Benchmark of a probabilistic fatigue software based on machined and as-built components manufactured in AlSi10Mg by L-PBF
Introduction
Metal additive manufacturing (AM) is nowadays considered a full-fledged technology taken into consideration for many industrial applications. In the recent years, most companies have switched from building demonstrators to actual production, and the number of AM parts currently in service has sensibly increased. In fact, most of the largest aerospace, automotive, and biomedical industries have now developed internal design practices and acceptability standards based on years of lessons learnt, growing process control capabilities, and huge amount of data collected and analyzed. For aerospace parts, the development of such know-how is expected to bring an increase of AM part criticality as this technology matures and gains widespread acceptance [1]. Despite this, the number of AM applications of critical or structural parts remains very limited. This is mostly due to insufficient regulatory framework for qualification and certification. Due to the high focus on quality coupled with low production volumes and strive for mass reduction, the space industry is leading the effort for closing this gap and space regulators are continuing the development of enabling standards and methods [2], [3]. At the same time, additional standardization efforts are ongoing, driven by other organizations among which ASTM and ISO [4], [5].
The main challenges of AM technology with respect to other legacy manufacturing methods are mostly related to damage tolerance and fracture control for mitigating catastrophic hazards resulting from the growth of an unknown pre-existing crack-like defect [6]. In fact, AM structural parts are prone to fatigue failure originated from anomalies despite several improvements are being introduced in the latest AM machines, e.g., sensors integration, which allows for a more robust implementation of in-situ monitoring and process control methodologies [7], [8], [9]. Therefore, a defect tolerant design becomes of primary importance at level of design and component qualification.
As a general statement, anomaly types can be subdivided in two categories: process anomalies and material anomalies. The first class refers to those process-induced anomalies which cause evident quality issues, e.g., build stop, build line skipped, cracking or deformation caused by residual stresses during cooling. On one hand, it is fundamental that the anomalies falling in this class are always avoided in service. In general, this can be obtained via non-destructive evaluation (NDE) and in-situ monitoring. On the other hand, the occurrence of such defects is usually minimized by the presence of a consolidated process, part production plan, and process simulation. Material anomalies due to AM processes can be further distinguished in volumetric or surface. The first category comprehends all those anomalies that can occur anywhere in the build, e.g., keyhole porosity, lack of fusion, inclusions [10], [11], [12]. Several works have been performed to model the effects of volumetric defects on fatigue based on fracture mechanics models [12], [13], [14], [15], [16] in which crack growth rate and thresholds account for the short crack effect (i.e., they are dependent on defect size). As for surface anomalies, this category comprehends all those anomalies that can occur only in the presence of a free surface, e.g., surface microcracks and protrusions, localized stresses caused by coarse surface roughness, or porosity placed below the outer skin. Also for these surface features a number of papers have shown the applicability of fracture-based approaches [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26].
Due to the random nature of material anomalies (not specific to AM materials), the FAA Advisory Circular 33.70-1 defining damage tolerance requirements for engine life limited parts states that “the probabilistic approach to damage tolerance assessment is one of two elements necessary to appropriately assess damage tolerance” [27]. In this regard, the most simple semi-probabilistic approach is the standard option for damage tolerance assessments in which the initial flaw size is conservatively assumed considering that the part contains the largest anomalies that the NDE can miss with a 90% probability of detection (PoD) and 95% confidence. The assessment is then performed adopting a minimum safety factor for the service life [28], [29].
The upper level of probabilistic analysis is to consider a fully probabilistic approach. The recent draft document by NASA [3] reports a complete probabilistic damage tolerant (PDT) analysis as an acceptable mean of compliance for fracture control of critical parts. To support such an assessment, an appropriate characterization of material anomalies is needed for developing the size distribution and frequency of occurrence of material anomalies. As discussed in [1], this information can be used to define an exceedance curve for a given class of material defects, which is the key input for probabilistic fracture mechanics-based assessments such as the one defined in the FAA Advisory Circulars 33.14-1 [30] and 33.70-2 [31] for specific types of material or manufacturing defects. In probabilistic terms, this input anomaly exceedance curve can be defined by inverting the PoD capability of the NDE methods adopted [3]. However, it should be noted that this procedure has two main drawbacks: (i) the level of conservatism might be, in some cases, excessive; (ii) multiple NDE techniques are usually necessary to cover all the possible surface and volumetric anomaly types, and the determination of a robust PoD for a generic geometry might become extremely challenging and expensive.
