1. Introduction
Polyethylene terephthalate (PET) is a semi-crystalline thermoplastic polymer with a high performance in terms of strength, stability, electrical properties, and the ability to resist ultraviolet (UV) light, also known as UV resistance. Furthermore, this material is fully recyclable and can be used for a broad range of applications with a long service life. Generally, plastic materials such as PET, polyethylene (PE), polyvinyl chloride (PVC) or polypropylene (PP) are used in the form of extensible or inextensible films for food packaging [
1], trash bags [
2], printed films, plastic cards, geomembranes, etc. Despite their high cost, the choice of PET-film solutions as protective layers for the retrofit of structural glass panels is typically suggested by strength quality and delamination properties. Moreover, tape manufactures usually take advantage of pressure sensitive adhesives (or PSAs) on their tape, which require slight pressure to adhere to most clean and dry surfaces. Anti-shatter safety films (ASFs) are thus a representative of the widespread application of PSAs, and their specific use for glass elements is rather common in civil engineering. These films can in fact be used for a multitude of applications, including to reduce transparency, obscure and improve the transmittance characteristics, or enhance safety levels against fracture.
It is, in fact, known that the majority of casualties caused by a sudden extreme event, of natural or anthropic origin, occur not due to structural collapse [
3,
4], but to falling rubble, tiles and glass fragments and shards [
5,
6]. This suggests that special attention should be paid not only to the (target) primary structure as a whole, but also to secondary components. The use of PET-films, in this regard, is known to reduce the possibility of flying glass debris following accidental actions of any nature, especially those of impulsive and unpredictable origin. For this reason, in addition to the multitude of efforts that have been made to improve energy saving features, various experimental studies have shown in the past that the use of protective films can increase the post-fracture residual performance of damaged ordinary glass elements. Many laboratory studies have been conducted to understand how the use of these films on glass members can affect the expected strength under impact [
7]. A ball-drop experimental program is presented in [
8] for traditional glass windows. The use of protective films proved to offer increased safety levels to window elements, and thus reduce the potential risk for occupants. Several authors have studied ways to improve the performance of structural glass based on thin films [
9]. Brueggeman et al. [
10] proposed an insulation system of panels to prevent damage. Other research studies have been dedicated to the detection of efficient methods for avoiding severe consequences for customers, that is using PET-films applied on both sides of glass panels [
11] or on the external surface only [
12,
13,
14]. Memari et al. [
14] explored the influence of films using a Racking Test Facility. The experiments demonstrated a greater strength for film-bonded glass elements, in addition to a limited ability to create flying debris, compared to ordinary glass members. On the other hand, literature efforts are still rather limited towards the generalized quantification of advantages in using similar protective films, as well as towards the definition of basic mechanical properties. In this regard, it is worth to note that a major issue regarding the performance of ASFs is that the quality of mechanical properties at the interface is affected by many factors, such as intrinsic material properties, composition, processing method and operational conditions [
15].
The present investigation studies how the influence of temperature and ageing time can influence the characteristics of basic material components, by taking into account a commercial multi-layer ASF product. The aim is to provide a complete characterization of the adhesive layer in direct contact with glass, by using a combination of experimental tests, theoretical assessment methods and Finite Element (FE) numerical parametric studies. This is achieved with peel adhesion testing methods, which is a traditional technique that can be used for assessing the characteristics of ASFs, as well as the effectiveness of aged ASFs [
15].
2. Background of Peeling Mechanics and Current Approach
Adhesion is an extremely complex process that concerns the creation and toughness of the bonding that can take place between any two materials. In general, two surfaces attract when the separation between them is within the range of interatomic distance: the surfaces are in contact with the intermolecular interaction forces of van der Waals. Among the many factors affecting adhesive properties, the three most important are: the viscoelasticity of the materials in contact, the surface roughness and the contact geometry.
In this paper, attention is focused on the study of the adhesion between a polymeric surface and a glass substrate. Adhesive properties are thus measured by peel testing, and the approach is suitable, especially when considering weak adhesion, as the deformation in the peel arm can be accounted for as elastic. To this aim, the mechanical relations of the peeling test are firstly introduced by following the theoretical and experimental evolution of the method from the mechanical point of view. Kinloch’s analysis is then addressed by describing in its essential points the energy balance on the peeling mechanics.
