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Aditya Vasudevan - One of the best experts on this subject based on the ideXlab platform.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part ii drift of fracture facets in mixed mode i ii iii
Journal of The Mechanics and Physics of Solids, 2020Co-Authors: Laurent Ponson, Alain Karma, Aditya Vasudevan, Jean-baptiste LeblondAbstract:Abstract In earlier papers (Leblond et al., 2011; 2019), we presented linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I+III, based on a “double” Propagation Criterion combining (Griffith, 1920)’s energetic condition and (Goldstein and Salganik, 1974)’s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its Propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part ii drift of fracture facets in mixed mode i ii iii
arXiv: Soft Condensed Matter, 2019Co-Authors: Aditya Vasudevan, Jean-baptiste Leblond, Laurent Ponson, Alain KarmaAbstract:In earlier papers (Leblond this http URL., 2011, 2019), we presented linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I+III, based on a "double'' Propagation Criterion combining Griffith (1920)'s energetic condition and Goldstein and Salganik (1974)'s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the "threshold'' value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its Propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.
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configurational stability of a crack propagating in mixed mode i ii iii
International Conference on Theoretical Applied and Experimental Mechanics, 2019Co-Authors: Jean-baptiste Leblond, Alain Karma, Laurent Ponson, Aditya VasudevanAbstract:In some previous papers, we presented some linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I + III, using a Propagation Criterion combining a Griffith-type energetic condition and Goldstein and Salganik’s “principle of local symmetry”. In the last one, the local value of the fracture energy was no longer considered as a constant but heuristically permitted to depend upon the ratio of the local mode III to mode I stress intensity factors. As a result, a much improved agreement of theory and experimental observations was obtained for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. This analysis is extended here to the situation, of considerable practical significance, where a small additional mode II loading component is present in the initially planar configuration of the crack. This component induces a small, general kink of this crack from the moment it is applied. The main novelty resulting from its application is that the instability modes, present above the threshold, must drift along the crack front during its Propagation. It is hoped that this prediction will be useful to theoretically interpret a number of experiments where such a drifting motion was indeed observed but left unexplained.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part i mixed mode i iii
Journal of The Mechanics and Physics of Solids, 2019Co-Authors: Jean-baptiste Leblond, Alain Karma, Laurent Ponson, Aditya VasudevanAbstract:Abstract In a previous paper (Leblond et al., 2011), we proposed a theoretical interpretation of the experimentally well-known instability of coplanar crack Propagation in mode I+III. The interpretation relied on a stability analysis based on analytical expressions of the stress intensity factors for a crack slightly perturbed both within and out of its original plane, due to Gao and Rice (1986) and Movchan et al. (1998), coupled with a double Propagation Criterion combining Griffith (1920)’s energetic condition and Goldstein and Salganik (1974)’s principle of local symmetry. Under such assumptions instability modes were indeed evidenced for values of the mode mixity ratio - ratio of the mode III to mode I stress intensity factors applied remotely - larger than some threshold depending only on Poisson’s ratio. Unfortunately, the predicted thresholds were much larger than those generally observed for typical values of this material parameter. While the subcritical character of the nonlinear bifurcation from coplanar to fragmented fronts has been proposed as a possible explanation for this discrepancy (Chen et al., 2015), we propose here an alternative explanation based on the introduction of a constitutive relationship between the fracture energy and the mode mixity ratio, which is motivated by experimental observations. By re-examining the linear stability analysis of a planar propagating front, we show that such a relationship suffices, provided that it is strong enough, to lower significantly the threshold value of the mode mixity ratio for instability so as to bring it in a range more consistent with experiments. Interesting formulae are also derived for the distributions of the perturbed stress intensity factors and energy-release-rate, in the special case of perturbations of the crack surface and front obeying the principle of local symmetry and having reached a stationary state (corresponding to instability modes in near-threshold conditions).