The second alternative available is deriving an exceedance curve based on the real anomaly distribution. It is interesting to highlight that the determination of an anomaly distribution for hard-alpha grains in titanium disks required years of collaboration by certification agencies, major aircraft engine manufacturers, and steel companies. On the other hand, characterizing anomalies in AM materials can be substantially easier due to the higher occurrence of anomalies, relatively low cost of in-house specimens production, and exploitation of more advanced NDE as X-ray micro computed tomography (CT) [10], [32], [33], [34], [35]. Once the anomaly distribution is known, statistical means can be successfully adopted to infer the critical defect size for larger volumes [10], [11], [35], [36]. Despite this approach might well cover the verification of actual build quality with respect to a qualified target for the selected AM machine and process (e.g., by analysis of witness samples [37]), the question remains if the distribution in the samples can cover the intrinsic variability of a complex component geometry when a detailed micro-CT characterization on the full part is not achievable. NASA draft [3] requires cut-ups on a sacrificial part to ensure that possible feature-dependent manufacturing issues are not present or covered by analysis. Such an approach would allow characterizing anomaly distributions in selected areas (e.g., highly stressed or complex to manufacture regions) with the aim of verifying buy-in with the qualified process curve or obtaining a more conservative anomaly exceedance curve option to be used for PDT analysis of the specific regions of interest.
Besides material anomalies, other sources of variability affect the fatigue resistance of AMed materials. Residual stresses, microstructural variations, and anisotropy are other important factors that should be accounted in the fatigue assessment [12], [38], [39], [40], [41]. Among these variables, residual stresses are considered one of the weakest points in the component assessment due to their uncertainty/variability [12]. Recent results [17], [42] for the fatigue strength of as-built surfaces in AlSi10Mg show that residual stresses play a role as important as surface features at the fracture origin. In this regard, the probabilistic approach is possibly the best suited to account for so many sources of variability without the excessive conservatism that would be caused by classical deterministic approaches based on safety factors.
Many different approaches are available in the literature for probabilistic assessment based on a FE structural analysis and the presence of defects/anomalies: (i) approaches based on weakest-link concepts and the underlying assumption of Weibull distributions [43], [44], [45]; (ii) weakest-link approach based on a fatigue model combined with extreme value statistics for defects [46]; (iii) explicit crack-growth simulations combined with Monte Carlo simulations [47], [48], [49], [50], [51], [52]. The weakest-link approaches have the advantage of implicit analytical formulations that drastically reduce the computational time, while the explicit crack growth simulations can precisely describe the life from the local stress field and they can be combined with analyses of defect detectability [53].
The real challenge is to apply these approaches using as an input the test campaign for process qualification and the data available from the component tests [2], so that they could become a support to design and qualification of components.
This is the topic of the research activity presented in this paper, where we discuss the application of ProFACE (Probabilistic Fatigue Assessment of engineering Components with dEfects), a tool developed by Politecnico di Milano for the fatigue assessment of AMed components [46]. Fig. 1 shows the schematic of ProFACE with the indications of the inputs/outputs and the methods. The basic inputs of the software (that is a post-processor of FE analyses) are the process signature, expressed by the distribution of defects and surface features due to the AM process and a suitable probabilistic model for fatigue strength in presence of defects (modeled as short cracks). The failure probabilities of the finite elements are then calculated with an approach based on extreme value statistics and then combined through a weakest-link model.
