by Song, Tae-Kwang; Kim, Yun-Jae; Kim, Jong-Sung; Jin, Tae-Eun

The present work provides mismatch limit loads and approximate J estimates for tensile plates with constant-depth, part-through surface cracks in the center of the weld metal. Based on systematic three-dimensional FE limit analyses, effects of strength mismatch related variables on limit loads are firstly quantified by the strength mismatch ratio and one geometry-related parameter. Mismatch limit loads for part-through surface cracks are then correlated to those for two-dimensional, through-wall crack problems. Based on the proposed limit load solutions, the applicability of the reference stress based J estimates is also investigated. When the reference stress is defined by the mismatch limit load, predicted J values agree overall well with FE results.

DOI: 10.1007/s10704-008-9206-6
Online Date: 4/25/2008
Print publication date: 12/1/2007
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by Bahat, Dov; Rabinovich, Avinoam; Frid, Vladimir; Brosch, Franz J.

A microscopic study reveals that when the curvature of striae that mark the fracture surface of PMMA glass with a chevron pattern increase beyond the critical angle, μc = 3° ± 2°, a breakdown into alternating tensile dark zones, and bright, ragged shear zones occurs. This breakdown was repeated in primary, secondary and tertiary cycles in diminishing scales. The secondary and tertiary breakdowns occurred exclusively in the shear zones. Similar breakdowns were found in chevron patterns on the fractured surface of a silicate glass ceramics. Due however to their different properties, certain differences were identified between the two materials in their breakdown characteristics, e. g. in the glass ceramic μc = 20° ± 2°. A similar primary breakdown was also identified on tensile fractures cutting rocks in geological outcrops. In the glass ceramic the interface angle $${\phi}$$, which the striae form with the fracture boundary, decreased from 32° ± 2°in the early stage of the striae growth at relatively low velocity, to 13° ± 2° during their advanced growth, at greater velocity, demonstrating that $${\phi}$$ is a good tool for monitoring the change in fracture velocity in a given material. It was found that four interconnected factors determine the geometries and breakdown styles of the chevron pattern: (1) the curvatures of the fracture front and that of the striae which intersect each other orthogonally, (2) the influence of the fracture boundaries, (3) the material properties, such as stiffness, and (4) the fracture velocity in the material.

DOI: 10.1007/s10704-008-9201-y
Online Date: 4/18/2008
Print publication date: 12/1/2007
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by Park, Soojae; Dillard, David A.

Characterizing the fracture energy of bonded adhesive joints over a range of mode mixities often requires special fixtures or a variety of test configurations. By pairing a tapered and a constant thickness adherend, a hybrid double cantilever beam (DCB) specimen is proposed. This asymmetric tapered DCB configuration can be used to determine the fracture energy as a function of mode mixity. As the debond propagates, the relative stiffness of the adherends varies in a systematic manner, resulting in a range of mode mixities from 0° to approximately 20°. Strain energy release rates were obtained using corrected beam theory and a finite element fracture analysis. Single-leg bending tests were used to determine the fracture energy at mode mixity up to 56°. Constant thickness and tapered DCB tests were used to determine the mode I fracture energy. The resulting fracture envelope was constructed in order to show the dependence of the fracture energy on mode mixity for a two part acrylic adhesive.

DOI: 10.1007/s10704-008-9200-z
Online Date: 4/9/2008
Print publication date: 12/1/2007
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by Chen, D. H.; Ozaki, S.

In this study, the general solution of stresses is derived for a T-shaped junction consisting of two thin plates with an adhesion crack. A shear force is applied to the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by the plane stress condition. The results obtained are verified by a numerical calculation based on the finite element method. Moreover, a singular stress field is obtained from the solution for the vicinity of the crack.

DOI: 10.1007/s10704-008-9194-6
Online Date: 4/8/2008
Print publication date: 12/1/2007
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by Shaheen, Ehab; Shrive, Nigel G.

Reactive Powder Concrete (RPC) is a special type of ultra high strength, superplasticized, silica fume concrete, often fibre-reinforced, with improved homogeneity because the traditional coarse and fine aggregate are replaced by fine sand with particle sizes in the range of 100–400 μm [4–16 thousandths of an inch]. RPC properties are attractive because compressive strengths up to 800 MPa [116 ksi] have been recorded, but more typically in excess of 200 MPa [29 ksi]. Flexural strengths up to 141 MPa [20.4 ksi] and fracture energy of 40 kJ/m²[kJ/in.²] have been reported—the latter achieved when steel or stainless steel fibres were included in the mix (Baché (1998) Proceedings of the 2nd international conference on superplasticizers in concrete, Ottawa, pp 35–41; Coppola et al. L’Industria Ital Cemento 707:112–125 (1996); Blais and Couture PCI J 44(5):60–71 (1999); Richard and Cheyrezy (1994) Proceedings of V. Mohan Malhotra symposium on concrete technology: past, present, and future (SP 144). American Concrete Institute, Detroit, pp 507–518; Richard and Cheyrezy Cement Concrete Res 25(7):1501–1511 (1995)). Ductal^®, a commercial RPC, has a compressive strength of approximately 150 MPa [22 ksi] with metallic or organic fibres. All tests described here were performed on 40 × 40 × 160 mm [1.6 × 1.6 × 6.3 in.] (Width (b) × Depth (d) × length (L)) prisms with Poly Vinyl Alcohol (PVA) fibres. Ductal^® is a family of RPC and micro-defect-free concretes containing micro silica, silica fume, cement, Quartz sand, superplasticizer, and PVA fibres. Mechanical and fracture parameters were investigated using four point bending. Low and high cyclic fatigue tests were conducted in three stages, starting from low to high strain cycles. Cracks generated by cyclic fatigue tests were monitored periodically in order to evaluate the rate of crack propagation. Cracks were also investigated using a high magnification microscope. Three pairs of specimens were tested, notched and un-notched to evaluate fracture parameters. Four point bending was used again because determination of the J-Integral (J

