PSI - Issue 74

Karel Slámečka et al. / Procedia Structural Integrity 74 (2025) 85 – 90 Karel Slámečka / Structural Integrity Procedia 00 (202 5 ) 000 – 000

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2. Finite-element model The finite-element (FE) model represents two spherical Ti powder particles, each ~28 µm in diameter, joined by a sintering neck with a minimum cross-section diameter of 20 µm. Owing to geometric symmetry, only one-eighth of the structure was simulated (Fig. 2). In the first simulation step, the system was initialised as stress-free at the nitriding temperature. Residual stresses were then evaluated across the smallest neck cross -section during cooling to room temperature. In the second step, a numerical uniaxial tensile test was performed to extract the effective composite stiffness from the simulated stress-strain response.

Fig. 2. Geometry and boundary conditions of the FE neck model. Two spherical Ti particles share a minimum-cross-section neck; symmetry limits the mesh to one-eighth. UY: Y -displacement; CPY: coupled Y DOFs. Axial load F starts at zero and increases in the tensile test.

The simulations considered five nitriding temperatures: 500 °C, 550 °C, 600 °C, 650 °C, and 700 °C. For 500 °C, 600 °C, and 700 °C, the thicknesses of the DZ and CL were taken from experimental measurements (Slámečka et al. (2025)). Intermediate values for 550 °C and 650 °C were interpolated (Table 1). At 500 °C, LT gas nitriding does not produce a distinct CL layer within 10 h (Roliński (2016), Unal et al. (2018), Slámečka et al. (2025)) , and the same assumption was adopted for 550 °C. In contrast, nitriding at 600 °C results in a multi-layered CL comprising the inner Ti 2 N and outer TiN layers (Fig. 1b), with possible presence of Ti oxides (Zhecheva et al. (2005), Zhao et al. (2020)). Beyond ~620 °C, the nitriding rate in open-microporous Ti increases markedly (Slámečka et al. (2025)) , justifying the use of CL and DZ thicknesses cl ose to those observed at 700 °C for 650 °C.

Table 1. Thicknesses of the DZ ( t DZ ), CL ( t CL ), and entire coating for each nitriding condition.

* Estimated values.

Nitriding temperature (°C)

t DZ (µm)

t CL (µm)

t DZ + t CL (µm)

500

1.0

0.0

1.0

* 550

* 1.8

* 0.0

* 1.8

600

2.5

0.8

3.3

* 650

* 2.9

* 1.1

* 4.0

700

3.1

1.2

4.3

The Ti core and DZ were modelled as bilinear elastic-plastic materials. The CL was considered a purely elastic, isotropic TiN layer with constant material properties (Table 2). The DZ corresponds to a solid solution of interstitial nitrogen atoms occupying octahedral sites in the hcp Ti lattice (Su shko et al. (2014)). To account for compositional gradients, the material properties within the DZ were scaled using a complementary error function (erfc), which is the solution to Fick’s second law for a semi -infinite domain: