The Inference of the Mechanical Properties of Materials at Micro and Meso-Scale via the Micro-Bending Technique



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Rapid advances in the field of material science have allowed for vast improvements in materials characterization. This relates to the development of novel experimental tools, techniques, as well as theories and numerical approaches to address the multi-scale mechanics of complex heterogeneous solids. In particular, the instrumented indentation has played a key role in providing researchers with unprecedented access to micro-mechanical properties of materials at various length scales. In this regard, given the scale separability conditions can be obeyed, the intrinsic phase properties e.g. elastic modulus, are obtained, and further used in the micromechanics upscaling schemes. However, in complex solids like cement-based materials, indentation testing at the micro- and mesoscale encounters several shortcomings, which if not addressed by the experimentalist may bias the entire analysis. Among them are cracking and material densification under the indenter at high loads, the pile-up of the material depending on its elastoplastic properties, or violation of the scale separability rule. In this work, the author proposes an original characterization method, coined here the micro-bending, and aiming at a reliable measurement of the elastic modulus of composite solids at micro and mesoscale using standard indentation tools, yet bypassing shortcoming related to the high-depth indentation. The proposed technique relies on measurements of deflection of the cantilever-type beam due to the concentrated load which is positioned at various spans. The method is adopted to the standard micro-indenter device, in which the rigid spherical probe is used to apply a point loads and the resulting deflections are monitored via the displacement transducer. The experimental outcome is analyzed following the original methodology in which the micro-cantilever bending is modeled within the framework of beams on the elastic foundation (Winkler type approximation). The inference of elastic modulus is carried out by postulating the inverse problem and solving it via the error minimization approach. The validation of the proposed approach is performed on the set of reference materials ranging from ceramics to metals. It is demonstrated, the proposed micro-bending test is capable of delivering highly accurate estimates of Young’s modulus, with estimated uncertainty well below 5% on homogeneous and more complex composite solids. Furthermore, the method is applied to cement-paste and cross-validated with the macro-scale ASTM testing in uniaxial compression. Finally, an extension of the micro-bending technique to study the flexural strength of cement-based materials is presented. The research findings reported in this thesis are complemented with the discussion of error analysis, the optimum experimental design of the micro-bending test, as well as discussion of technique extension to study visco-elastic, fracture, and fatigue phenomena at micro and mesoscale.



Micro-Bending, Material Characterization, Young's modulus, Modulus of Rupture, Flexural Strength