非晶合金泡沫作为新型结构材料，综合了金属泡沫与非晶合金两者的优点，实现了轻质与强韧的统一，近年来受到国内外学者的广泛关注。然而，由于其变形破坏具有跨尺度的特点，不仅包含纳米尺度剪切带内的塑性变形，还有孔壁断裂坍塌形成的宏观破裂带，目前相关研究仅仅停留在简单力学性能测试上，而对于深层次的材料变形、破坏、以及能量耗散机理却鲜有涉及，这极大地限制了非晶合金泡沫材料的工程应用。基于以上研究现状，本文围绕非晶合金泡沫材料的制备与性能优化，变形破坏过程中能量耗散的定量表征以及物理机制等方面开展系统研究。

本文首先以氧化铝空心球作为占位颗粒，成功制备出非晶合金复合泡沫材料。准静态压缩试验表明，该材料不仅拥有较高的屈服强度，同时兼具良好的变形稳定性，因而表现出优异的能量吸收性能。通过实验、力学分析与有限元模拟，并结合变形冻结与SEM显微形貌观察，揭示了非晶合金复合泡沫材料的强韧化机理：与低相对密度开孔泡沫孔壁的弯曲变形不同，中等相对密度非晶合金复合泡沫材料主要发生孔壁的剪切变形与破坏，这种变形模式充分利用了基体材料高强度的优势；另一方面，空心球的加入可以弥补材料内部孔隙分布不均匀导致的缺陷，有效避免形成宏观贯通的破裂带；第三，破碎后的小球仍然可以起到约束作用，激发非晶基体产生更多的剪切带，从而提高变形过程的稳定性。

利用非线性时间序列的分析方法，对非晶合金复合泡沫材料的变形动力学过程进行了定量化表征，通过计算最大Lyapunov指数、分形维、Hurst指数、以及多重分形分析，发现这些表征混沌吸引子结构的特征指数随着材料变形呈现出有规律的变化，对比实验表明这种趋势行为与非晶合金基体内的塑性变形有关。基于不同特征指数之间的分析结果可以互相应证，共同揭示材料微观变形机制，从而证明了非线性动力学分析方法在定量研究非晶合金复合泡沫材料这类极端非均匀材料变形破坏过程中的有效性。

无序材料的变形过程通常表现为间歇性的能量耗散。在外部扰动下，大量参与变形的单元通过级联形成跨尺度的“雪崩”，其尺寸分布满足自相似的G-R关系。经典的平均场理论通过忽略具体的物理细节，抓住长程弹性相互作用和材料非均匀性之间的竞争这一主要矛盾，推导出一系列普适的标度指数，并在大量脆性非均匀材料断裂实验中得到了验证。然而，与脆性材料实验结果不同，本文在研究非晶合金复合泡沫材料准静态压缩中的“雪崩”时，发现标度指数明显偏离了传统平均场理论的预测。通过进一步分析“雪崩”序列的时间关联性，包括等待时间概率分布以及余震序列随时间的演化特征，证明了这种反常的标度行为与非晶合金基体的塑性变形有关。对于非晶合金，高应力容易引起材料结构软化，导致粘-弹性的流变行为，并在系统内引入一个特征时间。基于这一特点，我们推导出了不同标度指数之间满足的标度关系，与实验结果十分吻合。有趣的是，这些反常标度行为与大地震统计规律之间表现出显著相似性。

基于以上实验分析，我们建立了考虑单元强度分布动态演化的粘弹性元胞自动机模型模拟非晶合金复合泡沫材料的变形破坏过程。在平均场近似下，可以进一步将复杂的多体问题简化为求解单个粒子。由此，我们推导了模型随机微分方程（SDE）及其主方程，它们构成了粘-弹性平均场理论。理论分析和数值模拟可以给出系统状态关于一个有效控制无量纲参数s的相图，其中，s为Deborah数与材料弹性极限应变之比。相图存在3个明显不同的区域：s > s_c，系统只有一个稳定的自组织临界状态；当s = s_c，系统将分出两个亚稳态，分别对应自组织临界状态和均匀粘流态；当s = s^* ，在粘-弹性驱动和单元强度分布动态演化共同作用下，系统发生saddle-node分叉，此时自组织临界状态不再稳定，当s < s^* 时，系统只存在一个均匀粘流态。在亚稳区s^* < s < s_c，系统在强扰动下表现出剧烈的应力震荡，伴随“雪崩”统计，我们发现了一系列与非晶合金复合泡沫材料以及大地震统计类似的反常标度行为。不仅如此，处于亚稳区的系统具有更高的平均应力，因而表现出更为优异的能量吸收性能，这对于如何进一步优化材料性能具有启发性。

