Nonlinear Field Theory of Fracture Mechanics for Paramagnetic and Ferromagnetic Materials

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
Xiaohong Chen
Keyword(s):  
Field Theory ◽  
Fracture Mechanics ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Ferromagnetic Materials ◽  
Nonlinear Field ◽  
Nonlinear Field Theory

A nonlinear field theory of fracture mechanics is developed for crack propagation in paramagnetic and ferromagnetic materials from the global energy balance equation and the non-negative global dissipation requirement. The crack-front generalized J̃-integral is equivalent to the generalized energy release rate serving as the thermodynamic driving force for crack propagation and also related to the generalized energy-momentum tensor in a way similar to the material force method. On the basis of the developed theory, the generalized energy release rate method, the generalized J̃-integral method, and the extended essential work of fracture method are proposed for quasistatic and dynamic fracture characterization of magnetosensitive materials in the presence of magnetothermomechanical coupling and dissipative effects. The present work overcomes the drawbacks and limitations of conventional fracture mechanics and resolves the controversial issues on magnetoelastic fracture criterion. Especially, the crack-front generalized J̃-integral has an odd dependence on the magnetic induction intensity factor for a Griffith-type crack in a magnetoelastic solid.

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

scholarly journals Effect of the Characteristic Size and Content of Graphene on the Crack Propagation Path of Alumina/Graphene Composite Ceramics

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 611
Author(s):  
Benshuai Chen ◽  
Guangchun Xiao ◽  
Mingdong Yi ◽  
Jingjie Zhang ◽  
Tingting Zhou ◽  
...  
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Volume Content ◽  
Phase Interface ◽  
Average Energy ◽  
Characteristic Size ◽  
Composite Ceramics ◽  
Graphene Composite

In this paper, the Voronoimosaic model and the cohesive element method were used to simulate crack propagation in the microstructure of alumina/graphene composite ceramic tool materials. The effects of graphene characteristic size and volume content on the crack propagation behavior of microstructure model of alumina/graphene composite ceramics under different interfacial bonding strength were studied. When the phase interface is weak, the average energy release rate is the highest as the short diameter of graphene is 10–50 nm and the long diameter is 1600–2000 nm. When the phase interface is strong, the average energy release rate is the highest as the short diameter of graphene is 50–100 nm and the long diameter is 800–1200 nm. When the volume content of graphene is 0.50 vol.%, the average energy release rate reaches the maximum. When the velocity load is 0.005 m s−1, the simulation result is convergent. It is proven that the simulation results are in good agreement with the experimental phenomena.

Nonlinear Approach for Strain Energy Release Rate in Micro Cantilevers

2010 ◽  
Author(s):  
Arash Kheyraddini Mousavi ◽  
Seyedhamidreza Alaie ◽  
Maheshwar R. Kashamolla ◽  
Zayd Chad Leseman
Keyword(s):  
Surface Roughness ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Rigid Substrate ◽  
Micro Cantilever

An analytical Mixed Mode I & II crack propagation model is used to analyze the experimental results of stiction failed micro cantilevers on a rigid substrate and to determine the critical strain energy release rate (adhesion energy). Using nonlinear beam deflection theory, the shape of the beam being peeled off of a rigid substrate can be accurately modeled. Results show that the model can fit the experimental data with an average root mean square error of less than 5 ran even at relatively large deflections which happens in some MEMS applications. The effects of surface roughness and/or debris are also explored and contrasted with perfectly (atomically) flat surfaces. Herein it is shown that unlike the macro-scale crack propagation tests, the surface roughness and debris trapped between the micro cantilever and the substrate can drastically effect the energy associated with creating unit new surface areas and also leads to some interesting phenomena. The polysilicon micro cantilever samples used, were fabricated by SUMMIT V™ technology in Sandia National Laboratories and were 1000 μm long, 30 μm wide and 2.6 μm thick.

Energy-based approach to fracture

2020 ◽  
pp. 506-528
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Fracture Mechanics ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Momentum Tensor ◽  
Linear Elastic Fracture Mechanics ◽  
J Integral ◽  
Linear Elastic ◽  
Energy Release Rates ◽  
Elastic Fracture

This chapter introduces the concept of energy release rates for linear elastic fracture mechanics. The concept of an energy release rate is defined and related to the criteria of Griffith with application in the context of bodies with point loads. Eshelby’s energy momentum tensor is also introduced and Rice’s path independent J-integral is derived, related to energy release rate, and applied to fracture problems.

Finite Element Modeling for Energy Release Rate in Human Cortical Bone

Volume 2 ◽  
2004 ◽  
Author(s):  
Saiphon Charoenphan ◽  
Apiwon Polchai
Keyword(s):  
Finite Element ◽  
Crack Propagation ◽  
Finite Element Modeling ◽  
Energy Release Rate ◽  
Cortical Bone ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Slow Crack Growth ◽  
Finite Element Models

The energy release rates in human cortical bone are investigated using a hybrid method of experimental and finite element modeling techniques. An explicit finite element analysis was implemented with an energy release rate calculation for evaluating this important fracture property of bones. Comparison of the critical value of the energy release rate, Gc, shows good agreement between the finite element models and analytical solutions. The Gc was found to be approximately 820–1150 J/m2 depending upon the samples. Specimen thickness appears to have little effect on the plane strain condition and pure mode I assumption. Therefore the energy release rate can be regarded as a material constant and geometry independent and can be determined with thinner specimens. In addition, the R curve resulting from the finite element models during slow crack growth shows slight ductility of the bone specimen that indicates an ability to resist crack propagation. Oscillations were found at the onset of the crack growth due to the nodal releasing application in the models. In this study light mass-proportional damping was used to suppress the noises. Although this techniques was found to be efficient for this slow crack growth simulation, other methods to continuously release nodes during the crack growth would be recommended for rapid crack propagation.

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