Linkage of Macro- and Micro-scale Modelling Tools for Additive Manufacturing

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INOM

EXAMENSARBETE MATERIALDESIGN, AVANCERAD NIVÅ, 30 HP

STOCKHOLM SVERIGE 2020,

Linkage of Macro- and Micro-scale Modelling Tools for Additive

Manufacturing

JULIA SJÖSTRÖM

KTH

SKOLAN FÖR INDUSTRIELL TEKNIK OCH MANAGEMENT

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Abstract

Additive manufacturing methods for steel are competing against commercial production in an increasing pace. The geometry freedom together with the high strength and toughness due to extreme cooling rates make this method viable to use for high-performance components. The desirable material properties originate from the ultrafine grain structures. The production is often followed by a post hardening heat treatment to induce precipitation of other phases. The printing process does however bring several challenges such as cracking, pore formation, inclusions, residual stresses and distortions. It is therefore important to be able to predict the properties such as temperature evolution and residual stresses of the resulting part in order to avoid time consuming trial-and-error and unnecessary material waste. In order to link different parts and length scales of the process, the integrated

computational materials engineering framework can be used where linkage tools couples results of different length scales.

18Ni300 maraging steel is a material that has been used extensively to produce parts by additive manufacturing, but there is still a wide scope for optimising the process and properties. In this thesis, the integrated computational materials engineering inspired framework is applied to link the process to the microstructure, which dictates the properties. Temperature evolution strongly influences the material properties, residual stresses and distortion in additive manufacturing. Therefore, simulations of temperature evolution for a selective laser melted 18Ni300 maraging steel have been performed by Simufact Additive and linked with the microstructure prediction tools in Thermo-Calc and DICTRA. Various printing parameters have been examined and resulting temperatures, cooling rates, segregations and martensitic start temperatures compared for different locations of the build part. Additionally, residual stresses and distortions were investigated in Simufact. It was found that higher laser energy density caused increased temperatures and cooling rates which generally created larger segregations of alloying elements and lower martensitic start temperatures at the intercellular region. There is however an impact from cooling rate and temperature independent of the energy density which makes energy density not an individual defining parameter for the segregations. By decreasing the

baseplate temperature, lower temperatures below the martensitic start temperature were reached, enhancing martensite transformation. Primary dendrite arm spacing calculations were used to validate the cooling rates. The cell size corresponded well to literature of <1 μm. Distortions and residual stresses were very small. The calibration was based according to literature and need experimental values to be validated. The integrated framework demonstrated in this thesis provides an insight into the expected properties of the additively manufactured part which can decrease and replace trial-and-error methods.

Keywords: Maraging steel, selective laser melting, temperature evolution, macro-scale modelling, segregation, ICME.

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Sammanfattning

Additiva tillverkningsmetoder för stål tävlar mot kommersiell produktion i en ökande takt. Geometrifriheten tillsammans med hög styrka och slagseghet på grund av

extrema kylhastigheter gör den här metoden intressant att använda för

högpresterande komponenter. De önskvärda materialegenskaperna härstammar från den ultrafina mikrostrukturen. Processen följs ofta av en värmebehandlande

härdning för att inducera utskiljningar av andra faser. Printing processen innebär dock flertalet utmaningar som exempelvis sprickbildning, porer, inneslutningar, restspänningar och förvrängningar. Det är därför intressant och viktigt att förutspå egenskaper såsom temperaturutveckling och restspänningar av den slutgiltiga

komponenten för att minska tidskrävande ”trial-and-error” och onödigt materialsvin.

För att länka ihop olika delar och längdskalor av processen kan ”the integrated computational materials engineering” strukturen användas där länkverktyg kopplar ihop resultat av olika längdskalor.

18Ni300 maraging stål är ett material som har använts till additivt tillverkade produkter i hög utsträckning men det finns fortfarande mycket utrymme för

optimering av processen och egenskaperna. I den här avhandlingen, den ”integrated computational materials engineering” inspirerade tillvägagångssättet används för att länka processen med mikrostrukturen, vilken bestämmer egenskaperna.

Temperaturutveckling påverkar kraftigt materialegenskaper, restspänningar och deformation vid additiv tillverkning. Förutsägelse av temperatur för ett selektivt lasersmält 18Ni300 stål har därför genomförts i Simufact Additive och länkats med mikrostruktursförutsägande redskapen Thermo-Calc och DICTRA. Olika

maskinparametrar har undersökts och efterföljande temperaturer, kylhastigheter, segregeringar och martensitiska starttemperaturer jämförts för olika delar av

geometrin. Tilläggningsvis var även restspänningar och deformationer undersökta i Simufact. Det konstaterades att högre energidensitet för lasern orsakade högre temperaturer och kylhastighet vilket generellt skapade mer segregeringar av

legeringsämnen och lägre martensitisk starttemperatur i de intercellulära områdena.

Det är däremot en gemensam påverkan av kylhastighet och temperatur vilket gör att energidensitet inte är den enskilda bestämmande parametern över segregeringarna.

Genom att sänka temperaturen på basplattan uppnåddes lägre temperaturer under den martensitiska starttemperaturen vilket förenklar den martensistiska

omvandlingen. Beräkningar av primär dendritisk armlängd användes för att validera kylhastigheterna. Cellstorleken överensstämde bra med litteraturen på <1 μm.

Deformationer och restspänningar var väldigt små. Kalibreringarna baserades på litteraturvärden och kräver experimentella värden för att valideras. Den integrerade strukturen som demonstreras i den här avhandlingen förser en insikt i de förväntade egenskaperna av en additivt tillverkad del vilket kan minska och ersätta ”trial-and- error” metoder.

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1 Introduction

As of today, a serious task of implementing “first-time-right” additive manufactured (AM) metallic components is faced. The relatively new manufacturing process brings several challenges to overcome in order to easily adopt this technology.

Microstructural challenges connected to high cooling rates, residual stresses and distortion are important to handle to fulfil part performance.

It is important that not only the geometrical tolerances are fulfilled after the

component is finished. Final microstructure will affect the material properties which need to attain sufficient values in order to reach performance requirements. The high cooling rates result in microstructure formation outside equilibrium. Convection, conduction and radiation will further affect the thermal history of the material, resulting in remelting, grain growth and recrystallization which also will impact final properties. The challenge is to control the process and know how different input printing parameters affect the build aiming to achieve desired microstructure.

