Pure Shear Loading Research Articles

Prediction of the initial thickness of shear band localization based on a reduced strain gradient theory

Plastic flow localization in ductile materials subjected to pure shear loading and uniaxial tension is investigated respectively in this paper using a reduced strain gradient theory, which consists of the couple-stress (CS) strain gradient theory proposed by Fleck and Hutchinson (1993) and the strain gradient hardening (softening) law (C–W) proposed by Chen and Wang (2000). Unlike the classical plasticity framework, the initial thickness of the shear band and the strain rate distribution in both cases are predicted analytically using a bifurcation analysis. It shows that the strain rate is obviously non-uniform inside the shear band and reaches a maximum at the center of the shear band. The initial thickness of the shear band depends on not only the material intrinsic length l cs but also the material constants, such as the yield strength, ultimate tension strength, the linear hardening and softening shear moduli. Specially, in the uniaxial tension case, the most possible tilt angle of shear band localization is consistent qualitatively with the existing experimental observations. The results in this paper should be useful for engineers to predict the details of material failures due to plastic flow localization.

Buckling analysis of Reissner–Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method

Buckling study of plates subjected to uniformly uniaxial, biaxial in-plane compression and pure shear loads using an efficient novel meshfree method is presented in this paper. The moving Kriging (MK) interpolation technique satisfying the Kronecker delta function property is employed to construct the shape functions. To allow for the effect of transverse shear deformation on thick plates, the first-order Reissner–Mindlin plate theory (FSDT) is adopted. The new formulation enables us to eliminate shear-locking demonstrated by various numerical examples involving both thin and moderately thick plates. It is found that the results achieved by the present approach match well with those obtained by other existing numerical approaches and analytical solutions, which illustrates the applicability, the effectiveness and the accuracy of the method.

Failure assessment of notched polycrystalline graphite under tensile-shear loading

The fracture load and the fracture initiation angle were experimentally measured for a V-notched specimen made of polycrystalline graphite under combined tensile-shear loading. The experimental results were obtained for several specimens with different notch angles and various notch tip radii. The experimental observations showed that for a constant notch tip radius, the fracture load in pure tensile loading conditions decreases as the notch angle increases. Moreover, for a constant notch angle, as the notch tip radius increases the fracture load in graphite specimens enhances in the entire domain between pure tensile and pure shear loading conditions. A recently developed failure criterion was then used to estimate the experimental values of the notch fracture resistance and the fracture initiation angle for the tested graphite specimens. The experimental results could be estimated very well by using the results of the proposed criterion.

Research Advances on Tension Buckling Behaviour of Aerospace Structures: A Review

This paper reviews most of the research done in the field of tensile buckling characteristics pertaining to aerospace structural elements with special attention to local buckling and parametric excitation due to periodic loading on plate and shell elements. The concepts of buckling in aerospace structures appear as the result of the application of a global compressive applied load or shear load. A less usual situation is the case, in which a global tensile stress creates buckling instability and the formation of complex spatial buckling pattern. In contrast to the case of a pure compression or shear load, here the applied macroscopic load has no compressive component and is thus globally stabilizing. The instability stems from a local compressive stress induced by the presence of a defect, such as a crack or a hole, due to partial or non-uniform applied load at the far end. This is referred to as tensile buckling. This paper discusses all aspects of tensile buckling, theoretical and experimental. Its far reaching applications causing local instability in aerospace structural components are discussed. The important effects on dynamic stability behaviour under locally induced periodic compression have been identified and influences of various parameters are discussed. Experimental results on simple and combination resonance characteristics on plate structures due to tensile buckling effects are elaborated.

Fracture mechanics model of a fault termination zone

AbstractA fault termination zone from Middle Eocene chalks near Beer Sheva, Israel, is analysed via a fracture mechanical technique. The zone consists of the end of the primary fault, three secondary faults and joints associated with these structures. We demonstrate that the shape of the first secondary fault can be obtained from theoretical fracture mechanical calculations. This shape also enables us to obtain the set of conditions which induced the observed structures. The technique reveals the relative importance of the different variables that appear in the theory. The most significant parameters in determining the shape of the first secondary fault are the vertical dimension of the primary fault, the ratio of the two horizontal differential stresses and the initiation angle of the secondary fault. Results indicate that the fault termination zone was created under an almost pure shear load. The true lateral displacement of the primary fault is unknown; hence, exact calculation of the stresses leading to the secondary fault is hardly possible. However, an estimation, based on a partial conversion of this displacement to an uplift, yieldsσ1andσ3values at initiation of between 3.8 and 7.6 MPa and 3.65 and 7.3 MPa, respectively.

