Dynamic quantized fracture mechanics

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Dynamic quantized fracture mechanics

Abstract A new quantum action-based theory, dynamic quantized fracturemechanics DQFMis presented that modifies continuum-based dynamic fracture mechanics DFM.

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The crack propaga-tion is assumed as quantized in both space and time. The static limit case corresponds to quantized fracture mechanics QFMthat we have recently developed to predict the strength of nanostruc-tures.

DQFM predicts the well-known forbidden strength and crack speedbands—observed in atom-istic simulations—which are unexplained by con-tinuum-based approaches.

Simple examples are discussed: i strengths predicted by DQFM for static loads are compared with experi-mental and numerical results on carbon nanotubes containing nanoscale defects; ii the dynamic frac-ture initiation toughness predicted by DQFM is compared with experimental results on microsec.

Documents: Advanced Search Include Citations. Abstract Abstract A new quantum action-based theory, dynamic quantized fracturemechanics DQFMis presented that modifies continuum-based dynamic fracture mechanics DFM. Powered by:.Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials.

It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. In modern materials sciencefracture mechanics is an important tool used to improve the performance of mechanical components. It applies the physics of stress and strain behavior of materials, in particular the theories of elasticity and plasticityto the microscopic crystallographic defects found in real materials in order to predict the macroscopic mechanical behavior of those bodies.

Fractography is widely used with fracture mechanics to understand the causes of failures and also verify the theoretical failure predictions with real life failures.

Fracture mechanics

The prediction of crack growth is at the heart of the damage tolerance mechanical design discipline. The processes of material manufacture, processing, machining, and forming may introduce flaws in a finished mechanical component. Arising from the manufacturing process, interior and surface flaws are found in all metal structures. Not all such flaws are unstable under service conditions. Fracture mechanics is the analysis of flaws to discover those that are safe that is, do not grow and those that are liable to propagate as cracks and so cause failure of the flawed structure.

Despite these inherent flaws, it is possible to achieve through damage tolerance analysis the safe operation of a structure. Fracture mechanics as a subject for critical study has barely been around for a century and thus is relatively new. Fracture mechanics should attempt to provide quantitative answers to the following questions: [2]. Griffith — thus the term Griffith crack — to explain the failure of brittle materials.

A theory was needed to reconcile these conflicting observations. Also, experiments on glass fibers that Griffith himself conducted suggested that the fracture stress increases as the fiber diameter decreases. Hence the uniaxial tensile strength, which had been used extensively to predict material failure before Griffith, could not be a specimen-independent material property.

Griffith suggested that the low fracture strength observed in experiments, as well as the size-dependence of strength, was due to the presence of microscopic flaws in the bulk material. To verify the flaw hypothesis, Griffith introduced an artificial flaw in his experimental glass specimens. The artificial flaw was in the form of a surface crack which was much larger than other flaws in a specimen. An explanation of this relation in terms of linear elasticity theory is problematic.

Linear elasticity theory predicts that stress and hence the strain at the tip of a sharp flaw in a linear elastic material is infinite. To avoid that problem, Griffith developed a thermodynamic approach to explain the relation that he observed. The growth of a crack, the extension of the surfaces on either side of the crack, requires an increase in the surface energy.

Briefly, the approach was:.It appears to me that there is more and more research done on discrete approaches to modelling fracture.

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Especially for brittle or quasi-brittle materials these methods are undergoing a revival. I am not sure why this is the case. I am also not in the position to judge if this revival is useful. I just had recently a look at some of these models and I found these discrete models to be suitable for description of fracture in heterogeneous materials, where cracks appear at many different positions. However, I am confused by literature in the field, even if I just focus on fracture.

There are models called lattice, particle, disctinct element, discrete element etc. These names seem to be used in different ways, which makes it difficult to communicate developments in this field. In a recent paper we have tried to distinguish between lattice and particle models for fracture in the following way:. In particle models, the arrangement of particles can evolve, so that neighbours of particles might change during analysis.

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Therefore, particle models are suitable to describe processes involving large displacements. On the other hand, in lattice models the connectivity between nodes is not changed during the analysis, so that contact determination is not required.

Consequently, lattice models are mainly suitable for analysis involving small strains. I was wondering if anyone would agree with the above classification. I think one should come up with something more refined and complete. Any suggestions? I have looked at lattice models for other purposesand especially the interesting work of Prof.

I can't comment on these methods perhaps Suku can tell us why lattice models are useful but just wanted to make the following comment. Other that the numerical methods you mentioned, there are fracture models that assume a minimum crack propagation length to avoid the nonphysical conclusion of Grifith's theory that predicts infinite strength for a vanishing crack size.

In other words, these models assume that crack propagation has a discrete nature. The idea started by the work of Novozhilov and has recently been investigated by several groups. In the literature these models are refereed to as "finite fracture", "quantized fracture", "discrete fracture", etc. After all, isn't it right in the classical analytical solid mechanics itself that a crack is rather unphysically defined as a hole that has zero as the radius of curvature?A new quantum action-based theory, dynamic quantized fracture mechanics DQFMis presented that modifies continuum-based dynamic fracture mechanics DFM.

The crack propagation is assumed as quantized in both space and time. The static limit case corresponds to quantized fracture mechanics QFMthat we have recently developed to predict the strength of nanostructures. DQFM predicts the well-known forbidden strength and crack speed bands — observed in atomistic simulations — which are unexplained by continuum-based approaches.

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Simple examples are discussed i strengths predicted by DQFM for static loads are compared with experimental and numerical results on carbon nanotubes containing nanoscale defects; ii the dynamic fracture initiation toughness predicted by DQFM is compared with experimental results on microsecond range impact failures of T3 aircraft aluminum alloy.