AM creates large temperature gradients and the thermal loads create residual stresses and distortion during printing and/or post processing. It is important to minimize these factors in order to stay within geometry tolerances, but it is a challenge since relaxation often lead to distortion. However, the use of specific printing strategies, support structures and laser settings can decrease the effect. By predicting the resulting part geometry deviation, it is possible to know if the printed component is within tolerances and if not, be able to compensate for before physical printing.

Residual stresses are also important for the component performance. Tensile residual stresses enhance fatigue crack growth while compressive stresses can impede crack growth. Stress relief most often results in unwanted distortions and an optimal balance of those are aspired. Simulations will help predict the residual stresses and design a suitable post processing step [1, 2].

AM technology for steels is rapidly developing and powder-based technologies in particular. Powder Bed Fusion (PBF) allows complex and precise geometries to be manufactured with exceptional properties suitable for many high-performance applications. The high cooling rate will create ultrafine grain structure increasing the strength. Maraging steels, and 18Ni300 specifically, are interesting AM materials since the high cooling rate together with the low carbon content create an almost fully martensitic structure without brittle carbide formation upon cooling. The low carbon content creates a softer martensite than for e.g. medium-carbon tool steels and necessary aging is usually needed to obtain required hardness. During aging,

intermetallics are, instead of carbides, formed as hardening mechanism. This creates high strength and toughness for complex parts suitable for aerospace and tool

industries which do not require large amounts [3].

The goal of this work is to ease the challenges mentioned by predicting the thermal evolution, element segregation and residual stresses and distortions of an additively manufactured 18Ni300 maraging steel part and thereby link macroscale simulation results with microstructural prediction tools. The procedure follows the integrated computational materials engineering (ICME) approach where different length scales are connected by linking computational tools to better understand the material behaviour. The process-structure-properties-performance linkages are important for additive manufacturing since trial and error is time-consuming and costly. The

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temperature history of 18Ni300 maraging steel will be investigated in order to find a pattern of temperature distribution throughout the build part. Temperature

dependent properties such as specific heat capacity and other necessary material information can be calculated and inserted in a FEM simulation and the subsequent FEM output can be analysed by CALPHAD (Calculation of phase diagrams)-based tools, that are used to link structure and process from thermodynamic and kinetic data. Simufact Additive and Thermo-Calc [4] tools were used to simulate the temperature history, residual stresses, segregation and martensite fraction in the printed 18Ni300 part under different conditions of selective laser melting.

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2 Literature Review

A lot of studies cover the basics of additive manufacturing and its problems. The printing method used in this work is selective laser melting (SLM) and several factors influencing the temperature history, residual stresses and other effects are further described. Material characteristics of 18Ni300 steel and why it is preferential for many SLMed products is discussed.

2.1 Selective Laser Melting

Additive manufacturing provides the ability to directly produce a complex geometry with no or less production steps such as machining in contrast to subtractive

manufacturing. The geometry freedom enables complex components to be made, saving material cost and weight and hence environmental impact but delivering the same or improved functionality.

SLM is a widely proven powder bed technique. The high solidification rate and temperature gradients lead to microstructures far away from equilibrium which are not desirable for many high-performance alloys. Moreover, the distinct temperature gradient leads to residual stresses and distortion of the build, as well as voids and anisotropy, after printing. These imperfections have negative influence on

mechanical strength, fatigue behaviour and elongation and can be controlled by post- processing such as heat treatments and hot isostatic pressing [5]. The build is created inside an inert gas chamber and the printer applies a thin 30-100 μm layer of powder onto a preheated baseplate, melts chosen parts based on a CAD-design by a laser beam, sinks down the base plate, applies a new powder layer and the procedure is repeated until the part is complete. Some important printing parameters are scan spacing, scan orientation, speed and intensity which all influence the quality of the end-product, such as surface roughness, microstructure, fatigue strength, density and hardness. If the scan spacing between the parallel vectors are too long, it will leave unmelted powder resulting in porosity and poor surface quality. If the spacing is too narrow, the energy consumption is unnecessarily large and the risk for evaporation larger. Similar consequences will rise if the scan intensity and speed are poorly selected in relation to material reflectivity and energy absorption. Other solutions to reduce the volume of pores are to efficiently dry the powder and have thorough control of the process parameters, optimizing scanning speed, path and overlap and to use hot isostatic pressing. The scan orientation or trajectory has shown to influence the residual stresses and distortions of the build. A chessboard design was proven to give the best result in a study, compared to uniform scanning vectors. Different scanning strategies are shown in Figure 1. Furthermore, the orientation of the build itself also affects the quality. Overhang and complex build conditions can be

facilitated by choosing a different build orientation. Additionally, also support structures are needed to avoid gravitational distortions and breakdowns [5-8].

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Figure 1. Examples of scanning strategies used in SLM [9].

The parameters influencing the laser energy density Ev (J/mm³)for SLM can be seen in Figure 2 and it is defined as equation 1 where P is the laser power in (W) , v is scanning speed in (mm/s) according to Equation 2, D is the point distance in (mm), θ is exposure time in (s), γ is stripe overlap, h is hatch spacing, t is layer thickness and δ is beam offset.

𝐸_v = ^𝑃

𝑣∗ℎ∗𝑡 (1)

𝑣 =^𝐷

𝜃 (2)

The energy density needed to melt the powder, Em (J/mm³), depends on the specific heat capacity c (J/Kg K), material density ρ (kg/mm³), melting temperature Tm (K) and the ambient temperature Ta (K) according to equation 3:

𝐸_m = 𝑐𝜌 (𝑇_m− 𝑇_a) (3)

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Figure 2. Printing parameters influencing the laser energy density.

These energy parameters are favourable to use while optimizing the SLM technique since they involve most process parameters. It has been found that by using the same resulting laser energy density value, similar build density and upcoming

microstructure were achieved. There is an optimal laser energy density which is high enough to avoid voids, porosity and partially melted powder but low enough to avoid evaporated elements, microsegregation, overmelting powder and too much tensile residual stresses based on the machine and material properties [5].

2.2 Residual Stresses

For powder bed fusion, the residual stresses are induced due to the expansion of the melted uppermost powder which is restrained by the underlaying solid substrate creating compressing stresses in the heated area. When the area cools down and shrinks, the shrinkage is restrained by the previous plastic strains caused by plastic relaxation during heating which results in tensile stresses in the area which are balanced with a compressive zone, see Figure 3 [10].

Figure 3. Residual stress formation during (a) heating and (b) cooling.

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This is a highly simplified model of residual stress formation. In reality, re-melting and re-solidification and cooling will affect the residual stresses, as well as

microstructure, further during the process. The accumulated heterogenous plastic stresses may lead to crack formation and decreased fatigue performance.

It should be mentioned that residual stresses appear in three different length scales.

The macrolevel, which is of most interest in this research but also microlevel related to anisotropy of grain structures and nanolevel due to coherency and dislocations, generally referred to as type I, type II and type III stresses.

Several factors affect the residual stresses during AM. The laser power will influence the molten pool and temperature of the whole powder bed. A higher intensity has shown to increase the melt pool size and the residual stresses for AlSi10Mg due to the increased thermal conductivity for the melted material than the powder [11]. The increased heat will decrease the material resistance to deformation in the laser area and cause more plastic compression. During the subsequent cooling, higher residual stresses occur as surrounding tensile stresses. Too high scanning speed also showed to increase the residual stresses since the shorter residence period lead to faster cooling rate and greater temperature gradients. However, an increase in laser energy density was shown to decrease the residual stresses in 316L stainless steel [12].The scanning strategy will affect the heat dissipation. By using shorter scanning length, less warping occured and a horizontal pattern resulted in less residual stresses compared to a tilted pattern [13]. The study also concluded that the stresses for a build gradually increases while printing due to accumulation effect from the above layers which reduces the cooling rate for the bottom part. The use of a preheated baseplate can also control the residual stresses [11].

Another research study indicates the same result showing that the reduction in stiffness for the upper layers increases the strain value gradually. A shorter build geometry hence resulted in less distortion than a taller build. Same study showed that using thinner powder layers for same laser power and speed results in higher

volumetric heat flux intensity and peak temperature. This, together with the higher printing time needed, tended to increase distortion but lower the residual stresses.

Same goes for heat input where a higher value reduces residual stresses but increases distortion [2]. Additionally, thinner-walled geometries have shown higher residual stresses in SLM processes [14].

There is a trade-off between distortion and residual stresses that needs to be considered for every build. The built up residual stresses will relax as the part is detached from the baseplate and cause distortion. During the build process, neighbouring tracks and underlaying tracks will be reheated and decrease elastic modulus which reduces residual stresses [15]. The aim is always to prevent the upcoming stresses by optimal printing parameters but post processing will also reduce the residual stresses such as heat treatments and peening. Here, tensile stresses can be modified to compressive stresses and hence prevent distortions after cutting the part from the baseplate and/or removal of support structures [16].

The martensitic phase transformation causes expansion forces as the specific

martensite volume is larger than austenite. Upon cooling, a net compressive residual stress state occurs when reaching the martensitic start (Ms) temperature. The heat affected zone (HAZ) may reach austenitizing temperature and transform back the

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martensite into austenite. However, the high-temperature austenite often experiences enough cooling rate to transform back into martensite. The amount of martensitic retransformation in the HAZs are lower than in the melt and does not cause enough expansion to generate compressive stresses. Instead, the HAZ has tensile stresses originated from thermal shrinkage restrained by the solid substrate [17].

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3 Maraging steel

Maraging steels possess properties suitable for airspace and aircraft components. It is therefore of particular interest to predict the thermal history, residual stresses and distortions, and accompanying microstructural changes in order to fulfil required performance. By aging a martensitic base structure, high strength, toughness, weldability and dimensional stability is obtained, together with low risk for

solidification cracking [18]. Due to the low carbon content and presence of Ni, Mo and Ti, nanosized intermetallic precipitates are created instead of carbides which increases the mechanical properties, hardenability and formability. The low carbon content further contributes to less thermal cracking during cooling [2, 19]. The chemical composition of 18Ni300 maraging steel is shown in Table 1.

3.1 Hardening Precipitates and Microstructural Characteristics

By 3D-printing maraging steels, the high cooling rate will induce highly dislocated metastable martensitic transformation enhanced by the high Ni content. This

transformation will obstruct the formation of Ni, Co, Mo precipitates and the alloying elements will stay in a supersaturated state. However, Al/Ti-rich nanoparticles were reported within the matrix of a laser PBF process [18].

Martensite without carbon is fairly soft and the subsequent aging time for the as-built part to form intermetallics is optimised for desired toughness, Young’s modulus, hardness etc. but is usually around 3-5 h at 450-550˚ C [20-22]. This will create Ni3(Al, Mo, Ti), (Fe)2(Mo, Ti) (Laves phase) and Fe7Mo6 (μ phase) precipitates and has also shown to increase the austenite fraction. By solution treating at 820˚ C for 1 h, the alloying elements dissolved homogenously in the solid austenite and all

austenite was transformed into martensite. Austenite reversion usually occurs during over-aging around a Ni- rich region of retained austenite and can be desired when high toughness is required due to higher ductility. The reversion is diffusion controlled when the temperature is between Ac1 and Ac3, austenite stabilizing elements will change the composition at the martensite-austenite interface. With time, Ni and Mn will segregate and further stabilize the austenite. At higher temperatures, above Ac3, the thermodynamic driving force dominates and the austenite transformation occurs through a shear mechanism, rather than through diffusion of elements [3, 23, 24]. The upper part of an SLMed build undergoes less intrinsic heating from above layers and is therefore less prone to form reverted austenite. This area is also shown to have less hardness due to less time for precipitation [25].

Ni3(Ti, Mo) are the main hardening precipitates which are the first to form upon aging. Initially, Ni3Mo may be formed due to the martensitic lattice coherence. The Ni and Ti interaction then quickly forms Ni3Ti. During over-aging, the metastable

Ni3(Mo, Ti) will dissolve, release Ni and form Fe2Mo which further enhances austenite reversion [26, 27].

The high cooling rate will create very fine dendritic/cellular grain structure,

increasing the strength and toughness compared to other manufacturing techniques.

