A Strain Gradient Model for Fracture Prediction in Brittle Materials

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Jia Li
Keyword(s):  
Stress Concentration ◽  
Strain Gradient ◽  
Brittle Materials ◽  
Main Idea ◽  
Gradient Elasticity ◽  
Critical Energy ◽  
Engineering Structures ◽  
Critical Energy Release Rate ◽  
Proposed Model ◽  
Two Parameters

In this paper, we present a new model to predict the fracture in brittle materials from a geometrical weakness presenting an arbitrary stress concentration. The main idea is to combine the strain gradient elasticity with a cohesive model that includes both the displacement and the rotation jumps between the cohesive surfaces in the separation law. Three material parameters were used in the establishment of the fracture criterion. The first two parameters are the commonly used σc, the ultimate stress, and Gc, the critical energy release rate. The third parameter is the characteristic length l as in most of the strain gradient models. The proposed three-parameter model enables to take the different stress concentration levels into account, thus providing a criterion to predict fractures for any stress concentration, whether it is singular or not. Experimental results were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed model is physically reasonable, highly accurate, and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle materials.

Applicability of the Critical Energy Release Rate for Predicting the Growth of a Crack in Nanoscale Materials Applying the Strain Gradient Elasticity Theory

2017 ◽  
Vol 754 ◽  
pp. 185-188 ◽  
Author(s):  
Michal Kotoul ◽  
Petr Skalka
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Elasticity Theory ◽  
Release Rate ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Critical Energy ◽  
Strain Gradient Elasticity ◽  
Critical Energy Release Rate ◽  
Gradient Elasticity Theory

The paper investigates the limits of applicability of the critical energy release rate for predicting the growth of a crack in nanoscale materials applying the strain gradient elasticity theory (SGET) capable to capture size effects, nonlocal material point interactions and surface effects in the form of (phenomenological) higher-order stress/strain gradients.

scholarly journals Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tom Vincent-Dospital ◽  
Alain Cochard ◽  
Stéphane Santucci ◽  
Knut Jørgen Måløy ◽  
Renaud Toussaint
Keyword(s):  
Growth Dynamics ◽  
Critical Energy ◽  
Affine Scaling ◽  
Critical Energy Release Rate ◽  
Spatially Correlated ◽  
Thermally Activated ◽  
Temporal Correlations ◽  
Fracture Dynamics ◽  
Proposed Model ◽  
Subcritical Fracture

AbstractWe present a subcritical fracture growth model, coupled with the elastic redistribution of the acting mechanical stress along rugous rupture fronts. We show the ability of this model to quantitatively reproduce the intermittent dynamics of cracks propagating along weak disordered interfaces. To this end, we assume that the fracture energy of such interfaces (in the sense of a critical energy release rate) follows a spatially correlated normal distribution. We compare various statistical features from the obtained fracture dynamics to that from cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such an approach could reproduce the mean advance of fractures and their local front velocity distribution. Here, we go further by showing that the proposed model also quantitatively accounts for the complex self-affine scaling morphology of crack fronts and their temporal evolution, for the spatial and temporal correlations of the local velocity fields and for the avalanches size distribution of the intermittent growth dynamics. We thus provide new evidence that an Arrhenius-like subcritical growth is particularly suitable for the description of creeping cracks.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

scholarly journals Enhanced Interfacial Shear Strength and Critical Energy Release Rate in Single Glass Fiber-Crosslinked Polypropylene Model Microcomposites

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2552 ◽  
Author(s):  
Uwe Gohs ◽  
Michael Mueller ◽  
Carsten Zschech ◽  
Serge Zhandarov
Keyword(s):  
Shear Strength ◽  
Electron Beam ◽  
Energy Release Rate ◽  
Glass Fiber ◽  
Release Rate ◽  
Interfacial Shear Strength ◽  
Glass Fibers ◽  
Critical Energy ◽  
Interfacial Shear ◽  
Critical Energy Release Rate

Continuous glass fiber-reinforced polypropylene composites produced by using hybrid yarns show reduced fiber-to-matrix adhesion in comparison to their thermosetting counterparts. Their consolidation involves no curing, and the chemical reactions are limited to the glass fiber surface, the silane coupling agent, and the maleic anhydride-grafted polypropylene. This paper investigates the impact of electron beam crosslinkable toughened polypropylene, alkylene-functionalized single glass fibers, and electron-induced grafting and crosslinking on the local interfacial shear strength and critical energy release rate in single glass fiber polypropylene model microcomposites. A systematic comparison of non-, amino-, alkyl-, and alkylene-functionalized single fibers in virgin, crosslinkable toughened and electron beam crosslinked toughened polypropylene was done in order to study their influence on the local interfacial strength parameters. In comparison to amino-functionalized single glass fibers in polypropylene/maleic anhydride-grafted polypropylene, an enhanced local interfacial shear strength (+20%) and critical energy release rate (+80%) were observed for alkylene-functionalized single glass fibers in electron beam crosslinked toughened polypropylene.

Scale-Dependent Crack Modeling for Investigation the Effect of Geometrically Necessary Dislocations in Micro/Nano Grain Size of Copper

2016 ◽  
Vol 15 ◽  
pp. 1-16 ◽  
Author(s):  
Amin Zaami ◽  
Ali Shokuhfar
Keyword(s):  
Grain Size ◽  
Stress Concentration ◽  
Strain Gradient ◽  
Stress Concentration Factor ◽  
Size Effects ◽  
Crack Tip ◽  
Length Scale ◽  
State Variables ◽  
Dependent Model ◽  
Homogeneous Strain

In this study, a scale-dependent model is employed to investigate the size effects of copper on the behavior of the crack-tip. This model includes the homogeneous and non-homogeneous strain hardening based on the wavelet interpretation of size effect. Introducing additional micro/nano structural considerations together with decreasing grain size, different size effects can be obtained. As the size dependency is not taken into account in conventional plasticity, an enhanced theory which is related to the strain gradient introduces a length scale will give more realistic representations of state variables near the crack-tip. Accordingly, the contribution of geometrically necessary dislocations (GNDs) activity on strengthening and stress concentration factor is identified in the crack-tip. Finally, the affected zone which is dominated by presence of GNDs is identified

scholarly journals Non-local criteria for the borehole problem: Gradient Elasticity versus Finite Fracture Mechanics

Meccanica ◽  
2021 ◽  
Author(s):  
A. Sapora ◽  
G. Efremidis ◽  
P. Cornetti
Keyword(s):  
Stress Concentration ◽  
Fracture Mechanics ◽  
Elastic Material ◽  
Fracture Criterion ◽  
Biaxial Loading ◽  
Gradient Elasticity ◽  
Energy Conditions ◽  
Material Behaviour ◽  
Finite Fracture Mechanics ◽  
Non Local

AbstractTwo nonlocal approaches are applied to the borehole geometry, herein simply modelled as a circular hole in an infinite elastic medium, subjected to remote biaxial loading and/or internal pressure. The former approach lies within the framework of Gradient Elasticity (GE). Its characteristic is nonlocal in the elastic material behaviour and local in the failure criterion, hence simply related to the stress concentration factor. The latter approach is the Finite Fracture Mechanics (FFM), a well-consolidated model within the framework of brittle fracture. Its characteristic is local in the elastic material behaviour and non-local in the fracture criterion, since crack onset occurs when two (stress and energy) conditions in front of the stress concentration point are simultaneously met. Although the two approaches have a completely different origin, they present some similarities, both involving a characteristic length. Notably, they lead to almost identical critical load predictions as far as the two internal lengths are properly related. A comparison with experimental data available in the literature is also provided.

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