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.

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.

Size Effects in Micro-bending Deformation of MEMS Devices Based on the Discrete Dislocation Theory

In the present research, the discrete dislocation theory is used to analyze the size effect phenomena for the MEMS devices undergoing micro-bending load. A consistent result with the experimental one in literature is obtained. In order to check the effectiveness to use the discrete dislocation theory in predicting the size effect, both the basic version theory and the updated one are adopted simultaneously. The normalized stress-strain relations of the material are obtained for different plate thickness or for different obstacle density. The prediction results are compared with experimental results.

Microdamage Evolution, Energy Dissipation and Their Trans-Scale Effects on Macroscopic Failure

The process of damage evolution concerns various scales, from micro- to macroscopic. How to characterize the trans-scale nature of the process is on the challenging frontiers of solid mechanics. In this paper, a closed trans-scale formulation of damage evolution based on statistical microdamage mechanics is presented. As a case study, the damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that the following dimensionless numbers: reduced Mach number M, damage number S, stress wave Fourier number P, intrinsic Deborah number D*, and the imposed Deborah number De*, govern the whole process of deformation and damage evolution. The evaluation of P and the estimation of temperature increase show that the energy equation can be ignored as the first approximation in the case of spallation. Hence, apart from the two conventional macroscopic parameters: the reduced Mach number M and damage number S, the damage evolution in spallation is mainly governed by two microdamage-relevant parameters: the Deborah numbers D* and De*. Higher nucleation and growth rates of microdamage accelerate damage evolution, and result in higher damage in the target plate. In addition, the mere variation in nucleation rate does not change the spatial distribution of damage or form localized rupture, while the increase of microdamage growth rate localizes the damage distribution in the target plate, which can be characterized by the imposed Deborah number De*.

Finite Boundary Effects in Problem of a Crack Perpendicular to and Terminating at a Bimaterial Interface

In this paper, the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries is investigated. The dislocation simulation method and boundary collocation approach are used to derive and solve the basic equations. Two kinds of loading form are considered when the crack lies in a softer or a stiffer material, one is an ideal loading and the other one fits to the practical experiment loading. Complete solutions of the stress field including the T stress are obtained as well as the stress intensity factors. Influences of T stress on the stress field ahead of the crack tip are studied. Finite boundary effects on the stress intensity factors are emphasized. Comparisons with the problem presented by Chen et al. (Int. J. Solids and Structure, 2003, 40, 2731-2755) are discussed also.

Fracture Mechanisms And Size Effects Of Brittle Metallic Foams: In Situ Compression Tests Inside Sem

In situ compressive tests on specially designed small samples made from brittle metallic foams were accomplished in a loading device equipped in the scanning electron microscopy (SEM). Each of the small samples comprises only several cells in the effective test zone (ETZ), with one major cell in the middle. In such a system one can not only obtain sequential collapse-process images of a single cell and its cell walls with high resolution, but also correlate the detailed failure behaviour of the cell walls with the stress-strain response, therefore reveal the mechanisms of energy absorption in the mesoscopic scale. Meanwhile, the stress-strain behaviour is quite different from that of bulk foams in dimensions of enough large, indicating a strong size effect. According to the in situ observations, four failure modes in the cell-wall level were summarized, and these modes account for the mesoscopic mechanisms of energy absorption. Paralleled compression tests on bulk samples were also carried out, and it is found that both fracturing of a single cell and developing of fracture bands are defect-directed or weakness-directed processes. The mechanical properties of the brittle aluminum foams obtained from the present tests agree well with the size effect model for ductile cellular solids proposed by Onck et al. (C) 2008 Elsevier Ltd. All rights reserved.

