The use of quarter point element in dynamic crack analysis

Boundary element method (BEM) formulations for transient dynamic crack analysis intwo-dimensional (2D) multifield materials are reviwed in this paper. Both homogeneous and lin-ear piezoelectric as well as magnetoelectroelastic material models are considered. Special attentionis paid to properly modeling the non-linear crack-face contact and semi-permeable electric/magneticboundary conditions. Implementation of the corresponding time-domain BEM(TDBEM) is discussedin detail. The proposed TDBEM uses a Galerkin-method for the spatial discretization, whilst thecollocation method is considered for the temporal discretization. Iterative solution algorithms aredeveloped to compute the non-linear crack-face boundary conditions. Crack-tip elements that ac-count for the square-root local behavior of the crack opening displacements (CODs) at the crack-tipsare implemented. In this way, stress intensity factors (SIF), electric displacement intensity factor(EDIF) and magnetic induction intensity factor (MIIF) may be accurately evaluated from the nu-merically computed CODs at the closest nodes to the crack-tips. Numerical examples involving sta-tionary cracks in piezoelectric and magnetoelectroelastic solids under different combined (mechani-cal/electric/magnetic) impact loadings are investigated, in order to illustrate the effectiveness of theproposed approach and characterize the influence of the semi-permeable crack-face boundary condi-tions on the dynamic field intensity factors.

A boundary element method using Laplace transform in time domain is developed for the analysis of fracture mechanic under coupled thermoelastic assumption. The transient coupled thermoelastic field is solved without need for domain discretization. The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by quarter-point elements. Thermal dynamic stress intensity factors for mode I are evaluated from computed nodal values, using the well-known displacement and traction formulas. The accuracy of the method is investigated through comparison of the results with the available data in literature. The conditions where the inertia term plays an important role is discussed and variations of the dynamic stress intensity factor is investigated.

Thermal shock fracture of a cylinder with a penny-shaped crack based on hyperbolic heat conduction

When computing the stress intensity factor (SIF) for high frequency loading it is important to consider dynamic effects such as inertia forces and damping. In the present study, different dynamic simulation procedures were carried out and the achieved SIF values were compared. Fast computation procedures such as modal analysis and direct steady-state analysis were compared to the computationally expensive transient dynamic analysis. Two different methods for calculating the SIF, the J-integral and the CTOD methods, were applied and compared and the results showed a near perfect agreement in calculation of the mode I SIF. The Rayleigh damping model was introduced into the dynamic computation to investigate its effect and the results revealed a clear effect on the SIF at 20 kHz frequency. The fast direct steady-state analysis showed good agreement to both modal and transient analysis with the different damping values used and is recommended as the most effective procedure.

Dynamic fracture behavior of functionally graded magnetoelectroelastic solids by BIEM

Stress intensity factors numerically investigated the Mode I loading of composite plates with an edge crack and repaired with a patch on a single side. The effect of the fiber orientation angle for both composite plate and the patch were analyzed with regard to crack length, adhesive properties, and plate thickness. The stress intensity factors were calculated by using the quarter point element that can be applied to 3D crack problems of homogeneous anisotropic materials.It was observed in this study that the fiber orientation angle affects the stress intensity factors significantly.

In order to investigate the effect of nozzle on stress concentration in pressure vessels, three dimensional finite element analyses were performed. The results were compared with those for corresponding two dimensional axisymmetric finite element analyses. A three dimensional finite element model with a surface crack was also designed to evaluate the effect of internal pressure and heat transfer on crack face, and the resulting stress intensity factors from the finite element analyses were compared with those for ASME Sec. XI and Raju-Newman's stress intensity factor solution. As a result, the validity of currently available stress intensity factor solutions for a surface crack was reviewed in the presence of geometrical complexity, heat transfer and internal pressure.

Elastic–plastic fracture mechanics as well as linear-elastic fracture mechanics may be applied to evaluate a flaw in ferritic low alloy steel components for operating conditions when the material fracture resistance is controlled by upper shelf toughness behavior. In this paper, the distribution of the stress intensity factor (SIF) along a corner crack using elastic–plastic fracture mechanics technique is investigated to assess the effect of a structural factor on mechanical loads in pressurizer vent nozzle penetration weld. For this purpose, the stress intensity factor and the plastic-zone correction of a corner crack are calculated under internal pressure, thermal stress, and residual stress in accordance with Electric Power Research Institute (EPRI) equation and Irwin’s approach, respectively. The resulting stress intensity factor and the plastic-zone correction were compared with those obtained from Structural Integrity Associates (SIA) and Kinectrics Inc., and were observed to be in good agreement with Kinectrics results.

Adaptive Gaussian process regression as an alternative to FEM for prediction of stress intensity factor to assess fatigue degradation in offshore pipeline

In this chapter, aspects of the finite element method for obtaining the displacement field of a body containing an interface crack are described. Square-root singular, quarter-point elements in two and three dimensions will be presented. Once the displacement field is found three methods are suggested for computing stress intensity factors; they include the displacement extrapolation (DE) method, the conservative interaction energy integral or M-integral, and the Virtual Crack Closure Technique (VCCT). The stress intensity factors are then employed to obtain the interface energy release rate and two phase angles.

Implementation of XFEM for dynamic thermoelastic crack analysis under non-classic thermal shock

At present, development of manufacturer’s ultrasonic cleaning tank (UCT) to match the requirements from consumers usually relies on computer simulation based on harmonic response analysis (HRA). However, this technique can only be used with single-frequency UCT. For dual frequency, the manufacturer used information from empirical experiment alongside trial-and-error methods to develop prototypes, resulting in the UCT that may not be fully efficient. Thus, lack of such a proper calculational method to develop the dual frequency UCT was a problem that greatly impacted the manufacturers and consumers. To resolve this problem, we proposed a new model of simulation using transient dynamics analysis (TDA) which was successfully applied to develop the prototype of dual frequency UCT, 400 W, 18 L in capacity, eight horn transducers, 28 and 40 kHz frequencies for manufacturing. The TDA can indicate the acoustic pressure at all positions inside the UCT in transient states from the start to the states ready for proper cleaning. The calculation also reveals the correlation between the positions of acoustic pressure and the placement positions of transducers and frequencies. In comparison with the HRA at 28 kHz UCT, this TDA yielded the results more accurately than the HRA simulation, comparing to the experiments. Furthermore, the TDA can also be applied to the multifrequency UCTs as well. In this article, the step-by-step development of methodology was reported. Finally, this simulation can lead to the successful design of the high-performance dual frequencies UCT for the manufacturers.

Evaluation of crack tip constraint using photoelasticity

Stress intensity factors for cracks emanating from a triangular or square hole in an infinite plate by boundary elements

Transient thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method