Stresses in an Infinite Strip Containing a Semi-Infinite Crack

1966 ◽  
Vol 33 (2) ◽  
pp. 356-362 ◽  
Author(s):  
W. G. Knauss
Keyword(s):  
Fracture Mechanics ◽  
Stress Field ◽  
Asymptotic Solution ◽  
Asymptotic Expansions ◽  
Region Of Interest ◽  
Graphical Form ◽  
Finite Width ◽  
Infinite Strip ◽  
Arbitrary Length ◽  
Laboratory Investigations

Stresses in an infinitely long strip of finite width containing a straight semi-infinite crack have been calculated for the case that the clamped boundaries are displaced normal to the crack. The solution is obtained by the Wiener-Hopf technique. The stresses are given in the form of asymptotic expansions in the immediate crack tip vicinity and for a larger region of interest in graphical form. The effect of prescribing displacements on the boundary close to a crack instead of stresses far away is discussed briefly. Together with an asymptotic solution for a small crack, the result is used to estimate the stress field around a crack of arbitrary length in an infinite strip. The usefulness of this crack geometry in laboratory investigations of fracture mechanics is pointed out.

scholarly journals RANDOM MATRIX MINOR PROCESSES RELATED TO PERCOLATION THEORY

2013 ◽  
Vol 02 (04) ◽  
pp. 1350008 ◽  
Author(s):  
MARK ADLER ◽  
PIERRE VAN MOERBEKE ◽  
DONG WANG
Keyword(s):  
Transition Probability ◽  
External Source ◽  
Finite Width ◽  
Infinite Strip ◽  
Determinantal Point Process ◽  
Last Passage Percolation ◽  
Common Features ◽  
Last Passage Times ◽  
Precise Relationship ◽  
Passage Times

This paper studies a number of matrix models of size n and the associated Markov chains for the eigenvalues of the models for consecutive n's. They are consecutive principal minors for two of the models, GUE with external source and the multiple Laguerre matrix model, and merely properly defined consecutive matrices for the third one, the Jacobi–Piñeiro model; nevertheless the eigenvalues of the consecutive models all interlace. We show: (i) For each of those finite models, we give the transition probability of the associated Markov chain and the joint distribution of the entire interlacing set of eigenvalues; we show this is a determinantal point process whose extended kernels share many common features. (ii) To each of these models and their set of eigenvalues, we associate a last-passage percolation model, either finite percolation or percolation along an infinite strip of finite width, yielding a precise relationship between the last-passage times and the eigenvalues. (iii) Finally, it is shown that for appropriate choices of exponential distribution on the percolation, with very small means, the rescaled last-passage times lead to the Pearcey process; this should connect the Pearcey statistics with random directed polymers.

Asymptotic analysis of the corner-behaviour of a rigid punch bonded to an elastic substrate

2007 ◽  
Vol 42 (5) ◽  
pp. 415-422
Author(s):  
L Bohórquez ◽  
D. A Hills
Keyword(s):  
Stress Field ◽  
Plastic Zone ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Half Plane ◽  
Poisson's Ratio ◽  
Rigid Block ◽  
Rigid Punch ◽  
Oscillatory Behaviour ◽  
Elastic Substrate

The contact between a flat-faced rigid block and an elastic half-plane has been studied, showing that an asymptotic solution correctly captures the stress field adjacent to the contact corners for all values of Poisson's ratio. It is shown that, in practical cases, the plastic zone, which is inevitably present at the contact corners, envelopes the oscillatory behaviour implied locally but is surrounded by an elastic hinterland correctly represented by the asymptote.

Investigation on Stress Field near Crack-Tip of Mode I in Shape Memory Alloy

2011 ◽  
Vol 142 ◽  
pp. 138-141 ◽  
Author(s):  
Bo Zhou ◽  
Xiao Gang Guo ◽  
Gang Ling Hou ◽  
Xu Kun Li
Keyword(s):  
Phase Transformation ◽  
Fracture Mechanics ◽  
Shape Memory Alloy ◽  
Stress Field ◽  
Shape Memory ◽  
Crack Tip ◽  
Complex Stress ◽  
Complex Stress State ◽  
Mode I ◽  
Transformation Equation

In this paper a phase transformation equation is supposed to describe the phase transformation behaviors of the shape memory alloy (SMA) under complex stress state. The stress field near crack-tip of mode I in SMA at various temperatures is investigated based on the supposed phase transformation equation and linear elastic fracture mechanics. Results show both the martensite region and the mixed region of martensite and austenite near the crack-tip become larger with the decrease of temperature. The fracture mechanics behaviors of SMA are much influenced by the temperature.

