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Article

Assessing the Fatigue Stress Behavior of Starch Biodegradable Films with Nanoclay Using Accelerated Survival Test Methods

by
Theofilos Frangopoulos
,
Sophia Dimitriadou
,
Joanis Ozuni
,
Anna Marinopoulou
,
Athanasios Goulas
,
Dimitrios Petridis
* and
Vassilis Karageorgiou
*
Department of Food Science and Technology, International Hellenic University, P.O. Box 141, 57400 Thessaloniki, Greece
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2024, 14(17), 7728; https://doi.org/10.3390/app14177728 (registering DOI)
Submission received: 25 July 2024 / Revised: 14 August 2024 / Accepted: 28 August 2024 / Published: 2 September 2024
(This article belongs to the Special Issue Synthesis and Application of Advanced Polymeric Materials)
Browse Figures
Review Reports Versions Notes

Abstract

:
A destructive degradation model was applied on films made from different concentrations of starch, glycerol and nanoclay using various elongation levels as a stress variable at different stress times and stretch cycles. The log tensile quotient (logarithm of the tensile strength to the corresponding break cycle) was recorded as the response variable. The log tensile quotient increased, and the log exact break time decreased, as the elongation level increased. The treatment containing the highest starch and nanoclay and lowest glycerol content proved to be the most resistant to stress conditions and the most versatile in relation to the varying log tensile quotients, while the treatments containing the lowest nanoclay and highest glycerol contents, regardless of the starch concentration, manifested the lowest log tensile quotient at higher levels of log exact break time. According to multiple regression findings, the break cycle governed mostly the stress conditions in the degradation model, followed by the sample ID and the log exact break time. The term log tensile quotient, attempted for the first time on data concerning biodegradable films enhanced with nanoclay, seems very promising for deeper research due to its ability to retrieve predictive information from survival equations and to discriminate the difference between film structures.

