In-plane Shear Stress Research Articles

Prediction of strength and fatigue life for 2D plain-woven high-alumina fiber reinforced alumina matrix composites under a complex in-plane stress state

This paper presents a strength criterion and fatigue life prediction method for 2D braided alumina matrix composites under a complex in-plane stress state. The static strength of the material was obtained by in-plane tensile, compression, and pure shear tests. Considering the difference between tensile and compressive properties of materials and the influence mechanism of in-plane tensile and shear coupling on material strength, a revised Hoffman strength theory was proposed. The predicted off-axis tensile strength is consistent with the test results, and the deviation is not more than 10%. Tensile fatigue tests were carried out with the off-axis angle θ=0°, 15°, 30°, 45°, the stress ratio R=0.1, and frequency f=10 Hz. The test results show that the fatigue life decreases with the increase of off-axis angle. Due to the in-plane shear stress component, the fatigue failure is gradually changed from fiber-dominated to fiber-matrix dominated mode. Based on a combination of the uniaxial tensile fatigue life curve, the Broutman-Sahu residual strength model, which is used to characterize the variation of the residual strength with the fatigue cycles, and the modified Hoffman strength theory, the paper proposes a fatigue life prediction model under complex in-plane loading conditions. The fatigue shear damage factor is defined to characterize the effect of the normal and shear stress interaction on fatigue life. The fatigue life prediction model is used to predict the fatigue life of specimens in the off-axis tensile fatigue tests. The predicted result agrees with the test result, and the deviation is within the 1-time life span. The results indicate that the proposed fatigue life prediction model can be used to predict the fatigue life of 2D braided alumina matrix composites under the complex in-plane stress condition with the given stress ratio, temperature, and fatigue load frequency.

Micromechanical Modeling of Unidirectional CFRP Composites with Proportional Stressing

In this paper, we present a computational micromechanical analysis of unidirectional (UD) carbon fiber-reinforced plastics (CFRPs) using representative volume elements (RVEs). The RVEs consist of randomly distributed fibers, matrix, and interfaces between the fibers and matrix. Periodic boundary conditions (PBCs) and proportional stressing are implemented to facilitate micromechanical analysis of the composites under controlled stress states. In particular, the failure mechanisms of the RVEs under combined transverse and in-plane shear stressing are investigated. The ratio of in-plane shear stress over transverse stress is kept constant during each simulation. By varying this ratio, the mechanical responses of composites under different stress states are systematically studied and the failure envelopes for different fiber volume fractions are extracted. We find the failure envelope converges as the fiber volume fraction increases. The framework developed in this study can be extended to different stress states allowing us to conveniently examine the failure criteria for UD CFRP composites comprehensively.

Molecular dynamics simulations of screw dislocation mobility in bcc Nb

The screw dislocation mobility in bcc Nb has been studied by molecular dynamics (MD) simulations at different strain rates and temperatures using an embedded-atom method (EAM) potential. Static properties of the screw dislocation, as determined with the EAM potential, are in agreement with previous density-functional-theory calculations. The elementary slip plane of the screw dislocation remains (110) for all studied strain rates (in the range 6.3 × 107–6.3 × 109 s−1) and temperatures (5 to 550 K). However, the consecutive cross-slip on different symmetry-equivalent (110) planes leads to an effective glide on (112) planes. It is demonstrated that the screw dislocation trajectories, velocities and waviness of the screw dislocation depend on the crystallographic indices, (110) or (112), of the maximum resolved shear stress plane. The waiting time for the start of the screw dislocation motion increases exponentially with decreasing strain rate, substantiating the necessity to apply in future accelerated MD techniques in order to compare with macroscopic stress-strain experiments.

