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In this paper, a strain gradient viscoelastic theory is proposed strictly, which can be used to describe the cross-scale mechanical behavior of the quasi-brittle advanced materials. We also expect the theory to be applied to the description for the cross-scale mechanical behavior of advanced alloy metals in linear elastic deformation cases. In the micro-/nano-scale, the mechanical properties of advanced materials often show the competitive characteristics of strengthening and softening, such as: the strength and hardness of the thermal barrier coatings with nanoparticles and the nanostructured biological materials (shells), as well as the strength of nanocrystalline alloy metals which show the characteristics of positive-inverse Hall-Petch relationship, etc. In order to characterize these properties, a strain gradient viscoelastic theory is established by strictly deriving the correspondence principle. Through theoretical derivation, the equilibrium equations and complete boundary conditions based on stress and displacement are determined, and the correspondence principle of strain gradient viscoelasticity theory in Laplace phase space is obtained. With the help of the high-order viscoelastic model, the specific form of viscoelastic parameters is presented, and the time curve of material characteristic scale parameters in viscoelastic deformation is obtained. When viscoelasticity is neglected, the strain gradient viscoelasticity theory can be simplified to the classical strain gradient elasticity theory. When the strain gradient effect is neglected, it can be simplified to the classical viscoelastic theory. As an application example of strain gradient viscoelastic theory, the solution to the problem of cross-scale viscoelastic bending of the Bernoulli-Euler beam, is analyzed and presented.

The stiff film/compliant substrate composite structure with a high modulus ratio finds a wide range of applications in production and in scientific research, and its indentation behavior cannot be described by the traditional theory when the film thickness is reduced from the millimeter scale to the micrometer or nanometer scale. In order to better understand the trans-scale indentation response of the composite structure caused by the reduction in the film thickness, this problem is solved analytically with the strain gradient theory and integral transformation. The gradient effect on the indentation response of the system is assessed in detailed from three aspects: load-displacement relationship, surface topography and distribution of bending moment on the film. In addition, the influences of film thickness, modulus ratio of the film to the substrate, contact radius and Poisson's ratio on the gradient effect are investigated. It is found that the gradient effect on the indentation response of the system, which is not sensitive to the contact radius and Poisson's ratio, is related not only to the film thickness but also to the modulus ratio of the film to the substrate. Based on the above analysis, a dimensionless number (g/l) is proposed to evaluate the gradient effect on the indentation behaviors of the system. And with the help of the dimensionless number, a new simple and accurate method for measuring the material length scale is proposed. Our research provides a theoretical basis for an in-depth understanding of the gradient effects on the indentation response of the stiff film/compliant substrate system and for the measurement of the material length scale.

Based on the assumption of constant-stress (Dugdale) interface bonding, a theoretical model is established in order to characterize the entire peeling response of an elastic film from a rigid substrate. The relationship between the peeling force and the peeling displacement and the relationship between the cohesive zone length and the peeling displacement at different peeling stages are analyzed. Closed-form solutions of the maximum peeling force and the maximum length of cohesive zone are further derived theoretically. It is found that both the maximum peeling force and the maximum length of cohesive zone depend on the interface strength, interface toughness and bending stiffness of the film. Combined with the classical Kendall's model, the cohesive zone length in the steady-state peeling stage is further given. A new method to simultaneously determine the interface strength and interface toughness is proposed, as long as the maximum peeling force, steady-state peeling force and film's bending stiffness are obtained from peeling tests. The results of this paper should be very helpful for interface performance prediction and interface design of film/substrate systems.

Cohesive zone models have been widely used to model interface crack initiation and propagation both in single-material media and bi-material systems. For single-material media with cohesive elements inserted into interface among segments, in order to ensure that the introduction of interface cohesive zone models does not affect the mechanical properties of single-material media before the softening stage of cohesive zone models, a selection criterion of stiffness of cohesive elements is proposed theoretically firstly based on the properties’ equivalence. Taking the softening stage into account, the mechanical responses of the overall stress-strain relationship of single-material media, for the cases of stable increase of strain and snap-back instability of strain, are both obtained, and the related energy mechanism are investigated. For bi-material systems with cohesive elements at interface between two materials, the thickness-dependent failure characteristics of systems in uniaxial tension are found, which is attributed to the difference of the releasing rate of elastic strain energy in the materials with different thicknesses. Furthermore, as a more complex application of cohesive elements, based on the selection criterion proposed, failure behaviors of the ceramic coating/substrate systems under three-point bending are modeled by finite element method and inserting cohesive elements into the coating segments and the coating/substrate interface simultaneously. The simulation results indicate the transition of dominated failure mode from coating cracking to interface delamination with increasing coating thickness, and show faster damage of thick coating systems, agreeing with experimental results. The effects of interface strength and toughness of cohesive elements on failure are also revealed. These results can provide guidance for the application of cohesive elements, and help us better understand the overall failure behaviors of interface systems.

Two types of peeling experiments are performed in the present research. One is for the Al film/Al2O3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al2O3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al2O3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case. (C) 2007 Elsevier Ltd. All rights reserved.

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

Plastic flow localization in ductile materials subjected to pure shear loading and uniaxial tension is investigated respectively in this paper using a reduced strain gradient theory, which consists of the couple-stress (CS) strain gradient theory proposed by Fleck and Hutchinson (1993) and the strain gradient hardening (softening) law (C-W) proposed by Chen and Wang (2000). Unlike the classical plasticity framework, the initial thickness of the shear band and the strain rate distribution in both cases are predicted analytically using a bifurcation analysis. It shows that the strain rate is obviously non-uniform inside the shear band and reaches a maximum at the center of the shear band. The initial thickness of the shear band depends on not only the material intrinsic length la but also the material constants, such as the yield strength, ultimate tension strength, the linear hardening and softening shear moduli. Specially, in the uniaxial tension case, the most possible tilt angle of shear band localization is consistent qualitatively with the existing experimental observations. The results in this paper should be useful for engineers to predict the details of material failures due to plastic flow localization. (C) 2011 Elsevier Ltd. All rights reserved.