scholarly journals Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops

2018 ◽  
Vol 12 (2) ◽  
pp. 91-95
Author(s):  
Heorgij Sulym ◽  
Viktor Opanasovych ◽  
Mykola Slobodian ◽  
Oksana Bilash
Keyword(s):  
Isotropic Plate ◽  
Constant Width ◽  
Plastic Hinge ◽  
Crack Opening ◽  
Linear Conjugation ◽  
Opening Displacement ◽  
Theory Of Plates ◽  
Crack Tips ◽  
Plastic Zones ◽  
Distributed Forces

Abstract Stress-strain state of isotropic plate with rectilinear through-crack at combined action of bending and tension, realized by applying distributed forces and bending moments at infinity, the vectors of which are parallel and perpendicular to the crack, is investigated. Under the influence of the internal stress the crack faces contacts on area of constant width near the upper base of plate, and plastic zones forms in its tips. Using methods of the theory of complex variables, complex potentials plane problem of elasticity theory and the classical theory of plates bending, solving of the problem is reduced to the set of linear conjugation problems and their analytical solution is built in a class of functions of limited plastic zones in the crack tips. The conditions of existence of the solution of the problem in these terms are determined. Using Treska plasticity conditions in the form of surface layer or the plastic hinge, the length of plastic zone and crack opening displacement are found analytically. Their numerical analysis for various parameters of the problem is conducted.

A new statistical distribution function for fracture toughness

1987 ◽  
Vol 410 (1839) ◽  
pp. 421-442 ◽  
Keyword(s):  
Distribution Function ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Parameter Distribution ◽  
Stress And Strain ◽  
Weibull Function ◽  
Opening Displacement ◽  
Total Failure ◽  
Crack Tips ◽  
Two Parameters

A statistical view of fracture at cracks is presented that is also appropriate for failures in singularity-dominated, self-similar fields other than those at crack tips. Consideration of the behaviour of the distributions of stress and strain near crack tips results in the development of a new two-parameter distribution function for the probability of failure. The two fundamental premises on which the function is based are, firstly, that the failure of any part of the material near to the crack tip leads to total failure along the whole crack front or at least represents total failure; and secondly, that the variability of strength in material is due to micro-structural inhomogeneity. The new function is tested by means of several large sets of toughness data from other workers, and is found to give with only two parameters better fits than can the three-parameter distribution function of Weibull. The Weibull function is capable of giving reasonable fits in its extremely flexible three-parameter form, but that very flexibility means that these fits may be no more than descriptions without theoretical foundation. It is found also that the new function is applicable equally to ceramics and steels. The very good fits afforded by the new function are further support for previous findings in two basic areas in the science of fracture. Firstly, previous work concerned with the distributions of stress and strain at crack tips and with crack-opening displacement upon which the new function is based, is supported, as is the idea that the crack-opening displacement is fundamental in determining the possibility and prob­ability of failure. Secondly, the present work is in agreement with widely accepted ideas concerned with stress-controlled mechanisms of failure in materials.

Interaction between a screw dislocation and a bridged crack with surface elasticity

2016 ◽  
Vol 22 (12) ◽  
pp. 2217-2239 ◽  
Author(s):  
Moxuan Yang ◽  
Xu Wang
Keyword(s):  
Screw Dislocation ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Surface Elasticity ◽  
Image Force ◽  
Opening Displacement ◽  
Crack Bridging ◽  
Line Force ◽  
Crack Tips ◽  
Crack Faces

