The deformation and fracture of balloons

Inflation of balloons provides a straightforward way of achieving large biaxial deformations. Previous studies have shown that when a balloon bursts, crack propagation occurs at very high speed – much higher than would be expected from the low strain modulus and elastic wave velocity of the rubber. The present paper is concerned with studies of the deformation and fracture of cylindrical balloons. On inflation, the deformations of such a balloon pass through an unstable region but subsequently increase monotonically with pressure. In this relatively high pressure region, the ratio of the longitudinal and circumferential extension ratios is broadly in accord with expectations from high-strain elasticity theory when the ratio of the corresponding stresses is taken into account. On bursting, crack speeds up to around 300 m/s in this region. It is shown that these speeds are in accord with large increase in incremental moduli for the highly-strained rubber. Marked changes in crack tip profile observed at very high crack speeds are consistent with control of the rate of growth by inertia rather than by the viscoelastic properties of the rubber (as is believed to be the case at lower speeds). Consistent with this, various elastomers having different glass transition temperatures show similar crack growth behaviour in the very high speed region.     

Energy release rates in rubber during dynamic crack propagation

The theoretical understanding of the fracture mechanics of rubber is not as well developed as for other engineering materials, such as metals. The present study is intended to further the understanding of the dissipative processes that take place in rubber in the vicinity of a propagating crack tip. This dissipation contributes significantly to the total fracture toughness of the rubber and is therefore of great interest from a fracture mechanics point of view. To study this, a computational framework for analysing high-speed crack growth in a biaxially stretched rubber under plane stress is therefore formulated. The main purpose is to investigate the energy release rates required for crack propagation under different modes of biaxial stretching. The results show, that inertia comes into play when the crack speed exceeds about 50 m/s. The total work of fracture by far exceeds the surface energy consumed at the very crack tip, and the difference must be attributed to dissipative damage processes in the vicinity of the crack tip. The size of this damage/dissipation zone is expected to be a few millimetres.     

Definition of a new predictor for multiaxial fatigue crack nucleation in rubber

From an engineering point of view, prediction of fatigue crack nucleation in automotive rubber parts is an essential prerequisite for the design of new components. We have derived a new predictor for fatigue crack nucleation in rubber. It is motivated by microscopic mechanisms induced by fatigue and developed in the framework of Configurational Mechanics. As the occurrence of macroscopic fatigue cracks is the consequence of the growth of pre-existing microscopic defects, the energy release rate of these flaws need to be quantified. It is shown that this microstructural evolution is governed by the smallest eigenvalue of the configurational (Eshelby) stress tensor. Indeed, this quantity appears to be a relevant multiaxial fatigue predictor under proportional loading conditions. Then, its generalization to non-proportional multiaxial fatigue problems is derived. Results show that the present predictor, which is related to the previously published predictors, is capable to unify multiaxial fatigue data.     

A multiaxial criterion for crack nucleation in rubber

The present paper is a first step towards the definition of a new multiaxial fracture criterion for rubber-like materials. Assuming that elastomers are subjected to a uniform distribution of intrinsic flaws, the framework of Eshelbian mechanics is considered. More precisely, the properties of the energy-momentum tensor are thoroughly studied to derive the criterion. A basic numerical example is presented and the qualitative discrepancy between the results obtained with this criterion and those relative to more classical approaches is highlighted.     

Stress state of a transversely isotropic magnetoelectroelastic body with a plane crack under antisymmetric loads

The static equilibrium of a transversely isotropic magnetoelectroelastic body with a plane crack of arbitrary shape in the isotropy plane under antisymmetric mechanical loading is studied. The relationships between the stress intensity factors (SIFs) for an infinite magnetoelectroelastic body and the SIFs for a purely elastic body with the same crack and under the same antisymmetric loading are established. This enables the SIFs for a magnetoelectroelastic body to be found directly from the analogous problem of elasticity. As an example of using this result, the SIFs for penny-shaped, elliptic, and parabolic cracks in a magnetoelectroelastic body under antisymmetric mechanical loading are found Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 37–51, October 2008.     

Stress response of a rubber block with frictional contact under axial loading

Rubber blocks (or springs) are structural components widely used in many applications. Design characteristics of a rubber block under axial loading are an apparent modulus (or compression modulus) and normal and shear stresses on contact surfaces. These are affected by a contact condition of the rubber block in contact with two rigid plates and the shape of the block. The problem of a rubber block bonded to two rigid plates has been solved using various approaches. In contrast, for a rubber block whose one surface is bonded to a rigid plate and the other surface in contact with a frictional surface, there is little work in spite of practical applications. For this contact condition, approximate solutions for rectangular blocks in plane strain and for axi-symmetric discs are derived under the assumption of Coulomb frictional contact. The problem is treated as an extension of the problem of an incompressible rubber block bonded to two rigid plates with one of the plates having a frictional interaction with the rubber block. In the linear range of deformation, finite element analysis and experimental results for rubber blocks with shape factors ranging from 1 to 6 are compared for the validation of analytic results. It is found that friction coefficients play important roles in the design characteristics of the rubber block.     

