Effects of Hydrostatic Stress on the A.C.Permeability of Mn-Zn Ferrite

Soft ferrites have excellent a.c.permeability, but it is reduced under stress.It has a hyperbolic re- lationship between permeability μ and stress σ or a linear increase of 1/μ with σ.It is also found that the stress sensitive factor α depends on sample porosity p.For fully densified Mn-Zn ferrites α is only 10^(-7)～10^(-8) MPa^(-1),but it increases to 6× 10^(-6) MPa^(-1) for samples containing closed porosity 6%.Such materials could be used as a sensor for measuring pressure。

Experimental study on the influence of hydrostatic stress on the Lode angle effect of porous rock

To investigate the deformation mechanisms of rock under hydrostatic stress, destructive experiments were conducted on sandstone under different levels of hydrostatic stress and stress Lode angles. The results reveal that the shape of the strength envelope on the π plane gradually changes from the shape of the Lade criterion to the shape of the Drucker-Prage criterion with an increase in hydrostatic stress.Normally, there exists a deviation between the strain and stress paths for porous rocks on the π plane,and the deviation decreases with an increase in stress Lode angle and hydrostatic stress. A rock failure hypothesis based on the rock porous structure was proposed to investigate the reasons for the abovementioned phenomena. It was found that the shear expansion in the minimum principal stress direction is the dominant factor affecting the Lode angle effect(LAE);the magnitude of the hydrostatic stress induces the variation of the porous structure and influences the shear expansion. Therefore, the hydrostatic stress state affects the LAE. The failure hypothesis proposed in this paper can clarify the hydrostatic stress effect, LAE, and the variation of the rock strength envelope shape.

Effect of hydrostatic stress on yield function and plastic constitutive relations

A new yield function taking effect of hydrostatic stress into account is presented through establishing and solving the functional equation satisfied by the yield function, and its characteristic is simple in form and strong in generality. In order to reveal its availability, a comparison is made between the results obtained with it and the experimental results of grey cast iron has be done, both seem to be in good agreement. At the same time, taking the yield function obtained here as a potential function, a new associative plastic constitutive equation taking effect of hydrostatic stress into account is built, and the plastic volume change ratio of plastic deformation is given.

Finite element simulation of hydrostatic stress in copper interconnects

This work focuses on numerical modeling of hydrostatic stress, which is critical to the formation of stress-induced voiding （SIV） in copper damascene interconnects. Using three-dimensional finite element analysis, the distribution of hydrostatic stress is examined in copper interconnects and models are based on the samples, which are fabricated in industry. In addition, hydrostatic stress is studied through the influences of different low-k dielectrics, barrier layers and line widths of copper lines, and the results indicate that hydrostatic stress is strongly dependent on these factors. Hydrostatic stress is highly non-uniform throughout the copper structure and the highest tensile hydrostatic stress exists on the top interface of all the copper lines.

Finite Element Modeling of Hydrostatic Stress Distribution in Copper Dual-damascene Interconnects

Hydrostatic stresses of copper dual-damascene interconnects are calculated by a commercial finite element software in this paper.The analytical work is performed to examine the effects of different low-k(k is permittivity)dielectrics,barrier layer and aspect ratio of via on hydrostatic stress distribution in the copper interconnects.The results of calculation indicate that the hydrostatic stresses are highly non-uniform throughout the copper interconnects and the highest tensile hydrostatic stress exists on the top interface of lower level interconnect near via.Both the high coefficient of thermal expansion and the low elastic modulus of the low-k dielectrics and barrier layer can decrease the highest hydrostatic stress on the top interface,which can improve the reliability of the copper interconnects.