by Verron, Erwan

The simple extension tear test-piece also referred to as the trousers sample is widely used to study crack propagation in rubber. The corresponding energy release rate, called tearing energy for rubber materials, was first established by Rivlin and Thomas (J Polym Sci, 10:291–318, 1953); a second derivation was proposed later by Eshelby (In G.C. Sih, H. C. van Elst, and D. Broek, editors, Prospects of Fracture Mechanics, 69-84, Leyden, 1975). We show here that the derivation of this result can be advantageously revisited through the scope of Configurational Mechanics. Our approach is based on the rigorous definition of the configurations of the body and on the physical significance of the configurational stress tensor. More precisely, it is demonstrated that the change in energy due to crack growth, and then the tearing energy, is directly related to the components of the configurational stress tensor in the body.

DOI: 10.1007/s10704-007-9165-3
Online Date: 11/28/2007
Print publication date: 9/1/2007
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by Hebel, Jochen; Hohe, Jörg; Friedmann, Valérie; Siegele, Dieter

In this study, several two-parameter- concepts are analyzed experimentally and numerically with respect to their capability of characterizing in-plane and out-of-plane crack tip constraint effects. Different approaches utilizing the second term T
_stress of the linear-elastic crack tip stress field, a higher term A
₂ of the power-law hardening crack tip stress field, a hydrostatic correction term Q for a reference stress field or the local triaxiality parameter h are compared. Experimental results for a pressure vessel steel 22NiMoCr3-7 are investigated by means of the different approaches regarding their capability of constraint characterization for enhanced transferability. Theoretical aspects are investigated in a modified boundary layer analysis and in three-dimensional nonlinear elastic-plastic finite element analyses of the specimens. It is found that, with respect to their capability of quantifying combined in-plane and out-of-plane constraint effects, the investigated concepts differ significantly.

DOI: 10.1007/s10704-007-9160-8
Online Date: 11/27/2007
Print publication date: 8/1/2007
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by Müller, Ralf; Gross, Dietmar; Schrade, David; Xu, B. X.

A phase field model for simulating the domain structures in ferroelectric materials is proposed. It takes mechanical and electric fields into account, thus allowing for switching processes due to mechanical and/or electrical loads. The central idea of the model is to take the spontaneous polarisation as an order parameter and to provide an evolution law for this parameter. The concept of evolving inhomogeneities (configuratioanl forces) can be used in this context, as the Spatial distribution of the spontaneous polarisation describes the inhomogeneity of the system. The evolution is found to be in agreement with the second law of thermodynamics and to resemble the (classical) Ginzburg-Landau equation. Numerical simulations show the features of the model and the interaction of domain structures with defects.

DOI: 10.1007/s10704-007-9153-7
Online Date: 11/27/2007
Print publication date: 9/1/2007
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by Li, Yong-Dong; Lee, Kang Yong

Treated was an anti-plane crack perpendicular to the interface of an exponential-type FGM strip bonded to another linear-type FGM substrate with infinite thickness. Through Fourier integral transform, the problem was reduced as a Cauchy singular integral equation, which was further solved numerically by the Lobatto–Chebyshev collocation method. Based on the numerical solution, the effects of the geometrical and physical parameters on the stress intensity factor (SIF) were analyzed and the following conclusions were obtained: (a) A notable discrepancy between the interface-perpendicular crack and the interfacial one is that, to reduce the weak-discontinuity of interface or to make the interface micro-discontinuous will not necessarily decrease the SIF of the former, but will surely decrease that of the latter. (b) When a crack tip is situated very near to the interface (or free surface), its SIF will be high and totally dominated by the interface (or free surface). (c) To increase the stiffness of the FGM on one side of the interface is beneficial to preventing the crack on the other side from growing toward the interface. Besides, some practical suggestions were further given for material design in the field of composites.

DOI: 10.1007/s10704-007-9161-7
Online Date: 11/27/2007
Print publication date: 8/1/2007
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by Kim, Yun-Jae; Song, Tae-Kwang; Kim, Jong-Sung; Jin, Tae-Eun

This paper presents plastic limit loads and approximate J estimates for axial through-wall cracked pipe bends under internal pressure and in-plane bending. These loads and estimates are based on small strain finite element limit analyses using elastic-perfectly plastic materials. Geometric variables associated with the crack and pipe bend are systematically varied, and three possible crack locations (intrados, crown and extrados) are considered. Effects of the bend and crack geometries on plastic limit loads are quantified, and closed-form limit load solutions are given. Based on the proposed limit load solutions, a reference stress based the J estimation scheme for axial through-wall cracked pipe bends under internal pressure and in-plane bending is proposed.