Retardation of a crack with connections between the faces using an induced thermoelastic stress field

This paper considers local temperature variations near the tip of a crack in the presence of regions in which the crack faces interact. It is assumed that these regions are adjacent to the crack tip and are comparable in size to the crack size. The problem of local temperature variations consists of delay or retardation of crack growth. For a crack with connections between the crack faces subjected to external tensile loads, an induced thermoelastic stress field, and the stresses at the connections preventing crack opening, the boundary-value problem of the equilibrium of the crack reduces to a system of nonlinear singular integrodifferential equations with a Cauchy kernel. The normal and tangential stresses at the connections are found by solving this system of equations. The stress intensity factors are calculated. The energy characteristics of cracks with tip regions are considered. The limiting equilibrium condition for cracks with tip regions is formulated using the criterion of limiting stretching of the connections.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 133–143, January–February, 2005     

Non-linear stresses in a rubber cylinder sheared by pressure at one end

Normal stresses are set up by shearing a rubber block or tube. They depend strongly on the end conditions, even for relatively long specimens [A.N. Gent, J.B. Suh, S.G. Kelly III, Mechanics of rubber shear springs, Int. J. Non-Linear Mech. 42 (2007) 241-249; J.B. Suh, A.N. Gent, S.G. Kelly III, Shear of rubber tube springs, Int. J. Non-Linear Mech. 42 (2007) 1116-1126]. We have now examined a solid rubber cylinder bonded within a rigid cylindrical tube and subjected to pressure at one end. In this case, the correct end conditions for a simple shear deformation are met, at least approximately. Theoretical analysis and finite element calculations show that inwardly directed second-order stresses are set up at the wall, in contrast to the outwardly directed stresses generated by shearing a block or tube. However, for the particular geometry considered, the stresses were rather small in comparison with the applied pressure. Conditions are described under which they would be significantly larger. Stresses in a non-linearly viscous fluid under steady shear flows are expected to be similar, depending strongly on the geometry, end shapes and stress conditions.     

Asymptotic mechanical fields at the tip of a mode I crack in rubber-like solids

Asymptotic analyses of the mechanical fields in front of stationary and propagating cracks facilitate the understanding of the mechanical and physical state in front of crack tips, and they enable prediction of crack growth and failure. Furthermore, efficient modelling of arbitrary crack growth by use of XFEM (extended finite element method) requires accurate knowledge of the asymptotic crack tip fields. In the present work, we perform an asymptotic analysis of the mechanical fields in the vicinity of a propagating mode I crack in rubber. Plane deformation is assumed, and the material model is based on the Langevin function, which accounts for the finite extensibility of polymer chains. The Langevin function is approximated by a polynomial, and only the term of the highest order contributes to the asymptotic solution. The crack is predicted to adopt a wedge-like shape, i.e. the crack faces will be straight lines. The angle of the wedge and the order of the stress singularity depend on the hardening of the strain energy function. The present analysis shows that in materials with a significant hardening, the inertia term in the equations of motion becomes negligible in the asymptotic analysis. Hence, there is no upper theoretical limit to the crack speed.     

Stress concentration around a spheroidal crack caused by a harmonic wave incident at an arbitrary angle

A method is proposed to study the stress concentration around a shallow spheroidal crack in an infinite elastic body. The stress concentration is due to the diffraction of a low-frequency plane longitudinal wave by the crack. The direction of wave propagation is established in which the combined concentration of mode I and mode II stresses is maximum __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 70–77, January 2006.     

Characterization of crack tip stresses in plane-strain fracture specimens having weld center crack

Fracture toughness of metals depends strongly on the state of stress near the crack tip. The existing standards (like R-6, SINTAP) are being modified to account for the influence of stress triaxiality in the flaw assessment procedures. These modifications are based on the ability of so-called ‘constraint parameters’ to describe near tip stresses. Crack tip stresses in homogeneous fracture specimens are successfully described in terms of two parameters like J–Q or J–T. For fracture specimens having a weld center crack, strength mismatch ratio between base and weld material and weld width are the additional variables, along with the magnitude of applied loading, type of loading, and geometry of specimen that affect the crack tip stresses. In this work, a novel three-parameter scheme was proposed to estimate the crack tip opening stress accounting for the above-mentioned variables. The first and second parameters represent the crack tip opening stress in a homogeneous fracture specimen under small-scale yielding and are well known. The third parameter accounts for the effect of constraint developed due to weld strength mismatch. It comprises of weld strength mismatch ratio (M, i.e. ratio of yield strength of weld material to that of base material), and a plastic interaction factor (I_p) that scales the size of the plastic zone with the width of the weld material. The plastic interaction factor represents the degree of influence of weld strength mismatch on crack tip constraint for a given mismatch ratio. The proposed scheme was validated with detailed FE analysis using the Modified Boundary Layer formulation.     

