Micro-spalling is a dynamic fragmentation process that is coupled with shock-induced overheating and melting. It has been observed in series of shock experiments and in several modern industrial applications such as inertial confinement fusion and laser-shock surface micromachining. Modeling micro-spalling is beyond the scope of traditional damage mechanics which ignores solid–liquid transformation.

Here, for the first time, we develop a continuum model of micro-spalling by coupling hydro-elastic–plastic-damage mechanics and high-pressure melting kinetics. A two-scale framework is proposed for modeling mechanical responses of partially melted materials in shock-induced micro-spalling. Temperature and pressure dependence of shock-induced melting rate is formulated. In modeling dynamic ductile damage, temperature and (partial) melting effects are involved.

The model is implemented into a finite element code and used as a predictive tool to simulate plate impact spalling experiments on aluminum. The simulations reveal typical characteristics of micro-spalling resulted from coupling effects of dynamic damage and melting, concerning evolutions of damage and phase distributions and thermodynamic paths. The simulations are in good agreement with previous experiments and molecular dynamics simulations. Particularly, the calculated free surface velocity profiles and spall strengths are quantitatively consistent with experimental measurements in a wide range of initial temperature up to the melting point. These results indicate that the present model is a reasonable uniform description of spalling process, covering transition from classical solid spalling to melting-accomplished micro-spalling.

微剥落是一个动态的破碎过程，伴随着震动引起的过热和熔化。在一系列冲击实验和一些现代工业应用（例如惯性约束聚变和激光冲击表面微加工）中已经观察到它。对微剥落进行建模超出了传统的破坏力学范围，后者忽略了固液转换。

在这里，我们首次通过耦合水弹塑性损伤力学和高压熔融动力学来建立微剥落的连续模型。提出了一个两尺度框架，用于在冲击引起的微剥落中模拟部分熔融材料的机械响应。公式化了温度和压力对冲击感应熔化速率的影响。在动态延性破坏建模中，涉及温度和（部分）熔化效应。

该模型被实现为有限元代码，并用作预测工具，以模拟铝板上的板冲击剥落实验。仿真揭示了动态损伤和熔化的耦合效应导致的微剥落的典型特征，涉及损伤和相分布以及热力学路径的演变。模拟与先前的实验和分子动力学模拟非常吻合。特别地，在直至熔点的宽范围的初始温度下，所计算的自由表面速度分布和剥落强度在定量上与实验测量一致。这些结果表明，本模型是剥落过程的合理统一描述，涵盖了从经典的固体剥落到熔融完成的微剥落的过渡。