Since LEFM has been successfully applied also at the geophysics size-scale, it is conceivable that DQFM theory can treat objects that span at least 15 orders of magnitude in size.

This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. A Carpinteri N Pugno ArticleTitle Are the scaling laws on strength of solids related to mechanics or to geometry? Nat Mat 4 — Occurrence Handle Freund LB Dynamic fracture mechanics. Cambridge University Press. Hellan K An Introduction to fracture mechanics. McGraw-Hill Book Company. Y Hirai et al. Google Scholar.

dynamic quantized fracture mechanics

Murakami Stress intensity factors handbook. Publ Pergamon, Oxford UK. Paris Productions Incorporated. Download references. Correspondence to N. Reprints and Permissions.

Dynamic quantized fracture mechanics

Pugno, N. Dynamic quantized fracture mechanics. Int J Fract— Download citation. Received : 06 May Accepted : 07 August Issue Date : July Search SpringerLink Search. Abstract A new quantum action-based theory, dynamic quantized fracture mechanics DQFMis presented that modifies continuum-based dynamic fracture mechanics DFM. Immediate online access to all issues from Then, static and dynamic three-point bending tests were conducted on these dynamically damaged specimens, respectively.

In the cyclic impact loading tests, the dynamic elastic modulus decreases gradually as the impact number increases, but dynamic cumulative damage exhibits a growing trend. In the static and dynamic three-point bending tests, when dynamic cumulative damage is less than 0.

Through the quantitative analysis of fracture surface morphologies, the roughness and area of the fracture surfaces increase with an increasing dynamic cumulative damage.

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Under the same dynamic cumulative damage of the specimens, both the roughness and area of the surfaces fractured by static three-point bending are larger than those fractured by dynamic three-point bending. With the increasing demand for the development of underground engineering, rock dynamics play an increasingly important role [ 1 — 4 ]. In this research field, the effects of environmental factors freeze-thaw cycles, chemical corrosion, and thermal damage on the rock dynamic fracture properties have been studied in depth.

For example, to study the couple effects of freeze-thaw cycles and dynamic loads on the fracture mechanism of sandstone, Chen et al. Yu et al. Li et al. In the field of rock statics, many scholars have made great efforts to study the rock static fracture properties and achieved many important results.

For example, Han et al. Hua et al. To study the effect of thermal damage on the fracturing properties of granite, Miao et al. To clarify the effect of the testing method type and specimen size on fracture toughness, Kataoka et al. To investigate the energy storage and dissipation characteristics during the tension-type failure process of marble, Gong et al. From the above discussion, it can be seen that the current studies mainly focus on the effects of environmental factors on rock dynamic and static fracture properties.

However, few studies have revealed the fracture properties of rocks after being damaged dynamically. After construction, the reserved surrounding rock bears the static load brought by the redistribution of the in situ rock stress for a long time, and it also encounters dynamic loadings from seismic activity. Once the defect area in the rock breaks, it may induce accidents.

Therefore, a comprehensive understanding of the static and dynamic fracture properties of rocks after being damaged dynamically and their differences are of great significance in engineering construction and accident prevention.

In this study, cyclic impact loading tests were first performed to prepare a batch of dynamically damaged NSCB marble specimens. Then, static and dynamic three-point bending tests were performed on these specimens to investigate the variations of the fracturing properties. On the aspect of fracture surface morphologies, the roughness and area of the fracture surfaces were quantitatively analysed. According to the contrast analysis results of static and dynamic fracture properties of the damaged marble, it can provide certain reference meaning for the construction and safety protection of rock engineering.

The rock material used in the tests was marble taken from a quarry in Dali, Yunnan Province, China. The marble block is white in colour, and its basic physical and mechanical properties were tested in the laboratory Table 1.Using an equivalent smooth blunt crack for a given fractal crack, we show that assuming that radius of curvature of the corresponding blunt crack is a material property, the crack roughens while propagating, i.

In other words, the presence of the Mirror-Mist-Hackle phenomenon for fractal cracks is analytically demonstrated. Unable to display preview. Download preview PDF.

dynamic quantized fracture mechanics

Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Finite Fracture Mechanics for Fractal Cracks. Conference paper. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Balankin, A. Physics of fracture and mechanics of self-affine cracks. Engineering Fracture Mechanics57 2 ,— Google Scholar. Barenblatt, G. Engineering Fracture Mechanics CrossRef Google Scholar.

Borodich, F. Fracture energy in a fractal crack propagating in concrete or rock. Doklady Akademii Nauk, — Some fractal models of fracture.Thanks for helping us catch any problems with articles on DeepDyve.

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Include any more information that will help us locate the issue and fix it faster for you. A new quantum action-based theory, dynamic quantized fracture mechanics DQFMis presented that modifies continuum-based dynamic fracture mechanics DFM. The crack propagation is assumed as quantized in both space and time. The static limit case corresponds to quantized fracture mechanics QFMthat we have recently developed to predict the strength of nanostructures.

DQFM predicts the well-known forbidden strength and crack speed bands — observed in atomistic simulations — which are unexplained by continuum-based approaches. Simple examples are discussed i strengths predicted by DQFM for static loads are compared with experimental and numerical results on carbon nanotubes containing nanoscale defects; ii the dynamic fracture initiation toughness predicted by DQFM is compared with experimental results on microsecond range impact failures of T3 aircraft aluminum alloy.

dynamic quantized fracture mechanics

Since LEFM has been successfully applied also at the geophysics size-scale, it is conceivable that DQFM theory can treat objects that span at least 15 orders of magnitude in size.

International Journal of Fracture — Springer Journals.

Basic fracture mechanics

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dynamic quantized fracture mechanics

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Terminology for discrete approaches to modelling fracture

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