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FRACTURE ANALYSIS FOR STEEL AND EPOXY MATERIAL

PLATE WITH EDGE CRACK

Kisan Patil1, Prof.C.S.Wadageri 2 1M.Tech.,Mechanical Engg. Dept., MMEC, Belagavi

2 Associate Prof. Mechanical Engg. Dept. MMEC, Belagavi

Abstract— The focus of this project is to investigate how a crack propagates and grows in Structural/Mild steel & Epoxy material plate. Edge crack this case will be performed for both

material to calculate stress intensity factor & J integral. FEA output will be compared with analytical

calculation to validate results. Finite element method software (ANSYS16) will be used to simulate

failure criteria and to compute the stresses and the stress-intensity factor.

So we have performed FEA analysis for both Mild steel and epoxy material. So we can understand

the propagation of crack & its growth in material plates.

Keywords— Edge crack, mild steel, epoxy material, propagation and growth of crack.

I. INTRODUCTION

Most of the structures are usually designed for taking loads to which they were subjected while in

service. The care has to be taken in order to avoid large stress concentrations and suitable margin of

safety is considered so that their values closed to maximum permissible stress are not going to

attained. But due to imperfections in materials that are arises during the production are unavoidable

and must taken in account.

The presence of crack and its propagation causes decrease in strength of material, on the other side if

flow is detected in structure that doesn’t implies that the structure is not safe.

The criterion is actually applicable to those materials which are expensive or structures whose

working is not economical to interrupt. Fracture mechanics here plays a major role, as fracture

mechanics approach has various concepts for structures analysis which contains the crack. Our aim is

to analyze and predict in what manner failure is going to occur.

Leonardo-da-Vinci was the first person to set up to measure strength of the wire. after experimenting

on wire he comes to the conclusion that wire strength is depends upon the length. wire quality in

those time is not good. and as length of wire is more it was found that it has more flaws. in those

days fracture was not a separate branch. Many bridges, locomotives, ships failed because of fracture

in 19th century. Locomotive which is the important industry in those days, it was found that the

various accidents took place because of failure of wheel and rails. Wohler who did experiment on

stress controlled cyclic loading on axles of locomotives. which leads to Goodman diagram analysis

for fatigue.

The modern fracture development was take place in year of 1948 when Irwin formulated and devised

parameters like stress Intensity factor and energy release rate. As initiation of fracture started, no. of

scientists started to research and it becomes the separate branch with no, of journals. Investigation

carried out by the Irwin was only for brittle. The analysis is restricted for engineering materials

which are generally ductile. Like ERR & SIF the other parameter such as CTOD & J-Integral, are

investigated for the crack tip where the large plastic zone is usually occur.

Fracture mechanics approach can also be applied for the different fields like piping rockets, nuclear

etc. where parts are critical which are manufactured from tough material and found to fail

catastrophically crack formed. To determine stress intensity factor various methods are available

International Journal of Recent Trends in Engineering & Research (IJRTER) Volume 02, Issue 10; Oct - 2016 [ISSN: 2455-1457]


such as finite difference method, finite element method, boundary element method. But FEM is most

commonly used tool for computation of SIF.

Adhesive/epoxy joint have found many applications in the field of aerospace, automobiles. As they

provide advantages w.r.t traditional joining technique. Which include less stress concentration,

distribution of load, reduction in weight, design flexibility? Standard test methods are used to find

strength of adhesive joints by considering no bond line defect. The strength of such joints was

greatly affected by the parameters such as incorrect or inappropriate bonding. Which leads to

occurrence of unbounded area which affects strength of joints? LEFM approach is widely used for

analysis of such joints.

Large numbers of uses were found over different traditional methods such as fasteners, welding,

brazing etc. Its advantage includes joining of dissimilar metals for weight reduction with stiff and

strong structure. Eg.honeycomb panels, polymeric adhesives can also be applied in case of joining

thin shits as it has low bearing strength and which cannot be joined with available technique. Also

adhesive bonding is one of the most suitable and economical technique for joining. also another

major advantage to use this technique is that operations can be automated. due to this advantages this

method is more commonly used in industries. E.g. aerospace, railway, trucks etc.

