Hetero-deformation induced (HDI) hardening does not increase linearly with strain gradient

Hetero-deformation induced (HDI) hardening has been attributed to geometrically necessary dislocations (GNDs) that are needed to accommodate strain gradient near the interfaces of heterostructured domains. Here we report that HDI hardening does not increase linearly with increasing strain gradient in the interface-affected zone. This is because some GND pileups may be absorbed by the interface and consequently does not contribute to HDI hardening with increasing strain gradient. Higher mechanical incompatibility across interface produces higher strain gradient. The strain gradient-dependent strengthening effect of heterostructured interface mainly originates from the development of HDI stress.