For the modelling of bulk material with very randomly varying internal structure, reliance on the RVE approach can be misleading. By defining a particular RVE, then the internal heterogeneous material structure of that RVE is defined, and then, as a result of the boundary condition symmetry assumptions, it is replicated across the infinite material domain. Thus the model is one of a patterned structure and not a random one. The same is also true for the case of a mixed dimensional problem, one concerned with bulk properties and also surface features or lead crack propagation, the assumptions made for boundary conditions in RVE modelling no longer apply. The reason for this becomes obvious if one again considers the two neighbouring notional RVEs: one is comprised only of bulk material, but the other includes a free surface. It is now clear that the assumption of similar levels of loading and deformation in these two RVEs is inappropriate, and so to make any assumption about stress-strain transfer at the boundary would be erroneous. In such a case, it is necessary to make a much larger domain model, and pad the boundaries with excess material, so that the areas of interest within the model are a long way away from the influence of any inappropriate boundary condition [56-58].

Surface roughness and surface effect representation

It is well-known that in fatigue coupon testing, the quality of the surface finish has a significant effect on the fatigue life achieved [33-34]. In classical stress analysis, it is well-known that surface notches create stress concentrations or raisers, and solutions for many particular geometrical shapes have been tabulated [59]. More recently, it has been suggested that surface roughness can be assessed using the same approach used for short cracks [60].
In order to replicate these observations in a model, it is necessary to have a means to characterise the surface texture of a typical engineering component [61]. Other authors have measured surface texture directly using a variety of methods, the highest precision method currently being Atomic Force Microscopy [62]. A recent review of surface texture of additively manufactured materials has been reported by Townsend et al. [35], providing many images of many surface textures pre- and post-finishing processing. Another recent report, by Triantaphyllou et al. , [36] focusses on metrology methods and provides some contrasting information. It is believed that surface roughness can be considered to be fractal, with similar geometric features appearing at different length-scales, and this is certainly a useful starting point for generating models of surface roughness [63-64]. Thus, although it is recognised that surface roughness is particularly significant, it is not entirely clear how fractal, or sub-surface phenomenology, such as surface braking cracks or porosity, should be included.

Material grain structure and methods of manufacture

It is reasonable to consider that the final surface texture of an engineering component might be significantly influenced by the particular material in question, the materials processing, the method of manufacture, any finishing techniques applied, and also any environmental effects to which it might have been subjected. This very rapidly leads an unwieldly set of parameters, each of which might have a relatively greater or lesser influence on the actual surface texture.
In conventional metallic component manufacturing, the materials processing leads to the development of a particular crystal grain structure. It is well-known that particular materials with particular grain structures have better fatigue performance than others that are chemically similar but structurally different [34]. There is also a consequence to the surface texture: the nature and typical size of the grain structure will have an effect on the particular surface finish that is obtained following subtractive processes such as machining, grinding or polishing. Thus, it is easy to see how the connection between fatigue performance and surface finish can become conflated with fatigue performance and grain structure. As a result, there are a number of authors developing detailed FEA models of crystal grain structure, but without including surface texture modelling [53-55]. The results of these analyses are qualitatively interesting and suggest phenomenological processes in the development of failure, but perhaps show only a part of the overall picture.
In Additive Manufacturing (AM), the process is quite different to the conventional processes, and it is recognised ‎[65] that AM processes produce microstructures that are different from those of conventionally manufactured materials. There are many different forms of AM, so it might be expected that the material produced would be quite different; however, it does seem from the consistency in the test evidence [5-12, 15-22, 66] that there is an implicit connection between microstructure and surface texture. Therefore, differences might be accounted for by parameter choice, rather than being due to significant differences in physics.

Surface geometry representation in fatigue modelling

Conventional fatigue theory is often based on the assumption of an initial crack, like EIDS. Gorelik suggests that the surface geometry can stand in place of the initial crack [60], but, as discussed above, it is still not clear quite what surface measurement would provide the associated EIDS. Describing a surface or a crack surface as“fractal” implies a non-integral dimension: something between a surface and a volume. The immediate sub-surface of a piece of material may contain flaws, porosity, and perhaps immediate sub-surface cracks. Considering the latter, before the surface is broken, these would be sub-surface phenomena, but as soon as the crack breaks the surface, the entire crack becomes part of the surface. Physically, these two situations are similar, so it seems that our understanding and representation of “surface geometry” might need to include the phenomenology of the immediate sub-surface porosity.
It has also been suggested [67] that, for the damage tolerant design of an AM part, the use of an EIDS of 1.27 mm is sufficiently large that the effect of surface roughness and near surface porosity can be ignored.
In the description here, we follow the ASTM E647-13a [68] definitions of “small” and “long” cracks. For small naturally occurring cracks, the influence of the microstructural size on crack growth has been found to be minimal [15]. For long cracks, the grain size can influence the crack growth rate significantly; however, since the focus in the present paper is on the surface geometry representation, and since, for small cracks, the effect of grain size is generally small [15], this suggests that modelling individual grains within the sub-surface would be unnecessary, at least in the first instance.