Multiscale modeling of irradiated polycrystalline FCC metals

We propose a set of models for the post-irradiation deformation response of polycrystalline FCC metals. First, a defect- and dislocation-density based evolution model is developed to capture the features of irradiation-induced hardening as well as intra-granular softening. The proposed hardening model is incorporated within a rate-independent single crystal plasticity model. The result is a non-homogeneous deformation model that accounts for defect absorption on the active slip planes during plastic loading. The macroscopic non-linear constitutive response of the polycrystalline aggregate of the single crystal grains is then obtained using a micro–macro transition scheme, which is realized within a Jacobian-free multiscale method (JFMM). The Jacobian-free approach circumvents explicit computation of the tangent matrix at the macroscale by using a Newton–Krylov process. This has a major advantage in terms of storage requirements and computational cost over existing approaches based on homogenized material coefficients in which explicit Jacobian computation is required at every Newton step. The mechanical response of neutron-irradiated single and polycrystalline OFHC copper is studied and it is shown to capture experimentally observed grain-level phenomena.     

Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals

In order to model the effects of grain boundaries in polycrystalline materials we have coupled a crystal-plasticity model for the grain interiors with a new elastic-plastic grain-boundary interface model which accounts for both reversible elastic, as well irreversible inelastic sliding-separation deformations at the grain boundaries prior to failure. We have used this new computational capability to study the deformation and fracture response of nanocrystalline nickel. The results from the simulations reflect the macroscopic experimentally observed tensile stress-strain curves, and the dominant microstructural fracture mechanisms in this material. The macroscopically observed nonlinearity in the stress-strain response is mainly due to the inelastic response of the grain boundaries. Plastic deformation in the interior of the grains prior to the formation of grain-boundary cracks was rarely observed. The stress concentrations at the tips of the distributed grain-boundary cracks, and at grain-boundary triple junctions, cause a limited amount of plastic deformation in the high-strength grain interiors. The competition of grain-boundary deformation with that in the grain interiors determines the observed macroscopic stress-strain response, and the overall ductility. In nanocrystalline nickel, the high-yield strength of the grain interiors and relatively weaker grain-boundary interfaces account for the low ductility of this material in tension.     

Multiscale modelling of the induced plastic anisotropy in bcc metals

This paper presents a new framework to predict the qualitative and quantitative variation in local plastic anisotropy due to crystallographic texture in body-centered cubic polycrystals. A multiscale model was developed to examine the contribution of mesoscopic and local microscopic behaviour to the macroscopic constitutive response of bcc metals during deformation. The model integrated a dislocation-based hardening scheme and a Taylor-based crystal plasticity formulation into the subroutine of an explicit dynamic FEM code (LS-DYNA). Numerical analyses using this model were able to predict not only correct grain rotation during deformation, but variations in plastic anisotropy due to initial crystallographic orientation. Optimal results were obtained when {1 1 0}〈1 1 1〉, {1 1 2}〈1 1 1〉, and {1 2 3}〈1 1 1〉 slip systems were considered to be potentially active. The predicted material heterogeneity can be utilised for research involving any texture-dependent work hardening behaviour, such as surface roughening.     

A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals

Modeling of scale-dependent characteristics of mechanical properties of metal polycrystals is studied using both discrete dislocation dynamics and continuum crystal plasticity. The initial movements of dislocation arc emitted from a Frank-Read type dislocation source and bounded by surrounding grain boundaries are examined by dislocation dynamics analyses system and we find the minimum resolved shear stress for the FR source to emit at least one closed loop. When the grain size is large enough compared to the size of FR source, the minimum resolved shear stress levels off to a certain value, but when the grain size is close to the size of the FR source, the minimum resolved shear stress shows a sharp increase. These results are modeled into the expression of the critical resolved shear stress of slip systems and continuum mechanics based crystal plasticity analyses of six-grained polycrystal models are made. Results of the crystal plasticity analyses show a distinct increase of macro- and microscopic yield stress for specimens with smaller mean grain diameter. Scale-dependent characteristics of the yield stress and its relation to some control parameters are discussed.     