1. Introduction

In recent years, with the change from conventional petrol-based food packaging materials such as polyethylene (PE), polyvinyl alcohols (PVA) and nylon [1], to biodegradable, natural and environmentally friendly counterparts, pressure has been observed in the food packaging industry to adapt to the responsibilities and duties of this new reality [2]. The food packaging industry has had many decades of studying and improving conventional plastic packages from the scope of improving mechanical, barrier and cost properties, which, in the case of biodegradable and environmentally friendly food packages, has not been observed to such an extent due to the great amount of time and testing needed on these products.
Research directions in food packaging include active (which modifies the condition of food to increase shelf life and safety) and intelligent (which monitors the condition of food) packaging. These directions, although widely explored in experimental studies, have not reached the market to a great extent [3]. Current issues in the food packaging industry that should be addressed by the development of biodegradable food packaging materials include greener packaging, waste reduction and sustainability [3]. Finally, a life cycle assessment of biodegradable food packaging materials should be studied in order to fully assess their environmental and ecological impact [4].
Between the varieties of biodegradable, natural film forming polymers, the most common one is starch because of several reasons, including its abundance, its ease of processing in order to produce films and the ability to customize the film forming procedure in order to manufacture films with different attributes. Starch, which is one of the most abundant natural polymers, consists of amylose and amylopectin. Amylose is the linear polysaccharide of starch, consisting of glucose units linked by a-(1→4) glycosidic bonds and is the main film forming factor, whereas amylopectin is the branched polysaccharide of starch consisting of both a-(1→4) and a-(1→6) glycosidic bonds [5].
The film forming procedure of starch includes the gelatinization of starch in an excess water content during heating at a specific temperature with the presence of a secondary plasticizer, such as glycerol. Starch is organized in granules, which in their physical state are semi-crystalline and insoluble in water. However, during heat treatment at a specific temperature for each starch species called gelatinization temperature, in an aqueous environment, starch granules tend to absorb water and swell, subsequently leading to their disruption and causing amylose chains to leach out into the solution. The gelatinization of amylose is the process that enables water absorption by amylose and the transition from a crystalline to amorphous state and, further, allows the formation of a continuous amylose matrix in which the water is entrapped [6]. The aqueous dispersion, which includes the gelatinized amylose with the secondary plasticizer, is called thermoplastic starch and, when it is dried, the films occur. As it happens with all natural systems, these non-spontaneous reactions based on thermodynamics—such as gelatinization, which needs energy to happen—are reversible, which means that, after some time, the amorphous state of starch is submitted to physicochemical reactions leading to retrogradation or a return to the crystalline state, which begins with the removal of water from the amylose matrix. Retrogradation has negative effects on the matrix and, therefore, on the occurring films, leading to the high brittleness and low integrity of the film. For these reasons, the use of secondary plasticizers, such as glycerol [7], is necessary, since they delay and hinder starch retrogradation by reducing the high intermolecular forces [8,9].
Due to their natural source, biodegradable starch films present poor mechanical and barrier properties, such as low tensile strength and elongation at break, and high water vapor and oxygen permeability [10]. Incorporation of secondary plasticizers, such as glycerol, is necessary to produce long-lasting films but, on the other hand, negatively affects water barrier properties and tensile strength. However, many ways of improving the mechanical and barrier properties of starch biodegradable films have been proposed in the literature. The most promising solution is the incorporation of nanoclay particles acting as nanofillers on the matrix that form stacked layers. Nanoclays can be classified as smectites, chlorites, kaolinites, illites and halloysites [4]. Negative charges, generated by isomorphic substitution within the interlayer spaces, are neutralized by alkali or alkaline earth cations. Apart from their contribution to improving the mechanical and barrier properties of food packaging materials, nanoclays have been shown to reduce the migration of chemicals from food packaging to food [11]. The most established nanoclay addition technology is organic surface modification, which enhances the intercalation of biopolymers within nanoclay platelets by increasing the interlayer spacing between them [12]. Current trends include the preparation of nanoclay hybrids with carbon nanomaterials and several metal or metal oxide nanoparticles, which increases surface area, heat resilience, loading and strength, and adds additional functionalities [12], and emulsion techniques such nano-emulsion and the Pickering emulsion, which contribute to the homogenous dispersibility of nanoclays in the food packaging matrix [13]. The migration/release of nanoclays from the food packaging material, during the