Comparisons between elastic and plastic constitutive models in smooth models 

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Specimens elaboration

The specimens used in this study were produced by the company PRISMADD (currently Weare Group), the manufacturing and post-treatment protocol is the one applied by the company to industrial parts made of 316L steel. This protocol consists in using a (new or recycled) powder volume N times until the oxygen rate becomes greater than 1000 ppm. The manufacturing parameters are also optimized by the company to minimize the porosity rate. A stress relieving heat treatment (in air) is then carried out before the parts are removed from the production tray by wire Electric Discharge Machining (EDM). This section is devoted to a description and an analysis of this protocol. The powder properties are first presented, then the manufacturing and post-processing parameters are detailed. The residual surface stresses after heat treatment are measured and analyzed.

Powder characterization

The precision and the quality of additive manufactured products are strongly influenced by the powder quality. Among the numerous characteristic parameters, the particle size is the most important one. The powder used in this study is an austenitic stainless steel 316L powder of industrial grade. It is a 12-times sieved (recycled) powder (with an oxygen rate less than 1000 ppm) seen by Weare Group as appropriate for providing quality AM parts. An analysis of the recycled powder chemical composition was performed. The nominal (normalized) and the actual (used) chemical composition of SS 316L is given in Table II-1. The chemical composition of the studied 316L powder is close to the nominal one.
Laser granulometry analysis was realized on two powder samples to make sure the repeatability (sample A and B whose distributions are displayed in Figure II-1). The particle size is described by D10-D90 where D10 is the equivalent volumetric diameter at cumulative probability of 10% and D90 is the equivalent volumetric diameter at cumulative probability of 90%. D50 (equivalent volumetric diameter at cumulative probability of 50% called also average equivalent diameter) can be used to compare between two powder distributions. The particle size in the delivery state (before recycling) is 5-25 μm, as can be seen in Figure II-1.

Fabrication of specimens

Two trays of around 80 specimens were manufactured with the same process parameters by the Weare Group. The SLM machine ProX DMP 320 (see Figure II-4a) was used with optimal parameters for SS 316L (listed in Table II-2). The powder melting and fusion was achieved by a laser with a spot size of 70 μm and with a power of 275 Watts. The laser scanning speed was 700 mm / s and the jumping speed 5000 mm / s. The hatch spacing was set to 70 μm and the layer thickness to 30 μm. The scanning strategy was hexagons, also known as random islands, with a recovery distance of 10 μm. Contouring was not applied here. Generally, the specimens used in the literature often experience contouring since it is a default configuration for most of the SLM machines. More exactly, this process step can improve the surface state. In our study, as we try to focus on the surface state effect, the choice is made to skip this step and hence to work with high roughness for the as-built configuration.

Microstructural characterization

The microstructures generated by SLM can be observed at two scales. We distinguish:
– The macrostructure generated by the passage of the laser spot and leading to fusion pools.
– The microstructure composed by grain crossing several melt pools and whose morphology and crystallographic texture are highly dependent on the cooling kinetics.
The observations were carried out on two planes (Figure II-9): (i) Z-plane also called manufacturing or lasing plane, this is the plane perpendicular to the manufacturing axis Z, it contains the history of a single layer; (ii) X/Y-plane, this is the plane perpendicular to X or Y and parallel to the Z axis. This
Microstructural characterization plane is constructed layer by layer during manufacturing and therefore contains the thermal history of all layers.

Macrostructure of the SLM SS 316L

The macroscopic structure of the Z-plane can be seen in Figure II-10. Using optical macroscopy, it is possible to distinguish weld beads corresponding to the main direction of the laser displacement. In this plane, the section of the grains is austenitic quadrangular. The optimized technique of 3D printing of metals consists of separating the manufacturing plane into several zones, generally of rectangular shapes. Once the laser finishes one zone it passes to the next one and can carry out the welding in the direction perpendicular to the preceding zone. This optimization reduces the residual stress in the final sample. The laser path is visible when changing directions (see « Laser spots » in Figure II-10).
With respect to the X/Y-planes (see Figure II-11), we can see ellipses, characteristic of the SLM process since they represent a section of the melt pools which appear during the passage of the laser. The macrostructure resembles fish scales. The observation of these planes makes it possible to clearly distinguish the interfaces between the layers, as well as, to see the elongated shape of austenitic grains crossing several layers. We can also observe the grains that are formed during the manufacturing process. Their growth direction roughly coincides with the Z-axis of the specimen.

Grain morphology and Crystallographic texture

To get a better knowledge of the microstructure, Electron Back Scatter Diffraction (EBSD) was used to observe the grain morphology and orientation. This analysis was carried out on a cylinder with a diameter of 8 mm and a height of 10 mm (see Figure II-15). The Z-plane was observed in the center of the specimen. While the X/Y-plane was observed in the bottom (corresponding to the first layers produced), in the middle and in the top (corresponding to the last layers produced).
The post-treatment of the results was performed by using the MTEX libraries. This post-treatment leads to EBSD mapping (with reconstituted grains) (Figure II-16 and Figure II-17), pole figures (Figure II-18a), and inverse pole figures (Figure II-18b). Based on this mapping, it is possible to reconstitute the grains by fixing the criterion of misorientation between two neighboring grains. In this study, this value of misorientation was taken equal to 6°.
The grain size is not homogeneous in the observed samples. Elongated columnar grains that cross several layers are visible. In Addition, no twin is present. The dislocation cells may be trapped in the dendritic structure leading to this absence.
With the exception of the grains in contact with the support and the grains of the extreme surface (where the cooling kinetics are different), all the other grains have a relatively identical morphology and size over the entire length of the cylinder. There is therefore no microstructure gradient along the sample.

