PSI - Issue 79

Davide D’Andrea et al. / Procedia Structural Integrity 79 (2026) 283–290

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Figure 1 . Parametric DBC’s section geometry . Copper is represented in orange while alumina in grey.

The Latin Hypercube Sampling (LHS) technique was employed to generate 500 parameter combinations spanning the defined domains. LHS divides the range of each variable into equal probability intervals and then randomly selects one value from each interval, ensuring that the full range of each variable is represented in the sample (Helton and Davis, (2003)). Dimensions dependent on the specific application, such as layers length and thickness, were treated as constants, whereas the dimple position was varied between 50 and 550 µm, the dimple radius between 100 and 290 µm, and the notch opening angle between 90° and 135°.

Table 1. Dimensions of the model.

2

Values 2500 3500 300 380 100÷290 90 ÷ 135 Unit

Parameter

Description

Copper layer’s length Alumina layer’s length Copper layer’s thickness Alumina layer’s thickness

2 3 2 3

Dimple’s radius

Bi-material notch opening angle Dimple’s minimum distance from corner 50÷550 A free quadrilateral mesh was employed to mesh areas distant from the notch tip, while in its vicinity a circular sector has been meshed with a very fine mesh converging at the centre of the opening angle. The radius of the Control area, R c , deriving from a preliminary analysis performed on specimens with various notch opening angle made in copper and alumina according to Berto, (2015), resulted to be equal to 1 µm. PLANE223 elements are second-order 2D finite elements specifically designed for coupled-field analysis, meaning they can simultaneously account for multiple physical effects, such as structural deformation and thermal conduction. These elements allow users to select a thermo-structural formulation, which couples thermal and mechanical behaviours, and can be used under the assumption of plane strain, suitable for modelling thick structures where deformation in the out-of-plane direction is negligible. Materi als properties deriving from literature’s work ( Gaiser et al., (2015); Pietranico et al., (2009); Xu et al., (2016)) are reported in Table 2. It should be noted that the two materials differ in both mechanical and thermal properties. Alumina exhibits brittle behaviour, whereas copper typically shows pronounced ductile behaviour. Under the assumption of negligible plastic deformation, only linear elastic simulations were performed.

Table 2. Materials properties

Material

Young’s [MPa] 127000 340000

Modulus

Poisson’s ratio [//]

Coefficient of Thermal Expansion [1/°C]

Copper (Cu) Alumina (Al 2 O 3 )

0.33 0.22

16.5e-6 7.3e-6