The higher the speed, the higher the cooling rate and hence finer structure leading to no time to form secondary dendrite arms [28, 29]. Typical cellular size is <1μm and more specifically reported as 0.2-0.6μm when evaluating the horizontal cross section

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[20, 30]. In many studies it is reported that the microstructure becomes slightly coarser in the positive build direction. This is explained by the higher conductivity of the baseplate used which will increase the cooling rate at the bottom and increase the temperature at the top [31]. Maraging steels also have low reflectivity and high

wettability making these suitable for powder bed fusion techniques [28]. Due to kinetic reasons, phases appearing as equilibrium phases in TC may not form during AM and in an as-built condition, such as Laves- and μ phase [32].

By being able to predict the temperature evolution and hence upcoming

microstructures, the process can be optimized and designed to skip or limit post heat treatments.

3.2 Martensite Fraction

As-built SLMed parts consist almost fully of martensite (94.2%) [20, 27]. The amount of retained and reversed austenite content correlates to the segregation during

solidification. During the cellular-dendritic growth, interdendritic regions tend to get increased amounts of austenite-stabilizing elements such as Ti, Mo and Ni. The remaining liquid is in other words obtaining increased amounts of solute elements through microsegregation, which lowers the martensitic start (Ms) temperature according to Equation 4 and makes austenite stable to lower temperatures than the matrix [33].

Ms(˚C) = 525-350(C-0.005)-45Mn-35V(Nb+Zr+Ti)-30Cr-20Ni-16Mo-8W-5Si+6Co+15Al (4) Where 0.005 <C<0.02 is the carbon content in wt%. According to [26], the Ms

temperature is 194 ˚C and Mf 62 ˚C implying full martensitic structure at room temperature. These values are experimentally based on a similar maraging steel and are thus used as comparison. The Ms temperature is also dependent on the prior austenite state. Larger austenite grains have shown to increase the Ms temperature. A higher temperature (over Ac3) will cause grain growth and reduce lattice

imperfections. This will lead to less energy required for martensite transformation.

Additionally, the high temperature will increase the frozen-in defects during cooling which will act as nucleation sites for the martensite. There are however studies implying that the Ms temperature is not affected by austenitizing temperature but grain size only [34].

Table 1 Composition of 18Ni300.

Ni Co Mo Ti Al Mn C Fe

wt% 18.5 9 4.8 0.6 0.1 0.1 0.03 balance

3.3 Post Processing

Post processing is necessary to achieve desired strength. The design of aging and solution treatment will affect the microstructure and precipitation outcome. For SLMed maraging steels, an incomplete recrystallization during solution treatment may enhance austenite reversion and retention due to less homogenization. The stability of reverted austenite is dependent on the temperature at which it was austenitized. A lower temperature close to Ac1 produces more thermally stable austenite compared to a temperature close to Ac3 [19].

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The thermal conductivity for a material is less in the powder state due to the lower density compared to the solid state at the same temperature. The powder density for a 18Ni300 alloy was 59.26% of the solid material. It is difficult to specify a

conductivity value since powder characteristics change but a general rule used is to set the conductivity to around 1-1.6 % of the solid material [6, 35]. In Simufact, no difference in properties due to the powder state is considered but only a function of temperature of solid material. Powder characteristics will be more important for micro- and mesoscale simulations using transient moving heat sources.

3.4 Previous Simulated Results

A FEM analysis was made for a maraging steel component in ANSYS [36]. The maximum temperature by using recommended printing parameters was 1617 ˚C and the thermal gradient was approximately 4x10⁷ K/m.

When evaluating the residual stresses for a 300 maraging steel, all build parameters resulted in compressive stresses at the surface varying between 14-322 MPa. By decreasing laser power and scan speed, the residual stresses were decreased due to lower thermal gradient and cooling rate. A thicker powder layer of 45μm also decreased the residual stresses compared to using 30μm as the energy density is decreased and affects the cooling rate and gradient. When evaluating distortions, the cantilevers warped upwards which would imply tensile stresses. Since the cantilevers are cut in the middle, the predominant net stresses causing distortions are tensile. An increase in scanning speed causing more porosity were found to relax the residual stresses and decrease distortions. Denser builds thus exhibit more residual stresses.

Comparing powder layer thickness, the 45μm layer decreased distortions significantly [37].

Another macro-scale model reported the resulting normal strain tensors for 18Ni300 steel to be 2.05e-3, 0.3e-3 and -2.35e-3 for the x-, y- and z-direction respectively.

However, the strain tensors were not calibrated experimentally and when validating the results from the inherent strain method, the part dimensions affected the results even though it should only depend on the thermal history which leaves the strain values unreliable [35].

A numerical investigation concluded a decrease in cooling rate for a stainless steel from approximately 5000 K/s for the second layer to 2325 K/s in the fifth layer. The ninth layer was further decreased to around 1000 K/s and the peak temperatures were simultaneously increasing from 1600 ˚C to 1750 ˚C from the first to the ninth layer. This is in accordance to [31], stating the reduced rate of heat transfer is connected to the increased build height [38].

The present thermal studies found are time consuming and not validated for maraging steels. The lack of printing conditions used and uncertainties in setup correspondence to reality and other simulation programs make the results less reliable and applicable in further research. The linkage to segregation analysis is also not found in previous studies. The connection between thermal history and

microstructure is necessary for fast performance prediction and is therefore covered in this study.

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4 Method

Several approaches have been used to predict the thermomechanical behaviour of additive manufactured components, many of which are mesoscopic and generate outputs about melt pool characteristics by using computational fluid dynamics. A commonly used software is ANSYS Fluent but other software such as ABAQUS [39], Sierra Multiphysics, Flow 3D, and ALE3D are also used in similar modelling

purposes [40]. These methods are time-consuming and alternative solutions such as Simufact Additive, 3DSIM, Additive Works and GEONX offer quicker macroscale results on the basis from the aforementioned thermo-mechanical software

approaches [41]. Necessary material input parameters for process simulation is calculated using Thermo-Calc software and the process output is then used as input for simulating the as-built microstructure in DICTRA and Ms temperature and martensite fraction. Thermo-Calc version 2020a and Simufact Additive 2020 were used on Windows 10 Version 1903 for x64- based systems and intel Core i5, 7th generation computer.

4.1 Simufact Additive

Simufact Additive is an MSC Software tool developed to quickly predict macroscale properties for powder bed based additive manufactured components with a user- friendly graphical interface. Since AM can be explained as countless microwelds experiencing the same temperature history, it uses the inherent strain method where every new layer is assumed to experience equal strain tensors to predict residual stresses and distortion. A mesoscale thermal calculation is also available [42].

