thank you a lot

Dear Ghadir,

there is a lot of interesting literature on this topic.

I suggest having a look at this book:

Modeling Damage, Fatigue and Failure of Composite Materials, Woodhead Publishing, edited by: Ramesh Talreja and Janis Varna

https://www.sciencedirect.com/book/9781782422860/modeling-damage-fatigue-and-failure-of-composite-materials

Here you´ll surely find what you are looking for and many more references.

thak you Dr . Abedin Gagani

Predicting the fatigue behavior of composite materials is quite a complicate task. The reason is that the properties of polymet based composites are dominated by manufacturing process. Each laminate gets its own properties , so that costly experimental campaign are required to characterize the fatigue behavior of composites. One should also recall that the "in service" loading are very far from the loading conditions visited during the experiments. Reliable models should be capable to redict the fatigue behavior under variable amplitude loadings.

Answers to the several questions that arise from the complexity of the subject can be found in the following papers:

- Alberto D’Amore , Massimiliano Giorgio, Luigi Grassia “Modeling the residual strength of carbon fiber reinforced composites subjected to cyclic loading” International Journal of Fatigue 78 (2015) 31–37

- D'Amore, A . Grassia, L. Phenomenological approach to the study of hierarchical damage mechanisms in composite materials subjected to fatigue loadings(Article) Composite Structures Volume 175 (2017) pp. 1-6

- Alberto D'Amore, Luigi Grassia "A method to predict the fatigue life and the residual strength of composite materials subjected to variable amplitude (VA) loadings, Composite Structures 228 (2019) 111338