Numerical Modelling Of The Selective Laser Melting (Finite Element Modelling) Essay Example


Numerical Modeling of the Selective Laser Melting (Finite Element Modelling): A Literature Review

Numerical Modeling of the Selective Laser Melting (Finite Element Modelling): A Literature Review


The manufacturing sector has made significant technological leaps. This sector has grown from simple manufacturing technologies to complex practices such as additive manufacturing and selective laser melting. Selective laser melting was first applied in Germany at the Fraunhofer Institute where it had discovered in the course of a German research project. Ever since this technology was discovered, it has been subject of numerous reviews and is one of the latest generative manufacturing technologies to be adopted by companiesi.

In light of this information, there is need to review scholarly articles and other literature reviews on the subject. The objective of this exercise is to summarize at least seven articles whose focus is this technology. To ensure that the information provided is both current and relevant the only articles published between 2007 and 2014 will be reviewed.

This review will be divided into six parts. The first section will focus on process parameters. This section will look at the effect of this technology on both the materials and the manufacturing process in general. Under specimen dimension, one of the objectives will be to identify some of the materials that can be subjected to this technology as well as highlight their properties. Since all journals contain specific findings, a brief comparison of what different authors have to say about SLM will be conducted under findings. Other topical areas that will be covered include mechanical properties, residual stresses, and microstructures. Finally, the conclusion will summarize the major points.

Process Parameters

Rajnikan, Rathod and Patel (2013) point out that the manufacturing parameters of an SLM machine affects the quality of materials or items producedii. In order to improve the quality of the products, it is critical that the SLM process is optimized. This activity is important because it helps to identify the correct adjustments to be made so that the highest quality standards are achieved. Not only does this activity improve the quality of the product, it assists manufacturers to operate in an economical and cost effective way.

The Taguchi method is one of the tools used in process optimization. One of the advantages of this tool is that it allows the experimental plan to be simplified. It also ensures that during the feasibility study, there is no interference between parameters. Besides the Taguchi method, other tools that can be used include; the factorial design, central composite design, and the response surface methodology (Rajnikan, Rathod & Patel, 2013).

Every parameter has a significant impact on the outcome of the optimization process. Therefore, during the activity engineers or technicians take keen note of how varying each parameter affects the outcome. For instance, experiments have shown that powder thickness influences the density of the item. Dingal et al (2008) as cited in Rajnikan, Rathod and Patel (2013) note the following as some of the important SLM process parameters. Laser characteristics include peak, time, or duration, speed, hatching distance and interval spot.

Material: density, particle size, and thickness

Specimen Dimensions for the SLM Process

Cellular dimension is an important factor in the SLM process. SLM technique influences the behavior of lattice structures when subjected to different stressors. Smith, Guan and Cantwell (2013) note that indeed research has been conducted to establish the potential of SLM built structures in the manufacture of lightweight structures that absorb energy. In their article, “Finite element modeling of the comprehensive response of lattice structures manufacturing using the selective laser melting technique” they point out those factors such as cell geometry affects a cell’s tensile strength and compressive conditions.

Metal foam is one of the lightweight energy absorbing materials. This material has exceptional electromagnetic properties, good sound properties, and thermal conductivity. It consists of an irregular structural lattice with localized weakness points. When subjected to elasticity and tensile tests metallic foam bends incurs a lot of deformation. Currently, experiments conducted on the same of the material reveal that it is possible to enhance its tensile strength and stiffness.

The octet-truss lattice is manufactured using the lost wax technique. This technique has heightened interest in the manufacture of the lightweight materials. Materials that have this structure have a tensile strength of between   ῥ2 and ρ
1.5(Smith, Gaus & Cantwell, 2013)iii. When subjected to stress, they undergo extensive bending and eventually get deformed. Truss structures exhibit better tensile properties. They do not deform as much as Octet truss lattices. Beryllium and Copper alloys contain truss structural conformations and when they were bent, compressed, and sheared the results were impressive.

Tetrahedral and pyramidal structural lattices have better performance compared to truss structures. Smith, Gaus and Cantwell (2013) note that when these structures are constructed using the investment casting technique; they acquire better compression, shear and bending abilities. This improved performance is attributed to increased resistance to plastic buckling (Smith, Gaus & Cantwell, 2013). The difference in performance can also be attributed to geometrical variances. Linearity is another material property that influences the structural properties (Contunzzi, Campanelli & Ludovico, 2011).