In the 1950’s, Gent was the first to propose a study on the peeling of an adhesive polymer from a surface with a constant peel angle [
16]. Later, Kaelble analysed the bond behaviour by introducing the role of microfracture mechanisms in the process [
17,
18,
19]. The study showed how peel rate and temperature can affect the failure at the interface for an adhesive system [
20]. In particular, Kaeble provided a complex expression for the calculation of peel force depending on the mechanical and rheological properties of the adhesive layer, and as a function of normal and shear stresses at the peel tip position. Furthermore, Gent and Petrich [
21] built a peeling model from a rigid substrate, in which the calculation of peel strength depended on parameters such as the thickness of the adhesive, the critical elongation to break or detach from the fibrillae, and efforts in fibrillae. The stronger the adhesive, the cavitation process and adhesive fibrillation develops during the test. The introduction of viscoelastic behaviour from the thin films resulted in the definition of the two transitions observed in similar materials, depending on the separation speed: the liquid-like delamination process was impacted by viscoelastic effects due to the deformation rate and adhesive stress–strain curve, which was rubber-like, associated with the transition of the elastomer adhesive to glass.
The peel test of flexible laminates as a fracture mechanics problem was introduced by Kinloch et al. [
22,
23]. Fracture mechanics is based on the basic assumption of continuous mechanics, thus the details of the molecular structure of the polymer are ignored and the subject of the study is seen as a single element with specific physical properties [
24].
According to the aforementioned approach, this energy-balance approach shows that the external work carried out by the peel force (
Uext) is the sum of the energy of creating a surface (
Ga [J/m
2]), the energy of extending the peel arm (
Us + Udt) and the energy of bending the peel arm (
Udb) [
22]:
where
b represents the width of the tape and
a corresponds to the surface involved in the delamination process.
Generally, the measured peel force
P is significantly dependent on geometry setup (peel angle, speed and laminated structure). As seen in the study by Kinloch, the total energy input for a single-arm peel test can be calculated as a function of peel strength
P,
b and the peel angle as in Equation (2), where the peel arm is considered inextensible [
22]:
However, there are no quantities in Equation (2) which can be attributed to the mechanical properties of the material, adhesive, or to the thickness of the strip. This limit depends on the simplified hypothesis of perfectly rigid in tension and completely flexible in bending tape, and therefore the external work is simply transferred to the surface at the separation point. On the contrary, by considering the tensile deformation of the tape, it is found that [
22]:
where
hs is the thickness of the peel arm and σ is the stress due to peel force which causes an elongation
εa. This results in an increase in travel distance of the peel force, which becomes
(1
+ εa − cos θ)a.
Moreover, the tape that is delaminated during the test (i.e., near the point of contact), is subjected to strong bending, particularly for a 90° peel test. This bending involves a loss of local energy that should be properly taken into account, so as to avoid the risk of erroneously higher measured values for
Gc. Thus, if plastic or viscoelastic bending of the peeling arm is taken into account [
22]:
where the contribution
Gdb denotes the total energy loss in the loading and unloading cycle per unit area.
Since the geometries of the case study are different from the issue discussed by Kinloch, a revised approach that can calculate each increment of energy based on the above formulation (Equations (1)–(4)) and take into account the variability of peel angle is needed.
In the present work, a discretization of the problem is in fact conducted with a variable
θ. For each time step of data acquisition an addendum of summation, for Equations (2) and (3), respectively, it can be calculated by:
It is worth noting that Equation (6) is valid in case of film with linear tensile deformation only (i.e., εa < εy). Due to the low force values applied during the peeling test, this is in fact what generally happens.
The final required term,
Gdb, cannot be evaluated through a simple summation, due to the assumed methodology to derive it. Thus, to obtain a consistent value of adhesion energy, which can be successively calibrated through FE numerical procedures, a mean of the peel angle is considered in order to apply the equations proposed in [
25], based on the elastic-plastic behaviour of the peeling arm modelled as a bilinear, work-hardening material (
E2 = α
E).
The adopted method consists of an iteration that accounts for the different loading states, as reported in [
22], that is:
Case #1—Elastic deformation during bending loading and unloading:
Case #2—Plastic deformation during bending loading and elastic deformation during bending unloading:
Case #3—Plastic deformation during bending loading and unloading:
where
k0 represents the rate between
R1, the radius of curvature related to the initial yielding of peeling arm, and
R0, the actual radius of the curvature at the peel tip position. Furthermore,
f1 and
f2 are a function of
k0 and the work-hardening parameter α according to the Kinloch method [
22].
The parameter θ0 (named root rotation) in the aforementioned expressions is herein introduced to denote a local angle and is thus substantially different from the imposed angle θ, which represents the rotation of the “beam” representing the peel arm. The limit condition θ0 = θ, in this regard, means that the peel arm has zero bending stiffness and acts as a string.
Although “Case #3” is generally the best representative of the loading and unloading of the peeling arm, “Case #1” represents more precisely the actual material behaviour for the polymeric materials involved in the present investigation.
