Pure Shear Conditions Research Articles

PERFORMANCE EVALUATION OF HYPERELASTIC MODELS FOR CARBON-BLACK–FILLED SBR VULCANIZATES

ABSTRACTThe performance of four recently developed hyperelastic material models (HM models) was evaluated by using stress–stretch relationships of filled styrene butadiene rubber vulcanizates with different contents of carbon black (CB) tested under uniaxial tension (UT), pure shear (PS), and equi-biaxial tensile (BT) conditions. The stress–stretch relationships for the PS and BT tests were obtained with a specially designed specimen having higher accuracy than those obtained with an ordinary specimen. The performances of the HM models were compared via the following three evaluations: (1) ability to reproduce the UT, PS, and BT tests; (2) ability to predict the PS and BT test results with material constants identified from the UT test; and (3) correlation between the identified material constants and CB contents. The evaluations based on a combination of the stress–stretch relationships with high accuracy and four recently developed HM models revealed that the HM model activates only the I1 term, which is the first invariant of the right Cauchy–Green tensor, exhibiting good reproducibility and predictability.

A Strain Rate Dependent Fracture Model of 7050 Aluminum Alloy

The purpose of this research is to predict fracture loci and fracture forming limit diagrams (FFLDs) considering strain rate for aluminum alloy 7050-T7451. A fracture model coupled Johnson-Cook plasticity model was proposed to investigate its strain rate effect. Furthermore, a hybrid experimental-numerical method was carried out to verify the strain rate-dependent fracture model by using fracture points of uniaxial tension, notched tension, flat-grooved tension, and pure shear specimens. The results show that the fracture points are in accordance with the fracture loci and FFLDs under different strain rates. The increasing strain rate decreases the FFLDs of aluminum alloy 7050-T7451. The difference of force-displacement responses under different strain rates is larger for notched tension and pure shear conditions.

Evaluation and improvement of macroscopic yield criteria of porous media having a Drucker-Prager matrix

A large number of analytical strength criteria have been developed for porous materials having a Drucker-Prager solid matrix by using different up-scaling methods. A number of representative exisitng criteria are selected and summarized. These criteria are first evaluated and compared both analytically and numerically with new FEM solutions obtained in this work. A wide variety of new numerical results are then provided from finite element simulations to enlarge the comparisons. In particular, the strength under the pure shear condition is discussed and studied in depth, either numerically and theoretically. Based on these comparisons, a new improvement of the prediction of pure shear strength is established. With this improvement, we derive a new macroscopic strength criterion for the porous materials with a Drucker-Prager type solid matrix. The new criterion is validated against those numerical solutions for a wide range of porosity and frictional coefficient. The special case of a porous material with a von Mises type solid matrix is also studied with a good validation.

CONSTRUCTION OF DEFORMATION DIAGRAMS OF CONCRETE UNDER SHEAR BASED ON THE AUTHOR'S THEORY OF ANISOTROPIC MATERIALS POWER RESISTANCE TO COMPRESSION AND DEFORMATION THEORY OF PLASTICITY

The Aim of this work was the construction of a concrete deformation diagrams under shear on the basis of two approaches: the theory of anisotropic materials force resistance in compression and deformation theory of plasticity with the use of state diagrams of concrete under tension and compression, obtained by the authors jointly with Acad. N.I. Karpenko earlier. For this purpose, in the framework of the first approach, the main computational expression of the author's model was written in the current deformations, which ultimately allowed to establish a relationship between the diagrams σb-εb, σbt-εbt and τb-γb and reveal the mechanics of destruction of concrete elements under compression. The second approach additionally takes into account the change in the coefficient of transverse deformations, µb, and shear modulus of deformations, Gb as the load increases, but does not take into account the presence of normal stresses affecting the stress-strain state. This approach recreates the conditions of pure shear, which is possible only theoretically, and in real designs is applicable with a certain degree of error. Nevertheless, both approaches provide almost identical data in the construction of diagrams «τb-γb», which differ from the experiment by no more than 13-15%. In this regard, they are recommended for implementation: the first-to perform engineering calculations «manually», the second-to develop computer programs that allow you to automate the calculation.