Grain Boundary Effects On Plastic Deformation And Fracture Mechanisms In Cu Nanowires: Molecular Dynamics Simulations

Metallic nanowires have many attractive properties such as ultra-high yield strength and large tensile elongation. However, recent experiments show that metallic nanowires often contain grain boundaries, which are expected to significantly affect mechanical properties. By using molecular dynamics simulations, here, we demonstrate that polycrystalline Cu nanowires exhibit tensile deformation behavior distinctly different from their single-crystal counterparts. A significantly lowered yield strength was observed as a result of dislocation emission from grain boundaries rather than from free surfaces, despite of the very high surface to volume ratio. Necking starts from the grain boundary followed by fracture, resulting in reduced tensile ductility. The high stresses found in the grain boundary region clearly play a dominant role in controlling both inelastic deformation and fracture processes in nanoscale objects. These findings have implications for designing stronger and more ductile structures and devices on nanoscale.

Interface Layer Effect On The Stress Distribution Of A Wafer-Bonded Bilayer Structure

The interface layer plays an important role in stress transfer in composite structures. However, many interface layer properties such as the modulus, thickness, and uniformity are difficult to determine. The model developed in this article links the influence of the interface layer on the normal stress distribution along the layer thickness with the layer surface morphology before bonding. By doing so, a new method of determining the interfacial parameter(s) is suggested. The effects of the layer thickness and the surface roughness before bonding on the normal stress distribution and its depth profile are also discussed. For ideal interface case with no interfacial shear stress, the normal stress distribution pattern can only be monotonically decreased from the interface. Due to the presence of interfacial shear stress, the normal stress distribution is much more complex, and varies dramatically with changes in the properties of the interface layer, or the dimensions of the bonding layers. The consequence of this dramatic stress field change, such as the shift of the maximum stress from the interface is also addressed. The size-dependent stress distribution in the thickness direction due to the interface layer effect is presented. When the interfacial shear stress is reduced to zero, the model presented in this article is also demonstrated to have the same normal stress distribution as obtained by the previous model, which does not consider the interface layer effect.

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.

Atomistic investigation of the effects of temperature and surface roughness on diffusion bonding between Cu and Al

Molecular dynamics (MD) simulations are carried out to analyze the diffusion bonding at Cu/Al interfaces. The results indicate that the thickness of the interfacial layer is temperature-dependent, with higher temperatures yielding larger thicknesses. At temperatures below 750 K, the interface thickness is found to increase in a stepwise manner as a function of time. At temperatures above 750 K, the thickness increases rapidly and smoothly. When surface roughness is present, the bonding process consists of three stages. In the first stage, surfaces deform under stress, resulting in increased contact areas. The second stage involves significant plastic deformation at the interface as temperature increases, resulting in the disappearance of interstices and full contact of the surface pair. The last stage entails the diffusion of atoms under constant temperature. The bonded specimens show tensile strengths reaching 88% of the ideal Cu/Al contact strength. (c) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

An analysis of the effects of symmetrical tilt grain boundaries on the plastic deformation

A numerical investigation on the simple polycrystals containing three symmetrical tilt grain boundaries (GBs) is carried out within the framework of crystal plasticity which precisely considers the finite deformation and finite lattice rotation as well as elastic anisotropy. The calculated results show that the slip geometry and the redistribution of stresses arising from the anisotropy and boundary constraint play an important role in the plastic deformation in the simple polycrystals. The stress level along GB is sensitive to the load level and misorientation, and the stresses along QB are distributed nonuniformly. The GB may exhibit a softening or strengthening feature, which depends on the misorientation angle. The localized deformation bands usually develop accompanying the GB plastic deformation, the impingement of the localized band on the GB may result in another localized deformation band. The yield stresses with different misorientation angles are favorably compared with the experimental results.

Fracture behavior of axisymmetrical bars under high triaxial stress and large strain cyclic loading

Axisymmetric notched bars with notch roots of large and small radii were tested under large strain cyclic loading. The main attention is focused on the fracture behaviour of steels having cycles to failure within the range 1-100. Our study shows that a gradual transition from a static ductile nature to one of fatigue cleavage can be observed and characterized by the Coffin-Manson formula in a generalized form. Both the triaxial tensile stress within the central region of specimens and static damage caused by the first increasing load have effects on the final failure event. A generalized cyclic strain range parameter DELTAepsilon is proposed as a measure of the numerous factors affecting behaviour. Fractographs are presented to illustrate the behaviour reported in the paper.