Smith, Gaus, and Cantwell (2013) note that BCC and BCC-Z structures have similar stress curves in the elasticity region. Both materials indicate similar plateau values when using the beam model. These structures also have excellent compression loading properties. Additionally the experiment results show that each unit cell absorbs up to fifty percent of the strain energy. This value was then used to estimate the normalized absorbed energy per material and this value was found necessary if one was to make direct comparisons between the two structures.

Numerical Modelling Of The Selective Laser Melting  (Finite Element Modelling)

Image borrowed from Smith, Gaus, and Cantwell (2011)

Van Belle, Vansteenkiste, and Boyer (2011) conducted an experiment to determine how SLM numerical modeling compares to one another. From the results, they were able to establish that 3D and 2D models have different thermal strain distributions. The results also showed that thermal expansion coefficient was not constant. This value fluctuated depending on the phase of the transformation. Their experiment established that the yield stress of any material is depended on temperature. This value was inversely proportional to temperature. The viscosity properties did not seem to be affected by temperature, hence, implying than material behavior was unaffected by temperature. The laser beam temperature had an impact on the geometrical orientation of the materials. Powder substances clamped together when heated and violent cooling resulted in the material obtaining a plastic tensile strain (Van Belle, Vansteenkiste& Boyer, 2011)iv.

Contunzzi, Campanelli, and Ludovio (2011) conducted an experiment to analyze melting of elements using the SLM process. The objective of the experiment was “to determine the profiles dimensions of the molten re-solidified zones in SLM Parts” (Contunzzi, Campanelli, & Ludovio, 2011). The model used in the experimented factored in geometry, layers and made provisions for transient effects. The results from the experiments proved that temperatures higher than 1400C lead to increased conductivity. Additionally, they demonstrated that temperature changes with depth. However, they discovered that these changes occurred when the temperatures were between 936C and 1471C and only within the third disposition layer.

Roberts, Wang, Esterlein, Stanford and Mynors (2009) found out that the role of time in the SLM process. Their research established that the time difference between heating and cooling during the SLM process was in terms of milliseconds. The cycles were very rapid resulting in extensive thermal stress on the material. These results meant that the skewed thermal profile is one of the characteristics of the process. Roberts, et al. (2009) noted that conductivity properties and untreated powder placed in front of the laser were the reasons behind the observations. Nonetheless, the experiment established that the findings only applied to thermal spots that far apart, those that were close together exhibited similar thermal cycles hence they recorded similar tendencies.

Temperature distribution varies according to material properties. Hussein, Hao and Everson (2013) were able to establish that the highest molten zone temperatures were 2600K which was higher than that of stainless steel (1672K). Materials with good conductivity properties demonstrated less temperature skewv.

They came up with a model that complies with the following conduction equation

Numerical Modelling Of The Selective Laser Melting  (Finite Element Modelling)  1

Gusarov and Smurov (2008) established that radiation transfer of the metallic powder is dependent on thickness or any other boundary conditions. The profile obtained from the experiment was bell shaped and bad a narrow flat top. The axial flux caused by the radiation transfer was highest on the surface; however, they noticed that the incident flux was less due to back scattering.

Tabular Comparison of the Findings


Effect of the Temperature


Directly proportional

Roberts, Wang, Esterlein, Stanford, & Mynors (2009).

Improves conductivity of materials

Increases in some materials

(Smith, Gaus & Cantwell, 2013)

Materials become malleable and easily deformed

(Gusarov & Smurov, 2008)


Unequal distribution (Hussein, Hao & Everson, 2013)

It varies with depth

(Contunzzi, Campanelli, & Ludovio, 2011)

Tensile strength

Decreases with increase in temperature

(Smith, Gaus & Cantwell, 2013)

Materials become more stiff and brittle (Gusarov & Smurov, 2008)

Numerical Modelling Of The Selective Laser Melting  (Finite Element Modelling)  2

Image extracted from Gusarov and Smurov (2008)

Mechanical Properties

Annealing temperature has an impact on the cumulated plastic strain. According to Van Belle, Vansteenkiste and Boyer (2011), when annealing temperature is equivalent to the melting temperature the maximum plastic strain rises by 40%. If the temperature is 1000C, the strain is reduces to 25%.