The Refined Theory of One-Dimensional Quasi-Crystals in Thick Plate Structures

For one-dimensional quasi-crystals, the refined theory of thick plates is explicitly established from the general solution of quasi-crystals and the Luré method without employing ad hoc stress or deformation assumptions. For a homogeneous plate, the exact equations and solutions are derived, which consist of three parts: the biharmonic part, the shear part, and the transcendental part. For a nonhomogeneous plate, the exact governing differential equations and solutions under pure normal loadings and pure shear loadings, respectively, are obtained directly from the refined plate theory. In an illustrative example, explicit expressions of analytical solutions are obtained for torsion of a rectangular quasi-crystal plate.

A Continuum-Based Cyclic Plasticity Model for AZ31B Magnesium Alloy under Proportional loading

This study investigates the cyclic plasticity of AZ31B extrusion under axial and shear loading conditions and presents a continuum-based cyclic plasticity model for the anisotropic behaviour of magnesium. An anisotropic form of the Armstrong-Frederick plasticity model is presented. It is shown that the model can independently produce hysteresis loops under pure axial and pure shear loading conditions. Two different parameters for loading and unloading were considered to address the asymmetric shape of the axial hysteresis loops. The model is evaluated by considering the cyclic stress-strain response of AZ31B extrusion in uniaxial and multiaxial loading cases. Stress amplitude, plastic energy and total energy densities are calculated using the proposed model and are compared with experimental results showing a good agreement.

Ultimate Load Analysis of RC Beam under Combined Action of Axial, Bending and Shear Loading

Based on Timoshenko beam theory, a section model for the ultimate load analysis of RC beam under combined action of axial force, bending and shear force is presented in this paper. Especially, the transverse deformation is considered with the appearance of diagonal cracks. The validity of the model is established by comparing its results with several tests. These simulations include ultimate bending moments of pure bending tests and ultimate shear loads with different shear-span ratios. The analytical results show excellent agreement with experimental data.

Computational Analysis of the AFM Specimen on Mixed-Mode II and III Fracture

Some results of 3D finite element analyses of the all fracture modes (AFM) specimen on mixed-mode II and III fracture are presented in this paper. The computational fracture analysis is based on the calculation of separated strain energy release rates (SERRs) along the crack front by the modified virtual crack closure integral (MVCCI)-method and the commercially available FE-code ANSYS. Calculation results show that under pure in-plane shear loading (mode II), not only the mode II, but also the mode III loading conditions, are generated owing to the Poission’s ratio effects. Similarly, under pure out-of-plane shear loading (mode III), besides the mode III, the mode II loading conditions are induced due to the global deformation. Nevertheless, once in-plane and out-of-plane shear loadings are superimposed, the fracture behavior appears more complex. Further discussion is given associate with some previous study.

Stress concentration around a hole in a radially inhomogeneous plate

The stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young’s modulus and Poisson’s ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson’s ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young’s modulus is obtained for the stress concentration factor in pure shear loading.

Improvement of the shear fixation stability of intramedullary nailing

Background The healing outcome of long bone fractures is strongly influenced by the mechanical environment. High interfragmentary movement at the fracture site is detrimental to the fracture healing process. Long bone fractures stabilized with thin intramedullary nails commonly used for unreamed intramedullary nailing might be very flexible in shear direction and therefore critical for the fracture healing outcome. The aims of this study were to simulate the shear interfragmentary movement during gait for a human tibia treated with intramedullary nailing and to investigate if this movement could be lowered by implant design modifications. Methods The shear movement was calculated with a 3D finite element model based on computer tomograph images of a cadaver bone–implant complex of a transverse tibia fracture treated with a Stryker T2 Standard Tibial Nail. This model was validated through in vitro test results under pure shear, axial, bending and torsional loading. Findings High shear movements of approximately 4 mm were calculated during gait. These shear movements could be reduced by approximately 30% either by implant modifications or the use of a 1 mm thicker nail. Combining the implant modifications with a 1 mm thicker nail, the shear movements could be reduced by 54%. Interpretation The increase of the fixation stiffness by using an implant material with a high Young's modulus in combination with an angle–stable nail–screw fixation helps to reduce the shear movement during gait and possibly to lower the risk of a prolonged healing time with unreamed intramedullary nailing.

