Significance: For centuries it has been a challenge to avoid strength–ductility trade-off, which is especially problematic for ultrastrong ultrafine-grained metals. Here we evade this trade-off dilemma by architecting a heterogeneous lamella structure, i.e., soft micrograined lamellae embedded in hard ultrafine-grained lamella matrix. The heterogeneous deformation of this previously unidentified structure produces significant back-stress hardening in addition to conventional dislocation hardening, rendering it higher strain hardening than coarse-grained metals. The high back-stress hardening makes the material as strong as ultrafine-grained metals and as ductile as coarse-grained metals.

Heterostructured materials have been reported as a new class of materials with superior mechanical properties, which was attributed to the development of back stress. There are numerous reports on back stress theories and measurements with no consensus. Back stress is developed in soft domains to offset the applied stress, making them appear stronger, while forward stress is developed to make hard domains appear weaker. The extra hardening in heterostructured materials is resulted from interactions between back stresses and forward stresses, and should be described as hetero-deformation induced (HDI) hardening and the measured ‘back stress’ should be renamed HDI stress. GRAPHICAL ABSTRACT Impact Statement The ‘back stress’ hardening in the literature can be described more accurately as hetero-deformation induced (HDI) hardening and the measured ‘back stress’ should be renamed HDI stress.

We report significant back stress strengthening and strain hardening in gradient structured (GS) interstitial-free (IF) steel. Back stress is long-range stress caused by the pileup of geometrically necessary dislocations (GNDs). A simple equation and a procedure are developed to calculate back stress basing on its formation physics from the tensile unloading–reloading hysteresis loop. The gradient structure has mechanical incompatibility due to its grain size gradient. This induces strain gradient, which needs to be accommodated by GNDs. Back stress not only raises the yield strength but also significantly enhances strain hardening to increase the ductility. Impact Statement: Gradient structure leads to high back stress hardening to increase strength and ductility. A physically sound equation is derived to calculate the back stress from an unloading/reloading hysteresis loop. GRAPHICAL ABSTRACT

Here we present a perspective on heterogeneous materials, a new class of materials possessing superior combinations of strength and ductility that are not accessible to their homogeneous counterparts. Heterogeneous materials consist of domains with dramatic strength differences. The domain sizes may vary in the range of micrometers to millimeters. Large strain gradients near domain interfaces are produced during deformation, which produces a significant back-stress to strengthen the material and to produce high back-stress work hardening for good ductility. High interface density is required to maximize the back-stress, which is a new strengthening mechanism for improving mechanical properties. GRAPHICAL ABSTRACT IMPACT STATEMENT Heterogeneous materials are becoming the next hot research field after the nanomaterials era.

Significance: Nature creates the gradient structure (GS) for a purpose: to make biological systems strong and tough to survive severe natural forces. For the grain-size GS, the deformation physics is still unclear. One wonders if the grain-size GS in the nanomicroscale would also benefit materials engineered by mankind. In this paper, a universal strain hardening mechanism is revealed in the GS. We discovered a unique extra strain hardening that is intrinsic to the GS. Its mechanism is the presence of strain gradient together with the stress state change. A superior combination of strength and ductility that is not accessible to conventional homogeneous materials is obtained. As a novel mechanism, extra strain hardening renders high ductility in the GS materials.