Thermal strain distribution in 3D and 2D models is because of mechanical loading. It was noted that plastic dissipation is weaker than the heating power, hence, causing a heat transfer issue. This led to the assumption that because powder is soft and elastic, it follows that it the stresses generated are bound to be weak. This in turn causes the layers to slide once the expansion process begins. The overall effect is the material becomes bendable and easily deformed.

The nature of the surface determines how much laser energy a material absorbsvi. Metals have varying surface properties, hence, absorbance values of pure titanium is used as the representative values when considering bulk metallic materials (Roberts, et al., 2009).

Porosity is another thermo-physical property that affects conductivity. Roberts, et al. (2009) note that loose metallic powders have better conductivity prospered since gases found within the pores enhance this property. Porosity is also influenced by pore geometries. Roberts, et al. (2009) point out that their complicated relationship is represented by the following equation

Numerical Modelling Of The Selective Laser Melting  (Finite Element Modelling)  3

Numerical Modelling Of The Selective Laser Melting  (Finite Element Modelling)  4 Represents powder bed

Numerical Modelling Of The Selective Laser Melting  (Finite Element Modelling)  5 Represents solid metal

Numerical Modelling Of The Selective Laser Melting  (Finite Element Modelling)  6Represents porosity terms

Residual Stresses

Residual stresses in SLM parts are one of the widely investigated topics (Van belle, Vansteenkiste & Boyer, 2013). Most of the research conducted have used destructive methods such as hole drilling method to measure the residual stressed generated during the SLM process. The method outlined in the removal layer theory is commonly used to gauge the amount of residual stress within a given part. It has been established that residual stress corresponds to elastic bending. Van belle, Vansteenkiste and Boyer (2013) note that the removal layer theory assumes the Young modulus, the Poisson ratio, and strain is proportional to residual stress. This relationship is demonstrated by the following equations.

σ1 (x n) = σ (x i) +
+ ∆σ (x .j)

σ2 (x n) =
σ (x n) +
N1ij+ ∆σ (x2 .j2)

σ1 (x n) represents the residual stress, σ (x n) additional stress created upon addition of an extra layer and σ (x i) is the additional stress due to the melted layer.

The deformity witnessed in the materials is as a result of excessive residual stress. The molten layers cause imbalances causing uneven distribution of pressure. Due to the un-uniform distribution, the certain adjustments have to be made to in order to account for the varying residual stressors. Normally, the linear stress is given a higher value since it has been established that the different layers experience different amounts of stress. A calculus distribution equation this then applied to correct the thermal strains recorded in the layers.

The Eigen stress is another residual stress factor that is influenced by the thickness of the materiaviil. Van belle, Vansteenkiste and Boyer (2013), notes that this type of stress is determined at the end of the process, and mostly is equal to half the thickness of the final support. They also point out that the type of residual stresses experienced by free surfaces is mostly tensile stresses. Any internal stress observed is as a result long cooling durations or other material properties.


The internal lattice structure of any material has a significant impact on the mechanical properties of the end product. The SLM process produces parts with different internal structuresviii. Temperature is one of the main factors that determine the type of lattice structure contained in SLM parts. The lattices have different density depending on the final volumes after undergoing compression. The geometrical properties influence their shape and size.

Compared to BCC, the BCC-Z lattice structure has a higher elastic modulusix. This difference is because BCC lattices lack vertical strands found in BCC-Z unit cells. These strands reinforce the structure’s strength by providing it with additional resistance force enabling it withstand higher stress levels. Compact structured tend to have greater stiffness. In addition, Smith, Gaus, and Cantwell (2009) noted that friction properties also affect the performance of different microstructures.


SLM is one the manufacturing practices that has got helped many companies cut costs and operate in an economical manner. Ever since its discovery, this technology has made significant contributions in engineering and other related fields. A lot of research has been conducted to determine how different aspects of this technology have contributed to the improvement of quality standards.

Process optimization is one of the activities under SLM that has made this technology cost effective. Optimization can be carried out using one of the following tools or methodologies; Taguchi, factorial design, central composite design or response surface methodology. The objective of this process is to improve the quality of the end product, as well as assist manufacturers to operate in an economical and cost effective way.

