dc.description.abstract
Concrete is primarily a matrix-inclusion composite consisting of cement paste and embedded aggregates. However, within a so-called interfacial transition zone (ITZ) of 15 microns around the surface of the aggregates, cement paste exhibits a larger porosity than in the bulk, stemming from segregation effects during production of concrete.<br />During monotonous increase of mechanical loads, onset of concrete microcracking is observed in the region of the ITZ. However, the exact location at which microcracking starts and the related failure mechanism are still unclear. Inspection of post-failure fragments of concrete allows for a posteriori identification of two possibilities: in some parts of the aggregates surface, a clean debonding from cement paste is observed, while in other parts, a very thin layer of cement paste remains attached to the aggregates. The former observation implies that onset of microcracking might be related to debonding in the two-dimensional interface between the aggregates and the surrounding ITZ, while the latter one suggests that also bulk failure of the thin ITZ is possible. This provides us with the motivation to study onset of concrete cracking by means of a micromechanics approach.<br />Herein, we develop tensile failure criteria (i) for debonding directly at the two-dimensional aggregate surface, and (ii) for bulk failure within the three-dimensional ITZ, respectively. Debonding is envisioned, once the maximum normal component of the traction vectors acting on the aggregate surface reaches a corresponding tensile bond strength. ITZ failure, in turn, is considered if the largest maximum principal ITZ stress reaches the tensile strength of the ITZ. The two failure criteria require access to traction vectors acting on aggregate surfaces and to the full three-dimensional stress states within the ITZs. This is provided by a continuum micromechanics model, resolving the microstructure of concrete, based on the separation of scales principle.<br />On the scale of several millimeters to centimeters, concrete is considered as a matrix-inclusion composite, where spherical aggregates are perfectly bonded to a matrix of cement paste. Since the thickness of the ITZ is negligible compared to the diameter of the aggregates and is significantly smaller than the typical mean inter-aggregate spacing, the ITZ is treated as a two-dimensional interface. On the much smaller scale of a few microns, the ITZ is represented as a three-dimensional spherical shell which exhibits a shell thickness of 15 microns, perfectly bonded to the aggregates. The described representation of concrete allows us to perform the scale transition from concrete-related macroloading down to microscopic traction vectors and ITZ stresses.<br />Based on continuum micromechanics-related estimates for strain concentration tensors, we first quantify the average stresses and strains of the aggregates. Since these stresses are also relevant for the aggregates' surfaces, we use Cauchy's formula in order to compute the orientation- I dependent traction vectors acting on the aggregate surface. Their normal components are involved in the aforementioned debonding criterion. Perfect bond-related continuity conditions for stresses and displacements, in turn, allow us to translate aggregate stresses and strains into three-dimensional, position-dependent ITZ stress states. A subsequent principal stress analysis delivers principal ITZ stresses which are involved in the aforedescribed ITZ failure criterion.<br />In real concretes, onset of microcracking manifests at the material scale of concrete as the onset of pre-peak nonlinearities in measured force-displacement diagrams, such that onset of microcracking refers to the elastic limit of concrete. Consequently, our two models result in estimates for two elastic limit surfaces in the macroscopic principal stress space. Considering typical concrete properties in order to compute model predictions, and comparing them with experimentally observed elastic limits of concrete under uniaxial tension and compression, respectively, allows us to conclude that ITZ failure is governing for onset of concrete microcracking under compression-dominated loading scenarios. For tension-dominated loading scenarios, in turn, both debonding and ITZ failure appear to be possible, and the relevant failure mode is governed by the ratio between the tensile strength values related to debonding and to ITZ failure, respectively. Finally, we study the sensitivity of our model predictions with respect to the properties of the constituents of concrete, including the stiffness of aggregates, of cement paste, and of the ITZ, as well as the dosage and the Poisson's ratio of the aggregates. This shows onset of microcracking in normal concretes is quite different from that of lightweight concretes.
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