We examine the contribution of crack bridging and surface elasticity to the elastic interaction between a mode III finite crack and a screw dislocation. The surface effect on the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. The crack faces are subjected to a bridging force which is assumed to be proportional to the crack opening displacement, whereas the bridging stiffness is allowed to vary arbitrarily along the crack. By considering a continuous distribution of both screw dislocations and line forces on the crack, the boundary value problem is reduced to two decoupled first-order Cauchy singular integro-differential equations. After the expansion of the unknown line dislocation and line force densities and the known variable bridging stiffness into Chebyshev polynomials, these singular integro-differential equations are solved numerically using the collocation method. Owing to the incorporation of surface elasticity, the stresses at the crack tips only exhibit the weak logarithmic singularity when the dislocation is located on the real axis where the crack is located, whereas in the case when the dislocation is not on the real axis, the stresses at the crack tips exhibit both the weak logarithmic and the strong square-root singularities. The two densities, the crack opening displacement across the crack faces and the image force acting on the screw dislocation are specifically calculated. We note that crack bridging only exerts an effect on the line dislocation density but has no influence on the line force density. In addition, we demonstrate that both surface elasticity and crack bridging can reduce the strengths of the logarithmic stress singularity at the crack tips and the magnitude of the crack opening displacement across the crack faces. Our results also clearly show that both crack bridging and surface elasticity exert a significant influence on the magnitude and direction of the image force acting on the screw dislocation.

An Arc-Shaped Debonding Crack Opened by Internal Pressure

1998 ◽  
Vol 14 (2) ◽  
pp. 83-89
Author(s):  
Ru-Min Chao
Keyword(s):  
Internal Pressure ◽  
Crack Opening ◽  
Stress Singularity ◽  
Crack Tip ◽  
Singular Integral Equations ◽  
Contact Length ◽  
Infinite Matrix ◽  
Closed Crack ◽  
Opening Displacement ◽  
Crack Tips

AbstractIn this paper, the problem of a debonding crack at the interface between a circular fiber and an infinite matrix opened by internal pressure is discussed. We concentrated on the effect of contact near the crack tips within the content of linear elastic fracture mechanics. The Muskhelishvili complex variable method is used in this analysis. The frictionless contact crack tip condition is adopted in this study in order to avoid the oscillatory stress singularity at the crack tip as shown in the classical solution. By using the crack opening displacement gradient as the primary variable, the problem is then reduced to two coupled singular integral equations, and the final discretization of the equations employs the method given by Erdogan and Gupta (1972). The comprehensive numerical results of stress fields and the mode II SIF at the closed crack tip will be given in the paper. It is also found from the numerical evidences that the contact length at the crack tip is independent of one of the Dundurs parameters, α.

scholarly journals Mode Stresses for the Interaction between Two Inclined Cracks in Bonded Two Half Planes

2020 ◽  
Vol 861 ◽  
pp. 524-528
Author(s):  
Khairum Bin Hamzah ◽  
Nik Mohd Asri Nik Long
Keyword(s):  
Numerical Solutions ◽  
Crack Opening ◽  
Mode Iii ◽  
Opening Displacement ◽  
Unknown Variable ◽  
Stress Mode ◽  
Crack Tips ◽  
The Right ◽  
Gauss Quadrature Rules ◽  
Inclined Cracks

The various mode of stresses for the interaction between two inclined cracks in the upper part of bonded two half planes which are normal stress (Mode I), shear stress (Mode II), tearing stress (Mode III) and mixed stress was studied. For this problem, the modified complex potentials (MCPs) method was used to develop the new system of hypersingular integral equations (HSIEs) by applying the conditions for continuity of resultant force and displacement functions with the unknown variable of crack opening displacement (COD) function and the right hand terms are the tractions along the crack. The curve length coordinate method and Gauss quadrature rules were used to solve numerically the obtained HSIEs to compute the stress intensity factors (SIFs) in order to determine the strength of the materials containing cracks. Numerical solutions presented the characteristic of nondimensional SIFs at the cracks tips. It is obtained that the various stresses and the elastic constants ratio are influences to the value of nondimensional SIFs at the crack tips.

scholarly journals Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 235
Author(s):  
Khairum Bin Hamzah ◽  
Nik Mohd Asri Nik Long ◽  
Norazak Senu ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Mathematical Model ◽  
Stress Intensity ◽  
Analytical Study ◽  
Crack Opening ◽  
Dissimilar Materials ◽  
Quadrature Formulas ◽  
Intensity Factors ◽  
Opening Displacement ◽  
Dimensionless Stress ◽  
Crack Tips