Jean-baptiste Leblond - One of the best experts on this subject based on the ideXlab platform.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part ii drift of fracture facets in mixed mode i ii iii
Journal of The Mechanics and Physics of Solids, 2020Co-Authors: Laurent Ponson, Alain Karma, Aditya Vasudevan, Jean-baptiste LeblondAbstract:Abstract In earlier papers (Leblond et al., 2011; 2019), we presented linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I+III, based on a “double” Propagation Criterion combining (Griffith, 1920)’s energetic condition and (Goldstein and Salganik, 1974)’s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its Propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part ii drift of fracture facets in mixed mode i ii iii
arXiv: Soft Condensed Matter, 2019Co-Authors: Aditya Vasudevan, Jean-baptiste Leblond, Laurent Ponson, Alain KarmaAbstract:In earlier papers (Leblond this http URL., 2011, 2019), we presented linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I+III, based on a "double'' Propagation Criterion combining Griffith (1920)'s energetic condition and Goldstein and Salganik (1974)'s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the "threshold'' value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its Propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.
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configurational stability of a crack propagating in mixed mode i ii iii
International Conference on Theoretical Applied and Experimental Mechanics, 2019Co-Authors: Jean-baptiste Leblond, Alain Karma, Laurent Ponson, Aditya VasudevanAbstract:In some previous papers, we presented some linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I + III, using a Propagation Criterion combining a Griffith-type energetic condition and Goldstein and Salganik’s “principle of local symmetry”. In the last one, the local value of the fracture energy was no longer considered as a constant but heuristically permitted to depend upon the ratio of the local mode III to mode I stress intensity factors. As a result, a much improved agreement of theory and experimental observations was obtained for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. This analysis is extended here to the situation, of considerable practical significance, where a small additional mode II loading component is present in the initially planar configuration of the crack. This component induces a small, general kink of this crack from the moment it is applied. The main novelty resulting from its application is that the instability modes, present above the threshold, must drift along the crack front during its Propagation. It is hoped that this prediction will be useful to theoretically interpret a number of experiments where such a drifting motion was indeed observed but left unexplained.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part i mixed mode i iii
Journal of The Mechanics and Physics of Solids, 2019Co-Authors: Jean-baptiste Leblond, Alain Karma, Laurent Ponson, Aditya VasudevanAbstract:Abstract In a previous paper (Leblond et al., 2011), we proposed a theoretical interpretation of the experimentally well-known instability of coplanar crack Propagation in mode I+III. The interpretation relied on a stability analysis based on analytical expressions of the stress intensity factors for a crack slightly perturbed both within and out of its original plane, due to Gao and Rice (1986) and Movchan et al. (1998), coupled with a double Propagation Criterion combining Griffith (1920)’s energetic condition and Goldstein and Salganik (1974)’s principle of local symmetry. Under such assumptions instability modes were indeed evidenced for values of the mode mixity ratio - ratio of the mode III to mode I stress intensity factors applied remotely - larger than some threshold depending only on Poisson’s ratio. Unfortunately, the predicted thresholds were much larger than those generally observed for typical values of this material parameter. While the subcritical character of the nonlinear bifurcation from coplanar to fragmented fronts has been proposed as a possible explanation for this discrepancy (Chen et al., 2015), we propose here an alternative explanation based on the introduction of a constitutive relationship between the fracture energy and the mode mixity ratio, which is motivated by experimental observations. By re-examining the linear stability analysis of a planar propagating front, we show that such a relationship suffices, provided that it is strong enough, to lower significantly the threshold value of the mode mixity ratio for instability so as to bring it in a range more consistent with experiments. Interesting formulae are also derived for the distributions of the perturbed stress intensity factors and energy-release-rate, in the special case of perturbations of the crack surface and front obeying the principle of local symmetry and having reached a stationary state (corresponding to instability modes in near-threshold conditions).
