טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAzulay Hay
SubjectEffect of Neighbor Morphology on Local Stresses in
Heterogeneous Materials
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Eli Altus
Full Thesis textFull thesis text - English Version


Abstract

The aim of this study is to evaluate the effect of stochastic heterogeneity on local stresses, in particular the neighbor heterogeneity which causes extreme local stresses. This topic is fundamental for a wide variety and scales of heterogeneous materials, from fiber composites to biological materials.

Local stresses or strains are common basis for design against failure. The strength and reliability is strongly dependent on localized stress concentrations in small regions having partially ordered (random) micro neighborhood.  Evaluating the effect of stochastic heterogeneity on local stresses can help designing improved materials by avoiding “dangerous” neighbor morphologies.

The study includes Finite Element Analysis (FEA) combined with analytical tools based on Functional Perturbation Method (FPM) and Monte Carlo Simulations (MCS). The von Mises local stress is selected as the "point of reference” and its sensitivity to model parameters is tested.

Two major complement objectives are pursued:

a.) Given a random morphology, find local neighborhoods which are more susceptible to failure and their probability of occurrence

b.) Given a macro geometry and external loading, find characteristics of morphologies with better resistance (strength)

The milestones for achieving these goals are:

a.) Find approximations for the local stress based on FPM and using MCS create a database of local stresses and matching morphologies

b.) Using (a), find analytically the amount and extent (in statistical terms) of high stress neighborhoods

c.) Test the accuracy and predictive capabilities of (a, b) with FEA results. Find analytically, and validate numerically, the size of neighborhood morphology which affects the local stress

It is found that:

a.)  The maximum local stresses occur when stiffer phase volume fraction is ~0.3

b.)  Second order stress prediction based on a local radius of ~3 “grains” is reasonably accurate

d.)  Fiber like morphologies parallel to the loading direction cause extreme stresses

e.)  Local stress distribution is found to be composed of two distinguishable parts which appear to be Gaussian sub-shapes, one for each phase

f.) "Crack" like morphologies of a “soft” fiber perpendicular to the external loading direction was found to cause extreme severity local stress

g.)  Morphologies related to extreme local stress and severity were found to be “mirror like” images

h.) Extreme stress morphologies were predicted using FD of the Taylor series. The stress predictions for these morphologies were found to match well the extremum values calculated numerically by the MCS and FE.