5.1. Ply Stacking Transverse of the Supporting Direction
In this section, we investigate the impact of the tiling in the transverse direction as present in the top and bottom flange of a web–core sandwich bridge deck panel. As noted in
Section 4.1, the majority of the 0° plies align with the global X-direction of the bridge deck. However, in the tensile tests performed in this section the local x-direction of the laminates aligns with the applied tensile force, as indicated in
Figure 13 and
Figure 14, which in this case lines up with the global Y-direction of the bridge deck perpendicular to the span direction. According to the findings of
Section 4.1, the fiber reinforcement is therefore mainly present in the local y-direction of the specimen. To maintain a limited amount of stiffness and strength of the specimens during the tensile testing, an additional 90°-ply (i.e., according to the global bridge deck coordinate system) is added to the laminate, as depicted in
Figure 13. In the following, the ply directions of the laminate configurations are given relative to the global bridge direction n. It should be noted that the stacking direction of the TL lines up with the longitudinal tensile direction of the specimens, requiring a 90° rotation of the laminate lay-up, as shown in
Figure 14.
The specimens are composed of multiple plies of E-glass fiber unidirectional (UD) material infused with polyester resin (specifically, Disititron 3501 LS1). This polyester resin undergoes solidification through cross-linking chains, facilitated by a catalyst, methyl ethyl ketone peroxide (MEKP). During the production process, a 2% MEKP solution, in conjunction with polyester resin, is employed to infuse the GFRP TL plates. The laminate configuration is composed of symmetrically positioned ply stacks, consisting of one quadriaxial ply with a [0/45/90/−45] arrangement and a total fabric weight of 600 g/m2, along with one UD ply with a fabric weight of 400 g/m2. This results in a laminate lay-up unit stack with a [0/45/90/−45/0] configuration. Three types of specimens are fabricated using the VARI technique: a PP reference specimen and two TL specimens with stacking angles of 2° and 4°.
The PP reference specimens consist of a total of four ply stacks, resulting in a laminate of 20 plies and a theoretical thickness of 4 mm. For constructing the TL with theoretical stacking angles of 2° and 4°, edge strips are employed at both ends in the longitudinal direction of the specimen, as depicted graphically in
Figure 15. These edge strips enable the creation of a specific thickness and length that determines the stacking angle of the laminate along the length of the TL specimen. During the cutting process of the specimen, the edge strip is first removed by making a transverse cut parallel to the local y-direction of the laminate, as indicated by scissor markings in
Figure 15. This results in a tiled stacking of the plies throughout the full length of the TL specimens, in contrast to the TL specimens in
Section 5.2. Subsequently, the TL specimens are cut parallel to the local x-direction of the laminate, as illustrated in
Figure 13 and
Figure 14, along the grey dotted lines marked with scissor symbols.
The overlap length between consecutive plies in the TL varies based on the laminate lay-up (i.e., the thickness of individual plies) and the chosen stacking angle, which in turn depends on the height of the edge strip. Additionally, the length of each ply in the TL depends on its position within the laminate, the desired length of the laminate, and the dimensions of the mold. As a result, each ply has a distinct length, making the construction of this type of TL complex. Depending on the stacking angle, different laminate thicknesses are achieved. Angled plies are positioned and added on top of the edge strip until four full ply stacks are obtained, totaling 20 individual plies. Subsequently, successive elongating plies are added in the x-direction over a predefined interval, which depends on the thickness of individual plies. Plies continue to be added until the desired length of the TL is reached, constrained by the mold’s dimensions. Once this length is achieved, the process is repeated in reverse order with a gradual reduction in the length of the individual plies. This construction method results in a layered structure of the laminate with a gradual emergence and disappearance of individual plies. Although this process leads to more ply ends on the top and bottom surfaces of the laminate, it reduces stress concentrations and creates a more uniform strain distribution across the sample, as will later be demonstrated by the findings of
Section 5.2.
Based on the dry weight of the fibers and the weight of the produced composite plate, the Fiber Volume Fraction (FVF) of the specimens is estimated. The FVF is found to fluctuate around 40% for both the PP and TL specimens. After cutting, the average cross-sectional area of the specimens is determined based on three measurements of width and thickness distributed along the longitudinal direction of the specimens.
Using the force data measured by the tensile machine and the displacements recorded by DIC across the entire field of the specimens, the stress–strain curves for the tensile tests conducted on the PP reference and TL specimens are established. The results are displayed in
Figure 16.
