Relation Between Stochastic Failure Location and Strength in Brittle Materials

2005 ◽  
Vol 73 (4) ◽  
pp. 698-701 ◽  
Author(s):  
Sefi Givli ◽  
Eli Altus
Keyword(s):  
Stress Field ◽  
Brittle Materials ◽  
Simple Function ◽  
Statistical Characteristics ◽  
Material Strength ◽  
One Dimensional ◽  
Specific Strength ◽  
Weakest Link ◽  
Average Variance ◽  
Failure Location

Statistical characteristics of failure location and their relation to strength in brittle materials are studied. One-dimensional rod and bending of a beam under arbitrary distributed loads are studied as examples. The analysis is based on the weakest link approach, and is not confined to specific strength distributions (such as Weibull, Gaussian, etc.). It is found that the statistical moments of the failure location (average, variance, etc.) are directly related to the area moments (centroid, inertia, etc.) of a simple function of the stress field. Therefore, important information related to material strength can be experimentally obtained based on measuring failure locations. Such experiments do not require the measurement of stresses, strains, or displacements, and are very attractive for MEMS/NEMS applications. The approach is general and can be applied to other types of testing specimens.

Study on Failure of Rock Mass around Deep Tunnel

2011 ◽  
Vol 99-100 ◽  
pp. 370-374 ◽  
Author(s):  
Yue Hong Qian ◽  
Ting Ting Cheng ◽  
Xiang Ming Cao ◽  
Chun Ming Song
Keyword(s):  
Rock Mass ◽  
Stress Field ◽  
Failure Modes ◽  
Shear Failure ◽  
Simple Function ◽  
Tensile Failure ◽  
Deep Tunnel ◽  
Main Mode

During excavating the problem of unloading is a dynamic one essentially. Assuming the unloading ruled by a simple function and based on the Hamilton principal, the distribution of the stress field nearby the tunnel is obtained. The characteristics of the failure nearby the tunnel are analyzed considering the shear failure and tensile failure. The results show that the main mode of the shear failure, intact and tensile failure occurs from the tunnel. The characteristic of the shear failure, intact and tensile failure are one of the likely failure modes.

Modeling of a Beam and a Rotor with an Edge Crack Using Dissimilar Elements

2003 ◽  
Vol 9 (10) ◽  
pp. 1159-1187 ◽  
Author(s):  
A. Nandi ◽  
S. Neogy
Keyword(s):  
Finite Elements ◽  
Stress Field ◽  
Edge Crack ◽  
Three Dimensional ◽  
Transition Element ◽  
Two Dimensional ◽  
Cracked Beam ◽  
One Dimensional ◽  
Beam Elements ◽  
Dimensional Plane

Vibration-based diagnostic methods are used for the detection of the presence of cracks in beams and other structures. To simulate such a beam with an edge crack, it is necessary to model the beam using finite elements. Cracked beam finite elements, being one-dimensional, cannot model the stress field near the crack tip, which is not one-dimensional. The change in neutral axis is also not modeled properly by cracked beam elements. Modeling of such beams using two-dimensional plane elements is a better approximation. The best alternative would be to use three-dimensional solid finite elements. At a sufficient distance away from the crack, the stress field again becomes more or less one-dimensional. Therefore, two-dimensional plane elements or three-dimensional solid elements can be used near the crack and one-dimensional beam elements can be used away from the crack. This considerably reduces the required computational effort. In the present work, such a coupling of dissimilar elements is proposed and the required transition element is formulated. A guideline is proposed for selecting the proper dimensions of the transition element so that accurate results are obtained. Elastic deformation, natural frequency and dynamic response of beams are computed using dissimilar elements. The finite element analysis of cracked rotating shafts is complicated because of the fact that elastic deformations are superposed on the rigid-body motion (rotation about an axis). A combination of three-dimensional solid elements and beam elements in a rotating reference is proposed here to model such rotors.

A Renewal Weakest-Link Model of Strength Distribution of Polycrystalline Silicon MEMS Structures

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Zhifeng Xu ◽  
Roberto Ballarini ◽  
Jia-Liang Le
Keyword(s):  
Experimental Data ◽  
Polycrystalline Silicon ◽  
Microelectromechanical Systems ◽  
Strength Distribution ◽  
Material Strength ◽  
Mems Devices ◽  
Efficient Computation ◽  
Weakest Link ◽  
Large Size ◽  
The Stability

Experimental data have made it abundantly clear that the strength of polycrystalline silicon (poly-Si) microelectromechanical systems (MEMS) structures exhibits significant variability, which arises from the random distribution of the size and shape of sidewall defects created by the manufacturing process. Test data also indicated that the strength statistics of MEMS structures depends strongly on the structure size. Understanding the size effect on the strength distribution is of paramount importance if experimental data obtained using specimens of one size are to be used with confidence to predict the strength statistics of MEMS devices of other sizes. In this paper, we present a renewal weakest-link statistical model for the failure strength of poly-Si MEMS structures. The model takes into account the detailed statistical information of randomly distributed sidewall defects, including their geometry and spacing, in addition to the local random material strength. The large-size asymptotic behavior of the model is derived based on the stability postulate. Through the comparison with the measured strength distributions of MEMS specimens of different sizes, we show that the model is capable of capturing the size dependence of strength distribution. Based on the properties of simulated random stress field and random number of sidewall defects, a simplified method is developed for efficient computation of strength distribution of MEMS structures.

Constitutive Inequalities for the Damage of Elastic-Brittle Materials

2011 ◽  
Vol 675-677 ◽  
pp. 891-899
Author(s):  
Qi Chang He ◽  
J.Z. Zhou
Keyword(s):  
Three Dimensional ◽  
Brittle Materials ◽  
Dimensional Case ◽  
Continuum Damage ◽  
One Dimensional ◽  
Damage Models ◽  
Constitutive Inequalities ◽  
The One

Starting from the requirement that the principle of determinism be satisfied, two constitutive inequalities are derived for one-dimensional strain- and stress-based continuum damage models. The one-dimensional constitutive inequality corresponding to the strain-based formulation turns out to be much less restrictive than the one associated to the stress-based formulation and is extended to the three-dimensional case. This extension gives a general constitutive inequality for the damage of elastic-brittle materials.

Statistical characteristics of the Poincaré return times for a one-dimensional nonhyperbolic map

2011 ◽  
Vol 82 (3-4) ◽  
pp. 219-225 ◽  
Author(s):  
V. S. Anishchenko ◽  
M. Khairulin ◽  
G. Strelkova ◽  
J. Kurths
Keyword(s):  
Statistical Characteristics ◽  
One Dimensional ◽  
Return Times

Basic Study of Caustics Properties under Thermal stress Fields : In Case of Axial Symmetrical one Dimensional Stress Field

2002 ◽  
Vol 2002.2 (0) ◽  
pp. 151-152
Author(s):  
Ahmad ALMALEH ◽  
Ahmad NAHHAS ◽  
Eitoku NAKANISHI ◽  
Yutaka SAWAKI ◽  
Kiyoshi ISOGIMI
Keyword(s):  
Thermal Stress ◽  
Stress Field ◽  
Stress Fields ◽  
Basic Study ◽  
One Dimensional
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