**1. Introduction**

In the last years a growing interest towards the development of new advanced biobased polymeric products that are sustainable, eco-friendly, eco-efficient and biodegradable has arisen for proposing valid alternatives in the global market, that is at present mainly dominated by petroleum-derived products. Thanks to new governments regulations not only researchers but also industries are seeking for more ecologically and friendly materials [1–3]. There are several market branches extremely valuable for biodegradable plastic materials such as single use items and those applications where collection and recycling are difficultly achieved, and then for a correct waste management compostability becomes an advantage; for this reason, it is expected that the biodegradable and biobased polymer market will increase in the coming years [4,5].

In this context, among biobased and biodegradable matrices which are industrially compostable and commercially available on the market, poly(lactic acid) (PLA) is one of the most attractive due to its relatively low production cost compared to other biobased polymers [6,7]. PLA exhibits very interesting mechanical properties (about 3 GPa as Young's modulus, 60 MPa as tensile strength and an elongation at break between 3–6%) [8,9]; however, it also presents some drawbacks to be overcome to reach end-users demands. In particular, PLA is very stiff and brittle and for this reason the addition of plasticizers and/or rubber particles is often required to enhance its elongation at break and tensile toughness [10–13].

An economic and assessed method to tune polymeric matrix properties is the polymers blending [14]. In literature many flexible biobased polymers have been successfully blended with PLA such as: poly(butylene succinate) (PBS) [15–17], poly(butylene succinate-*co*adipate) (PBSA) [18–20], polycaprolactone (PCL) [21–23] and poly(butylene adipate-*co*terephthalate) (PBAT) [24,25].

**Citation:** Aliotta, L.; Vannozzi, A.; Cinelli, P.; Coltelli, M.-B.; Lazzeri, A. Essential Work of Fracture and Evaluation of the Interfacial Adhesion of Plasticized PLA/PBSA Blends with the Addition of Wheat Bran By-Product. *Polymers* **2022**, *14*, 615. https://doi.org/10.3390/ polym14030615

Academic Editor: Jose-Ramon Sarasua

Received: 18 January 2022 Accepted: 1 February 2022 Published: 4 February 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In this article, on the basis of a previous study [18], a PLA/PBSA blend containing 60 wt.% of PLA and 40 wt.% of PBSA was selected as matrix due to its good flexibility and fracture properties. To this binary blend a by-product natural filler has been added. It is generally expected that the main address for a composite material is to exhibit enhanced physical and mechanical properties when it is compared to its individual components [26]. Nevertheless, in the case of very short fiber or particulate composites, the fibers cannot bear efficiently the load and their randomly orientation does not allow specific reinforcements along the fibers direction. In this case the benefit is related to the cost savings, lighter product weight, valorization of waste products and degradability promotion (in particular the final product disintegration) [27–31].

In response to the demand for extending biobased polymers applications while reducing the final materials cost, different studies are present in literature where the incorporation of low-cost and highly-available natural fillers and short fibers (derived from agricultural and or industrial waste) into a biobased polymeric matrices has been investigated [32–35]. More research is ongoing to optimize the valorization of agriculture residues as fillers in bio-composites. At this purpose, due to the large amount of grain by-products generated by the main food production, bran is very interesting due to its low cost and wide availability and it is a relevant cellulosic based filler for bioplastic production [36–39].

To improve the filler dispersion in the polymeric matrix and at the same time to counterbalance the stiffening effect caused by the bran addition, also improving the processability, a plasticizer was added. In particular, Triacetin was added considering the very interesting results found in literature in which Triacetin was added as plasticizer in natural fiber composites [40–42]. Ibrahim et al. [1], for example, demonstrated that PLA biocomposites with good mechanical and thermomechanical properties can be obtained using kenaf bast fiber as reinforcement and Triacetin as plasticizer. Furthermore, Pelegrini et al. [43] observed that Triacetin is a good processing aid and coupling agent that does not influence negatively the PLA biocomposites degradation.

In this study, after a preliminary characterization of wheat bran in which its granulometry and aspect ratio was determined; the effect due to the addition of different bran amount (from 10 to 30 wt.%) in a PLA/PBSA based polymeric matrix (plasticized with a fixed amount of Triacetin) was studied. Analytical models were applied in order to predict the mechanical characteristics and the interface adhesion between fibers and matrix that is fundamental to understand the interactions existing between the bran particles and the surrounding matrix. The mechanical properties, in fact, are connected to the fiber and matrix strengths, to the fibers distribution and to the interfacial shear strength (IFSS or τ) [6,27,44,45]. The last parameter, IFSS, is strictly related to different factors such as the interface thickness, the adhesion strength and the energy surface filler [27,46,47]. An IFSS good evaluation was obtained by the application of analytical models based on static and dynamical mechanical tests. Furthermore, for the first time for this biocomposites typology, the fracture toughness and crack resistance were investigated by the essential work of fracture (EWF) approach [48].