manufacture, use, disposal or weathering because of environmental conditions, is affected by temperature, the polymer/nanoclay interaction, mechanical impact and direct contact with food, and requires further investigation [13]. Finally, the potential toxicity of nanoclays is a research subject that has not been extensively studied due to the fact that the different toxicity profiles of nanoclays and modified nanoclays require a case-by-case evaluation [13]. Among nanoclay particles, montmorillonite (MMT) is the one that is used more frequently due to its low cost, large surface area and high cation exchange capacity [14]. In order to form nanocomposites of MMT–starch, and thus obtain the improved tensile and barrier properties, MMT needs to be intercalated through amylose chains, and this is facilitated by melt or solution intercalation at temperatures above 85 °C [15].
The international protocol of food packaging mechanical testing (ASTM D882), which is used by most packaging industries, subjects the film to tensile stress until disruption at a specific speed and, at the same time, the force needed to strain the film specimen, the distance and the time of the test are monitored. The tensile strength, elongation at break and Young’s modulus can be calculated from the stress–strain plot of the test, among others. Notwithstanding the fact that, with this test, the industry obtains an objective evaluation of the film tensile properties; in reality, the film is stressed in a very different way, meaning that the elongation ranges are substantially lower than the disruptive elongation ranges of the aforementioned test. Consumers reuse packages repeatedly, with different loads for different times and with repeating fatigue cycles [16], thus submitting the package to additive stress in lower elongations compared to the disruptive test and, consequently, this additive stress on the package will lead, after some time, to disruption. It is rational, then, that the food packaging industry, which uses biodegradable starch films, needs to be able to evaluate the stress behavior of these products at a range of stress levels, stress durations and cycles of stress.
When there is available time and space for the maintenance or operation of units, it is possible to adapt a life distribution model to the components over a long period, until the product’s warranty time or even until the end of its life under normal stress conditions. However, when it is impossible to collect sufficient data and, at the same time, a study of the behavior of units under stress conditions (temperature, pressure, electric voltage, humidity, vibration, strength and friction) is sought, then it is necessary to subject some units to increasing levels of stress for a short period of time so that expected failures can be adjusted to a life distribution model. Predicting the failure rate at high stress levels significantly reduces both the experimental time and the minimum necessary sample size of units. However, it is necessary to set the stress correctly at high levels, and the models that bridge the gap between high stress and normal stress are called acceleration models. The next move is to integrate the parameters of life distribution models into models describing the stress effect on the units. The most popular of these are the Arrhenius and Eyring models, and the selection of the most appropriate model that adjusts the data as a result of the units being subjected to stress is statistically estimated by applying either traditional regression (least squares) or, more precisely, by the maximum likelihood estimation (MLE) [17].
Regarding food packaging films, a fatigue cyclic stretching test has only been applied to a nanocellulose hydrogel for refrigerated chicken preservation; nevertheless, the study involved only the presentation of data for different hydrogel compositions, without any attempt to model fatigue behavior [18]. On the contrary, numerous studies have applied fatigue tests to investigate the thermal reliability of thin films that are used as coatings [19] or as parts of electronics packages and devices [20,21,22,23,24] using the reliability testing method [22] or the finite element numerical analysis method [20,21,23,24]. Fatigue models for metallic thin films are typically based either on the stress–cycle curve, in the case of high-cycle fatigue [21], or the Coffin–Manson equation, in the case of low-cycle fatigue [20], although other models—such as the strain envelope evolution model combined with critical fracture strain, in the case of a polyimide thin film [22]; the Engelmaier model, in the case of a film bulk acoustic resonator filter [23]; or the modified Basquin law for non-zero mean stress, in the case of inorganic coatings [19]—have been proposed.
The aim of this study was to evaluate the degradation—fatigue model of several starch biodegradable film treatments and examine the best fit distribution for regression analysis using the elongation level, break cycle and exact break time as fixed factors. Secondly, it tried to obtain better insight into the way that explanatory variables may influence the log tensile quotient (logarithm of the tensile strength to the corresponding break cycle (log[ts/bc])) through the employment of a multiple regression analysis using the forward selection of the most important variables to enter the model at a 0.05 probability level of significance. This combination of two response variables is attempted for the first time in this field. Finally, it should be addressed that it is the first time in the literature that this degradation model is applied on packaging materials.

