A hybrid approach for the efficient computation of polycrystalline yield loci with the accuracy of the crystal plasticity finite element method

Direct experimental evaluation of the anisotropic yield locus of a given material, representing the zeros of the material's yield function in the stress space, is arduous. It is much more practical to determine the yield locus by combining limited measurements of yield strengths with predictions from numerical models based on microstructural features such as the orientation distribution function (ODF; also referred to as the crystallographic texture). For the latter, several different strategies exist in the current literature. In this work, we develop and present a new hybrid method that combines the numerical efficiency and simplicity of the classical crystallographic yield locus (CYL) method with the accuracy of the computationally expensive crystal plasticity finite element method (CPFEM). The development of our hybrid approach is presented in two steps. In the first step, we demonstrate for diverse crystallographic textures that the proposed hybrid method is in good agreement with the shape of the predicted yield locus estimated by either CPFEM or experiments, even for pronounced plastic anisotropy. It is shown that the calibration of only two parameters of the CYL method with only two yield stresses for different load cases obtained from either CPFEM simulations or experiments produces a reliable computation of the polycrystal yield loci for diverse crystallographic textures. The accuracy of the hybrid approach is evaluated using the results from the previously established CPFEM method for the computation of the entire yield locus and also experiments. In the second step, the point cloud data of stress tensors on the yield loci predicted by the calibrated CYL method are interpolated within the deviatoric stress space by cubic splines such that a smooth yield function can be constructed. Since the produced yield locus from the hybrid approach is presented as a smooth function, this formulation can potentially be used as an anisotropic yield function for the standard continuum plasticity methods commonly used in finite element analysis.

Climate Change and Sustainability in Czech Wheat Production

The paper deals with the analysis of Czech wheat production and its determinants. We use the Just and Pope (1979) stochastic production function to estimate the effects of economic and weather variables, together with technological progress and climate change, on wheat yield in the Czech regions in the period 1961–2018. The results suggest that both economic and environmental factors play important roles in the wheat yield function. The output/input price ratio has a positive effect on the wheat yield. The effects of temperature and precipitation are month-specific and highly non-linear. Technological change also has a positive effect on yield, whereas climate change has a rather negative effect on wheat yield.

A thermo-viscoplasticity model for metals over wide temperature ranges- application to case hardening steel

In this contribution, a model for the thermomechanically coupled behaviour of case hardening steel is introduced with application to 16MnCr5 (1.7131). The model is based on a decomposition of the free energy into a thermo-elastic and a plastic part. Associated viscoplasticity, in terms of a temperature-depenent Perzyna-type power law, in combination with an isotropic von Mises yield function takes respect for strain-rate dependency of the yield stress. The model covers additional temperature-related effects, like temperature-dependent elastic moduli, coefficient of thermal expansion, heat capacity, heat conductivity, yield stress and cold work hardening. The formulation fulfils the second law of thermodynamics in the form of the Clausius–Duhem inequality by exploiting the Coleman–Noll procedure. The introduced model parameters are fitted against experimental data. An implementation into a fully coupled finite element model is provided and representative numerical examples are presented showing aspects of the localisation and regularisation behaviour of the proposed model.

Research on Fuzzy Plastic Constitutive Model Based on Membership Function

Soil has no obvious yield point, and the classical elastoplastic theory contradicts the uncertainty of the plastic yield point of the soil. Therefore, a fuzzy plastic Cambridge model based on the membership function was designed by combining the fuzzy mathematics with the Cambridge model. This model made the plastic membership function to correspond with the fuzzy yield function. The plastic strain at any stress state was calculated using the fuzzy Cambridge model and was compared with the indoor triaxial test results, and they were in good agreement. Therefore, it is appropriate to use fuzzy mathematics to express the unobvious soil yield property. The characteristics of soil yield in any stress state is reflected by the fuzzy plastic theory, which indicates that there is entirely no elasticity at any stress state. Moreover, the varying degrees of plasticity and the degree of plastic yield were uniquely determined by the plastic membership function. The fuzzy plastic model used the membership function change to replace the complex hardening. Additionally, the cyclic loading path was clear and appropriate for the cyclic loading and unloading calculations.

An extended super/subloading surface model for soft rock considering structure degradation

The strain-softening and dilatancy behavior of soft rock is affected by the loading history and the development of structure. This study regards soft rock as a structured and overconsolidated soil and develops a new elastoplastic model based on the classical super yield surface Cam-clay model. The proposed model is capable of capturing the effect of yield surface shape on the mechanical behavior of soft rock by introducing a new yield function. The proposed model is validated against the triaxial test results on different types of soft rocks under drained condition. The comparison results indicate that the proposed model is suitable for describing the constitutive behavior of soft rock.

Parameter Estimation and Application of Anisotropic Yield Criteria for Cylindrical Aluminum Extrusions: Theoretical Developments and StereoDIC Measurements

Theoretical and experimental studies are presented to characterize the anisotropic plastic response under torsion loading of two nominally identical aluminum Al6061-T6 extruded round bars. Theoretical models are developed using isotropic (Von Mises 1913) and anisotropic (Barlat 1991) yield criteria, along with isotropic strain hardening formulae, to model post-yield behavior under simple torsion loading. For the case of simple shear loading, incremental plasticity theory is used to determine the theoretical elastic, plastic, and total shear strains. A set of experiments are performed to calibrate Barlat’s 1991 yield function. Several specimens are extracted at different orientations to the longitudinal direction of each round Al6061-T6 bar and tested under uniaxial tension and simple torsion to optimally determine all anisotropic (Barlat 1991) yield function parameters. During loading, Stereo Digital Image Correlation (DIC) is used to quantify surface deformations for the torsion experiments and a baseline tension specimen to identify and correct measurement anomalies. Results show the isotropic yield model either underestimates or overestimates the experimental shear strains for both extrusions. Conversely, results using the Barlat 1991 anisotropic yield criteria are in excellent agreement with experimental measurements for both extrusions. The presence of significant differences in the anisotropic parameters for nominally similar extrusions confirms that plastic anisotropy is essential for the accurate prediction of mechanical behavior in longitudinally extruded Al6061-T6 bars.