MP21781 Understanding the Mechanical Properties of Additively Manufactured Lattice Structures with Testing and Simulation

Transcription

1 MP21781 Understanding the Mechanical Properties of Additively Manufactured Lattice Structures with Testing and Simulation Daniel Noviello Autodesk Advanced Consulting Learning Objectives Understand the challenges of mechanical characterization of metal additively manufactured structures Explore the impact that feature size has on mechanical properties Learn about elastic properties and failure modes of AM parts and lattice structures Investigate the application of current simulation tools when applied to lattices Description Autodesk has historically developed software and provided consulting services for metal additively manufactured (AM) lattice-type structures. Common powder-bed processes include SLM (Selective Laser Melting) / DMLS (Direct Metal Laser Sintering), and EBM (Electron Beam Melting). When considering real-life applications of these structures, many assumptions are made about the characteristics of the manufactured material. Among others, these include strength, elastic moduli, thermal properties, material density, surface finish, and structural stability. These characteristics are affected by many factors, including machine parameters, build orientation, and feature size. Your AU Expert(s) Daniel Noviello is a mechanical engineer in the Advanced Consulting Team at Autodesk, Inc., specializing in additive manufacturing, particularly finite element analysis (FEA) and stress analysis. He graduated from University of Queensland with a First-Class Honors in Mechanical and Space Engineering. After working for various aerospace/space companies, including GKN and Surrey Satellite Technology Limited, Daniel joined the Advanced Consulting Team to maximize in-house knowledge of stress and structural analysis, and bring key industry experience to the team. He has a passion for the practical application of new and emerging technologies to help advance the design and manufacturing industry. Page 1

2 The Challenge of Metal AM and Mechanical Properties Metal powder bed additive manufacturing (AM) poses a number of significant problems to the mechanical analyst wanting to simulate the behavior of a functional part. Conventional metallic wrought materials have well established analysis methods, and their material behaviors are very well understood. This is largely because the assumption of material isotropy yields practical and reliable results, and the manufacturing process is repeatable. When it comes to metal AM however, there is variability of material properties regardless if the same base material powder is used, and even if the same machine was used. The inability to get reliable material properties, and hence simulations, is a huge barrier to entry for industrial-use metal AM parts. We are currently in a situation where in most cases full destructive testing is the only way of verifying an AM part. What are some of the factors that determine my final part? Some of the main contributing factors include: 1. Laser spot size 2. Laser scan strategy 3. Laser power 4. Powder composition 5. Powder particle size and distribution 6. Part orientation 7. Porosity Important mechanical properties of the built material The above factors may have a direct or indirect effect on: 1. Elastic modulus 2. Poisson s ratio 3. Ultimate stress 4. Proof / Yield stress 5. Plasticity 6. Fracture toughness 7. Notch sensitivity 8. Fatigue endurance limits Metal AM and lattice-type structures Lattice structures are an efficient way of establishing high directional stiffness at a far reduced material volume. This makes them ideal for aerospace applications such as UAVs. They also have the virtue of a high surface area ratio making them ideal for heat exchanger applications. Another very important application of the metal AM lattice is in osteo-integration where fine trabecular lattice is used to stimulate bone in-growth. Page 2

3 FIGURE 1: LATTICE STRUCTURES USED IN (CLOCKWISE FROM TOP-LEFT): VEHICLE SUSPENSION MEMBER, ACETABULAR CUP, SPINAL CAGE IMPLANT, GEAR COG Physical testing for material properties For conventional metals, dog bone specimens are usually tested in tension to determine the quasi-static behaviour under load. The primary quantities measured are load and displacement. The load can be divided by the initial gauge area to get stress, and the displacement can be divided by the gauge length of the specimen to determine strain. This forms the basis of an engineering stress-strain curve. It is important to note that typical manufacturer dog bone test specimens have a gage diameter of 5mm or more (example, EOS). This is quite often beyond the scale of lattice members, which in many cases can be anywhere from 2mm down to 0.3mm diameter. Page 3