2. Materials and Methods

2.1. Materials

Starch was isolated from lentils (Lens culinaris) and chickpeas (Cicer aretinum) at a pilot plant scale according to the procedure described in the study of Frangopoulos et al. (2023) [25]. A separate extraction process was carried out for each legume. The extraction method included grinding, seed separation, sieving and sedimentation to clarify and remove impurities. The starches were dried in a lamina air flow tray dryer oven at 30 °C and stored at 25 °C for a week before analysis. The protein of the extracted starches was lower than 1.5%, indicating the purity of the isolated starch. Lentils and chickpeas are both legumes and exhibit similar structural and physical characteristics. Legume starches exhibit a C-type X-ray diffraction pattern [26]. The characteristic “C” pattern of legume starches, including black bean, chickpea and lentil starches, was also reported by Hoover and Ratnayake (2002) [27].
Glycerol was of 99% purity (Carlo Erba Reagents, SPA, Cornaredo, MI, Italy). The nanoclay used was montmorillonite (Bis(hydrogenated tallow alkyl)dimethyl salt with bentonite, <80 nm APS, 99% Purity, 1.98 g/cm3 density, <3% moisture) (Nanocel LG, Punjab, India).

2.2. Film Preparation

Biodegradable starch films with nanoclay were produced via the casting method. Briefly, starch aqueous solutions with different starch and glycerol concentrations were prepared. Also, nanoclay dispersions in water in concentrations up to 1% wt, which were stirred overnight and then sonicated for 15 min at 15,000 kHz, were added to the starch–glycerol mixture in different amounts. Starch aqueous solutions were thermally processed at 80 °C for 30 min on a magnetic stirrer inside a water bath in order to enable the starch gelatinization in the presence of glycerol. The thermoplastic starch was then further heated at 90 °C for 15 min under continuous stirring to achieve efficient intercalation of the nanosilicate sheets into the amylose matrix. Directly after heating, the thermoplastic starch was cast on 18 cm × 11 cm plexiglass trays and dried in an air circulating oven with a range of temperatures between 45 to 50 °C for approximately 24 h. Then the films were peeled off the plates and stored for 10 days at room temperature for moisture equilibration and further analyses. A schematic diagram of the film preparation is presented in Figure 1.

2.3. Thickness

The thickness of the films was measured with a digital electronic caliper (TESA, Brown & Sharpe Instruments, Grand Rapids, MI, USA) and a total of 12 measurements were taken from each film.

2.4. Tensile Properties

The mechanical properties and, more specifically, the tensile strength were determined using stress–strain graphs after tension tests. The tensile properties of the film samples were determined according to ASTM D882-10 [28] standard test methods for tensile properties. Briefly, film specimens were cut with a lancet to strips of 100 mm in length and 15 mm in width and were measured with a texture analyzer (TA-XT Plus, Stable Microsystems Ltd., Godalming, UK) with a 30 kg.f cantilever style loadcell and a cross-head speed (rate of grip separation) of 50 mm min−1. The measurements were performed at ambient temperature (23 °C).

2.5. Experimental Design

Based on preliminary experiments conducted with a definitive screening design (DSD), the best combinations of factors affecting starch biodegradable films’ mechanical and barrier properties were exported based on starch, glycerol and nanoclay concentrations. More specifically, starch biodegradable films containing 4 or 7% wt starch, 35 or 50% wt (on a dry starch basis) glycerol and 1 or 10.5% wt (on a dry starch basis) nanoclay were prepared. These values were chosen based on the optimization of previous experimental results [25]. Moreover, certain facts (e.g., films cannot be formed at starch concentrations higher than 7% wt and the application of these films in ongoing accelerated aging tests of rice at 70 °C for 3 weeks required a glycerol content as high as 50% wt (on a dry starch basis) in order to ensure the film integrity) determined some of these values. The film formulations are depicted in Table 1. Data were treated according to the conventional degradation model in which a stress variable is regressed against the destructive degradation time. A sample of 120 experimental film units for each treatment (see sample ID in Table 1) was subjected to 11 consecutive elongation levels starting from 5% (which was considered as the reference use) to 45% for 1, 3 or 6 stretch cycles that lasted from 1 to 22 min (Table 2). The log tensile quotient (logarithm of the tensile strength to the corresponding break cycle (log[ts/bc])) was the recorded stress variable, and the log exact break time that a unit broke was recorded as the exact break time corresponding to a particular elongation level. Also, the break cycle was recorded as the stretch cycles that a film unit survived until break. The elongation levels were further redefined to four meaningful groups, thus facilitating the formation of four regression lines in the degradation model. The effect of sample ID was also embedded in the degradation analysis using specific graphs.
To obtain better insight into the way the aforesaid explanatory variables may influence the log tensile quotient, a multiple regression analysis was employed using the forward selection of the most important variables to enter the model at a 0.05 probability level of significance.

