by Altus, Eli; Givli, Sefi

A Heterogeneous Double Cantilever Beam, commonly used for fracture energy measurements, is analyzed by the Functional Perturbation Method (FPM). External force and displacement are considered as functionals of materials morphology. Both stiffness and fracture energies are random fields, from which the average and variance of the external loading and displacement at the onset of crack growth are found explicitly. The inverse problem, in which the stochastic properties of the fracture energy (average and variance) are found from the load-displacement-crack length data, is also solved. The solution is given in terms of intrinsic correlation length, which is equivalent to ‘grain size’ in polycrystals. It is shown that a different characteristic length for the fracture energy and for moduli may exist. Special attention is given to very small or very large ‘grains’, for which an analytical approximation is permitted. It is shown that the ‘classical’ design loads for a common, fracture related reliability level, may be non-conservative and deviate significantly from the accurate value.

DOI: 10.1007/s10704-004-4029-6
Print publication date: 12/1/2004
View article on SpringerLink

by Broberg, K. B.

During dynamic crack propagation, several distinct changes in the morphology of the dissipative region near the crack edge occur, and they have a pronounced influence on the main propagation mechanism. There are also distinct morphological differences between mode I and mode II. For mode I crack expansion, four successive generations of localization may be observed: micro-separations coalescing with the main crack, protruding clusters of micro-separations, micro-branches, and finally (macro-)branches. The region of localizations is increasing laterally from the main crack plane with crack growth and velocity, as it appears, because of high normal stresses in planes normal to the crack direction. If sufficient space is available, an expanding mode I crack accelerates to a constant velocity, which appears to prevail even after branching and multiple-branching. This indicates an amazing self-similarity over the four generations of localization. The morphology changes during crack propagation depend both on the magnitude of the applied load and on the travelled length of the crack edge. For mode II, the energy dissipation seems generally to be much more concentrated to the crack plane than for mode I. A main reason appears to be that normal stresses in planes normal to the crack direction are comparatively small in front of the crack. Therefore, strong micro-separation localizations seem to appear mainly in shear planes parallel with the crack plane. The appearance of such localizations may be analogous to the remarkable flow velocity gradient discontinuity discovered in turbulent shear flow near a wall.As a consequence of the apparently stronger concentration of the dissipative region to the crack plane, a mode II crack can reach higher velocities than a mode I crack, and it may even reach intersonic velocities.

DOI: 10.1007/s10704-004-2825-7
Print publication date: 12/1/2004
View article on SpringerLink

by Kim, Yun-jae; Chung, Ki-hyun; Kim, Jin-su; Kim, Young-jin

Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE) analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plastic J and crack tip stresses for a plate with a through-thickness crack and semi-elliptical surface crack under positive biaxial loading. For the plate with a through-thickness crack, plate thickness and relative crack length are systematically varied, whereas for the plate with a semi-elliptical surface crack, the relative crack depth and aspect ratio of the semi-elliptical crack are systematically varied. It is found that the reference stress based approach for uniaxial loading can be applied to estimate J under biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected for positive biaxial loading, and thus elastic-plastic J for a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front.

DOI: 10.1007/s10704-004-2550-2
Print publication date: 12/1/2004
View article on SpringerLink

by Radi, Enrico; Gei, Massimiliano

The flow-theory version of couple stress strain gradient plasticity is adopted for investigating the asymptotic fields near a steadily propagating crack-tip, under Mode III loading conditions. By incorporating a material characteristic length, typically of the order of few microns for ductile metals, the adopted constitutive model accounts for the microstructure of the material and can capture the strong size effects arising at small scales. The effects of microstructure result in a substantial increase in the singularities of the skew-symmetric stress and couple stress fields, which occurs also for a small hardening coefficient. The symmetric stress field turns out to be non-singular according to the asymptotic solution for the stationary crack problem in linear elastic couple stress materials. The performed asymptotic analysis can provide useful predictions about the increase of the traction level ahead of the crack-tip due to the sole contribution of the rotation gradient, which has been found relevant and non-negligible at the micron scale.

