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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Fracture, Dissolution, and Cementation Events in Ordovician Carbonate Reservoirs, Tarim Basin, NW China

Ordovician carbonate rocks of the Yijianfang Formation in the Tabei Uplift, Tarim Basin, contain deeply buried (>6000 m), highly productive oil and gas reservoirs associated with large cavities (>10 m). Previous workers inferred that large cavities are paleocaves (paleokarst) formed near the surface and subsequently buried. Alternately, caves may have formed by dissolution at depth along faults. Using 227 samples from 16 cores, we document textures and cement compositions bearing on cavity histories with petrographic, high-resolution scanning electron microscopy (SEM), isotopic, and fluid inclusion microthermometric observations. Results show that dissolution occurred at depth and was caused by (1) acidic fluids derived from Middle-Late Silurian and/or Devonian-Permian hydrocarbon generation and maturation, (2) high-temperature fluids, of which some were associated with Late Permian igneous activity, and (3) Mg-rich fluids that accompanied Jurassic-Cretaceous deformation and the formation of partially open fractures and stylobreccias (fault breccias). The relative paragenetic sequence of the structure-related diagenesis suggests seven stages of fracturing, dissolution, and cementation. Mottle fabrics in the Yijianfang Formation contain argillaceous carbonate-rich silt and are bioturbation features formed within the marine environment. Those mottled fabrics differ from clearly karstic features in the overlying Lianglitage Formation, which formed by near-surface dissolution and subsequent infilling of cavities by allochthonous sediment. Mottle fabrics are crosscut by compacted fractures filled with phreatic-vadose marine cements and followed by subsequent generations of cement-filled fractures and vugs indicating that some fractures and vugs became cement filled prior to later dissolution events. Calcite cements in fractures and vugs show progressively depleted values of δ18O documenting cement precipitation within the shallow (~220 m), intermediate (~625 m), and deep (~2000 m) diagenetic environments. Deep (mesogenetic) dissolution associated with fractures is therefore the principal source of the high porosity-permeability in the reservoir, consistent with other pieces of evidence for cavities localized near faults.

58 GEOSCIENCES↗
DOE OSTI2022

Modeling Flow and Transport in Fractured Rock using Machine Learning [Slides]

Fractured systems in the subsurface play a role in many natural and engineered applications such as geologic carbon sequestration, hydraulic fracturing and underground nuclear test detection. Structural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Traditional modeling approaches either ignore or idealize structural information at these larger scales because we lack a computational framework that utilizes it in its entirety. The work presented here integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning.

58 GEOSCIENCES↗
DOE OSTI2023

Using Homogenized Models to Explore the Effect of Fracture Densities on Weathering

Despite its importance, only a few researchers have incorporated the effects of fracturing into models of reactive transport for rock weathering. Here we explore 2D simulations that describe weathering under conditions of diffusive and advective transport within heterogeneous media consisting of rocky blocks and fractures. In our simulations, the Darcy velocities vary in space and time and depend on weathering processes within the rock matrix. We explore simulations with saturated and unsaturated flow for weathering bedrock that consists of blocks separated by inert or weathered material. The simulations show that a simplified homogenized model can approximate exact solutions for some of the simulated columns and hills and can allow exploration of coupling between flow and reaction in fractured rock. These hillslope simulations document that, even in the presence of 2D water flow, i) an increase in fracture density results in faster weathering advance rates; and ii) the water table locates deeper for a rock system that is weathered and fractured rather than weathered and unfractured. Some of these patterns have also been observed for natural systems. But these simulations also highlight how simplified models that do not use appropriate averaging of heterogeneities can be inaccurate in predicting weathering rate for natural systems. For example, if water flows both vertically and laterally through the vadose zone of a hill, then a prediction of the depth of regolith that is based on modeling strictly unidirectional downward infiltration will be unrealistically large. Likewise, if the fracture density observed near the land surface is used in a model to predict depth of weathering for a system where the fracture density decreases downward, the model will overestimate regolith depth. Learning how to develop accurately homogenized models could thus enable better conceptual models and predictions of weathering advance in natural systems.

