skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Numerical Simulation of Fracture Initiation in Barre Granite using an Experimentally Validated XFEM Model
Fracturing in brittle rocks with an existing crack results in the development of a significant nonlinear region surrounding the crack tip called the fracture process zone. Various experimental and numerical studies have shown that the crack tip parameters such as the crack tip opening displacement (CTOD) and the fracture energy are critically important in characterizing the fracture process zone. In this study, numerical simulations of rock specimens with a center notch subjected to three-point bending were conducted using the extended finite element method (XFEM) along with the cohesive zone model (CZM) to account for fracture process zone. The input parameters of CZM such as the elastic and critical crack opening displacements were first estimated based on the results of three-point bending tests on the center notched Barre granite specimens. Displacements were measured using the two dimensional digital image correlation technique and used to characterize the evolution of the fracture process zone and estimate the parameters of the cohesive zone model. The results from the numerical simulations showed that CZM provided a good agreement with experimental data as it predicted all three stages of cracking from fracture process initiation to macro-crack growth.  more » « less
Award ID(s):
1644326
PAR ID:
10289895
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
54th US Rock Mechanics/Geomechanics Symposium
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, 55th US Rock Mechanics/Geomechanics Symposium)
    null (Ed.)
    Fracturing in brittle rocks exhibits a significant nonlinear region surrounding the crack tip called the fracture process zone (FPZ). In this study, the evolution of the FPZ under pure mode II loading using notched deep beam under three-point loading was investigated. The experimental setup included the simultaneous monitoring of surface deformation using the two-dimensional digital image correlation technique to characterize various crack characteristics such as its type and FPZ evolution in Barre granite specimens. Both displacement and strain approaches of the two-dimensional digital image correlation were used to identify the mode of fracture under pure mode II loading. Both approaches showed that the crack initiation occur under mode I despite the pure mode II loading at the notch tip. The displacement approach was used for characterizing the evolution of the FPZ which analyzed the crack tip opening displacement and crack tip sliding displacement to identify the transition between the three stages of FPZ evolution, namely, (a) elastic stage, (b) formation of the FPZ, and (c) the macro-crack initiation. The results showed that the evolution of the FPZ of mode I fracture under pure mode II loading is similar to cases of pure mode I loading of the same rock. 
    more » « less
  2. ; ; ; ; ; (, Proceedings of the National Academy of Sciences)
    The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials’ fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn’t this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress–displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed. 
    more » « less
  3. ; (, Journal of Applied Mechanics)
    Abstract Unlike micromechanics failure models that have a well-defined crack path, phase-field fracture models are capable of predicting the crack path in arbitrary geometries and dimensions by utilizing a diffuse representation of cracks. However, such models rely on the calibration of a fracture energy (Gc) and a regularization length-scale (lc) parameter, which do not have a strong micromechanical basis. Here, we construct the equivalent crack-tip cohesive zone laws representing a phase-field fracture model, to elucidate the effects of Gc and lc on the fracture resistance and crack growth mechanics under mode I K-field loading. Our results show that the cohesive zone law scales with increasing Gc while maintaining the same functional form. In contrast, increasing lc broadens the process zone and results in a flattened traction-separation profile with a decreased but sustained peak cohesive traction over longer separation distances. While Gc quantitatively captures the fracture initiation toughness, increasing Gc coupled with decreasing lc contributes to a rising fracture resistance curve and a higher steady-state toughness—both these effects cumulate in an evolving cohesive zone law with crack progression. We discuss the relationship between these phase-field parameters and process zone characteristics in the material. 
