A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. © 2022, The Author(s)

Interfaces in Dynamic Brittle Fracture of PMMA: a peridynamic analysis

Recent experiments in bonded PMMA layers have shown dramatic changes in dynamic crack growth characteristics depending on the interface location and toughness. In this paper we present a peridynamic (PD) analysis of this phenomenon and determine three elements that are essential in a model reproducing the observed fracture behavior: (1) softening near the crack tip to account for changes in PMMA due to heat-generation induced by the high strain rates reached around the crack tip in dynamic fracture; (2) independent extension (mode I) and shear (mode II) modes of fracture; (3) a two-parameter fracture model, which matches both strength and fracture toughness for any horizon size. Once these elements are in place, the PD model captures the experimentally observed dynamic fracture characteristics in bilayer PMMA: crack branching or not at the interface, depending on the interface location; crack running along the interface for a while before punching through the second PMMA layer; slight crack path oscillations near the far end of the sample. The computed crack speed profiles are close to those measured experimentally. The model produces an enlargement of the fracture process zone when the crack running along the interface penetrates into the second PMMA layer, as observed in the experiments. This is where nonlocality of the PD model becomes relevant and critical

A Fracture Multiscale Model for Peridynamic enrichment within the Partition of Unity Method

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of linear elasticity and zones where fractures occur. Here, the peridynamic (PD) model is used in regions of fracture and smooth PUM is used in the surrounding linear elastic media. The method is a so-called global-local enrichment strategy. The elastic fields of the undamaged media provide appropriate boundary data for the localized PD simulations. The first steps for a combined PD/PUM simulator are presented. In part I of this series, we show that the local PD approximation can be utilized to enrich the global PUM approximation to capture the true material response with high accuracy efficiently. Test problems are provided demonstrating the validity and potential of this numerical approach

Predictive Peridynamic 3D Models of Pitting Corrosion in Stainless Steel with Formation of Lacy Covers

In this work, the peridynamic corrosion model is used for 3D simulation of pitting corrosion in stainless steel. Models for passivation and salt layer formation are employed to predict detailed characteristics of pit growth kinetic in stainless steels, such as lacy cover formation on top of the pit, and the diffusion-controlled regime at the pit bottom. The model is validated against an experimentally grown pit on 316L stainless steel in NaCl solution. Lacy covers in this model are formed autonomously during the simulation process. They are remarkably similar to the covers observed on top of the real pits

Predictive Peridynamic 3D Models of Pitting Corrosion in Stainless Steel with Formation of Lacy Covers

In this work, the peridynamic corrosion model is used for 3D simulation of pitting corrosion in stainless steel. Models for passivation and salt layer formation are employed to predict detailed characteristics of pit growth kinetic in stainless steels, such as lacy cover formation on top of the pit, and the diffusion-controlled regime at the pit bottom. The model is validated against an experimentally grown pit on 316L stainless steel in NaCl solution. Lacy covers in this model are formed autonomously during the simulation process. They are remarkably similar to the covers observed on top of the real pits

Peridynamic Approaches for Damage Prediction in Carbon Fiber and Carbon Nanotube Yarn Reinforced Polymer Composites

Aerospace structures are increasingly utilizing advanced composites because of their high specific modulus and specific strength. While the introduction of these material systems can dramatically decrease weight, they pose unique certification challenges, often requiring extensive experimental testing in each stage of the design cycle. The expensive and time-consuming nature of experimental testing necessitates the advancement of simulation methodologies to both aid in the certification process and assist in the exploration of the microstructure design space. Peridynamic (PD) theory, originating from Sandia National Lab’s in the early 2000’s, is a nonlocal continuum-based method that reformulates the equation of motion into an integral equivalent form. The integral form, on which the theory is based, is well suited to explore discontinuity rich phenomena such as damage and material failure. This dissertation develops PD-based simulation approaches to investigate two polymer based composite material systems of different maturity: carbon fiber and carbon nanotube (CNT) yarn. For carbon fiber reinforced composites, simulation approaches were developed to predict damage resulting from low-velocity impact, an important part of the certification process because often damage associated with this loading goes undetected leading to premature structural failure. In contrast to the more established carbon fiber, CNT yarn is a promising constituent material still very much in the developmental process. With this in mind, PD simulation approaches were developed with a different objective, which was to systematically explore microstructure property relationships, providing early feedback in the material design process

Peridynamic Analysis of Rail Squats

Rail surface defects are a serious concern for railway infrastructure managers all around the world. They lead to poor ride quality due to excess vibration and noise; in rare cases, they can result in a broken rail and a train derailment. Defects are typically classified as ‘rail studs’ when they initiate from the white etching layer, and ‘rail squats’ when they initiate from rolling contact fatigue. This paper presents a novel investigation into rail squat initiation and growth simulations using peridynamic theory. To the best of the authors’ knowledge, no other comprehensive study of rail squats has been carried out using this approach. Peridynamics are well-suited for fracture problems, because, contrary to continuum mechanics, they do not use partial-differential equations. Instead, peridynamics use integral equations that are defined even when discontinuities (cracks, etc.) are present in the displacement field. In this study, a novel application of peridynamics to rail squats is verified against a finite element solution, and the obtained simulation results are compared with in situ rail squat measurements. Some new insights can be drawn from the results. The outcome exhibits that the simulated cracks initiate and grow unsymmetrically, as expected and reported in the field. Based on this new insight, it is apparent that peridynamic modelling is well-applicable to fatigue crack modeling in rails. Surprisingly, limitations to the peridynamic analysis code have also been discovered. Future work requires finding an adequate solution to the matter-interpenetration problem