4 FIGURE 2: TYPICAL DOG BONE SPECIMEN [1] FIGURE 3: GENERIC STRESS-STRAIN CURVE ISOTROPIC METAL [2] Objective of this study The study looks to firstly understand the correlation between mechanical properties and feature size by testing a number of differently sized dog-bone specimens. Next, the behaviour of lattice specimens in both tension and compression is investigated. Finally, it is considered how the tested mechanical properties can be used to simulate a lattice specimen. Where possible, testing methods are based on international standard ISO [5]. Page 4

5 Test specimens The study uses test specimens that are made from EOS AlSi10Mg powder on an EOSINT M 280. Dog bone specimens are of a typical cylindrical shape with three different gauge diameters of 0.6mm, 0.8mm, and 1.0mm. Lattice specimens are designed using Autodesk Within, and have a nominal volume of (25mm) 3 with 4x4x4 units of X-topology. FIGURE 4: LATTICE TEST SPECIMEN AND 1MM DOG-BONE SPECIMEN FIGURE 5: LATTICE TEST SPECIMEN DIMENSIONS Page 5

6 How Do Metal AM Material Properties Change with Feature Size? Typically, the mechanical analyst will use a materials database resource such as MMPDS and use key parameters to fully define the stress-strain curve for the material of choice. The analyst then uses the material curve as a series of data points for their analysis software such as Autodesk Nastran, or Autodesk Explicit. To test if material properties change with feature size for metal AM materials, three different dog bone specimen diameters are considered: 0.6 mm, 0.8mm, and 1.0mm. The aim is to obtain the stress-strain curve for a number of specimens of each size (5 in this case) and derive key quantities from the data. These are: Modulus of elasticity Yield stress Ultimate tensile stress Strain at break FIGURE 6: TENSILE DOG-BONE SPECIMENS Ramberg-Osgood Equation The Ramberg-Osgood ductile metal power law is used to describe the stress-strain curve for a number of materials including aluminum alloys. As per ESDU [3], it is defined as: f MPa Stress ε Strain E MPa Young's Modulus (Tensile strain 0.05 % %) m - Material characteristic (power-law, ESDU 76016) fn MPa Characteristic stress (power-law, ESDU 76016) As shown, with the Ramberg-Osgood relationship, the elastic-plastic stress-strain curve can be conveniently represented using just three material parameters E, m, and fn. There are however, some limitations with this equation for very high strains; this is discussed below. Page 6

7 Example test results: 1mm dog bone specimen The following plot shows the tensile stress-strain data obtained for the 1mm specimen. The calculated Ramberg-Osgood curve is shown in dashed red. Note the good repeatability of the test curves, with the exception of the final strain at break which varies most. The R-O curve however, tends to diverge after about a strain of mm/mm. This becomes important when deriving input material data points for simulation (more on this under heading Selecting the input points, page 15). FIGURE 7: 1MM TENSILE TEST RESULTS AND RAMBERG-OSGOOD MEAN FIT CURVE Feature size dependence example: ultimate tensile strength Consider the ultimate tensile strength (UTS). This is the maximum stress that the material can handle before failing. Figure 8 below shows mean tested values for the UTS against diameter. Notice the clear trend showing increasing modulus with measured diameter. The EOS datasheet value is shown for reference; it is based upon a 5mm diameter specimen. Note that this value is only indicative; the test conditions are likely to be very different to those used in this study. Page 7

8 FIGURE 8: TENSILE DOG-BONE SPECIMEN MEASURED UTS FOR 0.6MM / 0.8MM / 1.0MM NOMINAL DIAMETERS Why the trend? In order to gain insight as to why there is a trend with feature size, we took a closer look at the specimens. The following image shows a CT scan isosurface with a resolution of 4 μm. Note the clumpy nature of the material layup due to progressive solidification of melt pools. FIGURE 9: CT SCAN OF 1MM DOG 4MICRON RESOLUTION Among many other aspects, it can be hypothesized that the following affect drop-off of properties: The surface roughness Page 8

