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Simulation of Delamination Propagation in Composites Under High-Cycle Fatigue by Means of Cohesive-Zone Models

A damage model for the simulation of delamination propagation under high-cycle fatigue loading is proposed. The basis for the formulation is a cohesive law that links fracture and damage mechanics to establish the evolution of the damage variable in terms of the crack growth rate dA/dN. The damage state is obtained as a function of the loading conditions as well as the experimentally-determined coefficients of the Paris Law crack propagation rates for the material. It is shown that by using the constitutive fatigue damage model in a structural analysis, experimental results can be reproduced without the need of additional model-specific curve-fitting parameters.

Turon, Albert↗

Geomechanical and Hydrogeological Evaluation of a Shallow Hydraulic Fracture at the Devine Fracture Pilot Site, Medina County, Texas

UT-Austin’s Devine Fracture Pilot Site, 50 miles southwest of San Antonio, Texas, has been targeted for a comprehensive, multidisciplinary development of fracture diagnostic techniques that are cross-validated by ground-truth data acquisition near a recently created, 175-ft-deep, horizontal hydraulic fracture (Ahmadian et al. 2018 Demonstration of proof of concept of electromagnetic geophysical methods for high resolution illumination of induced fracture networks. In Proceedings of the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, 23–25 January 2018. SPE-189858-MS.). To evaluate the fracture diagnostic methods at this site, we conducted injection tests with a predefined volumetric flow-rate profile, resembling a diagnostic fracture injection test on September 2020. Subsequently, we developed hydrogeological and geomechanical models based on flow-rate and bottomhole-pressure measurements. History-matching efforts using a simplified layer-cake hydrogeological model resulted in the field-scale formation permeability of 9.87 × 10 –15 m 2 (10 mD) and Darcy-scale fracture permeability. The analysis of the bottomhole pressure and injection-rate history showed that (1) the newly created horizontal fracture was closed adjacent to the injection well pre-injection and (2) the initial pump-pressure increase at a nominal volumetric injection rate led to near-well fracture reopening, fluid conductivity increase, and abrupt injection-rate increase. To overcome hydrogeological-model limitations of predicting fracture reopening throughout injection, we extended the modeling to a finite-element, poroelastic analysis of horizontal-fracture growth using a cohesive-zone model. Using this fracture-reopening model, we improved the history match of the transient-pressure response during the experiment by adjusting the hydromechanical properties. Furthermore, post-injection pressure transient analyses helped reduce uncertainty in the overburden-stress gradient, and the initial hydraulic-fracturing simulation verified the plausibility of achieving the surveyed propped fracture area.

02 PETROLEUM↗

A smeared crack modeling framework accommodating multi-directional fracture at finite strains

A generic smeared crack modeling framework predicated on the deformation gradient decomposition (DGD) approach is proposed for use in dynamic fracture problems at finite strains, accommodating failure along multiple mutually orthogonal fracture planes embedded within an independently defined bulk material model. Within this constitutive framework, the traction equilibrium conditions imposed at each failure surface are used to determine the associated crack displacements stored as internal state variables. In general, the enforcement of interfacial equilibrium entails the implicit solution of a non-linear system of equations within the constitutive update procedure. However, if inertial effects arising due to the relative motion of the fractured material are incorporated within the model, the traction equilibrium conditions are shown to give rise to corresponding dynamic equations of motion governing the time-evolution of the crack opening displacements. For dynamic problems, an explicit time-integration procedure is devised to efficiently update the material state, subject to a set of internal frictionless contact constraints to prevent material inversion. Finally, the efficacy of the proposed modeling framework is investigated through several benchmark dynamic fracture problems run within the explicit finite element code DYNA3D.

42 ENGINEERING↗

Atomistic Cohesive Zone Models for Interface Decohesion in Metals

Using a statistical mechanics approach, a cohesive-zone law in the form of a traction-displacement constitutive relationship characterizing the load transfer across the plane of a growing edge crack is extracted from atomistic simulations for use within a continuum finite element model. The methodology for the atomistic derivation of a cohesive-zone law is presented. This procedure can be implemented to build cohesive-zone finite element models for simulating fracture in nanocrystalline or ultrafine grained materials.

Yamakov, Vesselin I.↗

Multiscale Modeling of Intergranular Fracture in Aluminum: Constitutive Relation For Interface Debonding

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction-displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum-atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum-atomistic interface, and continues its propagation in the atomistic environment. This study is a step towards relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.

Yamakov, V.↗

Non-conformal interface-cohesive modeling with the shifted boundary method

The accurate simulation of boundary- and interface-dominated problems on complex geometries remains challenging when boundary- or interface-fitted meshes are difficult to generate, particularly for curved boundaries, polycrystalline microstructures, and dense interface networks. The Shifted Boundary Method (SBM) alleviates this meshing burden by shifting the enforcement of boundary conditions from the true boundary to a nearby surrogate boundary and recovering the effect of the true boundary through geometric correction terms, thereby enabling standard finite element spaces on non-boundary-fitted meshes. In this report, we develop a general shiftedboundary and shifted-interface framework within the open-source MOOSE framework. We first present a general SBM implementation for complex geometries on non-boundary-fitted meshes. We then adopt the Shifted Interface Method (SIM) for internal interfaces and develop a unified shifted-interface treatment in which the interface law is enforced on a surrogate interface and the effect of the true interface is recovered through shifted jumps, fluxes, and tractions. This perspective brings scalar thermal-contact and vector-valued cohesive-zone mechanics into a single framework, the latter realized as the Shifted Cohesive Zone Method (SCZM) and coupled with history-dependent constitutive models from NEML2. We further extend the MOOSE mesh infrastructure to support cohesive-zone calculations on distributed meshes. The framework is verified and demonstrated through three progressive studies: Poisson’s equation on a smoothed starshaped domain, a manufactured thermal-contact problem on a non-interface-fitted mesh, and a two-dimensional polycrystalline representative volume element combining crystal plasticity with cohesive grain-boundary interfaces. Across these studies, the shifted formulations reproduce boundary- and interface-fitted reference solutions with high fidelity, indicating that the proposed framework provides an accurate and efficient route to boundary- and interface-dominated simulations on arbitrary geometries without requiring fitted meshes.

Yang, Cheng-Hau↗