Composite structures are often subjected not only to single impacts but also to repeated low-velocity impacts (RLVIs), which in this study refer to two successive impacts. This work investigates, both experimentally and numerically, the mechanical response and damage mechanisms of CFRP laminates under single impacts and RLVIs across various energy levels, with particular focus on non-uniform energies between the first and second impacts. The experiments focused on RLVIs under constant impact energy conditions, conducted at three energy levels of 10 J, 15 J, and 20 J. A complementary finite element model (FEM) incorporating a composite damage model was developed in ABAQUS/Explicit to simulate RLVIs using the restart technique. Based on this FEM, three impact energy scenarios were analyzed: (1) RLVIs with the same energy levels as the experiments; (2) highenergy (20 J and 30 J) second impacts following an initial low-energy (10 J) impact; and (3) low-energy (10 J) second impacts following high-energy (20 J and 30 J) initial impacts. The impact energies were classified as low or high depending on whether they were below or above the critical threshold (approximately 15 J) for fiber damage initiation. The qualitative effects of impact energy and sequence on the mechanical response were evaluated in terms of variations in impact force, displacement, absorbed energy, and response duration. Furthermore, the associated damage mechanisms, including fiber and matrix damage as well as delamination, were analyzed in detail.

This paper proposes an innovative frequency degradation model, termed the NTF (Number of load cycles, Temperature, real-time Frequency) model, for predicting the real-time frequencies, fatigue life (for the design stage), and residual fatigue life (during the service stage) of fiber reinforced polymer (FRP) laminates at various ambient temperatures (below the glass transition temperature). Built upon the traditional stiffness degradation model, the NTF model integrates the time-temperature superposition principle (TTSP) for frequency degradation along with a novel threshold frequency-based fatigue failure criterion. To validate the effectiveness of the proposed NTF model, tensile fatigue tests and modal tests on GFRP laminates at different ambient temperatures were conducted. The resultant experimental results indicate that higher-mode frequencies exhibit more stable degradation trends during temperature-influenced fatigue loading, establishing themselves as robust indicators for fatigue life prediction. Importantly, the validation results confirm that the proposed NTF model achieves satisfactory accuracy in predicting real-time frequencies (the highest average prediction error is below 1.40 %), fatigue life (about 90 % of the predicted data fall within the 2 times error band), and residual fatigue life (over 90 % of the predicted data fall within the 2 times error band). Notably, this study is the first to integrate the frequency degradation mechanism and the TTSP into a unified model for predicting the temperature-dependent fatigue life of FRP laminates.

This study proposes a novel stiffness degradation model, termed the NTSS (Number of load cycles, Temperature, loading Stress, and residual Stiffness) model, for predicting the residual stiffness and fatigue life of fiber reinforced polymer (FRP) composites under various ambient temperatures (below the glass transition temperature) and loading stresses. The innovation of the proposed model lies in its integrated consideration of both ambient temperature and loading stress. The proposed model has been validated for bending fatigue of CFRP and hybrid CFRP/GFRP laminates by using experimental data from the literature. The results show that the proposed model demonstrates satisfactory accuracy in predicting the residual stiffness (the maximum average prediction error is below 1.45 %) and fatigue life (over 75 % of the predicted data fall within the 2.5 times error band). In addition, the proposed model can also be applied to generate (S, Nf) data under different temperatures, thereby leading to the development of a new S-Nf curve model suitable for given temperatures. By integrating the threshold stiffness-based fatigue failure criterion, the developed S-Nf curve model is effective in guiding the design of FRP composites for long-term fatigue performance and in evaluating the long-term fatigue life.

The existing damage constitutive models for a composite lamina under impact loading have mainly considered four failure modes: longitudinal fiber failure in tension and compression, matrix failure in tension and compression along the transverse direction. However, when subjected to an impact load in the out-of-plane direction, through-thickness compression failure may also occur in laminates. Therefore, the present paper has established a damage constitutive model considering through-thickness compression failure and has compared it to those constitutive models without such consideration to see the improvement in the impact response analysis and to discuss the necessity of including through-thickness compression damage in the simulation. To this end, impact testing was conducted on manufactured composite panels, and the results were used to validate the finite element simulation of composite laminates under impact. The results showed that the constitutive model with the compression failure mode in the thickness direction had higher accuracy in predicting the impact force, displacement, damage, and energy absorption of laminates. The predicted results by the developed constitutive model showed that through-thickness compression damage indeed occurred in the laminates during the impact process, and it was mainly concentrated in the layers near the impact side. In the layers near the rear side, the tension damage of longitudinal fiber and matrix mainly initiated and developed in the annular region around the impact center on the laminates.

The lightweight design of railway vehicle components using fiber reinforced polymers (FRPs) has become a research hotspot due to the strong need for energy saving and environmental protection. This paper aims to evaluate the impact damage behavior of a carbon fiber reinforced polymers (CFRP) protection suspender, which is a component on railway vehicles to prevent the falling joist and bolster from touching the rails and to avoid the derailment of trains. A finite element (FE) model of the CFRP protection suspender, which considered varying bolt preloads was established in ABAQUS/Explicit. The bolt preload was successfully applied around the installation holes on the protection suspender by deliberately reducing the local temperature of the bolt shank to create shrinkage. The impact behavior of the protection suspender was then analyzed, and the impact-induced damage was governed by the Continuum Damage Mechanics (CDM) models, which include both intra-laminar damage and inter-laminar damage. The low-velocity impact response of the CFRP protection suspender was investigated with the lay-ups of [0]10 and [0/90/0/90/0]S under different bolt preloads (i.e. 0, 5 and 20 kN). The results showed that the vulnerable positions of the protection suspenders included the contact edge between the protection suspender and the impactor, the curved corner of the suspender, and the areas around the bolt holes. In addition, the protection suspender with the lay-up of [0]10 had better impact resistance than that with the lay-up of [0/90/0/90/0]S. By applying different preloads, it showed that the increase of bolt preloads could help to prevent the occurrence of crack damage around the installation holes, thus improving the structural safety when subjected to low-velocity impact. The present simulation results offered great value for the lightweight design and structural optimization of a protection suspender on railway vehicles that had to survive from sudden impact loads in service.

复合材料结构在疲劳过程中的累积损伤将导致结构刚度下降,并进一步引起结构的动态参数如频率发生衰减.因此,可以将结构疲劳状态与结构频率联系起来,基于频率预测结构的剩余疲劳寿命.本文首先基于复合材料在纵向、横向和面内剪切三个方向的疲劳特性,结合ABAQUS与Umat子程序开发了三维有限元模型模拟复合材料层合板中的疲劳损伤演变,并构建了不同疲劳状态下对应的模态分析模型,由此获得了疲劳过程中的频率衰减曲线.之后,基于疲劳过程的频率变化量训练了人工神经网络,用于预测玻璃纤维增强复合材料层合板的剩余疲劳寿命.特别地,在当前的数值模型中为每个单元分配了符合高斯正态分布的材料属性,以模拟实际情况下复合材料性能的离散性.结果表明,疲劳模型数值模拟结果与已有文献的疲劳实验数据吻合,基于频率变化量训练的人工神经网络可以成功预测玻璃纤维增强复合材料试件的剩余疲劳寿命.