Recently, IC-Peel software [
26] was provided by Imperial College in order to automate the necessary calculations by the numerical integration of the bilinear fit of the experimental material curve σ − ε (i.e., Young Modulus
E, in GPa, thickness
hs, in mm, and yielding stress
σy) and peel test geometry. As a benchmark for the present methodology, the aforementioned tool is herein employed, and a comparison of results is summarized in
Figure 1. In particular, the effects of the test rate (
v) and ageing conditions were considered relevant in the assessment of the adhesive behaviour, as several studies confirmed their influence. As explained in
Section 6.2, the different scenarios of ageing were chosen after
Tg (glass transition temperature) was identified by preliminary material investigations and within the general range of temperatures that glass is exposed to in buildings. It is worth noting the rather close correlation of calculated values, namely in the form of a rather small percentage variation in the proposed comparative charts.
3. Experimental Investigation
A commercial multi-layer film for safety glass applications was investigated in the present study. According to
Figure 2, the examined commercial tape was composed by two different layers made of PET, with a thickness of 0.11 mm (Layer 2) and 0.22 mm (Layer 1), and a PSA adhesive that was protected by environmental conditions by means of a removable release liner.
The first tests carried out included a tensile protocol, after treating the ends of the samples with glue (i.e., RS PRO Industrial Grade Adhesive 132633) in order to increase roughness and reduce slip to the grips. The tensile tests were conducted on five PET-film specimens, 350 mm in length (
Figure 3a), according to ASTM D882-02 [
27], which is adopted for plastics in the form of thin sheeting, including film with a thickness less than 1 mm. Each layer of the film samples was also analysed with Differential Scanning Calorimetry and Fourier Transform Infrared spectroscopy. Moreover, the delamination behaviour of the tape from a 100 × 40 × 6 mm
3 glass substrate was characterized by means of peel tests on rectangular specimens 25 mm in width (as shown in
Figure 3b and summarized in
Table 1) by taking into account testing and ageing influence. These tests involved a limited number of specimens, with identical geometric characteristics, but treated differently in the pre-test phases. Some specimens were in fact aged in a dry-heat chamber, ventilated with constant temperatures, and for different periods of exposure, from 3 to 168 h.
In this regard, it is important to clarify that the experimental setup of the peel test did not completely follow standard regulations. However, the sample preparation was considered necessary to minimize the influence of impurities or inclusions on the adhesion behaviour. The detailed dry lamination was carried out as in [
28]. Both peel tests and tensile tests were performed using a Schimadsu Autograph AFS-X universal testing machine at a crosshead speed of 25.4 mm/min.
4. Numerical Analysis
In support of the experimental methods, an FE numerical analysis was carried out in accordance with [
28]. A 3-dimensional model was built in Abaqus/CAE [
29] according to the layout and dimensions of the tape (total thickness of 36 µm) and the substrate, as described in
Figure 2 and shown in
Figure 4. Quasi-static analyses were carried out with the support of the Explicit solver.
The geometric model assembly (i.e.,
Figure 4a,b) consisted of C3D8R solid elements for glass substrates and the portion of film was expected to suffer from delamination, whereas the short vertical peel arm was represented in the form of S4R shell elements, to reduce the computational effort of the parametric peeling simulations.
As boundary conditions, the continuity restraint in the PET-film element was numerically described with a shell-to-solid connection. Furthermore, the lower surface of the glass substrate was clamped to reproduce the experimental setup.
The involved materials (glass, adhesive and PET) were modelled based on three different procedures. Glass was assumed to be linear elastic, with nominal mechanical parameters of annealed glass (
Eg = 70 GPa,
ν = 0.23, i.e., hypothesis of rigid substrate). For the description of PET behaviour, an elastic-plastic material constitutive law was taken into account and calibrated based on tensile tests outcomes (
EPET = 3.3 GPa,
εy_PET = 2.7% and
ν= 0.49), with the addition of subsequent considerations of the accelerated ageing effects. Finally, for modelling the adhesive layer with very thin thickness, a surface-based Cohesive Zone Modelling (CZM)-based behaviour technique was employed. Therefore, PSA was modelled as a surface-to-surface interaction between the two bonded surfaces, by using a traction-separation law (
Figure 4c), which consisted of three parts: a linear elastic behaviour, up to traction strength (
t0) representative of damage initiation, and its evolution down to separation failure (
δt). The elastic term is commonly defined by a constitutive matrix
K, as a function of film elastic moduli
Eadh and
Gadh, that relate the nominal stresses to the separation across the crack tip [
29]:
where
t and
δ represent stress and separation vectors, respectively. The former consists of three components: a normal traction
tn and two shear tractions,
ts and
tt. The corresponding separations, i.e., the relative displacements between the top and bottom surfaces of the cohesive layer, are denoted by
δn,
δs,
δt, respectively. Moreover,
Knn =
Eadh/
tadh;
Kss =
Kt t=
Gadh/
tadh.
