scholarly journals A Continuum Theory of Crack Shielding in Ceramics

1987 ◽  
Vol 54 (1) ◽  
pp. 54-58 ◽  
Author(s):  
M. Ortiz
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Constitutive Model ◽  
Closed Form ◽  
Applied Stress ◽  
Continuum Theory ◽  
Displacement Fields ◽  
Stress Strain ◽  
Macroscopic Crack

A phenomenological constitutive model is proposed which aims at describing the overall effect of microfracture in ceramics. Based on this model, the asymptotic stress, strain, and displacement fields at the tip of a stationary macroscopic crack are determined in closed form. The near-tip stress-intensity factor is computed and observed to be significantly smaller than the applied stress-intensity factor even for moderate amounts of damage.

scholarly journals The transition from subsonic to supersonic cracks

2015 ◽  
Vol 373 (2038) ◽  
pp. 20140122 ◽  
Author(s):  
Chris Behn ◽  
M. Marder
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Low Frequency ◽  
Continuum Theory ◽  
Vertical Displacement ◽  
Displacement Fields ◽  
Lattice Systems ◽  
Crack Motion ◽  
Rayleigh Wave Speed

We present the full analytical solution for steady-state in-plane crack motion in a brittle triangular lattice. This allows quick numerical evaluation of solutions for very large systems, facilitating comparisons with continuum fracture theory. Cracks that propagate faster than the Rayleigh wave speed have been thought to be forbidden in the continuum theory, but clearly exist in lattice systems. Using our analytical methods, we examine in detail the motion of atoms around a crack tip as crack speed changes from subsonic to supersonic. Subsonic cracks feature displacement fields consistent with a stress intensity factor. For supersonic cracks, the stress intensity factor disappears. Subsonic cracks are characterized by small-amplitude, high-frequency oscillations in the vertical displacement of an atom along the crack line, while supersonic cracks have large-amplitude, low-frequency oscillations. Thus, while supersonic cracks are no less physical than subsonic cracks, the connection between microscopic and macroscopic behaviour must be made in a different way. This is one reason supersonic cracks in tension had been thought not to exist.

The Importance of the Mode II Term on the Analysis of Angled Cracks in Unidirectional Carbon Fiber Composites

2021 ◽  
Author(s):  
Jacob Biddlecom ◽  
Garrett J. Pataky
Keyword(s):  
Stress Intensity Factor ◽  
Regression Analysis ◽  
Stress Intensity ◽  
Carbon Fiber ◽  
Intensity Factor ◽  
Fiber Composites ◽  
Shear Loading ◽  
Mode Ii ◽  
Carbon Fiber Composites ◽  
Displacement Fields

Abstract Carbon fiber reinforced polymers (CFRP) have been used in many high-performance applications where strength to weight ratio is an important characteristic. The goal of this research was to analyze the effects of Mode II, also known as shear loading, on the displacement fields surrounding a crack for unidirectional carbon fiber composites. Tensile and fatigue experiments were conducted on angled unidirectional CFRP coupled with digital image correlation (DIC) to analyze the full field displacement. Angled CFRP cracks experienced mixed mode loading which required addition insight due to the complex stresses on the fiber/matrix interface. The experimental displacement fields acquired from DIC were used as inputs for an anisotropic regression analysis to determine the mode I and mode II stress intensity factor ranges. The results from the regression analysis were used to predict the displacement fields around a crack. When comparing the experimental results with the predicted results, the inclusion of Mode II increased the agreement between predicted and experimental displacement fields around a crack tip for two different fiber orientation angles. Crack growth rate analysis and analytical stress intensity factor ranges were used to expand on the agreement of the results as well as bring to light CFRP specific fracture mechanisms that lead to disagreements.

