Papers by Keyword: Strain Gradient

Abstract: Beams find extensive applications in Nanoelectromechanical systems (NEMS) and Microelectromechanical systems (MEMS). The mechanical characteristics of these microstructures are significantly influenced by both their inherent microstructure and the forces acting at the micro/nano scales. Classical continuum theories fall short in capturing these small-scale effects due to the absence of a length scale parameter in their constitutive relations. To address this limitation, the existing literature primarily relies on the stress gradient nonlocal approach, which, however, has been found flawed and its universal applicability questioned in various scenarios. Therefore, the authors have endeavored to emphasize the strain gradient nonlocal approach, which has been relatively less explored. In this study, carbon nanotubes are modeled using the isotropic Timoshenko beam theory. To introduce the small-scale size effect into the model, the second-order negative strain gradient theory (NSGT) is employed. The Euler-Lagrange differential equations of motion and their corresponding boundary conditions are derived through Hamilton's principle. Analytical solutions are developed for static bending under uniformly distributed transverse load and free vibration problems using Navier's approach. Mathematical results are presented to validate the proposed solutions. Both analyses reveal that the nonlocal effect implemented in this study stiffens the structures, resulting in reduced static deflection and increased natural frequencies. It is noteworthy that beams with dimensions comparable to microstructural length scales exhibit a significant nonlocal effect, which diminishes as the structure's size increases. Additionally, the response obtained using the Timoshenko beam model is softer in comparison to the Euler-Bernoulli model due to the consideration of shear deformation.

Abstract: In this paper, a micromechanical finite element (FE) model has been proposed to investigate the effect of the nanoscale precipitates on the development of microplasticity for Inconel 718 (IN718) superalloy. A strain gradient crystal plasticity formulation has been developed with the considerations of the evolution of statistically stored dislocation density and geometrically necessary dislocation density. The mesh convergence has been examined, showing that sufficiently fine mesh is required in the FE model. The results show that the model with strain gradient effect incorporated shows less peak plastic strain and higher value of dislocation density than the model with no strain gradient effect. The present study indicates that the strain hardening process at the scale of strengthening precipitate is mainly governed by the evolution of geometrically necessary dislocation densities.

Abstract: Grain refinement by severe plastic deformation can make conventional metallic materials several times stronger, but it leads to dramatic loss of their ductility. Gradient structure through the thickness of processed material represents a new strategy for producing a superior combination of high strength and good ductility. In gradient metallic materials the grain size increases gradually from nanoscale at the surface to coarse-grained in the core. Strain gradient can be considered as a mechanism of creating of such microstructures. Providing of predetermined strain gradient in the metallic materials can be achieved by asymmetric rolling (AR), when circumferential speeds of the top and bottom work rolls are different. Since the AR is a continuous process, it has great potential for industrial production of large-scaled sheets. Searching the optimal process parameters which can provide special strain gradients through sheet thickness is very important. This paper presents the distributions of the effective strain through sheet thickness of low-carbon steel AISI 1015 processed by a single-pass AR. Influence of process parameters was investigated by the finite element method with using software DEFORM 2D. Extremely high strain gradient e ≈ 4...8 through sheet thickness during a single-pass AR was found. FE analysis of the deformation characteristics, presented in this study, can be used for optimization of the AR process as a method of fabrication of metallic materials with gradient microstructures.

Abstract: Damage and microcracks formed by rolling contact fatigue (RCF) were characterized for carburized SCM420 steel. A large number of microcracks were detected beneath the contact surfaces after RCF. The microcrack generation and strain distribution beneath the contact trail depended on the slip ratios of 0 %, -20% and -40 % in the roller pitting test. Such severe slip increased shear strain in the region higher than 160 µm in depth from the contact surface. Compressive stress also gave rise to strain in the region near the surface up to 100 µm in the depth. Those strain gradients may cause a strain incompatibility at the transition layer in which a crack branching was detected.

Abstract: Strain gradient is known as an important factor that influences springback of bent components in microscale. Compared with thicker foils, thinner foils usually indicate more strain gradient due to non-uniform material deformation. A resistance heating (RH) method is an effective approach to obtain homogenous material flow by heating foils within only several minutes. To predict springback of foils bent at elevated temperatures, an investigation of the influence of strain gradient on springback is indispensable. To achieve this, microbending tests assisted by RH were conducted at different temperatures ranging from 298 to 723 K in the present study. 0.05 mm-thick pure Ti foils with varying grain sizes of 2.7, 14.7, and 24.5 μm were used. As results, normalized bending moment decreased with increasing temperature and with increasing grain size. The less strain gradient of the foils with larger grain size and at elevated temperatures was confirmed to be the reason according to a theoretical analysis of springback using the constitutive model considering statically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs). The predicted normalized bending moment by theoretical calculation showed good agreement with experimental results at the temperature of 573 K or higher but not at the temperature lower than 573 K. It was found that the springback of the foils was influenced by the strain gradient at low temperatures. Furthermore, the size effects caused by strain gradient reduced as the bending temperature increases.