The off-diagonal terms in the stiffness matrix are zero due to uncoupled elastic behaviour assumption. Further elements are required to complete the CZM definition. Firstly, several damage initiation criteria are available in the Abaqus library, such as the maximum principal stress criterion (MAXPS), the maximum principal strain criterion (MAXPE), the maximum nominal stress criterion (MAXS), the maximum nominal strain criterion (MAXE), the quadratic nominal stress criterion (QUADS), and the quadratic nominal strain criterion (QUADE).
The first two criteria (MAXPE and MAXPS) refer to the main direction, and therefore the crack always develops in the orthogonal direction of deformation and stress to the main one, respectively. In the other criteria, instead, the user can choose the direction of crack. The maximum nominal stress (MAXS) criterion was used in the present analyses, based on the limit condition [
29]:
where
t0n,
t0s,
t0t denote the peak stresses related to pure failures (
n = normal direction;
t and
s = first or second shear directions) at the interface. These input parameters were computed from experimental peeling tests outputs, together with the fracture energy value
G, which was iterated to find a good match between experimental and numerical peel curves (starting from provisional values derived by the proposed theoretical approach).
Furthermore, it has to be noted that the damage evolution criterion is a function of fracture energy (
G). To follow the advancing crack tip, a scalar damage variable (
D) was hence provided during the numerical simulations (CSDMG parameter). It starts at a value of 0 at the initiation of damage, and then the
D-value monotonically increases until it reaches 1, so as to represent a fully damaged material and a complete loss of cohesive bond. This follows the degradation of material stiffness given by [
29]:
where
represents the stress predicted by the linear elastic traction-separation law.
In this study, an energy-based method was used. In particular, a Mode-Independent behaviour was considered in which the fracture energy G was set to correspond to the first mode energy, and to represent the work carried out by normal stress.
Following the above considerations, the detailed calibration of the reference FE model for peel test simulations was based on the experimental results from delamination tests, herein discussed (
Section 5 and
Section 6). This allowed the development of a consistent CZM law for the selected ASF product, and a realistic description of the stress state around the crack tip in different ageing conditions.
7. Conclusions
In this paper, the mechanical behaviour of unaged and aged multi-layer anti-shatter films (ASFs) for safety covers in structural glass applications was investigated based on experimental methods, theoretical approaches and Finite Element (FE) numerical modelling techniques. For a total of 52 small-scale samples, an alternative peeling setup was taken into account under various artificial ageing configurations.
Generally, both temperature and peel rate are known to significantly affect the mechanical behaviour of polymers. In this regard, the ASF-bonded glass specimens were grouped by peel rate (3 configurations) and time/temperature of ageing condition (8 in total). The relations between fracture energy and ageing conditions were investigated and it was observed that, as the period of heating exposure increases, it tends to obtain a higher value of Ga when the ageing temperature is sufficiently below the glass transition temperature. Furthermore, since the PSA model calibrated under the mode I failure showed a rather good agreement with the experimental experiences, it can be concluded that reliable FE numerical models of ASFs and ASF-bonded glass elements can be built. However, the limitation of the use of the Cohesive Zone Modelling (CZM) technique lies in the fact that it cannot fully seize the phenomena of crack propagation in the adhesive layer, and, for this reason, the calibration analyses should be carried out considering separately the detailing of each specimen. The experimental observations in fact highlighted that the ASF properties vary from specimen to specimen, and the variability was assessed by considering numerical and experimental outcomes on similar groups of samples/ageing conditions (5 per sample).
Generally, the peel tests showed that the adhesive fracture energy, as obtained according to the theoretical approach based on the Kinloch method, resulted in higher values than calibrated FE simulations. Moreover, in both cases, a certain upward trend of fracture parameters was observed for T = 50 °C, while an increasing Ga trend was observed for T = 70 °C in the range up to 24 h of heating exposure, and then followed by a degradation of adhesion properties.
Despite this, key parameters were properly detected to support critical design considerations, as well as to support the implementation of realistic FE numerical models for the study of ASF-bonded glass elements.
In the future, a possible extension of the present study should examine the cyclic response of PET-film samples, so as to capture experimentally and numerically a realistic measure of dissipation capacity in ASF-bonded glass elements, due to plastic deformations with a variable root rotation.
Similarly, the present outcomes will support an extension of the experimental and numerical analysis to the assessment of the dynamic performance of ASF-bonded glass elements in the post-breakage stage, or the impact response of full-size ASF-bonded glass members for structural applications in buildings.