Epoxy adhesives are one of the common structural adhesive here structural means that it is

polymerized. Elastic modulus and strength posses by the adhesive are high due to which load bearing

joint is formed.

1.1 MODES OF FRACTURE

Consider a plate having a crack. in order to study the in ehich way the force must be applied so that

crack can grow. Irwin who is responsible for classifying the different types of modes which are

shown in fig. according to Irwin there are three different modes of cracks which are Mode 1 , Mode

2 and Mode3.

In first mode component is subjected to tensile force due to which maximum displacement seen in y-

direction. The surfaces which are undergoes deformation are symmetric w.r.t plane perpendicular to

y & z direction.

In mode 2 component is subjected to shear forces which are parallel to the cracked serface and

displacent is seen in x direction in the plane. Deformed surfaces are diametric with plane ┴ to z axis

while is asymmetric about y axis.

In mode 3 the surfaces are loaded parallel to crack front and surfaces are slide in the z direction.

Surfaces which are subjected to deformation are asymmetric about both z & y axis

Mode 1 is most commonly observed type of fracture in most of the componts and is studied with

well developed models. Our aim is to calculate the stress intensity factor for mode 1 problems.



Fig 1.1: MODES OF CRACK

Our aim is to find the stress intensity factor for mode 1 problems as most of structures fails in tensile

loading.

II. FRACTURE MECHANICS OF PLATE WITH EDGE CRACK

Engineers need to study and analyze the cracks which are present in the structure resulting from the

manufacturing process or from fatigue. To avoid the failure of structure prior to its expected life in a

easy way. Strength of material approach is used in traditional design to access structural integrity.

Fracture mechanics approach is an important tool which include effect of flaws which becoming the

practice in a most of the industries.

Fracture mechanics can be explained using concept of applied mechanics & material science.

Propagation of a crack in a structure is a function of stress and flaws, and is represented by fracture

parameters.

stress intensity factors (K or SIFs): characterizes stress state near crack tip

J-Integral (J or JINT): contour‐integral around the crack tip that is equal to the change in

potential energy due to incremental crack advance

Energy release rate (G): Energy required to create newly formed crack surfaces

2.1 Fracture modes

Based on relative movement of two surfaces modes of fractures are classified as-

Mode I – Opening mode

Mode II – Shearing mode

Mode III – Tearing

Figure 2.1: Fracture Modes



2.2 Geometry details:

Plate with dimension 100*50*3 is modeled in Ansys design modular as below.

Fig 2.2: Geometry details

Analysis Is Performed For Below Cases, Table 2.1: Geometry Details

Mild Steel/EPOXY Material

Sr. No. a(mm) W(mm) Load(P)(N)

1 5 45 4680

2 10 40 5360

3 15 35 7040

4 20 30 10320

E(MPa) 206000/85000

Mu 0.3/0.35

B(mm) 3



2.3 Formulae to calculate Sif(K1) and J-integral(Jint)):

2.4 Materil properties Table 2.2: Material Properties

Mild Steel Epoxy Resin

Young’s Modulus(GPa) 206 85

Poisons ratio 0.30 0.350

Density 7850 (Kg/ ) 40 (Kg/ )

2.5 Static analysis:

Fracture analysis is combination of both fracture and stress analysis parameters calculations. The

analysis included may be non linear elastic or standard linear elastic analysis. Since the stresses at

the tip of the crack are too high, thus at the crack region finite element modeling requires special

attention

Fig 2.3: 3D model

2.6 Modeling the crack tip region:

Near the crack tip stress and displacement fields are of high gradients. The displacement and

stress fields are depends upon geometry and other factors. The relation between the displacement and

crack is it is vary with .

Stress, strains near the tip of crack varies as so as to generate the singularity in strains

and stress, meshing at the crack tip posses some characteristics:

Faces of the crack must be coincident.