Dynamic Steady-State Stress Field in a Web During Slitting

2005 ◽  
Vol 72 (2) ◽  
pp. 157-164 ◽  
Author(s):  
C. Liu ◽  
H. Lu ◽  
Y. Huang
Keyword(s):  
Steady State ◽  
Fracture Mechanics ◽  
Stress Field ◽  
Dynamic Fracture ◽  
Dynamic Stress ◽  
Razor Blade ◽  
Dynamic Fracture Mechanics ◽  
Mechanics Analysis ◽  
Dynamic Stress Field ◽  
The Web

Based on a dynamic fracture mechanics analysis, the stress field in a continuous film (called a web) during slitting (or cutting) is investigated. For a homogeneous, isotropic and linearly elastic web, the steady-state dynamic stress field surrounding the slitter blade can be related to the interacting traction between the moving web and the blade, and to the far-field tension that is parallel to the slitting direction. The interaction between the moving web and the blade also includes friction that is considered to be a Coulomb type. By solving an integral equation, the normal traction between the web and the blade can be expressed as a function of the blade profile and the web speed. Numerical calculations are performed for an ideal razor blade with the wedge shape. The analysis presented in this study indicates that the contact between the moving web and the blade does not start at the tip of the blade but rather starts at some distance behind the blade tip. Moreover, it is found that the distance from the point where the web begins to separate to the point where the blade and the web start to have contact, is controlled by the toughness of the web material and also by the web speed. Some characteristic nature of the dynamic stress field surrounding the slitter blade is investigated based on the dynamic fracture mechanics analysis results.

Neutron Diffraction Measurement of the Stress Field During Fatigue Cycling of a Cracked Test Specimen

1989 ◽  
Vol 166 ◽  
Author(s):  
M.T. Hutchings ◽  
C.A. Hippsley ◽  
V. Rainey
Keyword(s):  
Fracture Mechanics ◽  
Neutron Diffraction ◽  
Stress Field ◽  
Test Specimen ◽  
Maximum Stress ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
Diffraction Measurement ◽  
Tension Specimen ◽  
Neutron Diffraction Measurement

ABSTRACTThe triaxial stress field has been measured along the centre line of a compact tension specimen in the direction of cracking. The specimen had been subjected to ∼60,000 cycles at δK=31 and Kmax = 34 MPa mm½ and was bolted open at maximum stress. The field was remeasured after the stress had been fully relaxed. The results are discussed in terms of expectations from fracture mechanics calculations.

Technical Basis for Equations for Stress Intensity Factor Coefficients in ASME Section XI Appendix A

2004 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Programming Languages ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Graphical Form

The stress intensity factor (KI) equations in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field for a surface crack, and linear varying stress field for a sub-surface crack. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. For the buried elliptical flaw, the Gi coefficients are in graphical format. The tabular/graphical form makes the computation of KI tedious when determination of KI for various crack sizes is pursued. In this paper, closed-form equations are developed based on a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation within the current tables in Article 3320 of Appendix A. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. It is expected that the equations developed in this paper will be added to the Appendix A procedures. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently. This is especially useful in performing flaw growth calculations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming languages. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

scholarly journals ASYMPTOTICS OF STRESS AND CONTINUITY FIELDS NEAR A FATIGUE GROWING CRACK IN A DAMAGED MEDIUM IN CONDITIONS OF STATE OF PLANE STRESS

2017 ◽  
Vol 19 (9.2) ◽  
pp. 97-108
Author(s):  
S.A. Igonin ◽  
L.V. Stepanova
Keyword(s):  
Fatigue Crack ◽  
Asymptotic Solution ◽  
Plane Stress ◽  
Asymptotic Expansions ◽  
Asymptotic Representation ◽  
Stress Fields ◽  
Repeated Loading ◽  
Growing Crack

In the paper asymptotic solution to the problem of growth of fatigue crack in conditions of repeated loading in a damaged medium in the coupled elasticity-damage statement of the problem is given. Asymptotic expansions of stress fields and continuity fields in which two summands are retained in asymptotic representation are derived. The problems of determination of amplitude coeffl-cients of obtained asymptotic expansions are discussed.

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