Qualification of NSTX-U Inner TF Bundle Using Hi-Fidelity Models

The National Spherical Torus eXperiment Upgrade (NSTX-U) Recovery Project provides a national facility for the study of plasma confinement, heating, and current drive in a low-aspect-ratio, spherical torus configuration. For the NSTX-U Recovery Project, key system capabilities must be achieved in order to meet operational goals. The inner toroidal field (TF) bundle is part of the center stack with 36 pie-shaped wedges (TF inner legs) bonded into a cylindrical bundle. The inner bundle is connected to outer legs via flex straps, and an ohmic heating (OH) coil is wound around the inner TF bundle, with a layer of aquapour in between acting as a winding surface between TF-OH coils. The TF bundle for the Recovery Project underwent two expert reviews to gain an improved understanding of issues identified from the extent of condition and the magnet design verification and validation review; this was to ensure confidence in the ability of the TF-OH center stack assembly to meet physics requirements for operations. A hi-fidelity, finite element model was developed with appropriate detail for multiphysics analysis of the bundle and to provide a baseline model to use as a standard against which the allowable stresses were compared. The model was also used to understand mechanical behavior and to assess implications of hypothetical delamination to the machine operation. Normal tensile stress at the bundle stub was the result of a nonuniform resistive current distribution where a relatively cold region was formed when the TF coil was pulsed. The worst case occurred at the end of the pulse when the maximum temperature gradient was established at the bundle ends. The hot spot was in compression, and the cold region was in tension. The compressive stress, which had a maximum at the bundle stub, enhanced the insulation shear capability. The in-plane torsional shear stress peaked at the end corner of the inner leg outer diameter at end of flat top. The insulation tensile and shear stresses were extracted from the hi-fidelity model using orthotropic material properties derived from first principles, and these theoretical data were verified via material tests. Load path probes were used to quantify the redistribution of torsional loads between the bundle and the external load path for a hypothetical extreme delamination condition. The extent of possible delamination was limited to regions within the radius of the flex straps. There is no significant effect on the bundle inner leg copper stress. The differential movement between the flex straps in the hypothetical extreme delamination condition is far less than the toroidal gaps between them, so there is no risk of closing these electrical gaps between the bundle turns. There is thus no impact on machine operation or even hypothetical delamination to an extreme delamination beyond the simulation-predicted delamination boundary.

Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.

Phononic analyses of rectangular graphene and annular graphene under in-plane shear stress

In this work, the effects of in-plane shear stress on the thermal conductivities of two important kinds of graphene configurations (rectangular graphene and annular graphene) are investigated using molecular dynamics simulations. The various strain angles are set as θ = 0°, 3°, 5°, 10°, and 15° for rectangular graphene and θ = 0°, 3°, 5°, and 8° for annular graphene. A spectral energy density approach is applied to carry out phononic analyses of the two configurations under in-plane shear stress for the first time. It is found that for rectangular graphene, the thermal conductivity shows a significant decreasing trend from 239.6 to 79.1 W m−1 K−1 with the θ increasing from 0° to 15°. Besides, the application of shear stress can significantly widen the energy bands of branches, which indicates shorter phonon lifetimes. Further phononic analysis shows that most of the phonon scattering caused by in-plane shear stress emanates from the in-plane mode, which is an updated conclusion in this field. On the other hand, the thermal conductivity of annular graphene also shows a decreasing evolution with the increasing strain angles, but phonon transport in rectangular graphene is more susceptible to shear stress than in annular graphene due to a stronger phonon-boundary scattering in the latter configuration. In this work, the monotonically decreasing trends of the thermal conductivities of both graphene configurations with the increasing strain angle are different from the V-shape trend reported in the literature. Based on phononic analyses, it can be concluded that an abnormal increase of the thermal conductivities at a low shear stress can be attributed to the application of the AIREBO potential model in the literature.

Influence of uniaxial and biaxial pre-straining on the high cycle fatigue performance of DP590 steel

Present work aims to assess tensile and high cycle fatigue (HCF) performance of dual-phase (DP590) steel subjected to uniaxial and equi-biaxial pre-strain. Pre-strain increases material’s strength, reduces ductility and simultaneously enhances HCF performance, quantified by increased material’s tensile yield strength 12% & 21%, ultimate tensile strength 6% & 7%, endurance limit 11% & 18%, after 10% uniaxial and equi-biaxial pre-strain. The rotation of one maximum shear stress plane during uniaxial re-loading after equi-biaxial pre-strain results in increased fatigue life. Finite element analysis suggests an alteration in the location of deformation concentration zone during uniaxial fatigue cycling of equi-biaxial pre-strain material.

