Hydrogen Diffusion Towards the Fracture Process Zone

Mode I and mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity

Micromechanical modeling of damage evolution and fracture behavior in particle reinforced metal matrix composites based on the conventional theory of mechanism-based strain gradient plasticity

The effective threshold for fatigue crack propagation: a plastic size effect?

Modeling damage and fracture within strain-gradient plasticity

Mixed mode near-tip fields for cracks in materials with strain-gradient effects

Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations

Study on fracture parameters and fracture process zone of manufactured-sand recycled aggregate concrete

With introducing the strain gradient into plasticity theory, the crack field singularity at the crack tip changes. Characterization of the crack in strain-gradient dependent materials has not found a common consensus. In the present work the crack tip field is systematically investigated within the frame of the strain-gradient plasticity using the element-free Galerkin method. Under both small scale yielding and finite yielding conditions the crack field in strain-gradient plasticity consists of three zones: The elastic K-field, the known plastic HRR-field dominated by the known energy release rate, \({\mathcal G}\), and the hyper-singular stress field which cannot be characterized by the known fracture mechanics parameters. Effects of the finite strains have been considered for both small scale yielding and finite cracked specimens. The computational results show that the finite strains do not change the characterization of the crack tip fields under the strain-gradient plasticity. In all investigated cases the hyper-singular zone is small (\({r < \mathcal G/\sigma_0}\)) and well contained by the HRR zone under the \({\mathcal G}\) dominance condition. The hyper-singular zone is in the size of \({r/(\mathcal G/\sigma_0)}\) and may grow with the material length, but decrease with applied load. The known elastic-plastic fracture mechanics parameter, \({\mathcal G}\), can be directly applied to characterize the crack under strain-gradient plasticity, within the intrinsic material length much smaller than the overall component size, l < 0.1%L0. In this case the strain-gradient term in the gradient plasticity will not affect description of cracks.

Investigation of fine-scale dislocation distributions at complex geometrical structures by using HR-EBSD and a comparison with conventional EBSD

The Bauschinger and size effects in the thin-film plasticity theory arising from the defect-energy of geometrically necessary dislocations (GNDs) are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations (or pile-ups) moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the workconjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defectenergy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.

On the localisation of the FPZ under a pure mode II load identified by a hybrid method

Slip-discreteness-corrected strain gradient crystal plasticity (SDC-SGCP) theory

ABSTRACT: To study the effects of loading rate on the fracture characteristics, sandstone samples with a center notch were used in three-point bend experiment for the loading rates of 0.0004, 0.004, 0.04, 0.4 and 4mm/min of crack mouth opening displacement. We divided the fracture process zone into elastic zone (εxx &amp;lt; 0.08%), plastic zone (0.08% &amp;lt; εxx &amp;lt; 0.4%) and damage zone (εxx &amp;gt; 0.4%) based on the displacement and strain field around the fracture tip. The shape of the fracture process zone is candle-like, and the damage zone is within the plastic zone. The fracture process zone length and width are reduced by 36% and 23% when the loading rate increases by 3 orders of magnitude. The damage zone decreases from 56% to 40% with 3 orders' increase in loading rate; that is, the plasticity is enhanced from high fracture velocity. The rough fracture surface is induced by local microcrack slip and expansion in the fracture process zone from high loading rates. The proposed method of dividing the fracture process zone into a plastic-damage zone is of significance for studying the stress distribution and fracture energy calculation in the rock fracture. 1. INTRODUCTION The rock is a quasi-brittle material with mineral particles, cracks and pores, leading to a micro-crack zone in the fracture tip subjected to an external load, called fracture process zone (FPZ). FPZ generally refers to the region of fracture from fracture initiation to instability, and its length can be considered as subcritical propagation length. The mechanisms of microcrack, branching and slip along cracks lead to nonlinear fracture growth behaviors of rock. The stress-intensity factor (k) describes the elastic stress distribution with little yield zone at the crack tip. The crack growth occurs when k equals to fracture toughness (kc), a material property independent of fracture velocity. In general, the fracture velocity is positively correlated with loading rate. The relationship between fracture velocity and crack driving force is often described by a power law or an Arrhenius law (Ponson L, 2009). To involve the effects of fracture velocity, Paris, (1961) proposed the power law relationship between stress-intensity factor range Δk and crack growth rate da/dN to study fatigue failure. Atkinson, (1984) reviewed the experimental data on the subcritical crack growth in geological materials, indicating that a power equation (v∼kn) can be capable of describing fracture velocity - stress intensity factor. Zhou, (2009) et al. used three-point bend tests to determine the critical strain energy density factor of Huanglong limestone with loading rate ranging from 10-4∼10-1mm/s. A cohesive zone model (CZM) was proposed based on the traction-separation law (TSL) to study both crack initiation and propagation (Dugdale D S, 1960). To add rate effect to the CZM, two methods were raised, including the rate-dependent constitutive model in the bulk material and the rate-dependency in the TSL (Salih S, 2018). The non-negligible nonlinear deformation around the fracture tip, namely the FPZ, is responsible for rate-dependent rock fracture growth.