Pure Shear Strength of PVA Fiber Reinforced Concrete

Concrete is a compound which consists of binder with presence of water. The paper aims to investigate the influence of Poly Vinyl Alcohol (PVA) fiber on shear behaviour of concrete in structural element for which the conditions of pure shear established as an experiment without accompanying other stress components. The effect of PVA fiber with different dosages (0 - 0.3%) were analysed. The test was conducted to check failure in shear in an identified plane. Based on the test results of the investigation shear strength increased 20.78% and 43.18% for M20 and M50 grades of concrete respectively. The increment in dosage of fiber content reduces workability of fresh concrete. The empirical relationships have been established to calculate the values of shear strength for PVA fiber reinforced concrete in terms of fiber content.

Magnetic particle chains embedded in elastic polymer matrix under pure transverse shear and energy conversion

Abstract A model of structured Magneto-rheological Elastomer made of a soft matrix filled by magnetic particles was studied for energy harvesting, in pure shear condition. The particles were supposed to be aligned in a chain along which the magnetic field is applied and considering a shear strain applied in a plane perpendicularly to the chain. As the strain is applied and assuming the deformation is homogeneous and the particles remain aligned, both of the axis of their alignment and inter-distance between particles change, affecting their magnetic state. The aim of this work is to evaluate how far the magnetic induction variation induced by mechanical solicitation can be converted into electric signal. We firstly analyzed the magnetic susceptibility of a particle in the chain, and then derived an analytical expression for the composite permeability as a function of shear strain. FEM simulations taking into account the particle magnetic saturation was also performed to estimate the optimal conditions (magnetic field values, shear amplitude, etc.) maximizing the energy conversion potentials.

The dislocation behaviour and GND development in a nickel based superalloy during creep

In the current study, dislocation activity and storage during creep deformation in a nickel based superalloy (Waspaloy) were investigated, focussing on the storage of geometrically necessary (GND) and statistically stored (SSD) dislocations. Two methods of GND density calculation were used, namely, EBSD Hough Transformation and HR-EBSD Cross Correlation based methods. The storage of dislocations, including SSDs, was investigated by means of TEM imaging. Here, the concept of GND accumulation in soft and hard grains and the effect of neighbouring grain orientation on total dislocation density was examined. Furthermore, the influence of applied stress (below and above the yield stress of Waspaloy) during creep on deformation micro-mechanism and dislocation density was studied. It was demonstrated that soft grains provided pure shear conditions on at least two octahedral (111) slip systems for easy dislocation movement. This allowed dislocations to reach the grain boundary without significant geometrically necessary dislocation accumulation in the centre of the grain. Hence, the majority of the soft grains appeared to have minimum GND density in the centre of the grain with high GND accumulation in the vicinity of the grain boundaries. However, the values and width of accumulated GND depended on the surrounding grain orientations. Furthermore, it was shown that the hard grains were not favourably oriented for octahedral slip system activation leading to a grain rotation in order to activate any of the available slip systems. Eventually, (i) the hard grain resistance to deformation and (ii) neighbouring grain resistance for the hard grain reorientation caused high GND density on a number of octahedral (111) slip systems. The results also showed that during creep below the yield stress of Waspaloy (500 MPa/700 °C), the GND accumulation was relatively low due to the insufficient macroscopic stress level. However, the regions near grain boundaries showed high GND density. At 800 MPa/700 °C (above yield at this temperature), in addition to the movement of pre-existing dislocations (SSD and GND) at a higher mobility rate, large numbers of dislocations were generated and moved toward the grain boundaries. This resulted in a much higher GND density but narrower width of high intensity GNDs near the grain boundaries. It is concluded that although GND measurement by means of EBSD can provide great insight into dislocation accumulation and its behaviour, it is critical to consider SSD type which also contributes to the strain hardening of the material.

