# Role of cell structure in early-stage strengthening of L-PBF stainless steel 316L

Xiaobo Wang, Romain Quey, Venkata Karthik Nadimpalli, Dorte Juul Jensen, Tianbo Yu

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Xiaobo Wang, Romain Quey, Venkata Karthik Nadimpalli, Dorte Juul Jensen, Tianbo Yu. Role of cell structure in early-stage strengthening of L-PBF stainless steel 316L. 20th Nordic Laser Materials Processing Conference, Aug 2025, Kongens Lyngby, Denmark. pp.012017, 10.1088/1757-899X/1332/1/012017. hal-05213251

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# Role of cell structure in early-stage strengthening of L-PBF stainless steel 316L

X Wang<fnref n="1" />*, R Quey<fnref n="2" />, V K Nadimpalli<fnref n="1" />, D Juul Jensen<fnref n="1" /> and T Yu<fnref n="1" />

**Abstract.** This study investigates the influence of cell structure on the early-stage strengthening of stainless steel 316L produced by laser powder bed fusion. Two sets of samples were prepared: one as-printed, exhibiting a typical cell structure inside grains, and one subjected to a heat treatment, thus with cell-free grains. Tensile tests show about 150 MPa higher strength in the as-printed condition, corresponding to a 37% improvement as compared to the cell-free state. An analysis based on crystal plasticity simulations indicates that this corresponds to an increase in the critical resolved shear stress on the slip systems of 54 MPa. This value is consistent with the strengthening induced by the cell structure predicted by a simple dislocation forest hardening model, highlighting the significant effect of the cell structure on mechanical strength.

## 1. Introduction

Laser powder bed fusion (L-PBF) process introduces a hierarchical microstructure in stainless steel 316L [1]. This structure is composed of grains, each with a more or less uniform crystallographic orientations subdivided into micrometer-sized, slightly misoriented “cells”. Recently, the cell structure has gained significant interest [2]. Some studies attributed the enhanced tensile properties of L-PBF 316L compared to its conventionally manufactured counterparts to the cell structure [3], as it provides barriers to dislocation motion, thus increasing the yield strength. Furthermore, research on the thermal stability of the cell structure showed that it is eliminated after certain heat treatments, which in turn leads to a reduction in yield strength [4]. Although the presence of the cell structure has been correlated with improved mechanical properties, a quantitative understanding of its contribution to the early-stage strength remains limited.

In this study, we combine microstructural characterizations, tensile tests, and crystal plasticity (CP) simulations to investigate the role of the cell structure in enhancing strength of small strains, up to 1%, in L-PBF 316L. Additionally, a theoretical model based on dislocation forest hardening is employed to estimate the strengthening contribution of the cell structure. This integrated approach provides a solid understanding of the relation between cell structure and mechanical properties.

## 2. Experimental methods and simulation

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Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹Department of Civil and Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby DK-2800, Denmark</footnote>

<footnote n="2">²Mines Saint-Etienne, Univ Lyon, CNRS, UMR 5307 LGF, F - 42023 Saint-Etienne, France</footnote>

<footnote>*E-mail: xiawnga@dtu.dk (X Wang)</footnote>
## 2.1 Printing and post-print heat treatment

The powder employed was standard 316L powder from Höganäs, for details see [5]. The supplier provided the following particle size distribution information: $D_{10}$ = 25.1 µm, $D_{50}$ = 41.3 µm, and $D_{90}$ = 64.8 µm. The printing was carried out utilizing an open-architecture and open-source L-PBF system, which offers full experimental flexibility [6].

Cuboid samples (10x10x30 mm³) were printed, as illustrated in figure 1a. To print dense samples (<0.2% porosity), pre-optimized parameters were used: laser power $P$ = 250 W, scanning speed $s$ = 650 mm/s, layer thickness $t$ = 50 µm, and hatch distance $h$ = 100 µm [5]. The scanning direction was rotated 90° after each layer. The printing was done in a nitrogen atmosphere with a total oxygen level of <1000 ppm. Tensile specimens were extracted from the as-printed cuboids using electrical discharge machining. Figure 1b presents the geometry of the tensile specimen.

Two sets of samples, including tensile specimens and small cuboids for microstructure characterization, were extracted from two nominally identical cuboids. One set, referred to as AP (as-printed) was kept in the as-printed condition. The second set, referred to as HT (heat-treated), was subjected to heat treatment in a Nabertherm vacuum tube furnace (operated at 10⁴ torr) at 900 °C for 2 hours, followed by furnace cooling. The temperature and duration were chosen to eliminate the cell structure while maintaining the grain structure unchanged [7].