For all specimen types,
Figure 16 shows the presence of a knee point, distinguishing the initial linear elastic region from the region of transition stiffness. This knee point arises due to the matrix failure of the 0° plies (i.e., the 90°-plies in the global laminate directions are now aligned with the direction of tensile testing) within the laminate at an elongation of approximately 0.20%, resulting in a reduced stiffness. The initial stiffness is determined between 0.05% and 0.15%, while the transition stiffness after the knee point is determined between 0.40% and 0.60%. In addition to the stiffness, the first-ply-failure (FPF) and last-ply-failure (LPF) tensile strength and elongation are determined. The FPF strain is defined as the x-coordinate of the intersection of the linear trend lines representing initial and transition stiffness. The FPF stress is determined as the point where the curve intersects a vertical line drawn from the FPF strain on the x-axis.
Table 2 provides an overview of the mechanical properties of the PP reference and TL specimens.
Table 2 reveals that the tensile strength of a PP laminate is significantly larger than that of TLs. Additionally, increasing the stacking angle further reduces the LPF strength of the laminate. The tensile strength of TLs with stacking angles of 2° and 4° is 43% and 60% lower, respectively, compared to the PP reference laminate. Furthermore, the tensile strain at ultimate failure decreases by 56% and 66% for TLs with stacking angles of 2° and 4°, respectively. However, the initial stiffness remains nearly constant for different specimen types, at approximately 14.2 GPa.
The typical failure behavior of the PP reference and TL specimens is depicted in
Figure 17a,b. The failure mode aligns with the observations from
Section 5.2, with explosive fiber failure in the PP specimens and interlaminar shear between the individual plies of the TL specimens. The crack in the TL initiates at one of the plies end at the front and/or back of the specimen and then propagates under shear stresses in the thickness direction of the specimen. The final interlaminar crack within the specimen’s thickness direction can be seen in
Figure 17c. It is evident that the individual plies of the laminate exhibit a consistent stacking angle, in contrast to the TL specimens in
Section 5.2 where local angular rotations of different plies occurred.
The strain field and evolution along a longitudinal centerline of the specimens during the tensile tests are shown in
Figure 18 for the PP reference and TL specimens. As concluded in
Section 5.2, the strain field for the PP reference is nearly uniform across the specimen’s entire length. In contrast, the strain evolution for the TL specimens exhibits multiple peaks and valleys at the ply ends and beginnings. The TL specimens with stacking angles of 2° and 4° experience strain variations of 32% and 24%, respectively.
5.2. Ply Stacking in the Longitudinal Supporting Direction
In contrast to
Section 5.1, this section investigates the impact of the tiling in the longitudinal direction. Here, the loading direction (i.e., local x-direction of the laminate) during the tensile testing are aligned with the global X-direction of the bridge deck. Here, the specimens are comprised of repetitive 150 mm-long fabric stacks, each composed of four individual plies. Within each stack, there are two 0°-plies, one 45°-ply, and one −45°-ply, denoted as [0/45/−45/0], in accordance with the findings of
Section 4.1. These stacks are arranged in a tiled configuration with a predefined overlap length to create a TL with a specific stacking angle.
The plane parallel (PP) reference sample consists of three stacks sharing the same structural composition as described above. However, these stacks are arranged parallel to each other. Laminate plates, measuring 300 × 300 mm
2, are infused using a vacuum-assisted resin infusion (VARI) technique. After curing, they are meticulously trimmed to the prescribed coupon size, following ASTM D3039 guidelines, with a length of 250 mm and a width of 25 mm. The specimen’s thickness varies, depending on the build-up and overlap length. To ensure statistical robustness, we tested a minimum of five specimens per laminate type. Various specimen geometries and build-ups (as depicted in
Figure 19) underwent testing throughout this research.
To create diverse stacking angles within the tiled laminates, two techniques were employed. In the first technique, the thickness of a single stack was adjusted by doubling or tripling the build-up (indicated as TL1). In the second technique, the overlap length between the stacks was altered (indicated as TL2 and TL3), resulting in a gradual transition between the different stack layers. It is noteworthy that changing the overlap length of the stacks also increased the overall specimen thickness. The overall thickness indicated in
Figure 19 represents the average thickness across five tested specimens from a single manufactured plate, measured at three distinct points along the specimen’s length. Specimens labelled as TL1 feature a consistent overlap length of 50 mm for the stacks. However, the thickness of a single stack varies, as indicated by the suffixes t1, t2, and t3, representing one, two, and three times the original stack thickness, respectively ([0/45/−45/0], [0/45/−45/0]
2, and [0/45/−45/0]
3). Given that the 50 mm overlap length is a multiple of the total stack length (150 mm), it results in an abrupt transition between different stack layers, as depicted in
Figure 19b,d,f. For specimens TL2t1 and TL3t1, the overlap length between the stacks was altered to 40 mm and 20 mm, respectively, resulting in a gradual transition. The PP reference sample, featuring a stacking angle of 0°, serves as a benchmark for evaluating the global and local stiffness, as well as the strength at first ply and total failure of the TLs.