Florida's West Coast inlets: shoreline effects and recommended action

This report responds to the 1986 Beaches Bill which, in recognition of the potential deleterious impact on Florida's beaches of inlets modified for navigation, mandated a study of those inlets with identification of recommended action to reduce the impacts. This report addresses west Coast inlets; East Coast inlets are the subject of a companion report. There are 37 inlets along that portion of Florida's West Coast commencing from Pensacola Bay Entrance to Caxambas Pass at the south end of Marco Island. Compared to those on the East Coast, most West Coast inlets have not had the deleterious effects on the adjacent beaches, yet all modified inlets without proper management have the potential of impacting unfavorably on the adjacent shorelines. Moreover, at present there is interest in opening three West Coast entrances which either have been open in the past (Midnight Pass) or which have opened occasionally (Navarre Pass and Entrance to Phillips Lake). A review of inlets in their natural condition demonstrates the presence of a shallow broad outer bar across which the longshore transport Occurs. These shallow and shifting bar features were unsuitable for navigation which in many cases has led to the deepening of the channels and fixing with one or two jetty structures. Inlets in this modified state along with inappropriate maintenance practices have the potential of placing great ero$ional stress along the adjacent beaches. Moreover. channel dredging can reduce wave sheltering of the shoreline by ebb tidal shoals and alter the equilibrium of the affected shoreline segments. The ultimate in poor sand management practice is the placement of good quality beach sand in water depths too great for the sand to reenter the longshore system under natural forces; depths of 12 ft. or less are considered appropriate for Florida in order to maintain the sand in the system. With the interference of the nearshore sediment transport processes by inlets modified for navigation, if the adjacent beaches are to be stabilized there must be an active monitoring program with commitment to placement of dredged material of beach quality on shoreline segments of documented need. Several East Coast inlets have such transfer facilities; however. the quantities of sand transferred should be increased. Although an evolution and improvement in the technical capability to manage sand resources in the vicinity of inlets is expected, an adequate capability exists today and a concerted program should be made to commence a scheduled implementation of this capability at those entrances causing greatest erosional stress on the adjacent shorelines. A brief summary review for each of the 37 West Coast inlets is presented including: a scaled aerial photograph, brief historical information, several items related to sediment losses at each inlet and special characteristics relevant to State responsibilities. For each inlet, where appropriate, the above infor~tion is utilized to develop a recommenced action. (PDF has 101 pages.)

The mechanical effects of water flow on fish eggs and larvae

The impact of mechanical stresses upon ichthyoplankton entrained in power plant cooling systems has long been considered negligible. Arguments and evidence exist, however, to show that such a supposition is not universally true, especially in nuclear power plants. The mechanisms of mechanical damage can be detailed in terms of pressure change, acceleration, and shear stress with in the fluid flow field. Laboratory efforts to quantify the effects of mechanical stress have been very sparse. A well-planned bioassay is urgently needed. (PDF has 11 pages.)

Effects of shear on eggs and larvae of striped bass, morone saxatilis, and white perch, M. americana

Shear stress, generated by water movement, can kill fish eggs and larvae by causing rotation or deformation. Through the use of an experimental apparatus, a series of shear (as dynes/cm2)-mortality equations for fixed time exposures were generated for striped bass and white perch eggs and larvae. Exposure of striped bass eggs to a shear level of 350 dynes/cm2 kills 36% of the eggs in 1 min; 69% in 2 min, and 88% in 4 min; exposure of larvae to 350 dynes/cm2 kills 9.3% in 1 min, 30.0% in 2 min, and 68.1% in 4 min. A shear level of 350 dynes/cm2 kills 38% of the white perch eggs in 1 min, 41% in 2 min, 89% in 5 min, 96% in 10 min, and 98% in 20 min. A shear level of 350 dynes/cm2 applied to white perch larvae destroys 38% of the larvae in 1 min, 52% in 2 min, and 75% in 4 min. Results are experimentally used in conjunction with the determination of shear levels in the Chesapeake and Delaware Canal and ship movement for the estimation of fish egg and larval mortalities in the field.