Journal of Materials Research 2024 www.mrs.org/jmr Vol.:(0123456789) DOI:10.1557/s43578-024-01399-1 © The Author(s), under exclusive licence to The Materials Research Society 2024 Article Development of empirical models for estimation polymer indentation fatigue and validation with finite element simulation models Soumya Ranjan Guru 1,a) , Mihir Sarangi 1 1 Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India a) Address all correspondence to this author. e-mail: gsoumya03@iitkgp.ac.in Received: 1 March 2024; accepted: 11 July 2024 Multi-cycle micro-indentation tests were conducted on three polymers: Poly-ether-ether-ketone (PEEK), Poly (methyl methacrylate) (PMMA), and Poly (tetra-fluoroethylene) (PTFE). The load–displacement curve obtained from the indentation technique was used to evaluate the mechanical properties of these polymers. This study employed multi-cyclic indentation to establish a polymer fatigue model utilizing the indentation load–displacement curve. Currently, researchers are investigating fatigue life studies using stress- and energy-based approaches. Two empirical models for each approach were developed using the least-square curve-fitting method in this study. A simulation model based on finite element analysis has been utilized to verify the accuracy of these fatigue models for Vickers indentation. During the validation process, both models had a maximum error value of 2% compared to the experimental data, indicating a strong agreement with the simulation results. The generated models can evaluate polymer fatigue using non-destructive methodology. List of symbols A Contact area of indenter A i Vicker indenter area c 1 , c 2 , c 3 , c 4 , c 5 , c 6 Fitting constants E Elastic modulus of the material E i Indenter elastic modulus E r Reduced elastic modulus H Actual hardness of the material H = H P 1 Non-dimensional hardness h Indenter displacement on the material h c Indentation contact depth h f Indentation final depth h max Maximum indentation depth h s Recovery displacement due to material elasticity K 1 andK 2 Constant depends on the materials and indenter properties N Number of indentation cycles P Applied indenter load P = E*µ P 1 Experimental constant for fatigue model P 1 = P A i Indenter parameter coefficient P max Maximum indentation load W P Dissipated plastic hysteresis energy W e Dissipated elastic hysteresis energy W T Total absorbed energy of the materials W P = W P A i Non-dimensional plastic energy σ y Yield stress of the materials σ y = σ y P 1 Non-dimensional yield stress µ Poisson’s ratio of the materials µ i Poisson’s ratio of the indenter Introduction Material research and development have witnessed significant progress due to technological advancements. e popularity of destructive testing has seen a decline over time. Non-destructive testing (NDT) offers a clear advantage in terms of the reusability of the tested material. Micro-indentation testing is an NDT that can identify several mechanical properties, including hardness, elastic modulus, tensile strength, fatigue, and fracture toughness. is testing method is a well-known technique that involves determining penetration depth using an indenter. e penetra- tion depth could easily be utilized to calculate and analyze the elastic modulus (E) and hardness (H) of the materials, as well