The DIC measurements indicate variations in stiffness along the centerline of the specimen’s length, indicating distinct strain values at every position along the test specimen’s surface. Consequently, traditional point measurements using strain gauges or extensometers on the surface of a TL are deemed unreliable for determining laminate stiffness, a conclusion substantiated by the previous research in
Section 4.2. In this study, a comprehensive DIC measurement is opted for to capture the entire strain field of the specimen, providing a more accurate depiction of both global and local stiffness within the TLs. This enables the derivation of critical insights into the general stiffness and strength, concerning the first and last ply failures, influenced by the stacking angle. Here, the reference for these evaluations is the PP reference sample, which has a stacking angle of 0°.
Figure 20 presents the local Young’s modulus along the centerline of the plane parallel laminate and the different tiled laminates across a range of average global strains. The strains shown at regular interval, set at 20 s increments, commencing when a minimum strain threshold of at least 1000 με (0.1%) is attained to ensure a well-distributed strain profile along the specimen’s length. This interval is maintained until the specimen reaches its first failure. Importantly, at the point of failure, the speckle pattern is disrupted to such an extent that further pattern correlation becomes unfeasible. Consequently, at the location of the failure, a zero-strain value is recorded, which deviates from the reality of the situation, as substantial displacement typically occurs at that location. Consequently, the set of average strains may exhibit discrepancies across the graphs in
Figure 20.
Figure 20 not only reveals the presence of overlap regions in the TLs, indicated by peaks and valleys in the curves but also demonstrates that, as failure approaches (during the final time interval in the graphs), stiffness diminishes at the points of overlap. This reduction in stiffness is particularly pronounced at the overlap regions, as initial failure predominantly commences at the free edges of the top and bottom surfaces of the specimen, where a ply overlap terminates.
Figure 21 showcases the average stress–strain relationships for the PP reference sample and different TL specimens. Stress is computed by dividing the measured tensile force from the testing machine by the average cross-section along the specimen’s length. Strain, on the other hand, is directly derived from DIC measurements and is averaged across the full length of the specimen. It is important to note that the diagram represents only the elastic region of the stress–strain curve until the first failure occurs. Consequently, the maximal stress in this diagram does not correspond to the total tensile strength of the laminate specimen.
Applying Hooke’s law, the average Young’s modulus for the laminates is calculated, enabling the plotting of the relative stiffness for the PP reference sample as a function of the stacking angle in
Figure 22. This graph also includes relative strength data, both until the first failure (FF) and total failure (TF) in comparison to the PP reference sample. Notably,
Figure 22 reflects a marginal reduction in stiffness between the PP reference sample and various TLs. In contrast, a significant decline in strength until FF and TF are observed when the stacking angle deviates from 0°, represented by the PP reference sample. The stacking angle exerts a minor influence on the overall stiffness of the specimen, given that a PP laminate is only marginally stiffer than the TLs, by 10%. However, the difference in strength until TF is substantial, with a PP specimen being approximately 53% to 83% stronger than its TL counterparts.
From numerous microscopic images of the specimens, it is shown that the theoretically expected stacking angle of the specimens does not precisely match the actual local stacking angle following the production. The production process leads to a significantly larger local angle at an overlap location between two plies than the theoretical stacking angle. Additionally, the ply arrangement between two consecutive overlap regions in a TL aligns closely with that of a PP laminate. This correspondence can also be inferred from
Figure 20, which illustrates the local Young’s modulus along the centerline of the specimens.
In
Figure 23, the failure behavior of a PP reference sample (on the left) alongside two TLs (in the middle and on the right) can be observed. As expected, the PP reference sample exhibits fiber failure, accompanied by an explosive failure event, serving as the primary failure mode. In contrast, both the TL1t1 specimen with a lower thickness and a straight overlap and the TL3t1 specimen with a larger thickness and a more gradual overlap experience failure through shear between the different layers of a stack. It is noteworthy that there are slight variations in the failure behavior between the two construction methods. In the case of TL1, failure occurs more gradually and can be anticipated, whereas, in the case of TL2 and TL3, failure is abrupt, without any preceding deformation of the specimen. Given the preference in civil engineering for a more gradual failure, TL1 laminates are favored over the other two TL types.
Moreover, the local stacking angle exerts influence on the commonly observed fracture mechanism, as illustrated in
Figure 24. The tensile force applied results in substantial shear loading at the interfaces between the different plies, generating a shear-induced failure mechanism. Additionally, the applied tensile force leads to the straightening of the plies, involving a rotation and a local angle adjustment.
By straightening these plies and consequently reducing the local stacking angle, adjacent plies are pushed outward. This results in interlaminar failure (i.e., peel effect) at ply start/end locations, as depicted in
Figure 24a.