A continuum based microstructure model of inhomogeneous hardening and recovery as a pre-stage of recrystallization nucleation

AbstractStarting from the fundamental relation between the diffusion flux of point defects (vacancies, interstitials) and the gradient of the diffusion potential the diffusion equation is set up and applied to the calculation of the concentrations of both types of point defects. Thereby, all possible sources and sinks and their mutual effects are taken into consideration. These equations are coupled with the equations for the temporal derivatives of dislocation density, porosity, pore size and temperature. For the close-up region of spherical inhomogeneities (pores, hard inclusions) and a grain boundary this system of six partial differential equations is solved numerically. For simplicity a one dimensional model in space is used and uniaxial tension or pure shear load is assumed. Hardening and the simultaneous recovery are characterized by the local and temporal development of the point defect concentrations and especially of the dislocation density, which is proportional to the intrinsic strain energy. The gradients of both strain energy and lattice rotation determine the formation and growth of recrystallization nuclei. It is the aim of this work to present a new mathematical model and also to give a perceptual general view on the concerted action of the fundamental physical processes, which necessarily lead to hardening, recovery (softening) and recrystallization nucleation. Moreover it seems to be a basis of a future general theory of microstructure changes.

Development of interlocking mechanism for shear transfer in composite floor

Semi-pre-cast floor slab (called half slab in Malaysia) has been used widely in different parts of the world. It consists of a reinforced concrete pre-cast layer that acts initially as a formwork connected in situ with another concrete layer using shear connectors. Steel reinforcement (shear link, studs and/or steel truss) is commonly used to transfer the horizontal shear between the two composite layers. Longitudinal shear failure is the most common type of failure in the composite floor slab. This paper proposes a new system to transfer the horizontal shear between the interfaces of the pre-cast and cast in situ layers of concrete slab. The proposed system implements an interlocking concept and does not require any shear reinforcement. The composite floor slab used to illustrate the interlocking concept consists of a pre-cast inverted ferrocement layer interconnected with the cast in situ brick–mortar layer. The effectiveness of the interlocking mechanism in transferring the stresses developed due to the applied load is investigated. Eleven composite slab specimens having different shear connectors between the two layers were cast and tested under pure shear loading (push-off test). In the tested specimens, different interlocking mechanisms, continuous truss shear connectors and no connectivity between the two layers were used to connect the layers of slabs. The results indicate that the interlocking mechanism proposed is, as effective as, the steel trusses in resisting shear stresses and can be used to replace the steel trusses, which in turn will reduce the cost of the composite slab.

Loading Mixity on the Interfacial Failure Mode in Lead-Free Solder Joint

Abstract In this paper, single solder joints (SSJs) were subjected to moderate speed loading (5 mm/s) in different directions, from pure tensile mixity mode to pure shear. Fracture surfaces from different loading directions were examined both experimentally and numerically. The intermetallic compound (IMC) is formed between the solder alloy and the Cu pad, and the failure typically occurs at or near the solder/IMC/Cu interfaces of the board side. Pure tensile loading typically leads to interfacial fracture along the IMC/Cu interface. Mixity mode loading usually results in a mixture of interfacial and cohesive failure with damage propagating in a zigzag fashion between the solder/IMC interface and the solder alloy. Loading with higher shear component tends to result in more cohesive failure of the solder alloy near the solder/IMC interface. Under pure shear loading, failure is almost always cohesive within the solder alloy near the solder/IMC interface.

Emission of dislocations from nanovoids under combined loading

Among all directions available for dislocation emission from the surface of a cylindrical circular void, the direction of the most likely emission is determined. It is shown that this direction is different from the direction of the maximum shear stress at the surface of the void due to the applied loading. The critical stress and the direction of the dislocation emission are determined for circular nanovoids under remote uniaxial, pure shear, and arbitrary biaxial loading. The analysis includes effects of the loading orientation relative to the discrete slip plane orientation. It is shown that dislocations are emitted more readily from larger nanovoids and that wider dislocations are emitted under lower applied stress than narrow dislocations. Different mechanisms, under much lower stress, operate for growth of the micron-size voids.

Through-thickness strength measurements using Arcan’s method

This paper presents results obtained from the experimental study on the behaviour of glass/epoxy butterfly-shaped specimens tested under pure shear and biaxial loadings using an Arcan device. Notch-to-notch longitudinally and perpendicularly oriented fibre specimens, respectively referred to as Mat31 and Mat32 ones have been tested with different loading angles ranging from 0° to 90°. The fracture mode was more or less repetitive for Mat31 specimens whereas it depended on the loading direction for Mat32 type, for which the number of cracks and the obliqueness relative to the notch-to-notch line, decreased as the test angle increased. The comparison of failure envelopes has demonstrated that Mat31 specimens are much more resistant whatever the loading angle. However, strengths at failure of Mat32 type are in good agreement with Hashin’s failure criterion, for pure shear tests up to 30° loading angles. Mat31 specimens’ failure stresses were overestimated by the criterion, although similarities in trends were noticed.

