A novel numerical framework for simulation of multiscale spatio-temporally non-linear systems in additive manufacturing processes.

New computationally efficient numerical techniques have been formulated for multi-scale analysis in order to bridge mesoscopic and macroscopic scales of thermal and mechanical responses of a material. These numerical techniques will reduce computational efforts required to simulate metal based Additive Manufacturing (AM) processes. Considering the availability of physics based constitutive models for response at mesoscopic scales, these techniques will help in the evaluation of the thermal response and mechanical properties during layer-by-layer processing in AM. Two classes of numerical techniques have been explored. The first class of numerical techniques has been developed for evaluating the periodic spatiotemporal thermal response involving multiple time and spatial scales at the continuum level. The second class of numerical techniques is targeted at modeling multi-scale multi-energy dissipative phenomena during the solid state Ultrasonic Consolidation process. This includes bridging the mesoscopic response of a crystal plasticity finite element framework at inter- and intragranular scales and a point at the macroscopic scale. This response has been used to develop an energy dissipative constitutive model for a multi-surface interface at the macroscopic scale. An adaptive dynamic meshing strategy as a part of first class of numerical techniques has been developed which reduces computational cost by efficient node element renumbering and assembly of stiffness matrices. This strategy has been able to reduce the computational cost for solving thermal simulation of Selective Laser Melting process by ~100 times. This method is not limited to SLM processes and can be extended to any other fusion based additive manufacturing process and more generally to any moving energy source finite element problem. Novel FEM based beam theories have been formulated which are more general in nature compared to traditional beam theories for solid deformation. These theories have been the first to simulate thermal problems similar to a solid beam analysis approach. These are more general in nature and are capable of simulating general cross-section beams with an ability to match results for complete three dimensional analysis. In addition to this, a traditional Cholesky decomposition algorithm has been modified to reduce the computational cost of solving simultaneous equations involved in FEM simulations. Solid state processes have been simulated with crystal plasticity based nonlinear finite element algorithms. This algorithm has been further sped up by introduction of an interfacial contact constitutive model formulation. This framework has been supported by a novel methodology to solve contact problems without additional computational overhead to incorporate constraint equations averting the usage of penalty springs

Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation

Among the many additive manufacturing (AM) processes for metallic materials, selective laser melting (SLM) is arguably the most versatile in terms of its potential to realize complex geometries along with tailored microstructure. However, the complexity of the SLM process, and the need for predictive relation of powder and process parameters to the part properties, demands further development of computational and experimental methods. This review addresses the fundamental physical phenomena of SLM, with a special emphasis on the associated thermal behavior. Simulation and experimental methods are discussed according to three primary categories. First, macroscopic approaches aim to answer questions at the component level and consider for example the determination of residual stresses or dimensional distortion effects prevalent in SLM. Second, mesoscopic approaches focus on the detection of defects such as excessive surface roughness, residual porosity or inclusions that occur at the mesoscopic length scale of individual powder particles. Third, microscopic approaches investigate the metallurgical microstructure evolution resulting from the high temperature gradients and extreme heating and cooling rates induced by the SLM process. Consideration of physical phenomena on all of these three length scales is mandatory to establish the understanding needed to realize high part quality in many applications, and to fully exploit the potential of SLM and related metal AM processes

Mesoscale Calculations of the Dynamic Behavior of a Granular Ceramic

Mesoscale calculations have been conducted in order to gain further insight into the dynamic compaction characteristics of granular ceramics. The primary goals of this work are to numerically determine the shock response of granular tungsten carbide and to assess the feasibility of using these results to construct the bulk material Hugoniot. Secondary goals include describing the averaged compaction wave behavior as well as characterizing wave front behavior such as the strain rate versus stress relationship and statistically describing the laterally induced velocity distribution. The mesoscale calculations were able to accurately reproduce the experimentally determined Hugoniot slope but under predicted the zero pressure shock speed by 12%. The averaged compaction wave demonstrated an initial transient stress followed by asymptotic behavior as a function of grain bed distance. The wave front dynamics demonstrate non-Gaussian compaction dynamics in the lateral velocity distribution and a power-law strain rate–stress relationship

