The paper presents experimental and numerical characterization of damage evolution for ion-irradiated materials subjected to plastic deformation during nano-indentation. Ion irradiation technique belongs to the methods where creation of radiation-induced defects is controlled with a high accuracy (including both, concentration and depth distribution control), and allows to obtain materials having a wide range of damage level, usually expressed in terms of displacements per atom (dpa) scale. Ion affected layers are usually thin, typically less than 1 micrometer thick. Such a low thickness requires to use nano-indentation technique to measure the mechanical properties of the irradiated layers. The He or Ar ion penetration depth reaches approximately 150 nm, which is sufficient to perform several loading-partial-unloading cycles at increasing forces. Damage evolution is reflected by the force-displacement diagram, that is backed by the stress–strain relation including damage. In this work the following approach is applied: dpa is obtained from physics (irradiation mechanisms), afterwards, the radiation-induced damage is defined in the framework of continuum damage mechanics to solve the problem of further evolution of damage fields under mechanical loads. The nature of radiation-induced damage is close to porosity because of formation of clusters of vacancies. The new mathematical relation between radiation damage (dpa) and porosity parameter is proposed. Deformation process experienced by the ion irradiated materials during the nano-indentation test is then numerically simulated by using extended Gurson–Tvergaard–Needleman (GTN) model, that accounts for the damage effects. The corresponding numerical results are validated by means of the experimental measurements. It turns out, that the GTN model quite successfully reflects closure of voids, and increase of material density during the nano-indentation.

中文翻译：

---

离子辐照6061铝合金纳米压痕弹塑性损伤模型

本文介绍了在纳米压痕过程中经受塑性变形的离子辐照材料损伤演化的实验和数值表征。离子辐照技术属于以高精度控制辐射诱发缺陷的产生（包括浓度和深度分布控制）的方法，并且可以获得具有广泛损伤水平的材料，通常用位移表示每个原子 (dpa) 尺度。离子影响层通常很薄，通常小于 1 微米厚。如此低的厚度需要使用纳米压痕技术来测量辐照层的机械性能。He 或 Ar 离子穿透深度达到大约 150 nm，这足以在增加的力下执行几个加载-部分-卸载循环。损伤演化由力-位移图反映，这是由应力-应变关系支持的，包括损伤。在这项工作中，应用了以下方法：dpa 从物理学（辐射机制）中获得，然后在连续介质损伤力学的框架中定义辐射引起的损伤，以解决机械载荷下损伤场进一步演化的问题。由于空位簇的形成，辐射引起的损伤的性质接近于孔隙率。提出了辐射损伤 (dpa) 与孔隙度参数之间的新数学关系。然后通过使用扩展的 Gurson-Tvergaard-Needleman (GTN) 模型对纳米压痕测试期间离子照射材料所经历的变形过程进行数值模拟，该模型解释了损伤效应。通过实验测量验证了相应的数值结果。事实证明，GTN 模型非常成功地反映了在纳米压痕过程中空隙的闭合和材料密度的增加。