The enhanced strain-gradient plasticity theories formulate a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical plasticity and the classical continuum plasticity. To assess the size effects it is indispensable to incorporate an intrinsic material length parameter into the constitutive equations. However, the full utility of gradient-type theories hinges on one’s ability to determine the constitutive length-scale parameter. The classical continuum plasticity is unable to predict properly the evolution of the material flow stress since the local deformation gradients at a given material point are not accounted for. The gradient-based flow stress is commonly assumed to rely on a mixed type of dislocations: statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs). In this work a micromechanical model to assess the coupling between SSDs and GNDs, which is based on the Taylor’s hardening law, is used to identify the deformation-gradient-related intrinsic length-scale parameter in terms of measurable microstructural physical parameters. This work also presents a method for identifying the length-scale parameter from micro-indentation tests.

The last 3 decades of vigorous enforcement of U.S. antimerger laws is based on the market concentration doctrine, one of the oldest and most controversial propositions in industrial economics. This doctrine, which is an implication of oligopoly models in the tradition of Cournot ([1838] 1927) and Nash (1950), holds that the level of industry concentration is a reliable index of the industry's market power. The empirical implication is that a relatively high level of industry concentration, which in the presence of entry barriers is believed to facilitate intraindustry collusion or dominant-firm pricing, should be associated with relatively large industrywide monopoly rents.' Following Bain (1951), numerous The market concentration doctrine predicts that a horizontal merger is more likely to have collusive, anticompetitive effects the greater the merger-induced change in industry concentration. Since a collusive, anticompetitive merger generates an increase in the industry's quality-adjusted product price (or a decrease in factor prices), it also follows from the doctrine that the mergerinduced expected benefits to the product market rivals of the merging firms should be an increasing function of the concentration change. The empirical results of this paper, which are based on the industry wealth effect of a large sample of horizontal mergers, including cases found in violation of antimonopoly laws, fail to support this prediction. This conclusion is robust with respect to assumptions concerning the probability that a proposed merger will be prevented by the law enforcement agencies, and it continues to hold after transforming the industry wealth effect into a hypothetical, constant expected change in the industry's product price. The results imply that the levels of concentration and market shares found in the Department of Justice's merger guidelines are unlikely to identify truly anticompetitive mergers. * I wish to thank Paul Asquith, Gregg Jarrell, Rex Thompson, Walter Vandaele, the participants of the economics workshop at the Antitrust Division of the U.S. Department of Justice, and a referee of this Journal for helpful comments. Earlier drafts were presented at the 1983 meetings of the European Association for Research in Industrial Economics and at the 1984 meetings of the Western Finance Association. Financial support from the Social Sciences and Humanities Research Council of Canada (grant no. 494-83-0091) and the U.S. Federal Trade Commission is also gratefully acknowledged. 1. A closely related but somewhat less general prediction is that high levels of concentration should be associated with relatively high, supracompetitive product prices. Although