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1.
In this paper, stiffness reduction of general symmetric laminates containing a uniform distribution of matrix cracks in a single orientation is analyzed. An admissible stress field is considered, which satisfies equilibrium and all the boundary and continuity conditions. This stress field has been used in conjunction with the principle of minimum complementary energy to get the effective stiffness matrix of a cracked general symmetric laminate. Natural boundary conditions have been derived from the variational principle to overcome the limitations of the existing variational methods on the analysis of general symmetric laminates. Therefore, the capability of analyzing cracked symmetric laminates using the variational approach has been enhanced significantly. It has been shown that the method provides a rigorous lower bound for the stiffness matrix of a cracked laminate, which is very important for practical applications. Results derived from the developed method for the properties of the cracked laminates showed an excellent agreement with experimental data and with those obtained from McCartney’s stress transfer model. The differences of the developed model with McCartney’s model are discussed in detail. It can be emphasized that the current approach is simpler than McCartney’s model, which needs an averaging procedure to obtain the governing equations. Moreover, it has been shown that the existing variational models are special cases of the current formulation.  相似文献   

2.
The solutions of a boundary value problem are explored for various classes of generalised crystal plasticity models including Cosserat, strain gradient and micromorphic crystal plasticity. The considered microstructure consists of a two-phase laminate containing a purely elastic and an elasto-plastic phase undergoing single or double slip. The local distributions of plastic slip, lattice rotation and stresses are derived when the microstructure is subjected to simple shear. The arising size effects are characterised by the overall extra back stress component resulting from the action of higher order stresses, a characteristic length lc describing the size-dependent domain of material response, and by the corresponding scaling law ln as a function of microstructural length scale, l. Explicit relations for these quantities are derived and compared for the different models. The conditions at the interface between the elastic and elasto-plastic phases are shown to play a major role in the solution. A range of material parameters is shown to exist for which the Cosserat and micromorphic approaches exhibit the same behaviour. The models display in general significantly different asymptotic regimes for small microstructural length scales. Scaling power laws with the exponent continuously ranging from 0 to −2 are obtained depending on the values of the material parameters. The unusual exponent value −2 is obtained for the strain gradient plasticity model, denoted “curl Hp” in this work. These results provide guidelines for the identification of higher order material parameters of crystal plasticity models from experimental data, such as precipitate size effects in precipitate strengthened alloys.  相似文献   

3.
A new approach to modeling crystallographic texture evolution in Equal Channel Angular Extrusion (ECAE) is presented in this paper. The proposed approach utilizes an elastic–viscoplastic single crystal constitutive model implemented in a finite element framework. A representative volume element of the polycrystal is subjected to boundary conditions that simulate the approximate deformation history experienced by different regions of the sample (at different through-thickness depths) in both Route A and Route C processing. The proposed approach aims to capture the influence of the complex interactions that ensue among the constituent individual crystals of a polycrystal in controlling the texture evolution in the sample, while capturing the boundary conditions inherent to ECAE deformation. The predictions from the proposed approach are compared against previously reported experimental measurements in ECAE of copper. It is observed that the proposed approach provides significantly better agreement with the measurements when compared against previously reported model predictions.  相似文献   

4.
In this paper an Eulerian rate-dependent single crystal model that accounts for high-strain rates, large strains and rotations is developed. The viscoplastic law as well as the evolution equations for the lattice are written in terms of vectorial and tensorial quantities associated with the current configuration. The viscoplastic law is obtained from Schmid law using an overstress approach. Such an expression for the viscoplastic law is motivated by the microdynamics of crystal defects. A general analysis of the plane-strain response of the proposed rigid-viscoplastic single crystal model is presented. It is shown that only one differential equation, involving the orientation of one composite in-plane slip system, is necessary to describe the lattice evolution. Several two-dimensional boundary value problems, such as equal-channel die extrusion and channel die compression are selected to illustrate the predictive capabilities of the model. The results show that even at relatively low strain rates the viscosity plays an important role in the development of localized deformation modes. At high crosshead velocity, the plastic properties and crystal anisotropy are less important while inertia effects are dominant. Finally, the grains interaction is investigated by analyzing the compression of a grains multicrystal.  相似文献   

5.
We discuss methods to map crystallographic textures in crystal plasticity finite element simulations. Fourier-type series expansion methods which use spherical harmonic library functions as well as the direct pole figure inversion methods are not well suited to reproduce texture information in a sufficiently localized spherical form onto finite element grids. Mathematically compact Gauss-shaped spherical texture components represent a better approach for including textures in finite element models since they represent an excellent compromise between discreteness (spherical localization), compactness (simple functions), mathematical precision (very good approximation also of complex orientation distribution functions already with small sets of texture components), scalability (the number of used texture components can be systematically varied according to the desired exactness of the texture fit), conceptual simplicity (simple mathematical handling), and physical significance (texture components can be directly linked to characteristic metallurgical mechanisms). The use of texture component functions has also advantages over the use of large sets of discrete single orientations with equal scatter and height since they are more compact, practical, and provide better physical insight into microstructural mechanisms and composition sensitive effects. The article presents a new approach for the mathematical reproduction of such crystallographic texture components in crystal plasticity finite element simulations. It explains in some detail why they are particularly suited for this purpose and how they can be used to map and recover textures in/from plasticity simulations.  相似文献   