Cold-formed steel ledger-framed construction floor-to-wall connection behavior and strength

The objective of this paper is to investigate the moment-rotation behavior of floor-to-wall connections used in ledger-framed cold-formed steel building construction with full-scale experiments. Recently completed research employing full-scale shake table tests on a two-story ledger-framed cold-formed steel framed building utilizing oriented strand board (OSB) sheathed shear walls and floors exhibited beneficial lateral system response that exceeded predictions. One hypothesis is that the stiffness of the floor-to-wall connections, and the repetitive nature of this connection, provided beneficial semi-rigid frame response that augmented the designed shear walls. Monotonic and cyclic full-scale connections were tested and reported here to examine the connection strength and stiffness, so that this hypothesis may be explored further in the future. The test matrix is designed to evaluate the presence of OSB floor sheathing, applied moment/shear ratio of the joist, joist-to-ledger clip angle location (inside or outside of the joist section), presence of top and bottom screws connecting the joist and ledger flanges, and location of the joist relative to the studs. The results indicate how the connection details and loading conditions drive the moment-rotation response; in addition, several limit states not checked in current design were also observed. Current design for this connection assumes a pure shear condition governed by screw shear capacity. However, ledger-to-stud screw pull-out, ledger flange buckling, and stud web crippling limit states are all observed in the testing. Design methods to support strength predictions consistent with the observed limit states are developed and assessed. The testing provides needed characterization of cold-formed steel floor-to-wall performance and is augmented by improved design methods for this detail.

A Network Decomposition Model for Rubber-Like Materials Considering Topological Constraints

A molecular network constitutive model is proposed in this study. Based on the concept of molecular network decomposition, the molecular network was decomposed into a James–Guth 3-chain network model and an Arruda–Boyce 8-chain network model. Considering that the single molecular chain of rubber is constrained by the surrounding molecular networks, the 3-chain model and the 8-chain model were consequently modified using the tube theory. The proposed model contains four material parameters that were determined by fitting the uniaxial tensile test data from rubber-like materials, and the values of these parameters were utilized to determine the pure shear and the biaxial extension. The proposed model agrees well with the experimental data and can predict the test results of experiments performed under the conditions of pure shear and equi-biaxial deformation with acceptable accuracy.

Brittle failure of orthorhombic borides from first-principles simulations

The orthorhombic boride family $XM{\mathrm{B}}_{14}$, where $X$ and $M$ are metal atoms, have been of great interest in hard coating applications because of such novel properties as high thermal stability, low density, chemical stability, and a low friction coefficient. However, the brittle failure of orthorhombic borides limits their mechanical stability under working environments and prevents their extended engineering applications. To provide guidelines of improving their stability, we employed density functional theory (DFT) to examine the bonding character and mechanical response of $XM{\mathrm{B}}_{14}$ under pure shear, biaxial shear, and tensile loading conditions. Two typical $XM{\mathrm{B}}_{14}$ compounds, ${\mathrm{AlLiB}}_{14}$ and $\mathrm{A}{\mathrm{l}}_{0.75}\mathrm{M}{\mathrm{g}}_{0.78}{\mathrm{B}}_{14}$, were examined to illustrate the effects of intrinsic metal vacancies. We find that the ideal strength for ${\mathrm{AlLiB}}_{14}$ is higher than that for $\mathrm{A}{\mathrm{l}}_{0.75}\mathrm{M}{\mathrm{g}}_{0.75}{\mathrm{B}}_{14}$, suggesting that ${\mathrm{AlLiB}}_{14}$ is intrinsically stronger than $\mathrm{A}{\mathrm{l}}_{0.75}\mathrm{M}{\mathrm{g}}_{0.75}{\mathrm{B}}_{14}$. The failure mechanism of both ${\mathrm{AlLiB}}_{14}$ and $\mathrm{A}{\mathrm{l}}_{0.75}\mathrm{M}{\mathrm{g}}_{0.78}{\mathrm{B}}_{14}$ arises from deconstructing ${\mathrm{B}}_{12}$ icosahedra under pure shear and biaxial shear conditions, while the structural failure under tensile deformation arises from breaking interlayer bonds between icosahedral layers.

