Crack length versus time criterion for viscoelastic model 1

[doubleje]

In order of studying a crack propagation analysis of viscoelastic material (bituminous binder), I use crack length versus time criterion for my model of CAX4 elements that you can see in the image:

When I calculate the stress intensity factor and opening crack factor by extracting the displacement and the stress of nodes and elements corresponding, I have some remark that I wonder about:
In the image above, the crack tip is at the node 49 of element 49

• I found that in the element 49 for example, the values of maximal stress S22 of the point’s integration 1 and 2 are inferior to those of 3 and 4 although the position of these points 1 and 2 is more near from the cracktip than points 3, 4. Which point that I have to use to determine the stress intensity factor? In this case, how are the coordinates of point's Gauss (CAX4) in relation to the node's coordinates?
• When I specifies the Relative amplitude of the stresses at the contact interface due to bonding :

 *DEBOND, SLAVE=DBSLS, MASTER=DBSMS, FREQUENCY=1, OUTPUT=BOTH
0.0,1.
0.005,0.0

I found that the stress S isn’t null at the Crack surface. Do I have to reduce this amplitude till that the stress S is null?

Thanks in advance.

 

[xerf]

Some remarks:
- I think stress intensity factors (SIFs) make sense only for linear elastic materials.
- For linear elastic materials the crack surfaces (edges) should be stress free. Since the values on the element edges are obtained by extrapolation when you check the stresses on the crack surfaces you might get some small non-zero values.
- Are you sure of the order of integration points ? Have you check the nodal connectivity when you positioned the integration points. Even if you did, I think the positions of IP 3 and 4 in you plot should be ex-changed.
-Have you looked at *CONTOUR INTEGRAL, to have ABAQUS computing directly the SIFs ?

 

[doubleje]

Thank you for your pertinent answer that I’ve waited and checked for for every hours ). And I have some remark following :

I think stress intensity factors (SIFs) make sense only for linear elastic materials.
I agree with you that the SIFs is used in linear elastic fracture mechanics, but I think that stress intensity factors can be measured during quasi-stactic viscoelastic crack propagation at constant strain rates because of his propagation processes instantaneous.

I have a remark that in ABAQUS version 6.4, the Crack length versus time criterion for viscoelastic model can be done in a visco steps analysis but my current version of ABAQUS (6.6.3) did not take in account in this visco steps, and I’ve changed to static analysis.


For linear elastic materials the crack surfaces (edges) should be stress free. Since the values on the element edges are obtained by extrapolation when you check the stresses on the crack surfaces you might get some small non-zero values.

Fig. 2 : S22 - Point integration at crack edges.

You can see at Fig. 2, stress values at Point Gauss are not null. It may due to the relative amplitude of the stresses at the contact interface. However, this coefficient is small enough (I reduce 100% traction in 0.005s/20s of test’s time)


- Are you sure of the order of integration points ? Have you check the nodal connectivity when you positioned the integration points. Even if you did, I think the positions of IP 3 and 4 in you plot should be ex-changed.

Fig. 3 : Position of integration points for elements.

Element 49 CAX4 is defined like this :

49 ,49.57.58.50 (see also Fig. 2)

So I think this is the good order of integration points (Fig. 1).


-Have you looked at *CONTOUR INTEGRAL, to have ABAQUS computing directly the SIFs ?

I’ve looked at *CONTOUR INTEGRAL, but contour integral “can be used only with quadrilateral elements (in two dimensions) or brick elements (in three dimensions) – (ABAQUS Analysis User’s Manual)” and we must have contours surrounding the crack tip. So I wonder if I can use for CAX4 element for viscoelastic crack propagation to have SIFs ?


Thanks so much.

 

[xerf]

-CAX4 is a quadrilateral element.

-The GAUSS integration points are positioned within the element not on the edges of the element. (In the case of 4 points rule, the integration points are placed at +/- 1/Sqrt(3), from the element center, in the parent domain x,y=-1...+1). You have to use the nodal values of the stress field to check the stress on the crack edges.

-Within the element 49 you have a constant state of S22 stress component.

-If you look at numbering convention for the 4-node element in your second post, you can see that the IP3 and IP4 are numbered otherwise than in your first post. And as far as I see, the S22 is slightly grater at IP1 and IP3, than in IP2 and IP4.