3D XFEM Crack Tutorial

Abaqus Benchmarks Manual: Example 1.16.2

note: this figure shows a quarter symmetry model, we will be using a half-

symmetry model (H will be twice as large)

a=1in

c=4.16in

H=26.66in (53.33in in our model)

W=13.33in

t=1.66in

=1psi

Creating the model

Creating the Crack Domain The crack domain is the part that is cracked. It is initially modeled

without the crack, which is to be added later. Double-click on parts and

create a 3D Planar, Deformable, Solid part, name: plate, approximate

size: 200. Since this problem is symmetric about the y-axis only half of

the plate needs to be modeled (we choose left half). We cannot use

symmetry about the crack face for an XFEM analysis. Sketch the part as

seen in the Figure to the right, with a final extrude of 1.66in.

Creating the Crack A separate part is created to represent the crack. It is a 2D, deformable,

shell part, approximate size 40 (10.0in*4). We first draw an ellipse as seen in the figure below.

Then click on ShapeCutExtrude and draw the cut as shown below.

Specifying the Material Create a material named steel with Youngs Modulus E=30.0E+006psi,

and poissons ratio =0.3. Then create a solid, homogeneous section

of the material and assign it to the plate part.

Assembling the Model Instance the two parts into the assembly, and place the crack on the

midway point of the plate, intersecting one edge, as seen in the figure

to the right.

Creating the Analysis Step Create a Static, General step named Tension, accept all defaults.

Loading the model Double-click on Loads and create a Pressure Load named Tension,

select the top and bottom face of the plate and enter a magnitude of

-1.

Constraining the Model Double Click on Boundary Conditions and apply an XSYMM B.C. to

the Left Face of the plate. Once the mesh is created, we will create a

second B.C. constraining vertical motion

Requesting Field Output Double-Click on F-Output-1 under Field Output Requests and add the

output variables PHILSM and PSILSM under the Failure/Fracture

category.

Requesting Contour Integral

Output Double Click on History Output Requests

and make a request named SIF for the

tension step. Select Crack as the

domain from the drop-down list, output at

the last increment. Request 5 contours

and specify the type of contour integral as

Stress Intensity Factors. Repeat this step

for all desired contour integral types.

Partitioning the Model To simplify/optimize the meshing process

we create a series of partitions in the

crack domain which separate the cracked

region from the rest of the part. Here we choose the partition boundaries to be 2 inches from the crack

location, as seen in the figure. [Double-Click on Assembly, then ToolsPartitionFace-Sketch]. Then

choose toolspartitioncellextrude/sweep edges and individually sweep each of the three partition

lines through the thickness of the plate

Assigning Element Types Enter the mesh module, then select Assign Element Type from the toolbox on the right. Select the

entire model and assign reduced-integration first-order elements (C3D8R in this case). Then select only

the cracked region (region between partitions containing the crack) to be made of full-integration first

order elements (C3D8 in this case). This will help reduce computational cost since full integration

elements are only required where cracking takes place.

Meshing the Model In order to further reduce computational cost, we will make a refined mesh

only in the cracked region. The seeds are as follows:

Horizontal Left Edges (8 edges total): 40 elements

Horizontal Right Edges (8 total): 10 elements

Vertical Bottom&Top Edges (12 total): 20 elements

Vertical Middle Edges (6 total): 21 elements

Through Thickness: 15 elements

Constrain Vertical Movement We then create a node set in the assembly and select the two nodes (shown

in red) on the edge behind the crack, as shown in the figures below

Then create a Displacement/Rotation B.C. select the node set as the region, and constrain U2 and U3

Defining the Crack Create a set in the assembly named Crack and select the crack instance. Then under Engineering

Features double click on Cracks. Fill out the dialogue by creating an XFEM crack, choose the plate as

the crack domain and select the created set Crack as the crack location, then click OK.

Analyze the Model Create a job for the model, then right-click on the job and click submit.

Model Results

Viewing the Crack In some cases it is difficult to see the crack in the Visualization module, this problem can be solved by

using translucency and View Cuts.

1. Toggle on translucency

2. Click on the View cut manager

3. Select Options for the Crack view cut

4. Go to the On Cut tab and select Use these Options

5. In the Basic subtab select Filled and No edges

6. In the Color & Style subtab, change the Fill Color in filled/shaded plots and click apply. Try

different colors and translucencies to easily see the crack. (click Apply to view the changes)

Extracting Contour Integral Results All of the results can be found under ResultHistory

Output although organizing these results can take some

work. Before beginning, read the overview of the name

filter characters by clicking the light bulb.

Results are taken at certain points along the crack front,

each point has a specific XFEM label (XFEM_1, XFEM_2,

etc.) We will first determine the location of each point,

and then the distance along crack front can be

calculated.

1.

2.

3.

4.

5. 6.

First enter *_? in the name filter bar, this will show any results ending in an underscore followed by one

character. Select the x, y, and z coordinates for the first 9 XFEM points, click Save As,

append((XY,XY,)), then click OK.

Right-click on the newly-created XYData in the sidebar and click edit, then copy and paste the y values

column into excel. This gives 27 data points, 1 for each x, y, and z coordinate of the first 9 XFEM points.

In Excel, we then separate the column of 27 into 3 columns of 9.

We then collect the rest of the coordinates (assuming less that 100 XFEM points) by entering *_?? In the

Name Filter bar of the History Output dialogue box. Note that in this case, the coordinates end at

XFEM_34, this means that there are 34 XFEM points along the crack front. We then copy and paste

these data points to Excel by using the same method as before (edit XYData-2 this time!)

The distance along the crack front can now be readily calculated from the coordinates using the

following formula:

Di+1=Di+SQRT((x i+1-xi)2+(yi+1-yi)

2+(zi+1-zi)2))

Where Di is the distance along the crack front of the ith XFEM point. Note: D0=0

We are now ready to start collecting XFEM results. Starting with the first contour, enter *_1 i n the Name

Filter box of history output. Then select all data points except for the coordinates and the Crack

propagation direction. Paste these into excel and disperse them into the Countour#1 columns, as seen

below.

Repeat this step for all 5 contours and collection of the contour integral results is completed.

Compare Model Results The benchmarks example evaluates this problem by

plotting the contour integral results against the crack

front location in degrees, as seen by the graph to the

right. Depending on where and how the instances are

positioned relative to the assembly coordinate system,

the equation should look something like this:

i=ARCTAN[(z0-zi)/(xi-xfinal)]

The vertical axis is merely a normalized value of the

first stress intensity factor (K1), since and a are both

equal to 1, vertical axis values are just K1/()

As seen below, the results from our analysis are consistent with those from the benchmarks manual.

This verifies that the problem was accurately analyzed.

Our Results Benchmark Results