**1. Introduction**

Physical polymeric blends, constituted by a rubbery phase embedded in a more rigid matrix, are a long-lasting route for the preparation of new materials with a modulated balance of properties [1]. The advent of biobased and biodegradable polymers could positively affect the environmental profile of products, thanks to an improved carbon neutrality with respect to fossil-based counterparts and a more environmentally friendly end of life [2–4]. The increased interest towards biopolymers has resulted in a revival of blending technology and, in order to exploit their potential and enter new markets, the study of these materials is at the center of scientific research [5]. Improved knowledge of the mechanical behavior of biobased materials is fundamental for better exploiting their peculiar properties and comparing them with fossil-based ones, favoring the replacement of the latter in several application sectors.

In this context, it is beneficial to investigate micromechanical deformation processes that occur in physical polymeric blends, knowing that external stresses can be the cause of the starting point of numerous micromechanical deformation processes that play a critical role regarding the failure of pure heterogeneous systems [6]. The two basic micromechanical deformation processes in pure polymers are shear yielding and crazing [7], while in multiphase systems, it can also be active debonding and cavitation [8]. The debonding mechanism involves the formation of cavities/voids at the interface between the rubber

**Citation:** Aliotta, L.; Gigante, V.; Coltelli, M.-B.; Lazzeri, A. Volume Change during Creep and Micromechanical Deformation Processes in PLA–PBSA Binary Blends. *Polymers* **2021**, *13*, 2379. https://doi.org/10.3390/ polym13142379

Academic Editor: Andreia F. Sousa

Received: 29 June 2021 Accepted: 16 July 2021 Published: 20 July 2021

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phase and the matrix, while void formation occurring internally to the rubber particles is known as cavitation [9]. The expansion of the cavities occurs when the volumetric strain energy is greater than that required for the creation of the void surface area [10]. The parameter governing the cavitation or debonding mechanism is the value of the polymer/rubber interfacial adhesion: high adhesion values contribute to the internal cavitation of the rubber particles, while low values contribute to the debonding mechanism [11]. It is important to state that micromechanical deformations are competitive processes, the prevailing one is determined by the inherent properties of the matrix polymer and by local stress distribution [12]. The role and importance of void formation within or around the rubber particles in polymer blends are still not clear, but they have been at the center of academic interest in material science [13–16]. On the basis of energy balances, Lazzeri and Bucknall [17,18] developed the idea that cavitation/debonding of rubber particles arises at the crack tip and can be the cause of dilatational shear yielding and/or crazing in the matrix. The following matrix distortion is not homogeneous and becomes highly localized due to the formation of bands of voids and sheared material called "dilatational shear bands" or more simply "dilatational bands". The effect of cavitation is a local decreasing of the bulk modulus and hydrostatic stress components near the void and a corresponding growth of the stress deviatoric component. Higher elastic energy may then cause a faster advance of shear bands and, thus, a larger plastic zone form is attained [19].

In order to understand the micromechanical deformation processes that occur in particular polymeric blends, measurements and analysis of the volume change during uniaxial tensile or creep tests can lead to a better understanding of the deformation phenomena [20,21]. In particular, the theories existing in literature state that during shear yielding, the volume of the sample remains constant, while crazing, debonding, and cavitation are characterized by the increase in volume strain [22]. To make a "quantitative evaluation" of the deformation mechanisms effective in rubber-toughened systems, dilatometric studies of tensile creep have been carried out as function of the tensile stress or strain prior to fracture [23].

During uniaxial tensile testing, after that the rubber particles generate voids (by cavitation and or debonding), the voids elongate as the specimen extends. Generally, debonding or cavitation occurs before yielding [24]. The void growth mechanism is a second and successive deformation process that causes great differences in volume variation. Since this process occurs after yielding and it is in common to both cavitation and debonding phenomena, very interesting are creep studies in which different stress levels (below the yield stress) are investigated in order to identify the stress level for which the debonding or cavitation process begins.

In tensile creep experiments, the onset of dilatational yielding goes with a rapid increase in deformation; for this reason, the void volume will increase with strain in addition to the volume change of the matrix itself [20]. To avoid the drawbacks of mechanical extensometers, which include range limitations, recently video-controlled tensile testing equipment has been developed by G'Sell et al. [25,26] to optically evaluate the volumetric strain.

The abovementioned important concepts have been tested and developed on conventional polymeric systems; however, to the best of our knowledge, they have not been extensively explored on biopolymeric blends. In particular, coupling between the dilatometric volume measurement with an optical system performed in real time during creep tests of a biopolymeric blend is a novelty.

The present paper, starting from one of the author's own experience [27,28], aimed to explore the micromechanical deformation mechanisms of blends based on polylactic acid (PLA) and polybutylene succinate adipate (PBSA). These blends were recently considered for their potential use in packaging and personal care/sanitary applications [29], hence, in sectors where products have a short life thus highly contributing to the production of enormous amounts of waste [30]. In this paper, two formulations were studied in which PBSA was introduced at 15 and 20 wt.%, respectively.

Krishnan et al. [31], LeBarbe [32], and Nagarjan et al. [33] published exhaustive reviews regarding the problem of PLA toughening and the necessity of increasing the ductility without losing too many of the characteristics that make PLA interesting, i.e., high elastic modulus, good processability, high tensile strength (without forgetting biodegradability and biobased content).

In any case, while different researchers have investigated PLA toughened with biodegradable rubber, in which they stated that certainly the size of the dispersed particles, together with the quality of interfacial adhesion, determines the final toughening effect in PLA [34–40], only a few papers studied the short-time creep behavior of PLA-based blends [41–43], and none of them addressed the issue of relating micromechanical deformation phenomena with volumetric dilatometric variations from creep tests. For this reason, in this work, measurements of the volume strain, using an optical extensometer, were conducted with a universal testing machine in creep configuration to determine, accompanied by SEM images, the micromechanical deformation processes involved in a biopolymeric blend system.

Analytical models were also applied in order to correlate the creep to the dilatation variation; in particular, the Andrade equation [8] was applied and the *b* parameter for the polymeric systems was calculated. Plotting the *log b* against the applied stress, using an Eyring plot, a significant change in the curves was found, and it coincided with the onset of the cavitation/debonding mechanism. Furthermore, knowing the data of the pure matrix, from the Eyring relationship, the apparent stress concentration factor was calculated for the PLA binary blends with 15 and 20 wt.% of PBSA.
