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.

Vibration analysis of laminated shells using a refined shear deformation theory

A previously published refined shear deformation theory is used to analyse free vibration of laminated shells. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first-order shear deformation theory, hut the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of symmetric cross-ply laminated cylindrical shells, symmetric and antisymmetric cross-ply cylindrical panels is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.

Vibration analysis of laminated plates using a refined shear deformation-theory

A previously published discrete-layer shear deformation theory is used to analyze free vibration of laminated plates. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first order shear deformation theory, but the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of simply supported symmetric and antisymmetric cross-ply plates is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.

Strain gradient theory with couple stress for crystalline solids

A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.

The Flow Theory of Mechanism-Based Strain Gradient Plasticity

The flow theory of mechanism-based strain gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to strain gradient effect provides a means to explain the experimentally observed cleavage fracture in ductile materials [J. Mater. Res. 9 (1994) 1734, Scripta Metall. Mater. 31 (1994) 1037; Interface Sci. 3(1996) 169].

Shear deformation analysis on laser-induced reverse bulging and plugging

A new kind of failure mode is observed in circular brass foils in which their peripheries are fixed and their surfaces are subjected to a long pulsed laser over a central region. The failure is classified into three stages; they are referred to as thermal bulging, localized shear deformation and perforation by plugging. A distinct feature of the failure mode is that bulging and plugging occurred in the direction opposite to the incident laser beam. To study the failure mode, we investigate the non-linear response of heated, non-homogeneous circular plates. Based on the large deflection equations of Berger [J. Appl. Mech. 22 (3), 465-472 (1965)], Ohnabe and Mizuguchi [Int. J. Non-Linear Mech. 28 (4), 365-372 (1993)] and the parabolic shear deformation theory of Bhimaraddi and Stevens [J. Appl. Mech. 51 (1), 195-198 (1984)], we have derived new coupled governing equations of shear deformation and deflection. The new equations are solved, for the plate with a clamped edge, by the Galerkin and iterative methods. The numerical results for the shear deformation distribution are in good agreement with the experimental observation.

A new hardening law for strain gradient plasticity

A new hardening law of the strain gradient theory is proposed in this paper, which retains the essential structure of the incremental version of conventional J(2) deformation theory and obeys thermodynamic restrictions. The key feature of the new proposal is that the term of strain gradient plasticity is represented as an internal variable to increase the tangent modulus. This feature which is in contrast to several proposed theories, allows the problem of incremental equilibrium equations to be stated without higher-order stress, higher-order strain rates or extra boundary conditions. The general idea is presented and compared with the theory given by Fleck and Hutchinson (Adv. in Appl. Mech. (1997) 295). The new hardening law is demonstrated by two experimental tests i.e. thin wire torsion and ultra-thin beam bending tests. The present theoretical results agree well with the experiment results.

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.

Small scale, grain size and substrate effects in nano-indentation experiment of film-substrate systems

The mechanical properties of film-substrate systems have been investigated through nano-indentation experiments in our former paper (Chen, S.H., Liu, L., Wang, T.C., 2005. Investigation of the mechanical properties of thin films by nano-indentation, considering the effects of thickness and different coating-substrate combinations. Surf. Coat. Technol., 191, 25-32), in which Al-Glass with three different film thicknesses are adopted and it is found that the relation between the hardness H and normalized indentation depth h/t, where t denotes the film thickness, exhibits three different regimes: (i) the hardness decreases obviously with increasing indentation depth; (ii) then, the hardness keeps an almost constant value in the range of 0.1-0.7 of the normalized indentation depth h/t; (iii) after that, the hardness increases with increasing indentation depth. In this paper, the indentation image is further investigated and finite element method is used to analyze the nano-indentation phenomena with both classical plasticity and strain gradient plasticity theories. Not only the case with an ideal sharp indenter tip but also that with a round one is considered in both theories. Finally, we find that the classical plasticity theory can not predict the experimental results, even considering the indenter tip curvature. However, the strain gradient plasticity theory can describe the experimental data very well not only at a shallow indentation depth but also at a deep depth. Strain gradient and substrate effects are proved to coexist in film-substrate nano-indentation experiments. (c) 2006 Elsevier Ltd. All rights reserved.

表面热透镜技术应用于薄膜微弱吸收测量的理论和实验

由薄膜表面光热形变简化理论和表面热透镜衍射理论导出表面热透镜信号表达式,从理论上证明了表面热透镜信号和薄膜吸收率的线性关系.应用表面热透镜技术研制了薄膜吸收测量仪,测量结果表明其吸收率测量灵敏度和精度均达10-6量级.

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.

Deformation Monitoring and Forecasting Model Study Based on Grey System Theory

The grey system theory studies the uncertainty of small sample size problems. This paper using grey system theory in the deformation monitoring field, based on analysis of present grey forecast models, developed the spatial multi-point model. By using residual modification, the spatial multi-point residual model eras developed in further study. Then, combined with the sedimentation data of Xiaolangdi Multipurpose Dam, the results are compared and analyzed, the conclusion has been made and the advantages of the residual spatial multi-point model has been proved.

Real-Time Measurement on Deformation Fields of Hole-Excavated Samples under Impact Tension

In this paper, the real-time deformation fields are observed in two different kinds of hole-excavated dog-bone samples loaded by an SHTB, including single hole sample and dual holes sample with the aperture size of 0.8mm. The testing system consists of a high-speed camera, a He-Ne laser, a frame grabber and a synchronization device with the controlling accuracy of I microsecond. Both the single hole expanding process and the interaction of the two holes are recorded with the time interval of 10 mu s. The observed images on the sample surface are analyzed by newly developed software based on digital correlation theory and a modified image processing method. The 2-D displacement fields in plane are obtained with a resolution of 50 mu m and an accuracy of 0.5 mu m. Experimental results obtained in this paper are proofed, by compared with FEM numerical simulations.