Principal Shear Strain Research Articles

Estimation of crustal strain in Kashmir Himalayan region of north India using continuous GPS measurements

Global positioning system (GPS) measurements of crustal deformation provide insight into the crustal plate velocity and strain rate variation in the actively deforming Earth's crust. GPS measurements in the Kashmir Himalaya indicate that most of the crustal motion between the Indian Plate and southern China is accommodated along the Himalayan arc, resulting in the accumulation of crustal strain and locking of the Main Himalayan Thrust (MHT). Here, we present geodetically estimated spatial and temporal crustal strain rates in the Kashmir Himalaya from GPS measurements to understand the nature of crustal deformation. We processed and analysed GPS data from 21 sites across Kashmir Himalaya along with several IGS sites. We find that the average deformation rate of the GPS sites in Kashmir Himalaya with reference to the Indian Plate range between 2.8 and 15.5 ± 1 mm/year. The GPS results illustrate that the strain rate field is dominated by a compression component with its rate as 7.2 × 10−8 strain/year and the maximum shear strain, γmax, of 1.9 × 10−7 strain/year. The earthquake focal mechanisms suggest that earthquake activity in the Kashmir Himalaya is predominantly manifested in the form of thrust motion. The maximum principal shear strain value reflects that the Kashmir Himalaya is under NE–SW compressional regime. The spatial distribution of crustal strain indicates that the region north‐east of Kashmir Valley is accumulating maximum strain, resulting in the stress build‐up and could be the region of a future large earthquake.

Post-Forming Limits of Carbon Fibre Reinforced Thermoplastic Tubular Structures in a Rotary Draw Bending Process

This paper presents the post-forming limits of polyamide 6 carbon (CF/PA6) thermoplastic tubes to facilitate design and process optimisation of bent tubular CF/PA6 part manufacturing. Straight CF/PA6 tubes can be post-formed using rotary draw bending at elevated temperature to achieve desired curvatures. Forming limits of the tubes are predicted based on their winding angles, tube geometry, and bending radius, presented as the relation between tube winding angle and bending ratio. Additionally, the corresponding principal shear strain limits are derived from the winding angle limits and tube axial strains. Three sets of CF/PA6 tubes with the configurations of [±30°]4, [±45°]4, and [±60°]4 are heated to 220 °C and post-formed to a bending angle of 90° with a bending ratio of 2. Micro computed tomography imaging is performed to analyse tube geometry after forming to identify forming and failure modes for tubes beyond the forming limits.

主せん断ひずみエネルギーによる板材の成形限界の予測

主せん断ひずみエネルギーによる板材の成形限界の予測

主せん断ひずみエネルギーによる成形限界の評価

主せん断ひずみエネルギーによる成形限界の評価

Design criteria for electrochemical shock resistant battery electrodes

Mechanical degradation of electrode active materials (“electrochemical shock”) contributes to impedance growth of battery electrodes, but relatively few design criteria have been developed to mitigate fracture. Using micromechanical models and in situ acoustic emission experiments, we demonstrate and explain C-rate independent electrochemical shock in polycrystalline electrode materials with anisotropic Vegard coefficients. We conclude that minimizing the principal shear strain, rather than minimizing net volume change as previously suggested, is an important new design criterion for crystal chemical engineering of electrode materials for mechanical reliability. Polycrystalline particles of anisotropic Li-storage materials should be synthesized with primary crystallite sizes smaller than a material-specific critical size to avoid fracture along grain boundaries. Finally, we revise the electrochemical shock map construction to incorporate the material-specific critical microstructure feature sizes for C-rate independent electrochemical shock mechanisms, providing a simple tool for designing long-lived battery electrodes.

Plastic Anisotropy of A2024BE-T6 and O Aluminum Alloys

Multiaxial stress tests were carried out on thin-walled cylindrical specimens of the A2024BE-T6 alloy aged at 120°C for 1 hr and the A2024BE-O alloy fully annealed at 495°C for 1hr. The shear strength of these alloys is much lower than the tensile one, and the equi-strain surfaces in the tension-torsion stress field lie within Tresca's criterion. Planar anisotropy was determined from two types of multiaxial stress tests by means of the combined loading of axial load, internal pressure and torsion, referred to as “off-axis tension test” and “off-axis torsion test”. The degree of anisotropy is expressed by using two different measures : one is the proof stress and the other is the angle deviation between the directions of the principal stress (or principal shear stress) and principal strain increment (or principal shear strain increment). The A2024BE-T6 alloy exhibits more severe anisotropy than the A2024BE-O alloy and both alloys reveal more severe anisotropy in off-axis tension test than in off-axis torsion test. The plastic deformation behavior can be analyzed precisely by the constitutive equation derived from the anisotropic yield function, hardening law and associated flow rule.