Numerical quantification of damage accumulation resulting from blanking in multi-phase steel

The high potentials of utilizing high strength steels in the automotive industry have been proved. However, there are still some unsolved challenges. Forming of a component that has been produced by blanking is one of these. Blanking is commonly used in sheet metal forming as the initial cutting process. Yet, it introduces damage into the blanked edges that in subsequent forming steps may lead to crack formation. This problem arises in particular in modern multi-phase steels and can currently not be avoided thoroughly due to a lack of understanding of the relevant influences. In the present work, the effects of the blanking process on an HCT980XD sheet were therefore numerically investigated. To achieve this, the Edge-Fracture-Tensile-Test method was simulated. By using this method, a conventional uniaxial tensile specimen is manufactured with one milled side and one blanked side. This allows to highlight the effect of blanking in a subsequent tensile test. In order to investigate the damage process, the coupled Modified-Bai-Wierzbicki model was applied to simulate first the blanking process and then the tensile test. The results revealed that during the blanking process, the failure initiated from the surface elements near the punch and propagated through the thickness. Meanwhile, another crack initiated from the opposite side of the sheet. The elements of these cracks experienced near pure-shear condition at both damage initiation and fracture moments. At the end of this step, the remaining damage, which is considered as the predamage of the next step, was higher in the middle of thickness. During the subsequent uniaxial tension, the crack in the specimen initiated at a shear cut edge and crossed the width. The possible detailed resolution of loading paths and crack formation shows that the damage mechanics simulation provides researchers with a powerful tool for assessing limit states in forming processes.

Multi-scale strainfield analysis using geostatistics: Investigating the rheological behavior of the hot Variscan crust of the Pyrenees (Axial Zone)

The present study provides a quantitative way to analyze and interpolate strainfields from ductile fabric field measurements using geostatistics. Based on variogram analysis and kriging interpolations, the developed methodology allows computing automatic cleavage and lineation trajectory maps at different scales from a same field structural dataset. For the example provided by the hot Variscan crust of the Pyrenees, the analysis of cleavage/stretching lineations orientation and kinematic data document pure shear conditions recorded during convergence. Strain was vertically partitioned between an upper crust submitted to homogeneous thickening responding to N-S (orogen-normal) shortening and a hot and partially molten mid-lower crust affected by horizontal longitudinal (orogen-parallel) flow. The emplacement of plutons and gneiss domes generated heterogeneities in the upper crust and induced strain localization into steep anastomosed transpressional shear zones flanking those structures. The results show that geostatistics applied to structural geology are powerful tools for retrieving tectonic regimes of large orogenic segments by identifying and quantifying perturbations in the strainfields induced by protracted and potentially complex tectonic histories. The variogram analysis also gives first order clues to evaluate whether the considered structural domains underwent single continuous ductile or polyphased brittle-ductile deformation.

Material characterization and fracture prediction with advanced constitutive model and Polar EPS fracture diagram for AA 3104-H19

Material characterizations for plasticity and fracture have been conducted from uniaxial tensile tests, bi-axial bulge test, and disk compression test for a beverage can AA3104-H19 material. The results from the experimental tests are used to determine material coefficients for the Yld2004-18p model [1]. Finite element simulations are developed to evaluate the predicted earing profile. Excellent agreement with the experimental data for eight ears exhibited in AA3014-H19 is achieved using the Yld2004-18p constitutive model. Further mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on the samples with a central hole and notched specimens to achieve tensile and plane-strain conditions. A specially designed torsion test of a double bridge specimen is conducted to generate the points near pure shear conditions. The Nakajima test is also utilized to produce a bi-axial tension condition. The data from the experiments is used to generate the fracture locus in the principal strain space. Mapping from the principal strain space to Polar Effective Plastic Strain (PEPS) space is accomplished for a general yield function. Finite element modeling is used to validate the fracture diagram in the polar space. A hole expansion demonstrates the accuracy of the PEPS fracture theory for the direction for onset of failure.