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crack Propagation from a pre existing flaw at a notch root i introduction and general form of the stress intensity factors at the initial crack tip
International Journal of Fracture, 2000Co-Authors: Jean-baptiste Leblond, Pierre MouroAbstract:This paper and its companion are devoted to the study of crack kinking from some small pre-existing crack originating from a notch root (the notch root radius being zero). Both the notch boundaries and the initial crack are allowed to be curved; also, the geometry of the body and the loading are totally arbitrary. The ingredients required are knowledge of the stress intensity factors at the initial crack tip and use of a suitable mixed mode Propagation Criterion. This paper is devoted to the first point, and more specifically to establishing the general (that is, not yet fully explicit) form of the formulae giving these stress intensity factors. The method used is based on changes of scale (homogeneity properties of the equations of elasticity) on the one hand, and on continuity of the displacement and stresses at a given, fixed point with respect to the crack length on the other hand. The formulae derived for the stress intensity factors at the tip of the small crack are of universal value: they apply to any situation, whatever the geometry of the body, the notch and the crack and whatever the loading, the stress intensity factors depending always only upon the `stress intensity factor of the notch' (the multiplicative coefficient of the singular stress field near the notch root in the absence of the crack), the length of the crack, the aperture angle of the notch and the angle between its bisecting line and the direction of the crack.
Wei Dong - One of the best experts on this subject based on the ideXlab platform.
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on fracture process zone and crack extension resistance of concrete based on initial fracture toughness
Construction and Building Materials, 2013Co-Authors: Wei Dong, Xiangming Zhou, Zhimin WuAbstract:Abstract In this paper, a numerical approach is developed to investigate the evolution of fracture process zone (FPZ) during the complete fracture process in concrete structures by using stress intensity factor-superposition method. In this approach, the initial fracture toughness K IC ini , as an inherent material property, is introduced to form a crack Propagation Criterion for concrete. The developed numerical approach is then employed to analyze the complete fracture process of three series of notched concrete beams under three-point bending. It is found that the numerical results agree well with experimental ones published in literature through which the developed numerical approach, with an initial fracture toughness based crack Propagation Criterion, for fracture analysis of concrete is validated. The verified numerical approach is then utilized to simulate the complete fracture process of a series of concrete square plates with different sizes and/or initial crack length-to-depth ratio (a0/D). The effects of a0/D on evolution of FPZ length (aFPZ), especially after the FPZ is fully developed, are examined based on numerical analysis results. It is found that there are three different types of aFPZ variation with respect to a0/D, viz. (i) aFPZ keeps increasing after FPZ is fully developed. (ii) aFPZ turns to decrease from the peak value after FPZ is fully developed. (iii) FPZ is not fully developed. Finally, features of KR-curve for concrete are investigated based on the developed numerical method, and it is found that KR-curve of concrete is size-dependent when the effects of FPZ variation are taken into account.
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calculating crack extension resistance of concrete based on a new crack Propagation Criterion
Construction and Building Materials, 2013Co-Authors: Wei Dong, Zhimin Wu, Xiangming ZhouAbstract:Abstract A crack Propagation Criterion was proposed for model I crack in concrete by using the initial fracture toughness K IC ini as an inherent material property. Based on this Criterion, crack begins to propagate when the difference, between the stress intensity factors caused by the applied load K I P and that by the cohesive stress K I σ , exceeds K IC ini . Finite element analyses was then carried out to calculate the complete load vs. crack mouth opening displacement (P-CMOD) curve, the critical crack Propagation length ΔaC and the unstable fracture toughness K IC un for notched beams under three-point bending. It was found that numerical results showed a good agreement with the experimental ones. Based on this crack Propagation Criterion, crack extension resistance, in terms of stress intensity factor, KR being able to consider the variation of fracture process zone (FPZ) was employed for describing crack Propagation in concrete. KR is composed of K IC ini and K I σ , which is actually equal to the driving action of crack extension. It was concluded that given the elastic modulus E, the uniaxial tensile strength ft, the fracture energy GF and K IC ini , the complete fracture process in concrete and the KR-curve of concrete can be calculated based on the numerical method. Finally, discussion was made on the effects of fracture process zone, GF and specimens geometries on KR-curve.
Zhenjun Yang - One of the best experts on this subject based on the ideXlab platform.