DOI: 10.1007/s10704-007-9166-2
Online Date: 11/27/2007
Print publication date: 8/1/2007
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by Materna, Daniel; Barthold, Franz-Joseph

Variational design sensitivity analysis is a branch of structural optimization. We consider variations of the material configuration and we are interested in the change of the state variables and the objective functional due to these variations. In the same manner in configurational mechanics we are interested in changes of the material body. In this paper, we derive the physical and material residual problem by using standard optimization procedures and we investigate sensitivity relations for the physical and material problem. These sensitivity relations are used in order to solve the coupled physical and material problem. Both problems are coupled by the pseudo load operator, which play an important role for the solution of structural optimization problems. Furthermore, we derive explicit formulations for the variations of the physical and material problem and propose different solution algorithms for the coupled problem.

DOI: 10.1007/s10704-007-9142-x
Online Date: 11/23/2007
Print publication date: 9/1/2007
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by Zhu, Hao; Zhu, Liang; Chen, Jian-Hong; Lv, Xian-Feng

Fracture mechanisms in a 6063 aluminum alloy were investigated and analyzed carefully by in-situ tensile tests in SEM with a vacuum chamber. Specimens used were designed to produce different stress states. Studies indicated that with stress triaxiality (σ
_m/σ
_e) decreasing, the fracture modes changed from normal fracture to shear fracture and the fracture surfaces changed from the dimples and intragranular dominated fracture mode to the shear dominated fracture mode. The grain boundaries of the 6063 aluminum alloy were the weakest positions. In the case of high stress triaxiality, the grain boundary cracks were produced by normal stress or by the incompatibility of deformation between neighboring grains, and the normal stress dominated the crack propagation. In the case of low stress triaxiality, the boundary cracks were produced by the relative slipping of grains against neighboring grains, and the shear stress dominated the crack propagation. The final fracture of the specimens occurred by connections of cracks through transgranular cracking of the ligaments among these cracks.

DOI: 10.1007/s10704-007-9158-2
Online Date: 11/14/2007
Print publication date: 8/1/2007
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by Fett, Theo; Rizzi, Gabriele; Bahr, Hans-Achim; Bahr, Ute; Pham, Van-Bac; Balke, Herbert

An analytical solution for the linear-elastic problem of an edge-cracked semi-infinite body was given already in 1957. For the numerical evaluation of this solution an iteration procedure had to be applied. This might be the reason why the related analysis was not commonly used. By means of powerful mathematical tools developed in the last years it is now possible to evaluate highly-precise stress intensity factors, T-stress terms, weight functions etc. This will be shown in this paper in detail.

DOI: 10.1007/s10704-007-9152-8
Online Date: 11/13/2007
Print publication date: 8/1/2007
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by Tan, Henry; Huang, Young; Liu, Cheng; Ravichandran, Guruswami; Paulino, Glaucio H.

Debonding of particle/matrix interfaces can significantly affect the macroscopic behavior of composite materials. We have used a nonlinear cohesive law for particle/matrix interfaces to study the effect of interface debonding on the macroscopic behavior of particle-reinforced composite materials subject to uniaxial tension. The Mori–Tanaka method, which is suitable for composites with high particle volume fraction, is extended to account for interface debonding. At a fixed particle volume fraction, small particles lead to the hardening behavior of the composite while large particles yield softening. The interface sliding may contribute significantly to the macroscopic behavior of the composite.

DOI: 10.1007/s10704-007-9155-5
Online Date: 11/13/2007
Print publication date: 8/1/2007
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by Berezovski, Arkadi; Maugin, Gérard A.

The solution of the evolution problem of a discontinuity requires the formulation of a kinetic law of the progress relating the driving force and the velocity of the singularity. In the case of a crack, the energy-release rate can be computed (in quasi-statics and in the absence of thermal and intrinsic dissipations) by means of the celebrated J-integral of fracture that is known to be path-independent and, therefore, provides a very convenient estimation of the driving force once the field solution is known. However, the velocity at the crack tip remains undetermined. A similar situation holds for a displacive phase-transition front propagation. The driving force acting on the phase boundary can be determined, but not the velocity of the displacive phase-transition front. From the thermodynamic point of view, both the phase transition and the crack propagation are non-equilibrium processes; entropy is produced at the evolving discontinuity. Therefore, stress jumps are determined by means of non-equilibrium jump relations at the discontinuity. Then the kinetic relations can be obtained depending on the choice of excess stress behavior. The procedure is illustrated on the example of a phase-transition front propagation in a shape-memory alloy bar.

DOI: 10.1007/s10704-007-9159-1
Online Date: 11/13/2007
Print publication date: 9/1/2007
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