As a new type of structural material, metallic glass foams (MGFs), combining advantages of both metal foam and metallic glasses to achieve the unity of light weight and high toughness, have received extensive attentions in recent years. However, due to the deformation and failure of MGFs usually across many scales, range from the nanoscale plastic shear banding to the macroscopic collapse bands formed by fracture of the pore, the current research only stays at the level of simple mechanical testing, and there are few issues on mechanisms of materials’ deformation, failure, and energy dissipation, which limits their engineering applications. Based on the above status, in this article, we will intend to focus our research on the preparation and performance optimization of MGFs, the quantitative characterization of the energy dissipation, and the related physical mechanisms, etc.

In this paper, a metallic glass syntactic foam (MGSF) is fabricated with bulk metallic glass and alumina cenospheres. The quasi-static compression test shows that the MGSF combins high strength, stability, and ductility, and thus exhibits excellent energy absorption performance. Through experiments, mechanical analysis, and finite element simulation, combined with deformation freezing and SEM microscopic morphology, the mechanism of strengthening and toughening of MGSF is explored. Different from the elastic or plastic bending bending, MGSFs deform through shear banding and fracture of the cell walls, which can make full use of the strength of the matrix. Secondly, the addition of alumina cenospheres can compensate for the defects caused by the uneven distribution of pores, and effectively avoid the formation of macroscopic rupture bands across through the sample. Finally, the broken alumina cenospheres can still play a constraining role and stimulate the matrix to produce more shear bands, which improves the stability of the deformation process.

By using the analysis method of nonlinear time series, including the largest Lyapunov exponent, the fractal dimension, Hurst exponent, and multi-fractal analysis, the deformation dynamics of MGSF was studied quantitatively. It is found that the indexes characterizing the chaotic attractor structure change regularly with the deformation of MGSF. Through the comparative experiments on brittle porous materials, it is shown that this behavior is related to the plastic deformation in the metallic glass matrix. The analysis results based on different characteristic indexes are mutually corroborated and jointly reveal the microscopic deformation mechanism of the material, which proves that the analysis method of nonlinear time series is effective in studying the deformation and failure process of MGSF.

The deformation processes of disordered materials are usually through a intermittent energy dissipation, and under external disturbances, the large number of units participating in the deformation may form a cross-scale avalanche, which can be described by the scale free G-R relationship. The classical mean-field theory ignores any specific physical details, and chose to grasp the competition between long range elastic interactions and the material’s heterogeneity, which obtains a series of universal scaling exponents and is verified by many fracture experiments of brittle disordered materials. However, different from the brittle materials, the scaling law of avalanches in the compression of MGSF was found to significantly deviate from the prediction of the classical mean-field theory. Through further analyzing the time correlation of avalanche sequences, including the distribution of waiting times and the evolution of aftershocks, it is proved that this nontrival scaling exponent is related to the plastic deformation of the metallic glass matrix. For metallic glasses, high stress can easily cause a structure softening, which leads to a viscoelastic rheological behavior and introduces a characteristic time. Based on this feature, we deduced a scaling relationship correlating different scaling exponents, which is in good agreement with our experiments. Interestingly, there is a clear similarity between these non-trival scaling behaviors and the seismic statistics of large earthquakes.

Based on the experimental analysis, we establish a viscoelastic cellular automaton model with considering the dynamic evolution of strength distribution to simulate the deformation and failure of MGSFs. Under the mean field approximation, the complex multibody problem can be further simplified to solve a single particle. On this basis, we deduced the model’s stochastic differential equation (SDE) and its master equation, which constitute our viscoelastic mean field theory. The theoretical analysis and numerical simulations give a phase diagram of the system state versus an effective control dimensionless parameter, s, where s is the ratio of the Deborah number to the elastic limit strain of the material. As s > s_c, the only solution is the stable self organized critical state (SOCS). When s reaches s_c, the SOCS becomes metastable and gives place to a uniform viscous flow (UVF) under large perturbations. When s reaches s^*, under the combintion of the viscoelastic driven and the dynamic evolution of strength distribution, a saddle-node bifurcation occurs in the system, then the SOCS becomes no longer stable. When s < s^*, there will be only one stable solution of UVF. In the metastable range s^* < s < s_c, the system exhibits severe stress oscillations under strong disturbances, accompanied by a series of nontrivial avalanche statistics like those found in MGSFs and large earthquakes. Further, the system in the metastable region has a higher average stress, and thus exhibits more excellent energy absorption performance, which enlightens for how to further optimize material properties.