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Ferroelectric ceramics, such as barium titanate, have garnered significant interest due to their unique electrical and mechanical properties. In particular, their ability to undergo significant deformation under an applied electric field aids in their utilization in many applications, including actuators and sensors. The deformation behavior of ferroelectric ceramics is complex and is influenced by various factors, such as crystal structure, defect density, and processing conditions. This study focuses on the mechanics of ferroelectric ceramics and seeks to offer a thorough comprehension of the barium titanate’s deformation behavior. The study begins by discussing the crystal structure of barium titanate and how it influences the ferroelectric behavior of the material. It then delves into the various mechanisms of deformation, including domain wall motion, phase transformation, and twinning. The study also discusses the effects of temperature, electric field strength, and microstructure on the deformation behavior of barium titanate. Furthermore, the study explores the relationship between the deformation behavior and the mechanical characteristics of barium titanate, including Poisson’s ratio and Young’s modulus. Finally, the study concludes with a discussion of the potential applications of ferroelectric ceramics and the need for further research in this area. Overall, this study provides a comprehensive understanding of the deformation behavior of barium titanate showcasing distinct influences of grain size, texture, and anisotropy. Notably, varying grain sizes significantly impact deformation behavior. For instance, smaller grain sizes ($<10\mu$m) exhibit superior deformation characteristics, correlating with higher permittivity values (2731–5801) compared to larger grain counterparts (18.4$\mu$m). Additionally, transition temperatures ($T_{\mathrm{\text{O}}–\mathrm{\text{T}}}$) for different grain sizes (18.0–$30.1^{\circ }$C for smaller grains, 21.5–$30.6^{\circ }$C for larger grains) underscore the impact of phase transitions on grain size. These results underscore the paramount importance of grain size, texture, and anisotropy in governing the mechanical traits of barium titanate, emphasizing their consideration during fabrication and processing for optimal performance in diverse applications.

We perform tensile deformation studies on nanocrystalline twinning-induced plasticity (TWIP) steels using molecular dynamics (MD) simulations and observe significant volume changes during incremental deformation. The meta-atomic potential function is employed to define atomic interactions in TWIP steels. The nucleation and propagation of dislocations lead to a reduction in tensile stress, which is positively correlated with the average grain size. Tensile tests show that TWIP steels undergo a phase transformation during plastic deformation, primarily from the face-centred cubic (FCC) to the HCP phase. This transformation results in the formation of stacking faults (SFs) and twin boundaries (TBs). The slip of dislocations is intercepted by grain boundaries (GBs) and TBs, leading to stress concentration. When the stress reaches a critical threshold, cracks initiate and propagate at these weak points, causing volume expansion during plastic deformation. This volume change results from the interaction between the material’s complex microstructure and the generation and progression of cracks. In contrast, nanocrystalline Cu exhibits nearly constant volume during the plastic deformation stage, attributed to the insufficient dislocation slip and phase transformations in Cu. Overall, the observed volume increase is specific to TWIP steels and contributes to their high ductility.

Free-standing sub-micron Ti-5Al single crystal square pillars were fabricated along double slip and [0001] twinning orientations using FIB fabrication processes. Samples in range of 0.4 to 2.0µm were compressed. The yield stress increases much higher than their bulk counterpart as the specimen width decreases. The tendency of "smaller is stronger" is displayed in Ti-5Al single crystals loaded along and [0001] orientations. The number of slip systems is restricted by specimen physical size as it declines from 2µm to 0.5µm, when the specimens were subjected to double slip loading. Meanwhile, when sample size is less than 1.0µm, micro-pillars along twinning orientation have to compensate the incomplete twinning deformation via shearing due to geometrical restriction and dislocation starvation effects. This variation of deformation mode could be attributed to the starvation effect of dislocations.

