PSI - Issue 77

Alireza Shadmani et al. / Procedia Structural Integrity 77 (2026) 221–228 Shadmani et al. / Structural Integrity Procedia 00 (2026) 000–000

226

6

can be established as follows:

1 α

N N f

log(1 − (1 − e − α )

D = −

)

(6)

3. Results

A finite element model was developed to simulate the transient stress distribution within the PU coating resulting from a single raindroplet impact at a velocity of 110 m / s. The initial impact phase is dominated by a high-magnitude, localized compressive stress field of approximately -60.45 MPa, as shown in Fig. 4(a)-(b), at t = 1 × 10 − 7 s and t = 1.25 × 10 − 7 s. This intense stress localization forms at a subsurface location directly beneath the impact point, a direct consequence of the initial ”water hammer” shock pressure from the raindroplet. This subsurface localization is a critical feature, establishing the primary region where material damage is likely to initiate. Subsequently, the stress field rapidly evolves as the initial impact energy is converted into mechanical waves within the coating. The compressive peak attenuates while significant tensile stresses emerge at the surface, adjacent to the central impact zone, as depicted in Fig. 4(b). This signature, i.e., tension at the surface, is the characteristic profile of a Rayleigh surface wave propagating outwards from the impact location. This phenomenon is crucial as it transforms the initial compressive shock into a travelling wave that carries potentially tensile forces across the coating’s surface. Furthermore, to quantify this dynamic evolution, the stress-time histories were extracted along a path at the surface from the impact center (Fig. 4(c)). At the epicenter ( x = 0), the stress history is dominated by a sharp compressive spike, followed by a rapid return to near zero. This reflects the initial impact and subsequent relaxation. Moving outward, the stress profiles change markedly. At x = 2 . 5 mm , the compressive peak is lower, around -27 MPa, following tensile peaks that emerge after the compressive phase. This tensile peak is more pronounced at x = 5 mm , where the tensile stress reaches approximately 5.29 MPa. Further out, at x = 15 mm and x = 20 mm , the tensile peaks gets flattened and the compressive peaks diminish further. This progression illustrates the transformation of the stress field from a localized compressive shock to a broader tensile wavefront, which is critical for understanding the mechanisms of damage initiation and propagation in the PU coating.

(a)

(b)

(c)

7 s, (b) max. principal stress distribution at t

7 s, and (c) max. principal stress

Fig. 4: (a) Max. principal stress distribution at t = 1 × 10 − along the path on coating surface

= 1.25 × 10 −