3. Results and Discussion

The mechanical properties, water vapor permeability, optical properties, antimicrobial activity and biodegradability of these films have been analyzed in a previous study [25]. Table 3 presents the range of the thickness of the films that were tested in the present study.
As Table 2 and Figure 2 indicate, 11 elongation levels were used in the analysis, but, for reasons of expediency, 4 groups were chosen based on the ranges extended by the 3 mode frequencies of the exactly broken units per level, leaving only the level 5%: 8–14%, 15–20% and 23–45%. Of course, as would be expected when elongation is at high levels, meaning that external displacement increases, the deformation zone increases and the fracture of films inevitably occurs [29].
Both variables of the destructive degradation process were logarithmized to produce a better linear fit (b = 0.244, determined R2 = 0.485, p < 0.001), expressing a decline of the log tensile quotient as the log exact break time increased (Figure 3). Four regression lines were also embedded in the graph after separating the data in the four elongation groups. By consulting the regression slopes, it was deduced that the log tensile quotient declined more abruptly as the elongation groups decreased in size range. This decrease was particularly observed in the first two ranges (8–14% and 15–20%), whose 95% confidence intervals did not overlap with the other groups. It is worth mentioning the doubly steep descent of the reference elongation level 5% (b = 0.536) as compared to the highest ranges and the significant delayed time that elapsed until the first units commenced breaking (greater than 54.6 s, corresponding to antilog(4)), which is understandable due to the low stress intensity and the significant contribution of the break cycle.
More specifically, it can be observed in Figure 3 that there were very few ruptured films at low log exact break time values and low break cycles related to the elongation group 5%. Most of the destructed films at this elongation group existed at high break cycles and high log exact break times, which dragged the model line to a steeper trend. Generally, the stress levels that starch biodegradable films are subjected to should be at low levels, as is highlighted in other studies [30,31].
As the log exact break time increased, the level of break cycle also increased, reaching maxima approximately in the area confined by 5–9 log times and lower than 1 log tensile quotient, which means that the high-cycle force at levels within the elastic deformation caused a lesser degradation effect to the films than the intense low-cycle force and, eventually, increased the biodegradable starch film shelf life [32]. When the sample ID variable is involved in the analysis, some interesting observations are noted (Figure 4). More specifically, the sample 7_35_10.5 showed the most versatile capabilities, expanding over the whole range of the log tensile quotient, and was the treatment that had the most films that survived to the higher log tensile quotient values and higher log exact break time intervals compared to the other treatments. Moreover, it can be seen from Figure 5—which is an alternative version of the previous findings where the 95% confidence intervals per sample are deployed over the increasing range scale of log exact break time—that at all log exact break time intervals, the treatment 7_35_10.5 had the highest log tensile quotient. This treatment had a higher percentage of nanoclay and starch and the lowest percentage of glycerol. On the contrary, the samples 4_50_1 and 7_50_1 achieved the lowest log tensile quotients at all log exact break time intervals (Figure 5). Finally, the sample 7_50_10.5 exhibited the lowest expanding range over the log tensile quotient (Figure 4), thus showing the least response of potential effects and thereby being the least acceptable. These two treatments had the highest glycerol and nanoclay concentration, and the higher glycerol and lowest nanoclay concentration, respectively. Thus, it can be deducted that glycerol and nanoclay had an important influence on the films’ tensile properties and, more specifically, that increasing the nanoclay and decreasing the glycerol concentrations led to the increment of the films’ tensile strength. However, this also led to the decreasing of the films’ extensibility, which can be observed from the fact that the films with higher nanoclay and lower glycerol concentrations had more units that broke in the short log exact break time (Figure 4). Τhe increase in tensile strength induced by the addition of nanoclay and, on the other hand, the increase in elongation at break induced by increasing the glycerol content has also been observed in the work of Muller et al. (2014) [33]. The explanations for these phenomena are the roles of glycerol as a secondary plasticizer and its interaction with water, which reduces intermolecular forces, and nanoclay particles as junction zones that make the film matrix stronger [34].
Glycerol, which acts as a secondary plasticizer, interacts with water, causing a reduction in intramolecular forces and, consequently, a reduction in the tensile strength values and an increase in the elongation at break values.
Moreover, the maximal break cycle level appeared below the 0.5 log tensile quotient, therefore indicating that a great, time-independent resistance until failure occurred in parallel with higher break cycles. This also indicates that a long-lasting tensile load, applied consecutively and for equal durations, decreases the films’ tensile strength. The negative impact of cyclic loading of stress on polymeric materials’ tensile properties was investigated by Yashiro et al. (2010) [35], who reported that moderate cyclic stress loading on amorphous polyethylene causes decreasing stiffness and increasing plastic flow deformation. This gradual deformation of polymeric materials, like starch films with montmorillonite, under a steady stress load is called “creep deformation” [36].
Three explanatory variables entered the multiple regression model, explaining 74% of the total variation and, in decreasing order of importance: break cycle 51.6%, sample ID 16.2% and log exact break time 5.7%, while the elongation level was rejected from the model as not important. The reliability of the model is depicted in the plot created by the actual vs. predicted values (Figure 6a), and the scattered position of the residuals vs. the log tensile quotient (Figure 6b) indicates the variance homogeneity in the model. In Figure 6a, the 95% confidence intervals do not cross the horizontal line, and in Figure 6b, the points are evenly scattered around the horizontal line without outliers (values > 2 standardized residuals), indicating an adequate homogeneity of variance.
The regression model revealed an important prediction profile of the variables’ effects (Figure 7). The log tensile quotient decreased gradually as the log exact break time and break cycle increased, favoring the highest log tensile quotient values in the sample 7_35_10.5. The latter achieved a 3.91 log tensile quotient at a 4.73 log exact break time (antiloged 113 s) and at 3 break cycles. Furthermore, according to Tukey’s pairwise mean differences between sample IDs based on the error mean square of the ANOVA model, it possessed the highest mean value in the pattern of decreasing mean values (Table 4): 7_35_10.5 > 7_35_1 > 7_50_1 > 7_50_10.5 = 4_50_1.
Additionally, the treatment with the lowest least square means (LSM) was the sample 4_50_1, which, in combination with the almost inexistent higher break cycle levels (Figure 4), leads to the conclusion that it was the most vulnerable to premature rupture and had the poorest resistance to stress. These observations are mostly caused by the improving effect of the MMT addition on the structure and tensile properties of starch films at these levels of incorporation [34,37]. Also, the high glycerol content (%wt) based on dry starch weakens tensile properties through a reduction in intramolecular forces inside the amylose matrix induced by glycerol, which acts as a secondary plasticizer, leading to lower tensile strength, eventually [34,38]. Additionally, the very low starch concentration of this treatment reflects a weak amylose matrix, which, of course, has an impact on a film’s integrity and stiffness, as has also been observed in the literature [39].
Finally, an attempt was made to configurate the prediction profile of the most resistant sample (7_35_10.5) according to the log tensile quotient by entering the log exact break time 4.73 and increasing the level of the break cycle from 1 to 6 (Table 5). In general, the decreasing trend of the log tensile quotient, which indicates the mechanical resistance of films, in high log exact break times and break cycles is possibly attributed to the material fatigue effect after cyclic loads at a fixed frequency. This process, which generally comprises two steps, namely, initiation and propagation, involves changes on the microstructural level of the material, such as the generation of microcracks or other inhomogeneities, which occur at very low stress levels and, of course, below the ultimate tensile strength. Subsequently, the evolution and spread of these microflaws in the remaining material through repeated stretch cycles induces the weakening of the integrity and strength of the material and, inevitably, its fracture at low stress levels [40,41].
As discussed in the Introduction, data from fatigue tests have been modeled using other methods, such as the reliability testing method or the finite element numerical analysis method. Definitely, these methods analyze events at a microscale level using elaborate approaches, such as continuum damage mechanics, cohesive zone model elements and truss elements [42], and generate valuable data that can correlate microstructures with material behaviors. It should be mentioned, though, that statistical analysis is not necessarily applied to validate the reliability of these complicated models. In this study, we presented a simplistic and readily understandable approach that could be used as a tool to quickly produce information on fatigue behavior related to sample composition and experimental factors without requiring expertise in modeling, specialized software and computing power.

