We give an overview of the theory for generalized parton distributions. Topics covered are their general properties and physical interpretation, the possibility to explore the three-dimensional ...structure of hadrons at parton level, their potential to unravel the spin structure of the nucleon, their role in small-
x physics, and efforts to model their dynamics. We review our understanding of the reactions where generalized parton distributions occur, to leading power accuracy and beyond, and present strategies for phenomenological analysis. We emphasize the close connection between generalized parton distributions and generalized distribution amplitudes, whose properties and physics we also present. We finally discuss the use of these quantities for describing soft contributions to exclusive processes at large energy and momentum transfer.
► Extension of a spectral method to finite strains useful for crystal micro mechanics. ► Identical material model in comparison of finite element and spectral method solutions. ► Convergence with ...mesh/grid is faster than FEM. ► Stress equilibrium and strain compatibility is fulfilled much better. ► Computation time of 2563 grid comparable to that of 643 linear finite elements.
A significant improvement over existing models for the prediction of the macromechanical response of structural materials can be achieved by means of a more refined treatment of the underlying micromechanics. For this, achieving the highest possible spatial resolution is advantageous, in order to capture the intricate details of complex microstructures. Spectral methods, as an efficient alternative to the widely used finite element method (FEM), have been established during the last decade and their applicability to the case of polycrystalline materials has already been demonstrated. However, until now, the existing implementations were limited to infinitesimal strain and phenomenological crystal elasto-viscoplasticity. This work presents the extension of the existing spectral formulation for polycrystals to the case of finite strains, not limited to a particular constitutive law, by considering a general material model implementation. By interfacing the exact same material model to both, the new spectral implementation as well as a FEM-based solver, a direct comparison of both numerical strategies is possible. Carrying out this comparison, and using a phenomenological constitutive law as example, we demonstrate that the spectral method solution converges much faster with mesh/grid resolution, fulfills stress equilibrium and strain compatibility much better, and is able to solve the micromechanical problem for, e.g., a 2563 grid in comparable times as required by a 643 mesh of linear finite elements.
We study generalized parton distributions in the impact parameter representation, including the case of nonzero skewness \(\xi\). Using Lorentz invariance, and expressing parton distributions in ...terms of impact parameter dependent wave functions, we investigate in which way they simultaneously describe longitudinal and transverse structure of a fast moving hadron. We compare this information with the one in elastic form factors, in ordinary and in kT-dependent parton distributions.
Dual-phase (DP) steel is the flagship of advanced high-strength steels, which were the first among various candidate alloy systems to find application in weight-reduced automotive components. On the ...one hand, this is a metallurgical success story: Lean alloying and simple thermomechanical treatment enable use of less material to accomplish more performance while complying with demanding environmental and economic constraints. On the other hand, the enormous literature on DP steels demonstrates the immense complexity of microstructure physics in multiphase alloys: Roughly 50 years after the first reports on ferrite-martensite steels, there are still various open scientific questions. Fortunately, the last decades witnessed enormous advances in the development of enabling experimental and simulation techniques, significantly improving the understanding of DP steels. This review provides a detailed account of these improvements, focusing specifically on (
a
) microstructure evolution during processing, (
b
) experimental characterization of micromechanical behavior, and (
c
) the simulation of mechanical behavior, to highlight the critical unresolved issues and to guide future research efforts.
•Efficient spectral methods are developed based on direct and mixed variational approaches.•Equivalence of the proposed formulations with the original formulation is demonstrated.•Examples show ...improved performance for highly heterogeneous and non-linear materials.•Guidelines for composing favourable solution strategies are provided.
Efficient spectral methods are developed to predict the micromechanical behaviour of plastically deforming heterogeneous materials. The direct and mixed variational conditions for mechanical equilibrium and strain compatibility are formulated in a framework that couples them to a general class of non-linear solution methods. Locally evolving micromechanical fields in a sheared polycrystalline material governed by a phenomenological crystal plasticity constitutive law are used to validate the methods, and their performance at varying material heterogeneities is benchmarked. The results indicate that the solution method has a dominant influence on performance and stability at large material heterogeneities, and significant improvements over the conventional fixed-point approach are obtained when higher-order solution methods are employed. Optimal solution strategies are devised based on this and applied to an idealised dual-phase polycrystalline aggregate.
