Theoretical And Experimental Studies On The Cross-scale Strengthening,Softening And Viscoelasticity Of Advanced Materials

Micro/nano-structured advanced materials exhibit strong microstructural effects during micro-/nano-scale deformation,which include both strengthening and softening effects.The conventional continuum theory is unable to characterize these effects.Thus,researchers have proposed various strain gradient theories to characterize the strengthening effect of advanced materials,but these theories cannot explain the phenomenon of softening as the scale decreases(i.e.Hall-Petch effect and inverse-Hall-Petch effect).In this study,the in situ mechanical properties of polymeric materials were first tested using AFM to reveal the strong scale and viscoelasticity effects at the microscale.Then,the strain gradient viscoelasticity theory was derived using the energy principle for the strengthening-softening phenomenon of advanced materials.This theory considers the strain gradient,low-order viscous and high-order viscous effects,and it can explain the strengthening-softening effect.The main research works and results obtained are as follows:(1)Firstly,an in situ mechanical property test of PDMS polymer material was carried out with the aid of AFM,and a theoretical model of adhesive indentation applicable to a sharp indenter was proposed to calculate the elastic modulus and adhesive surface energy of the material in the indentation experiment.The calculation results showed that the elastic modulus of the material measured in the micro-scale experiment was much higher than the macroscopic elastic modulus of the material,and the material would exhibit obvious adhesion phenomenon or viscous effect in the micro-scale,i.e.,it revealed the strong scale effect and viscous effect that the material would exhibit in the micro-scale.(2)The strain gradient viscoelasticity theory is proposed,which considers the macroscopic and microscopic viscosity of the material,based on the traditional strain gradient elasticity theory and viscoelasticity theory,and introduces a gradient parameter that can portray the scale effect.The theory can be used to characterize the cross-scale mechanical behavior of quasi-brittle advanced materials,i.e.,for the viscous softening effect and the strain gradient strengthening effect at the nanoscale.In addition,the strain-gradient viscoelastic theory can be degraded to the conventional strain-gradient elasticity theory when the viscous effect is neglected,i.e.,the strain-gradient elasticity theory can be considered as a special case of this strain-gradient viscoelasticity theory.(3)The corresponding principles between the strain gradient viscoelastic theory and the conventional strain gradient elastic theory in the Laplace phase space are derived and presented.When the strain-gradient elastic solution of the corresponding problem is known,the strain-gradient viscoelastic solution of the problem can be obtained directly by using this correspondence.After deriving the strain gradient viscoelasticity theory,a hybrid finite element framework is completed to accompany the strain gradient viscoelasticity theory.The derivatives of strain gradient and higher-order stress are introduced into the hybrid finite element as additional nodal degrees of freedom,which reduces the requirement for continuity of the unit.(4)To obtain the mechanical theoretical explanation of the strengthening-softening effect of advanced materials,detailed analyses are carried out for the problems of thick-walled spherical shell cell and thick-walled cylindrical cell subjected to uniform compression,respectively.Furthermore,the theoretical results of strain gradient viscoelasticity in the thickwalled spherical-shell configuration are compared with the molecular dynamics simulation results of nanocrystalline copper,and the inflection point from the strengthening effect to the softening effect is determined by proposing a critical energy density criterion.The straingradient viscoelasticity theory can explain the strengthening-softening behavior.(5)Several typical cross-scale mechanical problems of advanced materials are solved using the strain gradient viscoelastic theory,including beam bending problems(pure bending,cantilever beam bending,and simply supported beam bending),and simple tensile problems of interlaced structural biomaterials.Meanwhile,the beam bending results calculated by the finite element model are compared with the theoretical results.In solving the simple tensile problems of staggered-structured bio-composites,the strain-gradient viscoelastic model corresponding to this type of material is proposed,and the equivalent modulus calculated by the theoretical model of strain-gradient viscoelasticity is compared with the experimental value,and it is found that the strain-gradient viscoelasticity results will be closer to the experimental value.