9 Surface cracks Void size Inclusion size Concentration of voids / inclusions Typically, a ductile fracture for a smooth specimen can start at internal voids and grow to the surface, or can start at the surface. In the case that the crack starts from the surface, the surface quality is of utmost importance as to how, and at what load a crack initiates. The following images show magnifications of a 1mm diameter specimen after failure. FIGURE 10: SPECIMEN FRACTURE SURFACE Simulation and surface defects To understand the degree to which the surface defects affect the formation of the fracture surface, a high resolution model (reconstructed from CT scan data) was analysed using Autodesk Explicit solver. The solver was run with quasi-static conditions and a strain-based element deletion criterion. The resultant failure simulation is shown below next to the actual failure. Since there are no microstructure models in this simulation, it suggests that the fracture initiates from the surface. FIGURE 11: COMPARISON OF SIMULATED FRACTURE SURFACE Page 9

10 Mechanical Properties and Failure Modes of Metal AM Lattices When considering the mechanical properties of lattices, an approach is taken that assumes uniform properties over the entire volume of the specimen. This means a single tension or compression stress-strain curve is obtained to represent the test volume. FIGURE 12: SCHEMATIC OF TENSION AND COMPRESSION LOADING APPLIED TO LATTICE SPECIMENS Test set up The lattice specimen was designed to be suitable for both tension and compression; pin holes used for tension and parallel machined surfaces used for compression. For tensile tests, a custom tension adaptor required design and manufacture. Figure 13 below provides images of both set ups. FIGURE 13: TEST SET-UPS; TENSION (LEFT), COMPRESSION (RIGHT) Page 10

11 Methods of displacement measurement Two measures of displacement measurement were used for the lattice specimens. 1. Cross head displacement This is the direct displacement reading from the testing machine. This displacement reading takes account of the stiffness of all parts attached to the load cell and base anchor. It thus gives a reading of entire assembly displacement (including all fixtures). 2. Advanced Video Extensometer (AVE) displacement The AVE displacement is calculated by tracking specific marks on the specimen. It continuously tracks the displacement of the pixels at a high frequency. The lattice specimens were tracked at the points indicated below: FIGURE 14: AVE TRACKING POINTS ON LATTICE SPECIMEN Tension results The force-displacement plots show a high level of non-linearity with a clearly defined ultimate (peak) load. The graph in Figure 15 shows an ultimate load at about 1mm displacement, after which failure initiates. The rough downward slope is indicative of individual lattice members progressively failing until there is complete separation of the specimen. Page 11

12 FIGURE 15: FORCE-DISPLACEMENT GRAPH OF LATTICE SPECIMEN IN TENSION Failure Mode Observation of the specimen shows some interesting features. Firstly, all members tend to fail at the end of the beams (at the junctions). Next, there tends to be a repeatable 45- degree failure in a V shape. FIGURE 16: LATTICE SPECIMEN FAILED IN TENSION Page 12

13 Compression results The compression force-displacement plots show some very interesting behaviour. We see an initial peak load at about 1mm (AVE) displacement followed by a steady collapse. The specimen then makes contact with itself in the collapsed area and begins to bear load again, then peaks at a higher load than the previous. After a second collapse, and subsequent re-bearing of load, the AVE loses track. The cross-head displacement however indicates a continuing increase in load as the lattice section of the specimen becomes compacted, thus making a transition to solid block compression. FIGURE 17: FORCE-DISPLACEMENT GRAPH OF LATTICE SPECIMEN IN COMPRESSION Failure Mode Once again we see a failure at a 45-degree shear plane, which is likely to be a result of the specific lattice topology. The progressive collapses occurred at perpendicular planes. The following image shows the compressive specimen after the first collapse: FIGURE 18: LATTICE COMPRESSION AFTER INITIAL COLLAPSE Page 13

