The effects of capillary force in micro or nano-indentation

Models describing wet adhesion between indenters and substrates joined by liquid bridges are investigated. The influences of indenter shapes and various parameters of structures on capillary force are focused. In the former, we consider several shapes, such as conical, spherical and truncated conical indenter with a spherical end. In the latter, the effects of the contact angle, the environmental humidity, the gap between the indenter and the substrate, etc. are included. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. Most interesting finding is that applying the present results to micro- and nano-indentation experiments shows the size effect in indentation hardness not produced but underestimated by the effects of capillary force.(4 refs)

Interface cracking and particulate size effect in particle-reinforced metal-matrix composites

The mechanical behaviors of the ceramic particle-reinforced metal matrix composites are modeled based on the conventional theory of mechanism-based strain gradient plasticity presented by Huang et al. Two cases of interface features with and without the effects of interface cracking will be analyzed, respectively. Through comparing the result based on the interface cracking model with experimental result, the effectiveness of the present model can be evaluated. Simultaneously, the length parameters included in the strain gradient plasticity theory can be obtained.

Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

Size Dependent Nanoindentation of a Soft Film on a Hard Substrate

Nanoindentation experiments on Al/glass systems show that, as the indentation depth increases, the hardness decreases during a shallow indentation, and increases when the indenter tip approaches the film–substrate interface. We associate the rise in hardness during two stages with the strong strain gradient effects, the first stage is related with the small scale effects and the second stage with the strain gradient between the indenter and the hard substrate. Using the strain gradient theory proposed by Chen and Wang and the classical plasticity theory, the observed nanoindentation behavior is modeled and analyzed by means of the finite element method, and it is found that the classical plasticity cannot explain the experiment results but the strain gradient theory can describe the experiment data at both shallow and deep indentation depths very well. The results prove that both the strain gradient effects and substrate effects exist in the nanoindentation of the film–substrate system.

Analysis of micro-indentation problem of a soft film on a hard substrate

Two stages have been observed in micro-indentation experiment of a soft film on a hard substrate. In the first stage, the hardness of the thin film decreases with increasing depth of indentation when indentation is shallow; and in the second stage, the hardness of the film increases with increasing depth of indentation when the indenter tip approaches the hard substrate. In this paper, the new strain gradient theory is used to analyze the micro-indentation behavior of a soft film on a hard substrate. Meanwhile, the classic plastic theory is also applied to investigating the problem. Comparing two theoretical results with the experiment data, one can find that the strain gradient theory can describe the experiment data at both the shallow and deep indentation depths quite well, while the classic theory can't explain the experiment results.

应变梯度理论进展

应变梯度理论是近10年来为解释材料在微米尺度下的尺寸效应现象而发展起来的一种新理论.首先综述了应变梯度理论近年的发展及其对材料力学行为研究方面的进展.其次主要介绍了不含高阶应力的一类应变梯度理论及其应用;最后对应变梯度理论的发展做了展望.

Effect of Particle Size on the Formation of Adiabatic Shear Band In Particle Reinforced Metal Matrix Composites

In this paper, the effect of particle size on the formation of adiabatic shear band in 2024 All matrix composites reinforced with 15% volume fraction of 3.5, 10 and 20 mum SiC particles was investigated by making use of split Hopkinson pressure bar (SHPB). The results have demonstrated that the onset of adiabatic shear banding in the composites strongly depends on the particle size and adiabatic shear banding is more readily observed in the composite reinforced with small particles than that in the composite with large particles. This size dependency phenomenon can be characterized by the strain gradient effect. Instability analysis reveals that high strain gradient is a strong driving force for the formation of adiabatic shear banding in particle reinforced metal matrix composites (MMCp).

A Study of Size-Dependent Microindentation

We recently proposed a strain gradient theory to account for the size dependence of plastic deformation at micron and submicron length scales. The strain gradient theory includes the effects of both rotation gradient and stretch gradient such that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the stretch gradient measures explicitly enter the constitutive relations through the instantaneous tangent modulus. Indentation tests at scales on the order of one micron have shown that measured hardness increases significantly with decreasing indent size. In the present paper, the strain gradient theory is used to model materials undergoing small-scale indentations. A strong effect of including strain gradients in the constitutive description is found with hardness increasing by a factor of two or more over the relevant range behavior. Comparisons with the experimental data for polycrystalline copper and single crystal copper indeed show an approximately linear dependence of the square of the hardness, H 2, on the inverse of the indentation depth, 1/h, I.e., H-2 proportional to 1/h, which provides an important self-consistent check of the strain gradient theory proposed by the authors earlier.

