Elastodynamic Fracture Analysis of Multiple Cracks by Laplace Finite Element Alternating Method

1999 ◽  
Vol 67 (3) ◽  
pp. 606-615 ◽  
Author(s):  
W.-H. Chen ◽  
C.-L. Chang ◽  
C.-H. Tsai
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Laplace Transform ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Alternating Method ◽  
The Laplace Transform

The Laplace finite element alternating method, which combines the Laplace transform technique and the finite element alternating method, is developed to deal with the elastodynamic analysis of a finite plate with multiple cracks. By the Laplace transform technique, the complicated elastodynamic fracture problem is first transformed into an equivalent static fracture problem in the Laplace transform domain and then solved by the finite element alternating method developed. To do this, an analytical solution by Tsai and Ma for an infinite plate with a semi-infinite crack subjected to exponentially distributed loadings on crack surfaces in the Laplace transform domain is adopted. Finally, the real-time response can be computed by a numerical Laplace inversion algorithm. The technique established is applicable to the calculation of dynamic stress intensity factors of a finite plate with arbitrarily distributed edge cracks or symmetrically distributed central cracks. Only a simple finite element mesh with very limited number of regular elements is necessary. Since the solutions are independent of the size of time increment taken, the dynamic stress intensity factors at any specific instant can even be computed by a single time-step instead of step-by-step computations. The interaction among the cracks and finite geometrical boundaries on the dynamic stress intensity factors is also discussed in detail. [S0021-8936(00)02103-6]

Use of Jˆ-Integral in Dynamic Analysis of Cracked Linear Viscoelastic Solids by Finite-Element Method

1982 ◽  
Vol 49 (1) ◽  
pp. 75-80 ◽  
Author(s):  
K. Kishimoto ◽  
S. Aoki ◽  
M. Sakata
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Computational Method ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Element Method

A computational method using the path (area)-independent Jˆ-integral is developed to analyze viscoelastic problems. Since the displacement field near the crack tip of a viscoelastic solid is dependent upon the complete past history of the dynamic stress-intensity factors, the Jˆ-integral is represented by a hereditary integral of the dynamic stress-intensity factors. We assume that the stress and strain rates vary in proportion to time during each increment of time and derive a formula to obtain the current value of the dynamic stress-intensity factor from the time increment of the Jˆ-value. Both pure and mixed mode problems of a suddenly loaded crack are analyzed by making use of the formula together with the conventional finite-element method. In order to demonstrate the capability and reliability of the present method, problems of a center crack and an oblique crack in viscoelastic rectangular plates are solved.

scholarly journals Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear

1997 ◽  
Vol 64 (1) ◽  
pp. 66-72 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Stress Intensity ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Dynamic Stress ◽  
Layered Medium ◽  
Transform Domain ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, the transient analysis of dynamic antiplane crack propagation with a constant velocity in a layered medium is investigated. The individual layers are isotropic and homogeneous. Infinite numbers of reflected cylindrical waves, which are generated from the interface of the layered medium, will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study, and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. The exact closed-form transient solutions of dynamic stress intensity factors are expressed in compact formulations. These solutions are valid for an infinite length of time and have accounted for contributions from all the incident and reflected waves interaction with the moving crack tip. Numerical results of dynamic stress intensity factors for the propagation crack in layered medium are evaluated and discussed in detail.

Modeling Crack Growth in Weld Residual Stress Fields Using the Finite Element Alternating Method

2011 ◽  
Author(s):  
F. W. Brust ◽  
T. Zhang ◽  
D.-J. Shim ◽  
G. Wilkowski ◽  
D. Rudland
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Stress Intensity ◽  
Crack Growth ◽  
Stress Intensity Factors ◽  
Corrosion Cracking ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Pressurized Water ◽  
Alternating Method

Flaw indications have been found in some nozzle to stainless steel piping dissimilar metal (DM) welds and reactor pressure vessel heads (RPVH) in pressurized water reactors (PWR) throughout the world. The nozzle welds usually involve welding ferritic (often A508) nozzles to 304/316 stainless steel pipe) using Alloy 182/82 weld metal. The welds may become susceptible to a form of corrosion cracking referred to as primary water stress corrosion cracking (PWSCC). It can occur if the temperature is high enough (usually >300C) and the water chemistry in the PWR is typical of operating plants. The weld residual stresses (WRS) induced by the welds are a main driver of PWSCC. Modeling the growth of these cracks in these WRS fields until leakage occurs is important for safety assessments. Currently, the prediction of PWSCC crack growth is based on the stress intensity factors at the crack tips. Several methods for modeling the crack growth through these WRS fields are possible, including using analytical, natural crack growth using finite element methods, and using the finite element alternating method. In this paper, finite element alternating method (FEAM) is used for calculating stress intensity factors and modeling the growth. First the FEAM method for growing cracks is presented. Next, several examples of modeling growth through control rod drive mechanism (CRDM) heads are presented. Finally, a short example examining multiple cracks in CRDM heads is presented. For many problems the FEAM approach for rapidly modeling crack growth is quite convenient, especially for difficult to mesh crack geometries.

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