IN DEGREE PROJECT MATERIALS DESIGN AND ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2018

Evaluation of residual stresses and distortions in additively manufactured components

SONJA JONSSON

SEBASTIAN KRAPPEDAL

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

Royal Institute of Technology

Master Thesis

SE202X

Evaluation of residual stresses and

distortions in additively manufactured

components

Author:

Sonja Jonsson

Sebastian Krappedal

Supervisor:

Pasi Kangas

Examiner:

Per-Lennart Larsson

June 25, 2018

Abstract

Additive manufacturing is a novel manufacturing technique, which has developed rapidlyin recent years. The additive manufacturing process produces complex geometries, lightweighted components and reduces the material waste. During the building process, a laserenergy source is commonly used to melt the metal powder. Due to the presence of ther-mal gradients, residual stresses resides in the final product. These residual stresses, whenreleased, result in a distortion of the product. To predict the appearing residual stressesand distortions, simulation tools can be used and prevent costly trials of failed printedproducts. This thesis investigates whether a good prediction of residual stresses and dis-tortions can be performed in additively manufactured components using MSC Simufact.The inherent strain method was used to predict the residual stresses and distortions of acantilever beam respectively a pipe. The printed components were then compared withthe simulations. The residual stresses were examined using a X-ray di↵ractometer and thedistortions were analyzed by a laser scanner.

Results showed that the predicted distortions of the pipe correlated well with the sim-ulations. However, the residual stresses were di�cult to compare with the simulations.The conclusion that Simufact Additive can predict distortions can thus be drawn.

Keywords: Additive manufacturing, selective laser melting, inherent strain, distor-tions, residual stresses, X-ray di↵raction, Simufact Additive.

Sammanfattning

Additiv tillverkning ar en modern tillverkningsteknik som har utvecklats snabbt de senastearen. Den additiva tillverkningen genererar komplexa geometrier, latta komponentersamt optimerar materialatgangen. Vid printingprocessen anvands en laserstrale som en-ergikalla for att smalta metallpulvret. Temperaturgradienten som uppkommer av styrkanpa laserstralen resulterar i restspanningar hos produkten. Dessa restspanningar frigorsnar man skar loss komponenten fran basplattan, vilket resulterar i deformationer. For attkunna forutspa dessa restspanningar och deformationer kan simuleringsprogram anvandas.Denna studie undersoker ifall man kan forutspa restspanningar i en kam och deforma-tioner i ett ror med hjalp av MSC Simufact. For att kunna forutspa restspanningarna hoskammen respektive deformationerna i roret anvands ”inherent strain” metoden. Resul-taten fran simuleringen jamfordes med de experimentella vardena dar restspanningarnauppmattes med hjalp av en rontgendi↵raktometer. Vid analys av deformationer anvandesen laserskanner.

Resultaten visade att deformationerna i roret stamde val overens med simuleringarna.Daremot var det svart att jamfora restspanningarna med vardena fran simuleringen.Sammanfattningsvis kan darfor Simufact Additive forutspa deformationerna i additivttillverkade komponenter.

Nyckelord: Additiv tillverkning, selektiv lasersmaltning, ”inherent strain”, deforma-tioner, restspanningar, rontgendi↵ratktometri, Simufact Additive.

Acknowledgement

This Master Thesis was carried out at the AM center at Sandvik, Sandviken, betweenJanuary and June 2018. The project was performed as a part of the Solid Mechanics trackin Materials Design and Engineering program at the Royal Institute of Technology (KTH).

We would like to sincerely thank our supervisor Pasi Kangas and the rest of the re-search group at the AM center at Sandvik for the enjoyable and challenging time at thecompany. It has been a new and rewarding experience researching within additive manu-facturing. We would also like to thank our supervisor at KTH Prof. Per-Lennart Larssonfor his support during the project. Also, a warm thanks to all the people at Sandvik Coro-mant in Vastberga for the positive and welcoming atmosphere. Finally a kindly thanksto Michele Antolotti and Martina Riccio at Beam IT who helped us with the additivemanufacturing part of this thesis.

Sincerely,Sonja Jonsson and Sebastian Krappedal

List of Figures

1 An overview of the AM process. . . . . . . . . . . . . . . . . . . . . . . . . . 12 The di↵erent steps in the AM product development cycle. . . . . . . . . . . 23 The di↵erent steps MSC Simufact executes in the product cycle development. 34 The di↵erent steps in a PBF process. . . . . . . . . . . . . . . . . . . . . . . 65 The base plate, support structure and the cantilever in the AM process. . . 76 The di↵erent support structures in relation to the cantilever beam. . . . . . 77 The scanning directions in the AM process. . . . . . . . . . . . . . . . . . . 88 The hatch angle in the AM process. . . . . . . . . . . . . . . . . . . . . . . 89 The hatch angle in relation to number of printed layers. . . . . . . . . . . . 910 The scanning strategies in the AM process . . . . . . . . . . . . . . . . . . . 911 The building direction in the AM process . . . . . . . . . . . . . . . . . . . 1012 Flow chart of FEM computation of stress with the inherent strains. . . . . . 1213 Microscopic modelling of the laser movement. . . . . . . . . . . . . . . . . . 1314 The element birth process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315 Calibration process of the cantilever beams. . . . . . . . . . . . . . . . . . . 1616 Voxel mesh in MSC Simufact . . . . . . . . . . . . . . . . . . . . . . . . . . 1717 Hexahedral elements with 8 and 27 control points. . . . . . . . . . . . . . . 1718 Schematic view of the plane of the specimen and the direction �. . . . . . 1919 The plots which are generated from the XRD analysis. . . . . . . . . . . . . 2020 Collection of 3D coordinates using a laser scanner. . . . . . . . . . . . . . . 2121 Triangulation principle using a laser scanner. . . . . . . . . . . . . . . . . . 2122 The building platform with the manufactured components. . . . . . . . . . 2423 The building directions of the cantilever beams for the calibration. . . . . . 2424 The cantilever beam in the xz-plane. . . . . . . . . . . . . . . . . . . . . . . 2525 The manufactured pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2526 The building platform with the 4 modules. . . . . . . . . . . . . . . . . . . . 2627 The reference markers for the laser scanning. . . . . . . . . . . . . . . . . . 2728 The electro polished zones of the cantilever beams in module 2. . . . . . . . 2729 The electro polished zones on the cantilever beams. . . . . . . . . . . . . . . 2830 The manufactured building platform. . . . . . . . . . . . . . . . . . . . . . . 3031 The cantilever beams after cutting it from the base plate. . . . . . . . . . . 3032 The pipe after cutting it from the base plate. . . . . . . . . . . . . . . . . . 3033 The residual stresses in the 45� direction of the printed cantilever beams. . 3134 The residual stresses in the 135� direction of the printed cantilever beams. . 3235 The residual stresses of the simulated cantilever beams using Stoney’s equa-

tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3336 A shape comparison of the printed pipe. . . . . . . . . . . . . . . . . . . . . 3537 A shape comparison of the simulated pipe. . . . . . . . . . . . . . . . . . . . 36A.1 The e↵ective stress of the simulated cantilever beam. . . . . . . . . . . . . . 42A.2 The stress state in x-direction of the simulated cantilever beam. . . . . . . . 42A.3 The stress state in y-direction of the simulated cantilever beam. . . . . . . . 43A.4 The shear stress in the xy-plane of the simulated cantilever beam. . . . . . 43A.5 The stress state of the simulated pipe. . . . . . . . . . . . . . . . . . . . . . 43

List of Tables

1 The printing settings for the cantilever beams using Ti-6Al-4V. . . . . . . . 252 The printing settings for the pipe using Ti-6Al-4V. . . . . . . . . . . . . . . 263 The scanning parameters for the XRD analysis. . . . . . . . . . . . . . . . . 284 The residual stresses of the printed cantilever beams in module 2. . . . . . . 315 The distortions and the residual stresses of the printed cantilever beams in

module 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 The shape deviation of the printed pipe in comparison with an undistorted

pipe without any support. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 The shape deviation of the printed pipe in comparison with an undistorted

pipe without any support. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36A.1 A comparison of the inherent strains for Al-Si-10Mg. . . . . . . . . . . . . . 41A.2 A comparison of the inherent strains for Ti-6Al-4V. . . . . . . . . . . . . . . 41A.3 The collected data when measuring the distortions in the cantilever beams. 41

