The constant efforts of today’s marine and shipbuilding industry to improve its efficiency and competitiveness are reflected in the efforts to implement new technologies, procedures, and organisational methods in design, production and product exploitation. Hence, the application of composite sandwich structures in marine applications has been recognised as a valuable contribution to such efforts.
Composite sandwich structures are well-used in smaller vessels, as they are primarily known for their lightweight construction and exceptional stiffness. Recent trends in the shipbuilding industry have followed the small craft well-established principle of using sandwich panels in need of structural weight reduction and stiffness. This new trend has opened up a new path for creating a standardised and reliable data source on construction material and construction and testing methods [1
]. The variety of materials used in composite production is increasing daily. Unlike in small craft production, where safety margins and risks are evaluated on a different level, and thus experimental evaluation of material properties is not mandatory, the production of large seagoing vessels needs reliable and accurate material data and approved testing methods. Collaboration between shipyards and class societies have yielded several projects and committees, like RAMSSES, ISSC, and increased practice of composites usage in parts or in large commercial and naval vessels, such as car decks in RO-Pax vessels [2
] or even parts of the superstructures, hatch covers or in the construction of the structure of large commercial and naval vessels [3
]. Therefore, composite sandwich panels and structures are an exciting go-to method for possible weight reduction issues.
The principle of sandwich structure is relatively simple, where the sandwich plate represents an I beam which consists of two faces (representing the flanges of the beam) on the top and bottom of the structure, having a core in between, acting as a web of I beams and making the necessary distance between flanges. The faces mostly take the normal stresses, while the core of the sandwich materials is usually stressed in shear. Therefore, the core is usually a different material from the faces spread out as continuous support for the faces [5
]. Most used cores in the marine industry are foams both metallic [6
] polymeric [2
] as well as balsa wood [7
] and honeycombs [7
]. Other arrangements such as corrugated steel sandwich panels can also be used [9
In the case of foam cores, mainly focusing on closed-cell PVC foams in marine structures, are predominantly cores of apparent densities ranging from 60 kg/m3
to 250 kg/m3
, but reliable data for such cores are usually extracted from manufacturer technical data sheets (TDS) as shown in [5
]. However, reliable stress-strain curves for these cores, especially shear stress-strain curves, are not readily available. The test results, curves and relevant data can be found for 80 kg/m3
to 250 kg/m3
(for Divinycell and DIAB foams) [10
], but data for lighter foams are scarce. For lightweight closed-cell PVC foams of 60 kg/m3
or less, usually, only limited data based on manufacturer TDS is available. Hence, a FlexyFoam M-55 closed-cell, lightweight PVC foam with an apparent density of 60 kg/m3
The shear properties of the core can be determined by following test and evaluation procedures described in [1
]. Several test methods were described, composed of several ASTM and ISO standards. The most widely used are flexural tests, which tend to extract shear properties through the flexion of the sandwich beams utilising the 3-point or 4-point bending test [13
]. Using the flexural test to extract the shear properties tends to be easier on the specimen production side, as the manufacturer of the vessel needs to provide just one type of testing specimen to extract multiple properties of the sandwich laminate. However, these tests provide approximate values as both the flexural and shear forces can influence the test results. Therefore, as advised in [15
], both flexural tests should be performed. Special care should be executed when designing the test specimens for flexural testing, especially when performing the 3-point bending test, as the failure mechanisms during the test can lead to core indentation, face wrinkling or dimpling. The results for lightweight cores with a density less than 100 kg/m3
in most cases exhibit indentation [16
], and therefore results obtained on these specimens cannot be taken into account when determining the shear properties of the core. The alternative testing methods for lightweight cores can be found in ASTM C273 [19
] and similar ISO 1922 [20
] standards. The test produces shear stress by moving the metal attachment plates parallel to the sandwich facing and covers the determination of shear strength parallel to the plane of the sandwich [19
]. Using the methods described in the ASTM C273 and ISO 1922 standards, shear properties can reasonably easily be calculated since the shear failure of the core occurs even on lightweight, lower density cores.
This paper aims to present the ASTM C273 standard test method used to determine the PVC foam core shear properties and the sample preparation details in particular. It is noted that standards usually lack detailed instructions regarding sample preparation. Therefore, the authors have provided detailed information about the manufacturing process of samples with checks and dimension checklists needed to reproduce the specimens successfully. Recent development in DIC technology in the field of composites, especially foams [20
], encouraged the authors to use the technology to evaluate the displacement of test specimens without the usage of different types of extensometers. Furthermore, shear tests were recorded using the DIC technology using 3D non-contact optical measurement based on the measured displacement field, thus enabling the calculation of shear stresses and shear modulus from DIC measurements. The shear modulus and the displacement of the grips on the testing machine were also recorded and compared to the values obtained with DIC measuring system. The difference was shown in shear test results for tensile and compressive loading arrangements, focusing mainly on the shear stress-strain curve and shear parameters for lightweight PVC foam core. In addition, DIC was used to visualise the strain field, animate the crack propagation, and monitor the parasitic effects that can occur at the core to adhesive interface [15
]. The presented approach is expected to improve the maritime structures and ships design process, especially related to the core foam selection and sandwich structures definition.