予ひずみを受けた軟鋼の多軸塑性挙動と６次後続降伏関数による解析

The subsequent yield function previously proposed by one of the authors is modified by introducing the fourth rank tensor of anisotropic moduli. This yield function accounts for the effects of the third deviatoric stress invariant and anisotropy and the Bauschinger effect. Multiaxial loading tests are carried out on tubular specimens of mild steel subjected to various amounts of torsional prestrain. Two modes of loading are used to assess the theoretical predictions: one is the combined tension- torsion and the other is off-axis torsion by means of the combined loading of compression, internal pressure and torsion. The equi-strain loci and strain behavior are examined as a function of prestrain at three levels of offset strain ranging from 0.002% to 2.0%. In the tension-torsion stress field, the equi-strain locus specified by a 0.002% offset forms a nose in the prestress direction and flattens on the opposite side. The locus expands with increasing offset strain, so that both the sharpness of nose and the degree of flattening decrease. The deviation between the directions of the principal shear stress and principal shear strain increment is determined from the off-axis torsion test. It rises to a maximum value with a change in the principal shear stress direction and then decreases. The maximum deviation is larger when a smaller offset strain is used, and it increases as the prestrain becomes larger. Such behavioral characteristics can be expressed precisely by the constitutive equation derived from the proposed yield function, hardening law and associated flow rule.

Off-Axis Torsion Tests on Tubular Specimens of Steel

In order to analyze the anisotropic hardening behavior of metals, an off-axis torsion test by combined loading is developed. In this test, the maximum shear stress direction φ can be changed from 0 deg to 90 deg while the ratio of maximum and minimum principal stresses is kept at −1. With increasing angle φ, the yield stress of the torsional-prestrained steel decreases; the difference between the directions of the maximum shear stress and principal shear strain increment rises to a maximum value and then decreases. It is experimentally verified that anisotropy is more severe when a smaller offset strain is used in defining the yield stress.

ｏｆｆ‐ａｘｉｓねじり試験による軟鋼の加工硬化，異方性およびバウシンガ効果の測定

When metallic materials are plastically deformed, the physical effects which are listed as work hardening, the development of anisotropy and the Bauschinger effect occur. In order to measure these effects off-axis torsion test by the combined loading is developed. In this test the principal shear stress direction φ can be changed from 0° to 90° while the ratio of maximum and minimum principal stresses is kept-1. Experiments were carried out on tubular specimens of fully annealed and torsional-prestrained mild steels, and the yield loci and strain behavior were examined at three offset levels. The yield stress of the prestrained steel decreases with increasing angle φ. The difference between the directions of the principal shear stress and principal shear strain increment rises to a maximum value and then decreases. The occurrence of this maximum difference corresponds to the angle where the slope of the tangent to the yield locus is steepest. These behaviors strongly depend on the offset value used in defining the yield stress, and severe anisotropy appears when the small offset strain value is used. It is shown that the proposed off-axis torsion test is a very useful method for analyzing the anisotropic hardening behavior of materials.

Character of strengthening of an initially orthotropic material when subjected to simple and complex loadings. Communication 3: Experimental study of mechanical anisotropy

The results of an investigation into plastic deformation of titanium alloy with initially anisotropic elastic mechanical characteristics are presented. The limit of applicability of classical plasticity theories for complex loadings is determined. A rating dependence is plotted in generalized coordinates: principal tangential stress and principal shear strain.

Deformation anisotropy of β-Sn crystals by microindenter

When a Vickers indenter is pressed into a surface of tin crystals, plastic strain below the impression distributes in a butterfly-like shape with open wings. The direction of principal shear strain changes greatly at regions under the impression toward the piled-up or the sunk-in surface. This finding suggests that the secondary slip system is activated following the primary slip system under the indenter, as it is penetrated. Observation using the etch-hillock technique supports the idea that dislocation substructure is formed just under the impression due to this mechanism.

Direct, Real-time Observation of Fatigue Crack Growth Behavior under Hi-Lo Two-step Loadings and Quantitative Analysis of Deformation near Crack Tip Using Image Processing Technique.

