Analysis of Strain-Hardening Viscoplastic Wide Sheets Subject to Bending under Tension

The present paper provides an accurate solution for finite plane strain bending under tension of a rigid/plastic sheet using a general material model of a strain-hardening viscoplastic material. In particular, no restriction is imposed on the dependence of the yield stress on the equivalent strain and the equivalent strain rate. A special numerical procedure is necessary to solve a non-standard ordinary differential equation resulting from the analytic treatment of the boundary value problem. A numerical example illustrates the general solution assuming that the tensile force vanishes. This numerical solution demonstrates a significant effect of the parameter that controls the loading speed on the bending moment and the through-thickness distribution of stresses.

Beyond strain release: Delocalisation-enabled organic reactivity

Strain energy has long been recognised as a fundamental driving force for organic reactions. However, the release of strain alone is an insufficient predictor of reactivity, as seen in the equivalent strain energies but disparate reactivity of cyclopropane and cyclobutane. Here we show that electronic delocalisation is a key factor that operates alongside strain release to boost reactivity, significantly lowering the energy required for bond-breaking in cyclopropanes, cycloalkynes and cycloalkenes. Consideration of thermodynamic and delocalisation parameters explains the relative rates of reaction of molecules containing these functional groups, leading to a ‘hierarchy of delocalisation’ and a rule-of-thumb model that accurately predicts activation barriers. The implications of these principles are demonstrated in the context of the reactions of strained building blocks commonly encountered in total synthesis, medicinal chemistry, polymer science and bioconjugation.

Influence of High Pressure Sliding and Rotary Swaging on Creep Behavior of P92 Steel at 500 °C

High-pressure sliding (HPS) and rotary swaging (RS) at room temperature were used to form severely deformed microstructures in martensitic creep-resistant P92 steel. The deformed microstructures contained markedly different ratios of low- and high-angle grain boundaries (LAGBs/HAGBs). The application of the RS method, with an imposed equivalent strain of 1.4, led to the formation of a heterogeneous microstructure with a high number of LAGBs, while the HPS method, with an imposed equivalent strain of 7.8, led to the formation of a relatively homogeneous ultrafine-grained microstructure with a significant predominance of HAGBs. Microstructure analyses after creep testing showed that the microstructure of RS- and HPS-processed P92 steel is quite stable, but a slight coarsening of subgrains and grains during creep testing can be observed. Constant load tensile creep tests at 500 °C and initial stresses ranging from 300 to 900 MPa revealed that the specimens processed by HPS exhibited higher creep strength (slower minimum creep rate) and ductility compared to the coarse-grained and RS-processed P92 steel. However, the HPS-processed P92 steel also exhibited lower values of stress exponent n than the other investigated states of P92 steel. For this reason, the differences in minimum creep rates determined for different states decrease with decreasing values of applied stress, and at applied stresses lower than 500 MPa, the creep resistance of the RS-processed state is higher than the creep resistance of the HPS-processed state.

An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow cylinder at large strains. The constitutive equations comprise the yield criterion and its associated flow rule. The yield criterion is pressure-independent. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution is facilitated using the equivalent strain rate as an independent variable instead of the polar radius. As a result, it reduces to ordinary integrals. In the course of deriving the solution above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. A practical aspect of the solution is that it readily applies to the preliminary design of tube hydroforming processes.

Study on Unloading Relaxation Characteristics of Columnar Jointed Rock Masses Based on Displacement Back Analysis

We aim to understand the relaxation of columnar joint rock masses during the excavation process of the diversion tunnel of the Baihetan hydropower station. This paper inverts the deformation parameters of the relaxed columnar joint rock based on the displacement monitoring data, and introduces a relaxation factor to describe the deterioration degree of anisotropic parameters of the relaxed columnar jointed rock. The equivalent strain is proposed as the criterion of unloading relaxation and the threshold is also given. Based on the software Flac3d, a program for calculating anisotropic elastoplastic model is developed. The distribution of the relaxation zone of the diversion tunnel after excavation is simulated, and compared with the results of the acoustic detection to verify the correctness and rationality of the program, which can provide a necessary reference for the design and construction of hydropower projects.