Simufact uses the Lagrangian computational framework by MSC Marc which allows for the easy activation/deactivation of elements technique saving computational cost [43]. The phase transformation is considered by using the Leblond model involving CCT and TTT diagrams [44].

Simufact assumes a flat powder and layer surface and does not consider element vaporization during the build. Additionally, the powder characteristics are not considered in simulations and does not possess any material differences from bulk material such as density and conduction. Densities for bulk material are however considered as temperature dependent for martensite and austenite as well as Young’s modulus [11]. The material database includes a variety of powder alloys with

properties calculated in JMatPro. The powder size distribution is neglected as well.

The thermal model does not consider the micro scale properties such as surface tension, evaporation, recoil pressure and Marangoni effect of the melt pool [43]. At the start of a scan track, it was shown that the temperature is less and may not lead to sufficient melting. This was explained by the decreasing thermal conductivity as more material is melted, increasing the temperature. This should be accounted for when setting up the build parameters for a real scan but is not considered in Simufact [45].

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5 Simulation Theory

There are various approaches to simulate AM processes. Those can be divided into micro-, meso- and macroscale and considers different input information for

calculation. The microscale level uses detailed information such as a moving heat source and fully thermo-mechanical coupled strategy to deliver results about the thermal history and microstructures. The mesoscale approach is simplified and uses an element layer technique instead of a moving heat source which can be activated sequentially for multiple elements at a time. The approach includes thermal history aspects to some extent but delivers faster results. In contrast to the two previous approaches, the macroscale determines residual stresses and distortion only from a mechanical perspective by using the inherent strain method first proposed by Keller et al [46].

The key is to connect the different length scales and use information given from a small specimen simulated from a microscale perspective as information for a macroscale calculation for a full component [47].

5.1 Thermo-Mechanical Coupling Analysis

In order to compute from a microscopic level, the temperature history from the heat source must be considered by finite element method (FEM). The non-linear transient thermo-mechanical calculation needs input regarding part geometry, mesh, initial and boundary conditions, loads and material properties. The partial differential equation is then discretized for each element and later connected as a global equation representing the whole part. A similar procedure of mechanical analysis is done to predict the distortion and residual stresses. The transient moving heat source is modelled as a conical Gaussian distributed heat flux with specific parameters deciding the melt pool characteristics. These parameters should be comparable to experimental values. The intensity I(r) in the radial distance from laser center is given by Equation 5.

𝐼(𝑟) = ^2𝐴𝑃

𝜋𝜔²exp (−^2𝑟²

𝜔²) (5)

Where A represents powder absorptivity, P laser power and ω the radius when the intensity is reduced by a factor of e² from the laser centre [48].

The heat transfer mechanism is calculated by using first law of thermodynamics considering conduction, convection and radiation to calculate the heat flux. In order to account for surrounding powder, a specific convection for the surrounding powder is applied [49]. The heat conduction is calculated by Fourier’s law according to

Equation 6 and by also including the solid-liquid transformation by adding the enthalpy change which is expressed as Equation 7, the resulting heat conduction equation is written as Equation 8.

∂

∂𝑥(𝑘^∂𝑇

∂𝑥) + ^∂

∂𝑦(𝑘^∂𝑇

∂𝑦) + ^∂

∂𝑧(𝑘^∂𝑇

∂𝑧) + 𝑞̇ = 𝜌𝐶_𝑝^∂𝑇

∂𝑡 (6)

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𝑑𝐻 = 𝐶_𝑝𝑑𝑇 (7)

∂

∂𝑥(𝑘^∂𝑇

∂𝑥) + ^∂

∂𝑦(𝑘^∂𝑇

∂𝑦) + ^∂

∂𝑧(𝑘^∂𝑇

∂𝑧) + 𝑞̇ = 𝜌^∂𝐻

∂𝑡 (8)

Where T is temperature, k thermal conductivity, q͘ is the added heat rate, ρ density, Cp

is specific heat capacity and t is the laser-powder interaction time [48].

The thermal history is then applied as a thermal load for the reduced model. By first simulating a small block of only a few layers, information for larger scale simulation is obtained. Each trajectory creates a transient moving melt pool which provides information about the powder to solid transformation stages. Additionally, the thermal history of a point is recorded and substituted by a load for scale up

simulations. This load can then be added as vectors representing each trajectory or as one or several layers for faster computing, taking specific convection for surrounding powder and top layer into account individually for a more reliable result [6].

The initial condition for temperature at t=0 is T(x,y,z,t)=T0, where T0 represents the ambient temperature. The boundary conditions for the top free surface is modelled as Equation 9 where heat losses occur through convection and radiation.

𝑘^𝜕𝑇

𝜕𝑛− 𝑞̇_𝑠+ ℎ(𝑇 − 𝑇₀) + 𝜎𝜀(𝑇⁴− 𝑇₀⁴) = 0 ∈ 𝑆 (9)

Where n is the normal vector of the surface S, 𝑞̇_𝑠 is the heat input rate of the laser, h is the heat transfer coefficient, σ is the Stefan-Boltzmann constant and ԑ is the

emissivity [48].

The meshed elements representing the not yet printed part of the geometry must not contribute to the whole part stiffness and therefore the calculation is done using the element birth and death technique. All elements are held deactivated until

solidification and then retain the stiffness when activated [48]. The material state function is defined as three cases; powder, liquid and solid and are based on the current temperature (Tc), maximum temperature (Tmax) and melting temperature (Tmelt). When Tmax is lower than Tmelt, the material is defined as a powder. When Tc is above Tmelt, the material state is liquid. The material is defined as solid when Tmax is higher than Tmelt and Tc is lower than Tmelt. The material state can then address the right material properties. The temperature can rise from ambient temperature to peak temperature within 0.4 milliseconds. This time is then applied as total exposure time for the heat flux when scaled up as a mesoscale layer approach. This body heat flux q is expressed as Equation 10.

𝑞 =

^𝐴×𝑃

𝑑_𝑠×𝑑_𝑚×ℎ (10)

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Where A is the laser absorption coefficient, P is the laser power, ds is the laser spot diameter, dm is the melt pool depth and H is the scan spacing [50].