Constitutive modeling of orthotropic sheet metals by presenting hardening-induced anisotropy

An essential work on the constitutive modeling of rolled sheet metals is the consideration of hardening-induced anisotropy. In engineering applications, we often use testing results of four specified experiments, three uniaxial-tensions in rolling, transverse and diagonal directions and one equibiaxial-tension, to describe the anisotropic features of rolled sheet metals. In order to completely take all these experimental results, including stress-components and strain-ratios, into account in the constitutive modeling for presenting hardening-induced anisotropy, an appropriate yield model is developed. This yield model can be characterized experimentally from the offset of material yield to the end of material hardening. Since this adaptive yield model can directly represent any subsequent yielding state of rolled sheet metals without the need of an artificially defined “effective stress”, it makes the constitutive modeling simpler, clearer and more physics-based. This proposed yield model is convex from the initial yield state till the end of strain-hardening and is well-suited in implementation of finite element programs.     

On the modeling of hardening in metals during non-proportional loading

The purpose of the current work is the formulation and initial application of a phenomenological model for hardening effects in metals subject to non-proportional loading histories characterized by one or more loading-path changes. This model is closely related to the incremental model of Teodosiu and Hu [Teodosiu, C., Hu, Z., 1995. Evolution of the intragranular microstructure at moderate and large strains: modelling and computational significance. In: Shen, S.F., Dawson, P.R. (Eds.), Simulation of Materials Processing: Theory, Methods and Applications. Balkema, Rotterdam, pp. 173–182; Teodosiu, C., Hu, Z., 1998. Microstructure in the continuum modelling of plastic anisotropy. In: Proceedings of 19th Risø International Symposium on Material’s Science: Modelling of Structure and Mechanics of Materials from Microscale to Product. Risø National Laboratory, Roskilde, Denmark, pp. 149–168]. Like their model, the current model captures in particular hardening stagnation after a load reversal as well as cross-hardening after orthogonal loading-path changes. On the other hand, the two models predict qualitatively different behavior during loading-path changes which take place purely in the inelastic range. Such is the case for example during orthogonal loading-path changes from uniaxial tension to simple shear without release, or during monotonic simple shear, or during deep-drawing. As shown by the experimental results reported on in the current work for the mild steel DC06, significant cross-hardening can occur during continuous orthogonal loading-path changes. Beyond this, the current model accounts in an approximate way for the possible effects of texture development on the material behavior with the help of the plastic spin. After investigating the behavior of the current model for various ideal two-stage loading histories (e.g., tension-shear), the current work ends with a comparison of standard combined hardening and current approaches in the context of the simulation of internal stress development and residual stresses during deep-drawing and the resultant springback after ring-splitting.     

Nucleation of micro-cracks for polycrystalline metal with anisotropy: micro-stress evaluation

Presented is the local stresses on the crystallographic plane as they are influenced by the metal fracture with anisotropy. It is based on the nucleation of micro-cracks and its unstable equilibrium in a polycrystal with texture. Crystallographic texture causes non-uniform distribution of the crack nucleus orientations owing to their preference to expand or open on certain crystallographic planes. This is the main cause of anisotropy of cleavage fracture stress of textured metal. “Oriented” micro-stresses in textured metal contribute to the anisotropic effect. In view of what has been said, accumulated plastic strains at fracture is analysed.     

Scattering of ultrasound by minority phases in polycrystalline metals

The scattering of ultrasound by minority phases in polycrystalline metals is discussed. For discrete inclusions, the scattering theory of Ying and Truell describes well the attenuation of longitudinal waves. To treat the scattering by a second phase formed by segregation at a grain boundary, the scattering by a spherical shell with density and elastic constants different from those of the surrounding medium is developed. Reflection of ultrasound at this boundary is found to enhance the attenuation at low frequencies in agreement with experiments of Kamigaki. Application is made to the scattering by manganese sulphide in free-machining steel.     

A review on the application of modified continuum models in modeling and simulation of nanostructures

Analysis of the mechanical behavior of nanostructures has been very challenging. Surface energy and nonlocal elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams,graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are mentioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomaterials are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires further applications of modified continuum models in modeling nanomaterials and nanostructures.     