Elements around tip of the crack must be quadratic nature, w.r.t mid side nodes placed at the quarter

points. (these elements are referred to be as singular elements.)



Fig2.4: Singular element

SOLID186 is more commonly used type of elememt. the brick element having 20-nodes shown in

above Figure 2.4: Singular Element, the first row must be surrounded by singular element around the

front crack. the element is of wedge shaped, with the KLPO face collapsed on the line KO.

2.7 Fracture analysis workflow:

The steps shown below describe setting up the fracture analysis when the location of crack is known.

The crack location and its alignment are dictated by the coordinate system selected by the crack

object.

1. In ANSYS Workbench, insert a Static Structural analysis in the project schematic.

2. Input geometry.

3. Locate a coordinate system with a graphic pick point, coordinates, or topology. We must locate

the co-ordinate system on the surface

4. Align axes of the co-ordinate system of crack. specified coordinate system's y-axis must be

pointing in the direction normal to the crack surface. For cracks lying on curved surfaces,

ensure that the coordinate system's x-axis is pointing normal to the surface of the body at the

coordinate system location. See Creating a Coordinate System Based on a Surface Normal for

details on how to orient such a coordinate system on a curved surface..

5. Insert a Fracture folder in the Tree Outline.

6. Insert a Crack object under the Fracture folder.

7. Specify the crack object details.

8. Generate the mesh by right-clicking the Fracture folder and selecting Generate All Crack

Meshes.

9. Apply loads and boundary conditions.

10. Apply any pressure on crack face if necessary.

11. Ensure the Fracture setting under Solver Controls in the Analysis Settings is turned on.

12. Solve.

13. Add the Fracture tool and Fracture Result.

14. Post process the Fracture Result.

15. Export to Excel or copy/paste from the chart if necessary.

2.8 Limitations of fracture analysis:

1. Fracture analysis does not support adaptive mesh refinement.

2. The Crack object is only supported for 3D analysis.

3. The Crack object can only be scoped to one body. The base mesh on that body must be

quadratic tetrahedron mesh.

4. The stiffness behavior of the scoped geometry selection of the Crack object must be flexible.

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5. The scoped crack front nodal selection of the Pre-Meshed Crack object must exist in geometries

with a flexible stiffness behavior definition.

6. Fracture parameter computations based on the VCCT technique are only supported for lower

order crack mesh. Hence, VCCT based fracture parameter computations are only supported for

Pre-Meshed Crack object.

7. Solution Restarts are not supported with the computation of fracture parameters. Solution

Restarts can be used for solving an analysis of cracks without computing the fracture parameters

by turning “Off” the “Fracture” setting under Solver Controls.

8. The Crack object only supports semi-elliptical surface cracks.

9. The crack top and bottom face nodes are not connected through any constraint equation. So the

nodes of the top face can penetrate the bottom face or vice versa based on the applied loads and

constraints. In these scenarios, you may need to create a constraint equation between crack faces

during solution using the Commands object.

10. The graphical view of the crack may differ from the generated mesh. For more information, see

the section on Cracks.

11. Crack object is not supported for Cyclic Symmetry Region and Structural Linear Periodic

Symmetry Region objects.

2.9 Meshing

Meshing is the process of dividing the structure into the number of small parts call as an

elements .this is done by meshing. In order to mesh a certain model element type has to be decided

first. In this case element type is solid186.

Fig 2.5: Meshing

2.10 Solid186 homogeneous structural solid element description

SOLID186 is a higher order 20-noded element which has quadratic displacement behavior. The

element posses 20 nodes with each node having 3-DOF. i.e. translatory in all three directions.

Element supports creep, plasticity and large strain capabilities.

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Fig 2.6: Solid186 element

2.11 Creating a finite element structure with pre-defined crack path

The energy release rate of structure having crack can be calculated with technique called as virtual

crack closure technique. And its been more commonly used in computing of composite laminates, by

assuming crack will grow in pre-defined path. This technique present with crossed technology linear

elements such as PLANE182 & SOLID186.

