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Stress mitigation for adhesively bonded photovoltaics with fibre reinforced polymer composites in load carrying applications
Composites Part B 177 (2019) 107420
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Stress mitigation for adhesively bonded photovoltaics with fibre reinforced polymer composites in load carrying applications Yiqing Dai a, Yu Bai a, *, Thomas Keller b a b
Department of Civil Engineering, Monash University, Clayton, VIC, 3800, Australia � Composite Construction Laboratory (CCLab), Ecole Polytechnique F�ed�erale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Building integrated photovoltaics (BIPV) Fibre reinforced polymer composites Solar cell Adhesive Bonding Compression Composite action
Structural loads, especially in-plane compression, may cause local buckling and debonding of the photovoltaic (PV) cells that are mechanically integrated with structural members and this may lead to degradation in their electrical performance. This paper proposes an approach to mitigate the strains transferred from structural members to PV cells through the partial composite action provided by low-modulus adhesives. Specimens were fabricated by bonding amorphous silicon (a-Si) PV cells to glass fibre reinforced polymer (GFRP) structural components by an adhesive layer of 0.5- or 2.0-mm thickness. Two types of adhesives were used including a twopart rigid epoxy adhesive and a low-modulus silicone adhesive. These integrations were then submitted to inplane compressive loadings. PV cells bonded by the silicone adhesive showed no damages during loading. While for PV cells bonded by epoxy adhesives, obvious electrical performance degradations were observed, when the strain reached 0.62% or 0.23% for specimens bonded by epoxy with a layer thickness of 0.5 mm or 2.0 mm respectively. Debonding and local-buckling of the PV cells were also witnessed. Theoretical analysis was con ducted to understand the strain mitigation of the adhesive as a result of the induced partial composite action. Results demonstrate that such strain differences between the GFRP and the bonded PV cell are dominated by the shear modulus and thickness of the adhesive layer as well as elastic modulus, thickness and length of the PV cell. The theoretical analysis was validated by finite element (FE) modelling and design suggestions are provided accordingly.
1. Introduction Building integrated photovoltaics (BIPV) are building components with integrated photovoltaic (PV) materials and they are used in parts of building envelops [1], such as roofs [2,3], windows [4], claddings [5] and facades [6]. Apart from functioning as building components, BIPV generate electricity by harvesting solar energy. In comparison to con ventional PV products standing on ground or structures, BIPV does not occupy additional space; and labor and cost can be reduced without mounting of individual PV cells. Quality of adhesive integration can also be assured in factory, since the PV cells are adhesively bonded with building components in factory and then the complete integration is installed onsite [7]. One of the practical methods for integration of such BIPV compo nents is to adhesively bond PV cells to exteriors of building materials and components [8]. Fibre reinforced polymer (FRP) composites are considered as the substrates in such integrations for their superior
strength-weight ratio and corrosion resistance, and some of them (e.g. glass fibre reinforced polymer, GFRP) are electrically insulating [9]. Due to such advantages, various profiles and components (e.g. flat plates [10, 11], rebars [12,13], square hollow sections [14,15] and sandwich structures [16,17]) made of GFRP composites have been implemented for structural applications including support systems for PV cells [18]. Translucent GFRP laminates were also proposed and developed to encapsulate translucent dye PV cells for BIPV applications [19–21]. In terms of the PV cells in BIPV components, different types have been employed in such integrations where mono-crystalline silicon (m-Si) PV cells are most commonly used because of their high PV efficiency [7,22]. However, BIPV components with m-Si PV cells are excluded from ap plications in load-carrying scenarios since m-Si PV cells are brittle and even small strains may cause their cracking, leading to degradation in electrical performance and functional failure [23]. For example, four-point bending experiments on m-Si PV cells samples indicated that they would break at 0.10%–0.15% tensile strains [24].
* Corresponding author. E-mail addresses: [email protected] (Y. Dai), [email protected] (Y. Bai), [email protected] (T. Keller). https://doi.org/10.1016/j.compositesb.2019.107420 Received 17 April 2019; Received in revised form 27 July 2019; Accepted 5 September 2019 Available online 6 September 2019 1359-8368/© 2019 Published by Elsevier Ltd.
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Several types of thin-film flexible PV cells capable of sustaining relatively large strains have shown potentials for such applications, for example amorphous silicon (a-Si) PV cells [25] and organic PV cells [26, 27]. In comparison to m-Si PV cells, they are much thinner and lighter in weight. Among thin-film flexible PV cells, a-Si PV cells are competitive since they are non-toxic and relatively cost effective [28]. The critical strain for initiation of electrical degradation in a-Si PV cells has been investigated in several studies. For example, tensile experiments were conducted on small-scale samples [29,30] and large-scale commercial products [31] of a-Si PV cells and consistent results suggested that the critical tensile strain was about 1.40%. Mechanical experiments on BIPV integrations of a-Si PV cells and FRP composites in tension have also been initiated in recent years. For example, a-Si PV cells were embedded in the wet face sheet resin, below a surface veil, of a GFRP sandwich structure with foam core and it was reported that no obvious change in the open-circuit voltage of the PV cell was observed when the service ability limit load of about 0.7 kN was applied [25]; while an elevated temperature up to 60–80 � C was identified when the structure was submitted to artificial sunlight. Tensile experiments were conducted on the integrations of carbon fibre reinforced polymer (CFRP) laminates and a-Si PV cells bonded by a two-part epoxy and up to 1.0% tensile strain did not affect much its electrical performance [32]. In-plane compressive strain was introduced to a-Si PV cells alone [33] and the critical compressive strain was found to be over 1.7%. Thus, in terms of in-plane compression, it seems possible for a-Si PV cells to work normally below the ultimate strain of GFRP materials (usually around 1% [34]). However, according to compression experiments on integrations of a-Si PV cells and GFRP substrates adhesively bonded by polyimide tapes, obvious decrease in open-circuit voltage was witnessed from 0.5% in-plane compressive strain and this was because of the debonding and local buckling of PV cells [29]. The in-plane compression is therefore a critical loading scenario for such integrations and rela tively small compressive strains may cause debonding or local buckling of the PV cells, resulting in compromise of their electrical performance or loss of their functionality. Thus, for the BIPV components used in compression scenarios, the adhesive layer plays an important role for the bonding and associated load transfer performance, while no much work was done to investigate the composite action and the resulting load transfer mechanism offered by the adhesives in the BIPV systems. Such results are important in the selection of an appropriate adhesive as well as its bonding geometrises (thickness, area, etc.) for better mechanical performance and electrical behaviour of such integrations under compression. In this study, a-Si PV cells and GFRP structural members with square hollow sections (SHS) were bonded by an adhesive of 0.5- or 2.0-mm thickness. Two types of adhesives were used including a rigid two-part epoxy adhesive and a ductile silicone adhesive. Such GFRP and PV in tegrations were then submitted to in-plane compressive loading in the longitudinal direction of GFRP SHS members. The electrical perfor mance of the specimens was continuously monitored during the me chanical loading (up to 80% of the ultimate load of the GFRP SHS) and unloading processes. A theoretical modelling was further developed to understand the strain transfer behaviour of the adhesive layer through the resulting full or partial composite action and to determine the dominant parameters for such load transfer mechanism. A finite element (FE) model was also developed to validate the theoretical results and the parametrical studies, together with the results received from the experiments.
tests were conducted using an Instron 50 kN machine and the load readout was recorded by a data logger (dataTaker DT515) at 1 Hz. Dog bone-shaped coupons with an overall length of 180 mm and a gauge length of 60 mm were prepared for the epoxy and silicone adhesives and reflectors with a spacing of about 40 mm were bonded to the surface of the coupons as shown in Fig. 1a and b. Specimens for the a-Si PV cell were also prepared with a dimension of 250 mm (length) � 25 mm (width) � 1 mm (thickness) and the spacing between the reflectors was about 50 mm as shown in Fig. 1c. An extensometer (MTS LX500) was used to monitor changes in spacing between the reflectors on the surface of the adhesive and PV cell coupon specimens; and the strain results were taken as the spacing change divided by the spacing length. For the adhesives, the tests were conducted with reference to ISO-527 at room temperature (about 22 � C) and the displacement rate was 1 mm/min. Tests for the PV cells were conducted with reference to ASTM D-882-12 [35]. Four steel plates (50 mm � 50 mm � 3 mm) with polished edges were bonded to both ends of the PV cells to protect the specimens and connecting wires. Open circuit voltage (VOC) of the PV cell coupon specimens were measured and recorded by the data logger. Two coupon specimens for each material were prepared and the adhesive coupons were cured for four weeks at room temperature before testing. The stress-strain results are shown in Fig. 2 for a-Si PV cells and the two types of adhesives. The epoxy specimens exhibit an approximate linear strain-stress behaviour up to the ultimate failure at 1.05% tensile strain and the elastic modulus can be determined accordingly. The sil icone adhesive specimens could be loaded up to large strain values over 100% while the elastic modulus would be then underestimated at large strains due to a reduction in the cross section. Thus, elastic modulus of the silicone adhesive was calculated based on its strain-stress behaviour within 2.0% strain (see Fig. 2). The a-Si PV cell exhibits a linear elastic behaviour until its yielding at about 0.21% tensile strain; and a strain hardening behaviour start from about 1.02% strain as shown in Fig. 2, since it comprises a steel substrate of around 0.07-mm thickness. Breakage of the a-Si PV cell happens at over 3.80% tensile strain. The resulting elastic modulus and strain characteristics on average of the repeating specimens are summarized in Table 1 and the results for the same GFRP SHS tested in [14] are also presented. It should be noted that, in the tensile tests for PV cells, no obvious change in VOC was observed until 1.4% tensile strain was reached. This result agrees with previous studies [29,30] and more detailed discussions of the voltage response to the tensile strain can be found from [29]. It also confirms the feasibility of a-Si PV cells for integration with GFRP composites in
2. Experimental investigations 2.1. Material properties The stress-strain behaviour and elastic modulus of the adhesives and the PV cells were determined individually by tensile coupon tests considering their similar properties in compression. As shown Fig. 1, the
Fig. 1. Experimental setup for material properties of (a) epoxy adhesive, (b) silicone adhesive, and (c) a-Si PV cells. 2
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thickness of 9.5 mm. The adhesive thickness was 0.5 or 2.0 mm for two types of adhesives, namely a two-part epoxy or a silicone adhesive. First, the potential GFRP interfaces for adhesive bonding were subjected to mechanical abrasion and cleaned. Second, for the specimens with the two-part epoxy, an epoxy resin (BPR 135G) and a curing agent from Epikote™ were mixed thoroughly and used as a bonding agent with a thickness of 0.5 or 2.0 mm. For the specimens with silicone, the Pattex® all-purpose silicone of 0.5- or 2.0-mm thickness was used, again after surface abrasion and cleaning. Two repeating specimens for each configuration and therefore a total of eight specimens were prepared. All the specimens were cured at room temperature for four weeks. The setup for compression experiments on the GFRP-PV integration is shown in Fig. 3b. A halogen lamp of 200 W was used to provide artificial sunlight to the PV cells considering it has similar spectrum with sunlight. A slight decrease of the open-circuit voltage (VOC) of the PV cells in association with the increase of their temperature (5–8 � C) was witnessed. After the VOC became stable, the compression load was applied at 0.5 mm/min using an Amsler 5000 kN testing machine. The specimens were loaded up to 800 kN (approximately 80% ultimate load of the GFRP section according to previous experimental results from the same GFRP SHS in compression [14,15]) and then unloaded gradually. Two strain gauges were installed on the centre of two adjacent surfaces of the GFRP SHS. No strain gauges were used on the PV cells since it is difficult to install the strain gauges on the textured polymer surface and the protective polymer may not fully transfer the PV cell strain to strain gauges. Instead, a laser extensometer (MTS LX500) was used to measure the change in distance between the two reflectors on the surface of PV cells. The compression load, distance change between the reflectors, strains of the GFRP SHS and VOC of the PV cells were recorded by a data logger (dataTaker DT515) at 1 Hz.
Fig. 2. Stress-strain relationships for PV cells, silicone adhesives and epoxy adhesives. Table 1 Mechanical properties of adhesives, PV cells and GFRP. Yielding strain Elastic modulus Ultimate strain
Silicone
Epoxy
PV cell
GFRP [14]
– 2.12 MPa >100.00%
– 3.54 GPa 1.05%
0.21% 20.98 GPa >3.80%
– 31.60 GPa 0.89%
tension as the latter usually have an ultimate tensile strain of around 1% [34]. Considering that elevated temperatures up to 60–80 � C may be reached for PV cells in BIPV applications [25], the glass transition temperature (Tg) for the epoxy used in this study is 81 � C according to the manufacturer and the temperature of working condition for the silicone ranges from 15 to þ200 � C.
2.3. Experimental results The stress-strain behaviour of the GFRP-PV specimens in the loading (left side) and unloading (right side) processes is shown in Fig. 4a and the specimens exhibit a linear stress-strain behaviour in both loading and unloading processes. The highly symmetric stress-strain curves in the loading and unloading processes indicates the deformation can be fully recovered. A maximum load of 800 kN was applied and thus the maximum axial stress is around 220 MPa. The maximum strain wit nessed ranges from 0.64% to 0.69% and the corresponding compressive
2.2. Specimens and experimental setup As shown in Fig. 3a, specimens were prepared using a-Si PV cells and GFRP SHS members. The a-Si PV cells with a dimension of 180 mm (height) � 60 mm (width) � 1.0 mm (depth) were bonded to the GFRP members with a section of 300 mm � 102 mm � 102 mm and a wall
Fig. 3. (a) Specimen configuration (side view) and (b) experimental setup for integration of a-Si PV cells and GFRP SHS components in compression. 3
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Fig. 4. Strain responses in loading and unloading processes of (a) GFRP and (b) PV cells of BIPV integration.
elastic modulus is around 32 GPa on average, which is in consistence with existing research [14–17]. Fig. 4b shows the correlation of the GFRP strain and PV cell strain during the loading and unloading processes. Due to the linear corre spondence between the compressive load and GFRP strain evidenced in Fig. 4a, the GFRP strain from Fig. 4b also represents the load level. It can be seen from Fig. 4b that strains in PV cells with epoxy adhesives are almost identical to those measured from GFRP; while the strains in PV cell with 0.5 mm or 2.0 mm thickness of the silicone layer are signifi cantly lower, with the maximum values of only 0.20% and 0.05% respectively. A strain transfer ratio (RS) can be defined as the ratio be tween the compressive strains in the PV cell and the GFRP strains at certain load level. Accordingly, at the maximum load (about 800 kN) in the experiments, RS for the epoxy adhesive with either thickness is around 1.0 (0.95–0.97); RS for the silicone adhesives of 0.5 mm is 0.29 and for the 2.0-mm ones is only 0.08. In this way, it can be demonstrated that RS or the PV cell strain can be effectively reduced using a silicone adhesive and RS is almost constant during the loading and unloading processes due to an approximate linear relation between the strains of PV cells and GFRP. When the applied compressive load was approaching 250 kN, local buckling of the PV cells was noticed from the GFRP-PV integrated specimen with 2.0-mm epoxy adhesive as indicated in Fig. 5a. Such local buckling was also associated with the debonding of the PV cell from the epoxy adhesive. For the specimens with 0.5-mm epoxy adhesive, local buckling of smaller scales was witnessed in only one or two spots from each specimen as presented in Fig. 5b. This may be associated with bonding imperfection in thicker epoxy layers since the voids and bubbles could hardly be completely eliminated in especially a thick adhesive layer due to high viscosity of epoxy in specimen fabrication. The PV cells
with silicone adhesives did not show visual buckling in the experiments, since only limited strains were transferred to the PV cells as the silicone adhesive was associated with small RS values. In terms of open-circuit voltage of the PV cells in the specimens with 0.5- or 2.0-mm silicone adhesive, hardly any change can be found as evidenced in Fig. 6a. However, obvious voltage degradation was wit nessed from the specimens with epoxy adhesives as shown in Fig. 6b. The voltage results in Fig. 6b are numbered, for example 0.5mm-1 represents the results from the first specimen with 0.5-mm thick epoxy adhesive. The critical strains for obvious voltage degradation are also presented in Fig. 6b, and for PV cells with 2.0-mm epoxy adhesive, voltages decrease severely from 0.20% to 0.25% GFRP strain and only about 20% voltage remains at the maximum GFRP strain of 0.68%. Limited voltage (less than 40%) recovered during the unloading process. For the PV cell integrated specimens with 0.5-mm epoxy adhesive, no degradation in voltage was noticed when the GFRP strain was below about 0.6% strain; after that, 83% or 50% voltage remained at the maximum GFRP strain for the two repeating specimens. During the unloading process, around 90% voltage was recovered. In a previous study [33], the electrical performance of a-Si PV cells was not affected by even 1.70% in-plane compressive strain; while the PV cells started degradation when only 0.22% strain was applied for the integration using 2.0-mm epoxy, or 0.61% applied for those with 0.5-mm epoxy in this study. This highlights that the voltage degradation in such PV cells should be associated with their local buckling induced by the compressive strains at the locations likely with bonding imper fections (see Fig. 5a and b). The silicone adhesives were evidenced to be capable of providing a strain mitigation effect (in addition to serving as lateral supports) for the integrated PV cells, thus this may provide an approach to ensure the PV cells under a low strain range in BIPV com ponents during service. 3. Modelling 3.1. Theoretical formulation Full composite action provided by the adhesive layer in the GFRP-PV integration results in identical axial strain in the PV cell and GFRP, i.e. the strain due to axial loading is fully transferred from the GFRP to PV cell through the adhesive layer. According to the results of the compression experiments as shown in Fig. 4b, full composite action was witnessed for the integrations with epoxy adhesive in this study. While partial composite action allows relative slips between the GFRP and PV cell and only a part of the GFRP strain can be transferred to the PV cell through the adhesive layer. A smaller strain was witnessed in the PV cells than GFRP from the compression experiments as shown in Fig. 4b, due to the partial composite action provided by the silicone adhesive layer. The full or partial composite action is therefore associated with the mechanical properties (shear modulus in particular) and dimensions
Fig. 5. Local buckling of a-Si PV cells in compressive specimens with (a) 2.0mm epoxy adhesive and (b) 0.5-mm epoxy adhesive. 4
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Fig. 6. Voltage responses of a-Si PV cells in relation of compressive strain of GFRP SHS for integration using (a) silicone and (b) epoxy adhesive.