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Tensile fatigue tests

The tensile fatigue tests are conducted in ambient air and temperature on a biaxial servo-hydraulic testing system, MTS® 809 (Figure II-29). The same machine was used for the monotonic tensile tests. The experiments are carried out under stress control at a load ratio R = -1 and a frequency of 15 Hz.
The target stress σ being defined, the cylindrical specimens of diameter D are subjected to the load F: 𝐹=𝜎𝜋𝐷24(𝐼𝐼𝐼.1).
The staircase method (appendix A.1) is applied to get the fatigue strength. The first specimen is subjected to a stress corresponding to the expected average fatigue strength. If the specimen survives 2*106 cycles, it is discarded and the next specimen is subjected to a stress that is one increment above the previous applied level, i.e. after a survivor the applied stress level is increased by one increment. The increment corresponds to the expected value of the standard deviation. When a specimen fails prior to reaching 2*106 cycles, the obtained number of cycles is noted, and the next specimen is subjected to a stress that is one increment below the previous applied level

Bending and torsional fatigue tests

A table resonant testing machine, Rumul® CrackTronic, is used (Figure III-1) to apply the bending and torsion loading modes.
Unlike servohydraulic fatigue set-ups, the Rumul® CrackTronic uses an electromagnetic driven resonator, built as a rotary oscillator, to create an appropriate bending or torsion moment. Independent to the dynamic drive, a static moment is possible to be applied to the specimen via a torsion rod. The test frequency is not controlled but depends on the specimen stiffness. In our experiments, the values reached were f = 96~98 Hz for the as built specimens and f = 94~96 Hz for the polished specimens. The resonant system allows crack initiation to be detected. For all our experiments, the tests are stopped and the number of cycles is recorded for a frequency drop of 0.1Hz. The corresponding detected crack is usually of a few millimeters long. A typical frequency curve is shown (Figure III-2).

Table of contents :

I.1. Generality
I.1.1. Selective laser melting of additive manufacturing
I.1.2. High cycle fatigue
I.1.3. Stainless steel 316L
I.2. The state-of-the-art research about fatigue behavior of SLM SS 316L
I.2.1. Effect of surface finish
I.2.2. Effect of heat treatment
I.2.3. Effect of building direction
I.2.4. Effect of processing parameters
I.2.5. Discussion
I.3. Summary
II.1. Specimens elaboration
II.1.1. Powder characterization
II.1.2. Fabrication of specimens
II.1.3. Heat treatment
II.2. Microstructural characterization
II.2.1. Macrostructure of the SLM SS 316L
II.2.2. Microstructure of the SLM SS 316L
II.2.3. Grain morphology and Crystallographic texture
II.3. Inherent defect characterization
II.3.1. Surface state characterization
II.3.2. Porosity characterization
II.4. Mechanical behavior
II.4.1. Hardness
II.4.2. Monotonic tensile test
II.4.3. Cyclic tensile test
II.5. Conclusions
III.1. Experimental fatigue test set-ups and conditions
III.1.1. Tensile fatigue tests
III.1.2. Bending and torsional fatigue tests
III.1.3. Surface preparation
III.2. Fatigue strength results and analysis
III.2.1. S-N curves
III.2.2. Effect of the surface state
III.2.3. Effect of loading type
III.2.4. Discussion
III.3. Fractographic analysis
III.3.1. Bending samples
III.3.2. Torsion samples
III.3.3. Summary
III.4. Correlation between defect size and HCF strength
III.4.1. Defect measurement
III.4.2. Kitagawa-Takahashi diagram
III.5. Conclusions
IV.1. Microstructure sensitive modeling framework for defective materials
IV.2. Explicit microstructure model and fatigue prediction approach
IV.2.1. Finite element model
IV.2.2. Material constitutive laws and fatigue approach
IV.3. Results
IV.3.1. Application and evaluation of non-local method based on experimental results
IV.3.2. Further investigation of the non-local method on the microstructure effect
IV.4. Conclusions
V.1. Preparatory investigations on the modeling of SLM steel 316L
V.1.1. Crystallographic orientation & grain morphology
V.1.2. Surface roughness & Pores
V.2. Modeling configurations
V.2.1. Design of geometrical models
V.2.2. Constitutive models
V.2.3. Loading condition
V.2.4. Fatigue criteria
V.3. Fatigue simulations of smooth models
V.3.1. Discussion on the experimental reference for simulation
V.3.2. Statistical method for microstructural heterogeneity
V.3.3. Investigations on R*
V.4. Fatigue simulations using models with roughness and defects
V.4.1. Models with artificial semi-ellipsoidal defects
V.4.2. Models with roughness
V.4.3. Models containing artificial defect and roughness
V.5. Role of plasticity in fatigue simulation
V.5.1. Comparisons between elastic and plastic constitutive models in smooth models
V.5.2. Comparisons between elastic and plastic predictions in defective models
V.5.3. Summary
V.6. Conclusions
Conclusions and prospects


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