The linear elastic solid approximation. Applications: brittle and quasi-brittle fracture; strength of structures

2014 ◽  
pp. 101-123
Author(s):  
G. I. Barenblatt
Keyword(s):  
Brittle Fracture ◽  
Fracture Strength ◽  
Elastic Solid ◽  
Linear Elastic

Crack-Path Effect on Material Toughness

1990 ◽  
Vol 57 (1) ◽  
pp. 97-103 ◽  
Author(s):  
Asher A. Rubinstein
Keyword(s):  
Crack Path ◽  
Numerical Procedure ◽  
Crack Tip ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Length Change ◽  
Curvilinear Crack ◽  
Linear Elastic ◽  
System Of Cracks ◽  
Remote Stress

The material-toughening mechanism based on the crack-path deflection is studied. This investigation is based on a model which consists of a macrocrack (semi-infinite crack), with a curvilinear segment at the crack tip, situated in a brittle solid. The effect of material toughening is evaluated by comparison of the remote stress field parameters, such as the stress intensity factors (controlled by a loading on a macroscale), to effective values of these parameters acting in the vicinity of a crack tip (microscale). The effects of the curvilinear crack path are separated into three groups: crack-tip direction, crack-tip geometry pattern-shielding, and crack-path length change. These effects are analyzed by investigation of selected curvilinear crack patterns such as a macrocrack with simple crack-tip kink in the form of a circular arc and a macrocrack with a segment at the crack tip in the form of a sinusoidal wave. In conjunction with this investigation, a numerical procedure has been developed for the analysis of curvilinear cracks (or a system of cracks) in a two-dimensional linear elastic solid. The formulation is based on the solution of a system of singular integral equations. This numerical scheme was applied to the cases of finite and semi-infinite cracks.

scholarly journals Study on Brittle Fracture Strength at Repair Weld of Thick Plate

1985 ◽  
Vol 1985 (158) ◽  
pp. 588-601
Author(s):  
Yukio Ueda ◽  
You Chul Kim ◽  
Katsuya Kajimoto ◽  
Masanao Kuroki ◽  
Yukito Hagiwara ◽  
...  
Keyword(s):  
Brittle Fracture ◽  
Fracture Strength ◽  
Thick Plate

scholarly journals The influence of elastic deformations in high-strength structural materials on the hydrogen transport

2021 ◽  
Vol 225 ◽  
pp. 01010
Author(s):  
Polina Grigoreva ◽  
Elena Vilchevskaya ◽  
Vladimir Polyanskiy
Keyword(s):  
Chemical Potential ◽  
Potential Gradient ◽  
Elastic Solid ◽  
High Strength ◽  
Ideal Gas ◽  
Linear Elastic ◽  
Coupled Diffusion ◽  
Elastic Boundary ◽  
Linear Effects ◽  
Solid System

In this work, the diffusion equation for the gas-solid system is revised to describe the non-uniform distribution of hydrogen in steels. The first attempt to build a theoretical and general model and to describe the diffusion process as driven by a chemical potential gradient is made. A linear elastic solid body and ideal gas, diffusing into it, are considered. At this stage, we neglect any traps and non-linear effects. The coupled diffusion-elastic boundary problem is solved for the case of the cylinder under the tensile loads. The obtained results correspond to the experimental ones. Based on them, the assumptions about the correctness of the model and its further improvement are suggested.

Effects of Specimen Size and Notch Acuity on the Brittle Fracture Strength of a Heat-Treated Steel

1961 ◽  
Vol 83 (4) ◽  
pp. 541-544 ◽  
Author(s):  
S. Yukawa ◽  
J. G. McMullin
Keyword(s):  
Brittle Fracture ◽  
Alloy Steel ◽  
Fracture Strength ◽  
Specimen Size ◽  
Root Radius ◽  
Lower Strength ◽  
Large Size ◽  
Treated Steel ◽  
Heat Treated ◽  
Heat Treated Steel

Effects of various methods of notch preparation on the notched slow bend fracture strengths of heat-treated alloy steel specimens were studied. The results indicate that several kinds of cracks result in about 35 per cent lower strength than a machined 0.005 in. root radius notch. The importance of testing sufficiently large size specimens to reveal this difference is shown.

Comparison of anterior capsulotomy techniques: continuous curvilinear capsulorhexis, femtosecond laser-assisted capsulotomy and selective laser capsulotomy

2019 ◽  
Vol 104 (3) ◽  
pp. 437-442 ◽  
Author(s):  
Sheraz Daya ◽  
Soon-Phaik Chee ◽  
Seng-Ei Ti ◽  
Richard Packard ◽  
David H Mordaunt
Keyword(s):  
New York ◽  
Femtosecond Laser ◽  
Fracture Strength ◽  
Study Groups ◽  
Study Group ◽  
Linear Elastic ◽  
Group 2 ◽  
Human Eyes ◽  
Anterior Capsulotomy ◽  
Fellow Eyes

