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Application Of ABAQUS To Analysis Of 3D Cracks And Fatigue Crack Growth Prediction

Chris Timbrell, Paul Claydon, Gerry Cook

of

Zentech International Limited, 103 Mytchett Road, Camberley, Surrey, GU16 6ES, U.K.

Abstract

A practical and well proven method is presented for generation of 3D meshes for modelling

cracks, including fully automatic techniques for 3D (non-planar) fatigue crack growth prediction.

The techniques, used successfully in various industries for a number of years, have recently been

applied for the first time with ABAQUS. Results are presented for a number of cases, including

comparisons against theoretical and experimental data.

Introduction

The finite element method has a long history in the field of fracture mechanics, but there are

specific problems when 3D cracks are considered. Not least of these is how to generate a

suitable finite element model in a sensible time scale. The difficulties are greatest for mixed

mode cases where both sides of the crack are modelled and the two adjacent crack faces must

remain separate. Even when this is achieved, a practical means must be found of using results of

the analysis to provide meaningful information on the crack configuration. For fatigue crack

growth prediction, it must also be possible to predict how the crack will advance and then to

generate a mesh for the new configuration.

A method has been developed which solves all of these problems using ABAQUS as the finite

element analysis tool. In this paper, emphasis has been placed on examples of the procedures

which have been developed. It is hoped that this will provide a more useful and interesting

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document than a detailed technical study of the methods used, although the basic concepts are

covered briefly.

Procedure

To alleviate the difficulties of generating 3D meshes containing cracks, a fully automated

procedure has been developed. This leads to subsequent fatigue crack growth prediction. The

full procedure, incorporated into the commercial package, ZENCRACK [5], is outlined in figure

1.

The user first generates an ABAQUS format mesh for the uncracked component. The mesh is

complete in its own right, containing the necessary loading, boundary conditions and material

specification. This is done using conventional methods. The mesh can consist of any element

type, but must contain 20 noded brick elements in the region(s) which will contain the crack(s).

To generate the crack front(s), one or more of these brick elements are replaced by 'crack-blocks'.

These crack-blocks are meshes of brick elements which are mapped into the original element

space and merged with the surrounding mesh. The user has control over the initial crack

orientation and size. Boundary conditions and loads are transferred to the crack-block elements

and a *J-INTEGRAL option is generated. If required, this updating procedure can be used to

apply pressure loading in the crack region, including the crack face. The result is a mesh

containing an initial defect.

This mesh is submitted for analysis by ABAQUS. The results of the *J-INTEGRAL evaluations

are processed by ZENCRACK and a new crack front position is calculated based on user defined

crack growth criteria. The mesh is automatically modified to contain this new crack position and

a further ABAQUS analysis is carried out. This process continues until user specified limits on

crack growth are reached.

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Crack Growth Prediction

For 3D models, the *J-INTEGRAL option in ABAQUS can be used to evaluate the distribution

of energy release rate along a crack front for a postulated crack front advance. For a symmetry

model, in which only one side of the crack is modelled, the direction of crack growth at each

node on the crack front is assumed to be in the crack plane and normal to the crack front. The

algorithms in ABAQUS automatically produce an energy release rate distribution which can be

used with a crack growth law to calculate fatigue the crack growth.

For mixed mode loading, in which both sides of the crack are modelled, it is not as easy to

identify how the crack will grow. The procedure used in ZENCRACK is to apply a 'fan' of

direction vectors on the *J-INTEGRAL option. For each node on the crack front, this yields a

series of energy release rate magnitudes and directions. These are processed to obtain the

distribution of the magnitude and direction of the maximum energy release rate. This is deemed

to be the direction in which the crack will grow. The result is the ability to predict non-planar

crack growth in a component under mixed mode loading.

Mesh Generation Examples

Examples are presented for generation of straight, elliptic and circular cracks. These demonstrate

the power and versatility of the mesh generation technique. The uncracked component mesh is of

a section of a cylinder. The model contains 32 brick elements and is shown in figure 2. In all

three examples, only one side of the crack is generated. This is for clarity and to allow the crack

fronts to be visible in the figures. It is just as easy to model both sides of the crack(s).

