Experimental And Theoretical Studies Of Anomalous Plasticity Of Micron-scale Metallic Wires

Many experiments have found that the plastic behavior of metals at the micron and sub-micron scales is obviously different from the classical plasticity. The study of anomalous plasticity of small-scale materials has become a significant frontier problem in mechanics and material science. In this dissertation, the anomalous plasticity of micron-scale metallic wires is systematically studied theoretically and experimentally. The main results are summarized as follows:(1) A high-accuracy fiber micro-tensile apparatus was developed. Load cell of the apparatus can be used to measure both the tensile force acted on the sample and the displacement of upper gripper, so force-displacement curve of sample may be obtained accurately. Tensile tests on micron-scale polycrystalline copper and gold wires, and316L stainless steel fibers were performed by using the apparatus. The results show that there is no significant size effect in the tensile responses of polycrystalline copper wires; and the Young’s moduli of copper wire and316L stainless steel fiber are smaller than their bulk values; and the yield strength of the polycrystalline gold wires is found to obey the classical Hall-Petch relation.(2) A torsion apparatus capable of performing monotonic and cyclic tests on small specimens was established based on the principle of torsion balance. An in-situ torsional vibration method for calibrating the torque meter with precision is addressed. This apparatus permits the measurement of torque to nN-m, as a function of torsional strain to a sensitivity of sub-microstrain. The classical work on wire torsion was repeated directly by using the apparatus. A size effect was observed in both the initial yielding and the plastic flow. The experimental result was then explained in terms of the couple stress strain gradient plasticity theory.(3) Both torsion and tensile tests were performed on polycrystalline copper wires with diameters in the range20-50μm. A significant size effect in both the initial yielding and the plastic flow is observed in torsion. In contrast, only a minor effect is seen in tension. The physical basis of the size effects in wire torsion is elucidated in the light of the geometrically necessary dislocation argument and of the critical thickness effect. Three phenomenological theories of strain gradient plasticity, due to Fleck and Hutchinson, to Chen and Wang and to Aifantis and co-workers, are assessed within the context of wire torsion, and the corresponding rigid-plastic solutions are derived. Distinctions between the theories are highlighted through comparison with experiment, emphasizing the difference in predicted trends in the size dependence of initial yielding and of hardening rate. The systematic experimental and theoretical assessment suggests that the size effect in the initial yielding is mainly due to the constraints that the external geometrical size put on a finite strained volume, while the size dependence in the plastic flow is principally owing to the geometrically necessary dislocations associated with the plastic strain gradients.(4) The plasticity of micron-scale Cu and Au wires under cyclic torsion is investigated for the first time using the torsion apparatus. In addition to a size effect, a distinct Bauschinger effect and an anomalous plastic recovery, wherein reverse plasticity even occurs upon unloading, are unambiguously revealed. These observations are in qualitative agreement with the molecular dynamics and discrete dislocation dynamics simulations. A nonlocal kinematic model involving both dissipative and energetic length scales is developed based on the Fleck-Willis framework. Systematic theoretical analysis implies that the geometrically necessary dislocations induced by the plastic strain gradients give rise not only to the size effect, but also to anomalous Bauschinger effect.(5) A unified treatment of double dislocation pileups experiencing non-uniform stress fields is given in terms of the Tricomi method. The boundary condition for a pure dislocation pileup is obtained. The complete fields for a double dislocation pileup are derived for situations where there are various gradients in applied stress. The corresponding dislocation distribution, the force on the leading dislocations, the plastic strain and the released energy in forming the pileup, and the number of dislocation pairs within the pileup are derived, respectively. A new law for stress gradient plasticity is deduced, which can predict the initial yield size effect in wire torsion and foil bending.(6) Following the guiding principle of the conventional theory of mechanism-based strain gradient plasticity (CMSG), a continuum theory of stress gradient plasticity incorporating both grain size and structure size is developed. The material length scale, the spacing of dislocation obstacles, is broadened to include sample size. The model is applied to interpret the size effects in wire torsion and film bending, and the predictions agree reasonably with the measurements.