58 GEOSCIENCES↗
DOE OSTI2023

Clinical effects of 3D printing-assisted posterolateral incision in the treatment of ankle fractures involving the posterior malleolus

Objective To explore the clinical outcomes of a 3D printing-assisted posterolateral approach for the treatment of ankle fractures involving the posterior malleolus. Methods A total of 51 patients with ankle fractures involving the posterior malleolus admitted to our hospital from January 2018 to December 2019 were selected. The patients were divided into 3D printing group (28 cases) and control group (23 cases). 3D printing was performed for ankle fractures, followed by printing of a solid model and simulation of the operation on the 3D model. The operation was then performed according to the preoperative plan, including open reduction and internal fixation via the posterolateral approach with the patient in the prone position. Routine x-ray and CT examinations of the ankle joint were performed, and ankle function was evaluated using the American Foot and Ankle Surgery Association (AOFAS) ankle-hindfoot score. Results All patients underwent x-ray and CT examinations. All fractures healed clinically, without loss of reduction or failure of internal fixation. Good clinical effects were achieved in both groups of patients. The operation time, intraoperative blood loss and intraoperative fluoroscopy frequency in the 3D printing group were significantly less than those in the control group ( p < 0.05). There was no significant difference between the two groups in the anatomical reduction rate of fractures or the incidence of surgical complications ( p > 0.05). Conclusion The 3D printing-assisted posterolateral approach is effective in the treatment of ankle fractures involving the posterior malleolus. The approach can be well planned before the operation, is simple to perform, yields good fracture reduction and fixation, and has good prospects for clinical application.

Zheng, Hongming↗
DOE OSTI2024

A multiscale anisotropic polymer network model coupled with phase field fracture

The study of polymers has continued to gain substantial attention due to their expanding range of applications, spanning essential engineering fields to emerging domains like stretchable electronics, soft robotics, and implantable sensors. These materials exhibit remarkable properties, primarily stemming from their intricate polymer chain network, which, in turn, increases the complexity of precisely modeling their behavior. Especially for modeling elastomers and their fracture behavior, accurately accounting for the deformations of the polymer chains is vital for predicting the rupture in highly stretched chains. Despite the importance, many robust multiscale continuum frameworks for modeling elastomer fracture tend to simplify network deformations by assuming uniform behavior among chains in all directions. Recognizing this limitation, our study proposes a multiscale fracture model that accounts for the anisotropic nature of elastomer network responses. At the microscale, damage in the chains is assumed to be driven by both the chain's entropy and the internal energy due to molecular bond distortions. In order to bridge the stretching in the chains to the macroscale deformation, we employ the maximal advance path constraint network model, inherently accommodating anisotropic network responses. As a result, chains oriented differently can be predicted to exhibit varying stretch and, consequently, different damage levels. To drive macroscale fracture based on damages in these chains, we utilize the micromorphic regularization theory, which involves the introduction of dual local-global damage variables at the macroscale. The macroscale local damage variable is obtained through the homogenization of the chain damage values, resulting in the prediction of an isotropic material response. The macroscale global damage variable is subjected to nonlocal effects and boundary conditions in a thermodynamically consistent phase field continuum formulation. Moreover, the total dissipation in the system is considered to be mainly due to the breaking of the molecular bonds at the microscale. To validate our model, we employ the double-edge notched tensile test as a benchmark, comparing simulation predictions with existing experimental data. Additionally, to enhance our understanding of the fracturing process, we conduct uniaxial tensile experiments on a square film made up of polydimethylsiloxane (PDMS) rubber embedded with a hole and notches and then compare our simulation predictions with the experimental observations. Furthermore, we visualize the evolution of stretch and damage values in chains oriented along different directions to assess the predictive capacity of the model. In conclusion, the results are also compared with another existing model to evaluate the utility of our model in accurately simulating the fracture behavior of rubber-like materials.

