Micromechanical Interpretation of the Dissipation Associated With Mode I Propagation of Microcracks in Brittle Materials

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
Bernhard Pichler ◽  
Luc Dormieux
Keyword(s):  
Tensile Strength ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Brittle Materials ◽  
Engineering Practice ◽  
Mode I ◽  
Zone Model ◽  
Cohesive Tractions

This paper deals with the dissipation associated with quasistatic microcracking of brittle materials exhibiting softening behavior. For this purpose an elastodamaging cohesive zone model is used, in which cohesive tractions decrease (during crack propagation) with increasing displacement discontinuities. Constant cohesive tractions are included in the model as a limiting special case. Considering a representative volume element containing a dilute distribution of many parallel microcracks, we quantify energy dissipation associated with mode I microcrack propagation. This is done in the framework of thermodynamics, without restricting assumptions on the size of the cohesive zones. Model predictions are compared with exact solutions, which are accessible for constant cohesive tractions. The proposed model reliably predicts both onset of crack propagation and the dissipation during microcracking. It is shown that the energy release rate is virtually equal to the area under the softening curve, if the microscopic tensile strength is at least twice as large as the macroscopic tensile strength. This result justifies approaches relying on the concept of constant energy release rate, such as those frequently used in the engineering practice.

A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION

2011 ◽  
Vol 21 (10) ◽  
pp. 2019-2047 ◽  
Author(s):  
GIULIANO LAZZARONI ◽  
RODICA TOADER
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
A Priori ◽  
Brittle Materials ◽  
Continuity Property ◽  
Vanishing Viscosity ◽  
Hausdorff Convergence ◽  
Linearized Elasticity

In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.

Effect of Characteristic Parameters of Exponential Cohesive Zone Model on Mode I Fracture of Laminated Composites

2012 ◽  
Vol 525-526 ◽  
pp. 409-412 ◽  
Author(s):  
Guo Wei Zhu ◽  
Yu Xi Jia ◽  
Peng Qu ◽  
Jia Qi Nie ◽  
Yun Li Guo
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Laminated Composites ◽  
Peak Load ◽  
Interfacial Strength ◽  
Critical Energy ◽  
Mode I ◽  
Zone Model ◽  
Critical Energy Release Rate

Delamination is a particularly dangerous damage mode of high performance laminated composites. In order to describe the composites ductile cracking and its progressive evolution accurately, the adjusted exponential cohesive zone model (CZM) is adopted, which correlates the tensile traction with the corresponding interfacial separation along the fracturing interfacial zone. At first the adjusted exponential CZM is used to simulate the mode I delamination of the standard double cantilever beam (DCB). The simulated results are in good agreement with the corrected beam theory and the corresponding experimental results. Then in order to research how the interfacial properties influence the mode I fracture, the interfacial strength and the critical energy release rate are studied. The main results are obtained as follows. The interfacial strength plays a crucial role in the laminated composites delamination onset, and it affects the peak load significantly if there is not a pre-crack. Once the delamination propagation begins to occur in the laminated composites, the responses of the load-displacement plots are relatively insensitive to the interfacial strength, and only the critical energy release rate is of critical importance. Furthermore, the peak load increases with the increase of the critical energy release rate and interfacial strength.

The Dynamic Energy Release Rate for a Steadily Propagating Mode I Crack in an Infinite, Linearly Viscoelastic Body

1990 ◽  
Vol 57 (2) ◽  
pp. 343-353 ◽  
Author(s):  
J. R. Walton
Keyword(s):  
Steady State ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Viscoelastic Body ◽  
Mode I ◽  
Mode I Crack ◽  
Failure Zone ◽  
Special Cases

An analysis is presented for the dynamic, steady-state propagation of a semi-infinite, mode I crack in an infinite, linearly viscoelastic body. For mathematical convenience, the material is assumed to have a constant Poisson’s ratio, but the shear modulus is only assumed to be decreasing and convex. An expression for the Stress Intensity Factor (SIF) is derived for very general tractions on the crack faces and the Energy Release Rate (ERR) is constructed assuming that a fully developed Barenblatt type failure zone with nonsingular stresses exists at the crack tip and the loadings have a simple exponential form. For comparative purposes, expressions for the ERR are derived for the special cases of dynamic steady-state crack propagation in elastic material and quasi-static crack propagation in viscoelastic material, both with and without a failure zone. Sample calculations are included for power-law material and a standard linear solid in order to illustrate the combined influence of inertial effects, material viscoelasticity, and a failure zone upon the ERR.

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.

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.

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.

The Edge Delamination Test: Measuring the Critical Adhesion Energy of Thin-Film Coatings, Part II: Mode Mixity & Application

1994 ◽  
Vol 338 ◽  
Author(s):  
Edward O. Shaffer ◽  
Scott A. Sikorski ◽  
Frederick J. McGarry
Keyword(s):  
Thin Film ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Mode I ◽  
Rigid Substrate ◽  
Edge Delamination

ABSTRACTThe edge delamination test (EDT) is being developed to measure the critical energy required to cause a thin film, under biaxial tensile stress, to debond from a rigid substrate[1]. The test uses circular features etched through biaxially stressed films adhered to a rigid substrate. If the stress is large enough, a stable debond ring grows radially about the feature. We use a finite element analysis to model the test, solving for the applied strain energy release rate as a function of crack length, feature hole radius and other geometrical parameters. The model identifies both mode I and mode II components of the strain energy release rate, and agrees with previous analytical solutions for the total debond energy. However, the model predicts, with a very refined mesh at the crack tip, the fracture process is pure mode I. To explore this result, critical strain energy release rates from the EDT and the island blister test (IBT) are compared. This agreement supports the model prediction that the failure process in the EDT is modeI peeling.

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