.

Furthermore, the increased shear toughness of the blended resin matrices suggests a potential increase of interlaminar shear strength of composites, which is mainly governed by the fracture and mechanical properties of the resin matrix under shear, assuming a robust bonding between fiber and matrix. As shown in the experimental results, blend 30E demonstrates the highest bond strength among the specimens that failed by CFRP delamination (20E, 30E, and 50E), which suggests a potential increase of interlaminar shear strength by using these blends. Since delamination is one of the dominant failure modes of fiber reinforced polymer composites under fatigue and impact loadings, these blended resin matrices with increased interlaminar shear strength may have the potential to enhance the fatigue life and impact resistance of fiber reinforced polymer composites.

CONCLUSIONS

The bond behavior of CFRP-steel DLS joints was examined, using newly developed phase separated IPNs of epoxy and PDCPD as the adhesive. Bond strengths of IPN adhesives with different epoxy and PDCPD compositions were characterized, and relationships between the bond strength and the bulk material properties were identified. A theoretical analysis using the classical Hart-Smith model was carried out to calculate the shear toughness and stress-strain distributions of the specimens. The major findings of this study are summarized as follows:

1. All epoxy-PDCPD phase separated IPNs adhesives performed better than either neat component. Among them, blend 30E exhibited the highest bond strength, representing an increase of ~35% compared to neat epoxy, and an increase of ~125% compared to neat PDCPD. Adhesive blends with moderate tensile strength, tensile modulus, and Mode I fracture toughness demonstrated the highest debonding strengths among the adhesives tested.

2. Debonding failure mode transitions were observed from steel--adhesive dominated failure to pure delamination failure, as the bond strength increased. This suggests that the steel-adhesive interfacial debonding strength increased when the IPNs adhesives were used.

3. A theoretical analysis by using the classical Hart-Smith model indicated that the blends have much higher shear toughness than their neat components, although additional testing is required to validate this finding. The potential bond strength can be even higher for specimens using blends with higher shear toughness, if the overlap length of DLS increases.

The findings of this research indicate that the newly developed epoxy-PDCPD blends are suitable for structural CFRP-steel bonding, due to the increase of bond strength, and preventing unfavorable steel-adhesive interfacial debonding. This IPN system can potentially be used for fiber-metal composite manufacturing. More broadly, the predicted high shear toughness of the IPNs offer a great potential as the matrix of fiber reinforced polymer composites, to increase their fatigue lives and impact resistances. The results highlight the importance of optimizing adhesive material properties collectively when developing new adhesives rather than maximizing a single parameter.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of the National Science Foundation (CMMI Award #1334838), and the Department of Civil and Environmental Engineering, Department of Chemical and Biomolecular Engineering, at the University of Houston.

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Meng Liu, (1) Brian J. Rohde, (2) Ramanan Krishnamoorti, (2) Megan L. Robertson (iD), (2) Mina Dawood (iD) (1)

(1) Department of Civil and Environmental Engineering, University of Houston, Houston, Texas, 77204-4004

(2) Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas, 77204-4004

Correspondence to: M. Dawood; e-mail: mmdawood@uh.edu and M. L. Robertson; e-mail: mlrobertson@uh.edu

Contract grant sponsor: National Science Foundation; contract grant number: 1334838.

DOI 10.1002/pen.25264

Published online in Wiley Online Library (wileyonlinelibrary.com).

Caption: FIG. 1. Illustration of the sequentially cured PCDPD-epoxy microphase separated IPNs [33, 34]. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 2. Trimmed fully cured fabricated specimen before testing. Excess resin is removed from the edges and chamfer and fillet effects are removed. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 3. Bond strength of phase separated IPNs as a function of epoxy resin volume percentage in the adhesive. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 4. Images of the select specimens highlighting the failure modes: (a) neat PDCPD with dominant adhesive-steel interface debonding failure. (b) blend 20E with complete CFRP delamination failure, (c) blend 30E with complete CFRP delamination failure, (d) blend 50E with dominant CFRP delamination plus minor area of adhesive-steel interfacial debonding, (e) blend 70E with dominant CFRP delamination failure plus partial adhesive-steel interfacial debonding, and (f) neat epoxy (DGEBA cured with NMA) with dominant CFRP delamination and partial adhesive-steel interfacial debonding. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 5. Bond strength as a function of (a) tensile strength, (b) Young's modulus, (c) tensile toughness, and (d) fracture toughness. Maximum bond strength is observed at intermediate tensile strength, modulus, and fracture toughness, whereas a decrease in bond strength is observed with increasing tensile toughness.

Caption: FIG. 6. Bond strength as a function of adhesive shear toughness. The solid line represents the maximum attainable bond strength with sufficiently long overlap (upper bound), see Eq. 5.

