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Introduction

Fiber-reinforced dental composites are used as dentinal replacements and are expected to perform as reliable substitute materials under the masticatory loads experienced in the mouth. Conventionally, dental composite contains reinforcing particulates in nano-, micro-, and macro-scale lengths in a resin matrix [ ]. The fillers significantly influence mechanical properties, contribute to isotropy, and supply sufficient strength as an essential requirement for restorative materials [ , ]. Furthermore, dental materials must possess fracture toughness or the ability to resist fracture [ ]. It is here that short fiber-reinforced composites (SFRC) demonstrate completely different toughening mechanisms from their particulate reinforced (PRC) conventional counterparts. The interactions between the high aspect-ratio fibers (with potential anisotropy with alignment) with the resin matrix contribute to rising fracture toughness values with crack extension [ , ].

During crack propagation, there are notably four contributions to the toughening of SFRC; strain energy stored in the fiber over the debond length contributing to elastic bridging, residual strain energy over the debond length which has a negative contribution to toughening when the fiber breaks/degrades, the energy creating the debond fracture surface, and the frictional energy in fiber pull out [ ]. Additionally, in a tradeoff between strength and toughness, the interface between fiber and matrix also plays an essential role in how the propagating crack moves. If the interface is too strong, the composite itself acts as a rigid, brittle material, and the high loads needed to overcome the glass fibers will cause fiber fracture. On the contrary, if this interface is too weak, fibers pull out without much frictional resistance, and the composite will exhibit overall low strength and low toughness [ , ]. However, at the right balance, optimal interfaces can be achieved to maximize the frictional resistance, dissipating energy through shear interfacial forces and effectively diminishing the crack advancing forces felt at the crack tip [ ].

We can use fracture mechanics to evaluate the material response to an existing crack. Linear-elastic fracture mechanics (LEFM) is used in the case of brittle materials; it is given as the critical stress intensity factor K _c or the critical energy release rate G _c . LEFM is widely used to characterize the localized stress at the crack tip in materials displaying a linear-elastic fracture response. LEFM is then not applicable in characterizing materials with larger process zones as it fails to account for the energy lost in plastic deformation. Instead, one applies elastic-plastic fracture mechanics (EPFM), which is commonly given by the path-independent line integral – J integral , and the essential work of fracture (EWF). Both EPFM methods are derived experimentally by calculating the area under the load-displacement curves, or work done; however, the difference is in testing methods and energy partitioning. J-integral is calculated as the potential energy difference between specimens with different crack lengths, which requires detection of cracking onset followed by test interruption. At each loading cycle, each load-displacement curve is partitioned into elastic and plastic components adhered to under ASTM E1820 [ ], resulting in the calculation of the critical energy release rate under mode 1 loading conditions, J _1c from the J _R – Δ a resistance curve (r-curve) [ ].

On the other hand, EWF originated from the idea of an inner autonomous region around the crack tip requiring increasing energy input to sustain crack growth, as the energy increasingly dissipates through the outer region [ ]. The inner region is energy partitioned as the essential work (W _e ), and the outer region is coined as the non-essential or plastic work (W _p ) component. The idea is that EWF partitions in the calculation of the specific essential work of fracture which is an inherent material property unaffected by specimen dimension or crack length, and simultaneously determines the plastic work as a function of ligament length (or uncracked portion of the specimen) [ , ]. Unlike the J-integral values requiring periodic test interruption for crack measurement, EWF values are derived experimentally by running a complete uninterrupted test of the specimen with different ligament lengths until failure. The total area under the load-displacement curve is the total work of fracture (W _f ).

SFRC materials, although composed of two constituents that would qualify individually for LEFM, are structured in a way that large amounts of energy are dissipated through fiber interactions as a pre-existing crack is loaded. Fracture mechanics of SFRC are better suited with EPFM. Previously, we measured the r-curve behavior of fiber-reinforced composites [ ], determined that different r-curves are created when fibers are aligned or randomly oriented [ ] and that the fiber-matrix interface is unaffected by water hydration [ ]. Fibers are known to be harmful to the lungs if inhaled due to their length and aspect ratio [ ]; therefore, it is precautionary to cover SFRC with a PRC material and prevent exposure to the oral environment. In practice, SFRC is confined to a finite space within a tooth cavity. Therefore it is of significance to understand the fracture mechanics in terms of thickness of SFRC and the thickness of the PRC covering of which is mandated for its use. As such, sufficient insight into the cover thicknesses and interface mechanisms to advancing cracks has not been effectively realized. Here we use the EWF method, as the conventional term ‘ligament’ translates to the clinical term ‘thickness’ of the SFRC and will hereafter be referred to as thickness. Therefore, this study investigates the thickness influence of the PRC material when veneered on the aligned SFRC using the EWF method. Moreover, we provide a discussion on the interface between the two composites, how it relates to clinical practice, and the feasibility and validity of our attempt to create an anisotropic structure with aligning fibers.

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Methods