5.2 Mechanical Layer Equivalent

Although thermomechanical approximation creates a good illustration of reality, the computational demand for additive manufactured parts is costly. In additive

manufacturing, the substantial temperature gradients occurring when the laser beam creates a liquid pool which heats the solidified underneath layer and quickly solidifies itself requires many iterations. The upcoming plastic deformations and strains from every added layer can instead be evaluated by using the mechanical layer equivalent method. The theory is based on the inherent strain method which considers the strains to be equal for points experiencing equivalent temperature history due to the location and distance from the heat source. The method uses the microscale results but applies them on a larger scale [46]. The sum of the plastic, thermal, creep and phase transformation strain is used as input for mechanical load and makes the FEM completely mechanical as opposed to the thermo-mechanical method. The inherent strains are dependent on the material properties, process parameters and the 3D- printer machine and can be measured in different ways.

One approach is to print actual specimens in three different orientations. More

specifically, three identical cantilever beams in 0˚, 45˚ and 90˚ angle from the x-axis.

Next step is to cut these off the base plate in the middle and measure the upcoming tip displacements. These values will be different depending on the scanning strategy.

It is found that the deviation is bigger for cantilevers printed lengthwise than for a cantilever printed parallel to the short side, as illustrated in Figure 4 [51]. The

deviation values can then be inserted as ԑxx, ԑyy and ԑzz inherent strains respectively in the Simufact software. A sensitivity analysis shows that varying the ԑzz strain has no effect on the final residual stresses and distortions and hence only the inherent stains in the x-y-plane are considered [35].

Figure 4. Upcoming distortions by printing a) parallel to short side and b) lengthwise direction [51].

In order to calculate the strains in the part, a voxel mesh is used. It divides the part up in cubes which senses the interaction between the part surface and the voxel mesh and calculates the solid fraction which is then considered when running the

simulation, see Figure 5 [47].

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Figure 5. Visualization of a voxel mesh.

This way, the computation is much faster and more suitable for industrial

environment as it produces macroscale results and does not use thermomechanical microscale information. The inherent strain method has traditionally been used for welding simulations and has shown to produce robust and realistic results [42].

When the software is calibrated according to the current conditions, the rest of the necessary parameters can be added. All printing parameters and values for heat treatment together with values for cutting off support structure and base plate are inserted. The post heat treatment will influence the distortion and must also be considered. The material properties such as Young’s modulus, conductivity and specific heat capacity change with temperature and are functions included in the material database. The direction in which the base plate and support structure are cut off will also affect the distortion. The software can compensate for the distortions and create a new model which considers the deviation and generates the new build

geometry in negative direction to the displacement [46, 52].

The inherent strain calculation is also based on the element birth and death method.

The FEM mesh is created layer by layer and discretizes the geometry. The layers are activated one by one and the inherent strain is inserted as mechanical load for each new activated layer before computing the mechanical equilibrium by von Mises flow rule [42].

5.3 CALPHAD

The ICME approach is a method to improve the process-structure-properties- performance linkages for materials by using models at the different length scales [53]. CALPHAD is one linkage tool to connect microstructure and process. CALPHAD tools have the possibility to predict temperature dependent properties for

multicomponent alloys by using thermodynamic databases. A mobility database can be used to predict diffusion coefficients and atomic mobilities. One such software is Thermo-Calc [4]. The thermodynamic equilibrium is based on minimizing the total Gibbs free energy of a system expressed as Equation 11 [54].

𝐺 = ∑_𝑖=1𝑛^𝜑𝐺_𝑚^𝜑(𝑇, 𝑃, 𝑥_𝑖^𝜑) (11)

Where n represents the number of moles of each phase φ and 𝐺_𝑚^𝜑 represents the molar Gibbs energy of phase φ at a certain temperature T and pressure P. The molar 𝐺_𝑖^𝜑 is in turn calculated for a solution according to Equation 12 [55].

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𝐺_𝑚^𝜑= ∑^𝑁_𝑖=1𝑥_𝑖^𝜑°𝐺_𝑖^𝜑+ 𝑅𝑇 ∑^𝑁_𝑖=1𝑥_𝑖^𝜑ln𝑥_𝑖^𝜑+ 𝐸𝐺_𝑚^𝜑 (12)

Where 𝑥_𝑖^𝜑 is the molar fraction of element i for phase φ, °𝐺_𝑖^𝜑 is the molar Gibbs

energy for a pure component i in the same phase at current pressure and temperature T, R is the gas constant and 𝐸𝐺_𝑚^𝜑 is the excess energy term which represents the interactions between different elements in a solution.

The Scheil-Gulliver model is used when considering microsegregation. Perfect mixing in liquid is assumed together with no diffusion in the solid phase. If diffusion is

considered, the (1 dimensional) DICTRA software is used. Mobility data in liquid and solid are included and local equilibrium at the interface is assumed. The kinetic and thermodynamic data are accessed from databases and used to calculate the diffusion- controlled transformations in multicomponent systems. The amount of diffusing species k passing per unit area perpendicular to the z-axis and time is expressed as Equation 13.

𝐽

_𝑘

= − ∑ 𝐷

_𝑘𝑗^{𝑛 𝜕𝑐}^𝑗

𝜕𝑧

𝑛−1𝑗=1 (13)

where cj is the concentration of either interstitial or substitutional element, 𝐷_𝑘𝑗^𝑛 is the diffusivity of the species in a volume-fixed frame of reference [56].

The high cooling rates in AM lead to less segregations than according to the Scheil model but Thermo-Calc includes a back-diffusion model which accounts for the subsequent diffusion in the primary phase during the fast solidification.

The Ms modelling is also based on Gibbs energy description. There is a chemical barrier for austenite to reach over in order to form martensite. At temperature T0, Gibbs energy for austenite and martensite are equal and the chemical driving force for martensitic transformation is zero. An undercooling from T0, representing the driving force, is needed to start the transformation. The Ms temperature is predicted based on empirical studies on critical driving force for martensite transformation.

The data is used to fit the interaction parameters in the excess Gibbs energy term of the critical driving force with the chemical barrier of the alloy. The chemical barrier information is stored in the thermodynamic database and the interaction parameters are functions of composition [57].