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automatic modelling of cohesive crack Propagation in concrete using polygon scaled boundary finite elements
Engineering Fracture Mechanics, 2012Co-Authors: Ean Tat Ooi, Chongmin Song, F Tinloi, Zhenjun YangAbstract:An automatic cohesive crack Propagation modelling methodology for quasi-brittle materials using polygon elements is presented. Each polygon is treated as a subdomain that is modelled by the scaled boundary finite element method (SBFEM). Generalised stress intensity factors (SIFs) based on matrix power function solutions of singular stress fields obtained from the SBFEM following standard finite element stress recovery procedures is used to evaluate the crack Propagation Criterion and determine the crack Propagation direction. Interface elements model the fracture process zones and are automatically inserted into the polygon mesh as the crack propagates. A shadow domain procedure couples the polygons and interface elements. It computes the load–displacement response and crack Propagation Criterion, taking into account the cohesive tractions on the crack edges that are modelled as side-face tractions in the SBFEM. Cracks are propagated using a simple, yet flexible local remeshing procedure that can remesh any arbitrary polygon. Only minimal changes are made to the global mesh structure each time the remeshing algorithm is called. Five cohesive crack Propagation benchmarks are modelled to validate the developed method and demonstrate its salient features.
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fully automatic modelling of mixed mode crack Propagation using scaled boundary finite element method
Engineering Fracture Mechanics, 2006Co-Authors: Zhenjun YangAbstract:Abstract The newly-developed scaled boundary finite element method (SBFEM) is able to calculate stress intensity factors directly because the singularity in stress solutions at crack tips is analytically represented. By taking this advantage, a mixed-mode crack Propagation model based on linear elastic fracture mechanics (LEFM) was developed in this study. A domain is first divided into a few subdomains. Because the dimensions and shapes of subdomains can be flexibly varied and only the domain boundaries or common edges between subdomains are discretised in the SBFEM, a remeshing procedure as simple as in boundary element methods was developed with minimum mesh changes whereas the generality and flexibility of the FEM is well maintained. Fully-automatic modelling of mixed-mode crack Propagation is then achieved by combining the remeshing procedure with a Propagation Criterion. Three mixed-mode examples were modelled. Comparisons of the numerical results with those from available publications show that the developed model is capable of predicting crack trajectories and load–displacement relations accurately and efficiently.
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finite element modelling of multiple cohesive discrete crack Propagation in reinforced concrete beams
Engineering Fracture Mechanics, 2005Co-Authors: Zhenjun Yang, Jian Fei ChenAbstract:Abstract This paper presents a finite element (FE) model for fully automatic simulation of multiple discrete crack Propagation in reinforced concrete (RC) beams. The discrete cracks are modelled based on the cohesive/fictitious crack concept using nonlinear interface elements with a bilinear tensile softening constitutive law. The model comprises an energy-based crack Propagation Criterion, a simple remeshing procedure to accommodate crack Propagations, two state variable mapping methods to transfer structural responses from one FE mesh to another, and a local arc-length algorithm to solve system equations characterised by material softening. The bond-slip behaviour between reinforcing bars and surrounding concrete is modelled by a tension-softening element. An example RC beam with well-documented test data is simulated. The model is found capable of automatically modelling multiple crack Propagation. The predicted cracking process and distributed crack pattern are in close agreement with experimental observations. The load–deflection relations are accurately predicted up to a point when compressive cracking becomes dominant. The effects of bond-slip modelling and the efficiency and effectiveness of the numerical algorithms, together with the limitations of the current model, are also discussed.
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fully automatic modelling of cohesive discrete crack Propagation in concrete beams using local arc length methods
International Journal of Solids and Structures, 2004Co-Authors: Zhenjun Yang, Jian Fei ChenAbstract:Abstract A finite element model for fully automatic simulation of multi-crack Propagation in concrete beams is presented. Nonlinear interface elements are used to model discrete cracks with concrete tensile behaviour represented by the cohesive crack model. An energy-based crack Propagation Criterion is used in combination with a simple remeshing procedure to accommodate crack Propagation. Various local arc-length methods are employed to solve the material-nonlinear system equations characterised by strong snap-back. Three concrete beams, including a single-notched three-point bending beam (mode-I fracture), a single-notched four-point shear beam (mixed-mode fracture) and a double-notched four-point shear beam (mixed-mode fracture), are modelled. Comparisons of the numerical results with experimental data show that this model is capable of fully automatically modelling concrete tensile fracture process with accurate pre/post-peak load–displacement responses and crack trajectories. Its mesh-objective nature, together with the high efficiency of the energy crack Propagation Criterion, makes using coarse meshes to obtain reasonably accurate simulations possible. The local arc-length numerical algorithms are found to be capable of tracking complex equilibrium paths including strong snap-back with high robustness, generality and efficiency.