3. Results and Discussion
Only the shear failure of the core was acceptable, while cohesive failure of the core to plate adhesive or adhesion failure of the core or plates was not acceptable according to the standard [19
Through thickness crack is clearly visible on specimens T2 and T4 to T7. Upon detailed inspection of all specimens, it was noted that T1 and T3 specimens did not experience the trough thickness shear failure. Failure in the T1 and T3 specimens occurred in the sandwich core material but was limited to the plane parallel to the loading plates, a millimetre from the core-adhesive interface. No cohesive or adhesion failure was spotted in T1 and T3 specimens. The images of the specimens loaded in the tensile direction after the test can be seen in Figure 4
. Specimens C1 to C10 all broke with the clear through thickness shear failure, as seen in Figure 5
The crack propagation could not be measured directly, as the paint fell off alongside the PVC foam particles during the crack propagation due to sandwich core material behaviour. The larger area around the crack lost the paint, so the very tip of the crack could not be located precisely. However, it was possible to observe discolouration of the specimen during the experiment, especially in the DIC post-processing stage. The discolouration of the surface (due to the paint erosion from the PVC foam) was in-line with the later observed crack. The initial crack on all specimens started similarly. The crack occurred in the corner of the core, near the core to the steel plate interface. The crack initiation started in the area of the core subjected to the tensile load, confirming the observations made by [12
] that the secondary stresses may occur in the core specimen, such that the tensile strain field may initiate the crack in the core. The tip of the crack was almost impossible to spot with the resolution and frequency of filming used in the current DIC measurement setup. However, the propagation of the crack and foam deformation was visible through the discolouration of the strain field.
a depicts the test’s initial configuration and starting point for specimens loaded in the tensile direction, with the surface component showing values of γxy
. Upon imposing the displacement on the movable loading plate, the crack on the specimen started to occur. The initiation and propagation of the crack could be made visible by tracking the grey areas on which software lost reference facets. Due to the nature of the sandwich core material, the loss of paint on surface components around the crack on PVC core foam was more significant than on the steel specimens. Therefore, the very tip of the crack was almost impossible to spot. However, the propagation path was clearly visible. The crack started near the lower edge of the core and propagated alongside the interface of core and adhesive in the direction of imposed displacement (visible in Figure 6
b). When the lower crack expanded to 1/3 of the specimen length, a new crack started to form on the upper part of the specimen, near the moving loading plate (visible in Figure 6
c). The test ended with trough thickness shear failure of the specimen, and through thickness crack is visible in Figure 6
d. A similar process was observed on specimens loaded in a compressive direction, although the initiation of the crack on the opposite side occurred much earlier. The DIC measurement on the compression samples can be visible in Figure 7
The images recorded with DIC were adequately synchronised with the force readings taken from the test machine during data post-processing. Overlapping timelines from the machine and DIC, it was possible to create load-displacement curves for each test. The shear stress τ, in MPa, and shear modulus G, in MPa, were calculated according to ASTM C273 standard. The average shear strength-strain curve was interpolated from experimental curves. The mean curve was interpolated using a Python script for curve interpolation created by authors. Inputs for the script were stress-strain curves for each group of specimens, thus calculating a separate mean curve for the tensile direction and a separate curve for the compressive direction of the applied load.
The resulting average shear stress-strain curve for specimens loaded in the tensile direction and curves for each specimen is shown in Figure 8
. Specimens T1 and T3 were not included in the calculation of the average curve, as the specimens did not experience proper shear failure.
According to the DIC system, the specimens T2 and T4 to T7 exhibited shear failure at different displacements (dDIC
) ranging from 4.68 mm to 7.06 mm. These values were compared to the measurements taken directly from the machine (dMACH
). The comparison table is presented below; see Table 3
, showing the difference Δd
and giving the average difference of −1.24 mm between the two measuring methods.
The comparison of calculated shear modulus for the specimens T2 and T4 to T7, using the values from the DIC measurement (GDIC
) and measurement calculated from the machine output (GMACH
), and difference (ΔG
) is presented in Table 4
with a calculated average difference of 2.6 MPa.
For specimens loaded in the compressive direction, the resulting average shear stress-strain curve and curves for each specimen separately are shown in Figure 9
Specimens C1 to C10 exhibited shear failure in elongation range from 6.00 mm to 9.51 mm. The comparison between values measured using DIC system (dDIC
) and measurements taken directly from the machine (dMACH
) is given by the difference Δd
value, see Table 5
. The average difference is somewhat smaller than in samples loaded in the tensile direction, with a value of −0.72 mm.
The comparison of calculated shear modulus for the specimens C1 to C10, using the values from the DIC measurement (GDIC
) and measurement calculated from the machine output (GMACH
), is presented in Table 6
. The average value of the difference is 6.8 MPa.