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6 Simulation Setup

In order to choose the right build parameters suitable for 18Ni300, a literature survey of previous SLM processes was made. The parameter optimization can be based on different backgrounds, usually the highest as-built part density is aimed for. Different laser energy densities have shown optimal part densities, but the range usually spans between 67-123 J/mm³. The recommended printing parameters reported in [5, 18, 22] were chosen for this project as stated in Table 2.

However, the energy density is highly dependent on the laser losses before reaching the powder and due to absorption/reflectivity in the powder bed. By using an

efficiency of 99.2% in Simufact, the energy density reached 67.47 J/mm³ as

recommended in [58, 59]. It is assumed that the energy density mentioned in reports is the one reaching the powder. Additionally, this energy density is enough to remelt the previous layer, ensuring a higher densification. The scanning strategy was set to

“stripe wise” in accordance to [31] and MS1 baseplate initial temperature to 200˚C as default.

The geometry used is shown in Figure 6 and the selected measuring points are shown in

Figure 7. The part was imported as a CAD-file and placed 3 mm above the baseplate.

An orientation assistant calculated the optimal geometry orientation considering support area and volume, projected area, design height, cost and local minima. A support structure of 0.12 mm radius was generated.

Figure 6. Part geometry used in simulations [60].

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Figure 7. Measuring points for temperature evolution of the geometry.

For the thermal and thermomechanical evaluation, the advanced option of austenite- martensite phase transformation in steels is considered and a copy of the MS1-MPM powder set as the material. The thermal conductivity and specific heat capacity of 18Ni300 are thermal dependent properties which highly influence the simulation results. In order to confirm reliable results, the predefined values in Simufact Material were compared to Thermo-Calc and literature. The conductivity, Young’s modulus and density were kept as the predefined values and the specific material properties such as solidus, liquidus, specific heat capacity and thermal expansion factor were investigated in Thermo-Calc and edited in the material database, see Table 3 and Figure 8, Figure 9 and Figure 10. Specific heat capacity and thermal expansion coefficient were calculated in the graphical mode by inserting the functions

“HW(fcc_a1).T” for specific heat capacity and “vm(fcc_a1).T/vm(fcc_a1)/3” for thermal expansion coefficient. Lastly, the numerical setting of time steps considered for each voxel layer was increased to 20.

The mechanical simulations were based on both calibrated inherent strains from distortion found in literature, and on inherent strains for a similar case used directly as input. These values were 2.05E-3, 0.30E-3 and -2.35E-3 for ԑxx, ԑyy and ԑzz

respectively [35]. The rotation angle between each scan was set to 67 ˚ and can only be considered for the mechanical simulations.

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Table 2. Recommended printing parameters for 18Ni300.

Laser power

Speed Beam width

Scan width

Scan overlap

Hatch distance

Layer thickness

Energy density 285 W 960

mm/s

0.15 mm

10 mm 0.08 mm 0.11 mm 0.04 mm 67.47 J/mm³

Table 3. Material properties for 18Ni300.

Solidus temperature [˚C]

Liquidus temperature [˚C]

Evaporation temperature [˚C]

Latent heat for melting [J/kg]

Latent heat for evaporation [J/kg]

1387.44 1440.77 2862 256400 6.09e+6

Figure 8. Thermal conductivity of maraging steel predefined in Simufact Material 2019.

0 5 10 15 20 25 30 35

0 200 400 600 800 1000 1200 1400 1600

Thermal conductivity [W/m*K)]

Temperature [˚C]

Thermal conductivity

Austenite Martensite

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Figure 9. Young’s modulus of maraging steel predefined in Simufact Material 2019.

Figure 10. Density of maraging steel predefined in Simufact Material 2019.

6.1 Sensitivity Analysis

By performing sensitivity analyses regarding mesh, material properties and build parameters, valuable information about the accuracy of the simulations is obtained. A too fine mesh will lead to unnecessary computational time, while a too coarse mesh will lead to unrealistic results. Voxel mesh sizes of 0.4, 0.5, 0.6, 0.7 and 0.8 were compared. The sensitivity of material properties is important due to the difficulties of finding relevant information on previous work. Laser power, speed, layer thickness and efficiency were varied. Thermal evolution results by using the predefined

maraging steel properties in Simufact obtained by JMatPro were compared to results by using properties obtained in Thermo-Calc. The specific heat capacity, thermal

0 50000 100000 150000 200000 250000

0 500 1000 1500 2000

Stress [MPa]

Temperature [˚C]

Young's modulus

7,2 7,3 7,4 7,5 7,6 7,7 7,8 7,9 8 8,1

0 500 1000 1500 2000

Density [g/cm3]

Temperature [˚C]

Density

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expansion coefficient and liquidus and solidus temperatures were updated for new simulations.

6.2 Calibration

After retrieving new updated values for specific heat capacity through Thermo-Calc, calibration was made. It is preferred to begin with a thermal calibration in order to retrieve the exposure energy fraction which is needed as input for a

thermomechanical calibration. This value splits the heat flux into two phases, one which melts the powder and the remaining reheats the surrounding material.

However, due to the lack experimental peak temperatures in literature, no reliable target could be inserted and the default value based on voxel mesh and layer thickness was used. The thermomechanical calibration will then use this value to adjust and find the optimized volumetric expansion coefficient. For the calibration process, the printing parameters were set equal to the values in Table 2, a voxel mesh size of 0.7 mm was used and the experimental feature of austenite-martensite phase transformation was considered. Two different baseplate temperatures were

compared, 100˚C and 200˚C.

The thermomechanical calibration requires a zmax target to aim for. This is the tip displacement achieved when printing and cutting off a cantilever using a specific machine. Since no experimental procedures were made, approximate values

according to [37] were chosen. No information of a specimen in another direction was reported and only one cantilever could be used for calibration. The end point was chosen as reference and a displacement of 1 mm was used. In order to more easily find the volumetric expansion factor, the initial value was lowered from default value to 0.3 and accepted deviation from zmax was 3%.

6.3 Thermal Simulations

When the sensitivity was investigated and mesh setting fixed to 0.7 mm, thermal simulations were performed to obtain the temperature histories at the same previously chosen points of the geometry. Power, efficiency, speed and baseplate temperature were changed to investigate the effect on temperatures, cooling rate and element segregations. The build parameters will influence the laser energy density and hence the temperature evolution. These parameters are vital for a good printing process and hence the variance in energy density was investigated in order to see how the results changed. Furthermore, investigating which parameters influence more than others are also of interest. The different build parameters used are listed in Table 4. Each printing condition has been addressed with a number for convenience.

