Unified Model for Fracture of Brittle Solids

2007 ◽  
Vol 280-283 ◽  
pp. 1739-1744
Author(s):  
Vladimir D. Krstić
Keyword(s):  
Residual Stresses ◽  
Crack Opening ◽  
Unified Model ◽  
Brittle Solid ◽  
Opening Displacement ◽  
Two Phase ◽  
Brittle Solids ◽  
Cylindrical Pores ◽  
Polycrystalline Solids ◽  
Phase Systems

A unified model for fracture of brittle solid based on crack opening displacement is presented. The model allows the prediction of elastic and fracture response of brittle materials containing spherical and cylindrical pores and polycrystalline solids containing anisotropic residual stresses. The analysis can also be used to predict spontaneous cracking and fracture of two phase systems possessing mismatch stresses.

A Simple Approach for Including Weld Residual Stresses in the Calculation of Pipe Circumferential Through-Wall Crack Opening Displacements

2016 ◽  
Author(s):  
Richard Olson
Keyword(s):  
Residual Stresses ◽  
Axial Force ◽  
Analytic Solution ◽  
Crack Opening ◽  
Bending Moment ◽  
Generalized Solution ◽  
Finite Element Analyses ◽  
Opening Displacement ◽  
Crack Face ◽  
Basic Equations

Current methodologies for predicting the crack opening displacement (COD) of circumferentially through-wall cracked pipe do not include the effect of weld residual stresses (WRS). Even the most advanced COD prediction methodology only includes the effect of applied axial force, bending moment, and crack face pressure. For some years, it has been known that weld residual stresses do alter the COD, but there has been no convenient way to include them in a COD prediction without doing case-specific finite element analyses. This paper documents a generalized solution for including WRS effects on COD. The model uses a closed-form analytic solution to approximate the crack face rotations that the WRS would induce which, subsequently, can be added to the typical axial force-bending-crack face pressure COD solution. The methodology is described and the basic equations for the solution are presented. Following this, application to cases to evaluate the efficacy of the approach are presented which show a mixture of results ranging from amazingly good to “of questionable value” with respect to the FEA results.

scholarly journals Nanobeams with Internal Discontinuities: A Local/Nonlocal Approach

Nanomaterials ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 2651
Author(s):  
Daniela Scorza ◽  
Sabrina Vantadori ◽  
Raimondo Luciano
Keyword(s):  
Convex Combination ◽  
Crack Opening ◽  
Integral Model ◽  
The Novel ◽  
Opening Displacement ◽  
Two Phase ◽  
Size Dependent ◽  
Mixture Parameter ◽  
Parameter Values ◽  
First Time

The aim of the present work is to extend the two-phase local/nonlocal stress-driven integral model (SDM) to the case of nanobeams with internal discontinuities: as a matter of fact, the original formulation avoids the presence of any discontinuities. Consequently, here, for the first time, the problem of an internal discontinuity is addressed by using a convex combination of both local and nonlocal phases of the model by introducing a mixture parameter. The novel formulation here proposed was validated by considering six case studies involving different uncracked nanobeams by varying the constrains and the loading configurations, and the effect of nonlocality on the displacement field is discussed. Moreover, a centrally-cracked nanobeam, subjected to concentrated forces at the crack half-length, was studied. The size-dependent Mode I fracture behaviour of the cracked nanobeam was analysed in terms of crack opening displacement, energy release rate, and stress intensity factor, showing the strong dependency of the above fracture properties on both dimensionless characteristic length and mixture parameter values.

Effect of Weld Induced Residual Stresses on Pipe Crack Opening Areas and Implications on Leak-Before-Break Considerations

2002 ◽  
Author(s):  
Lee Fredette ◽  
F. W. Brust
Keyword(s):  
Residual Stresses ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Crack Size ◽  
Battelle Memorial Institute ◽  
Pipe Material ◽  
Correction Factors ◽  
Opening Displacement ◽  
Leak Before Break ◽  
Current Guidelines

