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.

Mode I and Mode II Crack Tip Asymptotic Fields with Strain Gradient Effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

Onset of Adiabatic Shear Instability in Strain Gradient Dependent Metal Matrix Composites

In this paper, effect of strain gradient on adiabatic shear instability in particle reinforced metal matrix composites is investigated by making use of the strain gradient dependent constitutive equation developed by Dai et al. [9] and the linear perturbation analysis presented by Bai [10]. The results have shown that the onset of adiabatic shear instability in metal matrix composites reinforced with small particles is more prone to occur than in the composites reinforced with large particles. This means that the strain gradient provides a strong deriving force for onset of adiabatic shear instability in metal matrix composites.

Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i.e. a separation law and an integration Law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results([19]); the angular distributions of couple stresses are the same as the couple stress results([19]). For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion([19]), but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper.

The Influence of Strain Gradient on the shear Band in a Saturated Soil

The dynamic localization of saturated soil is investigated by considering the influence of higher strain gradient. It is shown that the strain gradient has a significant influence on the evolution of shear band in saturated soil and that the width of shear band is proportional to the square root of the strain gradient softening coefficient. The numerical simulation is processed to investigate the influences of shear strain gradient and other factors on the evolution of shear band.

In situ formation by laser cladding of a TiC composite coating with a gradient distribution

An in situ method was developed to produce an Ni alloy composite coating reinforced by in situ reacted TiC particles with a gradient distribution, using one-step laser cladding with a pre-placed powder mixture on a 5CrMnMo steel substrate. Dispersed and ultra-fine TIC particles were formed in situ in the coating. Most. of the TiC particles, with a marked gradient distribution, were uniformly distributed within interdendritic regions because of the trapping effect of the advancing solid-liquid interface. In addition, the TiC-gamma-Ni interfaces generated in situ were found to be free from any deleterious surface reaction. Finally, the microhardness also showed a gradient variation, with the highest value of 1250 Hv0.2 and the wear properties of the coating were significantly enhanced.

Probe for Measurements of Density/Conductivity in Flows of Conducting Fluids

A probe utilizing the bipolar pulse method to measure the density of a conducting fluid has been developed. The probe is specially designed such that the concentration of a stream tube can be sampled continuously. The density was determined indirectly from the measurement of solution conductivity. The probe was calibrated using standard NaCl solutions of varying molarity and was able to rapidly determine the density of a fluid with continuously varying conductance. Measurements of the conductivity profiles, corresponding density profiles, and their fluctuation levels are demonstrated in a channel flow with an electrolyte injected from a slot in one wall.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

(Ti,Al)N Film On Normalized T8 Carbon Tool Steel Prepared By Pulsed High Energy Density Plasma Technique

Under optimized operating parameters, a hard and wear resistant ( Ti,Al)N film is prepared on a normalized T8 carbon tool steel substrate by using pulsed high energy density plasma technique. Microstructure and composition of the film are analysed by x-ray diffraction, x-ray photoelectron spectroscopy, Auger electron spectroscopy and scanning electron microscopy. Hardness profile and tribological properties of the film are tested with nano-indenter and ring-on-ring wear tester, respectively. The tested results show that the microstructure of the film is dense and uniform and is mainly composed of ( Ti,Al)N and AlN hard phases. A wide transition interface exists between the film and the normalized T8 carbon tool steel substrate. Thickness of the film is about 1000 nm and mean hardness value of the film is about 26GPa. Under dry sliding wear test conditions, relative wear resistance of the ( Ti,Al)N film is approximately 9 times higher than that of the hardened T8 carbon tool steel reference sample. Meanwhile, the ( Ti,Al)N film has low and stable friction coefficient compared with the hardened T8 carbon tool steel reference sample.

Molecular Dynamics And Density Functional Studies Of A Body-Centered-Tetragonal Polymorph Of Zno

We report a previously unknown body-centered-tetragonal structure for ZnO. This structure results from a phase transformation from wurtzite in [0001]-oriented nanorods during uniaxial tensile loading and is the most stable phase for ZnO when stress is above 7 GPa. The stress-induced phase transformation has important implications for the electronic, piezoelectric, mechanical, and thermal responses of ZnO. The discovery of this polymorph brings about a more complete understanding of the extent and nature of polymorphism in ZnO. A crystalline structure-load triaxiality map is developed to summarize the relationship between structure and loading.

Enhanced cycling performance and high energy density of LiFePO4 based lithium ion batteries

LiFePO4 attracts a lot of attention as cathode materials for the next generation of lithium ion batteries. However, LiFePO4 has a poor rate capability attributed to low electronic conductivity and low density. There is seldom data reported on lithium ion batteries with LiFePO4 as cathode and graphite as anode. According to our experimental results, the capacity fading on cycling is surprisingly negligible at 1664 cycles for the cell type 042040. It delivers a capacity of 1170 mAh for 18650 cell type at 4.5C discharge rate. It is confirmed that lithium ion batteries with LiFePO4 as cathode are suitable for electric vehicle application. (c) 2007 Elsevier B.V. All rights reserved.

Anisotropic, gradient and metal-like mechanical behaviors of teeth and their implications on tooth functions

The anisotropy and gradient of the elastic modulus and the hardness of teeth were investigated by means of instrumented indentation method. Such properties are attributed to the unique microstructures of teeth based on scanning electron microscopic analysis. By comparing the relationship between the ratio of hardness to the reduced elastic modulus and the ratio of elastic unloading work to the total work of teeth in course of indentation to those of other materials, we found that the material behaviors of teeth display metal-like characteristics rather than ceramics as considered traditionally. These material behaviors and relevant functions are discussed briefly.

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.

Drop migration of middle Reynolds number in a vertical temperature gradient

The experimental investigation of the thermocapillary drop migration in a vertical temperature gradient uns performed on ground. Silicon oil and pure soybean oil were used as experimental medium in drops and as continuous phases, respectively, in the present experiment. The drop migration, under the combined effects of buoyancy: and thermocapillarity, was studied for middle Reynolds numbers in order of magnitude O(10(1)). The drop migration velocities depending on drop diameters were obtained. The present experimental results show relatively small migration velocity in comparison with the one suggested by Young et nl. for linear theory of small Reynolds number. An example of flow patterns inside the drop was observed by PIV method.

Experimental and theoretical study on numerical density evolution of short fatigue cracks

Fatigue testing was performed using a kind of triangular shaped specimen to obtain the characteristics of numerical density evolution for short cracks at the primary stage of fatigue damage. The material concerned is a structural alloy steel. The experimental results show that the numerical density of short cracks reaches the maximum value when crack length is slightly less than the average grain diameter, indicating grain boundary is the main barrier for short crack extension. Based on the experimental observations and related theory, the expressions for growth velocity and nucleation rate of short cracks have been proposed. With the solution to phase space conservation equation, the theoretical results of numerical density evolution for short cracks were obtained, which were in agreement with our experimental measurements.