Components fabricated using additive manufacturing (AM) processing routes are characterized by unique microstructures and the presence of irregularly shaped pores, but their quantification is currently insufficient for the operating and safety needs of fatigue critical components. Development of such tools or criteria to fulfill these needs are further challenged by the small sample sizes and limited range of testing conditions typical of AM experiments due to the cost and time associated with both AM manufacturing and fatigue testing. These limitations may in part be overcome by developing a statistical framework which provides a standardized method of aggregating, categorizing, and analyzing fatigue data to obtain broader trends across material systems. The framework originally developed on 316L stainless steel has been applied to powder bed fusion Ti-6Al-4V to quantify the scatter of fatigue life, contributions to mean fatigue life, and changes in the fatigue response. These analyses can be extended to incorporate fractographic information concerning fatigue crack initiating defects to help understand the role processing defects have on fatigue life scatter.
Fatigue data were aggregated from available sources for AM material processed by laser powder bed fusion (L-PBF) and electron beam powder bed fusion (E-PBF) Ti-6Al-4V. While not exhaustive, 124 individual data sets containing 1,082 data points were collected. Data points were manually extracted from digitized S-N plots. Categorization of data included testing setup, material properties, heat treatment, processing parameters, specimen design, and feedstock chemistries but were ultimately limited by variables commonly reported in literature. As such direct details about porosity and microstructure are not present because those are infrequently reported with fatigue data. Other variables such as feedstock chemistry were removed due to having over 1/3 of the values for data points missing (as an example, 2/3 of available data points did not report feedstock chemistry).
Fatigue response, mean fatigue life, and scatter of fatigue life were of interest for the statistical analysis. The slope of the S-N curve defines the fatigue response. General linear models were developed to define contributions to fatigue response and fatigue life. Model performance was then quantified by calculating the 95% confidence and prediction intervals, and adjusted and predicted correlation coefficients. Scatter of fatigue life was performed by splitting the data according to categorized variables and calculating an eigenvalue which acts as a succinct measure of scatter, taking into account both fatigue life and stress amplitude.
Validation data was obtained from five separate AM builds with 22 unique combinations of categorized variables. A subset of specimens were selected for quantitative fractography to investigate how characteristics of the crack initiating defects led to unexplained scatter after fitting the data to the fatigue life statistical model. A similar analysis was performed surface roughness specimens.
Results and Discussion:
Fatigue response is an important indicator of showing whether fatigue failures in aggregated data are driven primarily by defects or microstructure. Whereas in previous work a clear distinction could be made between two groups of fatigue response, no such clustering is observed in this data suggesting that despite various strategies to mitigate processing defects and surface asperities, whatever remains of these features acts to initiate fatigue failure. A general linear model was developed to better understand how categorized variables were influencing the fatigue response. Load ratio, UTS, and source power an layer thickness were found to be significant, though the model itself explained 37.2% of the total variation indicating that not all aspects of the variation were captured. However, each of these terms would correspond to an aspect of either concentrating stresses on processing porosity, decreasing notch sensitivity, or increasing the population of processing porosity.
A stronger statistical model was produced for mean fatigue life with approximately 70% of the total variation explained. Iterated 5-fold cross validation was performed to check model stability against outliers, and measurements of root mean square error (RMSE) supported such stability. The statistical model allows for discussion of how changes in testing setup, tensile properties, heat treatment, processing parameters, and specimen design impact mean fatigue life. For example, decreasing load ratio and increasing frequency on average produce higher fatigue lives, the latter quantification of which is noteworthy due to the increasing trend of using ultrasonic fatigue testing.
Eigenvalue analysis showed that processes like hot-isostatic pressing and shot-peening can substantially decrease the scatter in fatigue life. When comparing E-PBF and L-PBF, the E-PBF data published in literature tends to have lower fatigue lives.
Crack initiating defect location and circularity were investigated. When the predicted values from the fatigue life model were combined with the quantitative fractography metrics, residual sum of squares error decreased from 10.97 to 3.24. The additional role of pore characteristics on scatter can be quantified. This strategy also provides a potential way to incorporate higher quality data into statistical modeling through the use of secondary equations.
Existing fatigue data for AM materials are characterized by small sample sizes and a wide range of different testing conditions, which limit broader analysis of the mechanisms governing their fatigue performance. A methodology using a range of statistical and meta-analysis tools has been developed and tested to identify larger trends and discern mechanisms governing fatigue failure. The statistical analysis allowed interactions between the different categorical variable to be identified and highlighted sources of scatter in the larger data set, from which important effects on the resulting fatigue lives were identified. By expanding this statistical analysis to the measurement of crack initiating defects and surface roughness, insight regarding how the often unreported porosity and surface roughness metrics impact scatter in fatigue life were obtained. This research further develops the capability to construct a comprehensive fatigue database across material systems and suggest potential ways to incorporate new, pedigreed data sets into these relationships.
Keywords: titanium alloys, additive manufacturing, fatigue, statistics, defects, surface roughness