The reliability analysis of welded structure with embedded cracks by using three dimensional stochastic FEM

In this paper, the reliability of welded structure with an embedded elliptical crack was calculated by using three dimensional stochastic finite element method. This method has overcome the shortcomings of conservative results in safety assessment with deterministic fracture mechanics method. The calculation of reliability was based on three dimensional perturbation stochastic finite element program which was developed by ourselves. The effects of variables (such as fracture toughness K IC , load P, the ratio of minor axis to major axis a/c) on the structure reliability were also discussed. The calculation results indicate that among the three variables (K IC ,P, a/c) , the fracture toughness K IC has the greatest effect on the structure reliability. The next is external load P. The ratio of the a/c has lower effect on structure reliability than both K IC and P . The method has put forward a new way for safety assessment of welded structure with embedded elliptical cracks.

Numerical simulation on effects of embedded crack on rock fragmentation by a tunnel boring machine cutter

Based on the simplification of cutting process,a series of numerical simulations were conducted using a 2-D discrete element method to explore the effects of embedded cracks with different dip angles on the rock fragmentation process,cutting characteristics and breaking efficiency.The results show that the simulated results are in a good agreement with previous theoretical study.The main crack propagates to the top tip of embedded crack,except when the dip angle is 90°.Side cracks which are more fully developed in the rocks containing embedded cracks tend to propagate towards the free surface.According to the history of vertical cutting force,it is shown that the peak force is decreased by embedded cracks.The study on cutting efficiency was conducted by combining the quantity of crack and cutting energy.And the results show that breaking efficiency can be treated as a decreasing or a increasing function when the dip angle is less or larger than 30°,respectively.Breaking efficiency is higher than that in intact rock when the dip angle is larger than 45°.

Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.

Four-Beam Model for Vibration Analysis of a Cantilever Beam with an Embedded Horizontal Crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton＇s principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.

Temperature field at time of pulse current discharge in metal structure with elliptical embedding crack

Theoretical analysis is made on the temperature field at the time of pulse current discharge in a metal structure with an elliptical embedding crack. In finding the temperature field, analogy between the current flow through an elliptical embedding crack and the fluid flow through a barrier is made based on the similarity principle. Boundary conditions derived from this theory are introduced so that the distribution of current density and the temperature field expressions can be obtained. The study provides a theoretic basis to the applications of stopping spatial crack with electromagnetic heating.