Material specifications such as thickness, weight, density, and conductivity are critical to the SLM process. Each parameter influences a specific attribute of the final products. Temperature has a different impact on each of the mentioned parameters. For example, high temperature improves conductivity; however, its distribution is not equal across the different layers.

Under findings, it became evident that temperature variations were critical in the SLM process. These changes affected conductivity, and influenced lattice structures. However, there was no homogenous rule that could be applied to determine the outcome. Therefore, the authors came up with equations to demonstrate different phenomenon. The equations ranged from simple calculus equations to complex derivative equations.

The SLM process affected different mechanical properties to the materials. Some these properties included plastic strain, surface properties among others. Some of tensile strength was one of the residual stresses likely to be experienced on the surfaces of a material. Different structural lattices attribute their performance to the internal arrangement of particles. The geometrical arrangement of the atoms had a significant impact on the mechanical properties of the material.


Brodin, H., & Saarimäki, J. (2013). Mechanical properties of lattice truss structures made of a

selective laser melted superalloy. In ICF13.

Dingal, S., Pradhan, T. R., Sundar, J. S., Choudhury, A. R., & Roy, S. K. (2008). The application

of Taguchi’s method in the experimental investigation of the laser sintering process. The International Journal of Advanced Manufacturing Technology38(9-10), 904-914.

Gusarov, A. V., & Smurov, I. (2009). Two-dimensional numerical modeling of radiation transfer

in powder beds at selective laser melting. Applied Surface Science255(10), 5595-5599.

Hussein, A., Hao, L., Yan, C., & Everson, R. (2013). Finite element simulation of the

temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design52, 638-647.

Jun, T. S., & Korsunsky, A. M. (2010). Evaluation of residual stresses and strains using the

eigenstrain reconstruction method. International Journal of Solids and Structures47(13), 1678-1686.

Meier, H., & Haberland, C. (2008). Experimental studies on selective laser melting of metallic

parts. Materialwissenschaft und Werkstofftechnik39(9), 665-670.

Rajnikan, B., Rathod, R., & Patel, I. (2013). Process parameter optimization of SLM process and

application of Taguchi approach-The Review. International Journal for Scientific Research & Development1(4), 1008-1010.

Roberts, I. A., Wang, C. J., Esterlein, R., Stanford, M., & Mynors, D. J. (2009). A three-

dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing. International Journal of Machine Tools and Manufacture49(12), 916-923.

Smith, M., Guan, Z., & Cantwell, W. J. (2013). Finite element modeling of the compressive

response of lattice structures manufactured using the selective laser melting technique. International Journal of Mechanical Sciences67, 28-41.

Van Belle, L., Vansteenkiste, G., & Boyer, J. C. (2012). Comparisons of numerical modeling of

the Selective Laser Melting. Key Engineering Materials, 504, 1067-1072.

Van Belle, L., Vansteenkiste, G., & Boyer, J. C. (2013). Investigation of residual stresses

induced during the selective laser melting process. Key Engineering Materials554, 1828-1834.

Yan, C., Hao, L., Hussein, A., & Raymont, D. (2012). Evaluations of cellular lattice structures

manufactured using selective laser melting. International Journal of Machine Tools and Manufacture62, 32-38.

SLM process is applied in the additive manufacturing process.

The article by the authors highlights the importance of SLM optimisation

Structural lattices have different mechanical properties

The tensile properties are affected by temperature

Temperature distribution varies across the layers

vi. Experimental studies on selective laser melting of metallic parts, by Meier, H., & Haberland, C. (2008), Material wissenschaft und Werkstofftechnik, p. 665-670.

Evaluation of residual stresses and strains using the eigen strain reconstruction Jun, T. S., & Korsunsky, A. M., 2010,. International Journal of Solids and Structures, p. 1678-1686.

Mechanical properties of lattice truss structures made of a selective laser melted superalloy by Brodin, H., & Saarimäki, J. 2013,p. 13.

ix. Evaluations of cellular lattice structures manufactured using selective laser melting, Yan, C., Hao, L., Hussein, A., & Raymont, D. 2012, International Journal of Machine Tools and Manufacture, p. 32-38.