## 1 Introduction  
Lightweight design and manufacturing are the development direction of aerospace, transportation, and other fields, which can realize performance improvement, energy saving, and emission reduction [1; 2]. Carbon fiber reinforced polymer composites have the advantages of high specific strength, high specific stiffness, designable properties, and integral fabrication of components, making them the preferred materials for reducing weight and improving performance [3; 4]. Depending on the polymer matrix, such composites can be divided into thermosetting and thermoplastic. Both types of composites need to be used in applications with metals such as aluminum and titanium alloys, thus weakening the negative effects of strong anisotropy, low interlaminar shear properties, and the high manufacturing costs of composites [5; 6]. For instance, the fuselage of the Airbus A350 XWB airliner is mainly made of carbon fiber reinforced polymer composites, while aluminum and titanium alloys are used for the reinforcement of certain high-load-bearing structures [7; 8]. Compared with thermoset composites, carbon fiber reinforced thermoplastic (CFRTP) composites exhibit stronger impact resistance, as well as the advantages of heat molding,fusion joining, and recycling [9; 10; 11]. With the increasing maturity of raw material preparation and component molding, they are gradually used in aircraft flat tails, fuselages, etc., and face the same problem of joining with metals [12; 13; 14]. Mechanical joining methods such as bolting and riveting are commonly used for structures subjected to concentrated loads. For structures subjected to uniform or shear loads, fusion joining, which relies on interfacial bonding formed by molten thermoplastic polymers, is gaining importance. This approach avoids the performance degradation of CFRTP composites caused by material processing and reduces the use of adhesives and fasteners, thereby maximizing the effect of weight reduction [15; 16]. Depending on the heat source, fusion joining of CFRTP composites with metals can be categorized as friction joining, ultrasonic joining, laser joining, induction joining, and resistance joining. Among them, laser direct joining is the approach where a high energy density laser beam is used to heat the metal, putting the polymer matrix in contact with metal to melt and bond with metal to form a joint, with the advantages of good adaptability to material types and geometrical structures and easy automation [17; 18; 19; 20]. The joining temperature is the key to determining whether CFRTP composites and metals can be joined through fusion [21; 22]. Scholars have investigated the effect of joining temperature on the laser direct joining process using simulations and experiments. [PERSON] et al. equated the laser energy input to a Gaussian surface heat source and simulated the temperature field when laser direct joining PMMA and stainless steel [23]. To improve the accuracy of the temperature simulation, the temperature-dependent thermal properties and the anisotropy of the CFRTP composite were further considered, which allowed the average error between the simulated and measured temperatures to be less than 10% [24; 25]. Based on the temperature field simulation during laser direct joining, scholars investigated the relationship between temperature distribution and the melting and solidification process of CFRTP composites. [PERSON] et al. used the melting point of the polymer matrix as the melting boundary criterion in the temperature simulation, that is, 280 \({}^{\circ}\)C for the polyphenylene sulfide used, and found that the melting widths and depths obtained from the simulation agreed with the experiment [26]. Similarly, [PERSON] et al. used a melting temperature of 303 \({}^{\circ}\)C for a nylon 6T matrix as the melting boundary criterion, and the CFRTP composite solidification sequence during the laser direct joining was investigated [27].