Cosserat type continuum theories have been employed by many authors to study cracks in elastic solids with microstructures. Depending on which theory was used, different crack tip stress singularities have been obtained. In this paper, a microstructure continuum theory is used to model a layered elastic medium containing a crack parallel to the layers. The crack problem is solved by means of the Fourier transform. The resulting integrodifferential equations are discretized using the Chebyshev polynomial expansion method for numerical solutions. By using the present theory, the explicit internal length effects upon the crack opening displacement and stress field can be observed. It is found that the stress field near the crack tip is not singular according to the microstructure continuum solution although the level of the opening stress shows an increasing trend until it gets very close to the crack tip. The rising portion of the near tip opening stress is used to project the stress intensity factor which agrees fairly well with that obtained using the FEM to perform stress analyses of the cracked layered medium with the exact geometry. The numerical solutions also indicate that treating the layered medium as an equivalent homogeneous classical elastic solid is not adequate if cracks are present and accurate stress intensity factors in the original layered medium is desired.

DOI: 10.1007/s10704-009-9399-3
Online Date: 11/6/2009
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Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε

_θθ
ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.

DOI: 10.1007/s10704-009-9420-x
Online Date: 10/30/2009
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The paper focuses on experimental study of the effect of pore distribution on the mechanical properties of aluminum sheets containing multiple holes. Mechanical behavior of materials of uniform microstructure is compared with that of materials containing pore clusters of circular and elliptical shapes. The overall porosity of all specimens was 0.2. All the experiments were repeated 10 times. Our work demonstrates that overall elastic properties are almost insensitive to the actual distribution of pores – uniform or with distinguishable pore clusters. In contrast, fracture toughness of the specimens is strongly affected by the mutual positions of individual pores. Explicit connection between the fracture stress and minimum pore separation is obtained.

DOI: 10.1007/s10704-009-9416-6
Online Date: 10/30/2009
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In ferritic steels a propagating cleavage microcrack changes its propagation direction as it advances from grain to grain. This is due to differences in the orientation of the cleavage planes of two neighboring grains. In order to reach a cleavage plane in a new grain, a microcrack must first penetrate the grain boundary. Grain boundaries therefore act as natural barriers in cleavage fracture. The influence of a grain boundary and the associated misorientation in cleavage planes on crack arrest is here examined using a 3D finite element model with axisymmetric periodicity, representing two grains whose cleavage planes are tilted and twisted relative to each other. The temperature dependent mechanical properties of ferrite are modeled using a temperature dependent viscoplastic response. The development of the crack front as the microcrack penetrates through a grain boundary is here presented. The influence of the twist misorientation on the critical grain size, defined as the largest grain size that can arrest a rapidly propagating microcrack, is examined in a temperature range corresponding to the ductile to brittle transition (DBT) region. It is shown that when both tilt and twist misorientation are present, the influence of tilt and twist, respectively, on crack growth resistance can be decoupled.

DOI: 10.1007/s10704-009-9415-7
Online Date: 10/24/2009
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The ductile-to-brittle transition (DBT) in Fe-13Mn-1.3C (Hadfield steel, I) and Fe-13Mn-2.7 Al-1.3C (Hadfield steel, II) (wt.%) single crystals oriented along $${[011], [{\bar{{1}}}44]}$$, and [$${\bar{{1}}11}$$] directions was investigated under tension in the temperature interval of 77 to 673 K. The DBT temperature interval was found to be independent of single crystal orientation. The DBT temperatures were estimated (1) as the mean value between the temperature corresponding to the minimum crystal ductility and the one coinciding with the onset of the plateau of the $${\varepsilon}$$(T)-dependence (T_DBT1); and (2) as the temperature where the volume fraction of brittle failure on the fracture surfaces was 50% (T_DBT2). The DBT temperatures estimated this way, do not coincide for both steels. Mechanical twinning has been reported as the primary reason for the occurrence of the DBT in austenitic high-carbon Hadfield steel and appears to account for the difference in DBT temperatures as well. Alloying with aluminum partially suppresses twinning in steel (II). Twinning sets in only after a certain amount of dislocation slip, but still influences the fracture mechanism of steel (II).

