by Banichuk, N. V.; Ivanova, S. Yu.; Ragnedda, F.

Damage accumulation and fracture of structures represented an actual mechanical problem that is needed in development of theoretical and computational methods. One of the most important problems in this direction is the problem of optimal structural design, when in optimization process it is necessary to take into account initial structural defects, arising cracks and damage accumulation. This problem is characterized by incomplete information concerning initial cracks size, cracks position and its orientation. In this context it is necessary to develop the statements of the optimization problems based on guaranteed (mini–max), probabilistic and mixed probabilistic-guaranteed approaches for considered problems with incomplete information. For many realistic it is reasonable to use variants of the mini–max optimization, named as optimization for “the worst case scenario” (see Banichuk et al. Mech Struct Mach 26(1):149–188, 1997; Mech Based Des Struct Mach 31(4):459–474, 2003; Meccanica 40:135–145, 2005a; Mech Based Des Struct Mach 33(2): 253–269, 2005b). Considered problem consist in finding the shape and thickness distribution of axisymmetric quasi-brittle shells with arising cracks in such a way, that the cost functional (volume or weight of the shell material) reaches the minimum, while satisfying some constraints on the stress intensity factor and geometrical constraints. In the case of cycling loadings we consider the number of loading cycles before fracture as the main constraint. Some examples of problems formulations, analytical and numerical solutions based on genetic algorithm are presented.

DOI: 10.1007/s10704-008-9222-6
Online Date: 6/27/2008
Print publication date: 3/1/2008
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by Pineau, A.

Both scientists and engineers are very much concerned with the study of ductile-to-brittle transition (DBT) in ferritic steels. For historical reasons the Charpy impact test remains widely used in the industry as a quality control tool to determine the DBT temperature. The transition between the two failure modes, i.e. brittle cleavage at low temperature and ductile fracture at the upper shelf occurs also at low loading rate in fracture toughness tests. Recent developments have been made in the understanding of the micromechanisms controlling either cleavage fracture in BCC metals or ductile rupture by cavity nucleation, growth and coalescence. Other developments have also been made in numerical tools such as the finite element (FE) method incorporating sophisticated constitutive equations and damage laws to simulate ductile crack growth (DCG) and cleavage fracture. Both types of development have thus largely contributed to modeling DBT occurring either in impact tests or in fracture toughness tests. This constitutes the basis of a modern methodology to investigate fracture, which is the so-called local approach to fracture. In this study the micromechanisms of brittle cleavage fracture and ductile rupture are firstly shortly reviewed. Then the transition between both modes of failure is investigated. It is shown that the DBT behavior observed in impact tests or in fracture toughness specimens can be reasonably well predicted using modern theories on brittle and ductile fracture in conjunction with FE numerical simulations. The review includes a detailed study of a number of metallurgical parameters contributing to the variation of the DBT temperature. Two main types of steels are considered : (i) quenched and tempered bainitic and martensitic steels used in the fabrication of pressurized water reactors, and (ii) modern high-toughness line-pipe steels obtained by chemical variations and optimized hot-rolling conditions. An attempt is also made to underline the research areas which remain to be explored for improving the strength-toughness compromise in the development of steels.

DOI: 10.1007/s10704-008-9232-4
Online Date: 6/27/2008
Print publication date: 3/1/2008
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by Alexeev, A. D.; Revva, V. N.; Bachurin, L. L.; Prokhorov, I. Y.

Experimental results on rock deformation and fracture under true triaxial compression have revealed a misfit between strain state and stress state, strain state varying from generalized compression to generalized shear at σ₃ ≠ 0. This misfit can lead to data misinterpretation during the stress field reconstruction after unloading. Fracture of rock specimens under true triaxial compression occurs by a combined longitudinal/transverse shear and produces the highest dilatancy. An increase in the hydrostatic pressure level diminishes limiting values of shear strains and suppresses the dilatancy effect. A maximum of dilatancy coincides with a maximum of fresh surface area formed during the fracture of the rock. The generalized cleavage of rocks becomes energetically disadvantageous in a true triaxial compressive stress field. Some sandstone becomes more brittle under true triaxial compression (σ₂ ≠ 0) at low values of the minimal stress component (σ₃) due to high initial porosity and dilatancy.

