Improved Method For Predicting Fatigue Failure
The recent, rapid growth in additive manufacturing has brought a renewed interest in surface texture, particularly in how it relates to fatigue cracking.
A good deal of literature on crack development has focused on the depth of valleys in the texture. The roughness parameter ‘Rv,’ which reports the maximum valley depth, has been used to attempt to predict and prevent cracking. This approach, however, has significant shortcomings.
A better way to address cracking is to focus on sharpness along with the depth of the ‘sharp’ features rather than only tracking the depth of the deepest feature. Parameters that account for both depth and sharpness can lead to better control over the surface features that are most likely to lead to fatigue cracking.
Where Cracks Are Likely To Form
The deepest valley in a surface is often considered to be the most likely location for a crack to form. Because of this, designers will specify the ‘valley depth’ profile parameter Rv (or Sv for areal 3D measurements) to control the maximum depth.
The Rv parameter, however, has significant drawbacks. First, there are multiple definitions of Rv which produce considerably different results. For example, per the more popular (ISO-21920) definition, Rv is based on the average depth of several valleys, while the ASME B46.1 definition is based on the single, deepest valley. This discrepancy can be a recipe for confusion.
Second, these max depth parameters tend to focus on the single, lowest data point, which could easily be noise or bad data, making these parameters unreliable for controlling a process.
Third, and most fundamental: the deepest valley may not be the sharpest feature! Cracks may propagate from other, sharper valleys, as in Valley a in Figure 1. Or, because of the overall curvature of the surface, cracks may develop from sharp valleys (b, c) which appear shallower because of the part curvature.
Figure 1. A crack may form at a sharp, deep valley (a), but cracks may also form at sharp valleys that appear ‘shallower’ due to overall curvature of the surface (b), even at features that occur above the mean surface height (c).
Sharpness Is Better Predictor Than Depth
The ‘sharpness’ of a valley can be more likely to lead to cracking than depth alone. Consider a crack in metal. It may continue to propagate under stress. However, drilling a hole at the end of the crack can prevent it from propagating, because the hole increases the radius and thereby reduces the stress concentration. Figure 2 shows a similar situation, in which punching a hole in a chip bag stops a tear from propagating.
Figure 2. Punching a hole at the end of the tear in this bag increases the radius, which can stop the tear from propagating.
Since sharpness may predict cracking, we might try to calculate the radius of each valley in the texture in order to find the sharpest features. Unfortunately, because valleys are typically irregular in shape, it is difficult to reliably calculate a radius. A given valley could have many different radius values depending on the scale of interest and the data point spacing.
A better approach is to start by considering the smallest safe radius r, beyond which a surface may be ‘sharp’ enough to form a crack. We can apply a ‘closing filter’ to the measured profile by passing a mathematical disk of radius r over the measured data points (Figure 3). The path that the disk takes is called the ‘Closing Profile.’ This method is known as ‘morphological filtering,’ and it is described in the ISO 16610-49 and ISO 16610-85 standards.
Figure 3. A ‘closing filter’ results in a Closing Profile.
The voids between the Closing Profile and surface relate to crack formation.
In Figure 3, the valleys that are ‘sharper’ than the closing radius create ‘gaps’ or ‘voids’ under the Closing Profile. If we set the radius based on the safe curvature limit, the voids represent sharper regions that could relate to cracking and fatigue. Some of the deepest voids are shown in red in Figure 3. The ‘Maximum Void Depth’ is recorded after morphological filtering (Figure 3). Combining the maximum void depth and the related closing radius ties this notion of crack sensitivity to both depth and sharpness.
The Maximum Void Depth parameter (developed by Digital Metrology Solutions) is reported as ‘Wvdd’ for profile/2D analysis or as ‘Svdd’ for Areal/3D analysis. These parameters can be excellent predictors of cracking failure. The 2D parameter is based on a waviness ‘W’ profile. The use of a short wavelength limit is extremely helpful in controlling noise in the analysis. The cutoff wavelength for these short filters may lie in the typical roughness or waviness domains depending on the application.
