Fractal crushing of ice and brittle solids

1991 ◽  
Vol 433 (1889) ◽  
pp. 469-477 ◽  
Keyword(s):  
Fractal Dimension ◽  
Fragment Size ◽  
Special Role ◽  
Field Observations ◽  
Linear Elastic ◽  
Brittle Solids ◽  
Wide Range ◽  
Elastic Fracture ◽  
Ice Forces ◽  
Fractal Size

A significant ‘scale effect’ is observed when sea ice forces on structures are measured at field scale: the force per unit contact area is not independent of area, but decreases with increasing area. Fragments of broken materials are found to have a fractal size distribution, with a fractal dimension close to 2.5 over a remarkably wide range of fragment size. The research described in this paper brings these two observations together, and shows that they can be explained by a simple model of crushing, which incorporates the relation between fragment size and splitting force predicted by linear elastic fracture mechanics. The model indicates a special role for the fractal dimension of 2.5, and predicts a relation between force and area, consistent with field observations.

SIFs for Radial Cracks in Annular Discs Under Internal and External Shrinkage Pressure and Constant Angular Velocity

2007 ◽  
Author(s):  
A. Sakhaee-Pour ◽  
A. R. Gowhari-Anaraki ◽  
S. J. Hardy
Keyword(s):  
Finite Element ◽  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Coefficient Of Determination ◽  
Linear Elastic ◽  
Crack Configuration ◽  
Wide Range ◽  
Elastic Fracture ◽  
Radial Cracks

Finite element method has been implemented to predict stress intensity factors (SIFs) for radial cracks in annular discs under constant angular velocity. Effects of internal and external uniform pressure on the SIFs have also been considered. Linear elastic fracture mechanics finite element analyses have been performed and results are presented in the form of crack configuration factors for a wide range of components and crack geometry parameters. These parameters are chosen to be representative of typical practical situations. The extensive range of crack configuration factors obtained from the analyses is then used to develop equivalent prediction equations via a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 ≤ R2 ≤ 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. These equations for the SIFs enable designers to predict fatigue life of the components easily.

Fracture mechanics in design and service: ‘living with defects’ - Fracture mechanics of non-metallic materials

1981 ◽  
Vol 299 (1446) ◽  
pp. 59-72 ◽  
Keyword(s):  
Fracture Mechanics ◽  
Plane Strain ◽  
Design Criterion ◽  
Simple Extension ◽  
Metallic Materials ◽  
Environmental Behaviour ◽  
Linear Elastic ◽  
Wide Range ◽  
Elastic Fracture

An outline of linear elastic fracture mechanics (l.e.f.m.) is given with an emphasis on those aspects most relevant to non-metallic materials. Provided that the nonlinear zone of energy absorption surrounding the crack tip is small compared with other dimensions, then a K e or G e value may be used. A simple extension of this concept can include elastically nonlinear materials such as rubber. Examples of the use of this method are then given for polymers, rubber and wood, and include some discussion of the difficulties involving plane strain-plane stress transitions. The role of K e as a characterizing parameter in time-dependent, fatigue and environmental behaviour is then described with several examples, and it is concluded that plane strain fractures may be achieved with a wide range of values for any material. The consequences of this in choosing a design criterion are then discussed.

scholarly journals Peridynamic analysis of dynamic fracture: influence of peridynamic horizon, dimensionality and specimen size

2021 ◽  
Author(s):  
Sahir N. Butt ◽  
Günther Meschke
Keyword(s):  
Dynamic Fracture ◽  
Fracture Process ◽  
Three Dimensional ◽  
Specimen Size ◽  
Surface Topology ◽  
Linear Elastic ◽  
Brittle Solids ◽  
Non Local ◽  
Elastic Fracture ◽  
Three Dimensional Simulations

AbstractIn peridynamic models for fracture, the dissipated fracture energy is regularized over a non-local region denoted as the peridynamic horizon. This paper investigates the influence of this parameter on the dynamic fracture process in brittle solids, using two as well as three dimensional simulations of dynamic fracture propagation in a notched plate for two loading cases. The predicted crack speed for the various scenarios of the initially stored energy, also known as the velocity toughening behavior as well as characteristics of the crack surface topology obtained in different crack propagation regimes in 3D computational simulations are compared with the experimentally observed crack velocity and fracture surfaces for Polymethyl Methacrylate (PMMA) specimens. In addition, we investigate the influence of the specimen size on the dynamic fracture process using two dimensional peridynamic simulations. The fracture strengths and the velocity toughening relationship obtained from different specimen sizes are compared with the Linear Elastic Fracture Mechanics (LEFM) size effect relationship and with results from experiments, respectively.

A LEFM Based Study on the Interaction Between an Edge and an Embedded Parallel Crack

2013 ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Stress Intensity ◽  
Separation Distance ◽  
Multiple Cracks ◽  
Service Needs ◽  
Parallel Crack ◽  
Linear Elastic ◽  
Parallel Cracks ◽  
Wide Range ◽  
Two Parallel Cracks ◽  
Elastic Fracture

Parallel cracks are often detected in components of various pressurized applications using non-destructive methods. For non-aligned parallel cracks, on-site service needs to decide whether they should be treated as coalesced or separate multiple cracks for Fitness-for-Service. Criteria and standards for the adjustment of multiple nonaligned cracks are very different from one another in existing resources. And those criteria and standards are often derived from on-site service experience without rigorous and systematic verification. Based on this observation, in this study the interaction between an edge and an embedded parallel crack is investigated to correlate criteria and standards from various resources in order to recommend the usage of those standards for the purpose of Fitness-for-service and to classify them as either conservative or non-conservative. If H and S represent the horizontal gap and vertical separation distance, respectively, between the cracks, and a2 is the length of the dominant crack, a parametric study of parallel crack separation distance and gap on the crack stress intensity factor has been undertaken. Stress intensity factors (SIFs) have been acquired for a wide range of the normalized gap of H/a2 = 0.4∼2 and the normalized separation distance of S/a2 = −0.5∼2 between the two parallel cracks based on the principle of linear elastic fracture mechanics (LEFM). This study indicates that certain existing standards/criteria provide results that are much more conservative than others while certain ones do not provide adequate information for application.

