Constitutive Response of Passivated Copper Films: Experiments and Analyses

The constitutive behavior of passivated copper films is studied. Stresses in copper films of thickness ranging from 1000 nm to 40 nm, passivated with silicon oxide on a quartz or silicon substrate, were measured using the curvature method. The thermal cycling spans a temperature range from - 196 to 600°C. It is seen that the strong relaxation at high temperatures normally found in unpassivated films is nonexistent for passivated films. The copper film did not show any rate-dependent effect over a range of heating/cooling rate from 5 to 25°C/min. Further analyses showed that significant strain hardening exists during the course of thermal loading. In particular, the measured stress- temperature response can only be fitted with a kinematic hardening model, if a simple constitutive law within the continuum plasticity framework is to be used. The analytic procedures for extracting the film properties are presented. Implications to stress modeling of copper interconnects in actual devices are discussed.

Revised Cam-Clay Model

The Cam-clay models, or any other plasticity-based models, do not make distinction between the mode of stress transfer in coarse- and fine-grained soils. An examination of behavior at micro level in fine-grained soils, from the consideration of load transfer through physico-chemical interactions, suggests that the plastic compressions result from the grouping of particles into larger clusters and that elastic compressions result from the decrease in the spacing between particles. During shearing, these clusters gradually get dismembered, releasing the locked-in energy. The effect of such dismembering of clusters can be easily incorporated into the original Cam-clay model, and better predictions can be obtained with the associated flow rule, itself, for both normally and over consolidated states. The method essentially defines the hardening of yield surfaces with internal changes in the spacing between particles, instead of changes in externally observed plastic strains. The approach describes the behavior of over consolidated soils as yielding along successfively hardening Roscoe surfaces with gradually varying plastic properties.

A rational approach to model the behavior of bonded soils

The paper presents a rational approach to model the behavior of bonded soils within the frame work of hardening plasticity. The approach is based on the premise that the resistance of bonded materials is a superposition of the two components of cement bond strength and soil frictional strength and that the deformation of the soil is associated with the frictional component of stresses just as in the case of a remoulded soil, the bonds offering additional resistance at any given strain level. This concept is similar to two stiffnesses acting in parallel for the same strain response. The proposed model considers the constitutive laws separately for the two components (bond and frictional) and adds the two to get the overall response. The unbonded soil component is described by the well known 'modified Cam clay' model. The response of the bond component is also described by a strain softening elasto-plastic model, considering the behavior to be elastic up to the yield surface and elasto-plastic beyond yield surface. To illustrate the capability of the proposed, model some laboratory test results of both compression and-extension shear tests are predicted. Despite the model being simple, several typical features of the behavior of bonded materials are well reproduced. The model parameters are well defined and easily determinable.

Constitutive Model for Strength Characteristics of Municipal Solid Waste

This paper presents modification of the derivation of a previously proposed constitutive model for the prediction of stress-strain behavior of municipal solid waste (MSW) incorporating different mechanisms, such as immediate compression under loading, mechanical creep, and time-dependent biodegradation effect. The model is based on critical state soil mechanics incorporating increments in volumetric strains because of elastic, plastic, creep, and biodegradation effects. The improvement introduced in this paper is the modified critical state surface and considers five variable parameters for the estimation of stress-strain behavior of MSW under different loading conditions. In addition, an expression for the strain hardening rule is derived, with considerations of time-dependent mechanical creep and biodegradation effects. The model is validated using results from experimental studies and data from published literature. The results are also compared with the predictions of the stress-strain response obtained from a well-established hyperbolic model. (c) 2014 American Society of Civil Engineers.