Advanced high strength steels (AHSS) have been widely employed in the automotive industry to meet the requirements of improving crash performance while reducing vehicle weight. The excellent performance of AHSS in strength and ductility comes from a dedicated design of alloy composition and microstructure. However, the addition of some alloying elements may lead to poor weldability. Solidification cracking tends to occur in AHSS containing detrimental elements such as phosphorous or sulfur under unfavorable welding conditions.
Solidification cracking is a complex problem associated with multiple physical phenomena at different length scales. During welding, with a localized heat input, the material is heated to melt, forming a weld pool. Upon cooling, a mushy zone consisting of solid grains and liquid channels forms behind the weld pool. As temperature drops, solid grains in the mushy zone grow, which tends to close liquid channels in the mushy zone. However, during solidification, detrimental elements segregate in the liquid, inhibiting the closure of the liquid channel. Meanwhile, due to solidification shrinkage and thermal contraction, the liquid channels experience a tensile load, which tends to open the liquid channel. If there is insufficient liquid feeding, solidification cracking occurs. Solidification cracking can be avoided by controlling parameters including alloy composition, microstructure and processing conditions like power, welding velocity, laser beam shapes, etc.
Due to the complexity, an accurate prediction of solidification cracking under various welding conditions is challenging. A full-field simulation of a welded component which incorporates all the physical phenomena and is capable of handling various welding conditions is not realistic with current computational power. To achieve an accurate prediction of solidification cracking, approximations and simplifications must be made while major physical mechanisms are still properly captured. Moreover, existing modelling techniques should be improved or adapted to fulfill the requirements of welding simulations.
This research starts from explicitly modelling segregation and solidification during welding. In the literature, cellular automata (CA) models and phase field (PF) models have been widely used to simulate segregation and solidified microstructure. The CA method is more computationally efficient compared to the PF method and thus is mainly adopted in the current research. A cellular automata solidification model is developed, where the growth velocity is determined based on kinetic undercooling at the interface. The state-of-the-art model incorporates a decentered growth algorithm to suppress grid anisotropy and a generalized height function method to calculate curvature accurately. To remove the dependency on the mesh size, a new diffusion term is proposed to handle the diffusion between the interface cells and liquid cells. Moreover, a solute redistribution method has been applied for each interface cell to resolve the mass balance error introduced by the virtual liquid cell assumption. The developed CA model is validated by simulating single-dendritic solidification in an Al-3Cu (wt.\%) alloy. The simulated tip velocities agree with the prediction of the Kurz-Giovanola-Trivedi (KGT) model. With improvements in the aspects of mesh-size independency and mass balance, the developed CA model is suitable for solidification simulation with a high undercooling, as is common in welding. It also provides an easier way to achieve multi-component solidification simulation compared to conventional CA solidification models, which need to solve a system of mass balance equations in interface cells. Despite the improvements made, due to the poor discretization of the solid-liquid interface, the CA method is less accurate compared to the phase field method. Up to now, no CA models can reproduce the dendrite tip velocity predicted by a Green function method in single-dendritic solidification simulations.
For better accuracy, the research was extended with a focus on PF modelling of segregation in the liquid channels in the mushy zone during welding. Following the frozen temperature gradient approximation, the complex thermal conditions during welding are approximated with a directional solidification condition defined by a constant temperature gradient and pulling velocity, which is the moving velocity of the liquidus isotherm. Under directional solidification conditions, columnar dendrite grains form and liquid channels exist in between neighboring grains, where solutes accumulate. The liquid channel structure and segregation is simulated with the PF model, while the solidification cracking susceptibility (SCS) is then quantified by calculating the pressure drop from the dendrite tip to the coalescence point of the liquid channels with an analytical model, the Rappaz-Drezet-Gremaud (RDG) model. A larger pressure drop represents a larger SCS. With the modelling setup, the influence of the temperature gradient and the pulling velocity on SCS have been investigated. Increasing the pulling velocity or decreasing the temperature gradient increases the pressure drop from the dendrite tip to the coalescence point, leading to an increase in SCS. Decreasing the primary dendrite arm spacing (PDAS) decreases the permeability of the liquid channel and the liquid channel length at the same time, resulting in a decrease in the pressure drop and SCS when the PDAS is small. Consideration of the PDAS dependency on the temperature gradient and the pulling velocity influences the value of the pressure drop but does not change the tendency of the SCS. The findings indicate that solidification cracking can be avoided by either decreasing the pulling velocity or increasing the temperature gradient or refining the grain size, as supported by experimental results. However, due to the high computational cost, the size of the simulation domain is limited. Moreover, the influence of process parameters on SCS cannot be considered directly due to the lack of macroscopic modelling.