A crack perpendicular to and terminating at a bimaterial interface

Using dislocation simulation approach, the basic equation for a finite crack perpendicular to and terminating at a bimaterial interface is formulated. A novel expansion method is proposed for solving the problem. The complete solution to the problem, including the explicit formulae for theT stresses ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analysed in detail. It is found that normal stresses {ie27-1} and {ie27-2} ahead of the crack tip, are characterised byQ fields if the crack is within a stiff material and the parameters |p _T | and |q _T | are very small, whereQ is a generalised stress intensity factor for a crack normal to and terminating at the interface. If the crack is within a weak material, the normal stresses {ie27-3} and {ie27-4} are dominated by theQ field plusT stress. This work was supported by the Swedish Research Council for Engineering Sciences.     

Special approach for the determination of fracture mechanical parameters at an interface crack tip

An interface crack of finite length is considered between two semi-infinite planes with an artificial contact zone at one of the two crack tips. A transcendental equation and certain simple asymptotic formulas are established for the real contact zone (in the Comninou-Dundurs sense) in terms of the stress intensity factors (SIFs) of the considered model. In these terms analytical expressions are also provided for the energy release rate and for the SIF of the classical interface crack model with an oscillating singularity at the crack tip. The appropriate length of the artifical contact zone is shown to be attainable on the basis of the analysis of the stresses at the crack tip. The use of the proposed model is suggested for integrity assessment of inhomogeneous structural elements of composites containing interface cracks. Received 26 March 1997; accepted for publication 12 September 1997     

Stress field of a damaged material near the crack tip

In this paper, a deformation theory of plasticity for damaged materials is proposed. An asymptotic expression forH near a crack tip is obtained. Finally, the stress and strain fields near the crack tip are presented.     

Numerical analysis of quasi-static crack branching in brittle solids by a modified displacement discontinuity method

Mechanism of quasi-static crack branching in brittle solids has been analyzed by a modified displacement discontinuity method. It has been assumed that the pre-existing cracks in brittle solids may propagate at the crack tips due to the initiation and propagation of the kink (or wing) cracks. The originated wing cracks will act as new cracks and can be further propagated from their tips according to the linear elastic fracture mechanics (LEFM) theory. The kink displacement discontinuity formulations (considering the linear and quadratic interpolation functions) are specially developed to calculate the displacement discontinuities for the left and right sides of a kink point so that the first and second mode kink stress intensity factors can be estimated. The crack tips are also treated by boundary displacement collocation technique considering the singularity variation of the displacements and stresses near the crack tip. The propagating direction of the secondary cracks can be predicted by using the maximum tangential stress criterion. An iterative algorithm is used to predict the crack propagating path assuming an incremental increase of the crack length in the predicted direction (straight and curved cracks have been treated). The same approach has been used for estimating the crack propagating direction and path of the original and wing cracks considering the special crack tip elements. Some example problems are numerically solved assuming quasi-static conditions. These results are compared with the corresponding experimental and numerical results given in the literature. This comparison validates the accuracy and applicability of the proposed method.     

Dynamic fracture surface energy values and branching instabilities during rapid crack propagation in rubber toughened PMMA

An experimental device based on strip band geometry has been designed to explore the brittle behaviour of polymers during rapid crack propagation. The macroscopic crack speed is found to be quasi-constant along an entire RT-PMMA specimen, even in the case of crack branching and until arrest, if any. At the macroscopic branching velocity, the experimental fracture surface energy and the fracture surface roughness have no single values in RT-PMMA. In fact, the macroscopic fracture surface energy increases with the number of instabilities or frustrated micro-branches.     

Stress field at a tip of a prefabricated spiral V-notch

Based on the tranditional V-notched blasting, a technique of spirally V-notched blasting to loosen earth and rock was presented. Fracture mechanics and Westergaard stress function were adopted to build a complex stress function to derive the plane stress and strain fields at one tip of the crack under a quasi-static pressure. An expression was formulated to define the stress intensity factor of spiral V-notch loosen blasting. Factors that have effects on the stress intensity factor were studied. It is demonstrated that spiral V-notch loosen blasting is an extension of vertical V-notch blasting, straight cracking, and alike theories.     

Singular behaviour and asymptotic stress field of a crack terminating at a bimaterial interface

A crack terminating at an interface of two dissimilar elastic materials is investigated. It is found that the asymptotic stress field near the crack tip is in general composed of two parts with each part being characterized by one singularity. The detailed relation of the two singularities with the bimaterial properties is given for some special cases of the crack.     

虚拟裂纹闭合法在结构断裂分析中的应用

基于三维虚拟裂纹技术(3DVCCT),利用ABAQUS用户单元子程序(UEL)编写裂纹界面单元,使3DVCCT集成于ABAQUS软件中,直接计算出裂纹的断裂参数.采用此方法对连杆杆身表面裂纹进行研究,得到了连杆裂纹的应力强度因子的分布规律.     

Stress intensity factor in a contact problem for a plane crack under an antiplane shear wave

The frictional contact interaction of the finite edges of a plane crack under the action of a normally incident harmonic shear wave that produces antiplane deformation is studied. The influence of the forces of contact interaction on the stress intensity factor is analyzed Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 115–119, September 2007.