An approximate solution to the finite deformation of an elastic rectangular plate under static and dynamic transverse loadings

In the field of structure safety, the blast resistance of glazing is increasingly important. This problem could be simplified as a finite deformation rectangular plate under dynamic loading, whose traditional solution is still insufficient in accuracy. Based on von Kármán equations, this paper aims to offer an efficient and acceptable approximate solution. Two basic assumptions are adopted: a) the strain distribution along the principle direction of the mid-plane is uniform; b) the in-plane shear stress is ignored. The membrane stresses are expressed by the deflection of the plate, and then the von Kármán equations are de-coupled.Both static and dynamic solutions of current model are verified by finite element simulations, popularly used standards and experiment data. For the simply supported plates, the deflection and stresses predicted by current model are quite accurate. For the fully clamped plates, the deflection predicted is good, but the stress given has a big error, due to the lack of high order deflection modes. Besides, in predicting stresses, the effect of higher orders of deflection modes is discussed. It is confirmed that the accuracy of current approximate solution is sufficient to determine the maximum 1st principle stress of plates, and to give an efficient failure criterion of glazing under blast loading.

Persistent slip observed in TiZrNbHfTa: A body-centered high-entropy cubic alloy

Slip properties of TiZrNbHfTa were evaluated to obtain ψ–χ relationships, where χ is defined as the angle between the maximum shear stress plane and (1¯01). ψ is defined as the angle between the apparent slip plane and (1¯01). Bending tests were conducted with micrometer-sized cantilevers fabricated from a single grain with a focused ion beam. Slip bands appear to be straight on a micrometer length-scale, as for Fe–Si alloys, which suggests a persistent slip. However, the ψ–χ relationship indicated that ψ is nearly the same as χ, suggesting that there is no persistent slip. Detailed observations with an atomic force microscope confirm that cross-slipping is so frequent at a sub-micrometer length-scale that the slip bands appear to be straight and the maximum shear stress plane is observed on a micrometer length-scale. Here, TiZrNbHfTa shows abnormally frequent cross-slipping, which is a novel characteristic of high-entropy body-centered cubic alloys.

Influence of uniaxial and biaxial pre-straining on the low cycle fatigue performance of DP590 steel

The present work aims to examine the low cycle fatigue (LCF) behavior of dual-phase (DP590) steel subjected to different pre-straining (uniaxial and equi-biaxial) paths. The LCF tests reveal all specimens showed continuous cyclic softening throughout the fatigue life. However, the rate of cyclic softening is higher for the equi-biaxial pre-strain specimen. The rotation of one maximum shear stress plane during fatigue cycling after equi-biaxial pre-straining introduces non-proportional loading condition, thereby significantly reducing the fatigue life. The larger lattice rotation and in-grain misorientation due to the non-proportional loading is notable for the equi-biaxial pre-strain specimen.

A transversely hyperelastic constitutive model of flexible film composite

This paper presents a transversely hyperelastic constitutive model for predicting mechanical properties of flexible composites under unidirectional tension. A strain energy function which reflects the behavior of anisotropic elastic material is decomposed into three parts: matrix, fiber and fiber-matrix interaction. The fiber-matrix interaction was decomposed into in-plane shear stresses and out-of-plane shear stress, the in-plane shear stresses were related to the fiber elongation invariants, and the out-of-plane shear stress was related to the fiber elongation invariants and the matrix invariants. The fiber-matrix interaction considering shear factor was established. Based on fiber reinforced continuum mechanics, a transverse hyperelastic constitutive model including fiber, matrix and their interaction is developed. The transversely hyperelastic constitutive model is verified by the uniaxial tension tests. The constitutive model can be used to design the flexible structure of stratospheric airship.

Research on the Deformation Mechanism of Mining Roadway Stratiform Surrounding Rock with Nonuniform Stress Field

Aiming at the failure problems of mining roadway stratiform surrounding rock influenced by asymmetrical high stress, firstly, the rock instability conditions of different structural plane angles were summarized based on the mechanical model of rock joints and instability criterion. Secondly, stresses, plastic zone, and displacement of surrounding rock with different structural plane angles were calculated and analyzed with the theoretical calculation method or numerical simulation method, respectively. The distribution characteristics of plastic zone of surrounding rock under different influence factors are further studied, and the results show that the lateral pressure coefficient can change the size and shape of plastic zone at the same time. The damage mechanism was analyzed through the above study. Research studies show that the shear and tension failure area of plastic zone were directly determined by the maximum shear stress and the minimum principal stress. The effect of structure planes on stress has two sides, one to destroy the continuity and the other to strengthen discreteness and laddering nature. When the angle between maximum shear stress and structure plane increases, the extended mode and distribution pattern of plastic zone change substantially as well. The #15 haulage roadway is taken as engineering background, and the above research’s results are verified by the comprehensive analysis. The research results can enrich the butterfly plastic zone theory and provide the basis for roadway supporting design.