DOI: 10.1007/s10704-009-9414-8
Online Date: 10/22/2009
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This paper presents the extension of some finite elements with embedded strong discontinuities to the fully transient range with the focus on dynamic fracture. Cracks and shear bands are modeled in this setting as discontinuities of the displacement field, the so-called strong discontinuities, propagating through the continuum. These discontinuities are embedded into the finite elements through the proper enhancement of the discrete strain field of the element. General elements, like displacement or assumed strain based elements, can be considered in this framework, capturing sharply the kinematics of the discontinuity for all these cases. The local character of the enhancement (local in the sense of defined at the element level, independently for each element) allows the static condensation of the different local parameters considered in the definition of the displacement jumps. All these features lead to an efficient formulation for the modeling of fracture in solids, very easily incorporated in an existing general finite element code due to its modularity. We investigate in this paper the use of this finite element formulation for the special challenges that the dynamic range leads to. Specifically, we consider the modeling of failure mode transitions in ductile materials and crack branching in brittle solids. To illustrate the performance of the proposed formulation, we present a series of numerical simulations of these cases with detailed comparisons with experimental and other numerical results reported in the literature. We conclude that these finite element methods handle well these dynamic problems, still maintaining the aforementioned features of computational efficiency and modularity.

DOI: 10.1007/s10704-009-9413-9
Online Date: 10/18/2009
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The fracture behaviour of metal-piezoceramic interfaces under mechanical and electrical loading is examined by four point bending using commercial multilayer actuators. The experiments are performed under stable crack growth in a custom made very stiff testing machine. Besides mechanical loading, a constant electric field was methodically switched on in longitudinal specimen direction. Both poled and unpoled actuators were tested. The crack morphology and the fracture toughness depend on the type of the metal-ceramic interfaces. Assuming different electrical crack boundary conditions of a permeable and an impermeable crack, the field intensity factors K

_ic
, with i = 1, 2, 3, and energy release rates G

_c
(K

_ic
) at the measured critical loads are evaluated with linear-piezoelectric finite element calculations. Inside the bounds of the electrically induced mixed-mode angles, the permeable crack boundary condition yields a constant interface toughness Γ.

DOI: 10.1007/s10704-009-9408-6
Online Date: 10/13/2009
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In order to better understand the failure behaviour of brittle or quasi-brittle materials, we developed a numerical model to analyse the creation of a main macro-crack from a large number of micro-cracks. The boundary element method is used to simulate numerically the formation of a main macro-crack by the growth and the coalescence of the micro-cracks. Different two-dimensional panels in PMMA with initial micro-cracks are studied. The macroscopic responses of the panels are observed by simulating the damage process induced by the growth of micro-cracks. The ultimate tensile stress of the material can be then determined. The material toughness heterogeneity is taken into account in the developed model. The toughness heterogeneity is considered as existence of different energy barriers for the growth of micro-cracks. The influences of different parameters such as the level of local stress concentration, the density and the initial length of micro-cracks and the toughness heterogeneity on the failure behaviour of the materials are also studied. The numerical results show that the present model is realistic and efficient. It can be used to describe brittle or quasi-brittle material failure due to the creation of a main macro-crack from micro-cracks.

DOI: 10.1007/s10704-009-9412-x
Online Date: 10/9/2009
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This paper addresses the question of rate effects in the propagation of delamination cracks in Composite Fiber-Reinforced Plastics (CFRPs). In order to make use of a simple loading device, a mode-II case is used as the basis of the experimental study. The position of the crack is recorded quantitatively by means of a high-speed camera and dedicated image processing techniques. The delamination process is modeled by means of an interfacial Continuum Damage Model (CDM), similar to Cohesive Zone Model (CZM) approaches. In order to make suitable comparison between test and explicit finite element simulation of the test, criterai of proper temporal and spatial discretization have been derived. They ensure a fine description of the process zone and a proper description of the degradation evolution of the interface. Using such simulations and direct comparisons with the tests results, it is shown that the experimental results cannot be reproduced numerically without introducing rate effects. Then, it is proposed and identified by means of comparison between experiments and numerical simulation a bounded-damage-rate interfacial model. The main consequence of the proposed rate-dependent model is that it introduces a maximum crack velocity which is a function of the maximum damage rate. The dependence of the critical energy release rate on the crack’s velocity is analyzed, which leads to the identification of an equivalent rate-dependent fracture mechanics criterion.

DOI: 10.1007/s10704-009-9410-z
Online Date: 10/9/2009
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The paper provides statistical analysis on the effect of mutual positions of individual contacts on the overall resistance and incremental elastic stiffness of a cluster of contacts. We consider an example of a cluster with 76 contact spots of the same radii. The regular lattice of the contacts is compared with the perturbed ones (random clusters). The constriction resistance is determined as a sum of self resistance of the individual contacts and interactions between them. It is shown that the effect of perturbations is very small and, therefore, the mean distance between the centers of individual contacts can be used to estimate the overall cluster resistance. Using elasticity-conductivity cross-property connections, this result is transferred to the incremental elastic stiffness of the cluster. Thus, we established a correspondence between cluster of regular structure and cluster of randomly located contacts. The geometrical parameters governing elastic compliance and spreading resistance of the clusters are number of contact spots and the average distance between individual contacts.

DOI: 10.1007/s10704-009-9411-y
Online Date: 10/8/2009
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