1. Introduction
Aeronautics, in the special aeroengine subsector, is pushing hard to introduce powder bed 3D additive manufacturing (AM) because, with an optimal design, weight savings greater than 20% can be achieved in some cases [
1]. Inconel 718 used for aeroengine components is easy to cast but difficult to machine. Therefore, the AM technology is a great candidate for future designs. However, in the process, pores can appear if printing parameters are not fine-tuned.
Figure 1 shows some defects and pores due to lack of filling in layer-crossings, in this case, applying 67° between successive layers. The resolution of Digital X-Ray inspection cabins is usually not enough to detect pores, but it detects voids. Up to date, there is only a few works giving some values of probability of defects [
2,
3,
4,
5] and in many cases, in structural lattice made on purpose.
AM allows the replacement of various components welded and joined by just one single part [
6,
7]. Therefore, the AM technology eliminates the need of having large spare warehouses but it requires an additional reliability evaluation to update the failure rate and inspection intervals of the spare components. AM-components may contain undetected defects, because the non-destructive-testing methods available as UT [
8] and X-Ray computed tomography [
5,
9,
10] (used in
Figure 1) are not fully effective to detect AM lack of fusion [
10,
11] and AM porosity defects [
3,
4,
12]. Those defects can lead to unexpected component fracture and unscheduled replacement.
In additive SLM parts, all topics related to the influence of defects and surface quality are still under study. Some studies [
13,
14,
15] define coefficients to be applied in several surfaces affected by laser power and polishing; other works [
16] aimed at building orientation, heat treatment, surface quality, energy density, and service condition of the final product in steel SLMed components. Surface state was and it will be key in fatigue.
This paper develops a new probabilistic-fatigue-analysis method for AM-components, which follows the methodology used for welded structures explained by Coro et al. in [
17]. The methods applied in [
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45,
46,
47,
48,
49,
50,
51,
52,
53,
54,
55,
56], based in damage-tolerance analysis, wouldn’t consider any component coming from additive manufacturing.
The present approach suggests the possibility that several components are manufactured by the so-called powder-bed printing technique in Inconel 718; the methods developed in previous work by the authors [
17] for reliability updating, are upgraded now to include the AM design parameters, inspection methods, and component-loading conditions. The improved method incorporates a specific AM defect stress-intensity factor, and several specific AM volumetric probability-distribution-function (PDF): one for defects (pores or lack of fusion), another for inspection results (cracks), and the last for component stress. The proposed routine achieves a required reliability target, with minimum inspection and manufacturing cost for an AM-component.
The paper is structured as in [
17], and it is established upon the flowchart in
Figure 2, showing four loops that can be replayed separately or simultaneously during all of the AM-component life phases. The process is similar to the one presented in [
17], but with several substantial differences, highlighted in the following paragraphs.
The first loop, mandatory in the AM-component design process, defines the first inspection based on a required target reliability. As a first step, the AM-component target reliability is the same that the one of the welded-component by which is replaced, the weld concentration factor and angular misalignment parameters are removed, and the AM-component defect distribution is redefined by a volumetric distribution, as explained in
Section 2.1.1. In addition, the defect-growth laws are modified to remove the welded part geometrical characteristics, and the crack aspect ratio consideration is modified (as described in
Section 2.1.2). Finally, the reliability evaluation is performed in the same manner, and a comparison of this output with the required target reliability defines a first inspection schedule, and a comparison with the welded-component to replace.
The second loop remains the same; it is a sensitivity analysis of the manufacturing route of the AM-components. The AM-parameters and the defect-growth laws are used as input data, to evaluate the reliability and the parameter sensitivity study, as described in
Section 2.2. The results allow the definition of a new set of AM-parameters, the improvement of the inspections methods (to include the X-Ray computed tomography [
5,
9,
10] and ultrasonic testing (UT) [
8]), and the modification of the manufacturing route (to include Hot Isostatic Pressure (HYP) [
57,
58], annealed [
10]). The new AM-parameters can be used as feedback to replay the first loop or to redefine the inspection schedule.
The third loop corresponds to the update of a reliability estimate after each inspection. Again, the AM-parameters are the input data. A unique AM parameter
ai, that defines simultaneously the defect rate and size found during inspection is forecasted as explained in
Section 2.3 (in contrast, a welded-component needs two separate parameters to define the defect size
ai and rate
δ). Finally, the reliability evaluation is forecasted based on the removal of defective parts after each inspection, which provides a well-known saw-tooth reliability graph.
