Indentation scaling relationships provide normalized guidance for measuring and predicting mechanical properties in indentation experiments. At the nano-scale, the material size-effect is ...significant, while conventional scaling relationships fail to depict this phenomenon in nanoindentation precisely. In the present research, cross-scale indentation scaling relationships are investigated using a strain gradient theory. The nanoindentation response is found to be sensitive to different material parameters, including the material intrinsic length, yield stress, and work-hardening exponent across size-scales. If the strain gradient effect is ignored, the nanoindentation scaling relationships approach the macroscopic conventional ones. The cross-scale indentation scaling relationships obtained in the form of dimensionless functions in this work provide quantitative references to instrumented indentation tests on multiple size-scales, coinciding well with experimental results. The understanding of nanoindentation hardness is enhanced by the present work.
•The pre-stress loading method is proposed to obtain the acoustoelastic constant.•The longitudinal and transverse welding residual stresses are measured, respectively.•The finite element analysis ...model for laser ultrasonic measurement of welding residual stress is established.
Laser ultrasonic is a most promising method for non-destructive evaluation of residual stress. The residual stress of thin steel plate is measured by laser ultrasonic technique. The pre-stress loading device is designed which can easily realize the condition of the specimen being laser ultrasonic tested at the same time in the known stress state. By the method of pre-stress loading, the acoustoelastic constants are obtained and the effect of different test directions on the results of surface wave velocity measurement is discussed. On the basis of known acoustoelastic constants, the longitudinal and transverse welding residual stresses are measured by the laser ultrasonic technique. The finite element method is used to simulate the process of surface wave detection of welding residual stress. The pulsed laser is equivalent to the surface load and the relationship between the physical parameters of the laser and the load is established by the correction coefficient. The welding residual stress of the specimen is realized by the ABAQUS function module of predefined field. The results of finite element analysis are in good agreement with the experimental method. The simple and effective numerical and experimental methods for laser ultrasonic measurement of residual stress are demonstrated.
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 size and viscosity effects are noticeable at the micro-/nano scale. In the present work, the strain gradient viscoelastic solution of the mode-III crack in an infinite quasi-brittle advanced ...material is proposed based on the strain gradient viscoelasticity theory using the Wiener–Hopf method. The solutions to the gradient-dependent viscoelastic crack problem are obtained directly by using the correspondence principle between the strain gradient viscoelasticity and strain gradient elasticity in Maxwell’s standard linear solid model. In this model, the stress near the crack tip is time-dependent and size-dependent. Besides, the stress near the crack tip is more significant than that based on gradient elasticity theory. Compared with the elastic strain gradient effect, the viscous gradient effect makes the stress field at the crack tip harden. The location and the value of maximum stress change with time, which differs from the case in strain gradient elasticity theory. The time that the normalized stress takes to stabilize also changes with the distance from the crack tip. When the viscosity effect is neglected or time tends to infinity, the strain gradient viscoelasticity theory can be reduced to the classical strain gradient elasticity theory.
•The strain gradient viscoelastic solutions of the Mode-I and Mode-II crack in an infinite quasi-brittle advanced material are proposed based on the strain gradient viscoelasticity theory using the ...Wiener-Hopf method and the correspondence principle in Maxwell's standard linear solid model. The strain gradient viscoelasticity theory are successfully used to explain the fracture of microscale and nanoscale materials with viscosity and size effect.•The stress near the crack tip is time-dependent and size-dependent. The stress near the crack tip is more significant than that based on gradient elasticity theory. Compared with the elastic strain gradient effect, the viscous gradient effect makes the stress field at the crack tip harden.•The location and the value of maximum stress change with time, which differs from the case in strain gradient elasticity theory. The time that the normalized stress takes to stabilize also changes with the distance from the crack tip. When the viscosity effect is neglected or time tends to infinity, the strain gradient viscoelasticity theory can be reduced to the classical strain gradient elasticity theory.
The impacts of size and viscosity become distinctly evident when considering micro- and nano-scale phenomena for advanced materials with micro- and nanostructures. In this study, the mechanical behavior of the advanced material is characterized by using the strain gradient viscoelasticity theory, and a novel solution is presented for the mode-I and mode-II cracks, which is formulated based on the strain gradient viscoelasticity theory, employing the Wiener-Hopf method. Besides, the gradient-dependent viscoelastic crack solutions are directly derived by applying the correspondence principle that aligns strain gradient viscoelasticity with strain gradient elasticity within the Maxwell's standard linear solid model. Relative to the influence of elastic strain gradient effects, the involvement of viscous gradient effects instigates a reinforcement to the stress field around the crack tip, thereby offering a more reasonable representation of advanced materials crack behavior. When the viscosity effect is omitted or as time tends to infinity, the solutions based on strain gradient viscoelasticity theory converges to those on the classical strain gradient elasticity theory.