4. Conclusions

The aim of this study was to evaluate the degradation—fatigue model of several starch biodegradable film treatments with nanoclay and examine the best fit distribution for the regression analysis using the elongation level, break cycle and exact break time as fixed factors. Generally, it can be seen that the combination of low starch and nanoclay concentrations and a high glycerol concentration produced a weak film with a short lifespan and high vulnerability, whereas, when starch and nanoclay concentrations increased and glycerol decreased, the stiffness was maximized and the film units withstood long-term cyclic stresses more efficiently. Summarizing, it could be deducted that the present tool is useful to evaluate the stress fatigue and behavior of starch biodegradable films at different stress durations and life cycles and can be used to predict the optimum ranges of stress and fatigue cycles to increase the shelf life of biodegradable packaging materials based on starch. Future research directions should focus on industrial fields related to the degradation of biodegradable packaging materials under human and weather stress conditions such as temperature, humidity and UV exposure.

Author Contributions

Conceptualization, D.P. and V.K.; methodology, D.P. and V.K.; validation, D.P., V.K. and T.F.; formal analysis, T.F. and D.P.; investigation, T.F., S.D., J.O., A.M. and A.G.; resources, V.K., A.G. and D.P.; writing—original draft preparation, T.F. and D.P.; writing—review and editing, V.K. and D.P.; visualization, T.F.; supervision, V.K. and D.P.; project administration, V.K.; funding acquisition, V.K. All authors have read and agreed to the published version of the manuscript.

Funding

The authors would like to acknowledge the financial support from the “StActBioFP” (#Τ6ΥΒΠ-00270) research program funded by the European Union’s European Regional Development Fund and the Operational Program “Competitiveness, Entrepreneurship & Innovation” (EPAnEK) of the Partnership and Cooperation Agreement (NSRF) for the period 2014–2020.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article, and further inquiries can be directed to the corresponding authors.

Conflicts of Interest

The authors declare no conflicts of interest.