In figure 3, two elements are replaced to produce a straight radial crack front. Figure 4 shows an

elliptic crack at the outer surface and figure 5 a fully embedded circular crack. To further

demonstrate the simplicity of the method, table 1 lists the information required to generate the

mesh of figure 3 from the mesh of figure 2. This is the only information that is required above

and beyond the mesh of the intact component.

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Parametric Studies

The simplicity of the mesh generation technique makes it ideally suited to parametric studies

where different crack sizes need to be analysed in the same component. As an example, figure 6

shows a standard single edge notch specimen. This was analysed for different a/W ratios. The

same intact model was used for all analyses - the only differences in the input to ZENCRACK

were in the specification of the size of the defect (in this case it was necessary to change only two

numbers between each analysis). The model was analysed under plane strain conditions.

Theoretical values of stress intensity factor are compared against values calculated from

ZENCRACK interfaced to ABAQUS and MARC [4] in table 2 and figure 7. These show

excellent agreement for all a/W ratios.

Planar Crack Growth Prediction

An example of planar crack growth prediction is included for an initial semi-elliptic defect in a

bar under uni-axial tension, as shown in figure 8. This was selected on the basis of the

availability of experimental data for comparison [2]. Due to symmetry, only one quarter of the

bar was modelled, with a single crack-block used to model the crack front section (figure 10).

The model contained four elements along the crack front. Constraints were applied axially at the

loaded face to simulate the effect of clamping.

Figure 11 shows the meshing of the crack-block at the start of the analysis and part way through.

The advance of the crack front can clearly be seen. This analysis was continued for 17

increments (i.e. 17 finite element analyses), with the calculated crack growth history through the

section as shown in figure 12. Results for surface growth against number of fatigue cycles for

analyses with ABAQUS and MARC are shown in figure 13, plotted with the experimental data.

In both cases there is good agreement between the analytical and experimental results.

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Non-Planar Crack Growth Prediction

It is difficult to obtain experimental data for mixed mode fatigue crack growth prediction. As an

alternative, a case is presented where the general crack growth behaviour can be anticipated. An

analysis has been undertaken of a square bar containing a quarter circular corner crack. The bar

was loaded by in-phase cyclic tension and torsion. A schematic is shown in figure 9. Two crack-

blocks were used in the analysis, one for each side of the crack.

Figures 14 and 15 are results from the analysis of the initial configuration. These show the

behaviour that would be expected, namely symmetry along the crack front for magnitude of

energy release rate and asymmetry in the direction of maximum energy release rate. In other

words, the two ends of the crack will grow by equal amounts in opposite axial directions.

Figure 16 shows one of the crack-blocks after several increments of crack growth. This plot

demonstrates that as far as possible with the limited number of nodes available, the free crack

faces are maintained on the calculated crack history surface as the analysis proceeds. The

complete asymmetric crack growth history is shown in figure 17.

Conclusions

The methods described in this paper provide powerful additional capabilities to ABAQUS users

who are involved in analysis of 3D cracks. Three main capabilities can be identified :

• fast and easy generation of 3D meshes containing cracks

• analysis and processing of the initial cracked configuration

• automatic fatigue crack growth prediction with a mixed mode (non-planar) capability

References

1. Ewalds, H.L. & Wanhill, R.J.H. 'Fracture Mechanics', Edward Arnold (Publishers) Limited,

3rd imprint, 1986.

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2. Pang, H.L.J. 'Fracture Mechanics Analysis of Fatigue Failure in Cruciform Welded Joints',

PhD Thesis, Strathclyde University, Scotland, 1989.

3. Rooke, D.P. & Cartwright, D.J. 'Compendium of Stress Intensity Factors', 1974.

4. MARC software, MARC Analysis Research Corporation, Palo Alto, California, U.S.A.

5. ZENCRACK software, Zentech International Limited, U.K.

[ZENCRACK.MESH]FIG4 : output file reference 0,1,0,1,0,0,0, : general program options 2,2,2 : controls for crack-block mapping ST88X5.SUP : crack-block 1 is type ST88X5 25,209,157, : replace element 25, crack orientation via nodes 209 & 157 ST88X5.SUP : crack-block 2 is type ST88X5 29,214,162 : replace element 29, crack orientation via nodes 214 & 162 0.26,0.26, : define crack size - two ratios for crack-block 1 0.26,0.26, : define crack size - two ratios for crack-block 2

