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.

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.

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.

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.

Interaction between a nanocrack with surface elasticity and a screw dislocation

2016 ◽  
Vol 22 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Xu Wang ◽  
Hui Fan
Keyword(s):  
Screw Dislocation ◽  
Real Axis ◽  
Analytical Study ◽  
Logarithmic Singularity ◽  
Surface Elasticity ◽  
Spontaneous Generation ◽  
The Real ◽  
Crack Tips ◽  
Interaction Problem ◽  
The Continuum

In the present analytical study, we consider the problem of a nanocrack with surface elasticity interacting with a screw dislocation. The surface elasticity is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. By considering both distributed screw dislocations and line forces on the crack, we reduce the interaction problem to two decoupled first-order Cauchy singular integro-differential equations which can be numerically solved by the collocation method. The analysis indicates that if the dislocation is on the real axis where the crack is located, the stresses at the crack tips only exhibit the weak logarithmic singularity; if the dislocation is not on the real axis, however, the stresses exhibit both the weak logarithmic and the strong square-root singularities. Our result suggests that the surface effects of the crack will make the fracture more ductile. The criterion for the spontaneous generation of dislocations at the crack tip is proposed.

Uncertainty Characterization of the CrCOD Circumferential Crack Opening Displacement Module for xLPR

2015 ◽  
Author(s):  
Richard Olson ◽  
Paul Scott
Keyword(s):  
Crack Opening Displacement ◽  
Crack Opening ◽  
Opening Displacement ◽  
Crack Face ◽  
Pipe Surface ◽  
Circumferential Crack ◽  
The Us ◽  
Experimental Values ◽  
Metal Weld

The US NRC/EPRI xLPR (eXtremely Low Probability of Rupture) probabilistic pipe fracture analysis program uses deterministic modules as the foundation for the calculation of the probability of pipe leak or rupture as a consequence of active degradation mechanisms, vibration or seismic loading. The circumferential crack opening displacement module, CrCOD, estimates crack opening displacement (COD) at the inside pipe surface, at the mid-wall thickness location, and at the outside pipe surface using a combined tension/crack face pressure/bending GE/EPRI-like solution. Each module has an uncertainty beyond the uncertainty of the xLPR data inputs. This paper documents the uncertainty for CrCOD. Using 36 pipe fracture experiments, including: base metal, similar metal weld, and dissimilar metal weld experiments; bend only and pressure and bend loading; static and dynamic load histories; cracks that range from short to long, the uncertainty of the CrCOD methodology is characterized. Module uncertainty is presented in terms mean fit and standard deviation between prediction and experimental values.

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