Shear‐induced brittle failure of titanium carbide from quantum mechanics simulations

AbstractTitanium carbide (TiC) has a wide range of engineering applications such as structural components, protective coating materials for cutting tools and strengthening phase because of such superior properties as high wear resistance, high hardness, and good chemical resistance. However, the intrinsic failure mechanism of TiC remains unknown, which limits its extended engineering applications. Here, we used density‐functional theory (DFT) at the Perdew‐Burke‐Ernzerhof (PBE) level to examine the shear‐induced failure mechanism of TiC along various plausible slip systems. We found that the (110)[1 0] slip system has the lowest critical shear strength under both pure shear and indentation stress conditions, suggesting that it is the most plausible failure system under both conditions. The failure mechanism arises from the Ti–C bond stretching and finally breaking with the increase in shear strain. The deformation modes along other possible slip systems are also investigated, which illustrate the failure mechanism along other slip systems. Our results provide atomistic explanation of the brittle failure of TiC, which will be useful for designing TiC based hard materials with improved mechanical properties.

Plastic anisotropy and failure in thin metal: Material characterization and fracture prediction with an advanced constitutive model and polar EPS (effective plastic strain) fracture diagram for AA 3014-H19

Material characterizations for plasticity and fracture have been conducted from uniaxial tensile tests, bi-axial bulge test, and disk compression test for a beverage can AA3104-H19 material. The results from the experimental tests are used to determine material coefficients for the Yld2004-18p model (Barlat et al., 2005). Finite element simulations are developed to evaluate the predicted earing profile. It is shown that the Yld2004-18p model is capable of accurately predicting the complex earing profile. Excellent agreement with the experimental data for eight ears exhibited in AA3014-H19 is achieved using the Yld2004-18p constitutive model. Further mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on the samples with a central hole and notched specimens to achieve tensile and plane-strain conditions. A specially designed torsion test of a double bridge specimen is conducted to generate the points near pure shear conditions. The Nakajima test is also utilized to produce a bi-axial tension condition. The data from the experiments is used to generate the fracture locus in the principal strain space. Mapping from the principal strain space to stress triaxiality space, principal stress space, and Polar Effective Plastic Strain (PEPS) space is accomplished for a general yield function. Finite element modeling is used to validate the fracture diagram in the polar space. A model of a hole expansion during cup drawing demonstrates the robustness of the PEPS fracture theory for a condition with a highly anisotropic material and accurately predicts the direction for onset of failure.

Evolution of fabric in Chitradurga granite (south India) - A study based on microstructure, anisotropy of magnetic susceptibility (AMS) and vorticity analysis

In this paper, the fabric in massive granite (~2.6Ga) from the Chitradurga region (Western Dharwar Craton, south India) is analyzed using microstructure, anisotropy of magnetic susceptibility (AMS) study and kinematic vorticity analysis. The microstructural investigation on the granite shows a progressive textural overprint from magmatic, through high-T to low-T solid-state deformation textures. The mean magnetic foliation in the rocks of the region is dominantly NW-SE striking which have developed during regional D1/D2 deformation on account of NE-SW shortening. The plunge of the magnetic lineation varies from NW to vertical to SE, and interpreted to be a consequence of regional D3 deformation on account of NW-SE to E-W shortening. The vorticity analysis from magnetic fabric in the region reveals that the NW-SE oriented fabric formed under pure shear condition during D1/D2 regional deformation. However, some parts of the region particularly close to the adjacent Chitradurga Shear Zone show that the magnetic fabrics are oblique to the foliation as well as shear zone orientation and inferred to be controlled by simple shearing during D3 regional deformation. The shape preferred orientation (SPO) analysis from oriented thin sections suggest that the shape of the recrystallized quartz grains define the magnetic fabric in Chitradurga granite and the degree of the SPO reduces away from the Chitradurga Shear Zone. It is interpreted that the change in magnetic fabrics in some parts of the granite in the region are dominantly controlled by the late stage sinistral shearing which occurred during the development of Chitradurga Shear Zone.