Benefits Of Void Depth Parameter
The primary benefit of the Morphological Void Depth parameter is that it is based on both the sharpness and the effective depth of features. Traditional surface texture parameters treat the entire valley depth (relative to the meanline) as significant, which misrepresents feature depths. From a material perspective, the sharp region of the valley should be considered as the effective depth, not the entire valley. The Morphological Void Depth parameter more accurately accounts for the sharpest regions.
Another significant advantage of the Morphological Void Depth parameter is that it is not related to the meanline or mean plane of the surface. Sharp features will be detected regardless of their vertical position, so crack-causing features will be located even if they are not the absolute deepest valleys (Figure 4).
Figure 4. A closing filter locates the “deepest sharp voids” regardless of whether or not they are the deepest valley.
Taking Peaks Into Consideration
As we saw earlier, the closing filter mathematically applies a disk/ball to the measured profile or surface. If the ball encounters an extreme, sharp peak, large voids may be artificially created on either side of the peak. These artificial voids may represent the deepest voids, as shown in red on the top left in Figure 5.
One option for minimizing the influence of sharp peaks and artificial voids is to use an ‘alternating sequence’ filter. First, a closing filter is applied to produce a Closing Profile. Then, an ‘opening filter’ is applied, which acts like a disk/ball being pushed upward from below the Closing Profile. This combination of filters results in a more stable reference that is not influenced by extreme peaks (bottom left of Figure 5). In this profile, these false voids are now orange (indicating that they are no longer the worst voids) and the void on the right is now red (indicating that it is now the deepest void).
Figure 5. A sharp peak can cause artificial voids (in red) in the Closing Profile. An alternating sequence (closing/opening) filter can reduce the artificial voids and produce more reliable results on a surface with sharp peaks.
Figure 6 shows an example of Morphological Void Analysis applied to a 2D profile. For the 2D profile, the Closing Profile is shown in black on top of the red waviness profile (produced with a 0.025 mm short filter), highlighting the largest voids. A deep, sharp valley has been located, with an effective depth of 3.5 µm relative to a 25 µm closing radius. Note that the deepest void is in a different location than the deepest valleys!
Figure 6. A closing filter detects the most impactful valleys in a profile. Courtesy OmniSurf software, Digital Metrology Solutions.
Figure 7 shows how a closing filter can be used to locate potential crack sources in a complex surface. The original, areal/3D surface is shown on the left. A transparent blue, Closing Surface is superimposed in the middle, and the resulting voids are shown on the right.
Figure 7. Potential crack-causing valleys are hidden in a complex surface (a). Applying a Closing filter (b) reveals the most impactful valleys (c). Courtesy OmniSurf3D software, Digital Metrology Solutions.
Focusing on Functional Aspects of Texture
As we push for better performance from thinner and lighter components, it’s becoming even more essential to properly specify and control the surface texture. Parameters that focus on particular aspects of surface texture provide better process control than simple, general parameters such as “average roughness” (Ra). ‘Morphological Void Depth’ is a good example of an analysis that can locate surface features that are important from both a geometric and material perspective. By reporting valleys based on both depth and sharpness, this relatively new parameter can detect the features that are most likely to lead to cracking and potential failures.
For more information: www.digitalmetrology.com
About the authors
Mike Zecchino has been creating resources and technical content related to measurement and metrology for over 20 years. His articles have appeared in dozens of publications, and his training materials and videos support numerous measurement instruments and technologies.
mzecchino@digitalmetrology.com
Dr. Mark Malburg is the president of Digital Metrology Solutions. With over 30 years in surface metrology, he is the chief architect of a range of standard and custom software for surface texture and shape analysis. Dr. Malburg has consulted in numerous industries ranging from optics to aerospace. He is a frequent participant in standards committees and has helped shape many of the standards that govern surface specification and control.
mcmalburg@digitalmetrology.com