Contents

1 Introduction 11.1 Sandvik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.6 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Additive manufacturing 52.1 Powder bed fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Selective laser melting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.1 Parameters causing residual stresses . . . . . . . . . . . . . . . . . . 62.3.2 Scanning strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.3 Building directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Anisotropy of AM materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Finite element analysis 113.1 Thermo-mechanical simulations . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Inherent strain method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Software tool 164.1 Software calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.2 Mesh settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Measurement techniques 185.1 X-ray di↵raction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.1.1 Bragg’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.1.2 Strain measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.1.3 Residual stress determination . . . . . . . . . . . . . . . . . . . . . . 18

5.2 3D scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.2.1 Gom Atos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2.2 Stoney’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Theoretical reference frame 23

7 Method 247.1 Cantilever beams for calibration . . . . . . . . . . . . . . . . . . . . . . . . 247.2 Pipe for the deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257.3 Analysis of the printed components . . . . . . . . . . . . . . . . . . . . . . . 267.4 Laser scanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267.5 X-ray Di↵raction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

7.5.1 Electro polishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277.5.2 Residual stress analysis . . . . . . . . . . . . . . . . . . . . . . . . . 28

7.6 Analysis of the simulated components . . . . . . . . . . . . . . . . . . . . . 28

8 Results 308.1 Analysis of the cantilever beams . . . . . . . . . . . . . . . . . . . . . . . . 318.2 Analysis of the pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

9 Evaluation of the chosen method 38

10 Conclusions 39

11 Suggestions for further work 40

A Appendix 41A.1 Inherent Strains of the cantilever beams . . . . . . . . . . . . . . . . . . . . 41A.2 Distortions of the cantilever beams in modules 1 and 3 . . . . . . . . . . . . 41A.3 Simulated components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Bibliography 44

Abbreviations

AM Additive Manufacturing. 1

CAD Computer Aided Design. 2

EBM Electron Beam Melting. 5

FEM Finite Element Method. 11

LHI Least heat influence. 8

PBF Powder Bed Fusion. 5

SLM Selective Laser Melting. 3

XRD X-Ray di↵raction. 4

1 Introduction

1.1 Sandvik

This Master Thesis was carried out at the division for Additive Manufacturing (AM) atSandvik. The industrial company has a global profile focusing on engineering tools formining, equipment and tooling systems for metal cutting. The advanced stainless steel,special alloys and products for industrial heating are other core areas. Sandvik has threeR&D/sales servive business areas: Sandvik Materials Technology, Sandvik Mining & RockTechnology and Sandvik Machining Solutions. The division for AM is part of the SandvikMachning Solutions [1].

The company was founded in 1862 by Goran Fredrik Goransson, who initially focusedon drill steel for rock-drilling. This combined with high quality and added value, operating,investing in R&D and close customer service led to successful business [2]. Nowadays,Sandvik has developed a world wide brand with new and innovative techniques such asAM. The research center for AM was established in 2014 in Sandviken to develop newpossibilities of manufacturing complex geometries, which may benefit in comparison to amore traditional production approach [3].

1.2 Background

AM is a modern application, which has revolutionized the industrial production duringits existence and can be considered as one of the next pillars of the industrial revolution.The AM process creates possibilities such as: simplified logistics of spare parts, producingcomplex geometries of di↵erent components and reducing material consumption [4].

Furthermore, di↵erent kind of materials can be applied in the AM process dependingon the type of product and manufacturing process. Polymers, ceramics and metals aredi↵erent materials that can be integrated in the AM process [5]. Also, depending on howthe machine and the process parameters are designed, the material is either melted, bindedor polymerized in the manufacturing process. The material in an AM process can eitherbe liquid based, solid based or powder based [6]. An illustration of how the AM processis divided depending on material is shown in figure 1.

Figure 1: An overview of the AM process depending on the material [6].

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Moreover, there are number of di↵erent steps in the AM product development cycle,which are shown in figure 2. Initially, a design concept is made. Then, the following stageis to make a Computer Aided Design (CAD) of the component. Based on the modelledgeometry, a further analysis and an optimization is then performed. Afterwards, the soft-ware file is converted to the AM machine to build the component. When the componentis finished, it may need to undergo post-processing treatments to improve its mechanicalproperties. Finally, the prototype testing and evaluation is performed to investigate if theproduct fulfills the design criteria. If the design criteria is achieved, the component is thenconsidered as a final product. Otherwise, it is necessary to redo the product developmentcycle until the product meets the design criteria [7, 8].

Figure 2: The di↵erent steps in the AM product development cycle [7, 8].

In the process of building, presented in figure 2, the printed component may exhibitexcessive residual stresses. Post-processing heat treatments of the components are per-formed to reduce the magnitude of the residual stresses. Although heat treatment resultsin a more ductile material, some components may still crack or exhibit distortions as aresult of the remaining residual stresses [9].

Consequently, the possibility to predict residual stresses before building the componentin the manufacturing process is important. If the residual stresses appears to be too largein the simulation process, the building process or the design can then be re-constructed tocontrol the stress state. For example, the distortions may appear as a result of excessiveresidual stresses in the building process. Those type of errors can be reduced by modifyingthe support structure.

The software tool used in this study, MSC Simufact, has an application called additivemanufacturing, which is adapted to better understand the AM process. The softwaretool simulates parts of the product development cycle as shown in figure 3. Some ofthe design parameters that the software tool examines are: the material selection, laserpower, powder characteristics and hatch angles [10]. Therefore, comparing how the stressstate and distortions in the software tool corresponds to the actual stress state in the AMcomponent will be the main investigative part of this study.

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Figure 3: The di↵erent steps MSC Simufact executes in the product cycle development[11].

1.3 Aim

The aim of this study is to investigate whether a good prediction of residual stresses anddistortions can be performed in AM components, using the software tool MSC Simufact.During this study, cantilever beams will be manufactured using Selective Laser Melting(SLM) to compare the residual stresses with the simulation software and to generate theinherent strains. Also, to evaluate the distortions with the simulation software, a pipe ismanufactured.

To fulfill the aim, the SLM process will be studied further since it is the main manu-facturing process in this study. Creating an understanding of how the design parametersin the AM process correlate with the software tool, MSC Simufact, is required. Also, howto measure residual stresses and distortions in the manufactured components is examinedto yield relevant and su�cient results.

1.4 Problem statement

Based on the aim of this study, the following problem statements are defined to executethis thesis:

• Do the residual stresses and distortions in MSC Simufact correspond to the experi-mental measurements, which in this case are the printed AM components?

• Is MSC Simufact an e�cient software tool in AM processes concerning aspects as:user friendliness, yielding qualitative results and time management for simulations?

• Do the applied methods ensure that a good comparison can be made when comparingthe printed components with the simulations?

1.5 Limitations

For this study, only the metal powder Ti-6Al-4V will be studied. The main reason for thechoice of material relates to the AM process, where Ti-6Al-4V is commonly used. Also,titanium alloys are common materials for AM since it is light-weight, bio-compatible andcorrosion resistant, which is useful for the aerospace and medical industry [12].

Regarding the design of the machine, the SLM process melts the metal powder bya laser beam, which is the only studied energy source in this thesis. When evaluatingthe AM components, the examined parameters are residual stresses and distortions. Theresidual stresses causes distortions and sometimes even cracks in components.

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As for the experimental analysis, the residual stresses were measured implementingStoney’s equation and X-Ray di↵raction (XRD). The distortions were examined using a3D scanner.

