A Critical Distance Analysis of the Effect of Crack Length on Toughness and Fatigue in Compact Bone

2008 ◽  
Author(s):  
David Taylor ◽  
Saeid Kasiri
Keyword(s):  
Crack Length ◽  
Compact Bone ◽  
Cyclic Stress ◽  
Critical Distance ◽  
Short Crack ◽  
Stress Intensity Range ◽  
Distance Analysis ◽  
Short Cracks ◽  
Strain Fracture ◽  
First Time

The plane strain fracture toughness, KIC, has a constant value for long cracks, but when specimens containing short cracks are tested it is often found that the measured toughness is less than the long-crack value, and tends to decrease with decreasing crack length. A similar effect occurs when measuring the cyclic stress intensity range, ΔK, corresponding to a given rate of crack growth da/dN. Some experimental data are available in the published literature to show that cortical bone displays these short-crack effects for crack lengths of the order of millimeters or less. The hypothesis of the present work was that these effects can be predicted using an approach known as the Theory of Critical Distances. This is the first time that this approach has been used to predict short crack effects in bone.

Microstructural Parameters in the Theory of Critical Distances

2007 ◽  
Vol 567-568 ◽  
pp. 23-28 ◽  
Author(s):  
David Taylor
Keyword(s):  
Grain Size ◽  
Stress Concentration ◽  
Brittle Fracture ◽  
Damage Zone ◽  
Critical Distance ◽  
Microstructural Parameters ◽  
Short Cracks ◽  
Length Constant ◽  
Using Data ◽  
First Time

The work described below investigates, for the first time, the link between microstructural parameters such as grain size and the length constant L which is known as the critical distance. L is frequently used in the prediction of failure processes such as brittle fracture and fatigue, initiated at stress concentration features such as notches. Values of L were calculated using data from the literature on the effect of short cracks and notches in steels and ceramics. In some cases, simple relationships could be established between L and the grain size, or other microstructural features. Sometimes L was found to be much larger than anything in the microstructure and appeared to be related to the size of the damage zone at failure.

Dynamic Fracture of a Beam or Plate in Plane Bending

1976 ◽  
Vol 43 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. B. Freund ◽  
G. Herrmann
Keyword(s):  
Crack Length ◽  
Dynamic Fracture ◽  
Crack Tip ◽  
Bending Moment ◽  
Fracture Initiation ◽  
Fracture Plane ◽  
Multiple Reflections ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

Investigation to the Effects of Grain Misorientation on the Performance of Short Cracks

2007 ◽  
Vol 353-358 ◽  
pp. 1165-1168
Author(s):  
Yan Hai Xu ◽  
Hao Li ◽  
Li Guo
Keyword(s):  
Grain Boundary ◽  
Crack Propagation ◽  
Geometric Parameters ◽  
Short Crack ◽  
Short Cracks ◽  
Grain Orientations ◽  
Grain Misorientation

The influences of crystallographic and geometric parameters such as grain misorientation on the performance of short cracks are illustrated based on FEM in this paper. Firstly, the microstructure is simulated to account for the effects of grain misorientation on the performance of short cracks and the short cracks are initiated within the microstructure for the further investigation. The influence of grain misorientation is demonstrated by the change of neighboring grain orientations with an initiated short crack from 0° to 180°. The effects of the grain boundary on the short crack with the crack arrested or retarded are described by the crack propagation until it approached the grain boundary. The results will give more useful information such as crack arrested and retardation to the further research on the characteristics and evolution of short cracks.

scholarly journals Evaluation of Densitometric and Geometric Parameters of the Femur in 14-Month-Old Ostriches Depending on Sex with the Use of Computed Tomography

2013 ◽  
Vol 57 (2) ◽  
pp. 287-291 ◽  
Author(s):  
Anna Charuta
Keyword(s):  
Computed Tomography ◽  
Mineral Content ◽  
Compact Bone ◽  
Geometric Parameters ◽  
Bone Area ◽  
Bonferroni Correction ◽  
Strain Index ◽  
Multiple Group ◽  
First Time ◽  
One Way Anova

Abstract The aim of the study was to analyse densitometric and geometric parameters of the compact bone and the trabecular diaphysis of the femur of ostriches with the use of computed tomography. The method has been applied in ostriches for the first time. The study was conducted on the femur of 14-month-old ostriches of both sexes. The obtained results were analysed statistically using one-way ANOVA, with Bonferroni correction for multiple-group comparisons. It was stated that the mineral content (BMC) in the middle of the diaphysis of the femur was significantly higher in males (465.52 mg/mm) than in females (417.67 mg/mm). Similar tendencies were observed for the total bone area (TOT_ A), trabecular area (TRAB_ A), cortical area (CRT_ A), and strength strain index (SSI). The average area of the CRT_A for both sexes was 568.62 mm2 and was lower than the TRAB_A - 884 mm2, at P≤0.05. Moreover, it was found that strength strain index (SSI) of the diaphysis depended on the TOT_A and the TRAB_A. Both features positively correlated with SSI. Pearson’s correlation coefficient for both features was r = 0.97, at P≤0.01. Further research concerning the dynamics of changes of densitometric and geometric parameters occurring with age and involving both sexes is recommended, as there are many locomotion problems in ostriches, especially older ones, used intensively on farms for many years.