DOI: 10.1007/s10704-004-2549-8
Print publication date: 12/1/2004
View article on SpringerLink

by Kamaya, Masayuki; Kitamura, Takayuki

In order to keep high reliability of components in a nuclear power plant, it is important to understand the damaging process due to multiple small cracks. The growth shows random behavior because of the microstructural inhomogeneity and the interaction between cracks. The former includes the effects of crack kinking and anisotropic deformation in each crystal of polycrystalline. In this study, a Monte Carlo simulation method is developed in order to analyze the random behavior, taking into account the their influences on the stress intensity factor. The damaging process of mill-annealed alloy 600 in the primary water stress corrosion cracking (PWSCC) is numerically simulated by the proposed method. The crack size distribution obtained agrees well with the experimental observation, and the maximum crack size is statistically estimated on the basis of the Gumbel statistics.

DOI: 10.1007/s10704-004-2314-z
Print publication date: 12/1/2004
View article on SpringerLink

by Wang, Yue-Sheng; Huang, Gan-Yun; Gross, Dietmar

DOI: 10.1007/s10704-004-2620-5
Print publication date: 12/1/2004
View article on SpringerLink

by Dini, D.; Hills, D. A.

A solution procedure is developed for characterising the stress state at the root of a notionally sharp notch, but possessing a small root radius, using two nested asymptotic solutions: an outer asymptote representing a sharp semi-infinite V-notch and an inner solution representing a semi-infinite rounded notch. The two asymptotes are matched to each other remote from the notch root, and to an example finite notch using a generalised stress intensity factor. It follows that the characteristic, singular, sharp-notch field diverges from the rounded-notch solution very near the root. On the other hand, the notch in a finite body diverges from the sharp semi-infinite notch in the far field. Providing that the notch root radius is sufficiently small, it follows that there is an intermediate field where the singular field does characterise the behaviour of the finite radiused notch, and this is quantified.

DOI: 10.1007/s10704-004-2510-x
Print publication date: 12/1/2004
View article on SpringerLink

by Sumpter, J. D. G.

Crack stability in small scale yielding is traditionally analysed using the R-curve approach with toughness indexed by either of the linear elastic fracture mechanics parameters K or G. In ductile materials stable tearing commences well before crack instability and progresses under increasing GR. This is often assumed to mean that toughness is increasing with crack growth. It is shown in this paper that a rising GR curve is generated even when a crack propagates with constant toughness (constant energy dissipation rate). The paper demonstrates that this apparent anomaly occurs because G does not represent the energy input rate for a crack advancing under increasing load in an elastic-plastic material. The constant energy dissipation rate model is consistent with a size independent GR curve; also crack instability predictions are identical with both theories. The GR curve approach has practical advantages, but use of energy dissipation rate offers better physical insight and greater versatility when analysing tough materials.

DOI: 10.1007/s10704-004-2509-3
Print publication date: 12/1/2004
View article on SpringerLink

by Han, Jian-Jun; Dhanasekar, Manicka

This paper presents a method for tracking two-dimensional propagation of internal cracks, in particular vertical split head (VSH) defects, due to contact loading in railhead. Generalised curved crack is assumed to have present in the railhead and its propagation is simulated by solving interaction of arbitrary shaped cracks successively. Furthermore, the finite shape of the rail section is also modelled as the continuous distribution of dislocation within an infinite plane. Crack propagation is simulated using the criterion of vanishing of Mode II stress intensity factors (SIF) at crack tips. Examples are provided for tracking the propagation of pre-existing internal cracks in railheads turning into VSH defects under centric contact loading.

DOI: 10.1007/s10704-004-2508-4
Print publication date: 12/1/2004
View article on SpringerLink

by Momber, A. W.

The paper reports on the deformation and fracture of four rock materials and two cementitious materials due to the impingement of simulated liquid drops at velocities up to 900 m/s. For hard materials, the damage appeared in the form of an undamaged central region surrounded by rings of discrete microcracks. The size of the undamaged zone corresponded to the theoretical contact diameter for low and medium impact velocities, whereas the outer ring size corresponded to the simulated drop diameter. For soft materials, crack formation was obliterated by features of plastic flow. An elastic–plastic transition criterion was derived to explain these different types of response. Crack ring diameter increased as impact velocity increased. However, for rather non-homogeneous materials this relationship was very weak. Failure due to lateral jetting could be noted and was found to contribute significantly to the damage. Material was removed by two different modes: ‘drilling mode’ and ‘chipping mode’, respectively. The first mode applied to soft and porous materials, namely limestone and sandstone, whereas the second mode applied to rather dense and brittle materials, namely granite and feldspar.

DOI: 10.1007/s10704-004-2507-5
Print publication date: 12/1/2004
View article on SpringerLink