1.6 Contributions

This thesis will contribute to a better knowledge about the software tool MSC Simufact.The additive manufacturing part in MSC Simufact is a new tool for investigating AMparts. By evaluating how it works, the company will gain a better understanding of itsfunctions and if it is the most e�cient software tool on the market for AM components. Tomake the MSC Simufact classified as e�cient, the software tool needs to be user-friendly,present reliable results and be time e�cient in the simulation process.

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2 Additive manufacturing

AM is a manufacturing method based on additive incremental layer by layer manufactur-ing and di↵ers from conventional subtractive methods such as cutting or casting material.With the use of computer design models, this method can rapidly create components withhigh precision and without the need of many conventional processes and tools. Since AMcan be used to create complex and lightweight components that are created with less wastematerial and decreased energy usage, interest for using AM has increased within manyapplication areas [13].

Various methods using AM can be used depending on the input source material andthe energy source to form each layer, these two parameters are the main parameters forany metal in the AM process [14]. Di↵erent input source material may be in the form ofwire or powder. The AM process also requires a computer design model which is dividedinto di↵erent layers. The thickness of each layer is determined based on which sourcematerial is used and how other AM process parameters are set. When working with metalor alloy powders, Powder Bed Fusion (PBF) is a common AM method to print parts.Energy sources can either be in the form of laser or electron beams which uses thermal en-ergy, focused on select areas of the powder bed to fuse the powder and form each layer [15].

2.1 Powder bed fusion

PBF is an AM method where powder bed particles are selectively fused or fully meltedtogether in an inert gas atmosphere or vacuum depending on the energy source. Thepowder is put in two di↵erent chambers, one containing the powder stock and the otherone containing the build platform. As a layer is printed by the energy source accordingto the design model, the build platform is lowered and the powder stock piston movesupward to provide the build platform with more powder, usually with the help of a roller.The process, shown in figure 4, can then be repeated to create the next layer. CommonPBF methods using a laser beam include SLM [16].

2.2 Selective laser melting

SLM selectively prints each layer by fully melting the powder bed particles. The maindi↵erences when using laser beam as an energy source as opposed to an electron beaminclude energy beam intensity, build atmosphere, heating conditions as well as surfacefinish of the finalized component. Printed parts that are made with the use of SLM arecreated in an atmosphere with an inert gas whereas Electron Beam Melting (EBM) usesvacuum. Higher impurity levels and inclusions have therefore been seen in parts printedwith the SLM method [17]. Since the EBM uses higher energy intensity, there is anincreased build rate compared to SLM but the surface finish of the parts printed withSLM are finer [18]. Due to the high temperature heating and cooling when using SLMand EBM, temperature gradients occur in the printed parts. These thermal gradientsresults in large residual stresses in the printed part [19].

2.3 Residual stresses

During the process of PBF, large amounts of heat is applied at the top layer. As the buildcontinues, thermal convection of the material results in thermal gradients causing residualstresses where the magnitude will vary. The residual stresses are defined as the stresses,which remain in the material after the thermo-mechanical treatment has been performed

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(a) A powder layer is applied. (b) The layer is melted by the laser.

(c) A detailed overview of the laser melting pro-cess.

(d) The platform is lowered to apply anotherlayer.

Figure 4: The di↵erent steps in a PBF process [11, 17].

[20]. Moreover, there are three di↵erent types of residual stresses, namely type I, II andIII. Type I are long range stresses, which equilibrate over macroscopic dimensions. Thesetypes of stresses are calculated by applying continuum models, which does not take intoaccount the multiphase or polycrystalline behavior of a material. Type II is when residualstresses are dependent on the grain dimensions of a material whereas type III exists overatomic dimensions as dislocations [21].

The drawbacks with having excessive values of the residual stresses are resulting dis-tortions, thermal cracks and tensile stresses at the surface. This naturally causes problemswith producing high-quality components in the industry [20].

2.3.1 Parameters causing residual stresses

Furthermore, the appearance of the residual stresses may depend on a number of dif-ferent factors. Material properties, geometry of the components and the support, andthe process parameters are some of the aspects in SLM to consider [12]. The key factorcausing residual stresses in this study is the temperature gradient as mentioned in section2.2. Melting each powder layer in the machine by the laser generates molten pools withpeak temperatures, which exceeds 2000�C. The melted powder layer will then thermallyexpand, resulting in a compression of the surrounding solid material. Consequently, thecompression generates part-plastic and part-elastic strain behavior of the material. Whencooling the molten pool to its surrounding, where the temperature is approximately 100-200�C, the plastic strain causes a tensile strain in the melted parts and a compressivestrain in the surrounding area [22, 23].

Also, the design of the support structure and the base plate in the SLM process areother parameters contributing to residual stresses. The support structure is applied in

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the building process to avoid any bending or collapses of the component. Afterwards, thesupport is removed to finalize the component. The base plate usually has a traditionaldesign of a square with similar mechanical properties as the metal powder. What mightdi↵er is the choice of feedstock material when manufacturing the base plate in comparisonwith the metal powder. In the AM process, the base plate is pre-heated before buildingthe component. This is performed to decrease the gap between the temperatures of themelted layer and base plate and therefore reduce the temperature gradient. An exampleof the base plate and the support structure is presented in figure 5. Also, in figure 6 thereare two types of di↵erent support structures [12].

Figure 5: The base plate, support structure and the cantilever in the AM process [24].

(a) Conical support structure. (b) Thin wall support structure.

Figure 6: The di↵erent support structures in relation to the cantilever beam, which islater removed [12].

Moreover, the melting caused by the laser itself is dependent on di↵erent process pa-rameters such as laser power, scanning length of the laser, the scanning strategy and thebuilding direction. A larger laser power increases the output energy in the SLM process,which causes larger temperature gradients. Also, the increased scanning speed generatesa larger laser energy resulting in a melted top layer as well as bottom layers. As a result,the micro structure of the material changes, which a↵ects the mechanical properties dueto repeatable re-crystallization processes [25].

Additionally, the scan length vector is another important factor to consider when con-structing the design parameters for the SLM process. Longer scanning vectors generatesmore energy, which increases the temperature gradients and the stress state of the printedsample. Consequently, the deformation will increase for this case as well.

2.3.2 Scanning strategies

It is important to consider how the scanning strategy is combined in this case. Withinthe SLM process, there appears di↵erent kind of strategies resulting in varying stressstates and deformations [12, 23]. The most simple strategy is to determine direction ofthe scanning. For example, some of the scanning directions of a laser beam can either be

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unidirectional, bidirectional or spiral, which are presented in figure 7.

(a) Unidirectional.(b) Bidirectional.

(c) Spiral.

Figure 7: Some of the di↵erent scanning directions [11].

Another parameter, the hatch angle, ✓, shown in figure 8, describes the relation be-tween each printed layer in the SLM process. ✓ is the angle between the scanning directionin the initial layer and the following layers. If the hatch angle is 0, then the whole sampleis printed in one direction throughout the process. However, if the hatch angle is assumedto be set to 90� for a rectangular layer, then it will take 4 layers before the scanning direc-tion is the same as the initial layer [25]. This together with other printing combinationsare shown in figure 9.

Figure 8: An illustration of how the hatch angle relates to other printed layers [26].

Another type of scanning strategy is to change the printing directions within the layer.The most simple strategies are to print in one direction throughout the whole SLM processin either horizontal and vertical directions as shown in figures 10a and 10b. One of themore suitable scanning strategies within a layer is called Least heat influence (LHI). Thistype of pattern scans half of the layer in one direction and the other half is scanned inother direction as seen in figure 10c.

Another scanning strategy, the chessboard strategy, shown in figure 10d, is designedwith each sub square set up to scan in di↵erent directions. The aim with the chess boardconcept is to reduce the vector length and therefore decrease the laser energy in the man-

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Figure 9: Presentation of the relation between the hatch angle and the number of printedlayers [26].

ufacturing process [23].

