This document outlines a student's workplan to study the fracture of functionally graded materials. The plan includes conducting a literature review to identify gaps and objectives, modeling the material and analyzing it using software, performing parametric studies on properties like reinforcement size and volume fractions, and submitting a final report. Experimental results are also presented on a photoelastic model that show stress distributions and crack propagation under loading. Numerical finite element modeling is found to match the experimental photoelastic results to within 5-8 percent.

1. FRACTURE OF FUNCTIONALLY
GRADED MATERIAL
PRESENTED BY :-
Shambhu Kumar
REG. NO.-2014DN06
PRESENTED TO:-
Dr. Dharmendra Kumar
Shukla

2. LITERATURE SUVEY :-
 To make a survey research paper and all the relevant sources and find the
literature gap .
 To decide the objective of the thesis on the basis of literature survey.
MODELING :-
 Formulate the theoretical model.
 To create the specimen of Functionally graded polymer NanoComposite
material through coding software .
 To analyze the specimen using modeling software after the creating
specimen .
WORKPLAN FOR 3rd SEMESTER

3.  Following results can obtained through analysis
 Finding all aspects of fracture behaviour of FG-PNC including the
fracture mechanism and the effect of Nano-particle aspect ratio and
dispersion.
 Finding the failure strength of FG-PNC under the tensile and compressive
loads.
 Finding the Validate the model through experimental results.

4.  After the validation of model, I will start the parametric studies of that
model.
PARAMETRIC STUDIES
Following changes will be made in parametric studies :-
 shape & size of reinforcement .
 Volume fractions of composite.
 Thermal aspects of FG-PNC materials.
 Economical aspects of FG-PNC materials.
 Environmental aspects of FG-PNC materials
SUBMISSION OF REPORT
WORKPLAN FOR 4th SEMESTER

5. DETAILS OF PAPER SELECTED
 Topic:
 EXPERIMENTAL MODEL OF FRACTURE OF
FUNCTIONALLY GRADED MATERIALS
 Journal:
JOURNAL OF THEORETICAL AND APPLIED MECHANICS
48, 1, pp. 71-86, Warsaw 2010
 Published by: Mieczysław Jaroniek
Technical University of Lodz, Department of Materials and
Structures Strength, Lodz, Poland

6. OBJECTIVE
 This topic focus about the growth of crack in that
direction and main objective of this paper is
analysis of crack propagation of FGM three modes
of result study .
 Functionally graded materials are the material in which the
material properties vary in a given direction.

7. INTRODUCTION
 Functionally graded materials (FGM) can be obtained by
layered mixing of two materials of different thermo-
mechanical properties with different volume ratio by gradually
changing from layer to layer such that the first layer has only a
few particles of second phase and the last has the maximum
volume ratio of the first phase.

14. Material Properties
 Materials properties influence the stress distribution and concentration
,damage , process and load carrying capacity of elements.
 We consider a 4 layer of FGM material .
Mechanical properties of components of experimental model:-

15. Experimental results
 Dimension of a typical model used in the experiment and artificially initiated
small crack in the tension zone are given in the fig.
 Photoelastic models before test in a circular polariscope and in monochromatic
sodium light are presented ,from which we get isochromatics in the layer in the
initial phase .
 The stress distribution was determined by making use of method -
Shear Stress Difference Procedure (SDP):-Evaluation of complete stress stated
by means of isochromatics and angle of isoclines along the cuts.

16. PHOTOELASTICITY
 Photoelasticity is a branch of Photomechanics.
 Photomechanics entails experimental techniques that use properties of
light propagating through loaded or deformed components to
determine and analyze the relative displacements in the material in
order to establish their strain and stress fields
 The photoelastic response consists of two families of fringes –
isochromatic and isoclinic – which are observed in the polariscope.
 Isochromatics are the loci of the points along which the differences in
the first and second principal stress remain the same . Thus they are
the line which join the points with equal maximum shear stress
magnitude.
 Isoclinics are the loci of the points in the specimen along which the
principal stresses are in the same direction.

17. PHOTOELASTICITY
Example of Photoelasticity (a) stress concentration area of a sharp U-notch, (b) whole field
stress distribution image of a C-shaped model, (c) residual stresses in light bulbs caused by
the fabrication process.

18. PHOTOELASTICITY

19. PHOTOELASTICITY
 The circular polariscope is used for observing isochromatic fringe orders. The
name ‘circular’ comes from the fact that it uses circular propagating light in its
working field .
 A ¼ wave plate is placed with its fast and slow axes making a 45O angle to the
polarizer. This angle enables both amplitudes ES and EF to become equal.

20. Experimental results
 The Photoelastic model of a four layer beam with crack under four points bending, the
isochromatic patterns (σ1−σ2) corresponding to initiation of vertical cracks and tension
overcoat (layer 4) and compression of the substrate (layer 1) are presented in fig.
Experimentally obtained isochromatic pattern (σ1−σ2) according to the initial of crack
initiation of crack propagation

21. Experimental results
 In general cases (Sanford and Dally ,1979) Cartesian component of stress σx,σy
and τxy in the neighborhood of the crack tip are:-
Distribution of stresses in cross sections A-A and B-B with respect to crack
according to SDP evaluation .

22. Experimental results
 From the calculation
 And kσmi=σ1−σ2
 Then, r=rm, Θ=Θm
Three equation obtained that way have form

23. Experimental results

24. Experimental results

25. Numerical determination of stress distribution
 The distribution of stresses and displacements has been calculated using the
finite element method . Results in graphical form is

26. Numerical determination of stress distribution

27. conclusion
 We have shown in the whole paper FEM were performed in order to the
experimentally observed branching phenomena and the isochromatic
distribution observed during crack propagation. The results are agree with
numerically by FEM and determine photoelastically was found to be within 5-8
percent. Having use the stress-intensity factor criterion , the critical value of
stress and deformation fields charachterises the fracture toughness.

28. THANK YOU