PurposeTo compare the anterior capsulotomy edge tear strength created by manual continuous curvilinear capsulorhexis (CCC), femtosecond laser-assisted capsulotomy (FLACS), and selective laser capsulotomy (SLC).SettingSingapore National Eye Centre, Singapore and Excel-Lens, Livermore, California, USA.DesignThree armed study in paired human eyes.MethodsCapsulotomies were performed in 60 cadaver eyes of 30 donors using CCC, Victus Femtosecond Laser, (Bausch & Lomb, Rochester, New York, USA) or CAPSULaser, (Excel-Lens, Los Gatos, California, USA). Three pairwise study groups each involved 10 pairs of eyes. Study group 1: SLC eyes compared with fellow eyes with CCC. Study group 2: CCC eyes compared with fellow eyes with FLACS. Study group 3: FLACS eyes compared with fellow eyes with SLC.A shoe-tree method was used to apply load to the capsulotomy edge, and Instron tensile stress instrument measured distension and threshold load applied to initiate capsule fracture. Relative fracture strengths and distension of CCC, FLACS and SLC were determined. Scanning electron microscopy (SEM) of capsule edges were reviewedResultsAnterior capsulotomies behave as non-linear elastic (elastomeric) systems when exposed to an external load. The pairwise study demonstrated that the SLC fracture strength was superior to that of CCC by a factor of 1.46-fold with SLC 277±38 mN versus CCC with 190±37 mN. Furthermore, CCC fracture strength was superior to that of FLACS by a factor of 1.28-fold with CCC 186 + 37 mN versus FLACS 145 ± 35 mN (p < 0.001). This was determined by statistical analysis utilising the Wilcoxon matched-pairs signed-ranks test and in accordance with the Consolidated Standards of Reporting Trials guidelines. The capsule edge of SLC on SEM demonstrated a rolled over edge anteriorly and an alteration of collagen.ConclusionsThe strength of the capsulotomy edge for SLC was significantly stronger than that of CCC which and both were significantly stronger than FLACS. The relative strengths can be explained by SEM of each type of capsulotomy.

Study on the Relationship Between Interaction Factors and Stress Intensity Factor for Elliptical Flaws

2017 ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Kunio Hasegawa
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Elastic Solid ◽  
Element Analysis ◽  
Linear Elastic ◽  
Close Proximity ◽  
Interaction Factors ◽  
The Relationship

The interaction of multiple flaws in close proximity to one another may increase the stress intensity factor of the flaw in structures and components. This interaction effect is not distributed uniformly along the crack front. For instance, the strongest interaction is generally observed at the point closest to a neighboring flaw. For this reason, the closest point could show a higher value of the stress intensity factor than all other points in some cases, even if the original value at the point of the single flaw is relatively low. To clarify the condition when the closest point shows the maximum stress intensity factor, we investigated the interaction of two similar elliptical flaws in an infinite model subjected to remote tension loading. The stress intensity factor of the elliptical flaws was obtained by performing finite element analysis of a linear elastic solid. The results indicated that the interaction factors along the crack front can be expressed by a simple empirical formula. Finally, we show the relationship between geometrical features of the flaw and the stress intensity factor at the closest point to a neighboring flaw.

True bounds on Poisson's ratios for transversely isotropic solids

1992 ◽  
Vol 27 (1) ◽  
pp. 43-44 ◽  
Author(s):  
P S Theocaris ◽  
T P Philippidis
Keyword(s):  
Energy Density ◽  
Basic Principle ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Linear Elastic ◽  
Positive Strain ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

The basic principle of positive strain energy density of an anisotropic linear or non-linear elastic solid imposes bounds on the values of the stiffness and compliance tensor components. Although rational mathematical structuring of valid intervals for these components is possible and relatively simple, there are mathematical procedures less strictly followed by previous authors, which led to an overestimation of the bounds and misinterpretation of experimental results.

Separable K-Canonical Formulation of Rectangular Element and Symplectic Integration Method for Analysis of Laminated Plates

2011 ◽  
Vol 194-196 ◽  
pp. 1496-1505
Author(s):  
Guang Hui Qing ◽  
Liang Wang ◽  
Li Zhong Shi
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Canonical System ◽  
Laminated Plates ◽  
Linear Elastic ◽  
Canonical Formulation ◽  
Single Plate ◽  
Static Responses ◽  
Rectangular Element ◽  
Symplectic Schemes

In the state space framework, a separable K-canonical formulation of rectangular element and explicit symplectic schemes for the static responses analysis of three-dimensional (3D) laminated plates are proposed in this paper. Firstly, the modified Hellinger-Reissner (H-R) variational principle for linear elastic solid is simply mentioned. Secondly, the separable J-canonical system with Hamiltonian H and the separable K-canonical formulation of rectangular element are constructed. Thirdly, on the basis of the symplectic difference schemes, the explicit symplectic schemes are employed to solve the separable K-canonical governing equation for a single plate. Then, to obtain the high accurate numerical results, a multi-scale iterative technique is also presented. Finally, based on the interlaminar compatibility condition (displacements and stresses), the excellent performance of the method presented in this paper is demonstrated by several numerical experiments of the static responses of laminated plates.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

Influence of the Crack Opening Rate on the Fracture Toughness of Plain Concrete

1985 ◽  
Vol 64 ◽  
Author(s):  
P. Rossi ◽  
C. Boulay ◽  
P. Acker ◽  
Y. Malier
Keyword(s):  
Fracture Toughness ◽  
Brittle Fracture ◽  
Cantilever Beam ◽  
Double Cantilever Beam ◽  
Crack Opening ◽  
Plain Concrete ◽  
Elastic Behavior ◽  
Linear Elastic

ABSTRACTThree D.C.B. tests (Double Cantilever Beam) under different loading histories have shown that the applied crack opening rates can have an effect on the KIC fracture toughness values computed on the basis of linear elastic behavior of concrete. This assumption can be well justified for a certain range of crack opening rates, outside of which viscous phenomena must be taken in account. The concepts of ductile and brittle fracture appear then as related to the crack opening rate.

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