Microstructural evolution and flow behavior of twin-roll cast AZ41 magnesium alloy during hot compression were characterized by employing deformation temperature of 300°C, 350°C and 400°C, and strain rate ranging from 10^-3 to 10^-2s^-1. When compressed at different temperature (300°C, 350°C and 400°C) and strain rate (10^-3 and 10^-2s^-1) all stress strain curves showed a flow softening behavior before strained to 0.51 due to dynamic recrystallization, even though concurrent twinning was quite active. Twinning contributed to the flow hardening behavior appeared during the end of hot compression (ε > 0.51) at a strain rate of 10^-2s^-1 and elevated temperature (300°C, 350°C and 400°C) in spite of the softening effect of concurrently occurred dynamic recrystallization. TEM image showed that discontinuous recrystallization occurred when deformed at elevated temperature as high as 400°C and the strain rate ranging from 10^-2 to 10^-3s^-1. It is suggested that dislocation slip, twinning and recrystallization develop in a cyclic mode from initial stage to the end of hot compression.

Flow stress behavior during initial stage of hot compression of twin-roll cast ZK60 magnesium alloy was characterized by employing deformation temperature of 300°C and 400°C, and a given strain rate of 10^-2s^-1. A stress drop during initial stage of hot compression at 300°C, generally led by dynamic recrystallization, was found to be attributed to twinning, correspondingly to dynamic recrystallization as deformation temperature was raised to 400°C.

Layered metal composites have been widely used in various industries fields because of their excellent properties and are responsible for mechanical behavior of materials. This paper focuses on analyzing the deformation mechanism of the (110) interface under different loading states by MD. The results show that there are two yield points in the stress–strain curve under both Z- and Y-axis loading states. The first yield is the nucleation of dislocations at the interface, meantime the slip of dislocations and the extension of stacking faults begin at the Al layer. The second one, the dislocation passes through the interface, nucleates and emits toward the Cu layer at the interface, leading to a stress mutation. It is worth noting that during the stable rheological stage, the deformation mechanisms vary under different loading directions. Under Y-axis tensile loading, the phase transformation of FCC–HCP is present due to the interaction of dislocation movement and stacking fault. On the contrary, there are two twin paths A and B, improving the strength, during Z-axis compression loading. For other loading modes, there are three zones, namely the elastic stage, the release of energy, and strain hardening and dynamic softening. The interface plays the role of nucleation, annihilation and penetration of dislocations, and this interface-dislocation mechanism is reflected in the whole stage of plastic deformation. The results have an insight into the design and control in heterointerface.

In materials that undergo martensitic phase transformation, distinct elastic phases often form layered microstructures — a phenomenon known as twinning. In some settings the volume fractions of the phases vary macroscopically; this has been seen, in particular, in experiments involving the bending of a bar. We study a two-dimensional (2D) model problem of this type, involving two geometrically nonlinear phases with a single rank-one connection. We adopt a variational perspective, focusing on the minimization of elastic plus surface energy. To get started, we show that twinning with variable volume fraction must occur when bending is imposed by a Dirichlet-type boundary condition. We then turn to paper’s main goal, which is to determine how the minimum energy scales with respect to the surface energy density and the transformation strain. Our analysis combines ansatz-based upper bounds with ansatz-free lower bounds. For the upper bounds we consider two very different candidates for the microstructure: one that involves self-similar refinement of its length scale near the boundary, and another based on piecewise-linear approximation with a single length scale. Our lower bounds adapt methods previously introduced by Chan and Conti to address a problem involving twinning with constant volume fraction. The energy minimization problem considered in this paper is not intended to model twinning with variable volume fraction involving two martensite variants; rather, it provides a convenient starting point for the development of a mathematical toolkit for the study of twinning with variable volume fraction.

Push–pull tests of rolled magnesium alloy AZ31 were performed with a side-notch plate specimen to examine the crack growth behavior under negative mean stress conditions in conditions of high humidity. The effects of repetition of compression on crack growth were discussed. The geometry of the fracture surface and the changes in microstructure were related to the crack growth behavior. The crack growth rate varied even when the experimental conditions were the same. When the oxidized powder appeared from the cracked surface, the crack growth rate became lower. That was related to the changes in microstructure while the crack grew with local shear plastic deformation. The variation of crack closure point was related to the local shear plastic deformation.

