Review

Additive Manufacturing

Additive Manufacturing (AM) has become increasingly recognised as an important alternative method of manufacture, particularly for highly customised parts or parts with complex geometries [2]. The drivers for these first applications are practical issues, such as manufacturing flexibility, reduction in tooling costs, or better utilisation of material and sustainability [3]. As AM has become a more mature capability, more challenging applications are coming into consideration, such as components for aerospace or space vehicles, and with this, greater concern for the materials properties of the as-manufactured component [4]. The drivers for such applications include the environmental and material cost requirement to reduce the“buy-to-fly” ratio for expensive aerospace alloys, or to manufacture lightweight components with an internal hollow structure that are impossible to make any other way. Another emerging and important driver is the ability to manufacture parts in the field or at remote locations.
A more significant issue for AM for critical load bearing component applications is to know the mechanical performance of additively manufactured material. For the United States Air Force (USAF), the prediction of the Durability and Damage Tolerance (DADT) of a metallic part is based on linear-elastic fracture mechanics (LEFM) principles [5, 6]. This analysis process makes extensive use of what is termed the “equivalent initial damage size (EIDS)” , which represents the size of the damage that must be assumed to exist when the aircraft enters service. The size of the EIDS required for AM aerospace parts is discussed in [6].
It is well-known that surface finish has an influence on the fatigue performance of a test specimen, and so it is natural that the surface roughness of an as-manufactured AM component has received a great deal of interest from researchers looking to extend AM as a method of manufacturing aerospace parts [7, 8, 9, 10, 11, 12], for example, [8] stated:
“The surface roughness is the single most severe factor for fatigue for additive manufactured materials”.
The purpose of this current paper is to argue that surface roughness is not the only critical consideration, and to demonstrate that considering both surface roughness and sub-surface porosity can reveal more detail about the mechanism and development of damage accumulation in the material over multiple loading cycles. The published literature contains some indications of the significance of considering both surface roughness and sub-surface porosity together, rather than as two separate phenomena, but in general it does not seem to be generally recognised. For example, Masuo et al [13] investigated defects, surface roughness and HIPping of Titanium alloy AM. They describe two types of pores: gas pores and lack of fusion (LOF). They state, “Many defects which were formed at subsurface were eliminated by HIP and eventually HIP improved fatigue strength drastically…”, and note that surface polishing and HIPping substantially improve fatigue properties. On closer inspection of their stress-life (S-N) graphs it can be clearly seen that surface machining alone has a greater improvement than HIPping alone, but when both operations were performed the improvement was greater than might be assumed from summing the improvements from the two individual effects. In another example, Chan and Peralta-Duran [14] consider fatigue in AM parts, and use an analytical model to treat surface notches as fatigue crack nucleation sites. Their measured fatigue life results for as-built AM parts do not seem to follow the trend lines of their predictions, whereas the equivalent results for surface machined AM parts do. This seems to suggest that, in neglecting the combined surface morphology effects of neighbouring notches and sub-surface porosity, an important physical aspect is missing from their model.
It is hoped that the present computationally based study can help to identify the significant physical aspects that must be taken into account. Ideally, it would be desirable to be able to in link physical surface morphology feature measurements directly to the EIDS value used to certify AM parts for aerospace applications.

