On the influence of isotropic and kinematic hardening caused by strain gradients on the deformation behaviour of polycrystals

Ma, Anxin; Hartmaier, Alexander

doi:10.1080/14786435.2013.847290

Cited by 41 publications

(44 citation statements)

References 35 publications

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“…It has been well recognized that the back stress plays an important role in mediating the strengthening and strain hardening of heterostructured materials [27][28][29][30]. During the deformation of conventional polycrystals, remarkable strain inhomogeneity may take place at GBs with large misorientations [31]. However, owing to the easy plastic relaxation at GBs in the traditional coarse grains, the produced back stress and kinematic hardening are generally limited.…”

Section: Resultsmentioning

confidence: 99%

“…Considering that the deformation is mediated by threading dislocations gliding inside the twin lamellar channels, dislocations of the same slip system stored in the lamellae can result in self-hardening, while the pile-up of dislocations from other slip systems against TBs causes cross-hardening of the activated threading dislocations [31]. Figure 4(e) shows that a large number of dislocations can be observed at TBs in the specimen deformed at the high strain rate, while the twin lamellae are much cleaner in the specimen deformed at the low strain rate (Figure 4(f)).…”

Section: Resultsmentioning

confidence: 99%

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Kinematic and isotropic strain hardening in copper with highly aligned nanoscale twins

Wang

You

Lü

2018

Materials Research Letters

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The kinematic and isotropic strain hardening was investigated in columnar-grained copper with preferentially oriented nanoscale twins deformed at two different strain rates of 5 × 10 −5 and 5 × 10 −3 s −1 . A significant back stress is caused majorly by threading dislocation pile-up and accumulation at the grain boundaries and is strain rate independent. The isotropic hardening associated with an increment in the local effective stress stems from dislocation storage at twin boundaries, and a high strain rate is beneficial for enhancing isotropic strain hardening and tensile ductility. IMPACT STATEMENTLong-range back stress was detected to develop during plastic deformation of nanotwinned structures, majorly caused by pile-up and accumulation of threading dislocations at grain boundary regions. ARTICLE HISTORY

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Kinematic and isotropic strain hardening in copper with highly aligned nanoscale twins

Wang

You

Lü

2018

Materials Research Letters

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“…We choose a local crystal plasticity (CP) model without the effect of the strain gradient as described by Ma & Hartmaier (2014) for numerical modeling of material behavior. Here, an example of this process is presented for Rolled-Cu.…”

Section: Applicationmentioning

confidence: 99%

Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations

et al. 2020

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Crystallographic textures, as they develop for example during cold forming, can have a significant influence on the mechanical properties of metals, such as plastic anisotropy. Textures are typically characterized by a non-uniform distribution of crystallographic orientations that can be measured by diffraction experiments like electron backscatter diffraction (EBSD). Such experimental data usually contain a large number of data points, which must be significantly reduced to be used for numerical modeling. However, the challenge in such data reduction is to preserve the important characteristics of the experimental data, while reducing the volume and preserving the computational efficiency of the numerical model. For example, in micromechanical modeling, representative volume elements (RVEs) of the real microstructure are generated and the mechanical properties of these RVEs are studied by the crystal plasticity finite element method. In this work, a new method is developed for extracting a reduced set of orientations from EBSD data containing a large number of orientations. This approach is based on the established integer approximation method and it minimizes its shortcomings. Furthermore, the L 1 norm is applied as an error function; this is commonly used in texture analysis for quantitative assessment of the degree of approximation and can be used to control the convergence behavior. The method is tested on four experimental data sets to demonstrate its capabilities. This new method for the purposeful reduction of a set of orientations into equally weighted orientations is not only suitable for numerical simulation but also shows improvement in results in comparison with other available methods.

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“…The material behavior of the FE simulation is described by a phenomenologically based crystal plasticity model. To resolve the heterogeneous deformation resulting from abrupt changes in mechanical behavior across grain boundaries of the considered polycrystal and to consider size effects between small and large grains, a nonlocal crystal plasticity model proposed by Ma and Hartmaier (2014) is implemented. As the applied nonlocal crystal plasticity model is already described in Ma and FIGURE 1 | (A) Quasi-2D RVE with vertex nodes (V 1 , V 2 , V 4 , H 1 ) needed for the boundary conditions (see section 2.3.3); RVE with a mean grain size of 59µm and a standard deviation of 10µm contains 51 grains between 40 and 90µm, has a side length of 348.8µm and a thickness of 1.7µm and is used as model for the damage evolution (cf.…”

Section: Crystal Plasticity Modelmentioning

confidence: 99%

“…Hartmaier (2014), only an overview of the formulation is given. For further details on the non-local flow rule, the reader is kindly referred to Ma and Hartmaier (2014). In the following, quantities written in bold letters refer to vectors (small letters) and matrices of second rank tensors (capital letters).…”

Section: Crystal Plasticity Modelmentioning

confidence: 99%

Modeling Macroscopic Material Behavior With Machine Learning Algorithms Trained by Micromechanical Simulations

et al. 2019

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Micromechanical modeling of material behavior has become an accepted approach to describe the macroscopic mechanical properties of polycrystalline materials in a microstructure-sensitive way. The microstructure is modeled by a representative volume element (RVE), and the anisotropic mechanical behavior of individual grains is described by a crystal plasticity model. Such micromechanical models are subjected to mechanical loads in a finite element (FE) simulation and their macroscopic behavior is obtained from a homogenization procedure. However, such micromechanical simulations with a discrete representation of the material microstructure are computationally very expensive, in particular when conducted for 3D models, such that it is prohibitive to apply them for process simulations of macroscopic components. In this work, we suggest a new approach to develop microstructure-sensitive, yet flexible and numerically efficient macroscopic material models by using micromechanical simulations for training Machine Learning (ML) algorithms to capture the mechanical response of various microstructures under different loads. In this way, the trained ML algorithms represent a new macroscopic constitutive relation, which is demonstrated here for the case of damage modeling. In a second application of the combination of ML algorithms and micromechanical modeling, a proof of concept is presented for the application of trained ML algorithms for microstructure design with respect to desired mechanical properties. The input data consist of different stress-strain curves obtained from micromechanical simulations of uniaxial testing of a wide range of microstructures. The trained ML algorithm is then used to suggest grain size distributions, grain morphologies and crystallographic textures, which yield the desired mechanical response for a given application. For validation purposes, the resulting grain microstructure parameters are used to generate RVEs, accordingly and the macroscopic stress-strain curves for those microstructures are calculated and compared with the target quantities. The two examples presented in this work, demonstrate clearly that ML methods can be trained by micromechanical simulations, which capture material behavior and its relation to Reimann et al. Application of Micromechanical Modeling on Machine Learningmicrostructural mechanisms in a physically sound way. Since the quality of the ML algorithms is only as good as that of the micromechanical model, it is essential to validate these models properly. Furthermore, this approach allows a hybridization of experimental and numerical data.

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On the influence of isotropic and kinematic hardening caused by strain gradients on the deformation behaviour of polycrystals

Cited by 41 publications

References 35 publications

Kinematic and isotropic strain hardening in copper with highly aligned nanoscale twins

Kinematic and isotropic strain hardening in copper with highly aligned nanoscale twins

Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations

Modeling Macroscopic Material Behavior With Machine Learning Algorithms Trained by Micromechanical Simulations

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