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.

Martensitic transformation under impact with high strain rate

This paper deals with the quantitative prediction of the volume fraction of martensitic transformation in a austenitic steel that undergoes impact with high strain rate. The coupling relations between strain, stress, strain rate, transformation rate and transformed fraction were derived from the OTC model and modified Bodner-Partom equations, where the impact process was considered as an adiabatic and no entropy-increased process (pressure less than or equal to 20GPa). The one-dimensional results were found to model and predict various experimental results obtained on 304 stainless steel under impact with high strain rate.

Analysis of Dislocation-Induced Strain Field in an Idealized Wafer-Bonded Microstructure

The localized dislocation at the interface induces uneven strain distribution in two wafer-bonded layers. Because of the different elastic properties of two bonding layers and this uneven strain distribution, the bilayered microstructure deflects and deflection relaxes the strains. Depending on the microstructure dimensions, elastic properties and lattice parameters, the contribution of deflection to strain field can be very significant. The interface condition also plays an important role in relaxing strain. Two models capable of describing different interface conditions are used for the analysis and offer a more comprehensive study on the dislocation-induced strain field in a wafer-bonded bilayered microstructure. The combined effect of microstructure dimensions and interface condition on the strain is presented and compared.

Effect of polymer concentration on stabilized large-tilt-angle flexoelectro-optic switching

In this letter, the uniform lying helix (ULH) liquid crystal texture, required for the flexoelectro-optic effect, is polymer stabilized by the addition of a small percentage of reactive mesogen to a high-tilt-angle (φ>60°) bimesogenic chiral nematic host. The electro-optic response is measured for a range of reactive mesogen concentration mixtures, and compared to the large-tilt-angle switch of the pure chiral nematic mixture. The optimum concentration of reactive mesogen, which is found to provide ample stabilization of the texture with minimal impact on the electro-optic response, is found to be approximately 3%. Our results indicate that polymer stabilization of the ULH texture using a very low concentration of reactive mesogen is a reliable way of ruggedizing flexoelectro-optic devices without interfering significantly with the electro-optics of the effect, negating the need for complicated surface alignment patterns or surface-only polymerization. The polymer stabilization is shown to reduce the temperature dependence of the flexoelectro-optic response due to "pinning" of the chiral nematic helical pitch. This is a restriction of the characteristic thermochromic behavior of the chiral nematic. Furthermore, selection of the temperature at which the sample is ultraviolet cured allows the tilt angle to be optimized for the entire chiral nematic temperature range. The response time, however, remains more sensitive to operating temperature than curing temperature. This allows the sample to be cured at low temperature and operated at high temperature, providing simultaneous optimization of these two previously antagonistic performance aspects. © 2006 American Institute of Physics.

Interface crack problems with strain gradient effects

In this paper, the strain gradient theory proposed by Chen and Wang (2001 a, 2002b) is used to analyze an interface crack tip field at micron scales. Numerical results show that at a distance much larger than the dislocation spacing the classical continuum plasticity is applicable; but the stress level with the strain gradient effect is significantly higher than that in classical plasticity immediately ahead of the crack tip. The singularity of stresses in the strain gradient theory is higher than that in HRR field and it slightly exceeds or equals to the square root singularity and has no relation with the material hardening exponents. Several kinds of interface crack fields are calculated and compared. The interface crack tip field between an elastic-plastic material and a rigid substrate is different from that between two elastic-plastic solids. This study provides explanations for the crack growth in materials by decohesion at the atomic scale.

Microstructure, strain fields and flow stress in deformed metal matrix composites

An experimental study of local orientations around whiskers in deformed metal matrix composites has been used to determine the strain gradients existing in the material following tensile deformation. These strain fields have been represented as arrays of geometrically necessary dislocations, and the material flow stress predicted using a standard dislocation hardening model. Whilst the correlation between this and the measured flow stress is reasonable, the experimentally determined strain gradients are lower by a factor of 5-10 than values obtained in previous estimates made using continuum plasticity finite element models. The local orientations around the whiskers contain a large amount of detailed information about the strain patterns in the material, and a novel approach is made to representing some of this information and to correlating it with microstructural observations. © 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.

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.

Strain Rate Dependence of Plastic Flow in Ce-based Bulk Metallic Glass During Nanoindentation

The strain rate dependence of plastic deformation of Ce60Al15CU10Ni15 bulk metallic glass was studied by nanoindentation. Even though the ratio of room temperature to the glass transition temperature was very high (0.72) for this alloy, the plastic deformation was dominated by shear banding under nanoindentation. The alloy exhibited a critical loading rate dependent serrated flow feature. That is, with increasing loading rate, the alloy exhibited a transition from less prominent serrated flow to pronounced serrated flow during continuous loading but from serrated to smoother flow during stepped loading.

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.

The effect of straining mode on void growth

Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality: loading,while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results.

A new method for the acquisition of ultrasonic strain image volumes.

This article presents a new method for acquiring three-dimensional (3-D) volumes of ultrasonic axial strain data. The method uses a mechanically-swept probe to sweep out a single volume while applying a continuously varying axial compression. Acquisition of a volume takes 15-20 s. A strain volume is then calculated by comparing frame pairs throughout the sequence. The method uses strain quality estimates to automatically pick out high quality frame pairs, and so does not require careful control of the axial compression. In a series of in vitro and in vivo experiments, we quantify the image quality of the new method and also assess its ease of use. Results are compared with those for the current best alternative, which calculates strain between two complete volumes. The volume pair approach can produce high quality data, but skillful scanning is required to acquire two volumes with appropriate relative strain. In the new method, the automatic quality-weighted selection of image pairs overcomes this difficulty and the method produces superior quality images with a relatively relaxed scanning technique.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

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.