Effects of Loading Rate on Plastic and Damage Zones in Mode-I Crack Tip of Sandstone
Authors: Zhou Dawei , Zhang Guangqing , Sun Bin , Xie Pengxu , Lu Mingjing , Wang Dongying , Li Yuan 
Published: August 2024

ABSTRACT:
To study the effects of loading rate on the fracture characteristics, sandstone samples with a center notch were used in three-point bend experiment for the loading rates of 0.0004, 0.004, 0.04, 0.4 and 4mm/min of crack mouth opening displacement. We divided the fracture process zone into elastic zone (εxx &lt; 0.08%), plastic zone (0.08% &lt; εxx &lt; 0.4%) and damage zone (εxx &gt; 0.4%) based on the displacement and strain field around the fracture tip. The shape of the fracture process zone is candle-like, and the damage zone is within the plastic zone. The fracture process zone length and width are reduced by 36% and 23% when the loading rate increases by 3 orders of magnitude. The damage zone decreases from 56% to 40% with 3 orders' increase in loading rate; that is, the plasticity is enhanced from high fracture velocity. The rough fracture surface is induced by local microcrack slip and expansion in the fracture process zone from high loading rates. The proposed method of dividing the fracture process zone into a plastic-damage zone is of significance for studying the stress distribution and fracture energy calculation in the rock fracture.

1. INTRODUCTION
The rock is a quasi-brittle material with mineral particles, cracks and pores, leading to a micro-crack zone in the fracture tip subjected to an external load, called fracture process zone (FPZ). FPZ generally refers to the region of fracture from fracture initiation to instability, and its length can be considered as subcritical propagation length. The mechanisms of microcrack, branching and slip along cracks lead to nonlinear fracture growth behaviors of rock. The stress-intensity factor (k) describes the elastic stress distribution with little yield zone at the crack tip. The crack growth occurs when k equals to fracture toughness (kc), a material property independent of fracture velocity.
In general, the fracture velocity is positively correlated with loading rate. The relationship between fracture velocity and crack driving force is often described by a power law or an Arrhenius law (Ponson L, 2009). To involve the effects of fracture velocity, Paris, (1961) proposed the power law relationship between stress-intensity factor range Δk and crack growth rate da/dN to study fatigue failure. Atkinson, (1984) reviewed the experimental data on the subcritical crack growth in geological materials, indicating that a power equation (v∼kn) can be capable of describing fracture velocity - stress intensity factor. Zhou, (2009) et al. used three-point bend tests to determine the critical strain energy density factor of Huanglong limestone with loading rate ranging from 10-4∼10-1mm/s. A cohesive zone model (CZM) was proposed based on the traction-separation law (TSL) to study both crack initiation and propagation (Dugdale D S, 1960). To add rate effect to the CZM, two methods were raised, including the rate-dependent constitutive model in the bulk material and the rate-dependency in the TSL (Salih S, 2018). The non-negligible nonlinear deformation around the fracture tip, namely the FPZ, is responsible for rate-dependent rock fracture growth.