    more » « less
  4. ; ; ; (, Purdue University Research Repository)
    This publication documents measurement data for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy. Materials The diaphysis of a human (92-year-old, male) cadaveric femur was obtained through the Indiana University School of Medicine Anatomical Donation Program. Bars (nominally 4.0 mm x 4.0 mm cross section) were extracted from the diaphysis as demonstrated in Figure-samplelocation. Two single Edge Notch Bend, SEN(B), specimens for a load span s=20 mm were machined for a three-point bend fixture for crack growth in the transverse direction. SEN(B) specimens had the following dimensions (height d, depth b, initial crack length a0): beam 1 d=4.0 mm, b=4.0 mm, a0=1.8 mm, beam 2 d=4.1 mm, b=3.9 mm, a0=1.7 mm). Osteon diameter was measured was measured on polished sections by using backscatter SEM images following Britz (2009), Figure samplelocation.jpg. Using ImageJ, a grid is imposed on the images and On.Dm is determined as the Feret Diameter for at least 40 On.Dm measures. For beam 1 mean On.Dm is 242 micrometer and for beam 2 284 micrometer. Experiments and Data Fracture experiments were conducted with a Deben 5000 load rig in a Zeiss XRADIA 3D microscope. For system details see https://www.physics.purdue.edu/xrm/about-our-instruments/index.html. Data for these experiments is given in the two csv files of this project data set. In these experiments force F (load cell) data and image frame data are obtained as machine output. Crack mouth opening displacement (CMOD) is obtained from 3D X-ray images at frame numbers synchronized to force readings. Fracture process zone (FPZ) length L. FPZ length data is obtained from 3D image data in Gallaway, G. E.; Allen, M. R.; Surowiec, R. K.; Siegmund, T. H. (2025). 3D Image Data from In-situ X-ray Imaging Transverse Crack Growth Experiments in Human Cortical Bone. Purdue University Research Repository. doi:10.4231/94PZ-AB06 Code Code (Analysis_Main.m, Analysis_Func.m) takes data from the .csv files and determines the linear elastic fracture mechanics quantities (LEFM toughness), the quasi-brittle fracture mechanics quantities (QBFM toughness), and the tissue intrinsic (size-independent) fracture properties (tissue toughness, tissue strength, tissue lengthscale). Output is depicted as force-CMOD and fracture process zone length - CMOD records, and as crack growth resistance curves (quasibrittle energy release rate vs. fracture process zone length). In addition, the microstructure constant eta is obtained as the ratio between the tissue intrinsic lengthscale and the mean osteon diameter. Code (P_star.m) is provided to determine maximum sustainable load of a femoral shaft in three-point bending. It is assumed that the beam is a pipe with a surface crack of depth equal to the mean osteon diameter. This code can be used for sensitivity studies of the dependence of whole bone maximum sustainable load on cortical thickness, tissue intrinsic strength and microstructure constant eta. Example calculations are depicted in two relevant figures. 
    more » « less
  5. ; ; (, Polymer Engineering & Science)
    Abstract This study presents an experimental investigation to examine the mixed‐mode fracture behavior of fused filament fabrication printed acrylonitrile butadiene styrene (ABS). The single‐edge notch bending specimen configuration is employed to perform mixed‐mode fracture experiments. Four distinct printing orientations—90°, 0°, 45°/−45°, and 90°—are investigated. For each orientation, fracture studies are conducted under pure mode‐I loading (symmetric three‐point bending), mixed‐mode I/II, and pure mode‐II loading (asymmetric three‐point bending) to establish a mixed‐mode fracture criterion. The study evaluates the influence of printing orientation on fracture toughness, crack propagation behavior, and the mixed‐mode fracture criterion. Scanning electron microscopy (SEM) is utilized to analyze the fracture surfaces and correlate the observed fracture mechanisms with the measured fracture toughness values. The findings reveal that printing orientation significantly affects both the fracture toughness and the mixed‐mode fracture criterion. Among the orientations studied, the 90° specimens exhibit the highest fracture toughness and superior performance under all mixed‐mode conditions. SEM images of the fracture surfaces across different printing orientations show the formation of smooth shear zones of varying sizes near the crack tip under mixed‐mode and pure mode‐II conditions. These zones suggest an enhanced resistance to crack propagation, with the degree of improvement differing among the orientations. HighlightsMixed‐mode fracture behavior of 3D‐printed acrylonitrile butadiene styrene.Printing orientations have a major influence on mixed‐mode fracture criterion.90° printing orientation has the highest fracture toughness for mode‐mixities.0° printing orientation has the lowest fracture toughness for mode‐mixities.Fracture surface has dominant shear zone for all mode‐mixities except mode‐I. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email