Design for Additive Manufacturing – Material Characterization and Geometrical Optimization

The objective of the present study is to determine the effectiveness of AM technology as an alternative to chip removal processes. The focus is on the (experimental) characterization of the mechanical properties of a 17-4 PH SS, both in the AM versions and its wrought counterpart.

Selective laser melting (SLM) was used to manufacture two series of samples whose geometry was chosen according to the ASTM-E606 [1] standard. A third series turned from a cast material via turning operations.

Some scholars have observed a slight increment in the mechanical properties of AM 17-4 PH SS with respect to the traditional counterpart [2]. This evidence could be justified considering the manufacturing process characteristics. The AM, in fact, promotes a higher cooling rate that leads to a different microstructure [3]. The higher solidification rate that characterizes the SLM process impedes the formation of martensite promoting instead an austenitic microstructure [4–6]. As far as the structural properties of the AM 17–4 PH SS are concerned, the opinions of scholars differ. Some of them pointed out that they could be negatively affected by the porosities resulting from the production process [7–10], which act as nucleation sites. Others have instead proven how the presence of surface defects induced by the AM process could promote better lubrication [11].

AM, thanks to its flexibility, can be used to produce any kind of topology allowing the exploitation of lightened structures such as lattices and reticular. These latter structures have typically very small dimensions and, under operation, local plastic deformations could often not be avoided [12-14].

With these premises, to include all these effects in the design of a new AM component, the deep knowledge of the quasi-static (QS) and the cyclic and the fatigue behavior are fundamental.

In this paper, the results of the experimental characterization of an AM 17-4 PH SS are presented in the form of Ramberg-Osgood (RO) curves, Basquin-Manson-Coffin (BMC) curves [15], and Wöhler curves [16, 17].

In addition to the test on the AM as-build samples, the effect of the surface finishing was studied using the second series of samples manufactured via SLM and successively grinded. The knowledge of the characteristics is of fundamental importance, especially since in the majority of applications the lattice/reticular are set into operations without additional finishing processes. Finally, experiments were also conducted on a series of 17-4 PH SS turned from a casted bar.

Based on the results of the material characterization campaign, a geometry optimization of three mechanical components was done exploiting finite elements (FE). The optimization focuses on the strut's diameter and the size of the elementary cell. The optimization was aimed at reducing the component mass. The optimized geometries fulfill the requirements of the original counterparts. The original and the new designs were compared to evaluate the benefits of using AM as a substitution to traditional manufacturing.

Figure 1 shows the sample geometries used for the quasi-static (QS) and the low cycle fatigue (LCF) tests. In both cases, the samples have a cylindrical shape. The active length is 10 mm for the QS samples and 4.28 mm for the LCF samples. The lengths differ: 5 mm for the QS geometry and 2 mm for the LCF geometry. The geometry was selected according to the ASTM E606 standard [1].

Table 1 summarizes the chemicals of the AM powder.

At the Free University of Bolzano/Bozen, an electromechanical 5 kN testing machine is available, namely, a STEPLab UD04 (Fig. 2).

The QS tests were performed on this apparatus and fixed using mechanical clamping devices. During the QS test, the crosshead velocity was set to $0.1 \mathrm{~mm} / \mathrm{min}$ to avoid dynamic effects and local variation of the sample temperature. All broken samples (three repetitions) exhibit the cone-cup ductile fracture. The yielding for the AM 17-4 PH SS was quantified in 590 MPa , resulting below the one measured on the wrought 17-4 PH samples (980 MPa) [18-21] (Fig. 3). The measuring accuracy was about 2 N , i.e. about 0.1 MPa for the QS samples.

The LCF experiments were conducted under strain control on the STEPLAB UD04 tensile machine used for the QS characterization. The LCF tests were performed with a strain ratio $R_{\varepsilon}=-1$. The frequency for the tests was chosen according to the minimum value prescribed by the standard ASTM E606 [1], 0.1 Hz . All the tests were continued up to the failure. After approximately $1 / 3$ of the life, the hysteresis cycle resulted stable. These values were interpolated via the Ramberg-Osgood (RO) model (Fig. 4):

where $\varepsilon_{a e}$ and $\varepsilon_{a p}$ represent the elastic and plastic amplitudes of the strain, $\sigma_a$ is the stress amplitude, $E$ is the Young module, $K^{\prime}$ and $n^{\prime}$ are parameters [22]. Please be aware that, in the present form, $K^{\prime}$ and $n^{\prime}$ do not have the same meaning as the normally used Hollomon parameters [23].

The RO-tuned constants are shown in Table 2.

While the stable condition was exploited to tune the cyclic curve, the final failure of each sample (strain amplitude and the number of achieved cycles) is used to determine the coefficient of the Basquin–Manson–Coffin (BMC) equation.

The BMC equation consists of two parts. The first term $\frac{\Delta \sigma_f^{\prime}}{E}(2 N)^b$, called Basquin's term, refers to the elastic deformation. The second part of the equation is called MansonCoffins term and describes the plastic strain. The Basquin parameters $\sigma_f$ and b are called the fatigue strength coefficient and the fatigue strength exponent, respectively. The Manson-Coffin parameters $\varepsilon_f^{\prime}$ and c are instead the fatigue ductility coefficient and the fatigue ductility exponent. These values were determined based on 10 LCF tests for each material, following the ASTM 739 procedure [26].