Caption: FIG. 7. Theoretical stress and strain distributions along the overlap upon debonding: (a) shear stress distribution and (b) shear strain distribution. [Color figure can be viewed at wileyonlinelibrary.com]

TABLE 1. Mechanical and fracture properties of the resins. Sample Tensile Elongation at Modulus (MPa) strength (MPa) break (%) PDCPD (a) 53 [+ or -] 1 7.9 [+ or -] 0.7 1,610 [+ or -] 50 20E (a) 66 [+ or -] 1 5.7 [+ or -] 0.6 1960 [+ or -] 20 30E (a) 73 [+ or -] 1 5.6 [+ or -] 0.2 2,130 [+ or -] 30 50E (a) 76 [+ or -] 1 5.2 [+ or -] 0.2 2,260 [+ or -] 40 70E (a) 79 [+ or -] 2 5.1 [+ or -] 0.4 2,540 [+ or -] 50 Epoxy Resin 91 [+ or -] 8 5.1 [+ or -] 0.8 2,600 [+ or -] 100 (a) Araldite- 49 to 71 1.5 to 2.5 3,351 to 3,551 RT (b) Araldite- 80 to 84 5.7 to 5.9 2,999 to 3,199 80C (c) Sample Tensile toughness [K.sub.IC] (MPa (MPa) [m.sup.1/2]) PDCPD (a) 3.0 [+ or -] 0.3 2.7 [+ or -] 0.3 20E (a) 2.4 [+ or -] 0.4 2.29 [+ or -] 0.03 30E (a) 2.5 [+ or -] 0.1 2.07 [+ or -] 0.03 50E (a) 2.4 [+ or -] 0.2 1.51 [+ or -] 0.07 70E (a) 2.5 [+ or -] 0.3 1.3 [+ or -] 0.1 Epoxy Resin 2.7 [+ or -] 0.7 0.58 [+ or -] 0.09 (a) Araldite- N.A. N.A. RT (b) Araldite- N.A. 0.93 to 1.0 80C (c) (a) Data were taken from Ref. 34 for the epoxy resin prepared by curing DGEBA with NMA, along with the phase separated IPNs (curing protocol provided in experimental details). (b) Data were taken from Ref. 35 for Araldite 5052 cured under room temperature for 7 days. (c) Data were taken from Ref. 35 for Araldite 5052 cured under 80[degrees]C for 8 h. TABLE 2. Estimated longitudinal modulus of the outer adherend, [E.sub.0], of phase separated IPN DLS specimens (GPa) (a). PDCPD 20E 30E 50E 70E Epoxy resin 302.6 302.8 302.9 303.0 303.1 303.2 (a) The CoV of the longitudinal modulus of CFRP prepared by wet lay-up process is reported to be within 10% [43]. TABLE 3. Input for Hart-Smith model and the resultant shear properties under debonding failure loads. Matrix Shear modulus Shear strength Bond strength (a) [G.sub.a] (MPa) [[tau].sub.p] [P.sub.u] (kN) (b) (MPa) (c) PDCPD 597 [+ or -] 22 30.6 [+ or -] 0.6 30.9 [+ or -] 0.3 20E 726 [+ or -] 17 38.1 [+ or -] 0.6 63 [+ or -] 4 30E 789 [+ or -] 20 42.1 [+ or -] 0.6 69 [+ or -] 2 50E 837 [+ or -] 23 43.9 [+ or -] 0.6 68 [+ or -] 1 70E 941 [+ or -] 27 46 [+ or -] 1 64 [+ or -] 2 Epoxy 963 [+ or -] 43 53 [+ or -] 5 51 [+ or -] 4 Matrix Plastic shear Shear toughness (a) strain [[gamma].sub.p] [U.sub.shear] (%) (d) (MPa) (d) PDCPD 0 [+ or -] 0 0.46 [+ or -] 0.01 20E 2.2 [+ or -] 0.6 1.8 [+ or -] 0.2 30E 2.4 [+ or -] 0.3 2.1 [+ or -] 0.1 50E 1.9 [+ or -] 0.2 2.0 [+ or -] 0.1 70E 1.4 [+ or -] 0.3 1.7 [+ or -] 0.1 Epoxy 0 [+ or -] 0 1.0 [+ or -] 0.2 (a) The Poisson's ratio of DGEBA epoxies is typically in the range of 0.30-0.40 [44-461, and the Poisson's ratio of PDCPD is reported as 0.39 [47]. Therefore, it is reasonable to assume the Poisson's ratio of the IPN system is between 0.30 and 0.40. The Poisson's ratio will affect the shear modulus; however, it is independent from the shear toughness of specimens with sufficiently long overlap length (see Eq. 5). For the specimens studied here, the scatter of shear toughness by varying Poisson's ratio from 0.3 to 0.4 is less than 2%, which is consistently less than the error of the shear toughness calculated due to variability of bond strength. (b) Using Eq. 1. Means and standard deviations (error bars) were estimated using Monte-Carlo simulation considering the uncertainty of the input variables. (c) Using Eq. 2. (d) Determined numerically using equations in Ref. 16, appendix A. TABLE 4. Estimated maximum peeling stress of phase separated IPN DLS specimens (MPa). PDCPD 20E 30E 50E 17.7 [+ or -] 29.7 [+ or -] 33.5 [+ or -] 35.2 [+ or -] 0.5 0.7 0.8 0.9 PDCPD 70E Epoxy resin 17.7 [+ or -] 37.9 [+ or -] 38 [+ or -] 0.5 0.9 3