Fatigue crack growth tests under Hi-Lo two-step loadings were carried out on a 3% silicon iron in a scanning electron microscope, using the specially designed servo-hydraulic fatigue loading system. Fatigue crack growth behavior was discussed based on direct, real-time observation and microscopic quantitative analysis of principal shear strain distribution near the fatigue crack tip. which was obtained by a newly developed image processing technique. It was found that the delayed retardation behavior of crack growth occurred under Hi-Lo two-step loadings and the crack growth rate decreased as the frequency of crack branching increased. At the lowest growth rate, the interval of crack branching was found to be only about 4∼10μm. Principal shear strain distribution exhibited that the preferred slips occurred actively at not only the main crack tip but also the branched crack tips. Decentralization of the crack driving force may account for the retardation of crack growth rate.

Simulation of shear band formation in plane strain tension and compression using FEM

A phenomenological constitutive relation using the conventional J 2-flow isotropic hardening yield function as well as a threshold shear stress based yield function that governs a ‘directionally preferred plastic component’ of shear strain, developed by the authors in an earlier work, is used for the simulation of the shear band formation. The constitutive relation which is expressed as an explicit function of elastic constants, deviatoric stress state, direction of the principal shear strain and material flow stresses, is shown to be fully capable of capturing the formation of the shear band even under material hardening conditions and does not demand any prior knowledge of the orientation of the shear band. This dual yield constitutive relation is incorporated in an FEM procedure capable of handling large strains and rotations and a numerical simulation of a tensile and compressive deformation of a plane strain specimen is performed. It is demonstrated that the formation of the shear band can be captured more easily as a natural outcome of the simulation, without resorting to any instability criterion or ‘enriched’ elements that are usually employed in the contemporary procedures. Nevertheless, the usefulness of a ‘local instability criterion’ (Ortiz et al. (1987), Comp. Meth. Appl. Mech. Eng. 61, 189) is demonstrated in this study. The model is verified using the experimental data of Anand and Spitzig (1980, J. Mech. Phys. Solids 28, 113) and the agreement between the results of the simulation and the experimental data is found to be reasonably good.

Deformation of the cement mantle of tibial components following total knee arthroplasty: a laboratory study.

An in vitro model has been developed to measure in-plane strains of the cement mantle, sandwiched between the tibial component and the underlying cancellous bone following total knee arthroplasty. Maximal in-plane strains occurred in the cement mantle below the contact points between the femoral and tibial components. These strains were significantly reduced by increasing the thickness of the polyethylene and even more impressively by metal backing. Eccentric loading, by as little as 5 degrees, increased the strains in the loaded compartment by 26 per cent and decreased those in the unloaded compartment by 62 per cent. The addition of torsion to axial loading did not significantly alter the principal direct strains or the principal shear strains. Although surface-covering tibial components have been advocated, continuous support of the cortical rim did not appear to be important in reducing cement mantle strains. While other studies have emphasized the critical stresses that may occur in the polyethylene tibial components of total knee implants, this study highlights the potential for localized cement fatigue with improperly sized components or with eccentric loading.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

X-Ray Study on Plastic Deformation of Coarse Grained Aluminium under Tensile

Several studies have so far been reported on the distribution of elongation in individual grains of coarse grained aluminium specimen due to simple tension.In this study coarse grained flat aluminium specimens with grain sizes of about 2mm and 4mm were measured by the oscillating crystal method, specially using Cokα radiations for measurement of the six normal strains in random directions.From these measured strains and orientation of each crystal, longitudinal and lateral residual strains, principal residual strain, principal residual shear strain and the direction of principal maximum residual strains of individual grains were calculated based on the theory of elasticity.The experimental results obtained may be summarized as follows. The longitudinal as well as the lateral residual strains were in compression for smaller orientation function, and in tension for larger orientation function, their absolute values being proportional to the orientation function. Their principal maximum residual strains showed a similar tendency to the above longitudinal strains, while on the contrary their principal maximum residual shear strains showed an inverse trend. The angles between the direction of their principal maximum residual strain and longitudinal axis were larger for greater orientation function. These angles decreased with the increase of the applied strain. Both the defferences in their principal residual strains and their principal shear strains between the neighbouring grains were remarkable as the difference of orientation function increased.

Large Strain Creep of Rotating Cylinders

AbstractUsing the generally accepted assumptions of constant density, of equality of the ratios of principal shear stresses to the corresponding principal shear strain rates, and of existance of a relation between the significant strain rate and the significant stress, equations are developed for the strain rates, strains, and stresses of a rotating hollow cylinder made of an isotropic and homogeneous material which is subject to creep. The strains are considered large, requiring the use of finite‐strain theory. The application of the finite‐strain theory also permits the prediction of the time at which the cylinder will fail. The creep law ϵ = B σn is used in the derivation of the equations.