To include the influence of process parameters, macroscopic thermal-mechanical modelling and microstructure modelling of the whole weld pool are necessary. The former is relatively easy to achieve, while the latter is, nevertheless, not achievable with the aforementioned CA model or PF model, as both models require a fine mesh size to simulate the liquid channel structure and segregation within the liquid channels. Simulating the solidification microstructure for the whole weld pool or the whole mushy zone requires a huge amount of computational resources. As an alternative to the numerical solution, the segregation in the liquid channel can be calculated analytically with the Scheil-Gulliver calculation, while the remaining question is how to achieve the microstructure simulation of the whole weld pool.
Therefore, the research addressed microstructure modelling of the whole weld pool. To this purpose, a special kind of CA model is adopted, which calculates the growth velocity as a function of local undercooling based on analytical models (LGK model or KGT model). In this case, there is no need to solve the concentration profiles numerically, which permits a coarse mesh size and thus a reduction in the requirement of computational resources. These kind of CA models are called CAFE models, as such CA models are always coupled with a thermal finite element (FE) model. In this research, a CAFE model which is two orders of magnitude faster than conventional CAFE models has been developed. The acceleration comes from three different sources. Firstly, by adopting an exact temporal integration and a multi-layer capture algorithm, a large time step can be employed without compromising the simulation results. Secondly, the parallelism of the simulation codes is achieved in a shared-memory environment, enabling a more efficient load balance. Thirdly, a subdomain activation and deactivation method is employed to reduce the computation tasks. The proposed model is validated by simulating the grain morphology and texture of additively manufactured samples. A good agreement is achieved between the simulations and the experiments.
By coupling the CAFE model with a thermo-mechanical FE model and a granular model to calculate liquid pressure, a multi-physics multi-scale modelling framework is developed to predict solidification cracking. The thermo-mechanical FE model calculates the profiles of temperature and strain rate for the welded component during welding; the CAFE model simulates the solidification microstructure in the whole weld pool; and the granular model calculates the pressure drop in the liquid channel network determined based on the simulated microstructure and the Scheil-Gulliver calculations. The developed modelling framework is then validated by simulating welding experiments of a TRIP steel. With a constant ratio between the power and the welding velocity, increasing the welding velocity increases the maximum pressure drop in the mushy zone, indicating an increase in SCS. Grain refinement or decreasing the freezing temperature by changing the alloy composition leads to a decrease in the maximum pressure drop in the mushy zone, representing a decrease in SCS. The predictions from the modelling framework are supported by experimental findings in the literature.
In conclusions, the research starts from microstructure modelling of segregation and liquid channel structure with both the CA method and the PF method and finalizes with a multi-physics multi-scale modelling framework of solidification cracking. In this approach, several approximations and simplifications have been made to reach the final modelling framework for solidification cracking. The developed multi-scale multi-physics modelling framework incorporates major physical mechanisms at different length scales and paves a way to understand and predict solidification cracking under various welding conditions. It provides a theoretical basis to eliminate solidification cracking by tuning parameters including alloy composition, microstructure and processing parameters like power, welding velocity and laser beam shapes, etc. Moreover, with the acceleration in microstructure simulation, the developed CAFE model contributes to the development of a digital twin of additive manufacturing.