Generating printability maps for additively manufactured alloys

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A new approach to quantify the defects associated with AM process by mapping the process variables on a cartesian coordinate is suggested. Balling phenomenon, key hole formation and lack of fusion between the layers is addressed by taking into account the melt pool dimensions considering not only all the three modes of heat transfer(conduction, convection and radiation) but also vapourization. Mass and energy transport between the phases that is known to occur during keyhole formation is attributed to transition from surface to volumetric heating. A COMSOL heat transfer module that takes care of mass and energy transport during melting, solidification and keyhole formation is adopted to assemble a thermal modal that encompasses all the above mentioned intricacies. The Eagar-Tsai model[1] chosen to construct these printibility maps is found to be ineffective when compared with experimental observations. Uncertainity in material properties compounds to uncertain pritability maps hence melt pool dimensions are calibrated against 6 critical material parameters by using a gaussian process based surrogate model.



A ICME engineer is required to use his judgement supported by statistical tools to determine what to model? and what not to model?. AM processes can be modeled by using resource intensive techniques that are designed to incorporate laser interaction with the substrate by using power scale model or by simplifying the procedure to model it by using semi-analytical models. But a trade off between these two extremities bring us to a FEM based model which includes temperature dependant thermo-physical properties. Latent heat evolution during melting and solidification are inclusive of the model. From the temperature profile obtained from the model we can estimate the melt pool dimension and hence arrive at dimensionless ratios estimated based on length, width and depth of the melt-pool that can divide the process space of the printibality maps into defect free regions and cartesian space where defect can appear if the process parameters fall within this realm. The proposed model is compared with Eagar-Tsai model which assumes constant thermophysical properties, neglects phase change and energy deposition is considered to occur only on the surface which makes it impossible to study the laser penetration into the powder bed that are critical to the melt-pool dimensions and associated dimensionless ratios[2].

Results and Discussion

Printability maps are generated for two alloys: Ni-5wt.%Nb and CoCrFeMnNi alloy of equi-atomic composition. These maps are validated by experiments carried out across the process space. It is concluded that the model proposed has a superior predictive capability in comparision with the Eagar-Tsai model and can be extended to alloys of different composition. The uncertainity of the printability map boundaries(between safe and un-safe process conditions) can be calibrated by using a bayesian techniques. All material parameters are fixed and melt pool dimensions are calibrated by the surrogate model. A monte carlo simulation considering 10,000 sampling steps used here assumes all the 6 input material parameters to have a normal distribution. Since 95% confidence interval is chosen to evaluate the distribution of melt pool dimensions accurately fixing the map boundary is possible. Since the proposed model is quite inclusive in nature it is possible to develop variety of new alloy systems that are printable.

Printability maps that predict melt pool morphology regions for a Ni-5wt.%Nb alloy. Predicted regions are as follows: good quality (blue,G), keyholing (green,KEY), balling (purple, BALL), and Lack of Fusion (orange,LOF). Experimentally observed morphologies throughout the process parameters space are indicated by markers of different shapes following the same color scheme as the predicted regions.
Predictive accuracy of the Finite Element and Eagar-Tsai models for both melt pool width and depth for the CoCrFeMnNi high entropy alloy


  1. T.W Eagar and N.S Tsai "Temperature fields produced by traveling distributed heat sources: Use of gaussian heat distribution in dimensionless form indicates final melt pool shape can be predicted by for many welds and materials" Paper presented in 64th AWS convention, Philadelphia
  2. Luke Johnson, Mohamad Mahmoudi, Bing Zhang, Raiyan Seede, Xueqin Huang,Janine T. Maier, Hans J. Maier, Ibrahim Karaman, Alaa Elwany, Raymundo Arroyave "Assessing printability maps in additive manufacturing of metal alloys" Acta Materialia 176 (2019) Pg 199-210
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