Selective laser sintering (SLS) is a very popular and widespread technology among additive manufacturing, which is nowadays exploited in many different fields, from industrial design to architecture or medical devices. It enables the manufacture of complex geometries, which would be hard or even impossible to obtain through traditional subtractive techniques. The working principle of the SLS is based on the use of a laser to sinter powder layer-by-layer from the bottom-up, in this way, building the object section-by-section. One of its advantages is the capability of processing a large variety of materials [1
], such as metals, polymers, ceramics or wax. One drawback, however, is that the mechanical properties of the sintered product are anisotropic, depending on the direction in which the geometry is built up. As a consequence, the buildup direction is to be carefully chosen and becomes an important process parameter, in particular when dealing with the design of components characterized by their structural properties [2
]. In this work, the fracture mechanics properties of polyamide (PA), sintered via the selective laser sintering (SLS) technology, are investigated. The specimens have the peculiarity of being sintered with embedded crack-like notches (sharp notches). The advantage of directly sintering artificial crack is that this way, there is very little limitation in the position and orientation of the crack-like notch to manufacture, differently from the case in which traditional manufacturing methods are used. This allows one to be able to tackle even complex three-dimensional fracture mechanical problems. The possibility of sintering artificial crack-like notches during the SLS process was investigated by T. Brugo et al. [3
], showing the feasibility of the approach. The same method was then successfully applied in [4
] to study the fracture behavior of high-strength metallic material. A similar approach was also successfully applied to predict fracture loads of 3D-Printed ABS specimens, in which a pre-crack is embedded in the additive manufacturing process, this time using fused-deposition modeling (FDM) technology [5
In the literature, two main types of experimental setups can be found to investigate the fracture behavior of mode I/II mixity: the first one is based on asymmetrical rectangular specimens, such as [6
], the modified compact tension (CT) specimen [8
] or the mixed-mode bending (MMB) test [9
]. This latter method allows one to cover a spectrum of different mode ratios by varying the length of the loading lever. The second one exploits disc-like specimens, such as the Brazilian disc (BD) [10
], the semicircular bend (SCB) [11
] specimen, the asymmetric semicircular bend (ASCB) [12
] specimen and the Inclined edge-cracked semicircular bend (IASCB) [14
] specimen. In this study, the IASCB specimen subjected to three-point bend loading (the test configuration is described in detail in Section 2.2
) was used. This setup permits to study of a large range of mode I/II mixity levels without requiring an elaborate loading fixture. The IASCB specimens were sintered with different crack-like notch angles and tested on different support spans. In three of them (for pure mode I), the crack was manually induced, with the scope of carrying out a comparison with the ones with the sintered crack-like notch.
The digital image correlation technique (DIC) was exploited to determine the fracture behavior of the material. Together with the electronic speckle pattern interferometry (ESPI) [16
], the DIC is one of the most popular optical techniques used to evaluate the full displacement and strain field [17
]. The main advantage of the DIC is that it only requires cameras of adequately high resolution and an algorithm to perform the correlation between the images, which is carried out by exploiting a speckle pattern (usually spray-painted) on the surface of the sample. This pattern serves as an aid for the correlation algorithm, which is based on matching subsets of corresponding pixels in consecutive images. Consequently, the relative displacement may be measured and thus be used to quantify the deformation. In [18
], the DIC technique was used to investigate and characterize the fracture and fatigue behavior of a brittle material, namely the asphalt concrete, by exploiting the SCB test configuration. The DIC system used in [19
] has the peculiarity of being composed of two cameras, which makes it a stereo DIC system.