(a) Horizontal direction (b) Vertical direction

(c) LHI (d) Chess board

Figure 10: The di↵erent scanning strategies within a layer [27].

The following scanning strategies results in di↵erent stress states and distortions. De-pending on which direction the sample is measured, the stress state as well as the distor-tions may vary. However, it has been concluded that the most suitable scanning patternis the chessboard strategy [23, 27]. Additionally, the number of printed layers is anotherparameter to consider in this case. More printed layers results in better mechanical prop-erties of the material. The number of printed layers is combined with the hatch angle.The most suitable hatch angle is concluded to be 105� with 24 printed layers [27]. Havingthis type of set-up when printing components generates a material that is less anisotropicthan a material with less layers, which can be noted in figure 9.

2.3.3 Building directions

In addition to the di↵erent scanning strategies, the building direction within a planeis another parameter a↵ecting the residual stresses. The building direction is definedas the acute angle between the longitudinal axis and the vertical axis of a sample [25].The di↵erent building strategies in the varying planes are shown in figure 11. The mostsuitable building direction is in the vertical direction since it has larger tensile strengths

9

than the samples built in the horizontal direction. The vertical printed sample had ahigher elongation than the horizontally printed samples. Also, it is shown how the yieldstress changes depending on building direction. The optimal building direction is at 45�,which results in the perfect combination of ductile and strength behavior of the cantilever[28].

(a) Horizontal direction (b) Vertical direction

Figure 11: Examples of the di↵erent building directions within a plane[28].

2.4 Anisotropy of AM materials

Depending on the scanning strategy together with other design parameters in the AMprocess, anisotropic material properties may occur. The anisotropic behavior indicates amaterial with di↵erent mechanical properties in each direction [26]. Within the scanningstrategy, the number of printed layers and the hatch angle can be modified to reduce theanisotropy. Increasing the number of printed layers and having a varying hatch angle,shown in figure 9, results in less anisotropic behavior of the material [25].

10

3 Finite element analysis

Finite Element Method (FEM) softwares can be useful to predict the evolution of residualstresses in an early stage. Being able to modify and simulate the design parameters in themanufacturing process may thus, ensure the quality of the printed components. Residualstresses are permanent internal strains, caused by the thermal loads that are applied duringthe printing, which can be modelled on a macroscopic level. Other types of residual stressessuch as stresses induced by phase transformation, also occur during the manufacturing andprocessing. Phase changes in the material a↵ects the thermo-mechanical properties of thematerial and can be modelled on a microscopic level. Proper modelling of residual stresseson several levels is therefore important to avoid the dangers of high residual stresses [29].

3.1 Thermo-mechanical simulations

There are generally two methods to calculate the residual stresses in additive manufactur-ing using finite element analysis. The first method is a more conventional thermo-elastic-plastic method commonly used for calculation of welding distortions. This sequentiallycoupled thermo-mechanical approach can however be demanding on computational power.This is due to the transient nature of the moving heat source and the non linearity in thematerial properties. Accurate results of predicted residual stresses, are therefore verydependent on the precision in experimental measurements of thermal and mechanicalproperties. Due to the long computation time for the thermo-mechanical simulation andprediction of residual stresses, it is more suitable for smaller and less complex components.Since the AM process consists of multiple laser seams, a coupled thermo-mechanical sim-ulation approach would be heavy on computational power and require a lot of simulationtime [30].

3.2 Inherent strain method

The second method to determine the residual stress in components manufactured with AMis the inherent strain method. This method is beneficial due to the faster computationtime in comparison with the thermo-mechanical simulations. The inherent strain methodassumes that the laser seam in the AM process is very small in relation to the built com-ponents, and each laser seam has a similar thermo-mechanical history. The inherent strainmethod is therefore completely mechanical. The inherent strains have to be determinedinitially and can then be used to calculate the residual stress and distortion by imposingthe inherent strains on linear elastic FEM formulations [31].

The inherent strain are dependent on the material properties and the process param-eters and can be defined in the following way [31]:

The strain increment, d✏, in a thermo-mechanical formulation consist of an elasticstrain, d✏e, a plastic strain, d✏p, a thermal strain d✏thermal and a strain induced by phasetransformation d✏phase. The total residual strain, ✏

tot

, can be expressed as the summationof these increments according to the following equations.

✏tot

= ✏e + ✏p + ✏thermal + ✏phase (1)

The inherent strain, ✏⇤, is defined as the di↵erence between the total residual strainand the elastic strain as seen in equation 2.

✏⇤ ⌘ ✏tot

� ✏e (2)

11

The inherent strain is thus a sum of the plastic strains, thermal strains and phasetransformation induced strains as shown in equation 1. Using elastic FEM, the inher-ent strain can then be used to calculate the residual stresses according to the followingequations.

[K][u] = [f⇤], (3)

f⇤ =

Z[B][D][✏⇤]dV, (4)

Where [K] is the elastic sti↵ness matrix, [u] is the nodal displacement vector, f⇤ is thenodal force vector induced by the inherent strains. When the displacement vector [u] hasbeen solved using equation 3, the total strain, ✏, and consequently the residual stress, �,can be calculated.

✏ = [B][u] (5)

� = [De]([✏tot

]� [✏⇤]) (6)

Where [B] denotes the nodal deformation matrix and [De] denotes the material elasticmatrix [31]. The inherent strain, shown in figure 12, can be seen as the input for the FEMcomputation of the stresses and can be determined in either of the two ways, through athermal-elasto-plastic simulation or experimental measurements.

Figure 12: Flow chart of FEM computation of stress with the inherent strain as input[32].

The method of determining the inherent strain through FEM and using it for thecalculation of the stress can be summarized in the following manner:

1. A transient thermo-mechanical analysis is performed on a smaller specimen of a part.

2. After the whole part has cooled down to ambient temperature, the plastic straintensor and equivalent plastic strain are calculated.

3. The calculated plastic strains obtained from the specimen are then transferred tothe whole part.

12

4. Using elastic FEM with the whole part, computation of the macro model and itsdistortions and residual stresses can be made.

The modelling of the laser seam, shown in figure 13, can be described as follows. Ini-tially the trajectory of the laser seam on the powder bed is modelled. All of the elementsin the mesh of the powder bed layer are deactivated, meaning that there is no interac-tion with other elements. The elements remain deactivated until the laser trajectory haspassed by, the elements then become activated. The process of this layer based elementbirth technique is shown in figure 14. Afterwards, the resulting strains of the layer arecalculated. These strains are then used as inherent strains. As the build process continues,each layer of the build is activated sequentially. In order to account for changes of scanningstrategies for certain layers, rotation of the inherent strain vector can be performed andthe equivalent mechanical layer can be found [30].

Figure 13: Microscopic modelling of the laser movement [32].

Figure 14: The element birth process [30].

The inherent strain can also be determined experimentally by printing a specimen andmeasuring the inherent deformation due to the release of the residual stresses. When aspecimen containing residual stresses is cut the stress in the specimen will alter. Thismay be troublesome for many stress measurement techniques but is taken full use of inthe inherent strain method. In an ideal cutting process, the inherent strain in the original

13

specimen will not change even though the residual stress distribution does. The changein stress �� when cutting is used to calculate the inherent strain ✏⇤. A relation betweenthe stress state due to the cutting and the inherent strain can be represented in tensornotation as:

�� = f(✏⇤) (7)

To solve the equation and find the relation between the stress change and inherentstrain the material is regarded an elastic material. The relation can then be written as:

� = C(✏� ✏⇤) (8)

where:�=stressC=elastic constitutive tensor✏=total strain✏*=inherent strain

To find the elastic response function f(•) in equation 7, the inherent strain that causesthe change in stress is sought for. This can be done by the use of finite element analysisassuming the inherent strain and stress can be linearly interpolated between the elementsof the geometry. The stress can be determined experimentally at the nodes, while thestress and inherent strains in the elements are interpolated linearly from the nodal values.If every node is defined by a value of the stress, inherent strain and elastic responsefunction, the components of equation 8 can be indexed and rewritten as [33],

✏⇤ = ⌃✏⇤i

Ni

, (9)

� = ⌃�i

Ni

, (10)

f(•) = f(•)✏i

Ni

, (11)

where N is the specific interpolation function for each node.f(✏⇤) can be defined for any ✏⇤ and consequently,

Mij

= fi

(✏⇤ = ✏⇤j

Nj

|⇤✏

j

= 1), (12)

for every ✏⇤ = ⌃✏⇤i

Ni

with ✏⇤ = 1.