Closed-Form Stress Intensity Factor Solutions for Surface Cracks With Large Aspect Ratios in Plates

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Steven Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Influence Coefficient ◽  
Maximum Point ◽  
Surface Cracks ◽  
Fourth Degree ◽  
Aspect Ratios ◽  
Influence Coefficients

Abstract Alloy 82/182/600, which is used in light-water reactors, is known to be susceptible to stress-corrosion cracking. The depth of some of these cracks may exceed the value of half-length on the surface. Although the stress intensity factor (SIF) for cracks plays an important role in predicting crack propagation and failure, Section XI of the ASME Boiler and Pressure Vessel Code does not provide SIF solutions for such deep cracks. In this study, closed-form SIF solutions for deep surface cracks in plates are discussed using an influence coefficient approach. The stress distribution at the crack location is represented by a fourth-degree-polynomial equation. Tables for influence coefficients obtained by finite element analysis in the previous studies are used for curve fitting. The closed-form solutions for the influence coefficients were developed at the surface point, the deepest point, and the maximum point of a crack with an aspect ratio a/c ranging from 1.0 to 8.0, where a is the crack depth and c is one-half of the crack length. The maximum point of a crack refers to the location on the crack front where the SIF reaches a maximum value.

Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

2013 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Flat Plate ◽  
Closed Form ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Plate Geometry

The stress intensity factor (KI) equations for a surface crack 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. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is required and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The equations presented, represent a complete set of Ri/t, a/t, and a/l ratios and include those presented in the 2012 PVP paper [8]. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using 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. 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. The equations developed in this paper will be added to the Appendix A procedures in the next major revision to ASME Section XI. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful when performing flaw growth evaluations 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. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

Closed-Form Calculation of Stress Intensity Factor for an Axial ID Surface Flaw in Cylinder Subjected to Weld Residual Stresses

2013 ◽  
Author(s):  
Douglas A. Scarth ◽  
Steven X. Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Function Method ◽  
Current Method ◽  
Surface Flaw ◽  
Weight Function Method ◽  
Influence Coefficients

A method for calculating the stress intensity factor for linear elastic fracture mechanics based flaw evaluation is provided in Appendix A-3000 of ASME Section XI. In the 2010 Edition of ASME Section XI, the calculation of stress intensity factor for a surface crack is based on characterization of stress field with a cubic equation and use of influence coefficients. The influence coefficients are currently only provided for flat plate geometry in tabular format. The ASME Section XI Working Group on Flaw Evaluation is in the process of rewriting Appendix A-3000. Proposed major updates include the implementation of explicit use of Universal Weight Function Method for calculation of the stress intensity factor for a surface flaw and the inclusion of closed-form influence coefficients for cylinder geometry. The explicit use of weight function method eliminates the need for fitting polynomial equations to the actual through-thickness stress distributions at crack location. In this paper, the proposed Appendix A procedure is applied to calculate the stress intensity factors in closed-form for an axial ID surface flaw in a cylinder subjected to a set of nonlinear hoop weld residual stress profiles. The calculated stress intensity factor results are compared with the results calculated based on the current method in Appendix A using cubic equations to represent the stress distribution. Three-dimensional finite element analyses were performed to verify the accuracy of the stress intensity factor results calculated based on the current and proposed Appendix A procedures. The results in this paper support the implementation of the proposed stress intensity factor calculation procedure into ASME Code.

Closed-Form Relations for Stress Intensity Factor Influence Coefficients for Axial Outside Surface Flaws in Cylinders for Appendix A of ASME Section XI

2016 ◽  
Author(s):  
Steven X. Xu ◽  
Darrell R. Lee ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Inside Surface ◽  
Linear Elastic ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Elastic Fracture ◽  
Flaw Location

Linear elastic fracture mechanics based flaw evaluation procedures in Section XI of the ASME Boiler and Pressure Vessel Code require calculation of the stress intensity factor. Article A-3000 of Appendix A in ASME Section XI prescribes a method to calculate the stress intensity factor for a surface or subsurface flaw by making use of the flaw location stress distribution obtained in the absence of the flaw. The 2015 Edition of ASME Section XI implemented a number of significant improvements in Article A-3000, including closed-form equations for calculating stress intensity factor influence coefficients for circumferential flaws on the inside surface of cylinders. Closed-form equations for stress intensity factor influence coefficients for axial flaws on the inside surface of cylinders have also been developed. Ongoing improvement efforts for Article A-3000 include development of closed-form relations for the stress intensity factor coefficients for flaws on the outside surface of cylinders. The development of closed-form relations for stress intensity factor coefficients for axial flaws on the outside surface of cylinders is described in this paper.

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