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，但也有其他材料的特点是更大尺寸的夹杂物(集料)嵌入到更细的颗粒基质中。嵌入可能是完整的，即围绕着较大的颗粒，或者较细的基质可能只填充彼此接触的较大夹杂物之间的间隙。类似的情况也存在于许多天然岩石和冻结的沙子中。证据表明，夹杂物既可以强化材料，也可以削弱材料，即细晶材料随着夹杂物的加入而增强，反之亦然。夹杂物的影响可以通过微观连续或间断方法进行实验研究和分析预测：在微观连续方法中，颗粒被视为可变形基质中的刚性夹杂物。相反，也有可能出现较软的夹杂，但在本研究中不涉及这一点。通过应用均匀化方案，可以考虑裂纹密度对复合材料弹性性能的影响，最终对复合材料的破坏载荷的影响。然而，由于这涉及到体积平均，这涂抹了裂纹周围的应力强度，连续介质方法无法捕捉到裂纹的扩展和融合，从而导致裂纹网络。在不连续介质方法中，人们具体考虑裂纹的行为。当裂纹扩展时，它们会结合在一起，并最终形成彻底的破坏面。相反，扩展的裂纹将遇到更大的颗粒，进一步的扩展可能会被阻止。为了从这两种方法的相对优势中获益并消除它们的缺点，我们将把它们结合起来，开发出一种既准确又计算有效的预测模型。这种组合的优点是，微观连续体法能够捕捉含有刚性夹杂物的无裂纹基质的特征性质；这样的性质可以用于不连续体法。这项研究将包括实验和理论工作。实验将在含有夹杂物和预制裂纹的材料上进行，以研究相关的不连续行为。其他使用纳米压痕的实验将同时进行，以获得可用于约束裂纹扩展准则的信息。理论工作将利用实验结果来产生微观力学-不连续相结合的方法，该方法将通过与实验的比较来验证。这项研究将具有科学、实用的工程和教育影响。这项工作的科学益处和影响是更好地从根本上理解物质行为。具体地说，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具有极其重要的意义。-这项工作对执业专业的影响涉及何时采用连续体方法和何时采用非连续体方法以及界定两者之间的界限的问题。这个问题与结构和材料的合理分析和设计一样古老。这项研究虽然不意味着最终解决这个规模依赖的问题，但将提供机械的分析工具来选择适当的方法。事实上，它将更进一步，产生一种连续和不连续相结合的方法。这将在实践中产生重要影响的明显材料/结构是岩石和许多土壤以及混凝土--教育将受益于这一事实，即研究将由两名研究生(博士)进行，而且像往常一样，也将包括本科生。学生不仅会强烈参与研究工作，还会撰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.