14 Simulation Predominantly, the Autodesk Explicit solver was used to simulate the test specimens described. This is because of its ability to easily accept highly non-linear material data as an input, and to easily simulate self-contact and material failure. The analyst may however, have requirements for a much faster linear analysis, and be willing to accept a level of conservatism that this can provide. This is also the case for optimization analyses when the user needs to iterate several solutions as a design converges. Pertinently, a number of simulation techniques can be employed to analyse a lattice structure. Some examples are (in increasing levels of complexity): 1. Linear elastic tetrahedral element models (Nastran, Simulation Mechanical) 2. Non-linear elastic-plastic tetrahedral element models (Nastran, Simulation Mechanical) 3. Non-linear elastic-plastic tetrahedral element models with contact and material failure (Autodesk Explicit) This section will detail how test results are correlated using the Autodesk Explicit solver and how the correlated data can then be applied to each of the different solution types. Dog bone specimens The material curves of the dog bone specimens are correlated based upon feature size. Figure 19 shows the load-displacement plot for the 1mm specimens together with the simulated curve from a CT-scanned model using test-derived material data. FIGURE 19: DOG BONE TENSILE TEST DATA AND SIMULATION RESULT Page 14

15 FIGURE 20: CT-SCANNED MODEL: VON MISES STRESS OF DOG BONE IMMEDIATELY PRIOR TO FULL SEPARATION Selecting the input points The input data for simulation can be directly calculated from the Ramberg-Osgood equation with the mean values for m and fn. However, since the R-O curve deviates from the test data at higher strains, the final two data points are selected to be (a) the average stress at a strain of 0.03, and (b) the average ultimate stress-strain point. This allows for a repeatable and concise method of representing the test data as a single stress-strain relationship. The selected points are indicated in Figure 21 below. Page 15

16 FIGURE 21: SIMULATION INPUT DATA The above points typically need to be transformed into true stress and true plastic strain. This is the case for both Nastran and Autodesk Explicit (2 and 3 on the aforementioned list). The true stress and strains can be determined using the following equations. True stress: True strain: True plastic strain: σ t = σ(1 + ε) ε t = ln(1 + ε) ε t,plastic = ε t ln (1 + σ t E ) Where σ is the engineering (or measured) stress, ε is the engineering (or measured) strain, and E is the modulus of elasticity. Lattice Specimens Using the same material input data, Autodesk Explicit solver was used to simulate both tension and compression failure of the lattice specimens. For the tension case, this utilized the element deletion function whereby an element is effectively removed from the model upon reaching a certain failure strain level. The compression case required both element deletion, and selfcontact. Self-contact allowed the model to collapse on itself and exhibit realistic deformations. Tension The following image shows the final failed simulation next to the actual failed specimen. Notice similar behaviour where there is formation of 45-degree failure planes. As expected, each member fails at the junction (not through the span). Page 16

17 FIGURE 22: LATTICE SPECIMEN FAILED IN TENSION AND CORRESPONDING SIMULATION More importantly, the correlation of the load-displacement curve is reasonable. The simulation diverges from the test result around 0.5mm and the simulation achieves about a 10% higher ultimate stress. The subsequent decline in the load curve is much more rapid for the simulation. This is expected with the use of an element deletion failure model as material is made ineffective in discrete chunks (elements), as opposed to its continuous nature in test. FIGURE 23: LATTICE TENSION FORCE-DISPLACEMENT WITH SIMULATION RESULT Page 17

18 Compression The image below shows the compression simulation and test specimen subsequent to the first collapse. FIGURE 24: LATTICE SPECIMEN FAILED IN COMPRESSION AND CORRESPONDING SIMULATION While the simulation does not show a clear failure across a 45-degree plane, its behaviour is actually quite similar. This can be seen in the following force-displacement plot. FIGURE 25: LATTICE COMPRESSION FORCE-DISPLACEMENT WITH SIMULATION RESULT Page 18

