arXiv subjects

Subhrangsu Saha

Publications and source records attributed to Subhrangsu Saha.

3 recordsLinked to original sources

arXiv2026

A Guide to Fully Characterize the Fracture Properties of Cementitious Materials from Simple Experiments

Guided by recent advances in the understanding of nucleation and propagation of fracture in elastic brittle materials, this paper proposes a suite of three simple experiments that permit the measurement of the three macroscopic material properties governing when and where cracks nucleate and propagate in structures made of cementitious materials that are subjected to arbitrary monotonic quasi-static loading conditions. The first experiment is that of the uniaxial compression of a cylindrical specimen, which enables the extraction of the elastic properties -- namely, the Young's modulus and Poisson's ratio -- as well as the uniaxial compressive strength. The second experiment is the Brazilian fracture test, performed with flat platens on a material disk to determine the uniaxial tensile strength. Having knowledge of the uniaxial compressive and uniaxial tensile strengths then allows for the estimation of the strength surface of the material via interpolation (e.g., a Drucker-Prager fit). Finally, the third experiment is the wedge split test on a notched cube, which yields the fracture toughness. We demonstrate by means of direct comparisons with four-point and three-point bending tests on both unnotched and notched beams made of a 3D-printable mortar mixture that the elasticity, strength, and toughness properties obtained from the proposed tests are sufficient to predict the nucleation and propagation of fracture for any structure (granted separation of length scales) made of cementitious materials under any monotonic quasi-static loading condition.

cond-mat.soft↗

arXiv2026

Breaking Four-Point and Three-Point Bending Tests

Since their initial standardizations in the 1930s and 1950s, the so-called four-point and three-point bending tests on unnotched beams have been embraced by practitioners as two popular methods to indirectly measure the tensile strength of concrete, ceramics, and other materials with a large compressive strength relative to their tensile strength. This is because of the ease that the tests afford in both the preparation of the specimen (a beam of rectangular cross section) and the application of the loads (simple supports pressing on the specimen). Yet, this practical advantage has to be tempered by the fact that the observations from both of these tests -- being \emph{indirect} experiments in the sense that they involve \emph{not} uniform uniaxial tension but non-uniform triaxial stress states throughout the specimen -- have to be appropriately interpreted to be useful. By making use of the phase-field fracture theory initiated by Kumar, Francfort, and Lopez-Pamies (2018), which has been recently established as a complete theory of fracture capable of accurately describing the nucleation and propagation of cracks in elastic brittle materials under arbitrary quasistatic loading conditions, the main objective of this paper is to carry out a thorough 3D quantitative analysis of when and where fracture nucleates and propagates in four-point and three-point bending tests and thereby establish how to appropriately interpret their results. As a corollary, the analysis provides an explanation for why four-point bending tests typically yield smaller flexural strengths than three-point bending tests, a source of constant headaches for practitioners who have been left to wonder which test -- if any -- would be more appropriate for their purposes.

cond-mat.mtrl-sci↗

arXiv2024

A Griffith description of fracture for non-monotonic loading with application to fatigue

With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids \emph{not} just under monotonic but under general loading conditions, this paper puts forth a generalization of the classical Griffith energy competition in nominally elastic brittle materials to arbitrary \emph{non-monotonic} quasistatic loading conditions, which include monotonic and cyclic loadings as special cases. Centered around experimental observations, the idea consists in: $i$) viewing the critical energy release rate $\mathcal{G}_c$ \emph{not} as a material constant but rather as a material function of both space $\textbf{X}$ and time $t$, $ii$) one that decreases in value as the loading progresses, this solely within a small region $Ω_\ell(t)$ around crack fronts, with the characteristic size $\ell$ of such a region being material specific, and $iii$) with the decrease in value of $\mathcal{G}_c$ being dependent on the history of the elastic fields in $Ω_\ell(t)$. By construction, the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic, the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic, mortar, and PMMA.

cond-mat.other↗