Fatigue life testing, statistics and approaches for aircraft certification

However good a model is, the physical experiment is generally preferred because there may be parameters or effects within the real test specimen that are not measured or appreciated in the analysis but have a significant effect on the result obtained. Fatigue life prediction has always been built on test data and statistical analysis with the test specimens made from the same material and fabricated using the same manufacturing processes as the engineering component for which the fatigue life prediction is required. The practical attractions of Additive Manufacturing have to be tempered with the crucial requirement that the predicted operational life must be conservative. Since certification requires a damage tolerance/durability analysis [4, 5], there have been many test programmes from which the crack growth rate versus the stress intensity range during a load cycle curves,\(\frac{\text{da}}{\text{dN}}\) versus \(K\), have been generated for a range of metal alloys, and different Additive Manufacturing processes as well as for conventionally manufactured aerospace materials [15-22]. A review of the “state of the art” of the damage tolerant and durability analysis methodologies needed for aerospace applications is given in [22]. In this context [23-27] have shown that the Hartman-Schijve variant of the NASGRO crack growth equation can be used to represent crack growth in AM materials accurately as well as crack growth in parts repaired using additive metal deposition. The fact that the same formulation works so well for such a wide range of materials and manufacturing processes suggests that a phenomenologically based predictive understanding of fatigue life could be within grasp.
Regardless of which crack growth equation is used in the DTDA design/assessment of an AM part, or an AM repair to an existing part, the choice of the EIDS is a key factor in determining the operational life of the part. Here it is important to note that, as stated in the certification standard MIL-STD-1530D [5], the role of testing is merely to “validate or correct analysis methods and results” . This raises the question can we relate EIDS to a physical quantity?
As previously noted the certification requirements for AM components in military aircraft are enunciated in the recently published EZ-SB-19-01 [5], which is in-turn based on MIL-STD-1530D [5]. Prior to the introduction of EZ-SB-19-01, Structures Bulletin EZ-SB-13-001 [28] stated that AM is “NOT RECOMMENDED without extensive testing and AFRL/RX [Air Force Research Laboratory, Materials and Manufacturing Directorate] support” . Thus, while not recommended, the use of AM was not entirely ruled out. MIL-STD-1530D set out the evaluation requirements of (i) “Stability” (here this refers to process stability), (ii)  “Producibility” (the need to reproduce the same capabilities at volume production rates), (iii) “Characterization of […] properties” ,(iv) “Predictability of structural performance” , and (v) “Supportability” (product sustainment throughout the lifecycle).
The 2019 EZ-SB-19-01 [5] directive builds on these requirements, and discusses a range of aspects or features that might contribute or act as“surrogate damage” . To this end EZ-SB-19-01 cites “four attributes of surrogate damage: damage type, damage size, damage orientation, and damage location” . Thus, both surface roughness and defect size are considered together, and (to some extent) in the same way. It further discusses the damage tolerance approach and the requirement for an “Equivalent Initial Damage Size (EIDS)” . Here EIDS is defined as per MIL-STD-1530D [5], viz. :
“an analytical characterization of the initial quality of the aircraft structure at the time of manufacture, modification or repair. The EIDS distribution is derived by analytically determining the initial damage size distribution that characterizes the measured damage size distribution observed during test or in service.”
Given that the operational life of the structure is determined by analysis, this means that the EIDS is determined by the size of the initial flaw that will yield the measured test life. As explained by Lincoln [29], when the USAF adopted damage tolerance, they made the decision to separate the process for assessing safety from the process for assessing aircraft durability. Consequently, as shown in [29], EIDS can be a function of the \(\frac{\text{da}}{\text{dN}}\) versus\(K\) curve used in the analysis. Furthermore, Lincoln also revealed that for a durability analysis it is necessary to use the\(\frac{\text{da}}{\text{dN}}\) versus \(K\) curve corresponding to the growth of small naturally occurring cracks. This is explained in more detail in [13]. If this is not done then the EIDS values are a function of the test spectra [29]. On the other hand, if the small crack \(\frac{\text{da}}{\text{dN}}\) versus \(K\) curve is used in the DTDA analysis, then the EIDS is closely related to the actual size of the material discontinuities from which the cracks grow [16-17, 25-27, 29-32].
EZ-SB-19-01 notes that for AM parts surface roughness is a key physical property; however, surface roughness is strongly dependent on the AM process, and the choice of definition for roughness [33-36], with surface roughness sizes that can lie in the range of 10s to 100s of μm. In this context, the use of the fractal box dimension to characterize surface roughness is particularly appealing given its success in characterising crack growth [37-41], its ability to characterize the failure surfaces associated with additive metal deposition [40], and its role in the development of the Boeing Bogel surface treatment [42].
With regard to flaws such as defects, inclusions, porosity pores and surface breaking features, these are also typically in the size range 10s to 100s of μm. Finfrock et al. [43] describe the occurrence of porosity for parts made using Selective Laser Melting (SLM), highlighting the value of the HIPping process and the quality of the feedstock powder. Figure 1 illustrates the situation of porosity occurring close to the surface: the pore illustrated is roughly 50  μm across and centred at about 100  μm below the nominal surface. In another study by Du Plessis et al [44], using X-ray micro CT to examine AM Titanium alloy material subjected to HIPping, clusters of < 70 μm pores at a sub-surface depth of about 300 μm are illustrated. The authors explain, by analogy to similar observations made of cast components, that sub-surface pores that are connected to the surface by micro-cracks cannot be eliminated by HIPping. Tammas-Williams et al [45] and Léonard et al [46] also use X-ray CT to investigate defect location and type in Titanium alloy samples made using the SLM. Tammas-Williams et al state that the “majority of pores” are “spherical and relatively small (< 75 μm)” and that “only ~ 3% of pores” have an aspect ratio of greater than 1.5. In another interesting paper by Guo et al [47] laser shock peening of AM Titanium alloy is investigated. The paper illustrates a sub-surface pore of nearly circular form, with a diameter of approximately 5 μm, and situated about 30 μm beneath the surface. For further examples, Kruth et al [48] review a huge variety of AM process.
Finally, it should be noted that EZ-SB-19-01 [6] requires a minimal EIDS of 0.01 inches (0.254 mm), and that Airbus have stated that, for AM parts, an EIDS of greater than 0.5 mm is rarely seen [49]. This latter statement is important given the statement in EZ-SB-19-01 that for the damage size for durability crack growth analysis shall be based on a probability of exceeding the EIDS of 1x10-3.

Representative modelling approaches

There are two main areas of work on which this present work is based. Firstly, there is the body of work concerned with computational modelling of heterogeneous materials, in order to model their properties. The second area is concerned with the modelling of surface texture. In both cases, it is assumed that there would be a full computational analysis of the modelled geometry, probably using Finite Element Analysis (FEA), and probably including some non-linear elastic or elastoplastic material properties, to determine stresses and plastic strains. An interesting proxy approach is proposed [50] whereby the strain field can be related to a geodesic property, which might provide a faster but more approximate method for assessing such models.

Modelling of heterogeneous materials

The work in this area is very wide ranging, and includes heterogeneity in many forms, from the random patterns of metal crystal grain structure, porosity and modelling of foams, through to the regular structure of a perfect composite material. Authors typically model a Representative Volume Element (RVE) of material, applying boundary conditions based on symmetry conditions [50-55]. Where the objective is to understand bulk material properties based on a detailed local model, this is a sensible approach: consider a notional pair of neighbouring RVEs. Both would be undergoing similar levels of loading and deforming in a similar way. The boundary between them would transfer little overall stress or strain when averaged over its length.