19 Although there is quite some noise in the simulated curve, the drop off of load after initial collapse and then subsequent reloading can easily be observed. Notice also, like the tension case, the simulated ultimate stress is up to 10% higher than test, and the simulation result begins to diverge at about 5mm. Correlation in the linear region Consider the tension specimen; the force and displacement data is used to derive stresses using a reference area ((25mm) 2 nominal), and strains using a reference gauge length (initial measured distance of the AVE tracking points, nominally this would be 18.75mm). These stresses and strains are then plotted and used to determine the overall elastic modulus of the lattice test volume. The following graph shows the stress-strain curves and derived elastic modulus for both specimens and the simulated tension specimen. FIGURE 26: STRESS STRAIN OF THE LATTICE IN TENSION The Autodesk Explicit simulation shows good correlation with both the linear region (elastic) and commencement of the non-linear (plastic) region. The linear Nastran simulation also shows very good agreement for elastic deformation. This region however, is very limited, and does not continue past a strain of approximately mm/mm, which coincidentally corresponds with the typically accepted proof strain of most metals. This means that the lattice can be considered to have permanently deformed by this strain level. Page 19

20 Using a linear solution When using a linear solution (that Nastran can provide), results are very conservative for stresses beyond yield. This is because the change in elastic modulus at higher strains is not modelled. Consider the ultimate tensile strength (UTS). If a linear model is used, the UTS will correspond with a strain of approximately mm/mm, whereas the actual curve corresponds with a strain of mm/mm. UTS FIGURE 27: UTS CORRESPONDING TO LINEAR ELASTIC AND ELASTIC PLASTIC MODELS As is well-known, while elastic behaviour can be reasonably predicted by a linear solution, the strength margin can only be predicted by comparing stress to the material yield strength. This means that linear results can be used to suggest permanent deformation, but are very conservative for ultimate strength margins. Page 20

21 Summary In this handout, some of the key problems with characterizing metal AM parts have been identified. The resulting variation of material properties like elastic modulus and strength can be attributed to many factors, these included laser spot size, laser power, and metal powder. Specifically investigated were the effects on material properties due to differing feature size (sub 1mm). This showed a proportional relationship to feature size. This can be attributed partly to the resultant surface quality which, upon CT inspection, shows very discrete clumping due to successive melt pools. The Ramberg-Osgood equation and additional stress parameters were used to concisely describe the stress strain curve, and subsequently retrieve suitable data for simulation inputs. When considering built-up lattice parts, appropriate methods of testing the stiffness and strength have been discussed. Progressive failure modes for lattices in both tension and compression, and the degree of non-linearity were studied. In both tension and compression, the X-lattice has a tendency to fail across planes at 45-degrees to the load, and members fail at the junctions. The efficacy of using dog bone material data for a simulation of a lattice of similar member sizes was shown to be very good in both the linear and non-linear regimes. Autodesk Explicit solver was very capable in predicting detailed failure modes of the lattice specimen and loaddisplacement curves correlated very well with test. Likewise, Autodesk Nastran (linear solution sequence) was very good in predicting the linear region. The limitations of linear finite element solutions were discussed, and the linear region of the X-lattice specimen shown to be limited to strains below mm/mm. This study provides confidence in applying existing analysis techniques to complex AM structures, given that material properties are correctly quantified. It suggests that size effects can be modeled by applying material curves that are derived using specimens of the specific feature size. There is likely to be an upper limit on size, after which material properties no longer change, however this is yet to be determined. The study does not consider build direction which would add a layer of complexity that is not yet addressed. Future studies will consider methods by which metal AM material properties can be generalized so that the analyst no longer needs to perform physical testing prior to analysis. It is hoped that this will lead to the development of a reliable material database for which designers can use on metal AM parts at any scale. Further quantification of properties will also consider the effects of surface finishing, fatigue properties, and different materials. This is intended to advance the acceptance of structural metal AM parts in critical applications, particularly in aerospace. Page 21

22 References [1] By Wizard191 - Own work, CC BY-SA 3.0, [2] Campbell, F. C (2006). Manufacturing Technology for Aerospace Structural Materials. Oxford: Elsevier. [3] ESDU (1991). Generalisation of Smooth Continuous Stress-Strain Curves for Metallic Materials. ESDU. [4] EOS (May 2014). EOS Aluminium AlSi10Mg Material Data Sheet (with speed parameter set) [5] ISO (2009). International Standard ISO Metallic materials Tensile testing. Page 22