*3.2. Johnson-Cook Model*

As a result of very large magnitudes of the pressure load (several GPa) and a very short laser pulse duration (a few ns), extremely high strain rates (over 10<sup>6</sup> s<sup>−</sup>1) are reached in LIW process, similar to those in laser shock peening. Therefore, the rate-dependent Johnson-Cook (J-C) [43] material constitutive model was implemented to incorporate the e ffects of strain rate on material behavior. The J-C flow stress (<sup>σ</sup>*eq*) is given in Equation (6):

$$
\sigma\_{\varepsilon\eta} = \left( A + B \varepsilon\_{\varepsilon\eta}^{\text{II}} \right) \left[ 1 + C \ln \left( \frac{\dot{\varepsilon}}{\dot{\varepsilon}\_0} \right) \right] \left[ 1 - \left( \frac{T - T\_0}{T\_0 - T\_{\text{mclt}}} \right)^{\text{II}} \right] \tag{6}
$$

where parameters *A*, *B*, *n*, *C*, and *m* are quasi-static yield stress, hardening constant, hardening exponent, strain rate constant, and thermal softening exponent, respectively. These material constants are determined empirically. The rest of the parameters in the J-C model are equivalent plastic strain (<sup>ε</sup>*eq*), plastic strain rate (. ε), reference strain rate (. ε0), testing temperature ( *T*), reference temperature ( *T*0), and melting temperature ( *Tmelt*). J-C parameters of the materials used are listed in Table 3.

**Table 3.** J-C parameters [32], with permission from Elsevier, 2019.