Figure 24b–d illustrate the propagation of the crack due to shear stresses, culminating in the ultimate failure in
Figure 24e of the specimens. At the final stage, it is seen that the failure mode predominantly consists of interlaminar shearing between the ply stacks.
A plausible explanation for the peak and valley local stiffness values within a TL, as observed in
Figure 20, can be elucidated based on microscopic images taken at the overlap location in the TL2t1 specimen, as displayed in
Figure 25. On the flat side of the specimens (i.e., against the hard side of the mold during production), resin concentrations have developed between consecutive ply stacks, leading to localized cross-sectional reductions as can be seen from
Figure 25b. Due to this uneven arrangement of the different stacks and the variations in cross-section thickness at these points, an increase in local deformations and consequently, strains become apparent. This phenomenon, seen in
Figure 20, manifests itself as a reduction in local stiffness.
Based on the 3D DIC images, a complete strain field in the longitudinal direction of the specimen can be constructed, offering insights into the development of local strain concentrations on the specimen’s surface. To achieve this, εxx strain data obtained from the VIC-3D software (Version 9, Correlated Solutions, Columbia, SC, USA) are extracted at 200 points along a centerline in the longitudinal direction of the specimens. The strain pattern is analyzed at maximum load, just before ultimate failure, to gain a clear understanding of the occurring stress concentrations across the different specimens. In the following paragraphs, the strain pattern of one representative specimen from each type is assessed and discussed.
First, the reference PP sample is examined. From
Figure 26, it becomes evident that the strain field in the PP reference specimens displays nearly uniform distribution across the specimen’s surface, with an average standard deviation of merely 2% among the individual measurement points along the centerline. Slightly elevated local strain levels are only observable near the grips of the tensile machine.
Figure 26 showcases the strain field for a TL1t1 specimen. It confirms that the strain distribution across a TL’s surface is not uniform, corroborating the assumptions from the tensile tests conducted on transverse coupons from the top and bottom flange of a web–core sandwich panel, as highlighted in
Section 4.2. Additionally, overlap locations are discernible in the strain field, marked by reduced strain levels. Between consecutive overlap locations, the strain pattern exhibits a quasi-uniform evolution, akin to that observed in a PP laminate. Microscopic images in
Figure 5 suggest that these intermediate areas assume a quasi-PP laminate structure, with local angular rotations of plies occurring only at overlap locations. Manual production processes introduce an inherent challenge in achieving perfect transitions between successive stacks. Consequently, variations in thickness arise within the laminate, as illustrated in
Figure 25. These variations cause the local strain to decrease or increase, corresponding to decreases or increases in thickness. As a result, the ultimate failure location can be identified as the point with the highest strain. Given the unique laminate structure with pronounced stack transitions at overlap locations, a similar strain pattern emerges in
Figure 26 for the TL1t2 and TL1t3 specimens, respectively. However, the peaks and valleys in these laminate specimens occur more frequently and exhibit more pronounced extremes, owing to larger differences in cross-sectional thickness at overlap locations within the specimens. These extreme strain values are also reflected in the average standard deviation of the data along the centerline, amounting to 11%, 12%, and 14% for the TL1t1, TL1t2, and TL1t3 specimens, respectively.
In the second construction method (i.e., specimens labelled with TL2 and TL3) of the tiled laminates, a specific overlap length is introduced between the top stack’s initiation and the bottom stack’s termination within the TL. This results in a more gradual transition in thickness at the overlap locations and is also more forgiving in terms of potential errors during the placement of individual plies. Here,
Figure 26 demonstrates that the peaks and valleys in a TL2t1 specimen are considerably less pronounced compared to the TL1-type specimens, with a standard deviation of 10% for the TL2t1 specimens. Strain concentration continues to occur solely at the location of ultimate failure. It can be inferred that strain is more uniformly distributed in the longitudinal direction for this type of construction method for a TL.
A similar strain pattern can be observed in
Figure 26 for the TL3t1 specimens. However, no definitive failure location is evident in the strain field, and strain concentration spans the entire length of the specimens with overlap locations appearing in rapid succession in this case. The average standard deviation in strain along the longitudinal direction remains modest for the TL3t1 specimen, with a value of 9%.
An overall summary of the average microstrain interval and average strain just before ultimate failure for the different specimen types is depicted in
Figure 27. This reveals that PP specimens fail at the highest strain, while TL1t3 specimens fail at the lowest. Additionally, a decreasing trend is observed with increasing stack thickness in the TL1-type specimens. Furthermore, as previously established, TL2 and TL3 specimens fail at higher strains compared to TL1-type specimens with similar thickness and ply counts. Lastly, the scatter between the minimum and maximum strain is smaller for TL1t2 and TL1t3 specimens due to their lower strain at failure.