PhD Final Defense – Subhrangsu Saha

Fracture in Hard Elastic Brittle Materials Under Monotonic and Non-monotonic Loading

Advisor: Professor Oscar Lopez-Pamies

ABSTRACT

The main objective of this study is twofold: (i) to deploy the macroscopic theory of fracture

initiated by Kumar, Francfort, and Lopez-Pamies (2018) to explain long-standing problems in

hard elastic brittle materials subjected to monotonic quasi-static mechanical loading, and (ii) to

generalize that theory to non-monotonic loading conditions.

The first part of this study identifies a suite of three simple experiments to measure the

macroscopic material properties governing crack nucleation and propagation in structures made

of hard elastic brittle materials with a strong compressive-to-tensile strength asymmetry subjected

to arbitrary monotonic quasi-static loading. The first experiment, the uniaxial compression of

a cylindrical specimen, 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 is

the Brazilian fracture test, performed with flat platens on a material disk to determine the

uniaxial tensile strength. Knowing both the uniaxial compressive and tensile strengths allow for

the estimation of the material’s strength surface via interpolation (e.g., a Drucker-Prager fit).

Finally, a wedge-split test on a notched cube yields the fracture toughness. In addition, this

study resolves two long-standing problems of fundamental and practical significance: (i) how to

properly interpret peak load measurements (flexural strength) in beam bending tests, and (ii)

why four-point and three-point bending yield intrinsically different flexural strength results.

The second part of this study advances a generalized phase-field formulation capable of predicting

fracture nucleation and propagation under non-monotonic mechanical loading. Grounded in

extensive experimental observations, novel definitions for the strength surface and the critical

energy release rate are proposed as material functions of cumulative loading history. Specifically,

the material strength degrades from its initial undamaged state as a function of an accumulated

stress history variable, while the critical energy release rate degrades based on the elastic

strain energy within localized strain regions. This formulation generalizes the classical Griffith

energy competition to describe crack growth in nominally elastic brittle materials under general

loading. To circumvent the severe computational expenses inherent to phase-field modeling,

novel acceleration procedures are developed. These numerical schemes substantially reduce

computational execution times, particularly for high-cycle fatigue applications. The fidelity and

efficiency of the proposed framework are ultimately demonstrated through direct comparisons

with experimental benchmarks of fatigue fracture across a broad spectrum of hard materials.