DOI: 10.1007/s10704-008-9214-6
Online Date: 6/27/2008
Print publication date: 1/1/2008
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by Lei, Jun; Wang, Yue-Sheng; Gross, Dietmar

The hybrid time-domain boundary element method (BEM), together with the multi-region technique, is applied to simulate the dynamic process of crack deflection/ penetration at an interface in a bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations (BIEs) are employed with respect to the exterior boundaries; meanwhile, the non-hypersingular traction BIEs are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack tip and crack propagation in the matrix is modeled by adding new elements of constant length to the moving crack tip. The dynamic behaviours of the crack deflection/penetration at an interface, propagation in the matrix or along the interface and kinking out off the interface, are controlled by criteria developed from the quasi-static ones. The numerical results of the crack growth trajectory for different inclined interface and bonded strength are computed and compared with the corresponding experimental results. Agreement between numerical and experimental results implies that the present time-domain BEM can provide a simulation for the dynamic propagation and deflection of a crack in a bi-material.

DOI: 10.1007/s10704-008-9215-5
Online Date: 6/27/2008
Print publication date: 1/1/2008
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by Leguillon, Dominique; Murer, Sébastien

Cotterell and Rice theory (Int J Fract 16(2):155–169, 1980) on the kinking of a crack submitted to a biaxial loading in a homogeneous material is revisited. Using both an energetic and a stress fracture criteria (Leguillon, Eur J Mech A/Solids 21:61–72, 2002) allows defining a positive threshold of the T-stress T

_c
below which no branching can occur (Selvarathinam and Goree, Eng Fract Mech 60(5–6):543–561, 1998) provided the inhomogeneities size is small compared to the Irwin length. The absence of such a threshold would definitely condemn experimental procedures like the double-cantilever beam (DCB) or compact tension (CT) tests, which result in a positive T-stress at the crack tip. The stress intensity factors K

_I
and T are computed using a contour integral. Calculations provide a very good agreement with the analytical results of the infinite Centrally Notched (CN) plate in tension for instance. An asymptotic analysis makes it possible to define the branching angle as a discontinuous function of T with a jump from 0° to some significant positive value as T reaches T

_c
. Furthermore, for non vanishing K

_II
, a similar analysis is carried out, a positive T-stress increases the kinking angle due to K

_II
alone.

DOI: 10.1007/s10704-008-9231-5
Online Date: 6/26/2008
Print publication date: 3/1/2008
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by Lee, Kuk-Hee; Kim, Yun-Jae; Park, Chi-Yong

This paper provides plastic limit and TES (twice-elastic-slope) plastic load solutions for 90° pipe bends under combined pressure and out-of-plane bending, via three-dimensional non-linear FE analyses using elastic-perfectly plastic materials. Without internal pressure, a closed-form approximation is given. For combined pressure and out-of-plane bending, tabulated data are given, from which TES plastic loads can be interpolated. It is found that TES plastic loads for pipe bends under out-of-plane bending are lower than those under in-plane opening bending, but are higher than those under in-plane closing bending. It suggests that the in-plane closing bending mode is the most critical loading mode for 90° pipe bends, which is fully consistent to existing findings.

DOI: 10.1007/s10704-008-9217-3
Online Date: 6/26/2008
Print publication date: 1/1/2008
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by Jiang, L. Y.

This article provides a comprehensive investigation on the fracture behavior of cracked functionally graded piezoelectric materials (FGPMs). To account for the effect of dielectric medium inside the crack upon the fracture behavior of FGPMs, a dielectric crack model is used in this work, in which the electric boundary condition along crack surfaces is deformation-dependent and is nonlinear. The analytical formulations are developed using Fourier transform technique and solving the nonlinear singular equations using Chebyshev polynomials. A solution technique is developed to determine the desired deformation mode of the crack. Numerical simulations are given to show the effects of material gradient and the dielectric medium filling the crack upon the fracture behavior of FGPMs. The results obtained from this dielectric crack model clearly demonstrate how the transition between electrically impermeable and permeable crack models occurs with the change of crack opening displacement in response to the applied electromechanical loads. It is also observed that a critical state for the applied electromechanical loading exists for FGPMs that determines whether the impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric crack model considering the effect of dielectric medium filling the crack.

DOI: 10.1007/s10704-008-9236-0
Online Date: 6/26/2008
Print publication date: 1/1/2008
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