The development of an inhomogeneous damage field in an elastic-plastic model

By making use of the evolution equation of the damage field as derived from the statistical mesoscopic damage theory, we have preliminarily examined the inhomogeneous damage field in an elastic-plastic model under constant-velocity tension. Three types of deformation and damage field evolution are presented. The influence of the plastic matrix is examined. It seems that matrix plasticity may defer the failure due to damage evolution. A criterion for damage localization is consistent with the numerical results.

Morphological Stability of Epitaxial Thin Elastic Films by Van Der Waals Force

The morphological stability of epitaxial thin elastic films on a substrate by van der Waals force is discussed. It is found that only van der Waals force with negative Hamaker constant (A < 0) tends to stabilize the film, and the lower bound for the Hamaker constant is also obtained for the stability of thin film. The critical value of the undulation wavelength is found to be a function of both film thickness and external stress. The charateristic time-scale for surface mass diffusion scales to the fourth power to the wavelength of the perturbation.

Effective elastic moduli of two-dimensional solids with multiple cracks

An accurate method which directly accounts for the interactions between different microcracks is used for analyzing the elastic problem of multiple cracks solids. The effective elastic moduli for randomly oriented cracks and parallel cracks are evaluated for the representative volume element (RVE) with microcracks in infinite media. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method is simple and provides a direct and efficient approach to dealing with elastic solids containing multiple cracks.

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.

An Energy-Based Method for Analyzing Instrumented Spherical Indentation Experiments

Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic-plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

Analysis of indentation loading curves obtained using conical indenters

Using dimensional analysis and finite-element calculations we determine the functional form of indentation loading curves for a rigid conical indenter indenting into elastic-perfectly plastic solids. The new results are compared with the existing theories of indentation using conical indenters, including the slip-line theory for rigid-plastic solids, Sneddon's result for elastic solids, and Johnson's model for elastic-perfectly plastic solids. In the limit of small ratio of yield strength (Y) to Young's modulus (E), both the new results and Johnson's model approach that predicted by slip-line theory for rigid-plastic solids. In the limit of large Y/E, the new results agree with that for elastic solids. For a wide range of Y/E, some difference is found between Johnson's model-and the present result. This study also demonstrates the possibilities and limitations of using indentation loading curves to extract fundamental mechanical properties of solids.

Weibull modulus for diverse strength due to sample-specificity

By sample specificity it is meant that specimens with the same nominal material parameters and tested under the same environmental conditions may exhibit different behavior with diversified strength. Such an effect has been widely observed in the testing of material failure and is usually attributed to the heterogeneity of material at the mesoscopic level. The degree with which mesoscopic heterogeneity affects macroscopic failure is still not clear. Recently, the problem has been examined by making use of statistical ensemble evolution of dynamical system and the mesoscopic stress re-distribution model (SRD). Sample specificity was observed for non-global mean stress field models, such as the duster mean field model, stress concentration at tip of microdamage, etc. Certain heterogeneity of microdamage could be sensitive to particular SRD leading to domino type of coalescence. Such an effect could start from the microdamage heterogeneity and then be magnified to other scale levels. This trans-scale sensitivity is the origin of sample specificity. The sample specificity leads to a failure probability Phi (N) with a transitional region 0 < (N) < 1, so that globally stable and catastrophic modes could co-exist. It is found that the scatter in strength can fit the Weibull distribution very well. Hence, the Weibull modulus is indicative of sample specificity. Numerical results obtained from the SRD for different non-global mean stress fields show that Weibull modulus increases with increasing sample span and influence region of microdamage.

A New Version of Smoothed Point Method to Simulate Linear Elastic Wave Propagation

By using the kernel function of the smoothed particle hydrodynamics (SPH) and modification of statistical volumes of the boundary points and their kernel functions, a new version of smoothed point method is established for simulating elastic waves in solid. With the simplicity of SPH kept, the method is easy to handle stress boundary conditions, especially for the transmitting boundary condition. A result improving by de-convolution is also proposed to achieve high accuracy under a relatively large smooth length. A numerical example is given and compared favorably with the analytical solution.

The Size-Dependent Elastic Properties of Nanofilms with Surface Effects

Size-dependent elastic constants are investigated theoretically with reference to a nanoscale single-crystal thin film. A three-dimensional _3D_ model is presented with the relaxation on the surface of the nanofilm taken into consideration. The constitutive relation of the 3D model is derived by using the energy approach, and analytical expressions for the four nonzero elastic constants of the nanofilm are obtained. The size effects of the four elastic constants are then discussed, and the dependence of these elastic constants on the surface relaxation and the ambiguity in the definition of the thickness of the nanofilm are also analyzed. In addition, the elastic moduli of the nanofilm in two kinds of plane problem are obtained and discussed in the case of a special boundary condition.

Crack Tip Field and J-Integral with Strain Gradient Effect

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory Two typical crack Problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

Revelation of a Functional Dependence of the Sum of Two Uniaxial Strengths/Hardness on Elastic Work/Total Work of Indentation

Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength sigma(E,y) + engineering tensile strength sigma(E,b))/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the SUM sigma(E,y) + sigma(E,b) according to the data of an instrumented indentation test. The sigma(E,y) + sigma(E,b) value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.