Hi Torkan Shafighfard

As you mention "ply" I assume you are referring specifically to laminated composites. Due to heterogeneous nature, various micro-level failure mechanisms can occur within the laminate i.e. cracks, voids. Damage mechanics concerns the initiation and growth of such mechanisms to the point of ultimate laminate failure.

Ply discount method relates to progressive failure analysis. Consider, if you will, the case of a laminated pipe or vessel under internal pressure. It is straightforward to evaluate the pressure at which the first ply of the laminate will fail according to many established failure criteria. However, laminates can retain a certain level of load-bearing capacity beyond first-ply failure (FPF), therefore this approach can be overly conservative. Moreover, in the case of a pipe it may be more appropriate to treat failure as the loss of fluid-tightness; we could consider through-thickness cracking, that is, failure of all of the layers leading to leakage. This is where progressive failure and ply discount come in. We can evaluate FPF according to our chosen failure criteria. When a ply is deemed to have failed, its contribution to overall stiffness of the structure is effectively 'discounted'. Load is increased further and this is repeated until ultimate failure, i.e. the laminate can no longer sustain load.

In short, ply discount is not a failure criterion but a method of evaluating progressive failure in conjunction with chosen failure criteria that assess when each ply has failed and its stiffness is to be reduced. Note that the properties can be reduced instantly to zero or gradually degraded. Failure criteria such as Hashin, which distinguish heterogeneous fibre/matrix failure modes, can inform particular properties to reduce in the analysis.

Cheers,

JCH

James C. Hastie Thank you sir. So failure criterion just provides the load wherein the first lamina fails right? Therefore, it could not provide any important info since it is conservative and the load is not actually the load that failure occurs right? Also, sometimes they use hashin damage criterion is it different than hashin failure? if not, why they use same word?

Hi Torkan Shafighfard

Yes, the failure criterion will identify when the first ply has failed, but also can be used to identify when the next ply has failed, and the next.. and so on in the case of progressive failure analysis (PFA). Generally speaking, first-ply failure (FPF) is conservative because we know that laminates can still carry load to some extent if, for example, we are considering a laminate with 20 plies; we can easily envisage that failure of one ply resulting in its loss of load-bearing contribution will not render the laminate completely failed at that stage.

However, we must remember that it depends very much on the specific problem and we shouldn't always dismiss FPF as overly conservative and it can still have important practical value. For instance, the most obvious case would be a laminate with small number of plies, say four plies; we may find that FPF occurs very shortly before ultimate failure of the laminate. Therefore, FPF analysis may give a reasonable indication of true failure load and would certainly be less effort than PFA. Moreover, in practical applications it may be a requirement that the structure is designed based on FPF. In other words, certain industry standards or guidelines may dictate that a laminate structure cannot have a failed ply in service, even if in reality it may still carry some load. You can have a read of some of my papers on laminated composite pipes for oil and gas applications, in which we considered FPF on the basis that an "unfailed" pipe is desired in service.

The terms "damage" and "failure" appear to be used somewhat synonymously at times in the literature. "Hashin" should specifically refer to the Hashin criterion, which is used to evaluate fibre tension, fibre compression, matrix tension and matrix compression failures of a composite lamina. I imagine the authors have used "damage" in reference to occurrence of Hashin failure mode in a ply, e.g. "matrix damage in tension".

James C. Hastie Hello again sir. So, you know as I read there are three damage criteria called ply discount, maximum truncated strain, and discrete damage mechanics. So, for example hashin damage is inside these criteria or it is separate? Do you know any specific source to explain these? Or Continuum Damage Model is separate one from those?

Hi Torkan Shafighfard

It is important not to confuse the various terminologies. I recommend you digest the following useful article on the subject, which distinguishes between the various types and examples of failure criteria and damage mechanics approaches: https://doi.org/10.1177%2F0021998314553885

If you are currently deliberating a particular laminate problem, I suggest (as with generally most analyses) to keep the problem as simple as possible. First ply failure of a structural laminate under load is easily evaluated using any one of the various failure criteria involving principal stress (or strain) components. If you feel that first ply failure is too conservative, you can extend your model for progressive failure analysis in which the properties of a failed ply are reduced (i.e. ply discount), load is increased and this is continued until eventually the laminate as a whole can no longer carry load/fufil its design purpose.

In the above we are working at the macro or ply level, that is, we consider effective properties for the plies and do not have to consider fibre and matrix separately (as in micromechanics). I would only recommend a micromechanical failure/damage evaluation if you are interested in studying some particular phenomena associated with fibre, matrix or the interphase, rather than the structural response of the laminate as a whole (which is usually of greater practical interest for design purposes).

James C. Hastie

So, sir

ply discount, maximum truncated strain, and discrete damage mechanics are not only criteria for last ply failure right or these are just three that others are inside them? Thank you and I will read that paper :)

Hi Torkan Shafighfard

Ply discount method can be used to identify last ply failure based on the sequential failure of each individual ply. You will need to identify a suitable failure criterion to evaluate when each ply fails, as well as an appropriate degradation strategy to reduce properties of the plies upon their failure.

There are numerous failure criteria that can be used to identify ply failure (you can easily find these online). The simplest is the Maximum Stress criterion, which assumes failure occurs simply when any principal stress exceeds the corresponding strength. The Maximum Strain theory follows similar logic. I have not heard of the Truncated Maximum Strain theory previously, from the word 'truncated' I guess it is some slightly modified version of this. You should base your choice of criterion on experimental corroboration or at least sound justification from literature.

Rather than providing conditions at which certain failure mechanisms occur (as in the failure criteria), a damage mechanics approach users internal variables to capture and describe the evolution of damage for progressive failure analysis. I personally have not performed a damage mechanics-type analysis; I believe the popular composites textbooks should have a chapter or two on this.

James C. Hastie Hello again, could you also give me an overview of which experimental tests are required to have the material characterization for both damage and failure criteria?

Hi Torkan Shafighfard

Failure criteria, e.g. Maximum Stress alluded to earlier, require the tensile and compressive strengths of the lamina in each normal direction, i.e. 1, 2, 3, and shear directions, 12, 13, 23 (for plane stress, often assumed for laminate analysis, the coordinates 1, 2, 12 will suffice). These strengths be determined by straightforward tensile, compressive and shear experiments or from micromechanics (i.e. calculated based on strengths/properties of fibres and matrix and their associated volume fractions). If determining the lamina strengths by experiment we do not need to know the individual constituent strengths - we treat the material as homogeneous at the lamina level.

When analysing damage at the micro-level you will need to know the properties of the individual constituents.