6.
For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation (GND) densities supplement the conventional theory within a non-work-conjugate framework in which there is no need to introduce higher-order microscopic stresses that would be work-conjugate to slip rate gradients. We discuss its connection to a work-conjugate type of finite deformation gradient crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution for the small deformation theory. As in a previous formulation for small deformation, the present formulation applies to the context of multiple and three-dimensional slip deformations.  相似文献   

7.
Two explicit examples of live loadings, namely, uniform pressure and surface tension, are revised with a view towards postulating more general, and yet mathematically tractable, forms of surface loads of the live type having a surface potential  相似文献   

8.
A stochastic crystal plasticity model is proposed and applied within the rate-independent regime. As opposed to conventional deterministic algorithms wherein multiple slip systems are activated and redundant constraints may exist, the new Monte Carlo plasticity (MCP) paradigm is based on a stochastic chain of singly activated slip systems and thus avoids the possible ill-condition associated with multi-slip algorithms. The choice of the activated slip system is made at each Monte Carlo (MC) step based on the Metropolis algorithm. The MCP model is implemented within a Material Point Method (MPM) as a constitutive model to capture the elasto-plastic behavior of polycrystalline materials. A comparison with a commonly used singular value decomposition (SVD) algorithm indicates that MCP offers superior computational efficiency while maintaining comparable accuracy.  相似文献   

9.
Dislocations are the most important material defects in crystal plasticity, and although dislocation mechanics has long been understood as the underlying physical basis for continuum crystal plasticity formulations, explicit consideration of crystallographic dislocation mechanics has been largely absent in working constitutive models. Here, dislocation density state variables evolve from initial conditions according to equations based on fundamental concepts in dislocation mechanics such as the conservation of Burgers vector in multiplication and annihilation processes. The model is implemented to investigate the polyslip behavior of single-crystal aluminum. The results not only capture the mechanical stress/strain response, but also detail the development of underlying dislocation structure responsible for the plastic behavior.  相似文献   

10.
A finite-strain higher-order gradient crystal plasticity model accounting for the backstress effect originating from the existence of geometrically necessary dislocations (GNDs) is applied to plane strain finite element analysis. Different element types are tested to seek out an element formulation that is reliable and useful for solving problems involving severe plastic deformation. In the present finite element formulation, the GND density rates are chosen to be additional nodal degrees of freedom. Different orders of shape functions are employed for the interpolation of displacement rates and GND density rates. Their effects on solutions are examined in detail by considering three boundary value problems: a simple shear of a constrained layer (a film), a compression problem with loading surfaces impenetrable to dislocations, and a tension problem involving shear band formation. In all the cases, the formulation in which eight-node elements with reduced integration and four-node elements with full integration are used respectively for displacement rates and the GND density rates gives reasonable solutions. In addition to the discussion on the choice of finite elements, detailed behavior in gradient-dependent solids, such as the accumulation of GND density and the distribution of backstress on each slip system, is investigated by utilizing the reliable computational results obtained.  相似文献   

11.
12.
In this paper, an enhanced variational constitutive update suitable for a class of non-associative plasticity theories at finite strain is proposed. In line with classical numerical formulations for plasticity models, such as the by now established return-mapping algorithm, variational constitutive updates represent a numerical method for computing the unknown state variables. However, in contrast to conventional algorithms, variational constitutive updates are fully variational, i.e., all unknown variables follow jointly from minimizing a certain potential. In addition to the physical and mathematical elegance of these variational schemes, they show several practical advantages as well. For instance, numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem. Since mathematically, plasticity is a non-smooth problem and often, it leads to highly singular systems of equations as known from single crystal plasticity, a robust implementation is of utmost importance. So far, variational constitutive updates have been developed for different classes of standard dissipative solids, i.e., solids characterized by associative evolution equations and flow rules. In the present paper, this framework is extended to a certain class of non-associative plasticity models at finite strain. All models falling into this class show a volumetric-deviatoric split of the Helmholtz energy and the yield function. Typical prototypes are Drucker-Prager or Mohr-Coulomb models playing an important role in soil mechanics. The efficiency and robustness of the resulting algorithmic formulation is demonstrated by means of selected numerical examples.  相似文献   