Simulation of Titanium and Titanium Alloy Powder Compact Forging

Simulation can be divided into two types: physical simulation and interactive numerical simulation. Physical simulation depends on testing smaller or cheaper samples rather than real objects to simplify models; Interactive simulation, which is also been called numerical simulation is depending on mathematical models and computer program to get the detailed results of the model. In this thesis, 48 compression test samples of sintered powder compacts of pure titanium (HDH) and Ti-6Al-4V were tested by using Gleeble 1500 thermal simulation testing machine. The height reduction of all samples was set as 70% and the other experiment conditions were set as three different temperatures and two strain rates. The stress-strain curves of all samples have been collected in the computer which could be considered as basic for the 3D-FEM simulation. Metal plastic forming is a coupled thermo-stress process in which the workpiece is loaded and restricted in some boundary conditions which include force, temperature, velocity, geometry, friction and so on. Thus, the scientific objective of plastic forming simulation is to be able to predict and control these phenomenon and transformation.The upsetting of powder compacts of pure titanium (HDH) and Ti-6Al-4V (GA) was studied in this thesis based on theoretical and physical models and numerical simulation. Based on the constituent model in ABAQUS and the results of thermo-simulation, the upsetting of 3D-FEM model was built which involved heat transfer, deformation and densification. The temperature field, Mises stress field, strain rate field, strain field and relative density field of pure titanium (HDH) and Ti-6Al-4V (GA) powder compacts were attained. Comparing the density distribution of the metallographic phases in optical microscope with the results of simulation, basically, the experimental results are in general agreement with the results of simulation

Dislocation Density-Based Finite Element Method Modeling of Ultrasonic Consolidation

A dislocation density-based constitutive model has been developed and implemented into a crystal plasticity quasi-static finite element framework. This approach captures the statistical evolution of dislocation structures and grain fragmentation at the bonding interface when sufficient boundary conditions pertaining to the Ultrasonic Consolidation (UC) process are prescribed. The hardening is incorporated using statistically stored and geometrically necessary dislocation densities (SSDs and GNDs), which are dislocation analogs of isotropic and kinematic hardening, respectively. Since the macroscopic global boundary conditions during UC involves cyclic sinosuidal simple shear loading along with constant normal pressure, the cross slip mechanism has been included in the evolution equation for SSDs. The inclusion of cross slip promotes slip irreversibility, dislocation storage, and hence, cyclic hardening during the UC. The GND considers strain-gradient and thus renders the model size-dependent. The model is calibrated using experimental data from published refereed literature for simple shear deformation of single crystalline pure aluminum alloy and uniaxial tension of polycrystalline Aluminum 3003-H18 alloy. The model also incorporates various local and global effects such as (1) friction, (2) thermal softening, (3) acoustic softening, (4) surface texture of the sonotrode and initial mating surfaces, and (6) presence of oxide-scale at the mating surfaces, which further contribute significantly specifically to the grain substructure evolution at the interface and to the anisotropic bulk deformation away from the interface during UC in general. The model results have been predicted for Al-3003 alloy undergoing UC. A good agreement between the experimental and simulated results has been observed for the evolution of linear weld density and anisotropic global strengths macroscopically. Similarly, microscopic observations such as embrittlement due to grain substructure evolution at the UC interface have been also demonstrated by the simulation. In conclusion, the model was able to predict the effects of macroscopic global boundary conditions on bond quality. It has been found that the normal pressure enhances good bonding characteristics at the interface, though beyond a certain magnitude enhances dynamic failure. Similarly, lower oscillation amplitudes result in a lower rate of gap closure, whereas higher oscillation amplitude results in an enhanced rate of gap relaxation at the interface. Henceforth, good bonding characteristics between the constituent foils are found at an optimum oscillation amplitude. A similar analogy is also true for weld speed where the longitudinal locations behind the sonotrode rip open when higher weld speeds are implemented in the UC machine, leading to lower linear weld density and poor bonding characteristics