Fatigue Failure Analysis Using the Theory of Critical Distance

2011 ◽  
Vol 462-463 ◽  
pp. 663-667 ◽  
Author(s):  
Ruslizam Daud ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Al Emran Ismail
Keyword(s):  
Stress Concentration ◽  
Fatigue Failure ◽  
Notch Root ◽  
High Stress ◽  
Critical Distance ◽  
Future Research ◽  
Element Analysis ◽  
Linear Elastic ◽  
The Finite Element Analysis ◽  
Elastic Fracture

This paper explores the initial potential of theory of critical distance (TCD) which offers essential fatigue failure prediction in engineering components. The intention is to find the most appropriate TCD approach for a case of multiple stress concentration features in future research. The TCD is based on critical distance from notch root and represents the extension of linear elastic fracture mechanics (LEFM) principles. The approach is allowing possibilities for fatigue limit prediction based on localized stress concentration, which are characterized by high stress gradients. Using the finite element analysis (FEA) results and some data from literature, TCD applications is illustrated by a case study on engineering components in different geometrical notch radius. Further applications of TCD to various kinds of engineering problems are discussed.

scholarly journals New Insights into Molecular Mechanism behind Anti-Cancer Activities of Lycopene

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3888
Author(s):  
Boon-Peng Puah ◽  
Juriyati Jalil ◽  
Ali Attiq ◽  
Yusof Kamisah
Keyword(s):  
Immune Cells ◽  
Scientific Evidence ◽  
Special Role ◽  
Real Potential ◽  
Wide Range ◽  
Anti Cancer ◽  
The Family ◽  
The Relationship ◽  
Cancer Activity ◽  
Reduced Risk

Lycopene is a well-known compound found commonly in tomatoes which brings wide range of health benefits against cardiovascular diseases and cancers. From an anti-cancer perspective, lycopene is often associated with reduced risk of prostate cancer and people often look for it as a dietary supplement which may help to prevent cancer. Previous scientific evidence exhibited that the anti-cancer activity of lycopene relies on its ability to suppress oncogene expressions and induce proapoptotic pathways. To further explore the real potential of lycopene in cancer prevention, this review discusses the new insights and perspectives on the anti-cancer activities of lycopene which could help to drive new direction for research. The relationship between inflammation and cancer is being highlighted, whereby lycopene suppresses cancer via resolution of inflammation are also discussed herein. The immune system was found to be a part of the anti-cancer system of lycopene as it modulates immune cells to suppress tumor growth and progression. Lycopene, which is under the family of carotenoids, was found to play special role in suppressing lung cancer.

Local loads on a toroidal shell

1992 ◽  
Vol 27 (2) ◽  
pp. 59-66 ◽  
Author(s):  
D Redekop ◽  
F Zhang
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Elastic Shell ◽  
Toroidal Shell ◽  
Pipe Bend ◽  
Local Loads ◽  
Simply Supported ◽  
Linear Elastic ◽  
Wide Range ◽  
Theory Solution

In this study the effect of local loads applied on a sectorial toroidal shell (pipe bend) is considered. A linear elastic shell theory solution for local loads is first outlined. The solution corresponds to the case of a shell simply supported at the two ends. Detailed displacement and stress results are then given for a specific shell with loadings centred at three positions; the crown circles, the extrados, and the intrados. These results are compared with results for a corresponding cylindrical shell. The paper concludes with a table summarizing results for characteristic displacements and stresses in a number of shells, covering a wide range of geometric parameters.

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1429-1451 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Fractal Dimension ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Local Maximum ◽  
Fractal Dimensions ◽  
Dimension Formula ◽  
Phonon Spectra ◽  
Wide Range ◽  
Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

Investigation on Stress and Strain Singularity in LEFM

2006 ◽  
Vol 306-308 ◽  
pp. 31-36
Author(s):  
Zheng Yang ◽  
Wanlin Guo ◽  
Quan Liang Liu
Keyword(s):  
High Stress ◽  
Crack Tip ◽  
Plane Stress State ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Geometrical Nonlinear ◽  
Maximum Crack ◽  
Elastic Fracture ◽  
Plain Strain ◽  
Strain Singularity

Stress and strain singularity at crack-tip is the characteristic of Linear Elastic Fracture Mechanics (LEFM). However, the stress, strain and strain energy at crack-tip may be infinite promoting conflicts with linear elastic hypothesis. It is indicated that the geometrical nonlinear near the crack-tip should not be neglected for linear elastic materials. In fact, the crack-tip blunts under high stress and strain, and the singularity vanishes due to the deformation of crack surface when loading. The stress at crack-tip may still be very high even though the singularity vanishes. The low bound of maximum crack-tip stress is the modulus of elastic in plane stress state, while in plain strain state, it is greater than the modulus of elastic, and will increase with the Poisson’s ratio.

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