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: Delayed fracture caused by time-dependent damage in PDMS
An experimental and theoretical study of delayed fracture of polydimethlsiloxane (PDMS) is presented. Previous works have demonstrated that delayed fracture in single edge notch specimens is caused by time dependent damage due to chain scission. Here we study the interactions between damage and the elastic field using different specimens and crack geometries with blunt and sharp cracks. Our experiments show that initial toughness is not well defined, as stable slow crack growth can occur over a range of applied loads. Our experiments demonstrate that there is a universal relation between crack growth rate and applied energy release rate. A model coupling the nonlinear elastic deformation and rate dependent bond scission is proposed and is in good agreement with experimental data.  more » « less
Award ID(s):
1903308
PAR ID:
10498675
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Journal of the Mechanics and Physics of Solids
Volume:
181
Issue:
C
ISSN:
0022-5096
Page Range / eLocation ID:
105459
Subject(s) / Keyword(s):
delayed fracture Crack growth Catastrophic failure PDMS Time-dependent damage
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, International Journal for Numerical and Analytical Methods in Geomechanics)
    ABSTRACT Strongly anisotropic geomaterials, such as layered shales, have been observed to undergo fracture under compressive loading. This paper applies a phase‐field fracture model to study this fracture process. While phase‐field fracture models have several advantages—primarily that the fracture path is not predetermined but arises naturally from the evolution of a smooth non‐singular damage field—they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact. Building on a recently developed phase‐field model that accounts for compressive traction across the crack face, this paper extends the model to the setting of anisotropic fracture. The key features of the model include the following: (1) a homogenized anisotropic elastic response and strongly anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face. To test the model, we first compare the predictions to phase‐field fracture evolution calculations in a fully resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. Prior approaches to simulate wing cracks have treated the initial cracks as an external boundary, which makes them difficult to apply to general settings. Here, the effective crack response model enables us to treat the initial crack simply as a nonsingular damaged zone within the computational domain, thereby allowing for easy and general computations. 
    more » « less
  2. ; ; (, 54th US Rock Mechanics/Geomechanics Symposium)
    null (Ed.)
    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
  3. ; ; (, 56th U.S. Rock Mechanics/Geomechanics Symposium)
    ABSTRACT:Due to rock mass being commonly subjected to compressive or shear loading, the mode II fracture toughness is an important material parameter for rocks. Fracturing in rocks is governed by the behavior of a nonlinear region surrounding the crack tip called the fracture process zone (FPZ). However, the characteristics of mode II fracture are still determined based on the linear elastic fracture mechanics (LEFM), which assumes that a pure mode II loading results in a pure mode II fracture. In this study, the FPZ development in Barre granite specimens under mode II loading was investigated using the short beam compression (SBC) test. Additionally, the influence of lateral confinement on various characteristics of mode II fracture was studied. The experimental setup included the simultaneous monitoring of surface deformation using the two-dimensional digital image correlation technique (2D-DIC) to identify fracture mode and characterize the FPZ evolution in Barre granite specimens. The 2D-DIC analysis showed a dominant mixed-mode I/II fracture in the ligament between two notches, irrespective of confinement level on the SBC specimens. The influence of confinement on the SBC specimens was assessed by analyzing the evolution of crack displacement and changes in value of mode II fracture toughness. Larger levels of damage in confined specimens were observed prior to the failure than the unconfined specimens, indicating an increase in the fracture resistance and therefore mode II fracture toughness with the confining stress. 1. INTRODUCTIONThe fracturing in laboratory-scale rock specimens is often characterized by the deformation of the inelastic region surrounding the crack tips, also known as the fracture process zone (FPZ) (Backers et al., 2005; Ghamgosar and Erarslan, 2016). While the influence of the FPZ on mode I fracture in rocks has been extensively investigated, there are limited studies on FPZ development in rocks under pure mode II loading (Ji et al., 2016; Lin et al., 2020; Garg et al., 2021; Li et al., 2021). 
    more » « less
  4. ; ; ; ; ; ; (, Journal of Biomechanics)
    Quasi-brittle fracture mechanics is used to evaluate fracture of human cortical bone in aging. The approach is demonstrated using cortical bone bars extracted from one 92-year-old human male cadaver. In-situ fracture mechanics experiments in a 3D X-ray microscope are conducted. The evolution of the fracture process zone is documented. Fully developed fracture process zone lengths at peak load are found to span about three osteon diameters. Crack deflection and arrest at cement lines is a key process to build extrinsic toughness. Strength and toughness are found as size-dependent, not only for laboratory-scale experimental specimens but also for the whole femur. A scaling law for the length fracture process zone is used. Then, size-independent, tissue fracture properties are calculated. Linear elastic fracture mechanics applied to laboratory beam specimens underestimates the tissue toughness by 60%. Tissue fracture properties are used to predict the load capacity of the femur in bending within the range of documented data. The quasi-brittle fracture mechanics approach allows for the assessment of the combined effect of bone quantity and bone quality on fracture risk. However, further work is needed considering a larger range of subjects and in the model validation at the organ length scale. 
    more » « less
  5. ; ; ; (, 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
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email