In the case study, since the specimens exhibit a strong elastic-plastic behavior, the J-integral was chosen as the fracture characterization parameter. In fact, the stress intensity factors (SIFs) are suitable parameters only in the case of material that can be considered linear elastic. The J-integral, conversely, can be successfully used to characterize the fracture mechanics behavior of elastic-plastic material, such as a wide range of tough polymers, as stated in the standard ASTM D6068-96 [20
]. The J-integral was originally proposed by Rice [21
] and represents the strain energy release rate or energy per unit fracture surface area of a material. It is a common parameter to characterize near-crack-tip deformation filed in elastic and elastic-plastic material. Usually, the J-integral is calculated from the integration of the experimental load–displacement curve (henceforth named LDC), knowing the geometry factors previously obtained by finite element analysis (FEM). This procedure is usually adopted in standards such as the ASTM D6068-96 for CT and SEB specimens [20
]. However, this technique is suitable only for laboratory tests in which the geometry factors for the specific specimen geometry are previously known, and the loading-displacement curve can be measured. Conversely, on a complex structure under operating conditions, it is difficult or even impossible to compute the geometrical factors and the load–displacement boundary conditions for the specific spot in which the crack was nucleated. An alternative method consists of computing the J-integral from the displacement fields around the crack tip, measured by DIC. The main advantage of this technique is that it can be performed directly on the structure, without the need of previously knowing neither the geometrical factors nor the loading boundary conditions. The DIC-based methodology consists of numerically computing the J-integral along a rectangular contour of the DIC grid [22
]. For the J-integral calculation, displacement, strain and stress maps are needed. The displacement field is obtained directly from the DIC; the strain field can be computed by numerical differentiation of the former, whereas the stress maps can be computed from the strain maps, given that the constitutive equations of the material are known. The material has thus to be previously characterized, for example, in terms of Ramberg–Osgood parameters, as done for instance in [23
]. The J-integral values calculated by the DIC-based methodology were finally compared to the ones obtained employing the LDC method.
In Table 4
, the J-integral computed by the LDC and the DIC-based methods for different mode mixity is summarized. Figure 10
shows a comparison of the mean values obtained by the two methods. In Figure 10
a the comparison is made by a bar plot, whereas Figure 10
b has the mode mixity ratio Me
as the x-axis.
It can be observed that the difference between the values computed by the DIC-based method and the conventional LDC method (calculated as (DIC-LDC)/LDC*100) is comparable to the experimental errors of each method (calculated as the standard deviation of the three values obtained for each configuration). This can be visually observed in Figure 10
b, in which the error bands of the graphs of the two methods overlap to a significant extent.
Concerning the notch induction by the conventional subtractive method (by razor blade incision) or by additive method (by directly printing it), some considerations can be made. The J-integral mean value of the notch induced by the AM method is 12.2% higher than the one obtained by the SM method, but it is within the experimental error. This can be attributed to a less sharp crack-like notch in the case of AM specimens, which leads to a lower stress concentration in the area near the crack tip, and therefore to a higher apparent fracture toughness value.
By plotting the J-integral as a function of the mode mixity ratio Me
, it can be observed that the curve has a minimum at a mixity ratio equal to 0.77 and then it increases up to pure mode II. Generally, in the literature [4
], higher fracture toughness values are experimentally observed for mode II with respect to mode I. This is due to a wider stress state distribution for mode II than mode I, which leads to higher fracture toughness values.
In this work, the mixed-mode I/II J-integral was evaluated for polyamide ASCB specimens manufactured by the additive SLS process. A non-conventional method to produce crack-like notches during the manufacturing process, by embedding them in the geometrical modeling phase, was investigated and validated (the difference of the results in mode I of about 12%). The capability of manufacturing cracks with additive techniques is a powerful tool that can be useful for investigating the fracture mechanics behavior in the case of complex crack geometry, even three-dimensional and/or inside the structure.
Two different methods for evaluating the J-integral were compared: the conventional one based on the load–displacement curve and a less conventional one based on the evaluation of the J-integral contour by exploiting the measured full-field displacement and strain by DIC. The results obtained with this latter method were statistically comparable with the ones obtained with the former method, and the DIC method was thus demonstrated to be a valid option for investigating the fracture behavior in the case of sintered cracks on elastic–plastic material. The DIC methodology has the advantage of being contactless and can be used to evaluate the J-integral in a condition where it is not possible to use the conventional LDC method due to complex and often not known loading conditions of the structure. By combining the DIC methodology with the AM manufactured cracks, it is, therefore, possible to lay the foundations for an investigation approach that is more flexible than the standard one. Moreover, it can be easily implemented and be applied to a wider number of practical cases and real-world scenarios.