能量非局部模型和新的应变梯度理论

提出一种新的基于能量非局部模型的应变梯度理论,并应用此理论对多晶铜以及薄膜基底的微压痕硬度进行理论预测和数值分析.首先,提出了能量非局部模型,并由此模型,得出新应变梯度理论的本构关系;其次,由变分原理,得出相应的有限元公式;再次,给出了微压痕硬度的有限元分析方法;最后,将该理论预测结果与经典理论预测结果以及实验结果进行了对比.结果表明,计算结果与实验结果相符;而经典理论的预测结果远低于实验结果.

Structural ordering and interface morphology in symmetrically strained (GaIn)As/Ga(PAs) superlattices grown on off-oriented GaAs(100)

In this work we investigate the structural properties of symmetrically strained (GaIn)As/GaAs/Ga(PAs)/GaAs superlattices by means of x-ray diffraction, reciprocal-space mapping, and x-ray reflectivity. The multilayers were grown by metalorganic vapor-phase epitaxy on (001) GaAs substrates intentionally off-oriented towards one of the nearest [110] directions. High-resolution triple-crystal reciprocal-space maps recorded for different azimuth angles in the vicinity of the (004) Bragg diffraction clearly show a double periodicity of the x-ray peak intensity that can be ascribed to a lateral and a vertical periodicity occurring parallel and perpendicular to the growth surface. Moreover, from the intensity modulation of the satellite peaks, a lateral-strain gradient within the epilayer unit cell is found, varying from a tensile to a compressive strain. Thus, the substrate off-orientation promotes a lateral modulation of the layer thickness (ordered interface roughness) and of the lattice strain, giving rise to laterally ordered macrosteps. In this respect, contour maps of the specular reflected beam in the vicinity of the (000) reciprocal lattice point were recorded in order to inspect the vertical and lateral interface roughness correlation, A semiquantitative analysis of our results shows that the interface morphology and roughness is greatly influenced by the off-orientation angle and the lateral strain distribution. Two mean spatial wavelengths can be determined, one corresponding exactly to the macrostep periodicity and the other indicating a further interface waviness along the macrosteps. The same spatial periodicities were found on the surface by atomic-force-microscopy images confirming the x-ray results and revealing a strong vertical correlation of the interfaces up to the outer surface.

Enhanced Plasticity of Zr-Based Bulk Metallic Glass Matrix Composite with Ductile Reinforcement

A composite material containing uniformly distributed micrometer-sized Nb particles in a Zr-based amorphous matrix was prepared by suction cast. The resulting material exhibits high fractured strength over 1550 MPa and enhanced plastic strain of about 29.7% before failure in uniaxial compression test at room temperature. Studies of the serrations on the stress-strain curves and the shear bands on the fractured samples reveal that the amplitude of the stress drop of each serration step corresponds to the extent of the propagation of a single shear band through the materials. The composite exhibits more serration steps and smaller amplitude of stress drop due to the pinning of shear band propagation by ductile Nb particles.

Phase Transformation Accommodated Plasticity In Nanocrystalline Nickel

Based on detailed x-ray diffraction and transmission electron microscopy we have found body-centered-cubic (bcc) Ni upon room-temperature rolling of nanocrystalline (nc) face-centered-cubic (fcc) Ni. The bcc phase forms via the Kurdjumov-Sachs (KS) martensitic transformation mechanism when the von Mises equivalent strain exceeds similar to 0.3, much higher than accessible in tensile testing. The fcc and bcc phases keep either the KS or the Nishiyama-Wasserman orientation relationship. Our results provide insights into the deformation physics in nc Ni, namely, the fcc-to-bcc phase transformation can also accommodate plasticity at large plastic strains. (C) 2008 American Institute of Physics.

Asymptotic analysis of plane-strain mode I steady-state crack growth in transformation toughening ceramics (II)

Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strain mode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The stress singularity, the distributions of stresses and velocities at the crack tip are determined for various material parameters. The factors influencing the near-tip fields are discussed in detail.

Deflections and curvatures of a film-substrate structure with the presence of gradient stress in MEMS applications

The close form solutions of deflections and curvatures for a film-substrate composite structure with the presence of gradient stress are derived. With the definition of more precise kinematic assumption, the effect of axial loading due to residual gradient stress is incorporated in the governing equation. The curvature of film-substrate with the presence of gradient stress is shown to be nonuniform when the axial loading is nonzero. When the axial loading is zero, the curvature expressions of some structures derived in this paper recover the previous ones which assume the uniform curvature. Because residual gradient stress results in both moment and axial loading inside the film-substrate composite structure, measuring both the deflection and curvature is proposed as a safe way to uniquely determine the residual stress state inside a film-substrate composite structure with the presence of gradient stress.