Ferritic–martensitic dual phase (DP) steels deform spatially in a highly heterogeneous manner, i.e. with strong strain and stress partitioning at the micro-scale. Such heterogeneity in local strain ...evolution leads in turn to a spatially heterogeneous damage distribution, and thus, plays an important role in the process of damage inheritance and fracture. To understand and improve DP steels, it is important to identify connections between the observed strain and damage heterogeneity and the underlying microstructural parameters, e.g. ferrite grain size, martensite distribution, martensite fraction, etc. In this work we pursue this aim by conducting in-situ deformation experiments on two different DP steel grades, employing two different microscopic-digital image correlation (μDIC) techniques to achieve microstructural strain maps of representative statistics and high-resolution. The resulting local strain maps are analyzed in connection to the observed damage incidents (identified by image post-processing) and to local stress maps (obtained from crystal plasticity (CP) simulations of the same microstructural area). The results reveal that plasticity is typically initiated within “hot zones” with larger ferritic grains and lower local martensite fraction. With increasing global deformation, damage incidents are most often observed in the boundary of such highly plastified zones. High-resolution μDIC and the corresponding CP simulations reveal the importance of martensite dispersion: zones with bulky martensite are more susceptible to macroscopic localization before the full strain hardening capacity of the material is consumed. Overall, the presented joint analysis establishes an integrated computational materials engineering (ICME) approach for designing advanced DP steels.
The mechanical response of multiphase alloys is governed by the microscopic strain and stress partitioning behavior among microstructural constituents. However, due to limitations in the ...characterization of the partitioning that takes place at the submicron scale, microstructure optimization of such alloys is typically based on evaluating the averaged response, referring to, for example, macroscopic stress-strain curves. Here, a novel experimental-numerical methodology is introduced to strengthen the integrated understanding of the microstructure and mechanical properties of these alloys, enabling joint analyses of deformation-induced evolution of the microstructure, and the strain and stress distribution therein, down to submicron resolution. From the experiments, deformation-induced evolution of (i) the microstructure, and (ii) the local strain distribution are concurrently captured, employing in situ secondary electron imaging and electron backscatter diffraction (EBSD) (for the former), and microscopic-digital image correlation (for the latter). From the simulations, local strain as well as stress distributions are revealed, through 2-D full-field crystal plasticity (CP) simulations conducted with an advanced spectral solver suitable for heterogeneous materials. The simulated model is designed directly from the initial EBSD measurements, and the phase properties are obtained by additional inverse CP simulations of nanoindentation experiments carried out on the original microstructure. The experiments and simulations demonstrate good correlation in the proof-of-principle study conducted here on a martensite-ferrite dual-phase steel, and deviations are discussed in terms of limitations of the techniques involved. Overall, the presented integrated computational materials engineering approach provides a vast amount of well-correlated structural and mechanical data that enhance our understanding as well as the design capabilities of multiphase alloys.
Double hard scattering can play an important role for producing multiparticle final states in hadron-hadron collisions. The associated cross sections depend on double parton distributions, which at ...present are only weakly constrained by theory or measurements. A set of sum rules for these distributions has been proposed by Gaunt and Stirling some time ago. We give a proof for these sum rules at all orders in perturbation theory, including a detailed analysis of the renormalisation of ultraviolet divergences. As a by-product of our study, we obtain the form of the inhomogeneous evolution equation for double parton distributions at arbitrary perturbative order.
Typical hexagonal engineering materials, such as magnesium and titanium, deform extensively through shear strains and crystallographic re-orientations associated with the nucleation, propagation, and ...growth of twins. To accurately predict their deformation behavior it is, therefore, critical for constitutive models to incorporate these mechanisms. In this work an integrated approach for modeling the concurrent dislocation mediated plasticity and heterogeneous twinning behavior in hexagonal materials is presented. A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1¯012} tensile twins. A stochastic model is used to nucleate twins at grain boundaries, and their subsequent propagation and growth are driven by the Ginzburg–Landau relaxation of the system free energy which includes the orientation dependent twin interfacial energy and the elastic strain energy. Application of this novel and fully coupled model to the cases of magnesium single crystal, bicrystal, and polycrystal deformation is shown to demonstrate its predictive capability. Numerical simulations predict, in accordance with experimental observations, twin nucleation at grain boundaries followed by twin propagation into the grain interior and subsequent transverse twin thickening. Through this new combination of modeling approaches it is possible to systematically study the twin induced strain fields, the stress distribution along twin boundaries, and the spatial evolution of dislocation density within twins and parent grains.
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