Effect of Inclusions on Material Performance- Investigation Through Micro-Continuum, DIscontinuum and Nano-Indentation Approaches

许多人造材料，如混凝土，以及其他材料，其特点是在更细粒度的基质中嵌入更大尺寸的内含物（骨料）。嵌入可能是完整的，即包围较大的晶粒，或者更细的基体可能只填充彼此接触的较大夹杂之间的间隙。类似的情况也存在于许多天然岩石和冻沙中。有证据表明，夹杂物既可以增强材料，也可以削弱材料，即随着夹杂物的加入，细粒度材料的强度增加，反之亦然。夹杂物的影响可以通过微连续统或非连续统方法进行实验研究和分析预测：在微连续统方法中，晶粒被认为是可变形基体中的刚性夹杂物。相反的，即较软的内含物也是可能的，但这将不会在本研究中处理。通过采用均匀化方案，可以考虑裂纹密度对复合材料弹性性能的影响，并最终影响复合材料的破坏载荷。然而，由于这涉及到体积平均，从而抹去了裂纹周围的应力强度，因此连续体方法无法捕捉裂纹的扩展和合并，从而导致裂纹网络。在非连续介质方法中，人们专门考虑裂缝的行为。随着裂纹的扩展，它们合并并最终形成彻底的破坏面。相反，扩展的裂纹将遇到较大的晶粒，进一步的扩展可能会停止。为了从两种方法的相对优势中获益，并消除它们的缺点，它们将结合起来开发一个既准确又计算有效的预测模型。这种组合的优点是，微连续介质方法能够捕获具有刚性夹杂的未裂纹基体的特征特性；这样的性质可以用在非连续体方法中。这项研究将包括实验工作和理论工作。实验将在含有夹杂物和预制裂纹的材料上进行，以研究相关的非连续体行为。利用纳米压痕的其他实验将同时进行，以获得可用于约束裂纹扩展准则的信息。理论工作将使用实验结果来产生结合微观力学-非连续体方法，反过来，将通过与实验的比较来验证。这项研究将产生科学的、实际的工程和教育影响。这项工作的科学效益和影响是对材料行为的更好的基本理解。具体来说，这项研究将提高我们对夹杂物以及裂纹扩展和合并的影响的理解，这在许多天然和人造材料中都具有重要意义。-这项工作对执业专业的影响涉及到何时采用连续方法和何时采用非连续方法以及确定两者之间的界限的问题。这个问题与结构和材料的理性分析和设计一样古老。这项研究，虽然不意味着达到最终解决这个规模依赖的问题，将提供基于机械的分析工具来选择适当的方法。事实上，它将更进一步，产生一种连续-非连续相结合的方法。在实践中具有重要意义的明显材料/结构是岩石和许多土壤以及混凝土-教育将受益于这样一个事实，即研究将由两名研究生（博士）学生进行，并且像往常一样，也将包括本科生。学生们不仅要积极参与研究工作，还要写论文和做口头报告。

Many artificial materials such as concrete, but also others, are characterized by larger size inclusions (the aggregate) embedded in a finer grained matrix. The embedment may be complete, i.e. surrounding the larger grains, or the finer matrix may only fill the interstices between larger inclusions which are in contact with each other. Similar conditions exist in many natural rocks and frozen sands. Evidence indicates that inclusions can both strengthen and weaken a material, i.e. the finer grained material gaining strength as inclusions are added or vice versa. The effect of inclusions can be experimentally investigated and analytically predicted through either a micro-continuum or a discontinuum approach: In the micro-continuum approach, grains are considered as rigid inclusions in a deformable matrix. The opposite, i.e. softer inclusions are also possible but this will not be dealt with in this research. By application of a homogenization scheme, the effects of the crack density on the elastic properties, and eventually on the failure load of the composite can be taken into account. However, since this involves volume averaging, which smears out the stress intensity around cracks, the continuum approach cannot capture crack propagation and coalescence, leading to a crack network. In the discontinuum approach, one specifically considers the behavior of cracks. As cracks propagate, they coalesce and eventually form thoroughgoing failure surfaces. Conversely, propagating cracks will encounter the larger grains and further propagation might be stopped. To benefit from the relative advantages and to eliminate the disadvantages of both approaches, they will be combined to develop a predictive model which is both accurate and computationally effective. The advantages of such combination are that the micro-continuum approach is able to capture the characteristic properties of the uncracked matrix with rigid inclusions; such properties can then be used in the discontinuum approach. The research will consist of experimental and theoretical work. Experiments will be conducted on material containing inclusions and preformed cracks to study the associated discontinuum behavior. Other experiments using nano-indentation will be conducted simultaneously to obtain information which can be used to constrain the crack propagation criterion. The theoretical work will use the experimental results to produce the combined micromechanics-discontinuum approach which, in turn, will be validated through comparison with experiments. This research will have scientific, practical engineering and educational impacts. The scientific benefits and impacts of this work are a better fundamental understanding of material behavior. Specifically, the research will improve our understanding of the effects of inclusions and of crack propagation and coalescence, which are of utmost significance in many natural and artificial materials. - The impact of this work on the practicing profession relates to the question as to when to apply continuum approaches and when discontinuum approaches and to define the boundary between the two. This question is as old as rational analysis and design of structures and materials. This research, while not implying to reach a final solution to this scale dependent problem, will provide mechanically based analytical tools to select the appropriate approach. As a matter of fact, it will go a step further and produce a combined continuum-discontinuum approach. Obvious materials/structures where this will have important implications in practice are rocks and many soils as well as concrete - Education will benefit from the fact that the research will be conducted by two graduate (doctoral) students and, as usual, will also include undergraduate students. The students will not only be strongly involved in the research work but also in writing papers and making oral presentations.