Indentation scaling relationships intend to guide indentation experiments and help understand the indentation hardness. In the present study, dimensionless functions were obtained by fitting a series ...of numerical results of the cross-scale indentation tests based on a strain gradient plasticity theory. The closed-form indentation scaling relationships were found between dimensionless material properties and indentation responses, which were non-dimensionalised by a representative stress. The closed-form expressions were of high accuracy with both the numerical results and the experimental data. Forward and reverse analysis were then established and discussed, providing the indentation scaling relationships a quantitative result. The explicit definition of the representative stresses made it possible to obtain the specific relationship between indentation responses and each material parameter. Together with some pre-determined material parameters, the material intrinsic length was able to be derived from the indentation tests. The present work significantly enhanced the value of the cross-scale indentation scaling relationships, providing great convenience in guiding instrumented tests.
•The NS surface layer supported by CG substrate displays significant strain delocalization and achieves improved uniform elongation.•The strain delocalization is realized by forming dispersed stable ...strain bands (SBs) and promoting the deformation of non-strain banding zone.•The intra-layer microstructure inhomogeneity and the limited strain hardening capability of intra-layer domains lead to SBs nucleation.•The inter-layer microstructure inhomogeneity causes extra inter-layer shear constraints, which stabilize SBs and promotes the deformation of non-strain banding zone.•The NS indeed becomes ductile, due to the extensive nanotwinning and dislocation activity enabled by strain delocalization.
How to suppress strain localization in tensioned nanograined layer and make it ductile? This remains a great challenge. Here we explore the effects of microstructure inhomogeneity on the plastic behavior of nanostructured layer. A nanostructured CrMnFeCoNi high entropy alloy layer supported by coarse-grained substrate (in gradient architecture) is taken as an example. In the tensile deformation, strain examinations find that the nanostructure layer experiences significant strain delocalization by activating dispersed stable strain bands (SBs) and promoting the deformation of non-strain banding zone. Finite element analysis reveals that it is the intra-layer microstructure inhomogeneity which enables dispersed SBs nucleation from the mechanical weak sites. The inter-layer microstructure inhomogeneity introduces extra shear constraints from the coarse-grained substrate, which stabilizes SBs and improves the stress of non-strain banding zone, thereby suppressing the early catastrophic strain localization. Importantly, the strong nanostructure layer indeed becomes ductile (enables further work hardening) due to the activation of hierarchical nanotwinning and dislocation activity.
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The thick spherical shell cell is a common structural element employed routinely in constructing the new advanced materials. The strain gradient viscoelastic solution of a pressurized thick spherical ...shell cell is presented based on a strain gradient viscoelasticity theory. This solution captures the hardening and softening effects of materials by means of a gradient parameter, in which the higher-order viscosity is included by introducing a higher-order viscoelastic model. The hardening-softening behavior at the micro-/nano-scale is displayed, and the positive/inverse Hall-Petch character can be explained using the strain gradient viscoelastic model. During the derivation, the variational principle is used to obtain the governing equation and boundary conditions. The solution of the strain gradient viscoelastic problem with specific boundary conditions is then derived in detail by employing the Laplace transformation. Moreover, the strain gradient viscoelastic solution is obtained directly from the strain gradient elastic solution using the correspondence principle between the strain gradient viscoelasticity and the strain gradient elasticity. The stiffness of the pressurized spherical shell is discussed and compared with the result of the traditional simplified strain gradient elasticity. The strain gradient viscoelastic solution of stiffness is related to the material parameters with both time and scales.
•A pressurized thick spherical shell cell subjected to internal and external pressures is solved based on the strain gradient viscoelasticity theory.•A gradient viscoelastic parameter related to the material cell size and viscosity is involved.•The hardening-softening effect of advanced materials at the micro/nano-scale is presented.
Nanomechanical properties of polymer samples were calculated using an adhesive contact model appropriate for AFM indentation problems. A series of Polydimethylsiloxane (PDMS) samples were indented by ...the sharp indenter in the air by using an AFM, and dozens of the force-displacement curves of each sample were obtained. An adhesive contact model suitable for sharp indentation with adhesion was established based on the same assumptions of the JKR model which is only suitable for spherical indentation at small penetration depth. Differences between sharp indentation problems with and without adhesion were discussed, and the limitations of the traditional adhesion model were given. The elastic modulus was obtained by fitting experimental force-displacement curves with theoretical ones, and results were compared to those macroscopic values in literature. The adhesion energy between the indenter and the sample surface was accurately calculated using the adhesion model based on the calculated elastic modulus. The influence of the indenter tip angle on the calculation results of the elastic modulus was also discussed theoretically. In this study, the mechanical properties of polymer samples were calculated at the nanoscale considering the adhesion effect.
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