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Materials Science in Additive Manufacturing Defects in additively fabricated Al6061

pores based on the grayscale difference between results from sets 1 and 2. These models will be utilized in
screen pixels and their closest neighbors. The pixels multi-objective optimization to address the conflicting
that represent cracks have a lower grayscale difference objective of simultaneously minimizing porosity and crack
value than those in pores. In addition, if neighboring density.
pixels within 10 pixels of the radius exhibit a thin
feature with biased orientations based on distance and 2.4. Process parameter optimization
angle, the pixel is counted as part of a crack. A multi-objective optimization problem was established
(iii) Defect classification: Once the background is to optimize the conflicting objective of simultaneously
successfully removed, defects are classified. Pixels with minimizing the porosity and crack densities by identifying
grayscale values lower than the pre-defined grayscale the optimum decision variables. The decision variables of
color value and grayscale difference values below the the optimization problem were determined as the factors
set threshold are identified as pores. These pixels are of the experiments, P, v ,and h, and the objective functions
s
assigned a green color (Figure 1C). Conversely, pixels were developed using the predictive models for porosity
with grayscale values lower than the grayscale color and crack densities, as displayed in Equations III and IV.
value but with grayscale difference values (DGV) The mathematical expression of the established multi-
surpassing the threshold are recognized as cracks and objective optimization problem in this study is presented
assigned a red color (Figure 1C). in Equation II below.
(iv) Quantification of defect area fraction: To quantify Min.{ϕ (P,v ,h),ε (P,v ,h)}
the extent of each defect, the number of pixels 263≤P≤393 s rel s (II)
rel
corresponding to each category was analyzed. This 550≤v ≤2830
s
process enabled the determination of the area fraction 0.04≤h≤0.24
occupied by each type of defect. To optimize the conflicting objectives by identifying
In summary, the customized programming code has the optimum decision variables, we employed a multi-
facilitated the accurate identification and classification objective genetic algorithm (MOGA) in MATLAB
of defects within microstructures, encompassing “gamultiobj” (also used by Zhang et al. ) and a Pareto
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background removal, defect detection, and subsequent search algorithm in MATLAB “paretosearch” (also
defect quantification. The adaptability of threshold values used by Vora et al. ), and we compared the algorithms
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and parameters to each image ensured robust and tailored accordingly. MOGA essentially creates a random
defect analysis. initial population of solution sets from the decision
variable values and determines the fitness value of each
2.3. Process models solution inside that population. The fitness values are
The experimental design was utilized due to strict then converted into a functional range of values, called
limitations in possible L-PBF process parameter values expectations. Each solution is ranked according to their
and the number of experimental units, but it was sufficient expectation, and the “parent” solutions are selected
to generate effective second-order or quadratic response based on their expectations. The solutions with the
models. The general form of the second-order or lowest fitness values are labeled “elites” and directly
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quadratic model is given as: pass through to the next generation. Then, either by
combining the vector decision variable entries of pairs
y = β 0 ∑ k = i 1 β + i x i ∑ k = i 1 β + ii x i 2 + ∑ ∑ k i <= j 2 β ij i j + ε xx (I) of parents or by simply changing the decision variables
of the parents randomly, a new population of solutions
called “children” is formed. The former technique to
where y is the dependent output variable (e.g., porosity create children’s solutions is called “crossover,” whereas
[ϕ ], crack density [ε ]), β is the intercept, β is the the latter is called “mutation.” Finally, the elite and
rel
i
0
rel
regression coefficient or slope for linear terms, β is the children’s solutions form the next generation of solutions.
ii
regression coefficient for quadratic terms, β is the regression This algorithm is iterated until a stopping criterion
ij
coefficient for interaction terms (as estimated parameters in is met. Pareto search is an algorithm that initially
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the response), x is the independent process variable, and forms the feasible region of the solution set inside the
i
ε is the residual error. In the proposed experiment design, optimization problem boundaries with respect to the
three process parameters are considered (k = 3): laser power constraints and subsequently searches inside that region
(P), scan velocity (v ), and hatch distance (h). for all non-dominated solutions. A solution is considered
s
Response surface regression models for porosity and non-dominated if none of the objective function values
crack density were obtained using combined experimental of that solution can be improved without compromising
Volume 3 Issue 3 (2024) 6 doi: 10.36922/msam.3652