Effects of Ductility of Organic-Rich Shale on Hydraulic Fracturing: A Fully Coupled Extended-Finite-Element-Method Analysis Using a Modified Cohesive Zone Model

SPE Journal ◽  
2020 ◽  
Author(s):  
Chang Huang ◽  
Shengli Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cohesive Zone ◽  
Extended Finite Element Method ◽  
Cohesive Zone Model ◽  
Zone Model ◽  
Finite Element Method Analysis ◽  
Extended Finite Element ◽  
Method Analysis ◽  
Fully Coupled

Use of the Extended Finite Element Method in the Assessment of Delayed Hydride Cracking

2016 ◽  
Author(s):  
Martin Booth ◽  
Michael Martin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cohesive Zone ◽  
Zirconium Alloy ◽  
Extended Finite Element Method ◽  
Process Zone ◽  
Zirconium Hydride ◽  
Extended Finite Element ◽  
Delayed Hydride Cracking ◽  
Element Method

Zirconium alloys, as used in water-cooled nuclear reactors, are susceptible to a time-dependent failure mechanism known as Delayed Hydride Cracking, or DHC. Corrosion of zirconium alloy in the presence of water generates hydrogen that subsequently diffuses through the metallic structure in response to concentration, temperature and hydrostatic stress gradients. As such, regions of increased hydrogen concentration develop at stress concentrating features, leading to zirconium hydride precipitation. Regions containing zirconium hydride are brittle and prone to failure if plant transient loads are sufficient. This paper demonstrates the application of the Extended Finite Element Method, or XFEM, to the assessment of the DHC susceptibility of stress concentrating features, typical of those considered in the structural integrity assessment of heavy water pressure tube reactors. The method enables the calculation of a DHC threshold load. This paper builds on the process-zone approach that is currently used to provide the industry-standard DHC assessment of zirconium alloy pressure tubes and also recent developments that have extended the application of the process-zone approach to arbitrary geometries by the use of finite element cohesive-zone analysis. In the standard cohesive-zone approach, regions of cohesive elements are situated in discrete locations where the formation of zirconium hydride is anticipated. In contrast, the use of XFEM based cohesive formulations removes the requirement to define cohesive zones a priori, thereby allowing the assessment of geometries in which the location of hydride material is not known.

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