Necked areas in the pure shear tests?. Model to describe it?

[Fol]

Dear Dr. Bergstrom and other experts,


I’m really new in the field of rubber and in the field of FEA too so, I’ m sorry if my questions are too simple. I’m carrying out my Master Thesis (Diplomarbeit) and one area consists of validating the test data of a rubber obtained with pure shear tests (conventional device: load cell) using FEA and then using an optical device. The main problem of the test data obtained with the load cell is how to convert the engineering stress-strain to the real stress-strain, because of the appearance of a neck to low strains. Although there is a necked area and a heterogeneous distribution of the strain along the gage length, can I use the conventional equations s=s(e+1); e=ln(A0 / A) to obtain real stress-strain data?. Is there a mathematical model to obtain a corrected real strain-stress curve for necking, like Bridgman, Aronofsky, Tegart, … analysis in metals?. Any mathematical model to describe the stress state in the necked area and the influence of it in the test data results, for rubbers?. Bibliography?.
Another question: how does Abaqus interpret these necked areas in the job results (strains, stresses,…)?.

Thank very much for everything and for your great help.

David Fol

SF#

[Jorgen]

Hello David,

Here are a few comments:
:arrow: Is the necking problem that you mention from the pure shear experiments or some other type of experiments?
:arrow: If your specimen is inhomogeneosly deformed than you cannot use the conventional equations to convert from engineering stress and strain to true stress and true strain. In fact, I would say that if you have necking or some other inhomogeneous deformation field inside the gauge section, then you do not even know the engineering strain, unless you actually measure the dimensions of the neck during the deformation.
:arrow: If you cannot change the experimental setup to avoid the necking, then I would recommend that you either optically determine the stress and strain inside the neck during the loading, or perform FEA of the experimental setup. It is possible that the necking will not cause significant errors in the predicted stress and strain response.
:arrow: My understanding is that there are no well established theories for stress and strain distributions within a necked polymer specimen, primarily due to the wide range of viscoplastic deformation characteristics that polymers can exibit.
:arrow: I do not quite understand your ABAQUS question. You can simulate the neck formation and associated stresses and strains. Just create a FE model with a suitable geometric defect to force a specific neck location.

Jorgen

[Fol]

Hi Mr. Bergstrom,

1.- The necked areas appear in the rubber during the pure shear tests (tensile tests). I know that the dimensions of the specimens (length> 10*height) are designed to avoid the influence of these necked areas in the measurements, but I want to study or verify if they really not influence in the measurements. I am working to different specimen widths to see this influence; first with pure shear tests and then checking with Abaqus. I setup the experimental to cause the necking near the gauge area, so I don’t want to avoid it.

I would want to study too the stress state in these necks; this is the reason I’m looking for bibliography that explains the stress state of the necks in the rubbers and the influence of these stresses in the measurements.

I know Abaqus can gives me the information about the stress-strain in all the specimen and of course in the necked areas, but I look a pre-existing model only to check or verify.

2.- You explained to me that “you either optically determine the stress and strain inside the neck during the loading…”; sorry if it is an obvious ask but, how can I measure the stress& strain in the neck during the loading? Which device do I have to use?.

3.- How can I insert an image in this site?; a picture is worth a thousand words.


Thanks a lot.

David Fol

SF#

[Jorgen]

Hello David,

You might be interested in a recent paper written by Parson, Boyce and Parks: "An experimental investigation of the large-strain tensile behavior of neat and rubber-toughened polycarbonate", Polymer 45 (2004) 2665-2684.

Here's the abstract of that paper:

The large-strain tensile behavior of polycarbonate and polycarbonate filled with several volume fractions (f) of rubber particles is studied via an optical technique. Digital image correlation is used to determine, in two dimensions, the local displacement gradients and full-field displacements during a uniaxial tension test. Full-field strain contours, macroscopic true stress strain behavior, and local volumetric strain are reduced from the raw test data. Full-field strain contours exhibit a decreasing degree of localization with increasing f : The true stress strain results show a decrease in modulus, yield stress, post-yield strain softening, and subsequent strain hardening with increasing f : The volumetric strain decreases with increasing f as well. In the case of the neat polymer, comparisons are made to a three-dimensional finite element simulation.

Best of luck,
Jorgen

[Fol]

Thank very much Dr. Bergstrom. I will read carefully your suggested article.


Best wishes,

David Fol