42 ENGINEERING↗
DOE OSTI2021

An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes

Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of Ren et al. (2018) to admit fracture propagation (FP). The coupled XFEM-EDFM scheme utilizes a separate fracture mesh that is embedded on a static background mesh. The onset and dynamics of fracture propagation are governed by the equivalent stress intensity factor (SIF) criterion. A domain-integral method (J integral) is applied to compute this information. Additionally, an adaptive time-marching scheme is proposed to rapidly restrict and grow temporal resolution to match the underlying time-scales. The proposed model is verified with analytical solutions, and shows the capability to accurately and adaptively co-simulate fluid transport and deformation as well as the propagation of multiple fractures.

42 ENGINEERING↗
DOE OSTI2024

Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of ψ(t) ∝ t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail’s slope in three-dimensional fractured media. Here, in this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by con ducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural proper ties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical ψ(t) ∝ t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.

58 GEOSCIENCES↗
DOE OSTI2024

Cohesive phase-field chemo-mechanical simulations of inter- and trans- granular fractures in polycrystalline NMC cathodes via image-based 3D reconstruction

The optimal design and durable utilization of lithium-ion batteries necessitates an objective modeling approach to understand fracture and failure mechanisms. This paper presents a comprehensive chemo-mechanical modeling study focused on elucidating fracture-induced damage and degradation phenomena in the polycrystalline Li $\mathcal{x}$ Ni 0.5 Mn 0.3 Co 0.2 O 2 (NMC532) cathode. An innovative approach that utilizes image-based reconstructed 3D geometry as finite element (FE) mesh input is employed to enhance the precision in capturing the convoluted architecture and morphological features. For accurately representing the intricate crack configurations within the polycrystalline system, we adopted the cohesive phase-field fracture (CPF) model. Through the integration of advanced image-based geometry reconstruction technique and the promising CPF modeling approach, lithium (de)intercalation induced crack evolution (e.g., nucleation, propagation, branching and diverse modes including inter-/trans-(intra-) granular patterns) and the resulting chemical degradation can be precisely captured, which is also compared and validated with numerical predictions using a continuum damage model. In particular, this model predicts fracture induced degradation under varying fracture properties of grain boundaries and charging rates; the conclusion that NMC particles comprised of larger grains are predicted to have less degradation than those with smaller grains can also be drawn. This comprehensive analysis provides valuable insights into the fracture and degradation within polycrystalline NMC cathodes.

25 ENERGY STORAGE↗
DOE OSTI2021

Stratigraphically Controlled Stress Variations at the Hydraulic Fracture Test Site-1 in the Midland Basin, TX

We investigated the relationship between stratigraphy, stress, and microseismicity at the Hydraulic Fracture Test Site-1. The site comprises two sets of horizontal wells in the Wolfcamp shale and a deviated well drilled after hydraulic fracturing. Regional stresses indicate normal/strike-slip faulting with E-W compression. Stress measurements in vertical and horizontal wells show that the minimum principal stress varies with depth. Strata with high clay and organic content show high values of the least compressive stress, consistent with the theory of viscous stress relaxation. By integrating data from core, logs, and the hydraulic fracturing stages, we constructed a stress profile for the Wolfcamp sequence, which predicts how much pressure is required for hydraulic fracture growth. We applied the results to fracture orientation data from image logs to determine the population of pre-existing faults that are expected to slip during stimulation. We also determined microseismic focal plane mechanisms and found slip on steeply dipping planes striking NW, consistent with the orientations of potentially active faults predicted by the stress model. This case study represents a general approach for integrating stress measurements and rock properties to predict hydraulic fracture growth and the characteristics of injection-induced microseismicity.

microseismicity↗
DOE OSTI2026

Fracture Intersections under Stress: Laboratory Data and Code [Data set]