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Table 4. Build parameters used for different cases.

Case 1- refere nce

2- speed

3- efficie ncy

4- basepl ate

5- powe r

6- same original Ev

7- only power change Mesh,

mm

0.7 0.7 0.7 0.7 0.7 0.7 0.7

Power, W

285 285 285 285 400 400 400

Speed, mm/s

960 1000 1000 960 960 960 960

Efficien cy, %

99.2 99.2 80 99.2 80 70.68 99.2

Basepla te T, ˚C

200 200 200 100 200 200 200

Energy density, J/mm³

67.47 64.77 52.24 67.47 76.37 67.47 94.7

Influence of segregated elements on Ms temperatures for case 1, 4 and 5 were further compared. The segregation was investigated in Thermo-Calc. To consider the non- isothermal and time-dependent nature of additive manufacturing, the diffusion module DICTRA was used. The thermal histories achieved in Simufact were imported but the small time steps caused numerical problems and hence larger time steps were used as input. The temperatures were instead added as stepwise functions in the console mode ensuring that the cooling rates remained within around 30% of the average original cooling rate between the time steps. Only the last temperature peak over liquidus was used in each case. One region was entered with a width of 250 nm correlating to half of the cellular spacing. The grid was set to double geometric with 180 points and increasing denseness closer to each side of the grid by 10%. Liquid was entered as the active matrix phase and FCC#1 as an inactive phase allowed to form at the right interface boundary in an overall closed system. Fe, Ni, Co, Mo and Ti were expected to segregate and used in the simulations to also facilitate the calculations without affecting the results significantly.

Points A and D in the geometry were compared. Shortly before complete

solidification when the remaining liquid was between approximately 0.0005 and 0.05% of solid material, the simulation stopped for both points for case 5 and point A for case 1 and hence new simulations were needed to finish the processes. The reason is the segregation of elements during solidification which creates impossible

circumstances for DICTRA to find equilibrium for the last remaining liquid to

solidify. The solidified FCC composition profiles were saved and entered as new start compositions in a now slightly smaller region cell size representing the solidified FCC. The temperature profile started where the previous ended and the complete diffusion process was simulated to the last time step. Since the remaining liquid was neglected, only the active matrix phase of FCC was entered. The points investigated in

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DICTRA were Point A and D for the reference case 1, the increased energy density case 5 and for case 4, where a lower baseplate temperature for case 1 was used.

Different thermal profiles were used for investigation and the segregated compositions over distance were plotted and compared in tables. The new

compositions for case 1 and 5 were then correlated to Ms and Mf temperatures at point A and D by TC-Python, important for further microstructural investigations, together with the retained austenite fractions. The results were compared to previous experiments found in literature. Both TC and Simufact were used to calculate the martensitic volume fraction.

One way to investigate the reliability of the simulations is to calculate the primary dendrite arm spacing (PDAS), λ1 (μm), based on simulated thermal information and compare to micrographs. The equation is given as

𝜆₁ = 𝛼𝑇̇^−𝑛 (13)

where α and n are material specific constants set to 60 ms/K and 0.5 respectively and 𝑇̇ is the cooling rate. The n coefficient should be between 0.2 and 0.5 and α between 60-100 ms/K for steels [61]. The equation can also be used to connect the

temperature profiles from Simufact to the cell size used in DICTRA simulations.

Scheil simulations were also conducted to obtain composition during solidification.

All elements and phases were considered since each simulation computes relatively fast. Further investigation was done by allowing for back diffusion in the primary phase with cooling rates varying from 10000-30000 K/s.

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7 Results

The thermal Simufact simulations completed in 4-5 hours and thermomechanical calibrations up to a few days depending on initial reference value. All simulated data and files were saved on a separate hard drive for future use.

7.1 Material

The heat capacities and thermal expansion coefficients for austenite and martensite calculated using Thermo-Calc and the Calphad thermodynamic database TCFE10 and MOBFE5, are plotted in Figure 11 and Figure 12.

Figure 11. Thermo-Calc calculation of heat capacities for FCC and BCC of 18Ni300 using TCFE10 database.

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Figure 12. Thermo-Calc calculation of thermal expansion coefficient for FCC and BCC of 18Ni300 using TCFE10 database.

7.2 Sensitivity

Figure 13 shows the thermal history of all points including all temperature peaks.

Figure 14 illustrates the material sensitivity for the first peak only. The predefined material in Simufact is compared to only updated liquidus and solidus temperature and to the fully updated material, including also new thermal expansion coefficient and specific heat capacity. After updating the specific heat capacity and thermal expansion coefficient according to Thermo-Calc, the temperatures were decreased.

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Figure 13. Thermal history for all points, reference case 1.

Figure 14. Material dependent sensitivity using predefined MS1-MPM material, updating solidus and liquidus and also updating heat capacity and thermal expansion coefficient.

Figure 15 shows the mesh sensitivity of the first temperature peak for case 1

condition. The maximum temperature and cooling rate increased with smaller voxel size. Table 5 shows each maximum cooling rate after the corresponding temperature peak for the different mesh sizes. Considering temperature results and duration of one simulation the mesh size was set to 0.7 mm. Using 0.4 mm and 0.5 mm increased

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

0 2000 4000 6000 8000

Temperature [˚C]

Time [s]

Thermal history - Reference Case 1

Point A - Top Point B - Wall Point C - Protruding Point D - Bottom

100 600 1100 1600 2100 2600 3100 3600 4100 4600 5100

0 2 4 6 8 10 12 14

Temperature [˚C]

Time [s]

Reference Case 1 - Bottom Point D

Predefined

Solidus and liquidus Fully updated

Linkage of Macro- and Micro-scale Modelling Tools for Additive Manufacturing

Linkage of Macro- and Micro-scale Modelling Tools for Additive

Manufacturing

JULIA SJÖSTRÖM

Abstract

Sammanfattning

Table of Contents

1 Introduction

2 Literature Review

3 Maraging steel

4 Method

5 Simulation Theory

𝑞 =

𝐽

= − ∑ 𝐷

6 Simulation Setup

7 Results