Predicting the Hall–Petch effect in fcc metals using non-local crystal plasticity

Many conventional continuum approaches to solid mechanics do not address the size sensitivity of deformation to microstructural features like grain boundaries, and are therefore unable to capture much of the experimentally observed behavior of polycrystal deformation. We propose a non-local crystal plasticity model, in which the geometrically necessary dislocation (GND) density is calculated using a non-local integral approach. The model is based on augmented F^eF^p kinematics, which account for the initial microstructure (primarily grain boundaries) present in the polycrystal. With the augmented kinematics, the initial GND and the evolving GND state are determined in a consistent manner. The expanded kinematics and the non-local crystal plasticity model are used to simulate the tensile behavior in copper polycrystals with different grain sizes ranging from 14 μm to 244 μm. The simulation results show a grain size dependence on the polycrystal’s yield strength, which are in good agreement with the experimental data.     

A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation

This work is an attempt to answer the question:

Is there a physically natural method of characterizing the possible interactions between the slip systems of two grains that meet at a grain boundary—a method that could form the basis for the formulation of grain-boundary conditions?

Here we give a positive answer to this question based on the notion of a Burgers vector as described by a tensor field G on the grain boundary [Gurtin, M.E., Needleman, A., 2005. Boundary conditions in small-deformation single-crystal plasticity that account for the Burgers vector. J. Mech. Phys. Solids 53, 1-31]. We show that the magnitude of G can be expressed in terms of two types of moduli: inter-grain moduli that characterize slip-system interactions between the two grains; intra-grain moduli that for each grain characterize interactions between any two slip systems of that grain.We base the theory on microscopic force balances derived using the principle of virtual power, a version of the second law in the form of a free-energy imbalance, and thermodynamically compatible constitutive relations dependent on G and its rate. The resulting microscopic force balances represent flow rules for the grain boundary; and what is most important, these flow rules account automatically—via the intra- and inter-grain moduli—for the relative misorientation of the grains and the orientation of the grain boundary relative to those grains.     

Fatigue damage in polycrystals – Part 2: Intrinsic scatter of fatigue life

Part 2 deals with the evolution of plastic flow resistance with crack growth from its minimum value (fatigue limit) towards its saturated bulk value (cyclic yield stress). The far-field stress level, the geometry of the crack and the grain size distribution of the material are those parameters that control the area of crack tip plasticity and hence the rate towards saturation. The implication of the far-field stress is held responsible for the violation of the similitude concept and the failure of the stress intensity factor to describe conditions of short cracking. However, an engineering tool based on the stress intensity factor and being able to predict the fatigue life of short cracks can be constructed, considering that the distribution of crack growth rates is intrinsically defined by the material itself. The above allows the development of a set of equations able to construct the fatigue life scatter of the material.     

A Sulfur-Doped Copper Catalyst with Efficient Electrocatalytic Formate Generation during the Electrochemical Carbon Dioxide Reduction Reaction

Catalysts involving post-transition metals have shown almost invincible performance on generating formate in electrochemical CO₂ reduction reaction (CO₂RR). Conversely, Cu without post-transition metals has struggled to achieve comparable activity. In this study, a sulfur (S)-doped-copper (Cu)-based catalyst is developed, exhibiting excellent performance in formate generation with a maximum Faradaic efficiency of 92 % and a partial current density of 321 mA cm⁻². Ex situ structural elucidations reveal the presence of abundant grain boundaries and high retention of S−S bonds from the covellite phase during CO₂RR. Furthermore, thermodynamic calculations demonstrate that S−S bonds can moderate the binding energies with various intermediates, further improving the activity of the formate pathway. This work is significant in modifying a low-cost catalyst (Cu) with a non-metallic element (S) to achieve comparable performance to mainstream catalysts for formate generation in industrial grade.     

Crack growth versus blunting in nanocrystalline metals with extremely small grain size

Fracture of nanocrystalline metals with extremely small grain size is simulated in this paper by structural evolution. Two-dimensional scheme is formulated to study the competition between crack growth and blunting in nanocrystalline samples with edge cracks. The scheme couples the creep deformation induced by grain boundary (GB) mechanisms and the intergranular crack growth. The effects of material properties, initial configurations and applied loads are explored. Either the enhancement in diffusion mobility, or the deterrence in the grain boundary damage, would blunt the crack and decelerate its growth, and vice versa. The simulations agree with the analytical predictions as modified from that of Yang and Yang [2008. Brittle versus ductile transition of nanocrystalline metal. Int. J. Solids Struct. 45, 3897-3907]. Upon the suppression of dislocation activities, it is validated that the brittle versus ductile transition of nanocrystals is controlled by the development of grain boundary-dominated creep versus grain boundary decohesion. Further simulations found that either decreasing the grain sizes or increasing the dispersion of grain sizes would blunt the growing cracks.     

Vacancy effect on the elastic constants of layer-structured nanomaterials

Layer-structured nanomaterials where alternating layers of nanocrystallites meet along high angle grain boundaries constitute a special category of nanomaterials. In the present study we investigated the effect of the presence of a vacancy on the elastic constants of such materials by the use of atomistic simulation methods. The calculations were performed on a model system where atoms interact via a Lennard–Jones potential and the elastic constants were obtained in the frame of homogeneous deformations, for nanocrystallite layer widths ranging from 2.24 up to 37.12 nm. The results show that the favoured position of the vacancy is located in the GB core. The state of relaxation of the structure is an important factor that affects the obtained results. In both the unrelaxed and relaxed structures results converge to a given value after the 5th (3 1 0) layer. This value seems to depend on the size of the nanocrystallite L and approaches the bulk value above a given size L. It is also concluded that in the case of a relaxed system there is a smoother variation of the system energy and elastic constant as a function of the distance of the vacancy from the GB plane when the size L increases. The way that external stresses are applied on the system affects the values of the obtained elastic properties, with the elastic constants related to the characteristic directions of the grain boundary being the most affected ones. These findings are of particular interest for fabrication methods of nanostructured materials, experimental methods for the measurement of their elastic properties as well as multiscale modelling schemes.     

X-ray microdiffraction and strain gradient crystal plasticity studies of geometrically necessary dislocations near a Ni bicrystal grain boundary

We compare experimental measurements of inhomogeneous plastic deformation in a Ni bicrystal with crystal plasticity simulations. Polychromatic X-ray microdiffraction, orientation imaging microscopy and scanning electron microscopy, were used to characterize the geometrically necessary dislocation distribution of the bicrystal after uniaxial tensile deformation. Changes in the local crystallographic orientations within the sample reflect its plastic response during the tensile test. Elastic strain in both grains increases near the grain boundary. Finite element simulations were used to understand the influence of initial grain orientation and structural inhomogeneities on the geometrically necessary dislocations arrangement and distribution and to understand the underlying materials physics.     

Comprehensive loss modeling in Cu2ZnSnS4 solar cells

Thin film solar cells based on Cu₂ZnSnS₄ (CZTS) absorber material suffers from performance issues arising due to the presence of a non-optimal back contact barrier, low carrier lifetime, acceptor/donor point defects in bulk, interface defects at the absorber-buffer junction and grain boundaries within the absorber. We perform comprehensive simulations enumerating the impact of these performance limiting factors on CZTS solar cells. These simulations capture the experimentally observed anomalies in current-voltage (I–V) characteristics and the open-circuit voltage (V_OC) pinning in CZTS solar cells. These cause-effect relationships as elaborated in the findings are expected to be of great interest to the experimentalists working in this field.