Crack formation in composites through a spring model

Sadhukhan, Supti; Dutta, Tapati; Tarafdar, Sujata

doi:10.1016/j.physa.2010.10.032

Cited by 19 publications

(14 citation statements)

References 19 publications

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“…As drying continues, both for small and large disorder, the newly created free surfaces hinder the appearance of large avalanches by relaxing the stress in the remaining intact parts of the spring network. The overall shape of cracks is similar to what has been observed for drying processes in composite materials, where the disorder comes from random distributions of the three types of bonds representing the interaction between the ingredients of a composite (see [11][12][13]). …”

Section: Breakup Processsupporting

confidence: 69%

“…The quenched disorder of the material is represented by a random distribution of the bonds' breaking thresholds, and the amount of disorder is given by the distribution's width. There are numerous studies in the literature on the spatial arrangement of cracks [10][11][12][13][14][15]. Hereby, we focus on the temporal evolution of the crack by analyzing the statistics of avalanches of breaking bonds.…”

Section: Introductionmentioning

confidence: 99%

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Effect of disorder on temporal fluctuations in drying-induced cracking

2011

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We investigate by means of computer simulations the effect of structural disorder on the statistics of cracking for a thin layer of material under uniform and isotropic drying. For this purpose, the layer is discretized into a triangular lattice of springs with a slightly randomized arrangement. The drying process is captured by reducing the natural length of all springs by the same factor, and the amount of quenched disorder is controlled by varying the width ξ of the distribution of the random breaking thresholds for the springs. Once a spring breaks, the redistribution of the load may trigger an avalanche of breaks, not necessarily as part of the same crack. Our computer simulations revealed that the system exhibits a phase transition with the amount of disorder as control parameter: at low disorders, the breaking process is dominated by a macroscopic crack at the beginning, and the size distribution of the subsequent breaking avalanches shows an exponential form. At high disorders, the fracturing proceeds in small-sized avalanches with an exponential distribution, generating a large number of microcracks, which eventually merge and break the layer. Between both phases, a sharp transition occurs at a critical amount of disorder ξ(c)=0.40±0.01, where the avalanche size distribution becomes a power law with exponent τ=2.6±0.08, in agreement with the mean-field value τ=5/2 of the fiber bundle model. Moreover, good quality data collapses from the finite-size scaling analysis show that the average value of the largest burst ⟨Δ(max)⟩ can be identified as the order parameter, with β/ν=1.4 and 1/ν≃1.0, and that the average ratio ⟨m(2)/m(1)⟩ of the second m(2) and first moments m(1) of the avalanche size distribution shows similar behavior to the susceptibility of a continuous transition, with γ/ν=1, 1/ν≃0.9. These results suggest that the disorder-induced transition of the breakup of thin layers is analogous to a continuous phase transition.

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Section: Breakup Processsupporting

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Effect of disorder on temporal fluctuations in drying-induced cracking

2011

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“…In simulating the crack formation, we utilize the code for a 2-dimensional spring network, which was developed in [17] and used in [25]. It is modified here for application to a circular system, since the radial symmetry of the electric field must be implemented.…”

Section: A the Spring Network Modelmentioning

confidence: 99%

“…This form has been used in [25] as well as in the present paper. The parameters have been assigned values b = 0.10 and h = 1.02.…”

Section: The Desiccation Rulementioning

confidence: 99%

Electric-field-induced crack patterns: Experiments and simulation

et al. 2012

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We report a study of crack patterns formed in laponite gel drying in an electric field. The sample dries in a circular petri dish and the field is radial, acting inward or outward. A system of radial cracks forms in the setup with the center terminal positive, while predominantly cross-radial cracks form when the center is at a negative potential. The laponite accumulates near the negative terminal making the layer thicker at this end. A spring model on a square lattice is used to simulate the desiccation crack formation, with an additional radial force acting due to the electric field. With the radial force acting outward, radial cracks form and for the reversed field cross-radial cracks form. This conforms to the observation that laponite platelets become effectively positive due to overcharging and are attracted towards the negative terminal.

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“…to the problem are typically based on discrete models such as fiber bundles ( [5][6][7][8][9][10], and references therein) or lattices of springs [11], beams [12,13], and fuses [14]. In Monte Carlo and molecular dynamics simulations of such discrete models, the breaking of a single cohesive element can trigger an entire avalanche of failure events, which corresponds to the acoustic emissions observed in experiments [3,[15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Time evolution of damage due to environmentally assisted aging in a fiber bundle model

et al. 2013

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Damage growth in composite materials is a complex process which is of interest in many fields of science and engineering. We consider this problem in a fiber bundle model where fibers undergo an aging process due to the accumulation of damage driven by the locally acting stress in a chemically active environment. By subjecting the bundle to a constant external load, fibers fail either when the load on them exceeds their individual intrinsic strength or when the accumulated internal damage exceeds a random threshold. We analyze the time evolution of the breaking process under low external loads where aging of fibers dominates. In the mean field limit, we show analytically that the aging system continuously accelerates in a way which can be characterized by an inverse power law of the event rate with a singularity that defines a failure time. The exponent is not universal; it depends on the details of the aging process. For localized load sharing, a more complex damage process emerges which is dominated by distinct spatial regions of the system with different degrees of stress concentration. Analytical calculations revealed that the final acceleration to global failure is preceded by a stationary accumulation of damage. When the disorder is strong, the accelerating phase has the same functional behavior as in the mean field limit. The analytical results are verified by computer simulations.

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Crack formation in composites through a spring model

Cited by 19 publications

References 19 publications

Effect of disorder on temporal fluctuations in drying-induced cracking

Effect of disorder on temporal fluctuations in drying-induced cracking

Electric-field-induced crack patterns: Experiments and simulation

Time evolution of damage due to environmentally assisted aging in a fiber bundle model

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