A highly efficient computational framework for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

This article proposes a novel high-performance computing approach for the prediction of the temperature field in powder bed fusion (PBF) additive manufacturing processes. In contrast to many existing approaches to part-scale simulations, the underlying computational model consistently resolves physical scan tracks without additional heat source scaling, agglomeration strategies or any other heuristic modeling assumptions. A growing, adaptively refined mesh accurately captures all details of the laser beam motion. Critically, the fine spatial resolution required for resolved scan tracks in combination with the high scan velocities underlying these processes mandates the use of comparatively small time steps to resolve the underlying physics. Explicit time integration schemes are well-suited for this setting, while unconditionally stable implicit time integration schemes are employed for the interlayer cool down phase governed by significantly larger time scales. These two schemes are combined and implemented in an efficient fast operator evaluation framework providing significant performance gains and optimization opportunities. The capabilities of the novel framework are demonstrated through realistic AM examples on the centimeter scale including the first scan-resolved simulation of the entire NIST AM Benchmark cantilever specimen, with a computation time of less than one day. Apart from physical insights gained through these simulation examples, also numerical aspects are thoroughly studied on basis of weak and strong parallel scaling tests. As potential applications, the proposed thermal PBF simulation framework can serve as a basis for microstructure and thermo-mechanical predictions on the part-scale, but also to assess the influence of scan pattern and part geometry on melt pool shape and temperature, which are important indicators for well-known process instabilities

In Silico Analysis of Advanced Processing Methods for Light-weight Alloys Powders

Light-weight Al and Mg-based metal-matrix nanocomposites (MMNCs) are lauded as one of the most promising structural materials for vehicle, military, and construction applications. These MMNCs are often synthesized using the powder metallurgy (PM) process under liquid nitrogen cryogenic environments to control the grain sizes. It is believed that proper incorporation of the nitrogen species into the bulk lattice during processing could strongly enhance the mechanical properties of MMNCs by forming N-rich dispersoids. In this work, using the density-functional theory (DFT), the adsorption, absorption and diffusion behavior of nitrogen molecule/atoms have been studied and related to t Al and Mg MMNC PM processing. The study includes the impacts of binding sites, alloying elements (Al, Zn, and Y in Mg and Mg, Mn and Fe for Al), and surface crystallographic planes on the nitrogen molecule adsorption energies. The transition state (TS) behaviors for the bond breaking and lattice diffusion of nitrogen were examined. The results show that in presence of Mg (0001) or Al (111) surfaces, dissociation of $N_2$ to N atoms requires 1/9 to 1/5 of the isolated state energy , respectively. As a critical issue limiting the application of Mg-based MMNCs, the degradation (corrosion) of Mg alloys in aqueous media was modeled in this work. It is known that both the internal crystal structures and the impurity compositions/contents in the Mg alloys can affect the degradation rates. Density-functional theory (DFT) computation was utilized to understand the surface degradation behaviors with different crystallographic orientations and impurity elements from an atomistic standpoint. The adsorption response of the Mg alloy surface to the water molecule and the dissolution of surface atoms were studied to describe the degradation behavior of Mg and Mg alloys. The tendency for water molecule adsorption was quantified for Mg-based slab systems with low-index surface planes and various alloying elements including Al, Zn, Ca, and Y. The trends for surface degradation from these systems were examined using surface energy analysis and electrode potential shift analysis. The results showed that adding Ca and/or Y increases the propensity to attract a water molecule to the alloy surface. Also, it was generally found that the relative electrode potential shift of Mg-Y alloys is positive while those of all other alloys are negative. After having a comprehensive understanding about the atomistic behavior of metal powder in contact with the cryomilling media, the consolidation process was analyzed, including the melting and resolidification of powder through selective laser melting. At this stage of the work the concerns were to achieve the maximum connectivity between the powder layers after resolidification and to avoid extreme superheat. Since the efficiency of the MMNCs strongly relies on homogeneous distribution of reinforcement particles the SLM process was optimized to avoid any clustering of the reinforcement particles. Focusing on consolidation of MMNCS, Al10SiMg/AlN with weight ratio of 99:1 was chosen. AlSi10Mg with $10\%$ Si and $0.5\%$ Mg is one the most convenient compositions among the light weight alloys for laser melting processes, due to its narrow solidification range, that provides sufficient fluidity to produce sound products. Also, as the powder had been prepared via cryomilling process, the presence of AlN particles was proven based on the DFT calculations and experimental evidence described earlier. The laser power, scanning velocity and initial temperature of the powder were selected as the most important factors affecting the melting and solidification of the alloy powder. Finite volume analysis and experimental design were applied to optimize the SLM processing condition. Finite volume method was used to estimate the melt pool geometry, temperature profile of the part and velocity of solidification front. This information is necessary to produce strong parts with homogeneous properties all over the specimen, minimize energy consumption and avoid formation of defects in the sample. It was confirmed that even in the most extreme conditions the maximum temperature during the process would not exceed 1710K, which is roughly 460K below the melting temperature of the AlN reinforcement particles. The laser speed and power have significant effect on the melt pool geometry and maximum temperature of melt pool while the effect of initial powder temperature was insignificant for both of the response values. The AlN reinforcement particles are expected to have a homogeneous distribution since the velocity of the solidification front is higher than the critical calculated value of 5900 $\mu$ m/s. Results also showed that the solidification front velocity depends on the laser speed and the effects of laser power and initial temperature are insignificant. This work provides a comprehensive multiscale computational model tracking the Al and Mg based light-weight alloys from powder preparation stage to shaping the final product that considers potential gaps with focus on solidification process. These findings are particularly important to eliminate the extra processing steps to save time, energy and material maintaining the high quality of the final product