Exploration of subsequent yield surfaces through unit cell simulations

Subsequent yield surfaces of ductile solids, pre-strained in shear and/or tension, exhibit various characteristic features that depend on the proof strain used to detect yield. These features include kinematic hardening when the proof strain denoting yield is low, isotropic hardening when it is high, formation of a ‘nose’ in the loading direction and flattening of the rear part of the yield surface. With the aid of a computational homogenisation scheme that allows application of arbitrary macro stress or macro deformation gradient to a unit cell, we show that essential features of the subsequent yield surfaces owe their origin to the extent of plasticity accumulated within the unit cell. For instance, a simple unit cell containing a spherical void, where the void serves to create a heterogenous distribution of plastic strain, suffices to computationally reproduce the experimentally observed features. Moreover, in contrast to experiments which generally allow plotting of the yield surface in a normal stress – shear stress plane, the computational scheme allows fuller exploration of the subsequent macro yield surface in the macro stress space. We find that what seems to be a translation and distortion of the yield surface in experiments, is actually most pronounced near some critical octahedral planes characterised by levels of triaxiality induced by the pre-straining process. The evolution of the yield surface in regions where the triaxiality is higher is considerably different. Moreover, as homogeneous yielding is approached with loading of the unit cell, the material seems to forget the nature of the pre-straining process and undergoes isotropic hardening.

Fatigue property analysis of U rib-to-crossbeam connections under heavy traffic vehicle load considering in-plane shear stress

In this study, the fatigue property of U rib-to-crossbeam connections in orthotropic steel bridge (OSB) crossbeams under heavy traffic vehicle load was investigated considering the effects of in-plane shear stress. The applicability of an improved structural stress (ISS) method was validated for the fatigue behavior analysis of nonwelded arc-shaped cutout regions in multiaxial stress states. Various types of fatigue testing specimens were compared for investigating the equivalent structural stress, fatigue crack initiation positions, and failure modes with the unified standards. Furthermore, the implications of OSB crossbeams and specified loading cases are discussed with respect to the improved method. The ISS method is proven to be applicable for analyzing the fatigue property of nonwelded arc-shaped cutout regions in OSB crossbeams. The used method is essential for gaining a reliable prediction of the most likely failure modes under a specific heavy traffic vehicle load. The evaluated results using the used method are proven to be accurate with a slighter standard deviation. We obtained the trend of equivalent structural stress in arc-shaped cutout regions and validated the crack initiation positions and propagation directions by comparing them with the fatigue testing results. The implications of crossbeam spans on fatigue property are less significant than the effects of crossbeams.

A study of earthquake-induced vibration on laminated composite plates using finite element method

This study presents the dynamic response of an eight-noded composite plate under earthquake excitation. Koyna earthquake excitation frequency is considered for the present study. Central displacement and stresses at various positions are studied extensively. Variation in response under different boundary conditions and varying geometric conditions are presented. The ply angle in a lamina and the number of layers in a plate are also varied to observe their effect on displacement and stress. In almost all the cases, 45° lamination shows maximum displacement response, whereas 0°/90° lamination scheme always shows maximum normal stress values. On the other hand, inplane shear gives maximum response whenever a − 45° layer is present. The effect of plan dimension on displacement is also presented here. The displacement response is maximum when the plate becomes square for both cross- and angle-ply laminations. The displacement response with change in total thickness of the plate is presented in this article. The response increases drastically as the plate becomes thinner for angle and cross-ply laminations. The plate becomes unstable as the side to thickness ratio increases beyond 50. The variation of stresses for cross- and angle-ply laminated plates across their layers is reported here with different boundary conditions. A very important observation made through this comparison as a 45° clamped laminated plate should be designed under transverse shear stress, whereas the simply supported plate should be designed under inplane shear stress.

Failure Analysis of Unconfined Brick Masonry with Experimental Verification

The survival of low rise unconfined masonry structure against earthquakes is very rare even due to low or moderate intensity events. To understand the failure mechanism and cracking pattern of unconfined masonry, a scaled specimen of four unconfined brick was analyzed using finite element software in conjunction with experimental verification. This study started by developing 3D finite element model of unconfined masonry subjected to in-plane loading. Bricks and joints were modeled discretely in the model, allowing for nonlinear deformation characteristics of the both materials. This model exhibits the local effect and is capable of displaying the behavior of masonry walls in which high local stresses and stress gradients are presented in the color contour diagram. The overall result of stress is presented using the von Mises (distortion energy method). The analysis of the model concluded that the unconfined brick masonry specimen structure generally fails along the brick joints, although in-plane shear stresses can cause cracks through the brick in the translation to tensile stress zone.

