The stability of nanoscale devices is directly related to elasticity and the effect of temperature on the elasticity of thin films and nanocrystals. The elastic instability induced by rising ...temperature will cause the failure of integrated circuits and other microelectronic devices in service. The temperature effect on the elastic modulus of thin films and nanocrystals is unclear although the temperature dependence of the modulus of bulk materials has been studied for over half a century. In this paper, a theoretical model of the temperature-dependent elastic modulus of thin films and nanocrystals is developed based on the physical definition of the modulus by considering the size effect of the related cohesive energy and the thermal expansion coefficient. Moreover, the temperature effect on the modulus of Cu thin films is simulated by the molecular dynamics method. The results indicate that the elastic modulus decreases with increasing temperature and the rate of the modulus decrease increases with reducing thickness of thin films. The theoretical predictions based on the model are consistent with the results of computational simulations, semi-continuum calculations and the experimental measurements for Cu, Si thin films and Pd nanocrystals.
► We present a trans-scale mechanics model to characterize size effects of materials. ► We use the model to describe the mechanical behavior of the nanocrystalline metals. ► We use the cohesive zone ...model to describe the grain boundary damage. ► Stress–strain relations of nanocrystalline metals strongly depend on the grain sizes.
A trans-scale mechanics model considering both strain gradient and interface energy effects is presented for describing size effects in nanocrystalline and ultra-fine polycrystalline metals accompanying by intergranular fracture. A finite element method is developed which is suitable for describing the strain gradient and interface energy effects. Moreover, cohesive interface model is used to study the intergranular damage and fracture in polycrystalline metals with nanoscale and ultra-fine grains. A systematical study on the overall strength and ductility of polycrystalline aggregates which depend on both grain interiors and grain boundaries for different grain sizes and different interface properties is performed. The results show that the overall strength and ductility of polycrystalline aggregates with nanoscale and ultra-fine grains strongly depend on the grain size and grain hardening, interface energy density, grain boundary strength and toughness.
Interface delamination plays an important role on the failure of multi-layer parts, influences of interface properties and coating thickness on interface fracture of coating/substrate systems attract ...great attention. In this paper, interface fracture behaviors of ceramic coating/substrate systems under three-point bending were modelled based on finite element simulations with interface cohesive elements. Influences of coating thickness, interfacial strength and interfacial fracture toughness on interface crack evolution were studied. The simulations indicate that interface crack initiates earlier for the thicker coating systems or the systems with the smaller interface fracture toughness, and the influence of interface strength is more complicated. The simulation results are in agreement with the experimental results and instructive to understand interface failure behaviors of coating/substrate systems deeply.
In the present research, hierarchical structure observation and mechanical property characterization for a type of biomaterial are carried out. The investigated bioma- terial is Hyriopsis cumingii, a ...typical limnetic shell, which consists of two different structural layers, a prismatic ＂pillar＂ structure and a nacreous ＂brick and mortar＂ structure. The prismatic layer looks like a ＂pillar forest＂ with variationsection pillars sized on the order of several tens of microns. The nacreous material looks like a ＂brick wall＂ with bricks sized on the order of several microns. Both pillars and bricks are composed of nanoparticles. The mechanical properties of the hierarchical biomaterial are measured by using the nanoindentation test. Hardness and modulus are measured for both the nacre layer and the prismatic layer, respectively. The nanoindentation size effects for the hierarchical structural materials are investigated experimentally. The results show that the prismatic nanostructured material has a higher stiffness and hardness than the nacre nanostructured material. In addition, the nanoindentation size effects for the hierarchical structural materials are described theoretically, by using the trans-scale mechanics theory considering both strain gradient effect and the surface/interface effect. The modeling results are consistent with experimental ones.
Two types of peeling experiments are performed in the present research. One is for the Al film/Al
2O
3 substrate system with an adhesive layer between the film and the substrate. The other one is for ...the Cu film/Al
2O
3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al
2O
3 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.
•An analytical indentation model with the consideration of the surface effect for the composite structure is established.•The influence of the surface energy on the indentation response of the ...composite structure is investigated.•The factors influencing the surface effect are analyzed, systematically.•A dimensionless number is proposed to evaluate the influence of the surface effect on the composite structure.
The indentation behaviors of hard nanofilm/soft substrate composite structures which are widely used in production and in scientific research cannot be described by the conventional continuum theory due to the influence of surface energy under the micron scale. To better understand the indentation response of this composite structure under the influence of surface energy, an analytical indentation solution is obtained with the Hankel transform and the surface elasticity model developed by Gurtin and Murdoch. Based on the analytical solution, the influences of surface residual stress and surface elastic constant on the distribution of the bending moment in the nanofilm, the load-displacement relationship, and the surface morphology are investigated in detail. In addition, the influences of the film thickness, modulus ratio of the film to the substrate, contact radius and Poisson's ratio on the surface effect are studied. The results show that the influence of the surface effect on the indentation response of the system, which is insensitive to the Poisson's ratio and the contact radius, is not only sensitive to the thickness of the film, but also to the modulus ratio of the film to the substrate. Based on the above analysis, a dimensionless number (K2/(λ+6K1)1/3) is proposed to evaluate the influence of the surface effect on the indentation response of this composite structure. Our study sheds light on the understanding of the indentation behaviors of this composite structure under the influence of the surface effect and provides a theoretical guidance for the application of this composite structure.
The influence of the surface energy on the indentation response of a hard nanofilm/soft substrate system is studied in detail based on the theoretical model established by us. Display omitted
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
l
cs
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.
The elastic properties and the vibration characterization are important for the stability of materials and devices, especially for nanomaterials with potential and broad application. Nanomaterials ...show different properties from the corresponding bulk materials; the valid theoretical model about the size effect of the elastic modulus and the vibration frequency is significant to guide the application of nanomaterials. In this paper, a unified analytical model about the size-dependent elastic modulus and vibration frequency of nanocrystalline metals, ceramics and semiconductors is established based on the inherent lattice strain and the binding energy change of nanocrystals compared with the bulk crystals, and the intrinsic correlation between the elasticity and the vibration properties is discussed. The theoretical predictions for Cu, Ag, Si thin films, nanoparticles, and TiO2 nanoparticles agree with the experimental results, the computational simulations, and the other theoretical models.
PDF