A new mathematical model is developed for the analytical study of two cracks in the upper plane of dissimilar materials under various mechanical loadings, i.e., shear, normal, tearing and mixed stresses with different geometry conditions. This problem is developed into a new mathematical model of hypersingular integral equations (HSIEs) by using the modified complex potentials (MCPs) function and the continuity conditions of the resultant force and displacement with the crack opening displacement (COD) function as the unknown. The newly obtained mathematical model of HSIEs are solved numerically by utilizing the appropriate quadrature formulas. Numerical computations and graphical demonstrations are carried out to observe the profound effect of the elastic constants ratio, mode of stresses and geometry conditions on the dimensionless stress intensity factors (SIFs) at the crack tips.

A mode I crack with multiple islands of ideal contact between the crack faces: An asymptotic model

2021 ◽  
pp. 108128652110214
Author(s):  
Ivan Argatov
Keyword(s):  
Crack Opening ◽  
Reduction Factor ◽  
Mode I ◽  
Asymptotic Model ◽  
Mode I Crack ◽  
Opening Displacement ◽  
Multiple Contacts ◽  
Scaling Hypothesis ◽  
Penny Shaped Crack ◽  
Crack Faces

The problem of a mode I crack having multiple contacts between the crack faces is considered. In the case of small contact islands of arbitrary shapes, which are arbitrarily located inside the crack, the first-order asymptotic model for the crack opening displacement is constructed using the method of matched asymptotic expansions. The case of a penny-shaped crack has been studied in detail. A scaling hypothesis for the compliance reduction factor is formulated.

The Fracture Toughness of Hardened Tool Steels

1987 ◽  
Vol 109 (4) ◽  
pp. 314-318 ◽  
Author(s):  
D. F. Watt ◽  
Pamela Nadin ◽  
S. B. Biner
Keyword(s):  
Fracture Toughness ◽  
Crack Growth ◽  
Slow Crack Growth ◽  
Crack Opening ◽  
Compact Tension ◽  
Testing Procedure ◽  
Tool Steels ◽  
Opening Displacement ◽  
Tempering Temperature ◽  
Toughness Testing

This report details the development of a three-stage fracture toughness testing procedure used to study the effect of tempering temperature on toughness in 01 tool steel. Modified compact tension specimens were used in which the fatigue precracking stage in the ASTM E-399 Procedure was replaced by stable precracking, followed by a slow crack growth. The specimen geometry has been designed to provide a region where slow crack growth can be achieved in brittle materials. Three parameters, load, crack opening displacement, and time have been monitored during the testing procedure and a combination of heat tinting and a compliance equation have been used to identify the position of the crack front. Significant KIC results have been obtained using a modified ASTM fracture toughness equation. An inverse relationship between KIC and hardness has been measured.

Fatigue Crack Growth Tests on Glass Fibre Reinforced Polymer Matrix Composite

2005 ◽  
Vol 473-474 ◽  
pp. 189-194
Author(s):  
Zilia Csomós ◽  
János Lukács
Keyword(s):  
Cyclic Loading ◽  
Crack Opening Displacement ◽  
Matrix Composite ◽  
Glass Fibre ◽  
Crack Opening ◽  
Loading Conditions ◽  
Opening Displacement ◽  
Interfacial Cracks ◽  
Glass Fibre Reinforced ◽  
Number Of Cycles

E-glass fibre reinforced polyester matrix composite was investigated, which was made by pullwinding process. Round three point bending (RTPB) specimens were tested under quasi-static and mode I cyclic loading conditions. Load vs. displacement (F-f), load vs. crack opening displacement (F-v) and crack opening displacement range vs. number of cycles (ΔCOD-N) curves were registered and analysed. Interfacial cracks were caused the final longitudinal fracture of the specimens under quasi-static and cyclic loading conditions.

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