_IC
) requires the application of pure bending over a portion of the beam. Load was applied at the third points over a span (S) of 120 mm [4.7 in.], providing a span to depth ratio (S/d) of 3.0. Specimens were notched using a 1 mm [0.04 in.] thick diamond saw. The crack tip generated was circular and the crack length (s) was approximately 10 mm [0.4 in.]. Tests on the notched specimens included measurement of the crack mouth opening displacement (CMOD). Closed-loop testing was developed using a feed back signal from the (CMOD) clip gauge attached to the notched specimens and from strain gauges attached to the un-notched specimens. The weight (w) of each specimen was obtained prior to testing. Fracture parameters were calculated from the load–deflection curves obtained from the notched and un-notched specimens.

DOI: 10.1007/s10704-008-9199-1
Online Date: 4/8/2008
Print publication date: 12/1/2007
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by Andersons, J.; Timmermans, P. H. M.; Modniks, J.

In this work, the crack driving force for a tunnelling crack in a thin brittle layer confined by dissimilar thick, and more compliant, elastic layers is considered at tensile loading. The steady-state energy release rate is evaluated using distributed dislocation technique and series representation of the complex potentials for an isotropic trimaterial. Evolution of the energy release rate with the crack length is studied by means of FEM. The 3D FEM simulations for tunnel cracks suggest that the ERR can represented by a universal relation (mastercurve) in suitably normalised co-ordinates. An analytical approximation of the ERR mastercurve is obtained as a function of crack length, cracking layer thickness, and a non-dimensional steady-state ERR.

DOI: 10.1007/s10704-008-9197-3
Online Date: 4/8/2008
Print publication date: 12/1/2007
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by Chai, Herzl; Ravichandran, Guruswami

Chipping in glass plates from line-wedge contact loading is studied as function of the wedge’s subtended angle 2β, its inclination angle ϕ, and the distance h from a corner having a subtended angle 90° − θ A brittle-fracture analysis in conjunction with the FEM technique is used to elucidate the role of geometric variables on chip morphology and chipping load. Closed-form relations are developed for the latter by invoking the principle of geometric similarity and taking into consideration the details of contact forces transmitted to the crack mouth. The fracture progresses stably until surface effects alter the crack trajectory to form a chip. The latter conclusively occurs from the top surface if ϕ  >  β while from the side wall if ϕ  <  β. The fracture load for top-surface spalling scales with w
^1/2, where w is the indentation depth, and it monotonically declines with the offset angle ψ ≡ – ϕ
β, that for side-wall chipping scales with h
^1/2 and it is little sensitive to ϕ for moderate values of θ In both the cases, the chipping load increases with β. The results may provide insight into the mechanics of chipping in more complex anthropological, tribological, geological and biomedical applications, including flint-knapping, dental fracture, grinding and polishing and common cutting and machining operations.

DOI: 10.1007/s10704-008-9196-4
Online Date: 4/4/2008
Print publication date: 12/1/2007
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by Guerrero, Felicia; Sevostianov, Igor; Giraud, Albert

Transversely-isotropic material with an arbitrarily oriented penny-shaped crack is considered. We calculate fourth-rank compliance contribution tensor of the crack and second-rank crack opening displacement tensor and examine their dependence on crack orientation. It is shown that this dependence for the crack opening displacement tensor is negligible if transverse isotropy has elliptic character, i.e. if material symmetry can be described in terms of a certain second rank tensor.

DOI: 10.1007/s10704-008-9191-9
Online Date: 4/4/2008
Print publication date: 12/1/2007
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by Li, Zhonghua; Yang, Lihong; Li, Shu; Sun, Jun

Some approximate solutions for predicting the stress intensity factor of a short crack penetrating an inclusion of arbitrary shape have been developed under mode I and mode II loading conditions. The derivation of the fundamental formula is based on the transformation toughening theory. The transformation strains in the inclusion are induced by the crack-tip field and remotely applied stresses, and approximately evaluated by the Eshelby equivalent inclusion theory. As validated by detailed finite element (FE) analyses, the developed solutions have good accuracy for different inclusion shape and for a wide range of modulus ratio between inclusion and matrix material.

DOI: 10.1007/s10704-008-9198-2
Online Date: 4/4/2008
Print publication date: 12/1/2007
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by Weck, Arnaud; Segurado, Javier; LLorca, Javier; Wilkinson, David; Böhm, Helmut

Experiments on the growth and linkage of 10 μm diameter holes laser drilled in high precision patterns into Al-plates were modelled with finite elements. The simulations used geometries identical to those of the experiments and incorporated ductile damage by element removal under the control of a ductile damage indicator based on the micromechanical studies of Rice and Tracey. A regularization of the problem was achieved through an integral-type nonlocal model based on the smoothing of the rate of a damage indicator D over a characteristic length L. The simulation does not predict the experimentally observed damage acceleration either in the case where no damage is included or when only a local damage model is used. However, the full three-dimensional simulations based on the nonlocal damage methodology do predict both the failure path and the failure strain at void linkage for almost all configurations studied. For the cases considered the critical parameter controlling the local deformations at void linkage was found to be the ratio between hole diameter and hole spacing.

DOI: 10.1007/s10704-008-9195-5
Online Date: 4/1/2008
Print publication date: 12/1/2007
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