A New Model for Predicting the Maximum Gas Entrapment Concentration in a Yield Stress Fluid

SPE Journal ◽  
2022 ◽  
pp. 1-15
Author(s):  
Shaowei Pan ◽  
Zhiyuan Wang ◽  
Baojiang Sun
Keyword(s):  
Yield Stress ◽  
Maximum Error ◽  
Critical Distance ◽  
Single Bubble ◽  
Average Error ◽  
Two Phase ◽  
Yield Stress Fluid ◽  
Multiple Bubbles ◽  
Gas Entrapment ◽  
First Time

Summary Gas entrapment is a typical phenomenon in gas-yield stress fluid two-phase flow, and most of the related research focuses on the entrapped condition of the single bubble. However, the amount of entrapped gas, which is more meaningful for engineering, is rarely involved. In this paper, a theoretical model for calculating the maximum gas entrapment concentration (MGEC) is established for the first time. The critical distance between horizontal and vertical entrapped bubbles was determined by the yielded region caused by the buoyancy and the coupled stress field around the multiple bubbles. The MGEC is the ratio of a single bubble volume to its domain volume, which is calculated from the distance between the vertical and the horizontal bubbles. By comparing with the experimental results, the average error of MGEC calculated by this model is 4.42%, and the maximum error is 7.32%. According to the prediction results of the model, an empirical equation that can be conveniently used for predicting MGEC is proposed.

Material property controlling non-propagating fatigue crack length of mechanically and physically short-crack based on Dugdale-model analysis

2017 ◽  
Vol 90 ◽  
pp. 193-202 ◽  
Author(s):  
Naoki Fukumura ◽  
Bochuan Li ◽  
Motomichi Koyama ◽  
Tomohiro Suzuki ◽  
Shigeru Hamada ◽  
...  
Keyword(s):  
Fatigue Crack ◽  
Crack Length ◽  
Material Property ◽  
Model Analysis ◽  
Short Crack ◽  
Dugdale Model

scholarly journals Fatigue crack surface area and crack front length: new ways to look at fatigue crack growth

2018 ◽  
Vol 165 ◽  
pp. 13009
Author(s):  
Jesse van Kuijk ◽  
René Alderliesten ◽  
Rinze Benedictus
Keyword(s):  
Fatigue Crack ◽  
Crack Length ◽  
Crack Growth ◽  
Surface Area ◽  
Power Law ◽  
Crack Front ◽  
Crack Surface ◽  
Short Crack ◽  
Small Crack ◽  
Corner Crack

This paper discusses the appropriateness of crack length as a reference dimension for fatigue damage. Current discussion on short crack versus long crack data is still divided between various approaches to model small crack growth. A proper physical explanation of the probable cause of the apparent differences between short crack and long crack data is not yet provided. Long crack data often comprises crack growth in constant thickness specimens, with a through crack of near constant crack front geometry. This is not true for corner cracks or elliptical surface crack geometries in the small crack regime where the crack front geometry is not symmetric or through-thickness. This affects similitude parameters that are based on the crack length. The hypothesis in this paper is that a comparison between long crack data and short crack data should be made using similar increments in crack surface area. The work applied to the specimen is dissipated in generation of fracture surface, whereas fracture length is a result. The crack surface area approach includes the two-dimensional effect of crack growth geometry in the small crack regime. A corner crack and a through crack are shown to follow the same power law relationship when using the crack area as base parameter. The crack front length is not constant, and its power law behaviour for a corner crack is shown.

scholarly journals Molecular Structure of Nickel Octamethylporphyrin—Rare Experimental Evidence of a Ruffling Effect in Gas Phase

2021 ◽  
Vol 23 (1) ◽  
pp. 320
Author(s):  
Alexander E. Pogonin ◽  
Arseniy A. Otlyotov ◽  
Yury Minenkov ◽  
Alexander S. Semeikin ◽  
Yuriy A. Zhabanov ◽  
...  
Keyword(s):  
Gas Phase ◽  
Density Functional ◽  
Central Atom ◽  
Critical Distance ◽  
Problem Solution ◽  
Functional Theory ◽  
Inverse Problem Solution ◽  
Metal Porphyrins ◽  
First Time ◽  
Gas Phase Electron Diffraction

The structure of a free nickel (II) octamethylporphyrin (NiOMP) molecule was determined for the first time through a combined gas-phase electron diffraction (GED) and mass spectrometry (MS) experiment, as well as through quantum chemical (QC) calculations. Density functional theory (DFT) calculations do not provide an unambiguous answer about the planarity or non-planar distortion of the NiOMP skeleton. The GED refinement in such cases is non-trivial. Several approaches to the inverse problem solution were used. The obtained results allow us to argue that the ruffling effect is manifested in the NiOMP molecule. The minimal critical distance between the central atom of the metal and nitrogen atoms of the coordination cavity that provokes ruffling distortion in metal porphyrins is about 1.96 Å.

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