Thank you very much Dr. Hamed Ebrahimi for your kind reply. I will go through the document you have attached and if any doubt I will ask you again and if my problem solved, I will send you how it is solved. Thank you very much once again.

Dear Mathusuthanan:

In principle, if you are dealing with a structure made of a truly brittle material under a constant applied tensile load in an inert environment as low homologous temperatures, it will fail instantaneously if the stress intensity developed ahead of the crack exceeds the fracture toughness, KIc or Kc, i.e., if the local stress is sufficient to break an atomic bond at the crack tip. If the stress intensity is less than the fracture toughness, the structure in principle will never fail.

However, there are processes - primarily subcritical cracking processes - which permit crack advance at stress intensities less than this critical fracture toughness. It is these processes that determine the (damage-tolerant) life of a structure, which you can estimate in terms of measurements of the crack velocity as a function of the stress intensity (so-called v-K curves). These subcritical cracking processes include environmentally-assisted cracking (e.g., stress-corrosion and hydrogen-assisted cracking), creep crack growth and most importantly fatigue-crack growth (and of course combinations of these processes such as corrosion fatigue and creep-fatigue).

The question that you are actually asking is whether any of these processes can occur in a truly brittle material as again, in principle, the vast majority of these subcritical cracking processes rely on the existence of some degree of plasticity.

The answer to your question is therefore that you first need:

(i) to identify the subcritical cracking process(es) in your material that could extend any pre-existing crack to a length where K = KIc or Kc,

and then

(ii) determine the v-K curve in terms of rate of growth of such cracks as a function of the stress intensity (or stress intensity range if you're under cyclic loads) to enable the determination of how long that it will take before catastrophic failure can occur.

Admittedly, brittle materials are more likely to simply fracture once the stress intensity exceeds the critical value, but some subcritical cracking processes need to be considered. Environmentally-assisted cracking, especially involving hydrogen, is one such mechanism that can dramatically lower the toughness of most materials, including brittle ones. Creep-crack growth is less likely in a prototypical brittle material unless you're at a temperature on the order of at least half the melting temperature. However, although metal fatigue is promoted by local plasticity, such that brittle materials are far less susceptible, toughened ceramics can be prone to fatigue failure by a very different mechanism involving the cyclic degradation of (extrinsic) toughening mechanisms behind the crack tip. I don't believe that this is too pertinent to your problem if you're dealing with a purely brittle material, but if you're interested, the attached paper may provide some guidance.

ROR

Dear Mathusuthanan Mari,

It depends on the problem conditions: Stress life or strain life. You can use Basquin Equation, Coffin-Manson Equation, power law etc. You can find your answer if search for “how to calculate fatigue life” for your problem loading conditions.

Cheers.

well, maybe some partial answers/insights (or approaches) in publicly available articles and all also can be downloaded for free in researchgate that I have worked with:

Nemeth et al.; Stochastic Simulation of Mudcrack Damage Formation in an Environmental Barrier Coating (download February 2020 version) NASA/TP—2020-220185

Nemeth, Noel N., et al. (2016a): Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix and Polymer Matrix Composite Structures. NASA/TM—2016-219113.

Nemeth, Noel N., et al. (2016b): Stochastic-Strength-Based Damage Simulation of Ceramic Matrix Composite Laminates. NASA/TM—2016-219115. http://ntrs.nasa.gov/

Nemeth, Noel N.; Jadaan, Osama M.; and Gyekenyesi, John P. (2005): Lifetime Reliability Prediction of Ceramic Structures Under Transient Thermomechanical Loads. NASA/TP— 2005-212505.

and maybe more background but pretty pictures; Nemeth, Noel, et al. (2018): Simulation of Stochastic MudCrack Damage Formation in an Environmental Barrier Coating. Presented at the United States Advanced Ceramics Association (USACA) 42nd Annual Conference on Composites, Materials, and Structures, Cocoa Beach, FL

and more methodology explaining the multiaxial fracture criterion:

Nemeth, Noel, N. (2013b): Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws. NASA/TM—2013- 217810.

You can get crack initiation and stable growth or arrested growth depending on material system and (transient) loading conditions.

Regards, --noel

Dear Mathusuthanan Mari,

if you need to perform the tests in-situ, you may use a non destructive technique. I recommend the reading of our papers:

A lifetime prediction method based on Cumulative Flaw Length Theory

Article A lifetime prediction method based on Cumulative Flaw Length Theory

and

A statistical approach for the assessment of reliability in ceramic materials from ultrasonic velocity measurement: Cumulative Flaw Length Theory

Article A statistical approach for the assessment of reliability in ...

where we coupled fracture mechanics theory (Batdorf) with ultrasounds, and I found excellent confirmation studing the crack propagation in refractory plates.

Don't hesitate to contact me for further information.

Best regards,

Dino

Thanks to all for kind reply. I will go through it for my understanding and get back here if I have doubt as well as share my problem if I solved it.

There are some method to estimate the expected lifetime of components made of brittle materials (e.g. ceramics). The assumption of failure is based on the notion of a natural flaw reaching a critical length.

I would recommend reading the following two papers on the topic:

Article Lifetime prediction of ceramic components – A case study on ...

Article Probabilistic lifetime prediction for ceramic components in ...

Thank you very much @Iyas Khader. I will go through it.

This is a fatigue problem. You can use Paris formula to esitmate the expected lifetime of a structue if the external load is cyclic and below the critical value.

@r