Study On Dynamic Fracture In Viscoelastic Medium

In structure engineering,the increasing use of polymers and concrete demands a fundamental understanding of the response of cracked viscoelastic body to dynamic load.In earthquake engineering,rupture propagation can be regarded as the Mode II crack propagation.Classical dynamic fracture theories predict the surface wave speed to be the limiting speed for propagation of Mode II crack in linear elastic materials subjected to remote loading,howerver,Archuleta et al.find intersonic rupture velocities on the basis of their analyses of the earthquake data which exceed the surface wave speed.Rosakis et al.discovered Mode II cracks in polymers propagate faster than the speed of shear waves.Motivated by the theoritical and experimental observations,it is desirable to make a study of earthquake engineering by considering dynamic fracture in viscoelastic medium.Computation of the stress intensity factor(SIF)is one of the main aspects in fracture analysis,and it is necessary to obtain dynamic stress intensity factors(DSIFs)of three mode cracks imposed by dynamic load in viscoelastic medium.Previous work on DSIFs is mainly concerned with viscoelastic materials whose equations of motion are given in the form of wave equations and constitutive equations are given in the form of various models of linear viscoelasticity,in the present work,fractional differential constitutive models are introduced to analyze the semi-infinite Mode ?,?,? crack problem under impact loads in viscoelastic medium.For semi-infinite length Mode ?,?,? crack in infinite viscoelastic medium,the definition and properties of the fractional differention are described firstly,then,the wave-like fractional equations of motion are established,and Laplace and Fourier transforms are applied to the wave-like fractional equations and combined with the Wiener-Hopf to find the solutions for the DSIFs.Finally,analytical solutions of DSIFs in Laplace domain are obtained and solutions of DSIFs in time domain are obtained by the numerical technique of Laplace inversion.DSIFs are proportional to the parameters ?,b2,and inversely proportional to the parameters ?,b1.The gradients of DSIFs time history curve approach steady state after some time and parameters b1,b2 affect little on the gradient of the time history curves.Corresponding principle of DSIFs in elastic and viscoelastic medium is obtained by extending four parameters fractional differential constitutive models to the general fractional constitutive models.For the finite length crack,fractional differential constitutive models are introduced for transient problem of Mode ?,?,? finite length crack in viscoelastic medium.Firstly,the basic equations which govern the deformation behavior are converted to fractional wave-like equations,then,integral transform method reduces the problem to Fredholm integral equation of second kind,finally,dynamics stress intensity factors of Mode ? finite crack are obtained by numerical solution of Fredholm integral equation.The fractional differentiation order?,? have great effect on the gradient of the viscoelastic DSIFs curve.Parameters b1,b2 have some effect on gradient of viscoelastic DSIFs curve but little effect on the gradient of viscoelastic DSIFs after the peak of the DSIFs curve.A framework of damage mechanics in a related literature is introduced to geometric nonlinear analysis for mechanical performance of beam considering material degradation.The relationships of elastic modulus and poisson ratio before and after damage are derived,and damage evolution equations based on the displacement function are proposed.Computer programs are developed to analyze geometrically nonlinear damage behaviour of beam with update langrangian method considering shear deformation effect.Numerical example demonstrates the damage effect on load-displacement curve.Displacement of beam end affected by the damage threshold.