of the adhesive layer. A theoretical model with consideration of a range of major design parameters such as the shear modulus (GA) and thick ness (tA) of the adhesive layer is accordingly developed to understand the full or partial strain transfer behaviour through the adhesive layer in such BIPV integrations [36–39]. Fig. 7 shows a typical differential element in this study, where ‘y’ is the vertical distance to the centre of the PV cell (also see Fig. 3a); ‘x’ is the distance in thickness direction from the outer surface of the adhe sive; ‘LPV’ is the length of the PV cell; ‘tPV’ and ‘tA’ are thicknesses of the PV cell and adhesive respectively; ‘σ’, ‘τ’, ‘u’ and ‘ε’ are axial stress, shear stress, displacement and strain of the differential elements; ‘E’ is the elastic modulus and ‘G’ is the shear modulus; subscripts ‘G’, ‘A’ and ‘PV’ denote the layer of GFRP, adhesive and PV cell respectively. Due to the uniformly-distributed axial stress and strain on GFRP along the width direction (i.e. z direction shown in Fig. 3a) and the symmetrical loading and structural form in this regard, the variations of the stress and strain along the width direction (z direction) are minor and therefore neglected. The strain variation of PV cells in the thickness direction (x direction shown in Fig. 3a) is not considered because of their thin thicknesses and unconstrained outer surface. However, the strains along the axial direction (y direction shown in Fig. 3a) for the adhesive layer and PV cells caused by the axially applied load are not uniformly distributed, therefore such axial variations in stress and strain should be considered in the formulation. Also, the possible differences of strains between the GFRP and PV cell due to the partial composite action are taken into account through the strain transfer behaviour in the formu lation. As a result, based on the stress equilibrium in the longitudinal direction of the PV element shown in Fig. 7, Eq. (1) is obtained as below,
(1)
τPV ðyÞdy ¼ tPV dσPV ðyÞ
Where τPV(y) is the shear stress in the interface between the adhesive and PV cell, tPV represents the PV cell thickness, and σPV(y) is the axial stress of the PV cell. Similarly, τA(x,y), as the shear stress of the adhesive at a distance of x in the thickness direction from the outer surface of the adhesive layer, can be obtained as follows,
τA ðx; yÞ ¼ τPV ðyÞ þ x
dσ A ðx; yÞ ; ð0 � x � tA Þ dy
(2)
Where σA(x,y) is axial stress of the adhesive layer. Combining Eqs. (1) and (2), it gives
τA ðx; yÞ ¼
tPV dσ PV ðyÞ dσ A ðx; yÞ þx ; ð0 � x � tA Þ dy dy
(3)
Considering the stress-strain relationship of the adhesive and the PV cell, it gives � � t dε ðyÞ E dε ðx; yÞ (4) ; ð0 � x � tA Þ τA ðx; yÞ ¼ EPV PV PV þ x A A dy dy EPV Where εPV(y) and εA(x,y) are axial strain of the PV cell and adhesive respectively, and EA and EPV are their elastic modulus. Since the PV cell has a much higher elastic modulus than the adhesive according to Table 1, it gives EA �0 EPV
(5)
Therefore,
τA ðx; yÞ ¼ EPV tPV
dεPV ðyÞ dy
(6)
According to Eq. (6), shear stress of the adhesive layer, τA(x,y), may be independent of x along the thickness direction (i.e. the distance from the outer surface of the adhesive), considering the elastic modulus of the adhesive much lower than the PV cell. Therefore, the shear stress vari ation in the thickness direction (x direction) of the adhesive can be neglected and τA(x,y) becomes τA(y) only. Considering the relative displacement between the GFRP and PV cell in y direction (see Fig. 7), Eq. (7) can be obtained as uG ðyÞ
uPV ðyÞ ¼
τA ðyÞ GA
tA
(7)
where uG(y) or uPV(y) is the vertical displacement of GFRP or PV cell at the location with a vertical distance of y from the PV cell centre. Taking derivatives of y on both sides and substitution of Eq. (6) into Eq. (7) gives
Fig. 7. Illustration of strain transfer from GFRP to PV cell in a typical differ ential element where dy is a differential length, τPV is the shear stress between the adhesive and PV cell. 5
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εG
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εPV ðyÞ ¼
1 dτA ðyÞ 1 d2 εPV ðyÞ ¼ EPV tPV tA tA GA dy GA dy2
(8)
The Eq. (8) can be simplified as below, 2
d εPV ðyÞ þ k2 εPV ðyÞ ¼ k2 εG dy2
(9)
where k2 ¼
GA EPV tPV tA
(10)
The general solution for Eq. (9) as a second order differential equa tion of εPV in regard to y can be expressed as
εPV ðyÞ ¼
α sin hðkyÞ
(11)
β cos hðkyÞ þ εG
Considering the boundary conditions that the PV cell is free from axial stress at both ends, Eq. (12) can be formed as below, � � � � 1 1 (12) LPV ¼ 0 εPV y ¼ LPV ¼ εPV y ¼ 2 2 Thus,
α ¼ 0; β ¼
ε
2
3
6
cos hðkyÞ 7 � �7 5 cos h 12 kLPV
εPV ¼ εG 6 41
Fig. 8. FE modelling: loading, boundary conditions and meshing.
(13)
�G � cos h 12 kLPV
The adhesives used in this study were modelled as an elastic layer with the thickness ranging from 0.5 to 2.0 mm and elastic modulus ranging from 0.1 to 1000 MPa. Poisson’s Ratio was 0.50 for the adhe sives [41] and 0.20 for the PV cells. The ‘tie’ constrains and ‘rough’ frictional contact were used for the interfaces of the adhesive layer with the GFRP and the PV cell, i.e. considering no slips at the interfaces. As shown in Fig. 8, the FE models were meshed using C3D8 elements (8-node linear bricks) for the GFRP, adhesive and PV cell, resulting in 1 mm for one element of the PV cell or 5 mm for one GFRP element; the element sizes for the adhesive layer depended on its thickness and two element layers were considered in the meshing of adhesive through thickness. The uniformly distributed load up to 1000 kN (the ultimate load for the GFRP SHS according to [14–17]) was incrementally applied in compression on top of the GFRP SHS components. The specimens were supported on a rigid base plate with all displacements and rota tions constrained at the bottom of the base as shown in Fig. 8. The loading process was then solved using Krylov methods in ABAQUS.
(14)
Accordingly, the maximum strain in the PV cell happens at the centre of the PV cells (see Fig. 3a, namely y ¼ 0). Then the strain transfer ratio (RS) between the PV cell and GFRP at this location is given below, RS ¼
εPV ðy ¼ 0Þ ¼1 εG
1 � �¼1 cos h 12 kLPV
1 � qffiffiffiffiffiffiffiffiffiffiffiffi � 1 A cos h 2LPV EPVGtPV tA
(15)
As indicated in Eq. (15), RS or the strain transferred from the GFRP SHS to the PV cell is dominated by five factors, namely the shear modulus of adhesive (GA), adhesive thickness (tA) as well as the elastic modulus (EPV), thickness (tPV) and length (LPV) of the PV cell.
4. Results and discussion
3.2. FE modelling approach
4.1. Strain transfer ratio, RS
FE modelling based on ABAQUS was established to compare with experimental results for further parametric study and also to validate the theoretical formulation. A typical FE model with loading, boundary conditions and meshing methods are presented in Fig. 8. Dimensions of the FE model were defined according to the specimens in the experi ments (see Fig. 3a). Only for the parametric analysis on the influence of PV length, the GFRP component is modified to have a length of 500 mm to accommodate longer PV cells. The GFRP material was defined as linearly elastic and transversely isotropic, with the elastic modulus of 32 GPa in the longitudinal direction and 5 GPa in the transverse di rections. The interlaminar and in-plane shear moduli of the GFRP ma terial are 12 GPa and 3.5 GPa according to the experiments in [14–17]. The stress and strain constitutive relationship was defined in two stages for PV cells. The first one is described as linearly elastic with the elastic modulus of 21 GPa; and in the second stage, a yielding behaviour was considered with the modulus reduced to 0.4 GPa (2% of the modulus before yielding as suggested in [40]) after the linear stress-strain rela tion reaches 0.21% compressive strain according to the material testing of the PV cells (see Table 1). Strain hardening was not considered for the PV cells since this behaviour only happened for strain values over 1.0% while the GFRP strains in the experimental study were within 0.70%.
The correlations between strains of the GFRP and the PV cell of the GFRP-PV integration during the loading process are plotted in Fig. 9 based on the experimental results, theoretical formulation and FE modelling. A linear relationship between the strains of the GFRP and PV cells can be identified from those obtained by Eq. (15) and the FE modelling, where different loading levels ranging from 200 to 800 kN were applied and the strain transfer ratio (RS) can be obtained accord ingly. Such linear relationship is also supported by experimental results during the loading process for the GFRP-PV specimens with silicone and epoxy adhesives. The predicted PV cell strains from FE and theoretical methods are consistent with the experimental results especially at large load levels. Some differences within the prediction and experimental results are witnessed in Fig. 9 for especially the integrations with epoxy adhesives in small loading levels, possibly because the epoxy adhesive is not an idealized linear-elastic material as shown in Fig. 2. From Fig. 9, the aforementioned strain transfer ratio (RS) was calculated based on the consistent results from theoretical and FE modelling. For the scenario with a 2.0-mm adhesive thickness, this ratio is 0.08 for silicone and is 1.0 for epoxy; for an adhesive thickness of 0.5 mm, this ratio is 0.23 for silicone and is 1.0 for epoxy. These RS 6
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For the scenarios with silicone adhesives, as presented in Fig. 10a, the PV cell strains increase from the top or bottom end to its centre symmetrically and the maximum strain is witnessed in the centre. Such results agree with the theoretical results in Eq. (14). According to Fig. 10a, the maximum PV strain is about 0.5% for the PV cell with a length of 360 mm and an adhesive thickness of 0.5 mm; thus, even though a silicone adhesive has been applied, a relative high strain may still be received in a long PV cell. While the maximum PV cell strain can be reduced to 0.20% if the adhesive thickness is increased to 2.0 mm. For configurations with shorter PV length (180 mm) as shown in Fig. 10a, the PV strain values are smaller than 0.20% for both adhesive thick nesses (0.5 mm or 2 mm). It should be noted that these strain results are associated with a compression load of 1000 kN, corresponding to the ultimate compressive capacity of the GFRP SHS sections in use [14,15]. For the modelling results with 2.0-mm epoxy adhesives, as presented in Fig. 10b, the strain in the PV cell with a length of 360 mm increases sharply within about 10 mm from the top and bottom edges towards the centre of the PV cell. This strain value remains constant and consistent with the GFRP strain (0.87%) at the applied load of 1000 kN in most part (over 85%) of the cell. Thus, hardly any strain mitigation can be pro vided by epoxy adhesives and this rapid increase of strain of the PV cells to that of the GFRP is valid also for the PV cells of other lengths. In addition, according to the FE simulation and theoretical analysis, RS would not be affected by the width of the PV cell, thus a possible and practical solution may be to keep the longer edge of the PV cells perpendicular to the loading direction, therefore a shorter PV length is subjected to loading direction (resulting in less strain at the PV centre). It should be noted that the substrate of the a-Si PV cells in use is steel and it may yield after its strain reaches 0.21% (see Table 1). This may reduce its elastic modulus considerably and therefore the PV cell may easily buckle after the yielding of its substrate.
Fig. 9. Strain relationships between GFRP and PV cell integrated using silicone or epoxy with an adhesive thickness of 0.5 or 2.0 mm from experiments, FE simulation and theoretical methods.
values did not change with the load levels as the adhesive layer was modelled as linear elastic. Based on the validated theoretical and FE analysis, the effects of the material and geometric properties of the adhesives and PV cells (i.e. shear modulus and thickness of the adhesive as well as elastic modulus, thickness and length of the PV cell) can be further investigated to un derstand the strain transfer behaviour and provide suggestions for such applications. 4.2. Effects of PV cell length on RS
4.3. Effects of thickness and elastic modulus of PV cell on RS
In terms of the a-Si PV cells used in this research, several different dimensions are available in the market according to the manufactures, with the length ranges from 90 to 360 mm. Since the strain transfer ratio (RS) increases with the length of PV cells (LPV) according to Eq. (15), several PV lengths up to 360 mm were used in simulation to investigate the effect of PV length on the strain transfer behaviour. In the analysis, the GFPR SHS had a height of 500 mm to accommodate a maximum PV length of 360 mm and the adhesive thickness was 0.5 or 2.0 mm. A compression load of 1000 kN was then applied and the PV cell strains are presented in Fig. 10, where the vertical axis (y) represents the distance from the PV cell centre in height (see Fig. 3a) and negative values of y indicate the locations beneath the PV cell centre.