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Applsci 14 07728 g001
Figure 1. Schematic diagram of film preparation.
Figure 1. Schematic diagram of film preparation.
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Figure 2. Frequency distribution of the experimental units based on the elongation level (%).
Figure 2. Frequency distribution of the experimental units based on the elongation level (%).
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Figure 3. Degradation model plot of the log tensile quotient against log exact break time overlaid by the 4 elongation groups and the 3 break cycle levels, including the regression lines with 95% confidence bands.
Figure 3. Degradation model plot of the log tensile quotient against log exact break time overlaid by the 4 elongation groups and the 3 break cycle levels, including the regression lines with 95% confidence bands.
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Figure 4. Scatter plot of the log tensile quotient vs. sample ID overlaid by the 5 increasing levels of log exact break time and 3 levels of break cycle. Horizontal lines denote the means of the exact break time levels.
Figure 4. Scatter plot of the log tensile quotient vs. sample ID overlaid by the 5 increasing levels of log exact break time and 3 levels of break cycle. Horizontal lines denote the means of the exact break time levels.
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Figure 5. Mean changes and 95% confidence intervals of the log tensile quotient vs. sample ID along with the 5 increasing levels of log exact break time and the 3 increasing levels of break cycle. Error bars denote the 95% confidence intervals and means; those whose intervals do not overlap differ significantly.
Figure 5. Mean changes and 95% confidence intervals of the log tensile quotient vs. sample ID along with the 5 increasing levels of log exact break time and the 3 increasing levels of break cycle. Error bars denote the 95% confidence intervals and means; those whose intervals do not overlap differ significantly.
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Figure 6. Reliability of the regression model (red line ± 95% confidence band) explaining total variation. (a) Plot of actual vs. predicted values of the log tensile quotient. (b) Plot of residuals vs. predicted values of the log tensile quotient.
Figure 6. Reliability of the regression model (red line ± 95% confidence band) explaining total variation. (a) Plot of actual vs. predicted values of the log tensile quotient. (b) Plot of residuals vs. predicted values of the log tensile quotient.
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Figure 7. Prediction profile of the log tensile quotient as affected by log exact break time, break cycle levels and sample ID.
Figure 7. Prediction profile of the log tensile quotient as affected by log exact break time, break cycle levels and sample ID.
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Table 1. Formulation of film samples based on starch, glycerol and nanoclay concentrations.
Table 1. Formulation of film samples based on starch, glycerol and nanoclay concentrations.
Sample IDStarch Concentration (%wt)Glycerol Concentration (%wt) *Nanoclay Concentration (%wt) *
7_50_17501
4_50_14501
7_35_17351
7_50_10.575010.5
7_35_10.573510.5
* Glycerol and nanoclay concentrations were calculated on a dry starch basis.
Table 2. Experimental design of combinations based on stress time, number of stretch cycles and elongation level.
Table 2. Experimental design of combinations based on stress time, number of stretch cycles and elongation level.
Elongation Level (%)
Stretch CycleStress Time (min)58121415161820232545
1111111111111
411111111111
711111111111
1011111111111
1311111111111
1611111111111
1911111111111
2211111111111
3111111111111
411111111111
711111111111
1011111111111
1311111111111
1611111111111
1911111111111
2211111111111
6111111111111
411111111111
711111111111
1011111111111
1311111111111
1611111111111
1911111111111
2211111111111
Table 3. Thickness of the films.
Table 3. Thickness of the films.
Sample IDMean Thickness (Range) (mm)
7_50_10.21 (0.19–0.22)
4_50_10.11 (0.09–0.12)
7_35_10.20 (0.19–0.21)
7_50_10.50.23 (0.22–0.25)
7_35_10.50.23 (0.22–0.24)
Table 4. Tukey’s grouping of sample IDs based on the error mean square of the ANOVA regression model. Samples not sharing the same letter are significantly different.
Table 4. Tukey’s grouping of sample IDs based on the error mean square of the ANOVA regression model. Samples not sharing the same letter are significantly different.
Sample ID LSMLower 95%Upper 95%
7_35_10.5A 1.771.711.83
7_35_1 B 1.621.541.69
7_50_1 C 1.441.351.53
7_50_10.5 D1.241.161.32
4_50_1 D1.101.001.19
Table 5. Log tensile quotient of sample 7_35_10.5 in a fixed log exact break time at different break cycles.
Table 5. Log tensile quotient of sample 7_35_10.5 in a fixed log exact break time at different break cycles.
Log [Exact Break Time]Break Cyclelog[ts/bc]log[ts/bc]
Lower CI		log[ts/bc]
Upper CI
4.7317.116.637.63
4.7325.274.955.62
4.7333.913.604.25
4.7342.902.583.26
4.7352.151.832.52
4.7361.591.301.95
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MDPI and ACS Style

Frangopoulos, T.; Dimitriadou, S.; Ozuni, J.; Marinopoulou, A.; Goulas, A.; Petridis, D.; Karageorgiou, V. Assessing the Fatigue Stress Behavior of Starch Biodegradable Films with Nanoclay Using Accelerated Survival Test Methods. Appl. Sci. 2024, 14, 7728. https://doi.org/10.3390/app14177728

AMA Style

Frangopoulos T, Dimitriadou S, Ozuni J, Marinopoulou A, Goulas A, Petridis D, Karageorgiou V. Assessing the Fatigue Stress Behavior of Starch Biodegradable Films with Nanoclay Using Accelerated Survival Test Methods. Applied Sciences. 2024; 14(17):7728. https://doi.org/10.3390/app14177728

Chicago/Turabian Style

Frangopoulos, Theofilos, Sophia Dimitriadou, Joanis Ozuni, Anna Marinopoulou, Athanasios Goulas, Dimitrios Petridis, and Vassilis Karageorgiou. 2024. "Assessing the Fatigue Stress Behavior of Starch Biodegradable Films with Nanoclay Using Accelerated Survival Test Methods" Applied Sciences 14, no. 17: 7728. https://doi.org/10.3390/app14177728

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