金属玻璃是一种具有长程无序，短程有序结构的非晶材料，由于其具有许多优秀的性能，引起了许多科学家的关注。但是由于其缺乏位错滑移机制，室温下块体金属玻璃往往在高应力时出现由剪切带引起的脆性断裂，这一现象给金属玻璃的实际应用带来了巨大的挑战。因此有许多的研究工作试图理解和预测金属玻璃的形变以及断裂行为，提升金属玻璃的塑性能力。部分研究表明通过调整金属玻璃的成分等方法，可以使得块体金属玻璃具有一定的压缩塑性。并且金属玻璃在小尺寸时，剪切带的产生会被抑制使得金属玻璃变为均匀变形且具有可观的塑性。这些新的进展给金属玻璃带来广阔的应用前景，同时也给传统断裂准则以及微观变形机制的研究带来了新的问题与挑战。本文针对金属玻璃在复杂加载下以及不同尺寸时的力学行为进行了研究，以便于为金属玻璃在实际应用时的安全性提供理论依据。主要开展了以下几部分工作：

（1）我们提出了一个断裂角的普适公式以预测材料处于复杂加载时断裂面的位置。以椭圆准则为例，我们研究了两种典型金属玻璃的圆棒试样在轴向拉伸载荷叠加静水压力时的断裂行为。结果表明，块体金属玻璃在拉伸时的断裂是拉应力与剪应力共同作用导致。随后通过断裂角公式，我们得到了一个以平均应力和最大剪应力表征的新椭圆准则。由于平均应力和最大剪应力在外部载荷确定后就能直接得到，新的椭圆准则使用时将更为方便。

（2）随着大塑性块体金属玻璃的出现，它们的塑性不能再被忽略。并且许多块体金属玻璃在压缩屈服后表现为理想塑性，此时名义应力保持不变，而柯西应力由于横截面积的变大而减小。这样一来传统断裂准则将不再适用。基于以上情况，我们提出以应变来表征金属玻璃的断裂行为，并且提出了应变双曲线准则以及广义莫尔库伦应变准则。新的准则在考虑压力敏感性的同时，还可以描述不同材料的塑性能力以及材料的变形状态对断裂产生的影响。

（3）将上述两个准则与断裂角公式结合，我们对复杂压缩载荷下的圆棒试样进行分析，其理论预测结果与实验符合良好，揭示了复杂加载时金属玻璃强度以及塑性的变化规律。

（4）基于金属玻璃从液态到非晶态时的能量变化关系，我们得到了金属玻璃中软区的体积分数与材料特征尺寸之间的函数关系。通过将这一关系与Gurson的孔洞模型相结合，得到了金属玻璃尺寸相关的屈服准则，描述了金属玻璃强度的尺寸依赖关系。结果表明随着尺寸的减小，金属玻璃的强度会有所上升，而尺寸小到一个临界值时，将表现为尺寸无关，即屈服强度不发生变化，这一结论能与实验结果符合。进一步，结合剪切带的失稳条件，我们得到不同尺寸的圆棒试样剪切带失稳时的应力与应变状态。结果表明随着尺寸的减小，剪切带失稳时的轴向塑性应变会显著提高，而这剪切带的延后失稳使得金属玻璃变形机制发生转变（剪切带-均匀变形）。

   Metallic glasses (MGs) is a kind of amorphous material which process long-range disorder and short-range order structures.They have attracted wide attention of many scientists due to their other excellent properties. However, due to the absence of dislocation glide, brittle fracture induced by nanoscale shear band often occurs in bulk metallic glasses under high stress at room temperature. This phenomenon has brought great challenges to the practical application of bulk metallic glasses. Many researches have tried to study the laws of deformation and fracture of metallic glasses and to improve their plasticity. Some researches show that the plasticity of metallic glasses can be improved by adjusting their composition. The shear band of metallic glasses would be suppressed in small size so that the metallic glasses deformed uniformly with considerable plasticity. These developments have brought broad application prospects to metallic glass, and also brought new problems and challenges to the study of traditional fracture criteria and microscopic deformation mechanisms. In this paper, the deformation and fracture behavior of metallic glasses under complex loading and different sizes are systematically studied. The main work is as follows:

    A general formula of fracture angle is proposed to predict the location of fracture surface of bulk metallic glasses under complex loading. By combining the fracture angle formula with the ellipse criterion, the fracture behavior of round bar specimens of two typical metallic glasses was studied, which are under axial tensile loading and confining pressure. The results show that the fracture of bulk metallic glasses under tension loading is caused by the interaction of tensile stress and shear stress. In addition, by using the fracture angle formula, we obtained a new criterion, which takes the mean normal stress and maximum shear stress as independent variables. Since the mean normal stress and maximum shear stress can be obtained directly after knowing the external loading, the new ellipse criterion will be more convenient to use.

     Since bulk metallic glasses with large plasticity were prepared, their plasticity can no longer neglected after material yielding. In addition, the bulk metallic glasses show ideal elastic-plastic behavior after compression yielding, while the nominal stress remains unchanged, and the Cauchy stress decreases as the cross-sectional area increases. At this time, the traditional fracture criterion will not be suitable for describing the failure of metallic glasses. Based on these conditions, we proposed to use strain to describe the fracture behavior of metallic glasses, and put forward hyperbolic strain criterion and generalized Mohr-Coulomb strain criterion. The new fracture criterion not only consider the pressure-sensitivity of materials, but also describe the plasticity of different materials and the influence of deformation state to the fracture behaviors. By combining with the fracture angle formula,, we analyze the metallic metallic round bar specimens under complex compression loading, and reveal the influence of confining pressure on the strength and plasticity of metallic glasses. The theoretical results are in good agreement with the experiments.

     Based on the energy change of metallic glasses (from liquid to amorphous state), the functional relationship between the volume fraction of the soft zone in metallic glasses and the characteristic size of the material is obtained. By combining this relationship with Gurson's void model, the yield criterion related to the size of metallic glasses is obtained. The results show that the strength of metallic glasses increases with the decrease of size and remain unchanged while the size is small to a critical vaule. These results are in good agreement with the experimental results. Furthermore, combined with the shear band conditions proposed by Rice, we obtain the stress-strain states while shear bands instability of different sizes samples. It is found that the plastic strain while shear bands instability increases significantly with the decrease of sample size. It causes the change of deformation modes (shear band--uniform deformation) of metallic glasses when their size decrease.