There are different types of PV cells for building integration, for example both a-Si and organic PV cells have been used in BIPV com ponents in existing researches [18]. Comparing to a-Si PV cells, organic PV cells are usually much thinner and have a smaller elastic modulus (e. g. 0.1-mm thick with a modulus of 700–850 MPa in [42]) since plastic materials (e.g. polyethylene terephthalate, PET, with an elastic modulus of 1.7–2.5 GPa) are usually used as their substrates [43–45]. To compare the strain mitigation effect on different types of PV cells, PV cells with elastic moduli ranging from 0.1 to 100 GPa were considered with two PV cell thicknesses (0.1 and 1.0 mm). In this section, a 2.0-mm silicone adhesive with an elastic modulus of 2.1 MPa was used and a 1000-kN compression load was applied. The strains of the GFRP and PV cells were obtained and the resulting strain transfer ratio (RS) are calculated and presented in Fig. 11, with both FE simulation and theoretical results. It can be seen from Fig. 11, the strain transfer ratio (RS) of either PV thickness decreases with the increase of elastic modulus of PV cells. With a 2.0-mm silicone adhesive, RS is 0.08 for the a-Si PV cell while about 1.0 for the organic PV cell (0.1-mm thickness and 0.8-GPa elastic modulus), namely the GFRP strain is completely transferred to the organic PV cell. Thus the approach using such silicone adhesive for strain mitigation may not be effective for such organic PV cells because of their relatively low thickness and elastic modulus. While in terms of the a-Si PV cells with steel substrate, its high elastic modulus helps to mitigate the PV cell strain with low-modulus adhesives in compressive scenarios. In addi tion, the steel substrate can also protect the cells from potential puncture and fold risks during transportation and BIPV fabrication. 4.4. Effects of adhesive thickness and shear modulus on RS To understand the effects of thickness and shear modulus of adhe sives on RS, shear modulus values ranging from 0.1 MPa to 1.0 GPa were investigated in the numerical modelling, with the adhesive thickness of
Fig. 10. FE strain distribution along length of PV cells integrated with GFRP using (a) silicone and (b) epoxy adhesive. 7
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5. Conclusions An approach to mitigate the in-plane compressive strain of PV cells in BIPV applications was developed in this paper. It employs adhesives with low shear modulus to provide a partial composite action between the PV cell and the GFRP substrate when such BIPV integrations are under axial loading. BIPV integrations of GFRP SHS and a-Si PV cells were fabricated using two adhesives, namely a silicone adhesive with a shear modulus of about 0.7 MPa and an epoxy adhesive with a much higher shear modulus of about 1.2 GPa. The GFRP-PV integration specimens were submitted to a compression load up to 800 kN and then unloaded. Modelling based on theoretical methods and FE methods was further conducted to understand the strain transfer behaviour through the adhesive layer and the resulting strain mitigation on the PV cells. The following conclusions can be drawn: Fig. 11. Effects of thickness and elastic modulus of PV cells on strain transfer ratio for integration with GFRP, using a silicone adhesive of 2.0-mm thickness.
1. Debonding and local buckling of the PV cells were found from the GFRP-PV integration specimens bonded by the epoxy adhesive, causing the degradation of open-circuit voltage of the PV cells in such applications. The critical strains for the voltage degradation of the integrated a-Si PV cell in association with local buckling were about 0.23% for those with 2.0-mm epoxy and 0.62% for those with 0.5-mm epoxy. No debonding or local buckling was observed in the a-Si PV cells with a low-modulus silicone adhesive during the loading and unloading processes; therefore, no voltage degradation was witnessed. This is because a low-modulus adhesive provides a partial composite action between the GFRP and PV cell under loading, allowing relative slips and therefore inducing only limited axial compressive strain transferred from the GFRP to PV cell. 2. A strain transfer ratio (RS) can be defined as the ratio between strains of the PV cell and the GFRP. Consistent results from experimental, theoretical and FE methods suggest that RS is determined by the shear modulus and thickness of the adhesive as well as the elastic modulus, thickness and length of the PV cell. As far as a linear stressstrain behaviour was considered for the adhesive layer, RS is not affected by the load level and is about 1.0 for the integration with epoxy of a thickness of 0.5 or 2.0 mm. This ratio becomes 0.29 for those with 0.5-mm silicone or 0.08 for those with 2.0-mm silicone according to the experimental results on the GFRP-PV integration specimens. 3. When the GFRP-PV integration is subjected to axial compression, the PV cell strain increases from top and bottom edges to the centre and the maximum strain is found from the centre of the PV cell. A larger value of the maximum strain can be witnessed for the PV cell with a longer length. Using the proposed strain mitigation approach with a silicone adhesive of 2.0 mm, the strain of the integrated a-Si PV cell with length of 360 mm was received as 0.20%; while with the same PV length and adhesive thickness, such strain transfer ratio becomes 1.0 if using epoxy in the integration. From the theoretical and FE investigations, it was found that the width of the PV cell would not affect the strain distribution along its longitudinal direction. There fore, a practical suggestion may be to keep the longer edge of the PV cells perpendicular to the loading direction so that a smaller strain can be obtained in the centre of the PV cell. 4. Based on the theoretical and FE investigations, it can be seen that RS decreases with the increase of the elastic modulus and thickness of the PV cells. Thus, in comparison to the plastic substrates of relative low modulus used in organic PV cells for example, the steel substrate with a larger elastic modulus in the a-Si PV cells contributes to a much smaller RS, i.e. better strain mitigation effect, as evidenced in the experiments with the silicone adhesive of 0.5- or 2.0-mm thickness. 5. It is also seen from the theoretical and FE analyses that RS increases with the shear modulus of the adhesive but decreases with its thicknesses. As a result, some adhesives with a high shear modulus (e.g. two-part epoxy), because of their high strain transfer ratio, may
0.5 or 2.0 mm. RS was then calculated from the strains of the GFRP and PV cell. The RS results from FE and theoretical methods are presented in Fig. 12. Experimental results are also provided in Fig. 12 as red dots, where the shear modulus is taken as 0.70 MPa for silicone and 1.18 GPa for epoxy adhesive according to the elastic modulus in Table 1 and a Poisson’s Ratio of 0.50 [41]. As presented in Fig. 12, RS increases with the shear modulus of the adhesives and hardly any strain mitigation effect can be provided (i.e. RS becomes over 0.95) by adhesives with shear modulus over 100 MPa although a thickness of 2.0 mm is applied. Thus, some structural adhe sives used in engineering (e.g. two-part epoxy, polyester resin and pol yimides adhesive) may not be applicable for such applications since they usually have high shear moduli [46]. For adhesives with the same shear modulus, a smaller RS is obtained by a thicker adhesive as evidenced in Fig. 12, thus adhesive thickness helps to mitigate the PV cell strain. This also suggests the adhesive thickness as a design parameter in fabrication of the BIPV components to mitigate strains on PV cells. For example, a targeted RS can be determined according to the critical strains of the PV cell and the substrate; and then the adhesive thickness (tA) can be solved by Eq. (15) with given elastic modulus (EPV), thickness (tPV) and length (LPV) of the PV cell and shear modulus of adhesive (GA). In this study, based on the material properties in Table 1 (i.e. EPV ¼ 21.0 GPa and GA ¼ 0.7 MPa) and the dimensions in Fig. 1a (i.e. LPV ¼ 180 mm and tPV ¼ 1.0 mm) and if considering a RS value of 0.26 calculated from the ultimate GFRP strain of 0.87% [14,15] and the maximum PV strain reduced to 0.23% (in reference to Fig. 6a and b), a resulting adhesive thickness of 0.43 mm can be obtained.
Fig. 12. Effects of thickness and shear modulus of adhesives on RS for a-Si PV cells integrated with GFRP. 8
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not be able to offer satisfactory strain mitigation effects on PV cells integrated with GFRP substrates. The developed theoretical forma tion may also be used to estimate the minimum adhesive thickness required to achieve a favourable strain transfer ratio. For example, for given elastic modulus (EPV), thickness (tPV) and length (LPV) of the PV cell and shear modulus of adhesive (GA), a minimum adhesive thickness can be calculated by Eq. (15) to obtain a targeted RS.
