Size Effect And Constitutive Modeling Of Polymeric Materials In Deformation Of Microstructures

Nowadays,polymeric products with functional micro-structures on the surface are increasingly applied in micro optical device,micro biochemical reactor system and micro electromechanical system.The feature size of the functional micro-structure is mostly between 10 to 500 mm,which is so-called meso scale.Recently,the experimental studies demonstrate that the yield stress and the Young's modulus of the polymer increase as the feature size decreases in the meso scale and the polymers have size effect behaviors in meso scale.However,the traditional constitutive model of polymers cannot represent the size effect behaviors in meso scale,and also cannot provide precise predictions and theoretical guidance for the design and optimization of the micro embossing process of polymers.In this thesis,taking the size effect behaviors of polymers in meso scale as the research object,firstly,the elasto-viscoplastic model is proposed to represent the mechanical properties of polymeric materials in macro scale.Secondly,the size effect of polymers in meso scale is investigated based on the four points micro bending experiments.To predict the size effect behaviors,the strain gradient elasto-viscoplastic model is proposed by introducing the influence of the rotational gradient into the elastoviscoplastic model.After that,based on the strain gradient elasto-viscoplastic model,the finite element model with the consideration of the size effect of polymers is established.Lastly,micro embossing process of polymers in meso scale is studied via experiments and numerical methods.Main researches of this thesis focuse on the following aspects: 1.Investigation and analysis of the elasto-viscoplastic behaviors of polymeric materials in macro scaleFor the study of mechanical behaviors of polymers in macro scale,the uniaxial compression experiments of PMMA materials are performed and the influences of the strain rate on the mechanical behaviors of polymers are studied.Then,the elasticviscoplastic constitutive model of polymer in macro scale is established via introducing Hooke model,Eying model,internal variables and Langevin model to characterize the linear elasticity,the yield,the strain softening and the strain hardening of polymers.After that,the key parameters in the constitutive model are calibrated for PMMA materials and the influences of the key parameters on the stress-strain relation of polymer are discussed.2.Investigation and constitutive modeling of the size effect of polymeric materials in meso scaleThe four points micro bending platform is built to study the deformation behavior of polymers in meso scale.The variation of the curvature of the polymeric beam can be obtained via the digital camera and image process.With this platform,micro bending is conducted on PMMA films with different thicknesses and the experiment results show that both the elastic bending stiffness and the non-dimensional bending moment increase with the decreasing thickness of the film.In order to precisely model the deformation behavior of polymer in meso scale,the couple stress and the rotation gradient are introduced into the elastic-viscoplastic constitutive model,and then the strain gradient elastic-viscoplastic constitutive model is established.For PMMA materials,the material intrinsic length is then solved based on the experimental data of micro bending.The feasibility and the accuracy of the model are verified by the comparison between the experiment and the model.3.Numerical modeling of micro forming of polymers based on the strain gradient elasto-viscoplastic modelWith the help of UEL subroutine in ABAQUS FE tool,the plane strain element with the consideration of size effect of polymers is set up on the basis of the strain gradient elasto-viscoplastic constitutive model.With the proposed plane strain element,the FE model of the four points micro bending considering the size effect of polymers is then established and verified via comparison between the experimental and FE results.Lastly,the mechanism of the size effect of polymers in meso scale is revealed via numerical studies of micro bending.4.Experimental study of micro embossing process on polymer surfaceThe micro embossing experiments with various indentation depths are performed on the PMMA materials.The experiment results show that the hardening of the material behaviors in the micro embossing process is observed when the indentation depth decreases to the meso scale.Then,with the FE model based on the strain gradient elasto-viscoplastic model,the influence of the introduction of the rotation gradient on the simulation of micro embossing process of polymer is studied.Additionally,experimental studies of the roll-to-roll micro embossing on polymeric film are performed.Based on the response surface methodology,the regression model is established to describe the relationship between the height of the microstructures on the polymeric film and the processing parameters.Furthermore,the material flow behaviors of polymers in the roll-to-roll micro forming is analyzed by simulation.In summary,systematic researches are performed in this thesis focusing on study and constitutive modeling of the size effect of polymeric materials in meso scale which include four aspects: investigation and analysis of the elasto-viscoplastic behaviors of polymeric materials in macro scale,investigation and constitutive modeling of the size effect of polymeric materials in meso scale,numerical modeling of micro forming of polymers based on the strain gradient elasto-viscoplastic model and experimental study of micro embossing process on the polymer surface.It is believed that the research and the analysis method provide the base for the analysis of polymer deformation in meso scale and the design of micro embossing process for the functional micro structure on the surface of polymer.