Rewriting equation 7 as:

�i

= ⌃Mij

✏⇤j

(13)

the degrees of freedom ✏⇤j

can now be solved for using a finite element code.

In the case of anisotropic plasticity, which may occur in the additively manufacturedcomponents, yield criterion such as Hill’s and Barlat’s yield criterion may be used. De-pending on the process treatments other flow curve approaches may be applied [34].

F |�2��3|m +G|�1��3|m +H|�1��2|m + L|2�1��2��3|m +M |2�2��1��3|m +N |2�1��2��3|m0 (14)

Where F, G, H, L, M and N are experimentally determined constants.

14

f = |k1 + k2|a + |k1 � k2|a + |2k2|a = 2�ae

(15)

m and a are material parameters which are experimentally determined.

where:

k1 =�11 + �22

2

k2 =

s✓�11 � �22

2

◆2

+ �122

15

4 Software tool

MSC Software produces many tools for di↵erent kind of applications as: welding, joiningand additive. A large variety of treatments can be simulated to yield su�cient componentsto manufacture. Linear statics, thermal expansions, acoustics and failure analysis are someof the areas that can be simulated. Simufact Additive focuses on the AM process, morespecifically the SLM. MSC Simufact creates simulation possibilities such as [35]:

• Determination of the final shape by predicting distortions and residual stresses.

• Detection local hot spots and lack of fusion.

• Examination of the microstructure to evaluate the quality and appearing defects.

• Execution of additive simulation before building the component to verify that theprocess parameters are modified correctly.

4.1 Software calibration

The simulation of the AM process, using the inherent strain method, is an e�cient ap-proach when examining the printed components. However, the inherent strain needs tobe determined to perform the simulations. There are two di↵erent variants for doing thecalibration to determine the inherent strains. The first approach is when cantilever beamsare printed in both horizontal and vertical directions of the xy-plane for calibration. Athird cantilever beam can be printed in 45� direction for either calibration or validation.The same building platform could contain a fourth cantilever beam in arbitrary directionfor a final validation. This is shown in figure 15. When printing the cantilever beams 1-3,the same scanning strategy should be implemented where the hatch angle is 0�. Cantileverbeam 4 can be printed with the desired hatch angle [36].

Figure 15: The first method in how to perform a calibration [36].

The second approach calculates the average values of the inherent strains. This methodis used when components or the cantilever beams are built with varying hatch strategies,i.e chess board strategy. The inherent strains from this approach can only be imple-mented on components that are built the same way. In this case, only one cantilever beamfor calibration is required but having several beams built the same way is useful for thevalidation. Given the single printed cantilever beam, the measured distortion in the z-direction can then be implemented in the 0� and 90� cantilever beams in the software tool.

Once the process parameters and material properties have been calibrated, the soft-ware tool can now estimate the inherent strain by solving an optimization problem using

16

the least square method [35]. The optimization problem S can be formulated as follows,

S = minnX

i=1

r2i

(16)

Where ri

is the di↵erence between zi,sim

and zi,exp

. i is the number of running index,n represents the number of sample points, z

i,sim

is the simulated distortion and zi,exp

isthe measured distortion from the experiments.

4.2 Mesh settings

The surface mesh in MSC Simufact is built up by triangular elements. Hexahedral voxelelements, shown in figure 16, are then mapped on top of the surface mesh. These voxelelements create undistorted hexahedral element and can be mapped easily to complexcontours. The hexahedral element initially consists of 8 gauss points in the form of acube. The element can then selectively be sub-divided in 8 more sub-elements generating27 control points, see figure 17. The voxel elements use a volume fraction approach wherethe elements contain a solid fraction. Depending on a specified value of the solid fraction,the voxel element will be removed. Consequently the element sti↵ness has to considerthis volume fraction [35, 34]. Simufact additive meshes the surface mesh automatically,alternatively the geometry can be remeshed using other pre-processing softwares.

Figure 16: Voxel mesh of the pipe in MSC Simufact.

Figure 17: Hexahedral elements with 8 and 27 control points [35].

17

5 Measurement techniques

5.1 X-ray di↵raction

In order to validate the resulting residual strains and residuals stresses calculated fromthe simulations, the residual strains and thus the residual stresses need to be determinedexperimentally. A common method used to determine the residual strains is using XRD.The method can be used to measure the strains in the crystal lattice of the material.Residual stresses can then be calculated using constitutive equations for the stress strainrelationship in the appropriate crystal lattice planes [37]. The fundamentals of XRDdepend on the wave front interactions between the X-ray beam and the crystal lattice.The general application of the method can be described by Bragg’s Law [32].

5.1.1 Bragg’s Law

Crystalline materials consisting of atom lattice arranged structural patterns throughoutthe material. The planes of these atomic lattices can cause constructive or destructiveinterference through di↵raction. Bragg’s law deduces an equation for how the constructivedi↵raction can occur. This equation is expressed as the following:

n� = 2dsin(↵), (17)

where � is the wave length of the X-ray beam, n is an integer for the wavelength order,d is the inter-planar spacing between planes in the atomic lattice and ↵ is the angle of theincoming beam and the lattice planes [38].

5.1.2 Strain measurement

A material that is strain free has a characteristic di↵raction pattern for the unstrainedinter-planar spacing. By changing this inter-planar spacing or changing the wave lengthof the X-ray beam, di↵erent di↵raction patterns can be achieved. When a material isstrained, the elongations and contractions that occur in the crystal lattice will a↵ect theinter-planar spacing of the lattice planes and consequentially the di↵raction patterns. Bymeasuring this change of inter-planar spacing, the strain can be determined. By alteringthe tilt of the specimen within the di↵ractometer, plane measurements of di↵erent anglescan be made. Given a certain miller plane index (hkl), the lattice strain can be calculatedusing the following equation.

✏hkl

=d0 � d

hkl

d0(18)

where d0 refers to the inter-planar spacing in an unstrained state. In a similar mannerthe strain in the out of plane direction can be determined as following.

✏z

=dn

� d0d0

(19)

Where dn

can be determined using equation 17.

5.1.3 Residual stress determination

Once the lattice strains have been measured, the corresponding stresses can be calculated.A common way to do this using X-ray di↵raction is to implement the sin2 -method. The -angle is defined as the tilt-angle of the the specimen in the di↵ractometer. Measuringthe inter-planar spacing at several di↵erent tilt-angles will generate a curve. The residual

18

stresses can then be determined by calculating the gradient of that curve.

A relation between the measured inter-planar spacing and the stresses can be derivedusing the following equations [32, 39]. Hooke’s law gives:

�y

= E✏y

(20)

If the measurements have been made at the surface of the specimen, then a plane stressstate can be assumed, �

z

= 0. The strain ✏z

can then be determined as:

✏z

= �⌫(✏x

+ ✏y

) =�⌫E

(�x

+ �y

) (21)

A relation between the measured inter-planar spacing and the stresses can then beexpressed as:

dn

� d0d0

=�⌫E

(�x

+ �y

) (22)

For a plane-stress elastic model see figure 18 and using isotropic elasticity theory, thestrain expressed in the �-direction is found to be,

✏ �

=1 + ⌫

E(��

)sin2 � �⌫E

(�1 + �2) (23)

Figure 18: Schematic view of the plane of the specimen and the direction � [32].

When the angle is 90� the strain vector lies in the plane of the specimen surface.

��

= �1cos2�+ �2sin

2� (24)

To further derive the relation between the sin2 -angle and the and stress ��

, the fol-lowing equations are used.