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Acknowledgements The authors acknowledge the support from the Australian Research Council through the Discovery project (DP180102208). Thanks are also extended to the staffs in the Civil Engineering Laboratory of Monash University for the assistance in the experimental programme. References [1] Peng C, Huang Y, Wu Z. Building-integrated photovoltaics (BIPV) in architectural design in China. Energy Build 2011;43:3592–8. [2] Lu L, Yang H. Environmental payback time analysis of a roof-mounted buildingintegrated photovoltaic (BIPV) system in Hong Kong. Appl Energy 2010;87: 3625–31. � [3] Aguas H, Ram SK, Araújo A, Gaspar D, Vicente A, Filonovich SA, et al. Silicon thin film solar cells on commercial tiles. Energy Environ Sci 2011;4:4620–32. [4] Cannavale A, H€ orantner M, Eperon GE, Snaith HJ, Fiorito F, Ayr U, et al. Building integration of semitransparent perovskite-based solar cells: energy performance and visual comfort assessment. Appl Energy 2017;194:94–107. [5] Sun L, Lu L, Yang H. Optimum design of shading-type building-integrated photovoltaic claddings with different surface azimuth angles. Appl Energy 2012; 90:233–40. � � � Domjan S, Suklje [6] Medved S, Begelj Z, T, Cerne B, Arkar C. The dynamic thermal response model and energy performance of multi-layer glass and BIPV facade structures. Energy Build 2019;188:239–51. [7] Shukla AK, Sudhakar K, Baredar P. Recent advancement in BIPV product technologies: a review. Energy Build 2017;140:188–95. [8] Chen A, Yossef M, Zhang C. Strain effect on the performance of amorphous silicon and perovskite solar cells. Sol Energy 2018;163:243–50. [9] Li S, Tsang H-H, Cheng Y, Lu Z. Seismic testing and modeling of cylindrical electrical equipment with GFRP composite insulators. Compos Struct 2018;194: 454–67. [10] Satasivam S, Bai Y. Mechanical performance of modular FRP-steel composite beams for building construction. Mater Struct 2016;49(10):4113–29. [11] Ungureanu D, Ț� aranu N, Lup� așteanu V, Isopescu DN, Oprișan G, Mihai P. Experimental and numerical investigation of adhesively bonded single lap and thick adherent joints between pultruded GFRP composite profiles. Compos B Eng 2018;146:49–59. [12] Fava G, Carvelli V, Pisani MA. Remarks on bond of GFRP rebars and concrete. Compos B Eng 2016;93:210–20. [13] Kim B, Lee JY. Resistance of interfacial debonding failure of GFRP bars embedded in concrete reinforced with structural fibers under cycling loads. Compos B Eng 2019;156:201–11. [14] Xie L, Bai Y, Qi Y, Wang H. Pultruded GFRP square hollow columns with bolted sleeve joints under eccentric compression. Compos B Eng 2019;162:274–82. [15] Xie L, Bai Y, Qi Y, Caprani C, Wang H. Effects of width-thickness ratio on capacity of pultruded square hollow polymer columns. Struct Build 2018;171:842–54. [16] Satasivam S, Bai Y, Yang Y, Zhu L, Zhao XL. Mechanical performance of two-way modular FRP sandwich slabs. Compos Struct 2018;184:904–16. [17] Satasivam S, Bai Y, Zhao XL. Adhesively bonded modular GFRP web–flange sandwich for building floor construction. Compos Struct 2014;111:381–92. [18] Fang H, Bai Y, Liu WQ, Qi Y, Wang J. Connections and structural applications of fibre reinforced polymer composites for civil infrastructure in aggressive environments. Composites Part B 2019;164:129–43. [19] Pascual C, De Castro J, Schueler A, Vassilopoulos AP, Keller T. Total light transmittance of glass fiber-reinforced polymer laminates for multifunctional loadbearing structures. J Compos Mater 2014;48(29):3591–604. [20] Pascual C, De Castro J, Kostro A, Schueler A, Vassilopoulos AP, Keller T. Diffuse light transmittance of glass fiber-reinforced polymer laminates for multifunctional load-bearing structures. J Compos Mater 2014;48(29):3621–36.
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Contents lists available at ScienceDirect
Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Stress mitigation for adhesively bonded photovoltaics with fibre reinforced polymer composites in load carrying applications Yiqing Dai a, Yu Bai a, *, Thomas Keller b a b
Department of Civil Engineering, Monash University, Clayton, VIC, 3800, Australia � Composite Construction Laboratory (CCLab), Ecole Polytechnique F�ed�erale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Building integrated photovoltaics (BIPV) Fibre reinforced polymer composites Solar cell Adhesive Bonding Compression Composite action
Structural loads, especially in-plane compression, may cause local buckling and debonding of the photovoltaic (PV) cells that are mechanically integrated with structural members and this may lead to degradation in their electrical performance. This paper proposes an approach to mitigate the strains transferred from structural members to PV cells through the partial composite action provided by low-modulus adhesives. Specimens were fabricated by bonding amorphous silicon (a-Si) PV cells to glass fibre reinforced polymer (GFRP) structural components by an adhesive layer of 0.5- or 2.0-mm thickness. Two types of adhesives were used including a twopart rigid epoxy adhesive and a low-modulus silicone adhesive. These integrations were then submitted to inplane compressive loadings. PV cells bonded by the silicone adhesive showed no damages during loading. While for PV cells bonded by epoxy adhesives, obvious electrical performance degradations were observed, when the strain reached 0.62% or 0.23% for specimens bonded by epoxy with a layer thickness of 0.5 mm or 2.0 mm respectively. Debonding and local-buckling of the PV cells were also witnessed. Theoretical analysis was con ducted to understand the strain mitigation of the adhesive as a result of the induced partial composite action. Results demonstrate that such strain differences between the GFRP and the bonded PV cell are dominated by the shear modulus and thickness of the adhesive layer as well as elastic modulus, thickness and length of the PV cell. The theoretical analysis was validated by finite element (FE) modelling and design suggestions are provided accordingly.
1. Introduction Building integrated photovoltaics (BIPV) are building components with integrated photovoltaic (PV) materials and they are used in parts of building envelops [1], such as roofs [2,3], windows [4], claddings [5] and facades [6]. Apart from functioning as building components, BIPV generate electricity by harvesting solar energy. In comparison to con ventional PV products standing on ground or structures, BIPV does not occupy additional space; and labor and cost can be reduced without mounting of individual PV cells. Quality of adhesive integration can also be assured in factory, since the PV cells are adhesively bonded with building components in factory and then the complete integration is installed onsite [7]. One of the practical methods for integration of such BIPV compo nents is to adhesively bond PV cells to exteriors of building materials and components [8]. Fibre reinforced polymer (FRP) composites are considered as the substrates in such integrations for their superior
strength-weight ratio and corrosion resistance, and some of them (e.g. glass fibre reinforced polymer, GFRP) are electrically insulating [9]. Due to such advantages, various profiles and components (e.g. flat plates [10, 11], rebars [12,13], square hollow sections [14,15] and sandwich structures [16,17]) made of GFRP composites have been implemented for structural applications including support systems for PV cells [18]. Translucent GFRP laminates were also proposed and developed to encapsulate translucent dye PV cells for BIPV applications [19–21]. In terms of the PV cells in BIPV components, different types have been employed in such integrations where mono-crystalline silicon (m-Si) PV cells are most commonly used because of their high PV efficiency [7,22]. However, BIPV components with m-Si PV cells are excluded from ap plications in load-carrying scenarios since m-Si PV cells are brittle and even small strains may cause their cracking, leading to degradation in electrical performance and functional failure [23]. For example, four-point bending experiments on m-Si PV cells samples indicated that they would break at 0.10%–0.15% tensile strains [24].
* Corresponding author. E-mail addresses: [email protected] (Y. Dai), [email protected] (Y. Bai), [email protected] (T. Keller). https://doi.org/10.1016/j.compositesb.2019.107420 Received 17 April 2019; Received in revised form 27 July 2019; Accepted 5 September 2019 Available online 6 September 2019 1359-8368/© 2019 Published by Elsevier Ltd.
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Several types of thin-film flexible PV cells capable of sustaining relatively large strains have shown potentials for such applications, for example amorphous silicon (a-Si) PV cells [25] and organic PV cells [26, 27]. In comparison to m-Si PV cells, they are much thinner and lighter in weight. Among thin-film flexible PV cells, a-Si PV cells are competitive since they are non-toxic and relatively cost effective [28]. The critical strain for initiation of electrical degradation in a-Si PV cells has been investigated in several studies. For example, tensile experiments were conducted on small-scale samples [29,30] and large-scale commercial products [31] of a-Si PV cells and consistent results suggested that the critical tensile strain was about 1.40%. Mechanical experiments on BIPV integrations of a-Si PV cells and FRP composites in tension have also been initiated in recent years. For example, a-Si PV cells were embedded in the wet face sheet resin, below a surface veil, of a GFRP sandwich structure with foam core and it was reported that no obvious change in the open-circuit voltage of the PV cell was observed when the service ability limit load of about 0.7 kN was applied [25]; while an elevated temperature up to 60–80 � C was identified when the structure was submitted to artificial sunlight. Tensile experiments were conducted on the integrations of carbon fibre reinforced polymer (CFRP) laminates and a-Si PV cells bonded by a two-part epoxy and up to 1.0% tensile strain did not affect much its electrical performance [32]. In-plane compressive strain was introduced to a-Si PV cells alone [33] and the critical compressive strain was found to be over 1.7%. Thus, in terms of in-plane compression, it seems possible for a-Si PV cells to work normally below the ultimate strain of GFRP materials (usually around 1% [34]). However, according to compression experiments on integrations of a-Si PV cells and GFRP substrates adhesively bonded by polyimide tapes, obvious decrease in open-circuit voltage was witnessed from 0.5% in-plane compressive strain and this was because of the debonding and local buckling of PV cells [29]. The in-plane compression is therefore a critical loading scenario for such integrations and rela tively small compressive strains may cause debonding or local buckling of the PV cells, resulting in compromise of their electrical performance or loss of their functionality. Thus, for the BIPV components used in compression scenarios, the adhesive layer plays an important role for the bonding and associated load transfer performance, while no much work was done to investigate the composite action and the resulting load transfer mechanism offered by the adhesives in the BIPV systems. Such results are important in the selection of an appropriate adhesive as well as its bonding geometrises (thickness, area, etc.) for better mechanical performance and electrical behaviour of such integrations under compression. In this study, a-Si PV cells and GFRP structural members with square hollow sections (SHS) were bonded by an adhesive of 0.5- or 2.0-mm thickness. Two types of adhesives were used including a rigid two-part epoxy adhesive and a ductile silicone adhesive. Such GFRP and PV in tegrations were then submitted to in-plane compressive loading in the longitudinal direction of GFRP SHS members. The electrical perfor mance of the specimens was continuously monitored during the me chanical loading (up to 80% of the ultimate load of the GFRP SHS) and unloading processes. A theoretical modelling was further developed to understand the strain transfer behaviour of the adhesive layer through the resulting full or partial composite action and to determine the dominant parameters for such load transfer mechanism. A finite element (FE) model was also developed to validate the theoretical results and the parametrical studies, together with the results received from the experiments.