<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) Schematic illustration of a printed cuboid showing the extraction of the tensile specimen. (b) The tensile specimen (units in mm). (c) 3D tessellation generated by Neper, where each grain is colored according to its crystallographic orientation along the tensile direction.</figcaption></figure>

## 2.2 Microstructure characterization and tensile test

Both the AP and HT samples were prepared for microstructural characterization following the same preparation procedure. The samples for scanning electron microscopy (SEM) were prepared by grinding with SiC papers and then electrolytic polishing in Struers LectroPol-5. They were characterized in a Zeiss Sigma 300 microscope, equipped with an electron backscatter diffraction (EBSD) detector from Oxford Instruments using an acceleration voltage of 20 kV. To reveal the cell structure, the prepared samples were etched using a solution with HF:HNO₃:H₂O = 2:8:90 for 15 minutes. EBSD maps were obtained using a step size of 1 µm. The EBSD data were processed using the open-source MTEX software [8]. Samples for transmission electron microscopy (TEM) were cut out from the cuboids and were prepared through twinning using a 10% perchloric acid solution by Struers TenuPol-5 at a temperature of -25 °C [9].
A JEOL JEM-2100 microscope was used for the characterization at an acceleration voltage of 200 kV. All characterizations were conducted on the Y-Z plane (see figure 1a).

Tensile tests were performed at room temperature using an INSTRON 68TM-5 with displacement control. The sample strain was determined using a digital image correlation (DIC) system from LaVision, which captured specimen deformation during loading. The test was conducted at a constant crosshead speed of 0.6 mm/min, resulting in a strain rate of ~2×10⁻³ s⁻¹.

## 2.3 Crystal plasticity (CP) simulation

CP simulations were conducted to fit the experimental stress-strain curves and to estimate the critical resolved shear stress (CRSS) using the Neper/FEPX open-source software package [10,11]. The material behavior was described by an elastic response and a rate-dependent plastic response. The stress (σ) is related to the elastic strain (ε) by Hooke's law: σ = Cε, where C is the stiffness tensor, defined by the elastic constants C₁₁, C₁₂, and C₄₄ for cubic crystals. Assuming identical slip kinetics for all slip systems, the shear strain rate on slip system α is expressed as

$$ \dot{\gamma}^{\alpha} = \dot{\gamma}_{0} \left( \frac{|\tau^{\alpha}|}{g^{\alpha}} \right)^{\frac{1}{m}} \operatorname{sgn}(\tau^{\alpha}), \quad (1) $$

where $\dot{\gamma}_0$ is a fixed-rate strain rate scaling coefficient, $g^\alpha$ and $\tau^\alpha$ are the CRSS and current resolved shear stress of slip system α, and m is the strain-rate sensitivity exponent. The slip hardening is modeled by

$$ \dot{g}^{\alpha} = h_{0} \left( \frac{g_{s}-g^{\alpha}}{g_{s}-g_{0}} \right)^{n} \dot{\gamma}, \quad (2) $$

where $g_0$ and $g_s$ are the CRSS and saturation stress of slip system α, $h_0$ is the fixed-state hardening rate scaling coefficient, n is the non-linear Voce hardening exponent, and $\dot{\gamma}$ is calculated by $\dot{\gamma} = \sum_{\alpha} |\dot{\gamma}^{\alpha}|$. The material parameters [12] (excluding $g_0$) are shown in table 1.

<table><caption>**Table 1.** Elastic and elasto-viscoplastic model constants used in the simulation.</caption><thead><tr><th>C<sub>11</sub> [GPa]</th><th>C<sub>12</sub>[GPa]</th><th>C<sub>44</sub>[GPa]</th><th>h<sub>0</sub>[MPa]</th><th>g<sub>s</sub>[MPa]</th><th>m [-]</th><th>γ̇<sub>0</sub> [s<sup>-1</sup>]</th><th>n [-]</th></tr></thead><tbody><tr><td>204.6 × 10<sup>3</sup></td><td>137.6 × 10<sup>3</sup></td><td>126.3 × 10<sup>3</sup></td><td>171.7</td><td>291.7</td><td>0.05</td><td>0.0002</td><td>-1</td></tr></tbody></table>

The grain structure used in the CP simulation was generated using Neper, with a total of 1000 grains [10]. Although the grains in L-PBF 316L are typically elongated, a nearly equiaxed grain morphology was adopted here for simplification. The crystallographic orientations of the grains were obtained from the EBSD data, by uniformly selecting 1000 data points. The generated tessellation is presented in figure 1c, where each grain is colored according to its assigned orientation. The tessellation was then meshed into finite elements for simulation with FEPX [11]. To isolate the strengthening contribution of the cell structure, simulations were limited to small strains up to 1%, where the CRSS $g_0$ dominates the plastic response.

# 3. Results

## 3.1 Microstructural characterization

Figure 2 presents the microstructures of the AP and HT samples. From the SEM images, a pronounced cell structure is visible in the AP condition (figure 2a), while in the HT conditions (figure 2d), the cells are largely absent, while the grain boundaries remain. TEM images (figure 2b and 2e) further demonstrate this: The AP sample displays a high density of entangled
dislocations, forming cell boundaries. In contrast, the HT sample reveals a significant reduction in dislocation density, with only remnants of cell boundaries.