✏�

=d�

� d0d0

(25)

Substitution in equations 22 and 23 gives

d�

� d0d0

=1 + ⌫

E(��

)sin2 � �⌫E

(�1 + �2) (26)

19

And the lattice spacing for any direction defined in ( ,�) is given by,

d�

=1 + ⌫

E(��

)sin2 d0 ��⌫E

(�1 + �2)d0 + d0 (27)

Di↵erentiation of the lattice spacing in regard to the tilt-angle will finally give theexpression for the stress.

@d�

@sin2 = (

1 + ⌫

E)��

d0 (28)

��

=E

1 + ⌫

1

d0(@d

�

@sin2 ) (29)

It is important to note that the elastic constants E and ⌫ are specific for the crystal-lographic plane that is being studied and di↵ers from the bulk elastic components of thespecimen.

In the most simple case scenario, where there are no shear stresses nor inhomogenousstress states present in the material, the expression for the lattice spacing in relation tothe tilt angle will generate a linear curve. Anisotropy or shear stresses will induce a morecomplex curve which is presented below in figure 19 [39].

Figure 19: An illustration of the relation of the inter-planar spacing and the tilt angle ofthe specimen in XRD measurements for di↵erent stress states [32].

5.2 3D scanner

One of the alternatives to analyze the deformation of a component is to implement a laserscanner. This is a relatively simple method which gives qualitative results. The benefitsof using a laser scanner is the non-contact measuring approach and the possibilities ofscanning complex geometries. When scanning the surface of a component, a single pointdata is then obtained. The 3D coordinates of the collected point are described accordingto equation 30 [40].

20

x = rcos�cos✓

y = rsin�cos✓

z = rsin✓

9>=

>;(30)

Laser scanning is based on the principle of time measurement. The laser scanning beammeasures the distance to the examined point and generates the coordinates in relation tothe vertical and horizontal angle, namely ✓ respectively '. The operation of collecting 3Dcoordinates using laser scanning is shown in figure 20. When examining the deformation,the single points can either be applied as a point superposition or point comparison.

Figure 20: Collection of 3D coordinates using laser scanning [40].

5.2.1 Gom Atos

The laser scanning of the cantilever beams and the pipe can be performed by the scannernamed GOM Atos Compact Scan. This scanner with double sensor cameras and lightsource in the middle is based on triangulation principle when collecting points as shownin figure 21. To simplify the collection of the points for the cameras, markers are placedon the scanned component. A double laser beam is then projected on the object to collectthe di↵erent coordinates of the component. When both of the cameras images the area,the spotted zone is collected [41].

Figure 21: The triangulation principle when collecting a point P.

21

5.2.2 Stoney’s equation

When implementing a 3D scanning analysis on a component using laser, the residualstresses can alternatively be evaluated with Stoney’s equation. The laser scanner collectonly single points in comparison with XRD which is one of the drawbacks. To compensatefor this, several single points can be collected to calculate an average value of the residualstresses using Stoney’s equation, which is presented in equation 31. When using Stoney’sequation, two di↵erent states of a thin film are evaluated, namely the strip before theexperiment (t

s

) and after deposition (td

).

� =4E

s

t2s

3td

l2s

(31)

Where � is the residual stress in the collected point, Es

is the Young’s Modulus of thesubstrate, t

s

is the thickness of the substrate, is the deflection of the substrate. td

isthe thickness of the substrate after deposition, l

s

is the length of the substrate [42].

22

6 Theoretical reference frame

As stated in section 3.2, the inherent strain method is a time e�cient approach for an-alyzing the residual stresses and distortions of AM components in comparison to otherconventional methods. Therefore, the inherent strain of AM parts will be determined byusing the software tool MSC Simufact. Being able to analyze the residual stresses anddistortions of AM parts requires further research on how the AM process works and howthe di↵erent process parameters relates.

Given the knowledge of residual stresses and how it can be evaluated, the AM partswill be examined by comparing the results from the simulation in comparison with theexperimental test. The cantilever beams will be evaluated regarding the residual stressessince the geometry is relatively simple. The surface of the cantilever beam is a flat plane,which makes it easier to use the XRD machine. The printed pipe will be used to examiningthe distortions.

23

7 Method

For this study, simulations of the cantilever beams and the pipe were performed to evalu-ate the accuracy when determining residual stresses and deformations. Furthermore, theresults from the simulations were compared with the printed components. The simulationswere performed using the same set-up and process parameters as in the printing, which isshown in table 1.

Moreover, the printing was performed on a building platform with the dimensions250x250 mm using the Ti-6Al-4V material. There were 10 cantilever beams and one pipebuilt in the same material, which are illustrated in figure 22. The machine for printingthe components was EOS M290.

Figure 22: A sketch of the building platform with the components.

7.1 Cantilever beams for calibration

10 cantilever beams were printed accordingly to number 3 in figure 23. Cantilever beam 3,with a building angle of 45�, is a sum of 1 and 2. Figure 24 presents the printed cantileverbeams in the xz-plane. For the simulation and the printing part, the following designparameters were implemented on the cantilever beams, see table 1.

Figure 23: The building directions of the cantilever beams for the calibration.

24

Figure 24: Illustration of how the cantilever beams was printed in the xz-plane.

Table 1: The printing settings for the cantilever beams using Ti-6Al-4V. These are thestandard values for EOS M290.

Parameter Value

Length, [mm] 72Width, [mm] 12Height, [mm] 9Hatch angle, [�] 67Building direction, [�] 45Laser power, [W] 280Layer thickness, [µm] 60Scan width, [mm] 0.14Laser velocity, [mm/s] 1200Laser beam width, [mm] 0.1

7.2 Pipe for the deformation

Aside for the cantilever beams to calibrate for the inherent strains and measure the residualstresses, a pipe as shown in figure 25, was printed on the same building platform to examinethe distortion of the component. The settings for this component are presented in table2. The building direction was the same as for the cantilever beams, which was 45�.

Figure 25: Illustration of the pipe.

25

Table 2: The printing settings for the pipe using Ti-6Al-4V.

Parameter Value

Length, [mm] 90Thickness, [mm] 5Inner diameter, [mm] 35Hatch angle, [�] 67Building direction, [�] 45Laser power, [W] 280Layer thickness, [µm] 60Scan width, [mm] 0.14Laser velocity, [mm/s] 1200Laser beam width, [mm] 0.1

7.3 Analysis of the printed components

In order to fit the printed geometry to the XRD machine and the laser scanner, thebuilding platform was cut into four modules with a band saw according to figure 26. Thecantilever beams of module 2 were then investigated by the XRD where several strainmeasurements at di↵erent angles were made. Finally the stresses were determined usingthe sin2 method as presented in section 5.1.3.

Figure 26: The four di↵erent modules of the building platform.

For the pipe and the cantilever beams in modules 1 and 3, the components were cut outfrom the building platform using a band saw. The pipe was cut out completely whereas thecantilevers were cut until most of the teeth had been removed from the building platform.The cantilever beams were cut at the middle of the teeth section after the print had cooleddown to room temperature.

7.4 Laser scanning

The cantilever beams in modules 1 and 3 together with the pipe were investigated bya laser scanner. Several reference markers were placed on the components for the laserscanning, which is shown in figure 27. The laser scanning was performed by the scannernamed GOM Atos Compact Scan.

26

Figure 27: The reference markers for the laser scanning.

The maximum z-displacement of each cantilever beam was measured to determinethe inherent strain respectively the distortion. Also, the residual stresses implementingStoney’s equation were calculated based on the distortion of the cantilever beams in mod-ules 1 and 3. When the pipe with the support was scanned, the printed version wascompared with an undeformed pipe without any support structure.

7.5 X-ray Di↵raction

The residual stresses of the cantilever beams in module 2 were measured by a XRD ma-chine. Three zones at each cantilever beam were defined and electro polished before theXRD analysis. The defined zones are presented in figure 28. The analysis was carriedout in the 103 lattice plane using Cr K-↵ as the X-ray tube anode. Lattice materialparameters, Young’s modulus and Poisson’s ratio were 120919 Pa and 0.31 respectively.

