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: Sharp-interface limits for brittle fracture via the inverse-deformation formulation
We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Γ -convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local, non-convex stored energy of inverse strain, augmented by small interfacial energy, formulated in terms of the inverse-strain gradient. They predict spontaneous fracture with exact crack-opening discontinuities, without the use of damage (phase) fields or pre-existing cracks; crack faces are endowed with a thin layer of surface energy. The models obtained herewith inherit the same properties, except that surface energy is now concentrated at the crack faces in the Γ -limit. Accordingly, we construct energy-minimizing configurations. For a composite bar with a breakable layer, our results predict a pattern of equally spaced cracks whose number is given as an increasing function of applied load.  more » « less
Award ID(s):
2006586
PAR ID:
10525730
Author(s) / Creator(s):
; ;
Corporate Creator(s):
Editor(s):
NA
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Journal of the Mechanics and Physics of Solids
Volume:
190
Issue:
C
ISSN:
0022-5096
Page Range / eLocation ID:
105717
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. ; ; ; (, International Journal of Fracture)
    The Pure Shear (PS) crack specimen is widely employed to assess the fracture toughness of soft elastic materials. It serves as a valuable tool for investigating the behavior of crack growth in a steady-state manner following crack initiation. One of its advantages lies in the fact that the energy release rate (J) remains approximately constant for sufficiently long cracks, independent of crack length. Additionally, the PS specimen facilitates the easy evaluation of J for long cracks by means of a tension test conducted on an uncracked sample. However, the lack of a published expression for short cracks currently restricts the usefulness of this specimen. To overcome this limitation, we conducted a series of finite element (FE) simulations utilizing three different constitutive models, namely the neo-Hookean (NH), Arruda-Boyce (AB), and Mooney-Rivlin (MR) models. Our finite element analysis (FEA) encompassed practical crack lengths and strain levels. The results revealed that under a fixed applied displacement, the energy release rate (J) monotonically increases with the crack length for short cracks, reaches a steady-state value when the crack length exceeds the height of the specimen, and subsequently decreases as the crack approaches the end of the specimen. Drawing from these findings, we propose a simple closed-form expression for J that can be applied to most hyper-elastic models and is suitable for all practical crack lengths, particularly short cracks. 
    more » « less
  3. ; (, Materials)
    In this study, the fracture mechanics of eastern spruce were characterized in relation to end-grain orientation. Compact tension-type specimens with small pre-formed cracks were prepared such that grain angle varied relative to the load axis. Specimens were loaded under crack mouth opening displacement (CMOD) control as to maintain stable crack growth. Specimen fracture was characterized using both R-curve and bulk fracture energy approaches. The results showed that under a RT grain orientation, as well as grain deviations up to about 40∘, cracks will follow a path of least resistance in an earlywood region. As the grain angle exceeds 40∘, the crack will initially move macroscopically in the direction of maximum strain energy release rate, which extends in the direction of the pre-crack, but locally meanders through earlywood and latewood regions before settling once again in an earlywood region. At 45∘, however, the macroscopic crack takes a turn and follows a straight radial path. The results further show that RT fracture is macroscopically stable, while TR fracture is unstable. None of the end-grain fracture orientations showed rising R-curve behavior, suggesting that there is not a traditional fracture process zone in this orientation. 
    more » « less
  4. ; (, Journal of Materials Research)
    In this work, molecular dynamics simulations to explore the crack propagation and fracture behavior of Cu/Nb metallic nanolayered composites (MNCs) were performed. The results of this study are consistent with the previous experimental results, which illustrated that cracks in Cu and Nb layers may exhibit different propagation paths and distances under the isostrain loading condition. The analysis reveals that the interface can increase the fracture resistance of the Nb layer in Cu/Nb MNCs by providing the dislocation sources to generate the plastic strain at the front of the crack. Increasing the layer thickness can enhance the fracture resistance of both Cu and Nb layers, as the critical stress for activating the dislocation motion decreases with the increment of the layer thickness. In addition, grain boundaries (GBs) in polycrystalline Cu/Nb samples would decrease the fracture resistance of Nb layer by promoting the crack propagate along the GBs, i.e., intergranular fracture, while the effect of interface and layer thickness on the fracture resistance of MNCs will not be altered by introducing the GBs in MNCs. 
    more » « less
  5. ; ; ; ; (, ASM International)
    The deformation behavior of particles plays a significant role in achieving adhesion during cold spray. The deformation behavior of the particles is associated with the fracture of the oxide layer and recrystallization, which are the key elements of the quality of cold spray. Studies of particle compression have been made to understand the deformation behavior of a particle. However, the deformation behavior of particle under controlled load and precise and high strain rate is yet to be studied. Here, we show the oxide layer fracture pattern and recrystallization regime under controlled load with a precise and high strain rate. We found that the cracks in the oxide layer initially appeared on the equator of the particle and propagated towards the edge of the top surface. Meanwhile, on the top surface, the circumferential crack was developed. On the other hand, the nanoindentation result showed that the compressed particle under a high strain rate has an unusual load-displacement behavior. Our results demonstrate that the oxide layer fracture behavior corresponds to the adhesion mechanism suggested by previous studies. Our study also revealed that recrystallization takes place within the particle under a high strain rate. We anticipate this finding to give a general insight into the deformation behavior of particles during cold spray. For instance, since the recrystallization behavior at a given strain rate can be predicted through this study, the resultant grain size and shape, which is associated with mechanical properties, can also be predicted. Furthermore, the amount of strain and strain rate to form optimal adhesion can be evaluated. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email