Supporting Materials of the Article Entitled “Superior Tensile Ductility in Bulk Metallic Glass with Gradient Amorphous Structures” Q. Wang1*, Y. Yang2, H. Jiang3, C. T. Liu2, H. H. Ruan3 and J. Lu2* 1 Laboratory for Microstructures, Institute of Materials Science, Shanghai University, Shanghai 200072, China 2 Centre for Advanced Structural Materials, Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Hong Kong 3 Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong 1. Measurement of Tensile Strain of as-Cast and as-Treated BMGs with Digital Image Correlation (DIC) Tensile testing was carried out on a MTS™ Insight Electromechanical Tester (MTS, Eden Prairie, MN, USA). Tensile specimens with a 3-mm gauge length, 0.4-mm gauge thickness and 1-mm gauge width were wire cut from the as-cast and SMATed BMG plates, respectively, prior to the tensile tests. These BMG tensile samples were first preinstalled into a set of home-made jigs, which were then clamped to the MTS jaws for fixation. As the BMG tensile samples were too small for clamping an extensometer, the displacement or strain data were collected using an optical method. A series of pictures recording the deformation history of the BMG sample were first captured with a fast-rate camera and then analyzed using the commercial package Vic-3D™ (Correlated Solutions Inc., Columbia, SC, USA), which was developed based on the well-established digital image correlation (DIC) algorithm to extract the full-field displacements and strains of a deformed specimen1,2. Physically, the accuracy of our DIC-based strain measurement relies on the optical magnification and the resolution of the imaging sensor. For our case, the camera was set to an optical magnification of 1with a working distance of 65mm, which led to the correspondence of one pixel size with an area of 4.4m4.4m. Since the interpolation schemes and proper affine functions employed in the DIC algorithm enables an accuracy of 0.05 pixel, the typical displacement resolution in our measurement is ~0.22 m, corresponding to a strain resolution of ~73 micro-strains for a sample with a gauge length of 3mm, which is sufficient for our experiment as the yield/fracture strain of the BMG sample is on the order of 10,000 micro-strains. Furthermore, a direct-current (DC) regulated fiber optic illuminator was used to provide stable and even illumination of the sample surface. Figure S1 The displacement fields along the tensile direction overlaying the as-cast (a) and 25min-SMATed (b) BMG tensile sample at different levels of extension. In the tensile experiment, a strain rate of 0.01% per second was used and images were captured 1 frame per second. Figures S1 (a) and (b) show the typical displacement fields along the tensile direction, which were extracted by DIC at different levels of sample extension, overlaying the corresponding as-cast and 25min-SMATed samples under deformation, respectively. Within our expectation, it can be seen that the displacement fields along the tensile direction exhibit a linear distribution and their gradients then give rise to the overall mechanical strain experienced by the stretched BMG sample. 2. Achieving superior tensile ductility in a Zr55 Cu30Ni5Al10 BMG through SMAT Alloy ingots with a nominal composition of Zr55Cu30Ni5Al10 were prepared by arc-melting mixtures of pure metals (with the purity of above 99.9%) in Ti-gettered argon atmosphere. Each ingot was melted several times to obtain chemical homogeneity and finally cast into a water-cooled copper mold to obtain a rectangular plate with the dimension of ~80101 mm. The thickness is further reduced to 0.4 mm by grinding and mechanical polishing for mechanical characterizations such as tensile test and residual stress measurements. In the present study, the gradation of surface glassy structure and optimization of the pre-generated residual stress profile in the Zr based BMG plate (0.4mm by 10mm by 60mm in size) is performed by using surface mechanical attrition treatment (SMAT) with 512 stainless steel balls of 2mm (or 3mm) in diameter. In the SMAT processing, multi-directionally flying shots, which are activated by an ultrasonic vibration generator at a high frequency of 20k Hz, impact on the surface of a material repeatedly. Consequently, the severe surface plastic deformation is expected to alter the local material structure and residual stress profiles. The SMAT processing was lasted for 40, 60 minutes, respectively. Note that the process is stopped every 1.5 minutes in order to minimize the effects of overall temperature rising. For one of 60min-SMATed samples, a two-stage treatment route were adopted: 3mm- ball was used for 30min and then 2mm-ball for the remaining 30min. The amorphous nature of Zr based BMG plates before and after SMAT were confirmed by X-ray diffraction (XRD) using a diffractometer with Co-Kradiation, showing diffuse maxima without Brag diffraction peaks from crystal phases (See Fig S2 (a)). Fig. S2 Comparison of the experimental results obtained from the as-cast and SMATed 0.4-mm thick Zr55Cu30Ni5Al10 metallic glass. (a) the X-ray diffraction patterns confirming the amorphous structure of all BMG samples before and after the SMAT processes, (b) the variation of the residual stress distribution along the sample thickness with the SMAT time, (c) The room-temperature true stress-strain curves obtained at the strain rate of 110-4 s-1 (marks indicate where the stress-curve curves start to depart from a linear response) (d) The experimentally obtained yield/fracture strengths as a function of the BMG tensile ductility showing agreement with the theory. Figure S2 (b) shows the distributions of residual stress along thickness direction in the as-cast and SMATed Zr based BMG, which were also measured by using classic hole-drilling method. Compared to the SMATed Cu46Zr47Al7, the treated Zr-based BMGs exhibits similar residual stress distributions with a compressive stress maximum ranging from -210 to -430 MPa at 50 ~60 m depths. Note that after SMAT for 40min, the compressive stress maximum peaks at -320MPa, but further increasing of SMAT time up to 60min leads to its reduction to -210 MPa, implying that the treated Zr based BMG might have also undergone intense structural evolution with the severe surface plastic deformation caused by the SMAT process. The greater magnitude of compressive residual stress peak for the Zr based BMG subjected to two –stage treatment may be associated with the alternative use of 3mm and 2mm stainless steel ball, which could lead to a more pronounced graded glassy structure with larger volume fraction of liquid-like regions introduced into in the surface layers of the treated BMG. Figure S2 (c) displays the true stress-strain curves obtained from the as-cast and SMATed BMG samples using the real-time image correlation technique. It can be clearly seen that as-cast Zr55Cu30Al10Ni5 samples possesses a very limited plastic strain (<0.014%) prior to catastrophic fracture, which is common for many metallic glasses tested in tension at room temperature. However, similar to the Cu-Zr-Al BMG, the SMATed samples exhibit, more or less, a certain degree of strain hardening and tensile ductility. It is worthwhile to note that the measured tensile ductility attains about 3.6% (~4%) for the 60min-SMATed sample obtained through a two-step treatment approach. Moreover, compared to the Cu-Zr-Al BMG, the variation of strength with tensile ductility for Zr- based BMG also follows quite a similar rule(see Fig.2S(d)): as a result of strain hardening, the fracture strength of the SMATed BMG apparently rises with the tensile ductility; however, their yield strength declines as the fracture strength increases. Additionally, all of the Zr-based BMG samples failed via shear cracking during the room-temperature tensile tests. 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