Fatigue crack propagation in a quasi one-dimensional elasto-plastic model

TL;DR

This paper presents a combined numerical and analytical study of fatigue crack propagation in a simplified quasi-one-dimensional elasto-plastic lattice model, revealing mechanisms behind crack growth and fatigue phenomena.

Contribution

It introduces a novel lattice spring model with plasticity to analytically and numerically analyze fatigue crack growth, capturing key phenomenology like Paris law and overload retardation.

Findings

Model reproduces Paris law behavior.

Captures overload retardation effect.

Provides physical insight into fatigue crack mechanisms.

Abstract

Fatigue crack advance induced by the application of cyclic quasistatic loads is investigated both numerically and analytically using a lattice spring model. The system has a quasi-one-dimensional geometry, and consists in two symmetrical chains that are pulled apart, thus breaking springs which connect them, and producing the advance of a crack. Quasistatic crack advance occurs as a consequence of the plasticity included in the springs which form the chains, and that implies a history dependent stress-strain curve for each spring. The continuous limit of the model allows a detailed analytical treatment that gives physical insight of the propagation mechanism. This simple model captures key features that cause well known phenomenology in fatigue crack propagation, in particular a Paris-like law of crack advance under cyclic loading, and the overload retardation effect.