Shear buckling in foam-filled web core sandwich panels using a Pasternak foundation model

Web core panels, foam-filled sandwich panels with interior webs, are a structurally efficient option for transverse load bearing applications. In web core panels, the interaction between the webs and core material can have a substantial impact on web shear buckling strength and is a key element of lightweight structural design. The present work is an investigation of web buckling behavior in web core panels under a distributed load. To solve this problem, web shear buckling was analyzed for the case of pure shear loading with foam support, and this analytic model was extended to the case of panels with a transverse distributed load. The webs are modeled as simply supported plates resting on a Pasternak elastic foundation. To that end, a buckling model for plates on a Pasternak foundation is presented, along with closed-form approximations of the solution for square and infinitely long plates. An accurate model for the foundation constants is developed using energy methods. Applicability of the plate buckling model to web core panels with transverse loads is presented via a finite element study. In panels, the slenderness and spacing of the webs have a slight effect on the boundary conditions between the webs and face sheets. The effect is relatively small, however, and the model presented in this work underpredicts buckling strength by less than 25%. The model in this work is thus a reasonable approach to the practical design of web core panels.

Self-piercing riveting connections using aluminium rivets

The development of the self-piercing riveting (SPR) technology in recent years has broadened the application of the technology in the automobile industry. However, the SPR process currently utilises high-strength steel rivets; and the combination between steel rivets with an aluminium car body makes recycling a challenge. The possibility of replacing a steel self-piercing rivet with an aluminium one has thus been raised as an interesting topic. Within this framework, the objective of the present paper is to provide an experimental database on the riveting process using an aluminium self-piercing rivet. An experimental programme has been carried out, where two similar sheets in aluminium alloy 6060 in three different tempers (temper W, temper T4, and temper T6) have been joined by using a self-piercing rivet in three different alloys, i.e. 6082-T6, 7108-T5, and 7278-T6. The influence of the die shape on the SPR of aluminium sheets using aluminium rivets was also considered. Conventional rivets and dies according to the Boellhoff standards were employed. The test results were exploited in terms of the riveting force–displacement curves and cross-sectional geometries of the riveted joints. The test data were also used to validate a 2D-axisymmetric model, which was originally developed at SIMLab for modelling the riveting process using a steel rivet. Finally, the mechanical behaviour of a riveted connection using an aluminium rivet under quasi-static loading conditions (i.e. combined pure shear and pure opening loads) was experimentally studied and compared with corresponding tests using a steel rivet in terms of force–displacement curves.

Computational Fracture Analyses of a Compact Tension Shear (CTS) Specimen with an Inclined Crack Front

In this paper some results of 3D-finite element analyses of a modified CTS-specimen(MCTS) with an inclined crack front are presented. It will be shown, that through the inclination of the crack front, even under pure in-plane shear loading of the specimen, mixed-mode II and III loading conditions can be generated along the straight inclined crack front. Furthermore a superposition of all fracture modes I, II and III can be generated, if this MCTS-specimen is subject to an in-plane tension/shear loading. The computational fracture analysis is based on the calculation of separated energy release rates GI, GII and GIII along the crack front by the numerically highly effective modified virtual crack closure integral(MVCCI)-method and for the finite element(FE)-modelling the commercially available FE-code ANSYS is utilized.

Influence of adhesive bond line thickness on joint strength

While the geometry of aerospace assemblies is carefully controlled, for many industrial applications such as marine structures bond line thickness can vary significantly. In this study epoxy adhesive joints of different thicknesses between aluminium substrates have been characterized using physico-chemical analyses (differential scanning calorimetry, DSC; dynamic mechanical analysis, DMA; spectroscopy), nano-indentation and mechanical testing. Thermal analyses indicated no influence of thickness on structure. Nano-indentation revealed no evidence of an interphase at the metal/epoxy interface, nor any change in modulus for different thicknesses, though Raman spectroscopy suggested there may be slight variations in composition close to the substrates. However, mechanical testing using the modified Arcan fixture indicated a significant drop in strength and failure strain under pure tension and a smaller reduction for tension/shear and pure shear loads as thickness increased. Examination of sections through joints did not indicate any physical reason for this, but numerical analysis of the stress state revealed larger stress concentration factors for tensile loading in thick joints, which may explain the thickness effect. It is recommended that joint thickness should be kept below 0.8 mm to avoid obtaining artificially low values with the Arcan test.