The connectivity of natural and induced fractures governs the injection and withdrawal of fluids from subsurface reservoirs. Connectivity depends on intersections that control how fluids mix and move through the entire system. Here, we present data sets from 3D X-ray microscopy measurements of simple fracture networks under stress. 3D printing was used to create prismatic blocks that formed fracture networks composed of 2 orthogonal fractures. The network orientation was either "x" or "+" relative to an applied vertical stress. 3D data sets were collected for normal loads of 25, 100 and 200 Newtons for samples with fracture surfaces with either correlated or uncorrelated asperity distributions. The file contains data from the 12 samples analyzed along with an example code used to extract the intersection geometry. Additional experimental details can be found in the manuscript "Geologic Stress Modulates Fluid Mixing at Fracture Intersections" (10.1038/s43247-026-03525-9)and supplemental information to appear in Communications Earth & Environment in 2026.

02 PETROLEUM↗
DOE OSTI2021

A variational phase-field model For ductile fracture with coalescence dissipation

A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative where plasticity and fracture are strongly coupled. Several representative numerical examples motivate specific modeling choices. In particular, a linear crack geometric function provides an “unperturbed” ductile response prior to crack initiation, and Lorentz-type degradation functions ensure that the critical fracture strength remains independent of the phase-field regularization length. In addition, the response of the model is demonstrated to converge with a vanishing phase-field regularization length. Additionally, the model is then applied to calibrate and simulate a three-point bending experiment of an aluminum alloy specimen with a complex geometry. The effect of the proposed coalescence dissipation coupling on simulations of the experiment is first investigated in a two-dimensional plane strain setting. The calibrated model is then applied to a three-dimensional calculation, where the calculated load-deflection curves and the crack trajectory show excellent agreement with experimental observations. Finally, the model is applied to simulate crack nucleation and growth in a specimen from a recent Sandia Fracture Challenge.

42 ENGINEERING↗
DOE OSTI2024

Splitting tensile strength of shale cores: intact versus fractured and sealed with ureolysis-induced calcium carbonate precipitation (UICP)

Ureolysis-induced calcium carbonate precipitation (UICP) is a biomineral solution where the urease enzyme converts urea and calcium into calcium carbonate. The resulting biomineral can bridge gaps in fractured shale, reduce undesired fluid flow, limit fracture propagation, better store carbon dioxide, and potentially enhance well efficiency. The mechanical properties of shale cores were investigated using a modified Brazilian indirect tensile strength test. An investigation of intact shale using Eagle Ford and Wolfcamp cores was conducted at varying temperatures. Results show no significant difference between shale types (average tensile strength = 6.19 MPa). Eagle Ford displayed higher strength at elevated temperature, but temperature did not influence Wolfcamp. Comparatively, cores with a single, lengthwise heterogeneous fracture were sealed with UICP and further tested for tensile strength. UICP was delivered via a flow-through method which injected 20–30 sequential patterns of ureolytic microorganisms and UICP-promoting fluids into the fracture until permeability reduced by three orders of magnitude or with an immersion method which placed cores treated with guar gum and UICP-promoting fluids into a batch reactor, demonstrating that guar gum is a suitable inclusion and may reduce the number of flow-through injections required. Tensile results for both delivery methods were variable (0.15–8 MPa), and in some cores the biomineralized fracture split apart, possibly due to insufficient sealing and/or heterogeneity in the composite UICP-shale cores. Notably in other cores the biomineralized fracture remained intact, demonstrating more cohesion than the surrounding shale, indicating that UICP may produce a strong seal for subsurface application.

58 GEOSCIENCES↗
DOE OSTI2021

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.