It has been observed by experiments and computer simulations that deformation twinning and grown-in twins play important roles during the plastic deformation in nanocrystalline (nc) metals. In this study, molecular dynamics simulation is employed to investigate the role of grown-in twins in the tensile deformation of hexagonal close-packed nc cobalt. Plastic deformation processes in three types of nc samples, namely nc-cobalt without twins, with (0002) twin faults and with (1121) twins, are compared. The results show that the pre-existing twins significantly lower the mechanical strength and do not enhance the ductility of nc cobalt. Instead deformation induced hcp-to-fcc allotropic transformation is found to result in remarkable strain hardening in the modeled nc cobalt.

The large strain torsion of polycrystalline materials with the hexagonal close packed (HCP) crystallographic structure is numerically studied by using a special purpose finite element. All simulations are based on the recently developed large strain elastic visco-plastic self-consistent (EVPSC) model for polycrystalline materials. For the first time, the effect of twinning on the large strain torsion is assessed in the present study. It is found that the response of the large strain torsion of HCP polycrystals is very sensitive to the initial texture and texture evolution. Numerical results indicate that excluding texture evolution dramatically reduces the development of the second-order axial strain under free-end torsion, or the axial force under fixed-end torsion. It is also numerically demonstrated that twinning has a significant influence on the large strain torsion of HCP polycrystals. For the magnesium alloy AZ31 extruded bar, the predicted results are in good qualitative agreement with experimental observations.

Magnesium alloys exhibit significant inelastic behavior during unloading, especially when twinning and detwinning are involved. It is commonly accepted that noteworthy inelastic behavior will be observed during unloading if twinning occurs during previous loading. However, this phenomenon is not always observed for Mg sheets with strong rolled texture. Therefore, the inelasticity of AZ31B rolled sheets with different rolled textures during cyclic loading-unloading are investigated by elastic viscoplastic self-consistent polycrystal plasticity model. The incorporation of the twinning and detwinning model enables the treatment of detwinning, which plays an important role for inelastic behavior during unloading. The effects of texture, deformation history, and especially twinning and detwinning on the inelastic behaviors are carefully investigated and found to be remarkable. The simulated results are in agreement with the available experimental observations, which reveals that the inelastic behavior for strongly rolled sheets is very different than the extruded bars.

A constitutive framework based on concepts from phase field theory and pseudo-Finsler geometry is exercised in numerical simulations of deformation and fracture of ceramic polycrystals. The material system of interest is boron carbide, a hard but brittle ceramic. Some microstructures are enabled with thin layers of a secondary amorphous phase of boron nitride between grains of boron carbide. The constitutive theory accounts for physical mechanisms of twinning, crystal-to-glass phase transformations, cleavage fracture within grains and separation and cavitation at grain boundaries (GBs). According to the generalized Finsler approach, geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors, that enter the energy potential in a manner similar to order parameters of phase field models. A partially linearized version of the theory is invoked in finite element simulations of polycrystals, with and without GB layers, subjected to pure shear loading. Effects of grain size and layer properties — thickness, shear modulus and surface energy — are studied parametrically. Results demonstrate that twinning and amorphization occur prominently in nanocrystals but less so in aggregates with larger grains that tend to fail earlier by fracture. Structural changes occur readily in the latter at smaller applied strains only in conjunction with elastic shear softening in localized degraded or damaged regions. Hall–Petch scaling of peak shear strength with grain size is observed. Strength is increased via addition of amorphous layers that shift the failure mode from transgranular to intergranular and further by cavity expansion in layers that induces local elastic compression and suppresses crack extension. Stiff layers provide the largest peak strength enhancement, while elastically compliant layers may improve toughness and strength in the softening regime.