Abstract

This study presents two analytical models for the laser powder bed fusion (LPBF) process. To begin, the single layer’s dimensions were measured using principal operating conditions, including laser power, laser scanning speed, powder layer thickness, and hatch distance. The single-layer printing dimensions were transformed into multi-layer printing using the hatch distance. The thermal history of the printed layers was used as an input to the Johnson–Mehl–Avrami-Kolmogorov model to estimate the average dendrite grain size. LPBF experiments were conducted for a Cobalt–chromium (Co–Cr) alloy to validate the developed model. The average dendrite grain size was estimated using a scanning electron microscope (SEM) combined with “Image J” software. The Vickers hardness test was performed to correlate the average dendrite grain size and operating conditions. A 10–15% mean absolute deviation was presented between experiments and simulation results. In all samples, a Co-based γ-FCC structure was identified. An inverse correlation was established between the laser power and smaller average dendrite grain, while a direct relationship has been determined between laser scanning speed and average dendrite grain size. A similar trend was identified between hatch distance and average dendrite grain size. A direct link has been determined between the average dendrite grain size and hardness value. Furthermore, a direct relationship has connected the laser volume energy density and hardness value. This study will help experimentalists to design operating conditions based on the required grain size and corresponding mechanical characteristics.

Highlights

  • For multi-layers printing via the laser powder bed fusion (LPBF) process, an analytical model has been developed to estimate the dimensions of the deposited layers and corresponding average size and hardness

  • Study,two twoanalytical analyticalmodels modelshave havebeen beendeveloped developedfor forLPBF

  • The corresponding thermal history was used in the Johnson–Mehl–Avrami

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Summary

Introduction

Various experiments have been carried out to correlate the operating conditions with the average grain size. Experiments were performed to develop a correlation between number of the deposited layers and average grain size [18]. For multi-layers printing via the LPBF process, an analytical model has been developed to estimate the dimensions of the deposited layers and corresponding average size and hardness. For this purpose, an analytical solution was initially inferred to calculate the single layer’s dimensions, including height, width, and depth. The developed thermal history was used in correlation with the JMAK model [25] to calculate average grain size in the case of multiple layers. To develop a correlation between operating conditions and hardness value, Vickers hardness testing was carried out

Mathematical Modelling
Single Layer
Average Grain Dimension Estimation for Multi-Layers Printing
Material and Methods
Implementation
A Vickers
Results and Discussion
Morphologies
15. Relationship
Conclusions
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