42 ENGINEERING↗
DOE OSTI2022

Dynamic fracture of glass fiber-reinforced ductile polymer matrix composites and loading rate effect

Here, the dynamic fracture of S-2 glass fiber-reinforced polymer matrix composites (FRPMCs) was investigated in this study. The matrix ductility was improved by a recently developed network topology modification technique via mixing partially reacted substructures (mPRS). The composite material was manufactured and characterized by micro-CT scanning and scanning electron microscopy (SEM). Dynamic single-edge notched bending (d-SENB) experiments were performed on the composites by using a modified split-Hopkinson pressure bar. Each specimen’s fracture process was visualized by ultrafast X-ray imaging. Such in-situ radiography enabled identifying the damage initiation below 50-micron scale and inspecting its propagation through the internal structures of opaque composites, thereby accurately quantifying the composites’ mechanical properties. Furthermore, the identical d-SENB experiments were designed and the digital image correlation (DIC) was employed to monitor the stress wave propagation on the composite specimens. The force and deflection measurements were modified and correlated to the physical damage processes. Besides, quasi-static SENB experiments were conducted to identify the loading rate effects on the composites’ fracture behaviors. The force and deflection history, bending stiffness, energy dissipation, and fracture toughness at different loading rates were quantified and compared. Finally, post-fracture analysis by micro-CT scanning and SEM provided physical observations on the variation of the fracture morphology by different loading rates.

42 ENGINEERING↗
DOE OSTI2024

Impacts of irregularly-distributed acidified brine flow on geo-chemo-mechanical alteration in an artificial shale fracture under differential stress

The efficacy of geological carbon sequestration is reliant on the integrity of the caprock and its resistance to physical and chemical alteration. Caprocks with high abundance of reactive carbonates like calcite are susceptible to acid-promoted dissolution and can result in structural weakening. This work investigates the effect of acidified brine flow through an artificially fractured, high-carbonate (30 % by XRD) shale under differential compressive stress. Cylindrical samples were cut in half vertically and milled to create an artificial fracture with interlocking asperities and open channels. Samples were sheared with a single applied stress in a custom flow cell housed within an industrial CT scanner. Further, either acidic (pH 4) or reservoir-simulated (pH 9.5) brine was flowed through the artificial fracture for 7–8 days under reservoir pressure and room temperature. Model simulations indicate flow mainly occurred in open channels, with limited flow between overlapping asperities. Analysis of fracture surfaces by optical and scanning electron microscopy show increased surface alteration and roughness after exposure to pH 4 versus pH 9.5 brine indicating mineral dissolution/loss, and this effect is greater in areas that receive the highest brine flows. Similarly, surface analysis by scratch testing shows fracture toughness decreases more after exposure to acidic versus reservoir-simulated brine, with the greatest alteration in areas of highest acidic brine flows. Despite weakening, no shear slip occurred. Overall, the results indicate that acidified brine can result in significant physical and geomechanical alteration of irregular fracture surfaces in shale caprock, with greatest effects in preferential flow regions.

58 GEOSCIENCES↗
DOE OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Characterization of flow and transport in a fracture network at the EGS Collab field experiment through stochastic modeling of tracer recovery

Energy extraction from subsurface reservoirs is important for addressing the increasing energy demand and environmental concerns such as global warming. However, the characterization of subsurface reservoirs, particularly reservoirs dominated by fracture networks remains a challenge due to the lack of means to directly observe subsurface processes. This study explores the feasibility and efficacy of characterizing fracture flow and transport processes in an enhanced geothermal system (EGS) testbed through stochastic tracer modeling. There are two enabling factors that allow application of stochastic modeling to characterize a subsurface reservoir. First, an abundance of geological and geophysical measurements enables the development of a high-fidelity and well-constrained fracture network model. Second, high-performance computing (HPC) allows running massive realizations efficiently. Six conservative tracer tests were stochastically modeled and produced satisfactory realizations that successfully reproduce field tracer recovery data from each tracer test. The evolution of flow and transport processes in the fracture network was then analyzed from these satisfactory realizations. This work demonstrates that stochastic tracer modeling on a high-fidelity fracture network model is feasible and can provide important insights regarding flow and transport characteristics in subsurface fractured reservoirs.

58 GEOSCIENCES↗
DOE OSTI2021

Energy based fracture initiation criterion for strain-crystallizing rubber-like materials with pre-existing cracks

Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. Here in this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.

36 MATERIALS SCIENCE↗