Alain Karma - One of the best experts on this subject based on the ideXlab platform.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part ii drift of fracture facets in mixed mode i ii iii
Journal of The Mechanics and Physics of Solids, 2020Co-Authors: Laurent Ponson, Alain Karma, Aditya Vasudevan, Jean-baptiste LeblondAbstract:Abstract In earlier papers (Leblond et al., 2011; 2019), we presented linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I+III, based on a “double” Propagation Criterion combining (Griffith, 1920)’s energetic condition and (Goldstein and Salganik, 1974)’s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its Propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part ii drift of fracture facets in mixed mode i ii iii
arXiv: Soft Condensed Matter, 2019Co-Authors: Aditya Vasudevan, Jean-baptiste Leblond, Laurent Ponson, Alain KarmaAbstract:In earlier papers (Leblond this http URL., 2011, 2019), we presented linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I+III, based on a "double'' Propagation Criterion combining Griffith (1920)'s energetic condition and Goldstein and Salganik (1974)'s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the "threshold'' value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its Propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.
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configurational stability of a crack propagating in mixed mode i ii iii
International Conference on Theoretical Applied and Experimental Mechanics, 2019Co-Authors: Jean-baptiste Leblond, Alain Karma, Laurent Ponson, Aditya VasudevanAbstract:In some previous papers, we presented some linear stability analyses of the coplanar Propagation of a crack loaded in mixed-mode I + III, using a Propagation Criterion combining a Griffith-type energetic condition and Goldstein and Salganik’s “principle of local symmetry”. In the last one, the local value of the fracture energy was no longer considered as a constant but heuristically permitted to depend upon the ratio of the local mode III to mode I stress intensity factors. As a result, a much improved agreement of theory and experimental observations was obtained for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar Propagation becomes unstable. This analysis is extended here to the situation, of considerable practical significance, where a small additional mode II loading component is present in the initially planar configuration of the crack. This component induces a small, general kink of this crack from the moment it is applied. The main novelty resulting from its application is that the instability modes, present above the threshold, must drift along the crack front during its Propagation. It is hoped that this prediction will be useful to theoretically interpret a number of experiments where such a drifting motion was indeed observed but left unexplained.
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configurational stability of a crack propagating in a material with mode dependent fracture energy part i mixed mode i iii
Journal of The Mechanics and Physics of Solids, 2019Co-Authors: Jean-baptiste Leblond, Alain Karma, Laurent Ponson, Aditya VasudevanAbstract:Abstract In a previous paper (Leblond et al., 2011), we proposed a theoretical interpretation of the experimentally well-known instability of coplanar crack Propagation in mode I+III. The interpretation relied on a stability analysis based on analytical expressions of the stress intensity factors for a crack slightly perturbed both within and out of its original plane, due to Gao and Rice (1986) and Movchan et al. (1998), coupled with a double Propagation Criterion combining Griffith (1920)’s energetic condition and Goldstein and Salganik (1974)’s principle of local symmetry. Under such assumptions instability modes were indeed evidenced for values of the mode mixity ratio - ratio of the mode III to mode I stress intensity factors applied remotely - larger than some threshold depending only on Poisson’s ratio. Unfortunately, the predicted thresholds were much larger than those generally observed for typical values of this material parameter. While the subcritical character of the nonlinear bifurcation from coplanar to fragmented fronts has been proposed as a possible explanation for this discrepancy (Chen et al., 2015), we propose here an alternative explanation based on the introduction of a constitutive relationship between the fracture energy and the mode mixity ratio, which is motivated by experimental observations. By re-examining the linear stability analysis of a planar propagating front, we show that such a relationship suffices, provided that it is strong enough, to lower significantly the threshold value of the mode mixity ratio for instability so as to bring it in a range more consistent with experiments. Interesting formulae are also derived for the distributions of the perturbed stress intensity factors and energy-release-rate, in the special case of perturbations of the crack surface and front obeying the principle of local symmetry and having reached a stationary state (corresponding to instability modes in near-threshold conditions).
