scholarly journals Stress and Displacement Intensity Factors of Cracks in Anisotropic Media

2020 ◽  
Vol 25 (3) ◽  
pp. 212-218
Author(s):  
S. Kuznetsov ◽  
A. Karakozova
Keyword(s):  
Stress Intensity ◽  
Anisotropic Medium ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Displacement Discontinuity ◽  
Pseudodifferential Equation ◽  
Intensity Factors ◽  
Elastic Anisotropic Medium ◽  
Arbitrary Anisotropy ◽  
Vector Valued

AbstractA relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.

Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

2017 ◽  
Vol 29 (6) ◽  
pp. 1255-1271 ◽  
Author(s):  
MingHao Zhao ◽  
Yuan Li ◽  
CuiYing Fan
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Stress Intensity Factors ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Green Functions ◽  
Intensity Factors

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.

Natural Flaw Shape Development Due to Stress Corrosion Cracking

2008 ◽  
Author(s):  
D. Rudland ◽  
D.-J. Shim ◽  
A. Csontos
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Nodal Point ◽  
Nuclear Industry ◽  
Operating Conditions ◽  
Welding Residual Stress ◽  
Intensity Factors ◽  
Natural Manner ◽  
Flaw Shape

Typical ASME Section XI subcritical cracking analyses assume an idealized flaw shape driven by stress intensity factors developed for semi-elliptical shaped flaws. Recent advanced finite element analyses (AFEA) conducted by both the US NRC and the nuclear industry for long circumferential indications found in the pressurizer nozzle dissimilar metal welds at the Wolf Creek power plant, suggest that the semi-elliptical flaw assumption may be overly conservative in some cases. The AFEA methodology that was developed allowed the progression of a planar flaw subjected to typical SCC-type growth laws by calculating stress intensity factors at every nodal point along the crack front, and incrementally advancing the crack front in a more natural manner. Typically crack growth analyses increment the semi-elliptical flaw by considering only the stress intensity factor at the deepest and surface locations along the crack front, while keeping the flaw shape semi-elliptical. In this paper, a brief background to the AFEA methodology and the analyses conducted in the Wolf Creek effort will be discussed. In addition, the natural behavior of surface cracks under normal operating conditions (plus welding residual stress) will be investigated and compared to the semi-elliptical assumption. Conclusions on the observation of when semi-elliptical flaw assumptions are appropriate will be made. These observations will add insight into the conservatism of using an idealized flaw shape assumption.

An Efficient and Accurate Numerical Method of Stress Intensity Factors Calculation of a Branched Crack

2005 ◽  
Vol 72 (3) ◽  
pp. 330-340 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Extension ◽  
Crack Tip ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Displacement Discontinuity Method ◽  
Intensity Factors ◽  
Constant Displacement ◽  
The Right

Based on the analytical solution of Crouch to the problem of a constant discontinuity in displacement over a finite line segment in an infinite elastic solid, in the present paper, the crack-tip displacement discontinuity elements, which can be classified as the left and the right crack-tip elements, are presented to model the singularity of stress near a crack tip. Furthermore, the crack-tip elements together with the constant displacement discontinuity elements presented by Crouch and Starfied are used to develop a numerical approach for calculating the stress intensity factors (SIFs) of general plane cracks. In the boundary element implementation, the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called the hybrid displacement discontinuity method (HDDM). Numerical examples are given and compared with the available solutions. It can be found that the numerical approach is simple, yet very accurate for calculating the SIFs of branched cracks. As a new example, cracks emanating from a rhombus hole in an infinite plate under biaxial loads are taken into consideration. The numerical results indicate the efficiency of the present numerical approach and can reveal the effect of the biaxial load on the SIFs. In addition, the hybrid displacement discontinuity method together with the maximum circumferential stress criterion (Erdogan and Sih) becomes a very effective numerical approach for simulating the fatigue crack propagation process in plane elastic bodies under mixed-mode conditions. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the HDDM. Crack propagation is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented.

Mode Mixity for Circular Hollow Section X Joints With Weld Toe Cracks

2005 ◽  
Vol 127 (3) ◽  
pp. 269-279 ◽  
Author(s):  
X. Qian ◽  
Robert H. Dodds ◽  
Y. S. Choo
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Mixed Mode ◽  
Crack Depth ◽  
Intensity Factors ◽  
Mode Mixity ◽  
Hollow Section ◽  
Mode Stress ◽  
Circular Hollow Section

This paper describes the mode mixity of stress-intensity factors for surface cracks at weld toes located at the saddle point in circular hollow section X joints. The remote loading applies a uniform tensile stress at the end of the brace along its axis. The three-dimensional finite element models employ mesh tieing between a topologically continuous, global mesh and a separate, local crack-front mesh. Analyses of a simple plate model that approximates key features of toe cracks at the brace-chord intersection verify the negligible effects of the recommended mesh-tieing scheme on stress intensity factors. The linear-elastic analyses compute the mixed-mode stress intensity factors along the crack front using an interaction-integral approach. The mixed-mode stress intensity factors indicate that the crack front experiences predominantly mode I loading, with KIII→0 near the deepest point on the front (ϕ=π∕2). The total crack driving force, described by the J integral, reaches a maximum value at the deepest point of the crack for the crack aspect ratio a∕c=0.25 considered here. The mode-mixity angle, ψ=tan−1(KII∕KI), at ϕ=π∕2 is compared for a range of practical X-joint configurations and crack-depth ratios. The present study demonstrates that the mode-mixity angle ψ increases with increasing brace-to-chord diameter ratio (β) and decreasing chord radius to wall thickness ratio (γ). Values of the nondimensional stress intensity factors (FI=KI∕σ¯brπa and FII=KII∕σ¯brπa), however, show an opposite trend, with higher crack driving forces for small β and large γ ratios. The variations in the brace-to-chord wall thickness ratio (τ) and the crack depth ratio (a∕t0) do not generate significant effects on the mode mixity.

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