**5. Discussion**

Due to the significantly higher stiffness of the martensite phase and strong "elastic mismatch" in the DP steels, higher interfacial stresses are induced due to applied mechanical or thermal loading [44,45]. Therefore, when comparing the stress and strain fields of the martensite and ferrite phases, extremely higher stress (≈2500 MPa) and lower strain are achieved in the martensite phase. On the contrary, smaller stress (≈800 MPa) and larger strain can be identified in the ferrite phase.

From the current and previous studies [28,37,38,46,47], in 2D crystal plasticity simulation, the obvious stress and strain concentrations exist in the ferrite phase due to the absence of the third dimension. As depth increases, the stress and strain are more distributed, and the concentration generally transfers to the matrix/particle interfaces and triple points of grains with a low Schmidt factor. As the thickness increases, the matrix's stress field is phenomenally influenced by the adjacent inclusion. Chao et al. [48] indicated that the distance between two circular inclusions strongly provoked the stress field of the matrix and then interfered with the stress intensity factor of the crack.

Additionally, Diehl et al. [28] investigated the interaction between stress/strain conditions, the phase distribution of neighboring grain, and their crystallographic orientation. It was concluded that there is a drastic difference in local stress/strain distribution between 2D and 3D-RVEs results, which means it is difficult to validate simulation results with similar experiments. If 3D geometry is measured by slicing the surface, there is no same specimen available for the in situ tests. On the contrary, if the specimen is tested by deformation loading, 2D EBSD only can be obtained, and the corresponding 2D simulation result differs from the 3D distributions [28].

In the database of parameters from the proposed iterative method, as displayed in Tables 3 and 4, it can be examined that the *R*<sup>2</sup> *m* is practically similar in the same iterative step for ferrite phases regardless of total grain numbers, strain levels, and volume fractions. Additionally, the constants *am* and *bm* nearly have a consistency tendency regardless of total grain numbers and volume fractions. There is a difference in the case of strain levels. That is, the constant *am* and *R*<sup>2</sup> *m* display a similar value for different strain levels. Conversely, the constants *bm* demonstrates larger value at larger strain levels. It is exhilarating that the 3D distribution can be straightforwardly responded to by 2D result by the same iterative constant owing to the similar *am*, *bm* and statistical analysis, which means that the 3D distribution can be derived by the proposed iterative method regardless of total grain numbers and volume fractions.

The methodology of deriving 3D local distribution from 2D results has been thoroughly introduced. In the future, the constants *am* and *bm* can provide a helpful suggestion to predict the 3D local stress/strain from 2D local stress/strain. Henceforward, the derived 3D local stress and strain distribution can be an excellent validation of the experiment and further recommends the optimal design of the multiple phase steel with different grain orientation, total grain numbers, composition, and loading conditions by the proposed iterative method.