13.
An efficient new numerical integration scheme is presented for rate independent crystal plasticity theory. A key feature of this approach is the ability to identify active slip systems prior to determining their shearing rate. Options are described for various cases of slip system hardening, including self hardening and latent hardening. Alternatives for the constitutive update are explored, including hyperelasticity based on the multiplicative decomposition of the deformation gradient as well as application of the consistency condition in a much more efficient hypoelastic formulation. Several conclusions are drawn concerning the influences of elastic and plastic properties on the activation of slip systems and their subsequent shearing rates. Key among these is the fact that, once activated, shearing rates are independent of the levels of shear flow resistance on the slip systems, provided that the plastic hardening moduli are much less in magnitude than the elastic moduli, as is usually the case. Determination of active slip systems and their shearing rates depend on the degree of elastic anisotropy of the crystal, but not on the magnitude of elastic stiffness.  相似文献   

14.
材料的力学性能,尤其是在有限变形下所呈现的宏观各向异性,是材料结构设计和服役寿命考虑的关键因素。由于宏观模型不能较好地反映材料微观结构(晶粒的形貌和取向等)对宏观塑性各向异性的影响,因此,本文建立了能实际反映晶粒形貌的三维Voronoi模型,并基于晶体塑性理论对铝合金在有限变形下的响应进行计算。首先,建立反映材料微结构的代表性体积单元RVE模型进行计算,并与实验结果进行对比验证。然后,以单向拉伸为例,分析了有限变形过程中试件的晶粒形貌和取向分布等微观因素对宏观各向异性演化的影响,并从材料和结构两个层面讨论了微观结构对宏观力学性能的影响。结果表明,本文模型能够反映微观结构对宏观力学性能的影响,为实际生产制造领域构件的力学性能提供可靠的预测。  相似文献   

15.
Plasticity laws exhibiting non-linear kinematichardening are considered within the framework of infinitesimal deformations. The evolution equations governing the response of kinematic hardening are derived as sufficient conditions in order for the intrinsic dissipation inequality to be satisfied in every process. With a view to the extension to finite deformations, two basic possibilities are proposed. In every case, an isotropic elasticity law with respect to the so-called plastic intermediate configuration is assumed to hold. The theory applicable to finite deformations is based on the concept of so-called dual variables and associated time derivatives. Thus, the main difference between the present work and other contributions in this area is the choice of the variables used to formulate the theory. In fact, using dual variables, hardening rules are derived as sufficient conditions for the intrinsic dissipation inequality to be satisfied in every process. This is quite analogous to the case of infinitesimal deformation, but now the hardening rules take a very specific form which is explained in the paper. Received June 14, 1995  相似文献   

16.
A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack.  相似文献   

17.
A crystal plasticity finite element code is developed to model lattice strains and texture evolution of HCP crystals. The code is implemented to model elastic and plastic deformation considering slip and twinning based plastic deformation. The model accounts for twinning reorientation and growth. Twinning, as well as slip, is considered to follow a rate dependent formulation. The results of the simulations are compared to previously published in situ neutron diffraction data. Experimental results of the evolution of the texture and lattice strains under uniaxial tension/compression loading along the rolling, transverse, and normal direction of a piece of rolled Zircaloy-2 are compared with model predictions. The rate dependent formulation introduced is capable of correctly capturing the influence of slip and twinning deformation on lattice strains as well as texture evolution.  相似文献   

18.
A framework for material models describing finite plastic deformations is established by the assumption of isomorphic elastic ranges. The concepts of decomposition into elastic and plastic deformations is not needed, neither intermediate configurations. A comparison with other approaches is given and shows their range of validity.  相似文献   

19.
Micromechanical models aimed at simulating deformation textures and resulting plastic anisotropy need to incorporate local plastic strain heterogeneities arising from grain interactions for better predictions. The ALAMEL model [Van Houtte, P., Li, S., Seefeldt, M., Delannay, L. 2005. Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int. J. Plasticity 21, 589–624], is one of the models in which the heterogeneous nature of plastic deformation in metals is introduced by accounting for the influence of a grain boundary on the cooperative deformation of adjacent grains. This is achieved by assuming that neighbouring grains undergo heterogeneous shear rates parallel to the grain boundary. The present article focuses on understanding the plastic deformation fields near the grain boundaries and the influence of grain interaction on intra-grain deformations. Crystal Plasticity Finite Element Method (CPFEM) is employed on a periodic unit cell consisting of four grains discretised into a large number of elements. A refined study of the local variation of strain rates, both along and perpendicular to the grain boundaries permits an assessment of the assumptions made in the ALAMEL model. It is shown that the ALAMEL model imbibes the nature of plastic deformation at the grain boundaries very well. However, near triple junctions, the influence of a third grain induces severe oscillations of the stress tensor, reflecting a singularity. According to CPFEM, such singularity can lead to grain subdivision by the formation of new boundaries originating at the triple junction.  相似文献   

20.
THERANDOMVARIATIONALPRINCIPLEINFINITEDEFORMATIONOFELASTICITYANDFINITEELEMENTMETHODGaoHang-shan(高行山)(NorthwestenPolytechnicalU...  相似文献   

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