Table 1 - Data required to produce the mesh of figure 3 from the uncracked mesh of figure 2

a/W Ref. 1 Ref. 3 ABAQUS MARC 0.15 1.265 - 1.261 1.251 0.2 1.371 - 1.359 1.349

0.25 1.501 - 1.487 1.476 0.3 1.660 1.671 1.646 1.635

0.35 1.856 1.865 1.843 1.832 0.4 2.104 2.111 2.088 2.077

0.45 2.420 2.423 2.398 2.392 0.5 2.826 2.821 2.794 2.800

0.55 3.352 3.339 3.311 3.335 0.6 4.026 4.031 3.998 4.050

0.65 - 4.985 4.928 5.019 0.7 - 6.361 6.220 6.364

Table 2 - Theoretical and calculated values of KI/Ko for single edge notch specimen

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8

Figure 2

User supplied intact mesh

Figure 3

Straight through crack

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Figure 4

Elliptic crack at outer surface

Figure 5

Embedded circular crack

10

hW

aW

to

Ko

=

=

=

1 5

0 15 0 7

.

. .

σ πa

W

a2h

σ

0.0 0.2 0.4 0.6 0.8 0

2

4

6

8

Theoretical linesoverlay theanalysis results

MARC

ABAQUS

Single Edge Notch : Tension : Ki/Ko vs a/W Results for ZENCRACK with interface to ABAQUS and MARC

a/W

Ki/K

o

Figure 7 - Stress intensity factors for single edge notch specimen

Figure 6 - Geometry for single edge notch specimen

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2c

a

W

σ

σL

tLength, L,Width, W,Thickness, t,

700mm100mm25mm

initial c,initial a,

5.6mm4.6mm

Material, BS4360 grade 50D steelStress range, 0 - 144 Nmm -2

Figure 8 - Geometry for planar crack growth prediction example

Figure 9 - Geometry for non-planar crack growth prediction example

L

W

a

TC

initial quarter circulardefect, radius a

W 100mmWL

0.25

aW

0.2

E = 200000Nmm0.3

T 20NmmC 3200000Nmm

-2

2

=

=

=

=

==

−

ν

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View point -1.00E+00 -2.00E+00 -1.80E+00

X

Y

Z

Figure 10 - Uncracked mesh and initial cracked mesh

Initial meshing of crack-block Meshing of crack-block part waythrough the analysis

Figure 11 - Meshing near crack front at two stages of the analysis

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symmetry line

surface

Figure 12 - Crack growth pattern

0 5 10 15 0

10

20

30

Experimental

ABAQUSMARC

Semi-elliptic surface crack : Surface growth vs cycles Results for ZENCRACK with interface to ABAQUS and MARC

Number of cycles

Cra

ck g

row

th a

long

sur

face

, mm

(x10 5 )

Figure 13 - Calculated and experimental surface growth

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ABAQUSMARC

0 10 20 30 40 50 60 70 80 90 6

8

10

12

Square bar : Tension-torsion : Analysis of initial defect Results for ZENCRACK with interface to ABAQUS ans MARC

Angle around crack front, degrees

Max

imum

ene

rgy

rele

ase

rate

mag

nitu

de

(x10 -2 )

Figure 14 - Magnitude of maximum energy release rate along initial crack front

MARC ABAQUS

0 10 20 30 40 50 60 70 80 90 -40

-30

-20

-10

0

10

20

30

40

Square bar : Tension-torsion : Analysis of initial defect Results for ZENCRACK with interface to ABAQUS and MARC

Angle around crack front, degrees

Gro

wth

ang

le o

ut o

f the

initi

al c

rack

pla

ne, d

egre

es

Figure 15 - Magnitude of out-of-plane growth along initial crack front

15

X

Y

Z

View point -0.200E+01 0.100E+01 0.750E+00

Figure 16 - Meshing of one of the crack-blocks after 8 crack growth increments

X

Y

Z

View point -0.200E+01 0.100E+01 0.750E+00

Figure 17 - Crack growth history after 8 increments