tests were conducted using an Instron 50 kN machine and the load readout was recorded by a data logger (dataTaker DT515) at 1 Hz. Dog bone-shaped coupons with an overall length of 180 mm and a gauge length of 60 mm were prepared for the epoxy and silicone adhesives and reflectors with a spacing of about 40 mm were bonded to the surface of the coupons as shown in Fig. 1a and b. Specimens for the a-Si PV cell were also prepared with a dimension of 250 mm (length) � 25 mm (width) � 1 mm (thickness) and the spacing between the reflectors was about 50 mm as shown in Fig. 1c. An extensometer (MTS LX500) was used to monitor changes in spacing between the reflectors on the surface of the adhesive and PV cell coupon specimens; and the strain results were taken as the spacing change divided by the spacing length. For the adhesives, the tests were conducted with reference to ISO-527 at room temperature (about 22 � C) and the displacement rate was 1 mm/min. Tests for the PV cells were conducted with reference to ASTM D-882-12 [35]. Four steel plates (50 mm � 50 mm � 3 mm) with polished edges were bonded to both ends of the PV cells to protect the specimens and connecting wires. Open circuit voltage (VOC) of the PV cell coupon specimens were measured and recorded by the data logger. Two coupon specimens for each material were prepared and the adhesive coupons were cured for four weeks at room temperature before testing. The stress-strain results are shown in Fig. 2 for a-Si PV cells and the two types of adhesives. The epoxy specimens exhibit an approximate linear strain-stress behaviour up to the ultimate failure at 1.05% tensile strain and the elastic modulus can be determined accordingly. The sil icone adhesive specimens could be loaded up to large strain values over 100% while the elastic modulus would be then underestimated at large strains due to a reduction in the cross section. Thus, elastic modulus of the silicone adhesive was calculated based on its strain-stress behaviour within 2.0% strain (see Fig. 2). The a-Si PV cell exhibits a linear elastic behaviour until its yielding at about 0.21% tensile strain; and a strain hardening behaviour start from about 1.02% strain as shown in Fig. 2, since it comprises a steel substrate of around 0.07-mm thickness. Breakage of the a-Si PV cell happens at over 3.80% tensile strain. The resulting elastic modulus and strain characteristics on average of the repeating specimens are summarized in Table 1 and the results for the same GFRP SHS tested in [14] are also presented. It should be noted that, in the tensile tests for PV cells, no obvious change in VOC was observed until 1.4% tensile strain was reached. This result agrees with previous studies [29,30] and more detailed discussions of the voltage response to the tensile strain can be found from [29]. It also confirms the feasibility of a-Si PV cells for integration with GFRP composites in
2. Experimental investigations 2.1. Material properties The stress-strain behaviour and elastic modulus of the adhesives and the PV cells were determined individually by tensile coupon tests considering their similar properties in compression. As shown Fig. 1, the
Fig. 1. Experimental setup for material properties of (a) epoxy adhesive, (b) silicone adhesive, and (c) a-Si PV cells. 2
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thickness of 9.5 mm. The adhesive thickness was 0.5 or 2.0 mm for two types of adhesives, namely a two-part epoxy or a silicone adhesive. First, the potential GFRP interfaces for adhesive bonding were subjected to mechanical abrasion and cleaned. Second, for the specimens with the two-part epoxy, an epoxy resin (BPR 135G) and a curing agent from Epikote™ were mixed thoroughly and used as a bonding agent with a thickness of 0.5 or 2.0 mm. For the specimens with silicone, the Pattex® all-purpose silicone of 0.5- or 2.0-mm thickness was used, again after surface abrasion and cleaning. Two repeating specimens for each configuration and therefore a total of eight specimens were prepared. All the specimens were cured at room temperature for four weeks. The setup for compression experiments on the GFRP-PV integration is shown in Fig. 3b. A halogen lamp of 200 W was used to provide artificial sunlight to the PV cells considering it has similar spectrum with sunlight. A slight decrease of the open-circuit voltage (VOC) of the PV cells in association with the increase of their temperature (5–8 � C) was witnessed. After the VOC became stable, the compression load was applied at 0.5 mm/min using an Amsler 5000 kN testing machine. The specimens were loaded up to 800 kN (approximately 80% ultimate load of the GFRP section according to previous experimental results from the same GFRP SHS in compression [14,15]) and then unloaded gradually. Two strain gauges were installed on the centre of two adjacent surfaces of the GFRP SHS. No strain gauges were used on the PV cells since it is difficult to install the strain gauges on the textured polymer surface and the protective polymer may not fully transfer the PV cell strain to strain gauges. Instead, a laser extensometer (MTS LX500) was used to measure the change in distance between the two reflectors on the surface of PV cells. The compression load, distance change between the reflectors, strains of the GFRP SHS and VOC of the PV cells were recorded by a data logger (dataTaker DT515) at 1 Hz.
Fig. 2. Stress-strain relationships for PV cells, silicone adhesives and epoxy adhesives. Table 1 Mechanical properties of adhesives, PV cells and GFRP. Yielding strain Elastic modulus Ultimate strain
Silicone
Epoxy
PV cell
GFRP [14]
– 2.12 MPa >100.00%
– 3.54 GPa 1.05%
0.21% 20.98 GPa >3.80%
– 31.60 GPa 0.89%
tension as the latter usually have an ultimate tensile strain of around 1% [34]. Considering that elevated temperatures up to 60–80 � C may be reached for PV cells in BIPV applications [25], the glass transition temperature (Tg) for the epoxy used in this study is 81 � C according to the manufacturer and the temperature of working condition for the silicone ranges from 15 to þ200 � C.
2.3. Experimental results The stress-strain behaviour of the GFRP-PV specimens in the loading (left side) and unloading (right side) processes is shown in Fig. 4a and the specimens exhibit a linear stress-strain behaviour in both loading and unloading processes. The highly symmetric stress-strain curves in the loading and unloading processes indicates the deformation can be fully recovered. A maximum load of 800 kN was applied and thus the maximum axial stress is around 220 MPa. The maximum strain wit nessed ranges from 0.64% to 0.69% and the corresponding compressive
2.2. Specimens and experimental setup As shown in Fig. 3a, specimens were prepared using a-Si PV cells and GFRP SHS members. The a-Si PV cells with a dimension of 180 mm (height) � 60 mm (width) � 1.0 mm (depth) were bonded to the GFRP members with a section of 300 mm � 102 mm � 102 mm and a wall
Fig. 3. (a) Specimen configuration (side view) and (b) experimental setup for integration of a-Si PV cells and GFRP SHS components in compression. 3
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Fig. 4. Strain responses in loading and unloading processes of (a) GFRP and (b) PV cells of BIPV integration.
elastic modulus is around 32 GPa on average, which is in consistence with existing research [14–17]. Fig. 4b shows the correlation of the GFRP strain and PV cell strain during the loading and unloading processes. Due to the linear corre spondence between the compressive load and GFRP strain evidenced in Fig. 4a, the GFRP strain from Fig. 4b also represents the load level. It can be seen from Fig. 4b that strains in PV cells with epoxy adhesives are almost identical to those measured from GFRP; while the strains in PV cell with 0.5 mm or 2.0 mm thickness of the silicone layer are signifi cantly lower, with the maximum values of only 0.20% and 0.05% respectively. A strain transfer ratio (RS) can be defined as the ratio be tween the compressive strains in the PV cell and the GFRP strains at certain load level. Accordingly, at the maximum load (about 800 kN) in the experiments, RS for the epoxy adhesive with either thickness is around 1.0 (0.95–0.97); RS for the silicone adhesives of 0.5 mm is 0.29 and for the 2.0-mm ones is only 0.08. In this way, it can be demonstrated that RS or the PV cell strain can be effectively reduced using a silicone adhesive and RS is almost constant during the loading and unloading processes due to an approximate linear relation between the strains of PV cells and GFRP. When the applied compressive load was approaching 250 kN, local buckling of the PV cells was noticed from the GFRP-PV integrated specimen with 2.0-mm epoxy adhesive as indicated in Fig. 5a. Such local buckling was also associated with the debonding of the PV cell from the epoxy adhesive. For the specimens with 0.5-mm epoxy adhesive, local buckling of smaller scales was witnessed in only one or two spots from each specimen as presented in Fig. 5b. This may be associated with bonding imperfection in thicker epoxy layers since the voids and bubbles could hardly be completely eliminated in especially a thick adhesive layer due to high viscosity of epoxy in specimen fabrication. The PV cells
with silicone adhesives did not show visual buckling in the experiments, since only limited strains were transferred to the PV cells as the silicone adhesive was associated with small RS values. In terms of open-circuit voltage of the PV cells in the specimens with 0.5- or 2.0-mm silicone adhesive, hardly any change can be found as evidenced in Fig. 6a. However, obvious voltage degradation was wit nessed from the specimens with epoxy adhesives as shown in Fig. 6b. The voltage results in Fig. 6b are numbered, for example 0.5mm-1 represents the results from the first specimen with 0.5-mm thick epoxy adhesive. The critical strains for obvious voltage degradation are also presented in Fig. 6b, and for PV cells with 2.0-mm epoxy adhesive, voltages decrease severely from 0.20% to 0.25% GFRP strain and only about 20% voltage remains at the maximum GFRP strain of 0.68%. Limited voltage (less than 40%) recovered during the unloading process. For the PV cell integrated specimens with 0.5-mm epoxy adhesive, no degradation in voltage was noticed when the GFRP strain was below about 0.6% strain; after that, 83% or 50% voltage remained at the maximum GFRP strain for the two repeating specimens. During the unloading process, around 90% voltage was recovered. In a previous study [33], the electrical performance of a-Si PV cells was not affected by even 1.70% in-plane compressive strain; while the PV cells started degradation when only 0.22% strain was applied for the integration using 2.0-mm epoxy, or 0.61% applied for those with 0.5-mm epoxy in this study. This highlights that the voltage degradation in such PV cells should be associated with their local buckling induced by the compressive strains at the locations likely with bonding imper fections (see Fig. 5a and b). The silicone adhesives were evidenced to be capable of providing a strain mitigation effect (in addition to serving as lateral supports) for the integrated PV cells, thus this may provide an approach to ensure the PV cells under a low strain range in BIPV com ponents during service. 3. Modelling 3.1. Theoretical formulation Full composite action provided by the adhesive layer in the GFRP-PV integration results in identical axial strain in the PV cell and GFRP, i.e. the strain due to axial loading is fully transferred from the GFRP to PV cell through the adhesive layer. According to the results of the compression experiments as shown in Fig. 4b, full composite action was witnessed for the integrations with epoxy adhesive in this study. While partial composite action allows relative slips between the GFRP and PV cell and only a part of the GFRP strain can be transferred to the PV cell through the adhesive layer. A smaller strain was witnessed in the PV cells than GFRP from the compression experiments as shown in Fig. 4b, due to the partial composite action provided by the silicone adhesive layer. The full or partial composite action is therefore associated with the mechanical properties (shear modulus in particular) and dimensions
Fig. 5. Local buckling of a-Si PV cells in compressive specimens with (a) 2.0mm epoxy adhesive and (b) 0.5-mm epoxy adhesive. 4
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Fig. 6. Voltage responses of a-Si PV cells in relation of compressive strain of GFRP SHS for integration using (a) silicone and (b) epoxy adhesive.