A new approach to evaluate bending forces for deep-drawing operations of a TRIP700 +EBT steel sheet

In this work, a new approach was developed to determine the bending, unbending and friction forces involved in deep-drawing processes of metallic sheets based on a sheet drawing-bending test. The procedure used both the experimental and deduced behavior of sheets in bending and unbending processes under tension. To obtain experimental data, a new apparatus was built to measure the reactions forces in the bending tool. These tests were applied to a TRIP700 +EBT steel sheet in diverse pure shear deformation states, with two different lubricants. The effect of the back tension and the state of the material were also studied by bending and unbending processes using tensile tests under diverse pure-shear conditions. Deduced forces, like bending and unbending forces, were determined by introducing these experimental data into an expressly created numerical method. The obtained results allowed us to state that the TRIP700 +EBT steels sheet displayed evolutional mechanical behavior since the induced martensite phase transformation effect depended on the deformation mode and intensity, had good formability and a low friction coefficient with steel tools, which was almost constant and independent of the pressure in the bending tool.

A simplified model of plain weave fabric reinforcements for the pure shear loading

An analytical and non-linear finite element (FE) modelling approach of plain weave fabric reinforcements have been developed to predict shear force for pure shear condition. For simplicity two main components of force for shear deformation has been considered; one is force required for the elastic deformation and another is to overcome the frictional resistance. Coulomb friction model of ANSYS is used in the FE model whereas the boundary condition has been established using Lagrangian description. Modelling of frictional resistance due to contact between yarns and crossover are conducted by utilizing contact pair option in ANSYS. A good agreement between theoretical and FEA model have been obtained. To ensure pure shear deformation in the fabrics it has been proved that there are no stress (von Mises and normal) or tension exist in the deformed yarn.

Shape optimization of the hole in an orthotropic plate

ABSTRACTThe exploration in this work is how to minimize the stress concentration around the edge of the hole in an orthotropic plate. The study first presents the analytical solution of the stress distribution around arbitrary holes using the complex variable method and then carries out the shape optimization using the mixed penalty function method. In the optimization process, optimal holes and stress distributions under the different factors are investigated, i.e., the loading, the Young’s modulus, and the fiber direction. Finally, we come to the conclusion that in the biaxial compressive load state, the shape and the stress are mainly affected by the loading, followed by the fiber direction and the Young’s modulus. In the pure shear condition, all three factors determine the optimum results.

An incremental flow theory for crystal plasticity incorporating strain gradient effects

The present work investigates a new approach to formulating a rate-independent strain gradient theory for crystal plasticity. The approach takes as offset recent discussions published in the literature for isotropic plasticity, and a key ingredient of the present work is the manner in which a gradient enhanced effective slip measure governs hardening evolution. The effect of both plastic strains and plastic strain gradients are combined into this scalar effective slip quantity, the energy associated with plastic strain is dissipative (unrecoverable), while the energy from plastic strain gradients is recoverable (free). The framework developed forms the basis of a finite element implementation and is demonstrated on benchmark problems designed to bring out effects such as strengthening and hardening. Monotonic loading and plane strain deformation is assumed throughout, but despite this, non-proportional straining is predicted in the plastic regime even under pure shear conditions. Results of single slip and symmetric double slip reveal that strengthening and hardening are governed by the slip system orientation and the material length parameter only.