Figure 28: The electro polished zones of the cantilever beams in module 2 and the mea-suring directions of the residual stresses.

7.5.1 Electro polishing

The electro polishing was performed at three zones on each cantilever beam to avoidmeasuring the stress state at the surface of a component. Following parameter settingswere implemented:

• Room temperature = 25�C

• Electro polishing surface = 1 cm2

• Voltage = 38 V

• Flow rate = 12

27

A mixture of Electrolyte Streuers A2 = 730 ml ethanol + 90 ml distilled H2O + 100ml Butylcellosolve + 78 ml HClO4 was used when etching. When the cantilever beamswere etched around 30 seconds, the voltage of 38 V resulted in a current around 1.5 A.This resulted in a polished depth in z-direction which was approximately around 10µm,see figure 29.

Figure 29: The electro polished zones on the cantilever beams.

7.5.2 Residual stress analysis

When the sample has been prepared, the following parameters were implemented accordingto table 3 to run the XRD analysis.

Table 3: The implemented scanning parameters for the XRD analysis.

Parameter Value

Reflex Ti-103Source K↵Poisson’s ratio, ⌫ [-] 0.31Young’s Modulus, E [MPa] 1209192⇥ scan [�] 115-125Tilt angles, [�] 0, 20.7, 30.0, 37.8, 45.0, 52.2, 60.0Azimuth angle, � [�] 45 & 135

7.6 Analysis of the simulated components

When the deformation values of the cantilever beams had been achieved, the inherentstrains were calculated. When the simulations were performed, the pipe and the cantileverbeam were simulated separately on a building platform. Deformation of the building plat-form as well as the gravity was considered in the simulation. Also, the printed pipe wascompared with an original geometry without any support structure.

When the printed cantilever beams were compared with the simulations regardingthe residual stresses using Stoney’s equation, the e↵ective stress in MSC Simufact wasimplemented. For the residual stresses using XRD, the stress state in x- and y-directionas well as the xy shear stress were applied and then converted by equation 32 to the 45�

and 135� directions [43].

28

S0 =

2

4cos' sin' 0�sin' cos' 0

0 0 1

3

5

2

4�x

⌧xy

⌧xz

⌧yx

�y

⌧yz

⌧zx

⌧zy

�z

3

5

2

4cos' �sin' 0sin' cos' 00 0 1

3

5 (32)

Where S’ is the stress matrix.

29

8 Results

The obtained building platform with the cantilever beams and the pipe is illustrated belowin figures 30-32.

(a) From the side. (b) From above.

Figure 30: The manufactured building platform.

(a) Module 1. (b) Module 3.

Figure 31: The cantilever beams after cutting it from the base plate.

Figure 32: The pipe after cutting it from the base plate.

30

8.1 Analysis of the cantilever beams

Table 4: The residual stresses of the printed cantilever beams in module 2 where theresidual stresses were measured in 45�- respectively 135� direction.

Stress state Residual stress, � [MPa]

Direction 45� 135�

Value Error Value Error

Point 1 -32 225 796 108Point 2 -140 261 221 240Point 3 1041 529 19 127Point 4 310 186 622 70Point 5 526 217 370 180Point 6 565 103 284 176Point 7 465 393 586 181Point 8 263 212 -78 49Point 9 628 121 552 282

Figure 33: The residual stresses in the 45� direction of the printed cantilever beams inmodule 2. The red line represents the simulated results whereas the blue markers are theexperimental values of the printed parts with corresponding error margins.

31

Figure 34: The residual stresses in the 135� direction of the printed cantilever beams inmodule 2. The red line represents the simulated results whereas the blue markers are theexperimental values of the printed parts with corresponding error margins.

Table 5: The distortions and residual stresses using Stoney’s equation of the printedcantilever beams in modules 1 and 3.

Parameter Distortion, �z [mm] Residual stress, � [MPa]

Module 1Cantilever beam A 2.79 955Cantilever beam B 2.48 849Cantilever beam C 2.62 897Average value 2.63 900

Module 3Cantilever beam A 3.06 1047Cantilever beam B 2.61 893Cantilever beam C 2.73 934Average value 2.80 958

Total average value 2.72 929

Median 2.68 914Standard deviation 0.34 118Confidence interval 2.36-3.08 805-1053

32

Figure 35: The residual stresses of the simulated cantilever beams in modules 1 and 3using Stoney’s equation. The red line represents the simulated results whereas the bluemarkers are the analytic apporach based on the experimental distortions of the cantileverbeams in modules 1 and 3.

33

As noted in figures 33, 34 and table 4, the residual stresses di↵ers when comparingthe printed cantilever beams with the simulations. The results from the simulations andexperiments were di�cult to compare. This could be due to several reasons including bothexperimental errors as well as simulation software limitations. The results of the residualstresses that were given by the XRD were di�cult to measure. Also, the obtained resultsfrom the XRD were fluctuating and di�cult to compare with the simulated results. Thiscould be due to the X-ray not reaching deep enough in the z-direction of the component.Additional electro polishing on the surface using copper or cobalt radiation might havegiven more stable results. The purpose of using electro polishing is to avoid measuringonly surface stress and to reach deeper into the specimen. However, it is possible thatelectro polishing also a↵ected the stress state in the specimen.

The stress value from the XRD is also a surface value on the electro polished surface ofthe specimen since the method does not allow for deep penetration. The comparison withthe simulated surface value could therefore be a bad representation of the overall stress ofthe geometry.

Other factors that may have influenced the residual stresses and made the measure-ment more di�cult is the crystallographic texture. The grain size of the material is ofimportance when evaluating residual stresses since materials with larger grains have lessgrains that are contributing to the di↵raction peaks and obeying Bragg’s law. The resultof this is lower peak intensities, less accurate peak positions. The measurement of theresidual stress may therefore be very di↵erent depending on the tilt angle of the XRDmeasurement.

It is possible that both Ti-alfa and Ti-beta phases exists in the material. The mea-sured residual stress may then be determined from the di↵raction peak from one particularphase only. This may not have a good representation on the overall residual stress. Eachresidual stress related to a certain phase should be considered in relation to the volumefraction of the phase. A microscopic investigation on whether the material consists ofseveral phases prior to the XRD measurement may thus have given better residual stressresults.

Moreover, when examining the residual stresses in table 4, the experimental valuesof the cantilever beams from XRD showed di↵erent residual stresses depending on thedirection. This indicates an anisotropic material behavior.

Furthermore, the measured maximum z-displacement values that were measured onthe cantilever beams to give the inherent strain were measured using a ruler. The pre-cision of the measured values could therefore be questionable. The values from di↵erentcantilever beams were somewhat di↵ering and the average values was used to calculatethe inherent strain. The resulting inherent strain that was used for the simulation maynot have been fully accurate.

Additionally, the reason why the residual stresses were only examined at the cantileverbeams and not the component is because of the simplified geometry of the cantileverbeams. The surface of the cantilever beam in comparison with the pipe is plane, whichmakes it smoother using the XRD. It is preferable that the measurement surface is a flatregion. It is also recommended that the measurement is done a few millimeter from theedge to avoid residual stress relaxation. Out of simplicity, a pipe geometry was not opti-mal for residual stress measurements using a XRD.

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The residual stresses that are determined experimentally using XRD is lattice placespecific value converted to a mean stress of the specimen. How well the stress state corre-sponds with the calculated e↵ective stress through FEM is dependent on the precision ofthe material parameters such as the Young’s modulus as well as micro mechanical materialmodels.

8.2 Analysis of the pipe

Figure 36: A shape comparison of the printed pipe and a pipe without any support.

Table 6: The shape deviation of the printed pipe in comparison with an undistorted pipewithout any support.

