The Strengthening and Toughening of Biodegradable Poly (Lactic Acid) Using the SiO2-PBA Core–Shell Nanoparticle

The balance of strengthening and toughening of poly (lactic acid) (PLA) has been an intractable challenge of PLA nanocomposite development for many years. In this paper, core–shell nanoparticles consisting of a silica rigid core and poly (butyl acrylate) (PBA) flexible shell were incorporated to achieve the simultaneous enhancement of the strength and toughness of PLA. The effect of core–shell nanoparticles on the tensile, flexural and Charpy impact properties of PLA nanocomposite were experimentally investigated. Scanning electron microscopy (SEM) and small-angle X-ray scattering (SAXS) measurements were performed to investigate the toughening mechanisms of nanocomposites. The experimental results showed that the addition of core–shell nanoparticles can improve the stiffness and strength of PLA. Meanwhile, its elongation at break, tensile toughness and impact resistance were enhanced simultaneously. These observations can be attributed to the cavitation of the flexible shell in core–shell nanoparticles and the resultant shear yielding of the matrix. In addition, a three-dimensional finite element model was also proposed to illustrate the damage processes of core–shell nanoparticle-reinforced polymer composites. It was found that, compared with the experimental performance, the proposed micromechanical model is favorable to illustrate the mechanical behavior of nanocomposites.

grafting of the PBA polymer onto silica nanoparticle.

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In core-shell particle reinforced PLA model, the poly (n-butyl acrylate) shell is set as an isotropic 37 hyperelastic material, which exhibits very large strain and a strong non-linear stress-strain behavior.

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Hyperelastic material model is derived from a strain-energy density function

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The polymer matrix shows a rather brittle fracture behavior in uniaxial tension, but it shows 50 considerable plastic deformation in compression and pure shear [6][7][8]. Thus, the matrix is assumed 51 to behave as an elastic-plastic solid, moreover, it is found that the behavior of polymers is sensitive 52 to the hydrostatic pressure [9]. These characteristics can be captured via Mohr-Coulomb or Drucker-

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Prager yield criterion [10]. However, the Drucker-Prager criterion with circular cone yield surface is 54 more attractive in the numerical implementation than the Mohr-Coulomb criterion with hexagonal 55 cone yield surface, since it has a continuously varying normal [11]. Furthermore, the parameters of model. So, the extended linear Drucker-Prager model is employed to the matrix in this study, which 58 can be expressed as: where p is the hydrostatic stress, q is the Mises equivalent stress, r is the third invariant of deviatoric stress, β is the slope of the linear yield surface in the p -t stress plane, d is the cohesion of the material,

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and k is the ratio of the yield stress in triaxial tension to the yield stress in triaxial compression.

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The slope of β and yield stress ration of k can be determined by the following equations: where  is the internal friction angle of material, which is generally set as 15 o to represent the 64 polymer matrix [12], so it can obtain β=29.5 o , k=0.84.

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The matrix cohesion of d can be defined by the uniaxial tension strength t  : From the Equation (6)

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The criterion for damage initiation is met when the following condition is satisfied: where D  is a state variable that increases monotonically with the plastic deformation.

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After the onset of damage, the damage evolution is performed by a progressive failure 77 procedure, the stress-strain behavior of which is illustrated in Figure S3a. The solid curve in the figure   78 represents the damaged stress-strain response, while the dashed curve is the response in the absence      . The elastic stiffness of the interface element, K, is set as 10 8 GPa/mm in this 105 paper to ensure the displacement continuity around the particle at interface in absence of damage

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The degradation process of interface element will be initiated when its stresses and/or strains 108 satisfy certain damage initiation criteria. Here, the quadratic stress failure criterion is considered for 109 the damage onset of cohesive element, which can be represented as: where is the Macaulay brackets, which return the argument if positive and zero otherwise, to 111 impede the development of damage when the interface is under compression.
To describe the evolution of damage under a combination of normal and shear deformation across the interface, an effective displacement, m  is introduced: For computational convenience, the linear form of damage evolution law is based on effective