A convex fourth order yield function for orthotropic metal plasticity

Gotoh (1977) proposed the first fourth order polynomial yield function under plane stress states that could simultaneously represent both yield stress and r-value directional properties of orthotropic sheet metals. The parameter identification procedure of this model can result in unbalanced overall errors in the anisotropy description, and the convexity of this yield function is not guaranteed. In this regard, a direct method is proposed to uniquely determine the nine model parameters using four yield stress and three r-value measurements. Out of them, only three expressions are new, and the rest remain identical to the published version of Gotoh. However, it is necessary to check the convexity restrictions on the obtained model parameters. Therefore, model parameters of two dissimilar materials that violate these restrictions are accurately identified from the literature. And, an effective procedure to reestablish the yield function convexity using new bounds on equi-biaxial stress is suggested. In the second part, an inverse method for the identification of the yield function parameters is proposed. In this approach, seven nonlinear expressions are solved together to determine the nine parameters of the convex guaranteed Gotoh's yield function. The advantages and disadvantages of two methods are discussed in detail by comparing with the existing ones in recent literature. It is shown that both these methods are successful in representing the anisotropic behavior of both aluminum and steel experimental data's available in the literature. In addition, a new 3D extension of the Gotoh's yield function is suggested by introducing four additional parameters to capture the influence of out of plane shear stresses. When all the parameters are set to a unit value, the yield function exactly coincides with the 3D von-Mises yield function. Further, the direct approach is extended to account for distortional hardening behavior of fcc and bcc materials.

Examination of selected failure criteria with asymmetric shear stresses in the collapse analysis of laminated shells

The paper is concerned with failure analysis of composite shells performed with the usage of the nonlinear 6-parameter shell theory with drilling rotation degree of freedom. This special theory embodies naturally unlimited translations and rotations and is suitable for analysis of irregular shells for instance with various, particularly orthogonal, intersections. The presence of the drilling rotation is inherently accompanied with asymmetry of in-plane shear stresses and strains which must be taken into account in the composite failure criteria. In the paper in general two failure measures are applied: Hashin criterion and Tsai-Wu criterion which are appropriately modified to accommodate the stress asymmetry. It is shown, that depending on the used failure criterion, it is possible to obtain slightly different damage zones and values of the first ply failure and ultimate load. These values are compared with those obtained experimentally.

A unified approach to shear and torsion in reinforced concrete

Reinforced concrete (RC) beams can be subjected to a complex combination of shear forces (V), torsional moments (T), flexural moments (M) and axial loads (N). This paper proposes a unified approach for the analysis of these elements. An existing model for the analysis of orthogonally reinforced concrete membrane elements subjected to in-plane shear and normal stresses is generalized to apply to the case of beams subjected to the complex loading. The combination of V and T can be critical. Torsion is modelled using the hollow-tube analogy. A direct equation for the calculation of the thickness of the equivalent hollow tube is proposed, and the shear stresses caused by V and T are combined using a simple approach. The development and the evaluation of the model are described. The calculations of the model are compared to experimental data from 350 beams subjected to various combinations of stress-resultants and to the calculations of the ACI and the CSA codes. The proposed model provides the most favorable results. It is also shown that it can accurately model the interaction between V and T. The proposed model provides a unified treatment of shear in beams subjected to complex stress-resultants and in thin membrane elements subjected to in-plane stresses.

Shear friction capacity of self-consolidating concrete

Abstract An experimental research was developed to evaluate shear transfer in self-consolidating. Three concrete mixes were prepared, one conventional and two self-consolidating, differing on the proportion of the coarse and fine aggregate used. Nine push-off specimens, containing steel reinforcement passing through the shear plane, were tested, to evaluate the ultimate shear stress and shear plane displacements. Shear strength of self-consolidating concrete specimens were higher than conventionally vibrated concrete. The experimental results were compared to the shear strength estimated by literature and code based equations, yielding conservative results of these equations for both types of concrete, especially the models that disregard the compressive strength of concretes.