The determination of the Basquin coefficients ( $\sigma_f^{\prime}$ and b ) requires the knowledge of the yield stress $\sigma_Y$ and the fatigue limit $\sigma_F$ [27]. The Basquin term is used to break up the total deformation $\varepsilon_a$ into its elastic $\varepsilon_{a e}$ and plastic $\varepsilon_{a p}$ parts.

To estimate $\varepsilon_f^{\prime}$ and c , eqn 3 should be expressed as:

A and B are the maximum likelihood (ML) estimators defined as:

$\bar{X}$ and $\bar{Y}$ are the averaged dependent variable $x_i\left(\log \varepsilon_{a p}\right)$ and independent variable $y_i(\log N)$. The plastic strain amplitude (eqn 4) can be rewritten as:

The ML estimators of the coefficients $\varepsilon_f^{\prime}$ and c (eqn 3 ) of the Manson-Coffin equation are calculated as:

The parameters of the calibrated BMC curve are shown in Table 3.

From Fig. 5, it is possible to notice how the machined series of samples is better performing than the as-built one. The cast material (NO AM) shows the worst performance.

The flexibility of the additive manufacturing process [28] has opened up new possibilities promoting the optimization and redesign of components.

In the following chapter, the results of an optimization of three already existing components are summarized. As a benchmark, three components belonging to three completely different sectors were selected. Their shape was kept unaltered; the optimization process acted on the internal volume only. The optimization exploits the capability of AM to produce reticular/lattice structures in substitution to the traditional solid design leading to a significant reduction of the mass and the objects combined with material saving and a positive environmental impact.

The optimization procedure was applied to the elementary cells whose parameters were modified to fulfill the requirements in terms of resistance and stiffness. Three cell topologies, namely, the Body Centred Cubic, the Body Centred Cubic Z, and the Face Centred Cubic (Fig. 6) were selected as the most appropriate solutions for the optimization. A parametric archetypal of the elementary cell was modeled in the open-source environment SalomeMeca2020/Code_Aster [29]. The optimization was possible with the combination of the finite element (FE) software Code_Aster [30] and Dakota [31].

The optimization procedure started from the unitary loads that characterize the three components, such as hip prosthesis, blowing mold, and automotive gear.

After a preliminary simulation (for each component and cell topology combination), the diameter of the struts and the size of the elementary cell were modified. The following simulation was performed automatically. During the optimization procedure, two objective functions (mass minimization and stiffness maximization) were considered. The simulation parameters for the subsequent iterations were selected according to a MOGA approach (Pareto Front).

In case of monopodial loading, the force results in 7-10 times the body weight of a person. On these bases, the maximum load acting on the prosthesis was quantified in 6670 N (person of 85 kg ).

The contact area sandwiched between the femur head and the acetabulum cavity is around 0.003 . This results in contact pressure of about 2.2 MPa . This value was used as a constraint for the optimization.

The next component is a mold to produce plastic bottles (Fig. 8).

The material used for bottles is usually polyethylene terephthalate (PET). The production process consists of blowing pressured air into the PET into the stretching (Fig. 8) to let the sides stretch until they stick to the die. The pressure is typically 3.6 MPa.

The mechanical component representative of the series production is the fifth gear of the gearbox of an FCA GrandePunto gearbox (Fig. 9). Considering that the maximum torque that can be transmitted by the secondary shaft of the gearbox is equal to 378 Nm , the average shear stress in the gear rim can be estimated at about 7.0 MPa .

All the stress levels are below the fatigue limit of any commercial steel by one or two orders of magnitude and far below those of the 17-4 PH SS [32].

Overall, the three considered components exhibit huge margins of optimization.

The results of the optimization of the different cell types for the single-size batch component, such as the hip prosthesis, are summarized in Table 4 and depicted in Fig. 10.

The optimization of the three cell topologies for the die mold leads to the results shown in Table 5 and Fig. 11.

The optimization lead, for what concerns the gear, to the following results (Table 6 and Fig. 12).

Through the coupling of an open-source FE software and the optimization tool DAKOTA, it was possible to analyze the impact of a redesign for AM on three components representative of different production batches [33-37]. Considering that AM relies primary on the possibility to substitute the solid design with lattice structures or reticula and that those architectures could not be grinded and should be set into operations in the as-built condition, a preliminary testing campaign was performed to collect reliable data on the impact of the surface roughness on the material performance. Considering that AM parts could not be grinded, the testing campaign was performed on the as-built and machine AM samples. Moreover, in order to have a direct comparison with traditional manufacturing, the third series of samples manufactured starting from cast material was tested.

The original design of the three analyzed components was optimized exploiting the reticula. The optimization was performed ensuring the same reliability and maximum deformation of the original components. To achieve this goal, three reticular cell topologies such as BCC, BCCZ, and FCC were selected. Their strut diameters and cell size were changed based on FEM simulations combined with a multiobjective genetic algorithm.

A potential average weight reduction between $21 \%$ and $23 \%$ was obtained for each component.