**1. Introduction**

Three-dimensional printing (3D) has increasingly become one of the prevalent manufacturing methods for the development of tools and functional parts, particularly in the sectors entailing extensive customization, such as medical and aerospace [1–3]. However, there are currently various types of 3D printing techniques, including fused deposition modeling (FDM), stereolithography (SLA), and multi-jet fusion (MJF) that bring quite a number of uncertainties to the prediction of the outcome based on the mechanical engineering concepts [4,5].

Generally, 3D-printed parts fabricated by di fferent techniques di ffer in terms of strength, sti ffness, microstructure and material properties, so that it is necessary to investigate their behaviors through both experimental tests and finite element analysis (FEA) [6–10]. Fused deposition modeling 3D printing has shown promising capabilities to improve the specific mechanical properties of parts—such as fracture toughness—by optimization of extrusion deposition trajectories [11]. It is reported that the filament direction optimization contributed to a large deformation zone leading to "ductile-like behavior", which subsequently caused a slow crack propagation rate [9]. Also, using 3D printing for developing co-continuous composite or interpenetrating phase composite parts proved a significant increase of damage tolerance and fracture toughness compared to conventionally manufacture composite parts [12]. Rationally designed interpenetrating architectures enabled implementing diverse techniques of crack-deflection and crack-bridging to enhance fracture resistance in 3D-printed composites. Mechanical reliability is an essential aspect of various engineering applications. Catastrophic failures often occur due to unstable crack propagations and therefore, study of fracture of components is a vital component of engineering design. In this respect, to address the fracture behavior of 3D-printed

plastic components we used FDM and MJF techniques to manufacture notched samples and supported the experimental observations with a failure model.

Pre-existing cracks in di fferent materials can be induced by various circumstances. For instance, in composite materials defects can inadvertently be produced in the service life and also during the manufacturing process [13]. In ductile materials, cracks that originate from surface imperfections or notches often grow slowly, accompanied by significant plastic deformation. However, the rate of crack growth accelerates with the progressively increasing applied stresses [14].

A reliable method for evaluating the notched ductile parts before using them in real applications, i.e., grooves, threads, and shaft holes, was developed through fracture toughness experiments [15]. In earlier studies, mode I and mixed mode conditions have been practically used to determine the fracture behavior of materials [16–18]. Mode I fields are tensile stress normal to the plane of the crack symmetric with respect to the crack line, while the mode II fields are shear stress acting parallel to the plane of the crack and perpendicular to the crack front. Thus, the line ahead of the crack tip has the mixed mode I/II stress intensity factors. In these studies, the finite fracture theory was employed to investigate the fracture of rounded-tip notched samples with various notch radii and inclination angles under tensile loading. However, analysis of the fracture in ductile materials are more critical due to the plastic deformations as well as the stored elastic strain energy around the notch prior to the crack initiation [19]. For the analysis of fracture in notched ductile specimens, elastic-plastic fracture mechanics is usually employed, which is complex and time consuming. Therefore, an alternative method, known as equivalent material concept (EMC), was proposed where the elastic-plastic fracture mechanics analyses are circumvented with an equivalent virtual brittle material to predict ductile failure [20,21].

In this paper, we present an analysis of the fracture of U-notched 3D-printed thermoplastic components made by two di fferent 3D printing techniques. The equivalent material concept was employed to provide a new model in failure prediction. As the J-integral failure criterion is one of the most common brittle failure models used in the study of notched specimens, we investigated whether EMC could be combined with the J-integral failure principle to predict the fracture of U-notched 3D-printed specimens subjected to tensile loading. We present a study of the failure of U-notched 3D-printed rectangular nylon samples made by FDM and MJF under mode I and mixed mode I/II loading regimes within the framework of combined EMC and J-integral criterions. Nylon 12 filament and PA12 nylon powder were used for printing with centrally positioned notches. A series of tensile tests under static loading regime were performed, the results of which compared with that obtained by the EMC model combined with the J-integral criterion.

### **2. 3D Printing Samples**

Two di fferent types of 3D printing technologies were used to 3D print nylon samples. All the samples were first designed in a CAD platform and then saved in ".stl" format. The dogbone-type nylon samples were 3D-printed according to Type I ASTM D638 with a width of 13 mm, thickness of 5 mm and a gauge length of 50 mm as solid 100% infill rectangular plates, weakened by a centrally located bean-shaped slit with two U-shaped ends as shown in Figure 1, were 3D-printed by FDM and MJF with dimensions of 160 × 40 × 5 mm.

In FDM, nylon 12 samples were printed by a Fortus 450mc with nozzle and bed temperatures of 250 ◦C and 60 ◦C, respectively, nozzle speed 40 mm/s, infill percentage 100%, layer thickness 0.254, number of contours 1, and raster angle 0◦, whereas an HP 3D printer was used to produce the MJF PA12 samples with powder melting 187 ◦C and infill percentage 100%. The infill percentage was 100% for both samples. The average density of samples were measured using an electronic Qualitest Densimeter SD-200L as 1.019 gr/cm<sup>3</sup> and 0.984 gr/cm<sup>3</sup> for MJF and FDM 3D-printed specimens, respectively.

**Figure 1.** A schematic of centrally located bean-shaped notch with two U-shaped ends (dimensions in mm).
