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This is the second of two manuscripts that presents a computationally efficient full-field deterministic model for laser powder bed fusion (LPBF). The Hybrid Line (HL) thermal model developed in part I is extended to predict the in-process residual stresses due to laser processing of a nickel-based superalloy, RENÉ 65. The computational efficiency and accuracy of the HL thermo-mechanical model is first compared to the exponential decaying heat input model on a single-track simulation. LPBF thin-wall builds with three different laser powers and four printing patterns are evaluated in this study and compared with part-scale simulations. The simulations show good agreements with the experimental X-Ray diffraction measured residual stresses. Compared to the laser power, the scanning pattern is demonstrated to have significant effects on residual stresses. Laser scan patterns utilizing short laser paths generate lower tensile stress along the longitudinal direction of the part and higher compressive stress along the build direction.

This is the first of two manuscripts that presents a computationally efficient full field deterministic model for laser powder bed fusion (LPBF). A new Hybrid Line (HL) heat input model integrates an exponentially decaying (ED) heat input over a portion of a laser path to significantly reduce the computational time. Experimentally measured properties of the high gamma prime nickel-based superalloy RENÉ 65 are implemented in the model to predict the in-process temperature distribution, stresses, and distortions. The model accounts for specific properties of the material as different phases. The first manuscript presents the HL heat transfer model, which is compared with the beam-scale exponentially decaying model, along with the melt pool geometry obtained experimentally by varying the laser parameters. The predicted melt pool geometry of the beam-scale ED model is shown to have good agreement with experimental measurements. While the proposed HL model exhibits lesser accuracy in predicting the melt pool geometries, it can predict the cooling rates and nodal temperatures as accurately as to the ED model. Moreover, under large time integration steps, the HL model becomes more than 1,500 times faster than the ED model.

We study the Ozsváth-Szabó-Thurston transverse invariant in combinatorial link Floer homology for certain transverse cables L p,q of transverse link L in S 3 . Transverse cables L p,q are constructed from the grid diagram of L. The main result is θ(L p,q ) = 0 if and only if θ(L) = 0. We also prove a related result for invariants of Legendrian knots. Our proof uses an inclusion map i of certain grid complexes associated to L and L p,q . We prove that i induces inclusion on homology. We use these results to generate many infinite families of examples of Legendrian and transversely non-simple topological link types.

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