• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.557-568
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• 2007

The elastic T-stress is increasingly being recognized as an important second parameter to the stress intensity factor for fracture and fatigue assessments. In this paper, the mutual or M-contour integral approach is employed in conjunction with the Boundary Element Method (BEM) to determine the numerical T-stress solutions for cracks in plates with multiple holes. The problems investigated include plates of infinite width with multiple holes at which single or double, symmetric cracks have grown from. Comparisons of these results are also made with the corresponding solutions of finite plates with a single hole. For completeness, stress intensity factor solutions for the cracked geometries analyzed are presented as well. These results will be useful for failure assessments using the two-parameter linear elastic fracture mechanics approach.

• Proceedings of the KWS Conference
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• 2003.11a
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• pp.179-181
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• 2003

The present study focuses on the effect of geometrical discontinuity, strength mismatch, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the ductile crack initiation using two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.144-155
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• 2000

초록 The validity, of a single parameter such as stress intensity, factor K or J-integral in traditional fracture mechanics depends strongly on the geometry, and loading condition. Therefore the second parameter like T-stress measuring the stress constraint is additionally needed to characterize the general crack-tip fields. While many, research works have been done to verify, the J-T description of elastic-plastic crack-tip stress fields in plane strain specimens, limited works (especially. for bimaterials) have been performed to describe the structural surface crack-front stress fields with the two parameters. On this background, via detailed three dimensional finite element analyses for surface-cracked plates and straight pipes of homogeneous materials and bimaterials under various loadings, we investigate the extended validity or limitation of the two parameter approach. We here first develop a full 3D mesh generating program for semi-elliptical surface cracks, and calculate elastic T-stress from the obtained finite element stress field. Comparing the J-T predictions to the elastic-plastic stresses from 3D finite element analyses. we then confirm the extended validity of fracture mechanics methodology based on the J-T two parameters in characterizing the surface crack-front fields of welded plates and pipes under various loadings.

• Computers and Concrete
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• v.7 no.4
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.

• Tribology and Lubricants
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• v.36 no.6
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• pp.324-331
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• 2020

Wedging in a frictional elastic system is defined if the state of stick exists after the external loading on the system is removed. This paper presents a method to determine the critical coefficient of wedging for an elastic frictional system by considering the separation state. Wedging is always possible if the coefficient of friction exceeds a critical value known as the critical wedging coefficient. This method requires two concepts: a necessary and sufficient condition for wedging, which can be interpreted as positive spanning sets of constraint vectors existing in the wedged system, and the minimal positive basis that enables a minimum wedging coefficient. The algorithm based on the positive spanning concept is repeatedly executed after eliminating nodes from the contact stiffness matrix, for which the separation states are impending. The simulation results show that once a node enters the separation state, it never returns to the contact state again and the critical wedging coefficient reduces during repeated algorithm execution. The benefit of this method is that the computation time permits handling models with large numbers of contact nodes. The algorithm can also numerically find the critical wedging coefficient, thereby contributing to fastening and assembly performance improvements in mechanical systems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.756-763
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• 2001

In the process of integrity evaluation for nuclear power plant components, a series of fracture mechanics evaluation on surface cracks in reactor pressure vessel(RPV) must be conducted. These fracture mechanics evaluation are based on stress intensity factor, K. However, under pressurized thermal shock(PTS) conditions, the combination of thermal and mechanical stress by steep temperature gradient and internal pressure causes considerably high tensile stress at the inside of RPV wall. Besides, the internal pressure during the normal operation produces high tensile stress at the RPV wall. As a result, cracks on inner surface of RPVs may experience elastic-plastic behavior which can be explained with J-integral. In such a case, however, J-integral may possibly lose its validity due to constraint effect. In this paper, in order to verify the suitability of J-integral, tow dimensional finite element analyses were applied for various surface cracks. A total of 18 crack geometries were analyzed, and $\Omega$ stresses were obtained by comparing resulting HRR stress distribution with corresponding actual stress distributions. In conclusion, HRR stress fields were found to overestimate the actual crack-tip stress field due to constraint effect.

• Structural Engineering and Mechanics
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• v.34 no.2
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• pp.143-157
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• 2010

This paper presents theoretical solutions for the three-dimensional (3D) stress field in an infinite isotropic elastic plate containing a through-the-thickness circular hole subjected to far-field in-plane loads by using Kane and Mindlin's assumption. The dangerous position, where the premature fracture or failure of the plate will take place, the expressions of the tangential stress at the surface of the hole and the out-of-plane stress constraint factor are found in a concise, explicit form. Based on the present theoretical solutions, a comprehensive analysis is performed on the deviated degree of the in-plane stresses from the related plane stress solutions, stress concentration and out-of-plane constraint, and the emphasis has been placed on the effects of the plate thickness, Poisson's ratio and the far-field in-plane loads on the stress field. The analytical solution shows that the effects of the plate thickness and Poisson's ratio on the deviation of the 3D in-plane stress components is obvious and could not be ignored, although their effects on distributions of the in-plane stress components are slight, and that the effect of the far-field in-plane loads is just on the contrary of that of the above two. When only the shear stress is loaded at far field, the stress concentration factor reach its peak value about 8.9% higher than that of the plane stress solutions, and the out-of-plane stress constraint factor can reach 1 at the surface of the hole and is the biggest among all cases considered.

• Journal of the Korean Institute of Gas
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• v.25 no.6
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• pp.14-21
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• 2021

Inner shell material of LNG storage tanks that store ultra-low temperature LNG at -162℃ requires structural integrity assessment of a crack-like defect. From the viewpoint of conventional fracture mechanics, the assessment has mainly performed by single parameter using stress intensity factor K, J-integral and CTOD. However, the stresses in a material of crack tip are not unique caused by constraint loss due to size and geometry of the structure. Various attempts have been made to complement a single parameter fracture mechanics, typically with Q-stress. In this paper, we have performed a two-parameter approach by deriving the Q-stress coupling with J-integral suitable for the evaluation of the crack tip stress field in the non-linear elastic region. A quantitative evaluation of the constraint effect has performed by using the J-Q approach. It was evaluated that the SENB type specimen had a crack ratio of 0.1 to 0.7 and the wide type specimen had a crack ratio of 0.2 to 0.6.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1139-1153
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• 2016

Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.215-229
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• 2014

Due to the lack of effective longitudinal constraint for center tower, structural stiffness of three-tower suspension bridge becomes less than that of two-tower suspension bridge, and therefore it becomes more susceptible to the seismic action. By taking a three-tower suspension bridge-the Taizhou Highway Bridge over the Yangtze River with two main spans of 1080 m as example, structural dynamic characteristics and seismic performance of the bridge is investigated, and the effects of cable's sag to span ratio, structural stiffness of the center tower, and longitudinal constraint of the girder on seismic response of the bridge are also investigated, and the favorable structural system is discussed with respect to seismic performance. The results show that structural response under lateral seismic action is more remarkable, especially for the side towers, and therefore more attentions should be paid to the lateral seismic performance and also the side towers. Large cable's sag, flexible center tower and the longitudinal elastic cable between the center tower and the girder are favorable to improve structural seismic performance of long-span three-tower suspension bridges.