of the adhesive layer. A theoretical model with consideration of a range of major design parameters such as the shear modulus (GA) and thick ness (tA) of the adhesive layer is accordingly developed to understand the full or partial strain transfer behaviour through the adhesive layer in such BIPV integrations [36–39]. Fig. 7 shows a typical differential element in this study, where ‘y’ is the vertical distance to the centre of the PV cell (also see Fig. 3a); ‘x’ is the distance in thickness direction from the outer surface of the adhe sive; ‘LPV’ is the length of the PV cell; ‘tPV’ and ‘tA’ are thicknesses of the PV cell and adhesive respectively; ‘σ’, ‘τ’, ‘u’ and ‘ε’ are axial stress, shear stress, displacement and strain of the differential elements; ‘E’ is the elastic modulus and ‘G’ is the shear modulus; subscripts ‘G’, ‘A’ and ‘PV’ denote the layer of GFRP, adhesive and PV cell respectively. Due to the uniformly-distributed axial stress and strain on GFRP along the width direction (i.e. z direction shown in Fig. 3a) and the symmetrical loading and structural form in this regard, the variations of the stress and strain along the width direction (z direction) are minor and therefore neglected. The strain variation of PV cells in the thickness direction (x direction shown in Fig. 3a) is not considered because of their thin thicknesses and unconstrained outer surface. However, the strains along the axial direction (y direction shown in Fig. 3a) for the adhesive layer and PV cells caused by the axially applied load are not uniformly distributed, therefore such axial variations in stress and strain should be considered in the formulation. Also, the possible differences of strains between the GFRP and PV cell due to the partial composite action are taken into account through the strain transfer behaviour in the formu lation. As a result, based on the stress equilibrium in the longitudinal direction of the PV element shown in Fig. 7, Eq. (1) is obtained as below,
(1)
τPV ðyÞdy ¼ tPV dσPV ðyÞ
Where τPV(y) is the shear stress in the interface between the adhesive and PV cell, tPV represents the PV cell thickness, and σPV(y) is the axial stress of the PV cell. Similarly, τA(x,y), as the shear stress of the adhesive at a distance of x in the thickness direction from the outer surface of the adhesive layer, can be obtained as follows,
τA ðx; yÞ ¼ τPV ðyÞ þ x
dσ A ðx; yÞ ; ð0 � x � tA Þ dy
(2)
Where σA(x,y) is axial stress of the adhesive layer. Combining Eqs. (1) and (2), it gives
τA ðx; yÞ ¼
tPV dσ PV ðyÞ dσ A ðx; yÞ þx ; ð0 � x � tA Þ dy dy
(3)
Considering the stress-strain relationship of the adhesive and the PV cell, it gives � � t dε ðyÞ E dε ðx; yÞ (4) ; ð0 � x � tA Þ τA ðx; yÞ ¼ EPV PV PV þ x A A dy dy EPV Where εPV(y) and εA(x,y) are axial strain of the PV cell and adhesive respectively, and EA and EPV are their elastic modulus. Since the PV cell has a much higher elastic modulus than the adhesive according to Table 1, it gives EA �0 EPV
(5)
Therefore,
τA ðx; yÞ ¼ EPV tPV
dεPV ðyÞ dy
(6)
According to Eq. (6), shear stress of the adhesive layer, τA(x,y), may be independent of x along the thickness direction (i.e. the distance from the outer surface of the adhesive), considering the elastic modulus of the adhesive much lower than the PV cell. Therefore, the shear stress vari ation in the thickness direction (x direction) of the adhesive can be neglected and τA(x,y) becomes τA(y) only. Considering the relative displacement between the GFRP and PV cell in y direction (see Fig. 7), Eq. (7) can be obtained as uG ðyÞ
uPV ðyÞ ¼
τA ðyÞ GA
tA
(7)
where uG(y) or uPV(y) is the vertical displacement of GFRP or PV cell at the location with a vertical distance of y from the PV cell centre. Taking derivatives of y on both sides and substitution of Eq. (6) into Eq. (7) gives
Fig. 7. Illustration of strain transfer from GFRP to PV cell in a typical differ ential element where dy is a differential length, τPV is the shear stress between the adhesive and PV cell. 5
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εG
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εPV ðyÞ ¼
1 dτA ðyÞ 1 d2 εPV ðyÞ ¼ EPV tPV tA tA GA dy GA dy2
(8)
The Eq. (8) can be simplified as below, 2
d εPV ðyÞ þ k2 εPV ðyÞ ¼ k2 εG dy2
(9)
where k2 ¼
GA EPV tPV tA
(10)
The general solution for Eq. (9) as a second order differential equa tion of εPV in regard to y can be expressed as
εPV ðyÞ ¼
α sin hðkyÞ
(11)
β cos hðkyÞ þ εG
Considering the boundary conditions that the PV cell is free from axial stress at both ends, Eq. (12) can be formed as below, � � � � 1 1 (12) LPV ¼ 0 εPV y ¼ LPV ¼ εPV y ¼ 2 2 Thus,
α ¼ 0; β ¼
ε
2
3
6
cos hðkyÞ 7 � �7 5 cos h 12 kLPV
εPV ¼ εG 6 41
Fig. 8. FE modelling: loading, boundary conditions and meshing.
(13)
�G � cos h 12 kLPV
The adhesives used in this study were modelled as an elastic layer with the thickness ranging from 0.5 to 2.0 mm and elastic modulus ranging from 0.1 to 1000 MPa. Poisson’s Ratio was 0.50 for the adhe sives [41] and 0.20 for the PV cells. The ‘tie’ constrains and ‘rough’ frictional contact were used for the interfaces of the adhesive layer with the GFRP and the PV cell, i.e. considering no slips at the interfaces. As shown in Fig. 8, the FE models were meshed using C3D8 elements (8-node linear bricks) for the GFRP, adhesive and PV cell, resulting in 1 mm for one element of the PV cell or 5 mm for one GFRP element; the element sizes for the adhesive layer depended on its thickness and two element layers were considered in the meshing of adhesive through thickness. The uniformly distributed load up to 1000 kN (the ultimate load for the GFRP SHS according to [14–17]) was incrementally applied in compression on top of the GFRP SHS components. The specimens were supported on a rigid base plate with all displacements and rota tions constrained at the bottom of the base as shown in Fig. 8. The loading process was then solved using Krylov methods in ABAQUS.
(14)
Accordingly, the maximum strain in the PV cell happens at the centre of the PV cells (see Fig. 3a, namely y ¼ 0). Then the strain transfer ratio (RS) between the PV cell and GFRP at this location is given below, RS ¼
εPV ðy ¼ 0Þ ¼1 εG
1 � �¼1 cos h 12 kLPV
1 � qffiffiffiffiffiffiffiffiffiffiffiffi � 1 A cos h 2LPV EPVGtPV tA
(15)
As indicated in Eq. (15), RS or the strain transferred from the GFRP SHS to the PV cell is dominated by five factors, namely the shear modulus of adhesive (GA), adhesive thickness (tA) as well as the elastic modulus (EPV), thickness (tPV) and length (LPV) of the PV cell.
4. Results and discussion
3.2. FE modelling approach
4.1. Strain transfer ratio, RS
FE modelling based on ABAQUS was established to compare with experimental results for further parametric study and also to validate the theoretical formulation. A typical FE model with loading, boundary conditions and meshing methods are presented in Fig. 8. Dimensions of the FE model were defined according to the specimens in the experi ments (see Fig. 3a). Only for the parametric analysis on the influence of PV length, the GFRP component is modified to have a length of 500 mm to accommodate longer PV cells. The GFRP material was defined as linearly elastic and transversely isotropic, with the elastic modulus of 32 GPa in the longitudinal direction and 5 GPa in the transverse di rections. The interlaminar and in-plane shear moduli of the GFRP ma terial are 12 GPa and 3.5 GPa according to the experiments in [14–17]. The stress and strain constitutive relationship was defined in two stages for PV cells. The first one is described as linearly elastic with the elastic modulus of 21 GPa; and in the second stage, a yielding behaviour was considered with the modulus reduced to 0.4 GPa (2% of the modulus before yielding as suggested in [40]) after the linear stress-strain rela tion reaches 0.21% compressive strain according to the material testing of the PV cells (see Table 1). Strain hardening was not considered for the PV cells since this behaviour only happened for strain values over 1.0% while the GFRP strains in the experimental study were within 0.70%.
The correlations between strains of the GFRP and the PV cell of the GFRP-PV integration during the loading process are plotted in Fig. 9 based on the experimental results, theoretical formulation and FE modelling. A linear relationship between the strains of the GFRP and PV cells can be identified from those obtained by Eq. (15) and the FE modelling, where different loading levels ranging from 200 to 800 kN were applied and the strain transfer ratio (RS) can be obtained accord ingly. Such linear relationship is also supported by experimental results during the loading process for the GFRP-PV specimens with silicone and epoxy adhesives. The predicted PV cell strains from FE and theoretical methods are consistent with the experimental results especially at large load levels. Some differences within the prediction and experimental results are witnessed in Fig. 9 for especially the integrations with epoxy adhesives in small loading levels, possibly because the epoxy adhesive is not an idealized linear-elastic material as shown in Fig. 2. From Fig. 9, the aforementioned strain transfer ratio (RS) was calculated based on the consistent results from theoretical and FE modelling. For the scenario with a 2.0-mm adhesive thickness, this ratio is 0.08 for silicone and is 1.0 for epoxy; for an adhesive thickness of 0.5 mm, this ratio is 0.23 for silicone and is 1.0 for epoxy. These RS 6
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For the scenarios with silicone adhesives, as presented in Fig. 10a, the PV cell strains increase from the top or bottom end to its centre symmetrically and the maximum strain is witnessed in the centre. Such results agree with the theoretical results in Eq. (14). According to Fig. 10a, the maximum PV strain is about 0.5% for the PV cell with a length of 360 mm and an adhesive thickness of 0.5 mm; thus, even though a silicone adhesive has been applied, a relative high strain may still be received in a long PV cell. While the maximum PV cell strain can be reduced to 0.20% if the adhesive thickness is increased to 2.0 mm. For configurations with shorter PV length (180 mm) as shown in Fig. 10a, the PV strain values are smaller than 0.20% for both adhesive thick nesses (0.5 mm or 2 mm). It should be noted that these strain results are associated with a compression load of 1000 kN, corresponding to the ultimate compressive capacity of the GFRP SHS sections in use [14,15]. For the modelling results with 2.0-mm epoxy adhesives, as presented in Fig. 10b, the strain in the PV cell with a length of 360 mm increases sharply within about 10 mm from the top and bottom edges towards the centre of the PV cell. This strain value remains constant and consistent with the GFRP strain (0.87%) at the applied load of 1000 kN in most part (over 85%) of the cell. Thus, hardly any strain mitigation can be pro vided by epoxy adhesives and this rapid increase of strain of the PV cells to that of the GFRP is valid also for the PV cells of other lengths. In addition, according to the FE simulation and theoretical analysis, RS would not be affected by the width of the PV cell, thus a possible and practical solution may be to keep the longer edge of the PV cells perpendicular to the loading direction, therefore a shorter PV length is subjected to loading direction (resulting in less strain at the PV centre). It should be noted that the substrate of the a-Si PV cells in use is steel and it may yield after its strain reaches 0.21% (see Table 1). This may reduce its elastic modulus considerably and therefore the PV cell may easily buckle after the yielding of its substrate.