The assumptions involve in the technique are as follows

Propogation of crack occurs in a p redefined path.

The path is defined by means of interface elements.

analysis involved is quasi-static due to which transient effects are neglected

Fig 2.7: Crack path discretized with interface elements

2.12 Loads and boundry conditions

One end of plate is constrained in all direction & force is applied in other end.



Fig.2.8 BC's Fig 2.9 Cracks in FEA.

ANALYSIS IS PERFORMED FOR BELOW CASES,

Mild Steel/EPOXY Material

Sr. No. a(mm) W(mm) Load(P)(N)

1 5 45 4680

2 10 40 5360

3 15 35 7040

4 20 30 10320

E(MPa) 206000/85000

Mu 0.3/0.35

B(mm) 3



2.12 Static analysis result:

Table 2.3: Static Analysis Results for Epoxy

Sr No. a(mm) W(mm) Load(P)(N) SIFS (K1) J-Integral (JINT) SIFS (K1) J-Integral (JINT)

1 5 45 4680 439.139 1.5 437.69 1.5

2 10 40 5360 1070.95 8.8 1083 7.9

3 15 35 7040 3608.35 99.6 3465 91

4 20 30 10320 29724 6756.3 30056 7009

E(MPa) 85000

Mu 0.35

B(mm) 3

Analytical FEAEPOXY Material

Table 2.4: Static analysis results for mild steel

Sr No. a(mm) W(mm) Load(P)(N) SIFS (K1) J-Integral (JINT) SIFS (K1) J-Integral (JINT)

1 5 45 4680 439.139 0.7 440 0.64

2 10 40 5360 1070.95 3.9 995.8 3.6

3 15 35 7040 3608.35 44.2 3670.7 40.8

4 20 30 10320 29724 3002.2 29522 3163.4

E(Mpa) 206000

Mu 0.3

B(mm) 3

Analytical FEAMILD STEEL Material



Fig 2.10 Ansys results for edge crack

Fig 2.11 Ansys results for edge crack



2.13 CONCLUSION

For same loads epoxy resin material is observed having higher J-integral value, hence epoxy

material is better than steel. Crack will not propagate more in case of epoxy material.

This project investigates how the crack grows and propagates in two different materials and

their resulting stress distribution.

This study helps us in design of composite materials as we can use epoxy adhesives along with

steels to improve their toughness.

Also epoxy plates can be used in the areas where steel plates of same strength are currently in

use and failure comes due to cracks. This sudden failure or total shut down of unit due to one

part failure due to crack in mechanical systems is often. This can be avoided by replacing steel

with epoxy in those cases as per design considerations.

REFERANCES 1. J. Goodman, “Mechanics applied to Engineering”, Longmans green, London, 1899.

2. NegarullahNaseebullah Khan, Nitesh P. Yelve , “Analysis of Crack Propagation in Thin Metal Sheet, Three Point

Bend Specimen, and Double Cantilever Beam”,

3. H. Monajjemet. al, ‘Effect of notch depth and notch root radius on the J-integral in the plates made of functionally

graded steel’, MSc Student, Department of Mechanical Engineering/Amirkabir University of Technology, Tehran,

Iran, [email protected].

4. G. R. Irwin, “Fracture Dynamics, Fracture of Material”, American Society for Metals, Cleveland, 1948, pp. 147 –

166.

5. Wells, “Unstable crack Propagation in Metals: Cleavage and Fracture”, Proceeding of the Crack Propagation

Symposium, college of Aeronautics, Cranfeild, 1, 1961, pp. 210 – 230.

6. J. R. Rice, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and

Cracks”, Journal of Applied Mechanics, Transactions of ASME, 35, pp. 379 - 386, 1968.

7. Shawn A. English, Nagaraj K. Arakere& Phillip A. Allen, ‘J–Q characterized stress fields of surface-cracked

metallic liners – II. Composite overwrapped

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