Abstract: To evaluate the effect of the size of the microstructure on the mechanical property of the cavitated rubber blended (voided) amorphous polymer, the FEM simulation based on the rate form second-order homogenization method, in which rates of the macroscopic strain and strain gradient are given to the microstructure, was performed. Computational simulations of micro-to macroscopic deformation behaviors of amorphous polymers including different sizes and volume fractions of the voids were performed. Non-affine molecular chain network theory was employed to represent the inelastic deformation behavior of the amorphous polymer matrix. With the increase in the volume fraction of the void, decrease and periodical fluctuation of stress and localized deformation in the macroscopic field were observed, and were more emphasized with the increase in the size of the void. These results were closely related to the non-uniform deformation and volume increase of the void in the microscopic field.

Abstract: Plastic deformation induces various types of dislocation microstructures at different length scales, which eventually results in a heterogeneous deformation field in metallic materials. Development of such structures manifests themselves as macroscopic hardening/softening response and plastic anisotropy during strain path changes, which is often observed during forming processes. In this paper we present two different non-local plasticity models based on non-convex potentials to simulate the intrinsic rate-dependent and rate-independent development of plastic slip patterns, which is the simplified mechanism for the intrinsic microstructure development. For the sake of mechanistic understanding, the formulation and the simulations will be conducted in one-dimension which does not exclude its extension to multi-dimensions resulting in a crystal plasticity framework.

Abstract: According to the size and connecting characters of soil particles, soil is discomposed into two components as matrix and reinforcement particles respectively with a demarcation size fixed at 0.075mm to investigate the influence of the microstructures on soil strength. Based on the strain gradient theory, a multi-scale matrix-reinforcement particle model was established to study the trans-scale properties of soil strength which indicates that the soil strength is related to the intrinsic length scale, the strain gradient, the matrix properties and the gradation and size of reinforcement particles. A series of consolidated and undrained compression tests of unsaturated remoulded soil were designed to study the trans-scale properties of soil strength. The results showed that: the yield stress of soil increased as the reinforcement particle size decreased, displaying the trans-scale properties of soil strength. The research result is significant to the development of strength theory of soil.

Abstract: Studies of strain gradient plasticity theory have achieved considerable achievements in recent years. However, the combination of the mechanisms of the pressure-sensitive yielding and the size dependence of plastic deformation still remains an open challenge, especially in the relevant numerical simulation. In this paper, the finite-element formulation based on the flow theory of MSG plasticity for pressure-sensitive materials is set up. The elastic indentation response of the single crystal copper is computed using a user-defined eight-node isoparametric element through the USER-ELEMENT interface supported by the commercial software ABAQUS. The results of the numerical simulation show that the indenter load and the hardness have been slightly enhanced when the strain gradient is taken into account, compared to the results obtained from the CAX8R element.

Abstract: Gradient theories of plasticity play an important role in the description of inelastic behavior of materials. Usually, these theories involve space derivatives of stress or strain. On the other hand, conventional theories of plasticity can be divided into two groups, flow and deformation theories. Each of these groups has its own area of applications. The main conceptual difference between the theories belonging to the different groups is that the primary kinematics variables in deformation theories are displacements (or strains) whereas in flow theories velocities (or strain rates). Therefore, it is of interest to propose a gradient theory of plasticity involving space derivatives of a measure of strain rate (strain-rate gradient theory of plasticity) and to compare qualitative behavior of solutions for the strain-rate gradient theory of plasticity and an existing strain gradient theory of plasticity. One possible strain-rate gradient theory of plasticity is proposed in the present paper. The equivalent strain rate (second invariant of the strain rate tensor) is used as a measure of strain rate. The Laplacian operator is adopted to introduce the gradient term. An analytic solution for expansion of a hollow sphere is given for two strain-rate gradient theories of plasticity and one strain gradient theory. Comparison of the solutions shows that some qualitative features of the solutions for the strain-rate gradient theories are in better agreement with general physical expectations than those for the strain gradient theory.