Parameter Plane Deviation, � [mm]

Point 1 dXYZ 1.05Point 2 dXYZ 0.97Point 3 dXYZ 0.71Point 4 dXYZ -0.06Point 5 dXYZ -0.84Point 6 dXYZ -0.87Point 7 dXYZ -0.20

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Figure 37: A shape comparison of the simulated pipe.

Table 7: The shape deviation of the printed pipe in comparison with an undistorted pipewithout any support.

Parameter Plane Deviation, � [mm]

Point 1 dXYZ -0.10Point 2 dXYZ -0.15Point 3 dXYZ -0.12Point 4 dXYZ -0.14Point 5 dXYZ -0.76Point 6 dXYZ -0.75Point 7 dXYZ 0.10

When looking at the shape deviation of the pipe in figures 36 and 37, the distortionsfrom experimental measurements and simulations seem to be approximately the samewithin a millimeter. The pipe is seen to be deformed in the negative radial direction atthe sides, which applies for both the simulation and the experiment. However at the topof the pipe in figure 36, a distortion in the positive radial direction can be seen from thelaser scanning as well as by optical inspection. In figure 32, the top surface of the pipe hasbeen damaged and the thickness of the pipe appears to no longer be homogeneous. Thisdistortion hot spot is not visible in the results from the simulation in figure 37. The rea-son for this could be the support structure of the pipe, which is resisting the gravitationaldeformation in the z-direction. Normally, the pipe should deform downwards due to thegravitational forces on the pipe. However, the support structure generates a compressionin the negative radial direction resulting in a positive distortion in the z-direction. Apossible solution to this problem could be to implement a support structure inside thepipe. However, it might be complicated to remove this structure when the pipe has beenmanufactured.

Another reason for this problem could be that some kind of damage has occurred inthis area which could not be simulated in the software tool. The additive part in MSCSimufact does not simulate any kind of damages that are on a microscopical level. There-

36

fore, some faults may occur on a microscopical level that cannot be simulated in this case.For example, the top of the pipe presents a rougher surface which might be due to porositythat is on a microscopical level.

It is possible that cutting the building platform into the 4 modules, induced residualstresses that resulted in this distortion, which is something that could not be simulatedin the software. This is unlikely since the distortion of the pipe in this area was observedprior to cutting. The residual stresses in the base plate were also very low.

Also, the distortion values given by the laser scanner were in some areas hard to cap-ture due to the geometry of the pipe but the areas of interest were captured successfully.Values depend on resolution and performance of laser scanner which also might explaindi↵erences from the simulation values.

Another possibility as to why the distortion at the top of the pipe could not be seenin the simulation is due to possible printing process errors. This includes over-heating ofthe top layer surface, meaning that too much energy was applied from the laser. Problemswith the heat flow output could be a reason why this surface of the pipe is somewhatdiscolored and rough.

Prior to cutting the pipe from the building platform, large stresses beyond the yieldstress were seen in the simulation around the support structure, see figure A.5. This couldbe the reason for the small cracks that appeared in the support structure. These crackscould have a↵ected the stress state of the pipe and caused the distortion in the top surface,something that was not observed in the simulation since Simufact additive does not handlecrack propagation.

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9 Evaluation of the chosen method

The applied experimental methods to measure distortions and residual stresses were laserscanning and XRD. The results from these methods were compared to simulated results,where the fully mechanical and macroscopic inherent strain method was used. Regardingthe distortions, laser scanning seemed to give results that corresponded well with the sim-ulation and were easy to compare. Laser scanning is a quick and easy way to measure thedistortions in a component. The method that was used to measure the residual stresses,XRD, was however more complicated. The applied method generated only surface valueswhich did not correlate well with the simulation. This could be due to di�culty in reachingdeep into the specimen with electro polishing. Therefore, electro polishing the specimendeeper or reconsider another geometry might render results that are easier to compare.

The inherent strain method is a fast method and easy to use compared to other anal-ysis methods for residual stresses in additively manufactured components. The methodis preferable in regard to time management when analyzing complex geometries. Thesimulation software is user-friendly, where the process steps are easy to follow as they aredivided into the same order as in the printing procedure.

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10 Conclusions

• An evaluation of residual stresses and distortions in additively manufactured com-ponents using the software tool MSC Simufact was performed in this study.

• The experimental values of the cantilever beams from XRD showed di↵erent residualstresses depending on the direction. This indicates an anisotropic material behavior.

• The applied experimental methods to measure distortions and residual stresses werelaser scanning and XRD. The residual stresses of the printed cantilever beams dif-fered in comparison with the simulations whereas the distortions of the pipe weresimilar in all areas except for the top layer when evaluating the printed part withthe simulation.

• The inherent strain method is a fast method and easy to use compared to otheranalysis methods for residual stresses in additively manufactured components. Themethod is preferable in regard to time management when analyzing complex geome-tries. The simulation software is user-friendly, where the process steps are easy tofollow as they are divided into the same order as the printing procedure.

• Simufact Additive is an easy to use software tool for the AM process. The softwaretool follows the real process work flow of the SLM process. Using the inherent strainsgenerates time e�cient simulations.

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11 Suggestions for further work

Initially, the project, which included modules as 3D printing, XRD analysis and laser scan-ning of the components, was performed in di↵erent environments. Therefore, having anexperimental set-up for all of these steps in a homogeneous environment would reduce thepossibilities of damaging the building platform with the components when transportingthe AM components.

Furthermore, as stated in section 7.1, only cantilever beam 3 was printed for thisproject. For further work can even cantilever beams 1 and 2 be printed and evaluated tocalibrate and validate the inherent strains. Also, a fourth cantilever beam with an arbi-trary direction can be printed for further validation. However, it requires more buildingplatforms and printing times to do this implementation. Thus, the results may becomemore accurate.

Also, the geometry for the residual stress analysis could be reconsidered. Instead ofhaving the cantilever beam for the XRD, perhaps a traditional beam could be printed andcut out to implement an analytical solution. Additionally, a phase analysis of the printedcomponents could be considered when examining the residual stresses.

To ensure that the printing process does not cause any material failure, the processparameters should be optimized prior to the printing. Running a thermo-mechanical anal-ysis in Simufact additive may help to understand the heat influence and if it will causeproblems running a fully mechanical simulation.

Additionally, since heat treatment is implemented on AM components to reduce theresidual stresses, the heat treatment process tool could also be evaluated to examine theperformance of the software tool.

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A Appendix

A.1 Inherent Strains of the cantilever beams

Table A.1: A comparison of the inherent strains for Al-Si-10Mg where the values from thesimulations are the standard parameters.

Inherent strain, ✏ [-] Value

Simulation✏x

-0.008✏y

-0.003✏z

-0.03

Experimental✏x

-0.000288559✏y

-0.00247046✏z

-0.0315875

Table A.2: A comparison of the inherent strains for Ti-6Al-4V where the values from thesimulations are the standard parameters.

Inherent strain, ✏ [-] Value

Simulation✏x

-0.008✏y

-0.003✏z

-0.03

Experimental✏x

-0.00534233✏y

-0.003✏z

-0.03

A.2 Distortions of the cantilever beams in modules 1 and 3

Table A.3: The collected data when measuring the distortions in the cantilever beams.

Parameter Initial height, z0[mm] Height after cutting, z1[mm] Distortion, �z [mm]

Module 1Cantilever beam A 9.08 11.87 2.79Cantilever beam B 9.15 11.63 2.48Cantilever beam C 8.96 11.58 2.62

Module 3Cantilever beam A 9.08 12.08 3.06Cantilever beam B 9.14 11.75 2.61Cantilever beam C 9.18 11.91 2.73

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A.3 Simulated components

Figure A.1: The e↵ective stress of the simulated cantilever beam.

Figure A.2: The stress state in x-direction of the simulated cantilever beam.

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Figure A.3: The stress state in y-direction of the simulated cantilever beam.

Figure A.4: The shear stress in the xy-plane of the simulated cantilever beam.

Figure A.5: The stress state of the simulated pipe.

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