In conventional metals, there is plenty of space for dislocations-line defects whose motion results in permanent material deformationto multiply, so that the metal strengths are controlled by dislocation interactions with grain boundaries 1,2 and other obstacles 3,4 . For nanostructured materials, in contrast, dislocation multiplication is severely confined by the nanometre-scale geometries so that continued plasticity can be expected to be source-controlled. Nanograined polycrystalline materials were found to be strong but brittle 5-9 , because both nucleation and motion of dislocations are effectively suppressed by the nanoscale crystallites. Here we report a dislocation-nucleation-controlled mechanism in nano-twinned metals 10,11 in which there are plenty of dislocation nucleation sites but dislocation motion is not confined. We show that dislocation nucleation governs the strength of such materials, resulting in their softening below a critical twin thickness. Large-scale molecular dynamics simulations and a kinetic theory of dislocation nucleation in nano-twinned metals show that there exists a transition in deformation mechanism, occurring at a critical twin-boundary spacing for which strength is maximized. At this point, the classical Hall-Petch type of strengthening due to dislocation pile-up and cutting through twin planes switches to a dislocation-nucleationcontrolled softening mechanism with twin-boundary migration resulting from nucleation and motion of partial dislocations parallel to the twin planes. Most previous studies 12,13 did not consider a sufficient range of twin thickness and therefore missed this strength-softening regime. The simulations indicate that the critical twin-boundary spacing for the onset of softening in nano-twinned copper and the maximum strength depend on the grain size: the smaller the grain size, the smaller the critical twinboundary spacing, and the higher the maximum strength of the material.Ultrafine-grained Cu with nanoscale thin twins embedded in individual grains has recently been synthesized, achieving a strength increase by a factor of 7 to 10 relative to conventional coarse-grained polycrystalline Cu, as well as considerable ductility and high electrical conductivity 10,11 . More interestingly, the strength of such nanotwinned Cu first increases as the twin-boundary spacing l decreases, reaching a maximal strength at l 5 15 nm, then decreases as l is further reduced 11 . The trend of increasing strength in nano-twinned ultrafine-grained Cu with decreasing l can be relatively well explained by the Hall-Petch effect because the twin planes can serve as barriers to dislocations gliding on inclined slip planes. However, the strength softening with a further decrease of l from 15 nm to 4 nm is intriguing.For nanocrystalline metals without nano-twin substructures, molecular dynamics simulations 6-9 have shown a strength softening mechanism as grain size is reduced to about 10 nm in Cu, which has been attributed to a transition from dislocation-mediated plastic deformat...

The two-dimensional crystalline structures in graphene challenge the applicability of existing theories that have been used for characterizing its three-dimensional counterparts. It is crucial to establish reliable structure-property relationships in the important two-dimensional crystals to fully use their remarkable properties. With the success in synthesizing large-area polycrystalline graphene [1][2][3][4][5] , understanding how grain boundaries (GBs) in graphene [2][3][4] alter its physical properties 5-13 is of both scientific and technological importance. A recent work showed that more GB defects could counter intuitively give rise to higher strength in tilt GBs (ref. 10). We show here that GB strength can either increase or decrease with the tilt, and the behaviour can be explained well by continuum mechanics. It is not just the density of defects that affects the mechanical properties, but the detailed arrangements of defects are also important. The strengths of tilt GBs increase as the square of the tilt angles if pentagonheptagon defects are evenly spaced, and the trend breaks down in other cases. We find that mechanical failure always starts from the bond shared by hexagon-heptagon rings. Our present work provides fundamental guidance towards understanding how defects interact in two-dimensional crystals, which is important for using high-strength and stretchable graphene 14 for biological and electronic applications.Among the remarkable physical properties 15-20 observed in graphene, the high strength reported in pristine graphene 19 is stimulating great interest in applying high strength and stretchable graphene for various applications such as in biological membranes and electronic devices 14 . For example, monolayer graphene can have a loading capacity comparable to a 50-nm-thick film (for example, copper or silicon) with a strength of about 200 MPa. However, the presence of GBs in large-area polycrystalline graphene raises a fundamental question as to whether polycrystalline graphene for engineering practice can be as strong as pristine graphene. Although there is a good understanding on how typical defects such as dislocations and GBs influence the strength of three-dimensional polycrystals, how GB defects such as pentagonheptagon rings in two-dimensional graphene influence its mechanical properties remains unknown. In this work, we address how and why pentagon-heptagon defects in a tilt GB may enhance or weaken the strength of graphene through both molecular dynamics (MD) simulations and continuum mechanics analysis.To gain some insight into the influence of GB defects on the mechanical strength of graphene, we perform MD simulations for the dependence of GB strengths on grain misorientation for graphene with both armchair and zigzag tilt GBs. Simulation details are given in the Methods and Supplementary Information. At the atomic level, GBs in graphene are usually formed by typical defects of pentagon-heptagon rings [5][6][7][8][9][10][11][12][13] . We construct a series of both low-angle and...