by Oleaga, Gerardo E.

In this note we study a basic propagation criterion for quasi-static crack evolution in Mode III. Using classical techniques of complex analysis, the assumption of stable growth is expressed in terms of the parameters defining the elastic field around the tip. We explore the consequences of the local condition obtained and analyse its role as a crack propagation law. In particular, we herein extend to bounded domains a number of results previously obtained for the whole plane.

DOI: 10.1007/s10704-007-9121-2
Online Date: 9/28/2007
Print publication date: 9/1/2007
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by Epstein, Marcelo

For evolutionary processes of material remodelling and growth, a comparison is drawn between a conventional formulation and one that postulates the existence of additional balance laws for the configurational forces.

DOI: 10.1007/s10704-007-9119-9
Online Date: 9/28/2007
Print publication date: 9/1/2007
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by Ryvkin, Michael; Aboudi, Jacob

Two approaches are combined to investigate the effect of localized thermomechanical loadings of periodic multiphase materials. The first one, referred to as the representative cell method, reduces the infinite domain problem to a problem for the periodicity cell by means of the discrete Fourier transform. This problem is solved by the discretization of the cell into several subcells and a second order expansion of the displacements transform vector in terms of local coordinates. Results for boron/epoxy and glass/epoxy composites subjected to localized mechanical and thermal loadings are presented, and they are compared with analytical solutions for homogeneous materials.

DOI: 10.1007/s10704-007-9123-0
Online Date: 9/28/2007
Print publication date: 6/1/2007
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by Sevostianov, Igor; Kachanov, Mark

For two rough plates pressed against one another, two types of contacts can be distinguished: Hertzian ones and “welded” areas. We find that the two types produce the same effect on the incremental stiffness of the interface and on the effective conductivity across it if their contact areas are the same.

DOI: 10.1007/s10704-007-9122-1
Online Date: 9/28/2007
Print publication date: 6/1/2007
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by Pitti, R. Moutou; Dubois, F.; Petit, C.; Sauvat, N.

An analytical and numerical procedure based on an independent integral path and finite element analysis for mixed-mode fracture in viscoelastic orthotropic media is developed. The separated method employs virtual mechanics fields induced by the classical singular analytical forms. The viscoelastic generalization uses a thermodynamic approach by defining an energy release rate only taking into account a perfect uncoupling between free and viscous energies. The implementation of the Mθ-integral in finite element software and its integration into the viscoelastic incremental formulation are presented. As results, the analytical and numerical solutions are compared by the way of the energy release rate in pure mode I, pure mode II and mixed modes. In shows that, the developed model lead to accurate and efficient separated fracture mode in viscoelastic materials.

DOI: 10.1007/s10704-007-9111-4
Online Date: 9/27/2007
Print publication date: 6/1/2007
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by Zavattieri, Pablo D.; Hector, Louis G.; Bower, Allan F.

A finite element model of crack propagation along a sinusoidal interface with amplitude A and wavelength λ between identical elastic materials is presented. Interface decohesion is modeled with the Xu and Needleman (J Mech Phys Solid 42(9):1397, 1994) cohesive traction–separation law. Ancillary calculations using linear elastic fracture mechanics theory were used to explain some aspects of stable and unstable crack growth that could not be directly attained from the cohesive model. For small aspect ratios of the sinusoidal interface (A/λ ≤ 0.25), we have used the analytical Cotterell–Rice (Intl J Fract 16:155–169, 1980) approximation leading to a closed-form expression of the effective toughness, K

_Ic
, given by $$K_{Ic}\sqrt{(1-\nu^{2})/E\phi_n}=2/\left(1+\left[1+4\pi^{2}(A/\lambda)^{2}\right]^{-1/2}\right),$$ where $$\phi_n$$ is the work of separation, E is Young’s modulus, and ν is Poisson’s ratio. For A/λ > 0.25, both the cohesive zone model and numerical J-integral estimates of crack tip stress intensity factors suggest the following linear relationship: $$K_{Ic} \sqrt{(1-\nu^{2})/E\phi_n}=0.81+1.89(A/\lambda).$$ Parametric studies show that the length of the cohesive zone does not significantly influence K

_Ic
, although it strongly influences the behavior of the crack between the initiation of stable crack growth and the onset of unstable fracture.

DOI: 10.1007/s10704-007-9109-y
Online Date: 9/20/2007
Print publication date: 6/1/2007
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by Kim, Y.; Chao, Y. J.

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A
₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A
₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A
₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.

DOI: 10.1007/s10704-007-9114-1
Online Date: 9/18/2007
Print publication date: 6/1/2007
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by Seelig, Thomas; Giessen, Erik

Numerical simulations are performed in order to gain a better understanding of the effects of various microstructural features and toughening mechanisms in amorphous PC/ABS polymer blends. Crack tip loading under global small-scale yielding conditions is considered with the blend microstructure explicitly resolved in the near-tip process zone. Constitutive models are employed which account for large visco-plastic deformations, the characteristic softening- rehardening behavior of glassy polymers, as well as the effect of plastic dilatancy in the ABS phase due to rubber particle cavitation. The influence of blend composition and morphology on the local stress distribution and the development of the plastic zone at a stationary crack tip are analyzed. Furthermore, crack propagation and the evolution of fracture toughness are studied using different cohesive surface models for failure in the different phases of the blend microstructure.

DOI: 10.1007/s10704-007-9117-y
Online Date: 9/14/2007
Print publication date: 6/1/2007
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by Chai, Herzl; Lawn, Brian R.

An earlier analysis of chipping fracture in brittle solids is here extended to include the case of blocks with inclined side faces and non-normal contact loading. The simple relation P
_F =  β K
_c
h
^3/2 for the critical chipping load P
_F in terms of indent location h and material toughness K
_c is preserved, with angular coordinates simply incorporated into the β coefficient. Chipping fracture tests using a Vickers indenter near the edges of glass blocks with non-orthogonal faces is used to validate the analysis. Implications of the results in relation to practical engineering, biomechanical and anthropological structures are indicated.

DOI: 10.1007/s10704-007-9113-2
Online Date: 9/12/2007
Print publication date: 5/1/2007
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by Ahn, D. C.; Sofronis, P.; Dodds, R.

This paper presents a finite element study of the hydrogen effect on ductile crack propagation in metals and alloys by linking effects at the microstructural level (i.e., void growth and coalescence) to effects at the macro-level (i.e., bulk material deformation around a macroscopic crack). The purpose is to devise a mechanics methodology to simulate the conditions under which hydrogen enhanced plasticity induces fracture that macroscopically appears to be brittle. The hydrogen effect on enhanced dislocation mobility is described by a phenomenological constitutive relation in which the local flow stress is taken as a decreasing function of the hydrogen concentration which is determined in equilibrium with local stress and plastic strain. Crack propagation is modeled by cohesive elements whose traction separation law is determined through void cell calculations that address the hydrogen effect on void growth and coalescence. Numerical results for the A533B pressure vessel steel indicate that hydrogen, by accelerating void growth and coalescence, promotes crack propagation by linking simultaneously a finite number of voids with the crack tip. This “multiple-void” fracture mechanism knocks down the initiation fracture toughness of the material and diminishes the tearing resistance to crack propagation.

DOI: 10.1007/s10704-007-9112-3
Online Date: 9/12/2007
Print publication date: 5/1/2007
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