EBSD inverse pole figure (IPF) coloring maps (relative to the building direction) are shown in figure 2c and 2f for the AP and HT samples, respectively. The figures reveal that, despite the pronounced changes in cell morphology and dislocation density mentioned above, the grain structure remains largely unchanged after the heat treatment. The selected heat treatment therefore allowed to eliminate the cell structure while avoiding recrystallization and grain growth.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Microstructural characterization of the material in the AP and HT conditions. (a, d) SEM images showing cell morphology for AP and HT, respectively. (b, e) TEM bright-field images showing dislocation structures. (c, f) EBSD IPF coloring maps based on the crystallographic orientation of the building direction, with boundaries (>2°) overlaid in black, showing the grain structure in AP and HT, respectively.</figcaption></figure>

## 3.2 Tensile curves and crystal plasticity simulation to 1% strain

Figure 3 presents the engineering stress-strain curves up to 1% strain for both the AP and HT samples, based on two experimental repetitions. The AP samples exhibit a significantly higher strength compared to the HT ones. This difference is directly related to their microstructures. As the grain structures are similar in the two types of samples, it is reasonable to expect that the change in tensile properties is mainly induced by the cell structure. The AP samples contain cell structures with high dislocation densities, which enhance strength by impeding dislocation movement. In contrast, the cell structure is largely eliminated in the HT samples, resulting in reduced strength.
Figure 3 also includes the simulation results (dashed lines) for both the AP and HT samples, fitted to the experimental stress-strain data. Good fits are obtained in both cases. In this strain range, the dominant parameter influencing the model response is the CRSS ($g_0$). A good match with the experimental curves for the AP condition was achieved with a $g_0$ value of 190.3 MPa, while the HT condition was best represented with a lower $g_0$ of 136.7 MPa. This difference of 53.6 MPa in the fitted CRSS, $\Delta g_{0fit}$, directly reflects the strengthening effect provided by the cell structure.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Engineering stress-strain curves for the AP and HT conditions. Solid lines represent experimental results from two samples (exp1 and exp2), while dashed lines show the corresponding simulation results (sim).</figcaption></figure>

## 4. Theoretical analysis

To further evaluate the contribution of the cell structure to the early-stage strengthening, a theoretical approach was used to estimate the CRSS $g_0$ directly from the experimental microstructure. According to the literature, the dominant strengthening mechanism associated with the cell structure is the dislocation forest effect, where dislocations act as obstacles to gliding dislocations [4]. Therefore, a model based on dislocation hardening is used, where the total $g_0$ is expressed as [13]:

$$g_0 = g_0^{\text{const}} + \chi b \mu \sqrt{\rho}. \quad (3)$$

Here, $g_0^{\text{const}}$ represents the baseline CRSS that includes all strengthening contributions except that from the cell structure. The strengthening due to cell structure is captured by the second term, where $\chi$ is the dislocation interaction coefficient (taken as 0.24), $b$ is Burgers vector (0.256 nm), $\mu$ is the shear modulus (78 GPa) [14], and $\rho$ is the estimated dislocation density derived from geometrical considerations of the cell structure.

Assuming the cells have a n-gonal prism-like 3D morphology [5] and the cell walls have a mixed tilt and twist character, the dislocation density can be calculated using the relation [15]:

$$\rho = 2\sqrt{3} \frac{\theta}{db}. \quad (4)$$
Assuming an average cell equivalent diameter *d* of 0.5 µm and a misorientation angle *θ* of 0.4–0.5° [16], the estimated dislocation density is in the range of 1.9–2.4×10¹⁴ m⁻². Substituting this value into the hardening model (equation 3) gives a theoretical increase in CRSS due to the presence of the cell structure, Δ*g*₀*theo*, of 66–74 MPa. This estimation aligns reasonably well with the Δ*g*₀*fit* identified from the stress–strain data fitting. The discrepancy may be attributed to simplifications in the model or to the selected parameter values, e.g., *χ*, *θ*, or *d*.

Overall, the agreement between the analytical model and the simulated fit highlights the dominant role of the cell structure in strengthening L-PBF 316L. It provides a quantitative basis for understanding how the cell structure contributes to macroscopic mechanical performance. It also confirms that the observed increase in CRSS in the AP samples can be reasonably attributed to the high dislocation density associated with the cell structure.

**5. Summary**

This study investigates the role of the cell structure in strengthening L-PBF 316L stainless steel. SEM and TEM images confirm the presence of a cell structure in the as-printed condition, and that it can be removed by heat treatment at 900 °C for 2 hours. Tensile tests to 1% strain show a decrease of about 150 MPa in strength as a consequence of removal of the cell structure. Crystal plasticity simulations quantified this change as a 53.6 MPa decrease in the CRSS $g_0$. A theoretical dislocation forest hardening model, using experimentally estimated dislocation densities, predicts a similar contribution in CRSS from cell structure (66–74 MPa). These findings confirm that the cell structure has a dominant strengthening contribution in L-PBF stainless steels.

**Acknowledgements**

The work of XW and TY was supported by the Independent Research Fund Denmark DFF-FTP [grant number 2035-00061B], while Villum Fonden [MicroAM - grant number VIL54495] supported the work of VKN, and DJJ. Part of this research was carried out during the stay of XW at CNRS/Mines Saint-Etienne.

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