by Ju, S. H.; Chung, H. Y.

To evaluate the three-dimensional (3D) stress intensity factors (SIFs) of a sharp V-notch using the finite element result is limited in the literature. Thus, this study developed a least-squares method to solve this problem as well as study its restriction and accuracy. First, the William’s eigenfunction and complex stress function approach are deduced into a least-squares form, and then stress field from the finite element analysis is substituted into the least-squares equation to evaluate the 3D SIFs. Numerical simulations in this article show that the least-squares method can be used to calculate SIFs accurately if more than two stress terms are included. The calculated SIFs of this least-squares method are not sensitive to the maximum and minimum radiuses of the area from which data are included. The major advantage of the proposed method is that the procedure is simple and systematic, so it can be applied to any finite element code without difficulties.

DOI: 10.1007/s10704-008-9193-7
Online Date: 3/27/2008
Print publication date: 11/1/2007
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by Brinckmann, Steffen; Giessen, Erik

Although a thorough understanding of fatigue crack initiation is lacking, experiments have shown that the evolution of distinct dislocation distributions and surface roughness are key ingredients. In the present study we introduce a computational framework that ties together dislocation dynamics, the fields due to crystallographic surface steps and cohesive surfaces to model near-atomic separation leading to fracture. Cyclic tension–compression simulations are carried out where a single plastically deforming grain at a free surface is surrounded by elastic material. While initially, the cycle-by-cycle maximum cohesive opening increases slowly, the growth rate at some instant increases rapidly, leading to fatigue crack initiation at the free surface and subsequent growth into the crystal. This study also sheds light on random local microstructural events which lead to premature fatigue crack initiation.

DOI: 10.1007/s10704-008-9190-x
Online Date: 3/26/2008
Print publication date: 11/1/2007
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by Alan, Tuncay; Zehnder, Alan T.

Experiments show that the strength of nanostructures can be very high and that strength statistics are dominated by surface flaws. To understand the dependence of strength on the surface morphology, a series of fracture mechanics based Monte-Carlo simulations were performed. The surfaces of previously tested Si nanobeams were measured, statistically characterized and equivalent surfaces were generated. The surface profiles consist of bunched steps with varying heights and widths. At the root of each step, there is a stress singularity defined by a stress intensity factor. The beams were assumed to fail when the stress intensity factor anywhere on the surface exceeds the fracture toughness. In agreement with experiments, simulations show that even a small increase in the surface roughness results in a significant reduction in the strength of nanostructures. Thus, careful attention to the surfaces is essential for optimum strength and reliability at the nanoscale.

DOI: 10.1007/s10704-008-9184-8
Online Date: 3/18/2008
Print publication date: 11/1/2007
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by Gerberich, W. W.; Mook, W. M.; Carter, C. B.; Ballarini, R.

Increasingly, the essential, robust character of many nanoscale devices requires knowledge of their fracture toughness. For most brittle materials the technique of choice has been indentation mechanics but little insight into the fracture mechanism(s) has resulted since these have generally been treated as brittle fracture dominated by the true surface energy. Linear elastic fracture mechanics approaches have been invoked to describe indentation fracture but do not address why the surface energy from fracture toughness is most often slightly or even substantially greater than the true surface energy. In the present study we invoke a crack extension force correlation that demonstrates why this is the case at least in fracture measurements based on indentation mechanics. The proposed correlation is different from previous ones in that it focuses on observations of indentation-induced dislocation activity prior to fracture. Allowing the resistance side of the crack extension force analysis to incorporate small amounts of plasticity gives a relationship that is consistent with 22 relatively brittle intermetallics, semiconductors and ceramics. This explains why measured strain energy release rates can be 2 to 5 times as large as surface energies measured in vacuum or calculated by pseudopotentials using the local density approximation.

