EN EL CURRÍCULO

From the shadow measurement method as discussed in the previous section 2.3.2, it was shown that there were irregularities along the outer surfaces of the struts. As mentioned by Van Bael et al. (2011), waviness and roughness of strut surfaces, due to attached powder particles, will result in local heterogeneities and stress concentrations leading to a lower stiffness and lower compressive strength of the material. Moreover, it will complicate the accurate prediction of mechanical properties by means of analytical models and finite element analysis (FEA). Therefore, on top of the determination of strut diameter, the surface roughness profiles of the SLM Ti-6Al-4V struts in this research were also deduced from the shadow measurements, as shown in Table 2.8.

Table 2.8: Surface roughness profiles and parameters that were deduced from shadow measurement method for both the as-received and heat-treated SLM Ti-6Al-

4V struts (200 W and 1000 µs manufacturing parameters, at 35° build angle) [S(1- 15)-35-200-1000-AR and S(1-9)-35-200-1000-HT(B)]

As-received micro-strut Heat-treated micro-strut

Outer surface variation Outer surface variation

Outer diameter shadow Outer diameter shadow

Surface roughness profile of as-received

strut Surface roughness profile of heat-treated strut

Ra = 16.8 µm Ra = 11.5 µm Ry = 70 µm Ry = 60 µm Rz = 59 µm Rz = 46 µm

The standard surface topography components; average roughness (Ra), peak-to-

valley height roughness (Ry), and 10-point roughness (Rz); are represented by the

following equations:

| | [2.7] | | [2.8] ∑ ∑ [2.9]

Figure 2.22 further explains the surface roughness parameters definitions. Based on the standard equations, surface roughness parameters for the as-received and heat- treated SLM Ti-6Al-4V micro-struts were determined. Differences of Ra, Ry and Rz

between the as-received and heat-treated struts were 31.5%, 14.3% and 22% respectively, as shown in Table 2.8.

Figure 2.22: Arbitrary surface profile and the standard surface roughness parameters [Adapted from Arola and Williams (2002)]

There was also an interest to study the stress concentrations along the micro-struts surfaces due to the surface roughness. A semi empirical relationship for surface stress concentration factor, Kt, using standard roughness parameters was given by

Neuber rule, as being applied by Arola and Williams (2002), as shown in Equation 2.10.

1 [2.10] Where Rz is the 10-point surface height, ρ is the notch root radius, n is the stress state

(n=1 for shear and n=2 for tension), and λ is the ratio between spacing and height of surface irregularities.

An alternative expression which was more suitable for the stress concentration imposed by surface texture was given by Arola-Ramulu model [Arola and Ramulu (1999)]. The effective stress concentration, , for a process-dependant surface texture was defined in terms of dominant profile valleys and the corresponding average valley radii, as in Equation 2.11.

1 [2.11] Where Ra, Ry and Rz are the average roughness, peak-to-valley height, and 10-point

roughness respectively; parameter is the effective profile valley radius determined from the dominant profile valleys as shown in Figure 2.23; and n is the stress state (n=1 for shear and n=2 for tension).

Figure 2.23: Definitions of effective profile valley radius [Arola and William (2002)]

By referring to Arola and Williams (2002), the effective notch root radius was estimated from the surface profiles using a graphical radius method. A best-fit circle defined by the maximum area of contact was inscribed in the root of at least three deepest valleys of the examined profile. The average of these profile valley radii was then calculated to establish for both the as-received and heat-treated struts. The value for the as-received strut was estimated as (36.7 ± 9.5) µm, and the value for the heat-treated strut was estimated as (32.3 ± 3.4) µm. The effective stress concentration factors, , for both the as-received and heat-treated SLM Ti-6Al-4V struts surfaces were calculated using the Arola-Ramulu model according to Equation 2.11 and were related to the surface roughness as shown in Figure 2.24 below. It was shown that the stress concentration was higher for the higher surface roughness of the as-received strut. This means that, the strength of the as-received strut would be lower as compared to the heat-treated strut. The effects of surface roughness on the properties of the SLM Ti-6Al-4V micro-struts will be discussed in Section 2.5. Figure 2.25 shows the relation between the surface roughness and the ultimate strength of the micro-struts in this study.

Figure 2.24: The stress concentration of the as-received and heat-treated SLM Ti- 6Al-4V struts (200 W and 1000 µs, at 35° build angle) [S(1-15)-35-200-1000-AR and S(1-9)-35-200-1000-HT(B)] given as the effective stress concentration factors,

, in terms of the average surface roughness, Ra

Figure 2.25: The effect of surface roughness Ra on the ultimate tensile strength σUTS

of the SLM Ti-6Al-4V struts (200 W and 1000 µs, at 35° build angle) [S(1-15)-35- 200-1000-AR and S(1-9)-35-200-1000-HT(B)] As‐received  strut Heat‐treated  strut 1.6 1.8 2 2.2 2.4 10 12 14 16 18 20 Effective   Stress   Concentration,   K ̅t

Average Surface Roughness, Ra(µm)

As‐received  strut Heat‐treated  strut 0 100 200 300 400 500 600 10 12 14 16 18 20 Ultimate   Tensile   Strength,   σ UTS   (MPa)  

2.3.5 Comparison between the As-Received and Heat-treated Microstructure of