Fig. 9. Strain relationships between GFRP and PV cell integrated using silicone or epoxy with an adhesive thickness of 0.5 or 2.0 mm from experiments, FE simulation and theoretical methods.
values did not change with the load levels as the adhesive layer was modelled as linear elastic. Based on the validated theoretical and FE analysis, the effects of the material and geometric properties of the adhesives and PV cells (i.e. shear modulus and thickness of the adhesive as well as elastic modulus, thickness and length of the PV cell) can be further investigated to un derstand the strain transfer behaviour and provide suggestions for such applications. 4.2. Effects of PV cell length on RS
4.3. Effects of thickness and elastic modulus of PV cell on RS
In terms of the a-Si PV cells used in this research, several different dimensions are available in the market according to the manufactures, with the length ranges from 90 to 360 mm. Since the strain transfer ratio (RS) increases with the length of PV cells (LPV) according to Eq. (15), several PV lengths up to 360 mm were used in simulation to investigate the effect of PV length on the strain transfer behaviour. In the analysis, the GFPR SHS had a height of 500 mm to accommodate a maximum PV length of 360 mm and the adhesive thickness was 0.5 or 2.0 mm. A compression load of 1000 kN was then applied and the PV cell strains are presented in Fig. 10, where the vertical axis (y) represents the distance from the PV cell centre in height (see Fig. 3a) and negative values of y indicate the locations beneath the PV cell centre.
There are different types of PV cells for building integration, for example both a-Si and organic PV cells have been used in BIPV com ponents in existing researches [18]. Comparing to a-Si PV cells, organic PV cells are usually much thinner and have a smaller elastic modulus (e. g. 0.1-mm thick with a modulus of 700–850 MPa in [42]) since plastic materials (e.g. polyethylene terephthalate, PET, with an elastic modulus of 1.7–2.5 GPa) are usually used as their substrates [43–45]. To compare the strain mitigation effect on different types of PV cells, PV cells with elastic moduli ranging from 0.1 to 100 GPa were considered with two PV cell thicknesses (0.1 and 1.0 mm). In this section, a 2.0-mm silicone adhesive with an elastic modulus of 2.1 MPa was used and a 1000-kN compression load was applied. The strains of the GFRP and PV cells were obtained and the resulting strain transfer ratio (RS) are calculated and presented in Fig. 11, with both FE simulation and theoretical results. It can be seen from Fig. 11, the strain transfer ratio (RS) of either PV thickness decreases with the increase of elastic modulus of PV cells. With a 2.0-mm silicone adhesive, RS is 0.08 for the a-Si PV cell while about 1.0 for the organic PV cell (0.1-mm thickness and 0.8-GPa elastic modulus), namely the GFRP strain is completely transferred to the organic PV cell. Thus the approach using such silicone adhesive for strain mitigation may not be effective for such organic PV cells because of their relatively low thickness and elastic modulus. While in terms of the a-Si PV cells with steel substrate, its high elastic modulus helps to mitigate the PV cell strain with low-modulus adhesives in compressive scenarios. In addi tion, the steel substrate can also protect the cells from potential puncture and fold risks during transportation and BIPV fabrication. 4.4. Effects of adhesive thickness and shear modulus on RS To understand the effects of thickness and shear modulus of adhe sives on RS, shear modulus values ranging from 0.1 MPa to 1.0 GPa were investigated in the numerical modelling, with the adhesive thickness of
Fig. 10. FE strain distribution along length of PV cells integrated with GFRP using (a) silicone and (b) epoxy adhesive. 7
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5. Conclusions An approach to mitigate the in-plane compressive strain of PV cells in BIPV applications was developed in this paper. It employs adhesives with low shear modulus to provide a partial composite action between the PV cell and the GFRP substrate when such BIPV integrations are under axial loading. BIPV integrations of GFRP SHS and a-Si PV cells were fabricated using two adhesives, namely a silicone adhesive with a shear modulus of about 0.7 MPa and an epoxy adhesive with a much higher shear modulus of about 1.2 GPa. The GFRP-PV integration specimens were submitted to a compression load up to 800 kN and then unloaded. Modelling based on theoretical methods and FE methods was further conducted to understand the strain transfer behaviour through the adhesive layer and the resulting strain mitigation on the PV cells. The following conclusions can be drawn: Fig. 11. Effects of thickness and elastic modulus of PV cells on strain transfer ratio for integration with GFRP, using a silicone adhesive of 2.0-mm thickness.
1. Debonding and local buckling of the PV cells were found from the GFRP-PV integration specimens bonded by the epoxy adhesive, causing the degradation of open-circuit voltage of the PV cells in such applications. The critical strains for the voltage degradation of the integrated a-Si PV cell in association with local buckling were about 0.23% for those with 2.0-mm epoxy and 0.62% for those with 0.5-mm epoxy. No debonding or local buckling was observed in the a-Si PV cells with a low-modulus silicone adhesive during the loading and unloading processes; therefore, no voltage degradation was witnessed. This is because a low-modulus adhesive provides a partial composite action between the GFRP and PV cell under loading, allowing relative slips and therefore inducing only limited axial compressive strain transferred from the GFRP to PV cell. 2. A strain transfer ratio (RS) can be defined as the ratio between strains of the PV cell and the GFRP. Consistent results from experimental, theoretical and FE methods suggest that RS is determined by the shear modulus and thickness of the adhesive as well as the elastic modulus, thickness and length of the PV cell. As far as a linear stressstrain behaviour was considered for the adhesive layer, RS is not affected by the load level and is about 1.0 for the integration with epoxy of a thickness of 0.5 or 2.0 mm. This ratio becomes 0.29 for those with 0.5-mm silicone or 0.08 for those with 2.0-mm silicone according to the experimental results on the GFRP-PV integration specimens. 3. When the GFRP-PV integration is subjected to axial compression, the PV cell strain increases from top and bottom edges to the centre and the maximum strain is found from the centre of the PV cell. A larger value of the maximum strain can be witnessed for the PV cell with a longer length. Using the proposed strain mitigation approach with a silicone adhesive of 2.0 mm, the strain of the integrated a-Si PV cell with length of 360 mm was received as 0.20%; while with the same PV length and adhesive thickness, such strain transfer ratio becomes 1.0 if using epoxy in the integration. From the theoretical and FE investigations, it was found that the width of the PV cell would not affect the strain distribution along its longitudinal direction. There fore, a practical suggestion may be to keep the longer edge of the PV cells perpendicular to the loading direction so that a smaller strain can be obtained in the centre of the PV cell. 4. Based on the theoretical and FE investigations, it can be seen that RS decreases with the increase of the elastic modulus and thickness of the PV cells. Thus, in comparison to the plastic substrates of relative low modulus used in organic PV cells for example, the steel substrate with a larger elastic modulus in the a-Si PV cells contributes to a much smaller RS, i.e. better strain mitigation effect, as evidenced in the experiments with the silicone adhesive of 0.5- or 2.0-mm thickness. 5. It is also seen from the theoretical and FE analyses that RS increases with the shear modulus of the adhesive but decreases with its thicknesses. As a result, some adhesives with a high shear modulus (e.g. two-part epoxy), because of their high strain transfer ratio, may
0.5 or 2.0 mm. RS was then calculated from the strains of the GFRP and PV cell. The RS results from FE and theoretical methods are presented in Fig. 12. Experimental results are also provided in Fig. 12 as red dots, where the shear modulus is taken as 0.70 MPa for silicone and 1.18 GPa for epoxy adhesive according to the elastic modulus in Table 1 and a Poisson’s Ratio of 0.50 [41]. As presented in Fig. 12, RS increases with the shear modulus of the adhesives and hardly any strain mitigation effect can be provided (i.e. RS becomes over 0.95) by adhesives with shear modulus over 100 MPa although a thickness of 2.0 mm is applied. Thus, some structural adhe sives used in engineering (e.g. two-part epoxy, polyester resin and pol yimides adhesive) may not be applicable for such applications since they usually have high shear moduli [46]. For adhesives with the same shear modulus, a smaller RS is obtained by a thicker adhesive as evidenced in Fig. 12, thus adhesive thickness helps to mitigate the PV cell strain. This also suggests the adhesive thickness as a design parameter in fabrication of the BIPV components to mitigate strains on PV cells. For example, a targeted RS can be determined according to the critical strains of the PV cell and the substrate; and then the adhesive thickness (tA) can be solved by Eq. (15) with given elastic modulus (EPV), thickness (tPV) and length (LPV) of the PV cell and shear modulus of adhesive (GA). In this study, based on the material properties in Table 1 (i.e. EPV ¼ 21.0 GPa and GA ¼ 0.7 MPa) and the dimensions in Fig. 1a (i.e. LPV ¼ 180 mm and tPV ¼ 1.0 mm) and if considering a RS value of 0.26 calculated from the ultimate GFRP strain of 0.87% [14,15] and the maximum PV strain reduced to 0.23% (in reference to Fig. 6a and b), a resulting adhesive thickness of 0.43 mm can be obtained.
Fig. 12. Effects of thickness and shear modulus of adhesives on RS for a-Si PV cells integrated with GFRP. 8
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not be able to offer satisfactory strain mitigation effects on PV cells integrated with GFRP substrates. The developed theoretical forma tion may also be used to estimate the minimum adhesive thickness required to achieve a favourable strain transfer ratio. For example, for given elastic modulus (EPV), thickness (tPV) and length (LPV) of the PV cell and shear modulus of adhesive (GA), a minimum adhesive thickness can be calculated by Eq. (15) to obtain a targeted RS.
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