The USNRC is anticipating updating their leak-before-break (LBB) procedures. One of the technical areas of concern in the existing procedures is the prediction of the crack-opening-displacements (COD) needed for estimating the postulated leakage crack size for a prescribed leakage detection capability. If cracks develop in the welded area of a pipe, as is often the case, residual stresses in the weld may cause the crack to be forced closed. Earlier studies have shown that pipe welding produces high residual stresses with a sharp stress gradient ranging from tension to compression through the thickness of the welded area of the pipe. The current guidelines are inadequate to predict crack size based on leak rates for cracks in welded areas of pipes. The current guidelines rely on the calculation of the crack-opening-displacement as related to pipe loading. Values from the current guidelines are used to predict a crack’s cross sectional area and, in turn, to determine the severity of an existing crack by monitoring in-service leakage rates. The equations currently in use are applicable to service loaded pipe material only. Residual stresses caused by cold work, welding, etc. are neglected. This study uses two and three dimensional finite element models and weld residual stress calculation software created at Battelle Memorial Institute to develop correction factors to be used with the traditional design equations. The correction factors will compensate for the effects of welding induced residual stresses on cracks in pipe welds. This study concentrates on type 316 stainless steel material properties, but the COD corrections should be equally applicable to all stainless steels, and also can be used for ferritic steels. A test matrix of pipe radius, thickness, and crack size was used to develop the equation correction factors. Pipe wall thicknesses (t) of 7.5 mm (0.295 in.), 15 mm (0.590 in.), 22.5 mm (0.886 in.), and 30 mm (1.181 in.) were studied in pipes with mean radius to thickness ratios of 5, 10, and 20. Cracks with half-lengths in radians of π/16, π/8, π/4, and π/2 were introduced in these virtual pipes. The matrix of results was used to produce correction factors for crack opening displacement equations applicable to a broad range of pipe sizes.

Recent Ideas in Plastics for Aircraft Structures

1956 ◽  
Vol 60 (547) ◽  
pp. 476-481
Author(s):  
J. E. Gordon
Keyword(s):  
High Strength ◽  
Common Salt ◽  
Brittle Solid ◽  
Two Phase ◽  
Aircraft Structures ◽  
Brittle Solids ◽  
Inherent Strength ◽  
Glass Metal ◽  
Very High

SummaryStrong plastics consist of two-phase arrangements of pairs of brittle solids which in combination may be very tough. Improvement now depends upon an understanding of brittle solid theory. The strength of brittle solids is generally very low but may occasionally approach the very high theoretical values. This is due to the high inherent strength being generally marred by tiny defects. When these defects are removed or contained high strength may be achieved. The various mechanisms by which this may be done are exemplified in mica, common salt, glass, metal whiskers and so on. The relevance of these substances and mechanisms to the manufacture of plastics is discussed.

Microcracking in Polycrystalline Solids

1988 ◽  
Vol 110 (2) ◽  
pp. 101-104 ◽  
Author(s):  
N. Laws ◽  
J. R. Brockenbrough
Keyword(s):  
Grain Boundary ◽  
Residual Stresses ◽  
Grain Boundaries ◽  
Applied Load ◽  
Process Zone ◽  
Crack Density ◽  
Hexagonal Array ◽  
Brittle Solid ◽  
Micro Cracks ◽  
Polycrystalline Solids

A polycrystalline brittle solid may undergo grain boundary micro-cracking due to residual stresses or applied load. This paper contains some results pertaining to the loss of macroscopic stiffness of such solids when all micro-cracks are open and when some may be closed and be subject to frictional sliding. Two specific models are investigated: first micro-cracking on the grain boundaries of a regular hexagonal array, second, micro-cracks which are randomly located and oriented. It is shown that for many purposes the two models give identical results. The paper concludes with some analysis of the possible toughening due to process zone micro-cracking at the tip of a macroscopic crack. It is found that toughening can only occur if the saturation crack density is very large.

Welding Residual Stresses and Effects on Fracture in Pressure Vessel and Piping Components: A Millennium Review and Beyond

2000 ◽  
Vol 122 (3) ◽  
pp. 329-338 ◽  
Author(s):  
P. Dong ◽  
F. W. Brust
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Pressure Vessel ◽  
Crack Opening ◽  
Opening Displacement ◽  
Stress Effects ◽  
Weld Residual Stress ◽  
Growing Crack ◽  
Critical Issues ◽  
Stress Prediction

In this paper, the recent advances in weld residual stress modeling procedures are first reviewed within the context of pressure vessel and piping applications. A typical pipe girth weld was then used as an example to highlight some of the critical issues in weld residual stress prediction, measurement, and residual stress effects on various aspects of fracture behaviors from stress intensity factor solutions for a growing crack to crack-opening displacement calculations for leak-before-break assessment. Finally, the future needs in improved fracture mechanics procedures by incorporating the rapidly expanding knowledge on weld residual stresses are summarized with respect to pressure vessel and piping applications. [S0094-9930(00)02103-X]

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