An official website of the United States government
Abstract Shrimali and Lopez-Pamies (2023, “The ‘Pure-Shear’ Fracture Test for Viscoelastic Elastomers and Its Revelation on Griffth Fracture,” Extreme Mech. Lett., 58, p. 101944) have recently shown that the Griffith criticality condition that governs crack growth in viscoelastic elastomers can be reduced to a fundamental form that involves exclusively the intrinsic fracture energy Gc of the elastomer, and, in so doing, they have brought resolution to the complete description of the historically elusive notion of critical tearing energy Tc. The purpose of this article—which can be viewed as the third installment of a series—is to make use of this fundamental form to explain one of the most popular fracture tests for probing the growth of cracks in viscoelastic elastomers, the trousers test.
more »
« less
Validating Griffith fracture propagation in the phase-field approach to fracture: The case of Mode III by means of the trousers test
Abstract At present, there is an abundance of results showing that the phase-field approach to fracture in elastic brittle materials — when properly accounting for material strength — describes thenucleationof fracture from large pre-existing cracks in a manner that is consistent with the Griffith competition between bulk deformation energy and surface fracture energy. By contrast, results that demonstrate the ability of this approach to describe Griffith fracturepropagationare scarce and primarily restricted to Mode I in the setting of infinitesimally small deformations. Aimed at addressing this lacuna, the main objective of this paper is to show that the phase-field approach to fracture describes Mode III fracture propagation in a manner that is indeed consistent with the Griffith energy competition. This is accomplished via direct comparisons between phase-field predictions for fracture propagation in the so–calledtrouserstestand the corresponding results that emerge from the Griffith energy competition. The latter are generated from full-field finite-element solutions that — as a second main contribution of this paper — also serve to bring to light the hitherto unexplored limitations of the classical Rivlin-Thomas-Greensmith formulas that are routinely used to analyze the trousers test.
more »
« less
- Award ID(s):
- 2308169
- PAR ID:
- 10632657
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- International Journal of Fracture
- Volume:
- 249
- Issue:
- 3
- ISSN:
- 0376-9429
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Many geo‐engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase‐field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase‐field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy‐based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase‐field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase‐field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. The comparison of numerical results for two‐dimensional test cases with existing analytical solutions demonstrates that the proposed phase‐field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three‐dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.more » « less
-
We briefly review the Γ-convergence of phase-field fracture to Griffith fracture, and describe how softening and nucleation occur when implementing phase-field models. An example is given of how this softening and nucleation can be completely stopped, while preserving crack growth and Γ-convergence. We then show how nucleation can locally be turned back on, based on any criterion, such as a stress threshold. Again, these modifications preserve Γ-convergence, and they can be applied to static, quasi-static, and dynamic models. Additionally, we describe why these modifications can be expected to improve the convergence of phase-field models.more » « less
-
- (Ed.)Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system.more » « less
-
It is now a well-established fact that even simple topology variations can drastically change the fracture response of structures. With the objective of gaining quantitative insight into this phenomenon, this paper puts forth a density-based topology optimization framework for the fracture response of structures subjected to quasistatic mechanical loads. One of the two key features of the proposed framework is that it makes use of a complete phase-field fracture theory that has been recently shown capable of accurately describing the nucleation and propagation of brittle fracture in a wide range of nominally elastic materials under a wide range of loading conditions. The other key feature is that the framework is based on a multi-objective function that allows optimizing in a weighted manner: ( ) the initial stiffness of the structure, ( ) the first instance at which fracture nucleates, and ( ) the energy dissipated by fracture propagation once fracture nucleation has occurred. The focus is on the basic case of structures made of a single homogeneous material featuring an isotropic linear elastic behavior alongside an isotropic strength surface and toughness. Novel interpolation rules are proposed for each of these three types of material properties. As a first effort to gain quantitative insight, the framework is deployed to optimize the fracture response of 2D structures wherein the fracture is bound to nucleate in three different types of regions: within the bulk, from geometric singularities (pre-existing cracks and sharp corners), and from smooth parts of the boundary. The obtained optimized structures are shown to exhibit significantly enhanced fracture behaviors compared to those of structures that are optimized according to conventional stiffness maximization. Furthermore, the results serve to reveal a variety of strengthening and toughening mechanisms. These include the promotion of highly porous structures, the formation of tension-compression asymmetric regions, and the removal of cracks and sharp corners. The particular mechanism that is preferred by a given structure, not surprisingly, correlates directly to the elastic, strength, and toughness properties of the material that is made of.more » « less