Characterization of macroscopic tensile strength of polycrystalline metals with two-scale finite element analysis

The objective of this contribution is to develop an elastic-plastic-damage constitutive model for crystal grain and to incorporate it with two-scale finite element analyses based on mathematical homogenization method, in order to characterize the macroscopic tensile strength of polycrystalline metals. More specifically, the constitutive model for single crystal is obtained by combining hyperelasticity, a rate-independent single crystal plasticity and a continuum damage model. The evolution equations, stress update algorithm and consistent tangent are derived within the framework of standard elastoplasticity at finite strain. By employing two-scale finite element analysis, the ductile behaviour of polycrystalline metals and corresponding tensile strength are evaluated. The importance of finite element formulation is examined by comparing performance of several finite elements and their convergence behaviour is assessed with mesh refinement. Finally, the grain size effect on yield and tensile strength is analysed in order to illustrate the versatility of the proposed two-scale model.     

Liquid and gas flows in porous media with allowance for induced anisotropy

The changes in the permeability of a porous medium resulting from the reorientation of the solid matrix particles under the influence of the percolating flow are considered. The mathematical model also contains the angular momentum equation, including the moment of the viscous flow forces. The state of the elastic matrix is characterized not only by the repacking strains but also by the particle orientation vector. The latter determines the anisotropy of the permeability tensor. The effective stress, strain, pore pressure and orientation vector fields in the neighborhood of an operating well are constructed. The effect of the induced permeability anisotropy on well productivity is noted.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 96–103, May–June, 1992.The authors are grateful to G. A. Zotov and V. A. Chernykh for their interest and support.     

Assessment of the anisotropy of the crack resistance of plastically anisotropic metals

The applicability of the structural-mechanical approach to the assessment of the indices of crack-resistance anisotropy under plane-strain and plane-stress conditions is confirmed by an example of plastically anisotropic semi-finished products and articles made from aluminum alloys of a wide class. These parameters are determined as functions of the anisotropy indices of the yield stresses due to monoaxial tension of crack-free specimens and processing strains, which can be determined by the metallographic method. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 137–144, April, 2000.     

A two-dimensional dislocation dynamics model of the plastic deformation of polycrystalline metals

Two-dimensional dislocation dynamics (2D-DD) simulations under fully periodic boundary conditions are employed to study the relation between microstructure and strength of a material. The material is modeled as an elastic continuum that contains a defect microstructure consisting of a preexisting dislocation population, dislocation sources, and grain boundaries. The mechanical response of such a material is tested by uniaxially loading it up to a certain stress and allowing it to relax until the strain rate falls below a threshold. The total plastic strain obtained for a certain stress level yields the quasi-static stress-strain curve of the material. Besides assuming Frank-Read-like dislocation sources, we also investigate the influence of a pre-existing dislocation density on the flow stress of the model material. Our results show that - despite its inherent simplifications - the 2D-DD model yields material behavior that is consistent with the classical theories of Taylor and Hall-Petch. Consequently, if set up in a proper way, these models are suited to study plastic deformation of polycrystalline materials.     

Effect of texture smearing on the anisotropy of cleavage-stress of metals and alloys

The effect of crystallographic texture smearing on the anisotropy of fracture stress of metals is analyzed. It is found that texture smearing leads to an appreciable decrease in the value of the coefficient of cleavage-stress anisotropy compared with that for metals with very sharp textures. The magnitude of this effect depends on the initial plastic strain (that depends on the breadth of texture component) and the level of stress triaxiality.     

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets: Application to sheet springback

The constitutive model for the unusual asymmetric hardening behavior of magnesium alloy sheet presented in a companion paper (Lee, M.G., Wagoner, R.H., Lee, J.K., Chung, K., Kim, H.Y., 2008. Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheet, Int. J. Plasticity 24(4), 545–582) was applied to the springback prediction in sheet metal forming. The implicit finite element program ABAQUS was utilized to implement the developed constitutive equations via user material subroutine. For the verification purpose, the springback of AZ31B magnesium alloy sheet was measured using the unconstrained cylindrical bending test of Numisheet (Numisheet ’2002 Benchmark Problem, 2002. In: Yang, D.Y., Oh, S.I., Huh, H., Kim, Y.H. (Eds.), Proceedings of 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Jeju, Korea) and 2D draw bend test. With the specially designed draw bend test the direct restraining force and long drawn distance were attainable, thus the measurement of the springback could be made with improved accuracy comparable with conventional U channel draw bend test. Besides the developed constitutive models, other models based on isotropic constitutive equations and the Chaboche type kinematic hardening model were also considered. Comparisons were made between simulated results by the finite element analysis and corresponding experiments and the newly proposed model showed enhanced prediction capability, which was also supported by the simple bending analysis adopting asymmetric stress–strain response.