DOI: 10.1007/s10704-008-9177-7
Online Date: 3/18/2008
Print publication date: 11/1/2007
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by Bennett, Terry; Gitman, Inna M.; Askes, Harm

Dispersive wave propagation is simulated with a continuum elasticity theory that incorporates gradients of strain and inertia. The additional parameters are the Representative Volume Element (RVE) sizes in statics and dynamics, respectively. For the special case of a periodic laminate, expressions for these two RVE sizes can be provided based on the properties of the two components. The fourth-order governing equations are rewritten in two sets of coupled second-order equations, whereby the two sets of unknowns are the macroscopic displacements and the microscopic displacements. The resulting formulation is thus a true multi-scale continuum. In a numerical wave propagation example it is shown that the higher-order continuum model provides an excellent approximation of an explicit model of the heterogeneous laminate.

DOI: 10.1007/s10704-008-9192-8
Online Date: 3/18/2008
Print publication date: 11/1/2007
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by Zappalorto, M.; Lazzarin, P.

An analytical study is carried out on the elastic–plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material is thought of as obeying an elastic-perfectly-plastic or a strain hardening law. When the notch root radius becomes zero, the analytical frame matches the solutions for the crack case due to Hult–McClintock (elastic-perfectly-plastic material) and Rice (strain hardening material). The analytical frame provides an explicit link between the plastic stress and the elastic stress at the notch tip. Neuber’solution for blunt notches under antiplane shear is also obtained and the conditions under which such a solution is valid are discussed in detail by using elastic and plastic notch stress intensity factors. Finally, revisiting Glinka and Molski’s equivalent strain energy density (ESED), these factors are used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case.

DOI: 10.1007/s10704-008-9185-7
Online Date: 3/11/2008
Print publication date: 11/1/2007
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by Delaplace, A.; Desmorat, R.

It is proposed to use a discrete particle model as a complimentary “numerical testing machine” to identify the hydrostatic elasticity-damage coupling and the corresponding sensitivity to hydrostatic stresses parameter. Experimental tri-axial tensile testing is difficult to perform on concrete material, and numerical testing proves then its efficiency. The discrete model used for this purpose is based on a Voronoi assembly that naturally takes into account heterogeneity. Tri-tension tests on a cube specimen, based on a damage growth control, are presented. A successful identification of the hydrostatic sensitivity function of a phenomenological anisotropic damage model is obtained.

DOI: 10.1007/s10704-008-9183-9
Online Date: 3/11/2008
Print publication date: 11/1/2007
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by Dascalu, C.; Bilbie, G.

A two-scale homogenization method is used to construct a damage model in the framework of configurational mechanics. The upscaling procedure allows for the identification of damage configurational forces as the result of the microscopic fracture analysis. The obtained damage equation incorporates stiffness degradation, material softening, unilaterality, induced anisotropy. The balance of configurational forces naturally captures a microscopic length, leading to size effects in the overall damage response. The new approach is illustrated in the case of brittle damage, for a three point bending test. Extended finite elements are used for the numerical modeling of macro-crack initiation and growth. The influence of the microscopic size on the failure initiation stress is analyzed and it is shown that this dependence follows a Hall–Petch type rule.

DOI: 10.1007/s10704-008-9189-3
Online Date: 3/4/2008
Print publication date: 9/1/2007
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by Mahnken, Rolf

This work describes the computation of fracture parameters in functionally graded materials (FGMs) with stationary cracks. To this end the continuum concept of material forces is employed, such that the corresponding balance equation can be discretized with a standard Galerkin finite element procedure. A domain-type formulation is used for evaluation of a vectorial J-integral, where in the practical implementation the material nodal forces of the finite element discretization are summed up in a finite region of the crack-tip. In this way the numerical calculation is completely independent from the alignment of the finite element mesh or any selected integration contour, which is most attractive for adaptively refined finite element meshes. For illustrative purpose the accuracy of the method is discussed for two examples based on comparison with available theoretical and numerical solutions.

DOI: 10.1007/s10704-008-9175-9
Online Date: 3/4/2008
Print publication date: 9/1/2007
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by Dascalu, C.; Maugin, G. A.

DOI: 10.1007/s10704-008-9179-5
Online Date: 3/4/2008
Print publication date: 9/1/2007
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