The grouping of the results for C1 to C5 (presented in red) and C6 to C10 (presented in blue) is also clearly visible. Due to the limited amount of sandwich core sheets available for testing, the sandwich core material for specimens was sampled on various positions on two different core sheets. Sandwich core material for specimens C1 to C5 was taken from one sheet, and for C6 to C10 specimens from another sheet. Due to manufacturing methodology, different parts of PVC foam can have slightly different properties, as PVC foam is usually cast into large blocks, and then they are cut in thin sheets prepared for sandwich construction, which may be the cause of the anisotropy and heterogeneity of core materials [28
]. According to the author’s experience in the manufacturing procedures of the composite vessels, it is almost impossible for the vessel manufacturer to know the exact position of the sheets in the initial foam block. Therefore, the sampling process should involve samples from several sources and include different batches of the available core material.
The shear modulus calculated from the average curve of the specimens loaded in the tensile direction is 10.6 MPa. The lowest shear modulus of 9.9 MPa is calculated on specimen T5, whereas the highest shear modulus value is 11.9 MPa, calculated on T4. The shear modulus calculated from the average curve for the specimens loaded in compressive direction is 22.1 MPa. The lowest value for specimens loaded in compressive direction is 18.8 MPa, calculated for the C6 specimen. The highest shear modulus is 22.3 MPa, calculated for the C8 specimen. The average shear modulus calculated for all specimens is 16.4 MPa.
The shear modulus designated by the manufacturer in the product TDS [26
] is 22 MPa, calculated using ASTM C393 standard. The average shear modulus for specimens loaded in the tensile direction is 52% lower than designated in the TDS [26
]. The average shear modulus for specimens loaded in compressive direction differs from the designated modulus for just 0.5%, and it is slightly higher than stated in TDS [26
]. However, the values provided by the author can also be compared to the values provided in [10
], where shear modulus for foam with an apparent density of 80 kg/m3
is calculated at 18 MPa, while for foam with an apparent density of 100 kg/m3
shear modulus is around 25 MPa. TDS from yet another manufacturer [29
] for the PVC foam cores provided a minimal value of 14 MPa, the maximal value of 21 MPa, and an average value of 17 MPa for shear modulus for foams with an apparent density of 60 kg/m3
, tested and calculated using the ASTM C273 standard. These values indicate that the shear modulus for PVC foam of apparent density of 60 kg/m3
should be somewhat lower than 22 MPa in the expected range from 10 MPa to 20 MPa. Hence, it can be concluded that the specimens loaded in the tensile direction tend to give conservative values for the shear modulus of the foam. In contrast, values provided by specimens loaded in compressive direction are almost 20% higher than the shear modulus calculated for PVC foam of the apparent density of 80 kg/m3
provided in [10
]. Such differences can result from different loading conditions occurring due to the loading in tensile and compressive directions. While cell walls of the closed-cell foams subjected to pure shear are subjected only to pure bending [30
], the tensile or compressive components are added to total stress when parasitic stresses occur. Cell walls subjected to compression densify, thus adding to the strength of the material, while cell walls subjected to the tensile loading bend and stretch. Thus, additional stress predominant in the tensile direction causes brittle fracture of the cell walls, while additional compressive stress causes progressive crushing [30
], which was somewhat captured using DIC. However, further study on the microscopical level is advised.
The authors of that article used the ASTM C273 standard to determine the shear properties of PVC foams, while the core manufacturer used ASTM C393 standard to determine the shear modulus. The ASTM C393 calculates the sandwich panel’s shear properties using the beam flexure, which includes yet another parameter to the equation, a sandwich panel facings. An expected facing ultimate strength needs to be known to correctly calculate shear modulus, while ASTM C273 standard does not include any additional material in the calculation. The authors’ shear modulus values are in line with known data for cross-linked, closed-cell PVC foams, especially if the mean value is calculated using the specimens loaded in the tensile and compressive direction.
The shear modulus values calculated from the machine given results tend to give a conservative estimation of the sandwich core shear modulus compared to the DIC measuring system method. The shear modulus of the specimens loaded in the tensile direction was lower by about 23% on average to DIC values, while for the specimens loaded in the compressive direction is about 32% on average lower than DIC values. Thus, a direct measurement from the machine could be taken for engineering purposes and a quick estimation of the properties of the lightweight sandwich material.
The shear stress values for each specimen are shown in Table 7
, as well as the average values for specimens loaded in the tensile direction and specimens loaded in the compressive direction.
According to TDS provided by the manufacturer [26
], the ultimate shear strength of the foam is 0.8 MPa. At the same time, average values for both types of specimens are lower than specified, 5.9% lower for specimens loaded in the tensile direction and 3.6% lower for specimens loaded in the compressive direction. However, they are higher than 0.7 MPa, provided in [5
], and in line with recommended values from TDS [29
], where 0.6 MPa is the minimal, and 0.77 MPa is the maximal value of the shear strength of the core.