On the origin of the back stress in heterogeneous structure: intergranular residual stress and intragranular back stress

Back stress has been proven to be the primary mechanism for superior mechanical properties of heterogeneous structures, but its quantitative contribution remains vague. The main purpose of this work is to clarify the contributions of back stress components, i.e., intergranular residual stress and intragranular back stress, to the mechanical properties of heterogeneous structures based on the crystal plasticity theory. The results show that the intragranular back stress is smaller than the intergranular residual stress but contributes significantly to the strain hardening of the heterogeneous bimodal structures. In addition, the contributions of misorientation and grain size to back stress are quantitatively analyzed, and the near-linear relationship between hetero-deformation induced hardening and strain gradient is found. These findings emphasize the essential role of the intragranular back stress induced by strain gradient and provide an in-depth understanding of the elaborate roles of back stress in heterogeneous structures.