A Study to Derive Equivalent Mechanical Properties of Porous Materials with Orthotropic Elasticity

The need for diverse materials has emerged as industry becomes more developed, and there is a need for materials with pores in various industries, including the energy storage field. However, there is difficulty in product design and development using the finite element method because the mechanical properties of a porous material are different from those of a base material due to the pores. Therefore, in this study, a Python program that can estimate the equivalent property of a material with pores was developed and its matching was verified through comparison with the measurement results. For high-efficiency calculation, the pores were assumed to be circular or elliptical, and they were also assumed to be equally distributed in each direction. The material with pores was assumed to be an orthotropic material, and its equivalent mechanical properties were calculated using the equivalent strain and equivalent stress by using the appropriate material property matrix. The material properties of a specimen with the simulated pores were measured using UTM, and the results were compared with the simulation results to confirm that the degree of matching achieved 6.4%. It is expected that this study will contribute to the design and development of a product in the industrial field.

The Central Strain Analytical Modeling and Analysis for the Plate Rolling Process

The strain after rolling plays an important role in the prediction of the microstructure and properties and plate deformation permeability. So it is necessary to establish a more accurate theoretical strain model for the rolling process. This paper studies the modeling method of the equivalent strain based on the upper bound principle and stream function method. The rolling deformation region is divided into three zones (inlet rigid zone, plastic zone, and outlet rigid zone) according to the kinematics. The boundary conditions of adjacent deformation zones are modified according to the characteristics of each deformation zone. A near-real kinematics admissible velocity field is established by the stream function method on this basis. The geometric boundary conditions of the deformation region are obtained. The deformation power, friction power and velocity discontinuous power are calculated according to the redefined geometric boundary conditions. On this basis, the generalized shear strain rate intensity is calculated according to the minimum energy principle. Finally, the equivalent strain model after rolling is obtained by integrating the generalized shear strain rate in time. The plate rolling experiments of AA1060 and the numerical simulations are carried out with different rolling reductions to verify the analytic model precision of the equivalent strain. The results show that the minimum and maximum relative equivalent strain deviation between the analytic model and the experiment is 0.52% and 9.96%, respectively. The numerical calculation and experimental results show that the model can accurately calculate the strain along the plate thickness. This model can provide an important reference for the rolling process setup and the microstructure and properties prediction.

Two-dimensional ferroelasticity in van der Waals β’-In2Se3

Two-dimensional (2D) materials exhibit remarkable mechanical properties, enabling their applications as flexible and stretchable ultrathin devices. As the origin of several extraordinary mechanical behaviors, ferroelasticity has also been predicted theoretically in 2D materials, but so far lacks experimental validation and investigation. Here, we present the experimental demonstration of 2D ferroelasticity in both exfoliated and chemical-vapor-deposited β’-In2Se3 down to few-layer thickness. We identify quantitatively 2D spontaneous strain originating from in-plane antiferroelectric distortion, using both atomic-resolution electron microscopy and in situ X-ray diffraction. The symmetry-equivalent strain orientations give rise to three domain variants separated by 60° and 120° domain walls (DWs). Mechanical switching between these ferroelastic domains is achieved under ≤0.5% external strain, demonstrating the feasibility to tailor the antiferroelectric polar structure as well as DW patterns through mechanical stimuli. The detailed domain switching mechanism through both DW propagation and domain nucleation is unraveled, and the effects of 3D stacking on such 2D ferroelasticity are also discussed. The observed 2D ferroelasticity here should be widely available in 2D materials with anisotropic lattice distortion, including the 1T’ transition metal dichalcogenides with Peierls distortion and 2D ferroelectrics such as the SnTe family, rendering tantalizing potential to tune 2D functionalities through strain or DW engineering.

Effects of Shear Deformation of Struts in Hexagonal Lattices on their Effective In-Plane Material Properties

Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.