The upgraded ProFACE 2.0 version (including surface features and residual stresses) was tested in the framework of a benchmark activity funded by ESA, in which special demonstrators were printed and tested in the machined and as-built surface states, along with fatigue coupons aimed at calibrating the material properties and establish the anomaly distributions [54]. This paper is structured as follows:
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Section 2: the test campaign aimed at generating a set of fatigue data on specimens and on a specially designed benchmark component;
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Section 3: the new features of the software, with its capabilities to handle the presence of residual stresses and the distribution of superficial features associated to the as-built surface state;
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Section 4: application of ProFACE to the ESA benchmark campaign by analyzing specimens and components;
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Section 5: a sensitivity analysis on the two most significant variables, i.e., the residual stresses and anomaly distributions.
Section snippets
Benchmark experimental database
This section summarizes the experimental results obtained in the framework of a benchmark activity between ESA, the Manufacturing Technology Center (MTC, Coventry) and Politecnico di Milano [54]. This benchmark activity was aimed at preparing an experimental database for validating fracture-based fatigue assessments and probabilistic analyses through the ProFACE software. Duties for the benchmark campaign were the following: MTC was in charge of project management, specimen and component
ProFACE: inputs and models
The backbone of ProFACE is the weakest-link model, based on which the component is considered as a chain of small sub-parts, each connected to the others with their own failure probability. According to this model, the loaded component fails if one element of the chain fails. The ingredients required to implement this approach are a fatigue strength model which links the stress associated with each sub-part with the dimension of the critical defect (), and a suitable defect distribution. The
Application of ProFACE
ProFACE was used to estimate the fatigue life of standard uniaxial fatigue specimens and wishbones, in both machined and as-built state. These two different external surface states are featured by a different population of defects as well as different residual stress fields. The analyses were performed considering the defect distributions obtained from the dimension of the defects at the fracture origin of the specimens and the residual stress fields evaluated from the experimental measurements
Sensitivity analysis
Fatigue tests are typically affected by a certain level of uncertainty. Besides the presence of manufacturing defects, variability of the material resistance , and possible uncertainty on the applied stress, which were all included in the first version of ProFACE [46], other variables might affect the final life prediction. In the previous section it was shown how the effect of residual stresses can influence the fatigue resistance of specimens and components. Moreover, it is well known
Limitations and future developments
The hypotheses on which the software is based (namely the description of fatigue life through the normalized S-N diagram in Fig. 7) limit its present capabilities to engineering applications in HCF. ProFACE aims at covering the present gap between simple weakest-link analyses and detailed probabilistic crack growth tools with a quick post-processor based on defect-tolerance concepts. Future developments, aimed at keeping this main peculiarity, will extend its capabilities in the following
Conclusions
AMed metal parts have opened new design possibilities to solve engineering problems based on geometry optimization and high structural strength over weight ratio. However, there is the need (reflected in guidances developed by NASA and ESA) of design rules able to account for the presence of volumetric and surface anomalies, and the presence of residual stresses. If fracture-based life estimations work well for AMed materials at the specimen level, the application of similar approaches to
CRediT authorship contribution statement
F. Sausto: Software, Numerical analyses, Writing – original draft. S. Romano: Designed the benchmark component, Software, Writing – original draft, Writing – review & editing. L. Patriarca: Supervision, Writing – original draft, Writing – review & editing. S. Miccoli: Code optimization, Software, Writing – review & editing. S. Beretta: Directed this research activity, Software, Writing – original draft, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors acknowledge the support of the European Space Agency trough contract n. 4000120221-17-NL-LvH, in which MTC contracted Politecnico di Milano for “ProFACE Benchmark” according to ESA-TRP-TECMSP-SOW-009494, and contract n. 4000133245/20/NL/AR/idb, in which MTC contracted Politecnico di Milano for “ProFACE surface features extension” according to ESA-TRP-TECMSP-SOW-009494. The authors thank the European Space Agency, especially Dr. Tommaso Ghidini, for permission to publish the results
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Current address: GE Avio s.r.l., Via Primo Maggio 99, 10040, Rivalta di Torino (TO), Italy.