ORIGINAL RESEARCH A Numerical Study of Cracks Appearance on Tungsten Surface After High Intense Pulsed Ion Beam Irradiation Ijaz Shahid 1,2,3 • Jie Shen 1,2,3 • Xiao Yu 1,2,3,5 • Jie Zhang 1,2,3 • Haowen Zhong 1,2,3 • Xiaojun Cui 1,2,3 • Guoying Liang 1,2,3 • Wanying Huang 1,2,3 • Shijian Zhang 1,2,3 • Sha Yan 4 • Xiaofu Zhang 1,2,3 • Xiaoyun Le 1,2,3 Ó Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Due to the outstanding physical properties, Tungsten has been proposed for use in the divertor of future fusion devices. However, tungsten shall face strong particle bombardment from the plasma, which causes severe damage to the material. The purpose of this work is to build such an accurate analytical model which can predict the damages in target material like crack production and propagation after high intense pulsed ion beam irradiation. Hence, a two-dimensional finite element method is used to study the effect of high intense pulsed ion beam on tungsten surface numerically. To judge temperature and stress distribution in material, thermal conduction model is combined with non-linear fracture mechanics model and J-Integral parameter is used as a criterion to judge the crack propagation. Simulation results reveal that different crack heights and sizes can affect the results and there is a critical depth for crack propagation. The model gives good results to real experimental observations and has potential applications for different intense pulsed electron/plasma beams and different target materials as well. Keywords Tungsten Á High intense pulsed ion beam Á J-integral Á Finite element method Á Fracture toughness Introduction During the development of nuclear fusion reactor, one of the most urgent problems is to obtain material which are capable to operate for a long time under neutron irradiation damage, plasma attacks and two kinds of strong thermal irradiation i.e., steady state and transient state, which shorten the life time of plasma facing component (PFC’s) and cause serious security issues. Therefore, material with excellent resistance to irradiation damage is needed. This problem has been motivated to investigate materials for this purpose. Tungsten due to its comparatively good physical and mechanical properties, as shown in Table 1 gets extensive attention to be proposed as a most promising armor material for plasma facing components (PFC’s) in fusion devices [1] and possibly as a first wall material [2]. The long-life use of materials like tungsten for nuclear fusion devices is still under investigation. So, in this regard to study the effect of irradiations on candidate material can be carried out by simulating the interaction between tungsten and high intense pulsed ion beam (HIPIB) with different conditions. HIPIB is an emerging technology which primarily involved in nuclear fusion and high energy physics research [3]. This technology is the combination of charged ion beam like carbon and proton, with intensity (1–10 4 A/ cm 2 ), high power density (10 6 –10 10 W/cm 2 ) and short duration pulse (B 1 ls). During the irradiation process fast & Xiaoyun Le xyle@buaa.edu.cn 1 School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, People’s Republic of China 2 International Research Center for Nuclei and Particles in Cosmos, Beihang University, Beijing 100191, People’s Republic of China 3 Beijing Key Laboratory of Advanced Nuclear Energy Materials and Physics, Beihang University, Beijing 100191, People’s Republic of China 4 Institute of Heavy Ion Physics, Peking University, Beijing 100871, People’s Republic of China 5 Tomsk Polytechnic University, Tomsk 634050, Russia 123 Journal of Fusion Energy https://doi.org/10.1007/s10894-018-0186-x