Nanostructured Mg-ZK50 Sheets Fabricated for Potential Use for Biomedical Applications

Magnesium (Mg) alloys are widely used in biomedical applications thanks to their combination of exceptional mechanical properties, biocompatibility, and biodegradability. Mg-ZK alloy series; for instance, ZK40, ZK60 and ZK61; is an example of the most commonly used Mg bio-alloy. Zirconium (Zr) acts as a grain refiner when added to Mg, which manipulates the material structure by producing a refined internal structure and enhancing its properties. In addition, when Zinc (Zn) is added to a Mg-Zr alloy, strength is improved. Therefore, given the favorable properties of ZK alloys in biomedical applications, the current research aimed for the fabrication and the evaluation of a new ZK alloy with a new composition; ZK50, as a potential biomaterial for biomedical applications. Three stages were implemented in order to achieve the objective of this study. In the first stage, ball milling process was used to synthesize nanostructured Mg-ZK50 alloy from elemental powders (Mg, Zr, and Zn). The produced powders (BM) were studied using SEM, XRD and TEM to determine the internal structure refinement as well as the phase development due to milling. In the second stage, Powder-in-Tube (PIT) rolling process followed by annealing was applied to produce consolidated thin sheets from the BM powders. Accordingly, in the third stage, the effect of annealing on the internal structure, mechanical properties, corrosion behavior and cytotoxicity was evaluated. The mechanical milling of the elemental powders produced a nanostructured alloyed powder after 45 hrs of milling with a crystallite size of 8.83 nm, which is considered the finest internal structure for Mg and Mg based alloys to date. Afterwards, nanostructured thin sheets were successfully produced using PIT at 300 °C with 67% reduction percent. The modulus of the sheets was found matching to that of human bones. It is worthy to note that annealing was found to have a detrimental effect on the corrosion behavior of the alloy. However, a hydroxyapatite layer was formed which indicated that the produced sheets induced osteoinductivity of the bone. Moreover, cytotoxicity of the sheets was not affected by the sheets and all the produced sheets showed an acceptable toxicity level within the cells. In conclusion, the produced Mg-ZK50 nanostructured alloyed sheets are considered a new potential biomaterial for orthopedic implants that induces osteoinductivity and prevent stress shielding