The fourth loop focus on the service-support process of AM-component. An AM-component has more undetectable defects than a welded-component. In addition, the AM-component has smaller defect size, and then a component testing is needed because of the reduced inspection effectiveness in the beginning of the component life. At this stage, the defect size evaluated in loop 3 (
Section 2.3) is compared with the inspection findings (
Section 2.4). Thus, by using the maximum likelihood analysis, the AM-parameters can be updated, and loops 1, 2 and/or 3 can be replayed to achieve an “Inspection scheduling based on reliability updating for AM-components”.
As outlined in the previous paragraphs, the paper highlights the novelties of the methodology in order to be applied in AM components, taking as baseline the method developed for welded components.
Section 2.1 and
Section 2.2 explain the damage-growth model, which originally incorporate the AM-component parameters as volumetric defect size, finding size, and stress probabilistic distribution. In addition, it contains the defect-growth model, that incorporates a specific SIF for AM pores and lack of fusion defects in an AM-plate, and the innovative reliability estimation method, that uses FORM + fracture method in AM component.
Section 2.3 explains the process to evaluate and forecast the reliability after each inspection, which uses FORM method in AM component.
Section 2.4 explains the method to predict inspection findings, and an innovative FWMSV maximum-likelihood-estimator methodology to update the defect-growth model considered.
Section 3 compares the numerical example of a pressure-containment case reported in [
17], and manufactured by electron-beam welding process, with the same component manufactured by power bed 3D AM.
Section 4 contains the main conclusions of the work.
3. Results and Discussion
This section presents a numerical example to evaluate the reliability of an AM jet engine case based on the developed methodology by Coro et al. in [
17]. The example allows the comparison between AM-component and electron-beam welded-components because the load and dimensions are the same that the electron-beam weld case reported in [
17]. The evaluated geometry corresponds to an AM cylindrical case of 500 mm height, 707 mm diameter, and 2.2 mm thickness (see
Figure 3) of a nickel-based alloy. The loads are generated by the temperature gradient between the atmosphere and the jet engine during a flight cycle. Each flight has a single load cycle, which gets null load at the beginning and maximum stress level at take-off. Skin loads are distributed in 36-mm lengths, with 60 MPa inside and 100 MPa outside the AM cylindrical case, and as seen in
Figure 4, they follow a parabolic stress distribution circumferentially.
The PDF (mean and standard deviation values) of the parameters considered in the AM-case calculation are summarized in
Table 2. The unique AM-component area has a resultant
ai PDF mean value of 150 μm and a PDF standard deviation of 20 μm. They have been evaluated by the evaluation of AM component cut-ups. The AM-case volume under stress is 39,600 mm
3 (2.2 × 36 × 500), and it has the same amount of defects per unit of volume as the reference [
2], that reports an
ai PDF mean value of 20 μm and a PDF standard deviation of 30 μm in a volume of 0.325 mm
3.
The stresses
σa and
σb agree with stress occurrence per unit of volume shown in
Figure 3 and
Figure 4. They have been evaluated by FEM statistical stress distribution. The geometry acceptance criterion restricts the thickness reduction and misalignment to 6%, and it depends of the AM manufacturing parameters and the rejections requirement. In addition, the defect POD has a PDF mean value of ln(0.38) mm with a PDF standard deviation of 0.677 mm [
56]. The POD curves are defined in the industrial NDT standards, or after a statistical hit-miss analysis of a test component inspection finding.
The Paris constant
c incorporates the defect-growth variability, and the Paris constant
n has a constant value of 3.0. The fracture toughness
KIc accounts the scatter of the final flaw size before failure. Both parameters have been obtained by standard test method to measurement fracture-toughness and fatigue [
36,
37]. As discussed in
Section 2.1.1, the effect of the AM-components anisotropy [
59], defect-growth threshold, residual stresses, and defect-growth retardation effect due to compressive loads, are considered negligible during the fatigue-crack growth evaluation.
It is considered that AM-case thickness tolerance is the double of welded-case one and the AM-case method uncertainties are a half of those in the welded-case because of the removal of the weld-stress concentration-factor (AM avoids weld root and crown geometry).
The AM case failure probability target is 1.4 × 10
−4 during the first 300 flight cycles, the same that the welded component reliability requirement to replace [
17]. A single defect-propagation analysis, which considers the PDF mean value of the parameters in
Table 2, predicts a structural fracture of the AM-case at 2152 load cycles.