Continuum Damage Mechanics References

TD 2022-02-07

This post is intended to pull together some valuable resources and references on the subject of continuum damage mechanics, aka ductile damage of metals. From the Abaqus 2022 GA docs, Materials > About Progressive Damage and Failure:

There has been some confusion in the past because the above stress-strain curve is a true stress-true strain curve. The point "C" is NOT ultimate. Ultimate occurs much earlier on the curve.

In the near future, we will update this part of the Abaqus docs to look like the image below.

"The nominal (engineering) stress reaches a maximum (ultimate tensile strength) value at point $x$ , corresponding to the onset of incipient necking. Beyond this point, deformation localizes in a neck region and the stress-strain state is not uniform in the specimen. Therefore, after point $x$ , the curve is no longer representative of the actual stress-strain state at any given location of the specimen. ... Point $c$ in this curve identifies the material state at the onset of damage"

Construction of a ductile damage model in Abaqus for metals such as steel, aluminum, etc, can be thought of in four steps (following the docs, but adding a few more details):

1) Create an elastic-plastic material model that is valid well past ultimate into the necking region of the deformation. This is a key ingredient, perhaps the most important step.

a) It is useful to begin this process by using uniaxial tensile test data up to ultimate. This step can be accomplished quickly using the material calibration app in the 3DExperience platform.

b) Use the uniaxial test data up to damage initiation to further define the elastic-plastic model. The most common way of doing this is using an FE simulation of the test, using what is often called an inverse method. This step can be accomplished using the FE-mode calibration in the calibration app, an example is shown here: Necking of a titanium dogbone specimen

c) Validate, or refine this elastic-plastic model by simulating all of the various tests that have been performed. It is well known that the damage for most metals is dependent upon the state of stress triaxiality, thus various test specimen geometries are used to understand this dependence. The failure strain may also be dependent upon the Lode angle, and perhaps the strain-rate. Thus additional tests, with additional specimen geometries, may also be used.

2) Determine the parameters for the *Damage Initiation behavior of the material. We are in the process of adding this capability to the material calibration app (for the relatively new Hosford-Coulomb damage model). For every test specimen geometry used:

a) Determine the location of incipient failure. This is usually done by using information from both the test observations and the FE models of the specimen. For some frequently used specimens, this location is well documented. For instance for a uniaxial pull test the location of incipient failure is at the center of the bar/rod.

b) Using the FE model, loaded to incipient failure, understand the state of: plastic strain (PEEQ), triaxiality (TRIAX), Lode angle (LODE), and perhaps plastic strain rate (PEEQR) at this element. If the test specimen has necked (typical), the PEEQ value cannot be read from a plot of the macro test response. It must be determined from the FE model response at the location of incipient failure.

3) Determine the parameter(s) for the *Damage Evolution behavior of the material.

4) A choice of element deletion.

Learning resources:

Review of Advanced Materials Modeling Capabilities in Abaqus 2014 (lists some good reference papers)

2012 Sandia Fracture Challenge (lists some good reference papers)

Identification of Ductile Damage Parameters ; 2013 conference paper

Tech Briefs are typically created to show what can be done with the advanced technology in Abaqus, but are not intended to teach the how.

Tech Brief: Pipeline Rupture in Abaqus/Standard with Ductile Failure Initiation

Tech Brief: Simulation of the ballistic perforation Video

Damage model calibration and application for S355 steel (2016)

João Ribeiroa, Aldina Santiago, Constança Rigueiro

The numerical prediction of ductile fracture of martensitic steel in roll forming (2018)