Strain Localization Initiation Research Articles

Effect of friction welding conditions on joint properties of austenitic stainless steel joints by friction stud welding

ABSTRACTThis study focuses on the opening mode of induction bends; this mode represents the deformation outside a bend. Bending experiments on induction bends are shown and the manner of failure of these bends was investigated. Ruptures occur at the intrados of the bends, which undergo tensile stress, and accompany the local reduction in wall thickness, i.e. necking that indicates strain localization. By implementing finite element analysis (FEA), it was shown that the rupture is dominated not by the fracture criterion of material but by the initiation of strain localization that is a deformation characteristic of the material. These ruptures are due to the rapid increase in local strain after the initiation of strain localization and suddenly reach the fracture criterion. For the evaluation of the deformability of the bends, a method based on FEA that can predict the displacement at the rupture is proposed. We show that the yield surface shape and the true stress–strain relationship after uniform elongation have to be defined on the basis of the actual properties of the bend material. The von Mises yield criterion, which is commonly used in cases of elastic–plastic FEA, could not predict the rupture and overestimated the deformability. In contrast, a yield surface obtained by performing tensile tests on a biaxial specimen could predict the rupture. The prediction of the rupture was accomplished by an inverse calibration method that determined the true stress–strain relationship after uniform elongation.

Influences of loading direction and intermediate principal stress ratio on the initiation of strain localization in cross-anisotropic sand

Since cross-anisotropic sand behaves differently when the loading direction or the stress state changes, the influences of the loading direction and the intermediate principal stress ratio (b = (σ 2 − σ 3)/(σ 1 − σ 3)) on the initiation of strain localization need study. According to the loading angle (angle between the major principal stress direction and the normal of bedding plane), a 3D non-coaxial non-associated elasto-plasticity hardening model was proposed by modifying Lode angle formulation of the Mohr–Coulomb yield function and the stress–dilatancy function. By using bifurcation analysis, the model was used to predict the initiation of strain localization under plane strain and true triaxial conditions. The predictions of the plane strain tests show that the major principal strain at the bifurcation points increases with the loading angle, while the stress ratio decreases with the loading angle. According to the loading angle and the intermediate principal stress ratio, the true triaxial tests were analyzed in three sectors. The stress–strain behavior and the volumetric strain in each sector can be well captured by the proposed model. Strain localization occurs in most b value conditions in all three sectors except for those which are close to triaxial compression condition (b = 0). The difference between the peak shear strength corresponding to the strain localization and the ultimate shear strength corresponding to plastic limit becomes obvious when the b value is near 0.4. The influence of bifurcation on the shear strength becomes weak when the loading direction changes from perpendicular to the bedding plane to parallel. The bifurcation analysis based on the proposed model gives out major principal strain and peak shear strength at the initiation of strain localization; the given results are consistent with experiments.

A study of the influence of REV variability in double‐scale FEM ×DEM analysis

SummaryIn this work, the consequences of using several different discrete element granular assemblies for the representation of the microscale structure, in the framework of multiscale modeling, have been investigated. The adopted modeling approach couples, through computational homogenization, a macroscale continuum with microscale discrete simulations. Several granular assemblies were used depending on the location in the macroscale finite element mesh. The different assemblies were prepared independently as being representative of the same material, but their geometrical differences imply slight differences in their response to mechanical loading. The role played by the micro‐assemblies, with weaker macroscopic mechanical properties, on the initiation of strain localization in biaxial compression tests is demonstrated and illustrated by numerical modeling of different macroscale configurations. Copyright © 2016 John Wiley & Sons, Ltd.

Rupture prediction for induction bends under opening mode bending with emphasis on strain localization

This study focuses on the opening mode of induction bends; this mode represents the deformation outside a bend. Bending experiments on induction bends are shown and the manner of failure of these bends was investigated. Ruptures occur at the intrados of the bends, which undergo tensile stress, and accompany the local reduction of wall thickness, i.e., necking that indicates strain localization. By implementing finite element analysis (FEA), it was shown that the rupture is dominated not by the fracture criterion of material but by the initiation of strain localization that is a deformation characteristic of the material. These ruptures are due to the rapid increase of local strain after the initiation of strain localization and suddenly reach the fracture criterion. For the evaluation of the deformability of the bends, a method based on FEA that can predict the displacement at the rupture is proposed. We show that the yield surface shape and the true stress–strain relationship after uniform elongation have to be defined on the basis of the actual properties of the bend material. The von Mises yield criterion, which is commonly used in cases of elastic–plastic FEA, could not predict the rupture and overestimated the deformability. In contrast, a yield surface obtained by performing tensile tests on a biaxial specimen could predict the rupture. The prediction of the rupture was accomplished by an inverse calibration method that determined the true stress-strain relationship after uniform elongation. As an alternative to the inverse calibration, a simple extrapolation method of the true stress-strain relationship after uniform elongation which can predict the rupture is proposed.

Strain Localization Kinetics in a Metal Strip in Tension

Simulation results for strain localization in a metal strip are obtained with analytical and numerical methods. The initiation of strain localization is shown to be determined by the initial nonuniformity of material properties and by loading conditions. The more uniform material properties, the higher the strain level at which localized flow starts to develop. Metal heating under adiabatic deformation (as a result of the thermal plastic strain effect) causes a decrease in a strain level at which its localization starts. The pulse current passage, accounting for its thermal effect, exerts a similar influence.

Gradient plasticity modeling of geomaterials in a meshfree environment. Part I: Theory and variational formulation

Deformation and strength behavior of geomaterials in the pre- and post-failure regimes are of significant interest in various geomechanics applications. To address the need for development of a realistic constitutive framework, which allows for an accurate simulation of pre-failure response as well as an objective and meaningful post-failure response, a strain gradient plasticity model is formulated by incorporating the spatial gradients of elastic strain in the evolution of stress and gradients of plastic strain in the evolution of the internal variables. In turn, gradients of only kinematic variables are included in the constitutive equations. The resulting constitutive equations along with the balance of linear momentum for the continuum are cast as a coupled system of equations, with displacements and plastic multiplier appearing as the primary unknowns in the final governing integral equations. To avoid singular stress fields along element boundaries, a finite element discretization of the governing equations would require C 2 continuous displacements and C 1 continuous plastic multiplier, which is undesirable from a numerical implementation point of view. This issue is naturally resolved when a meshfree discretization is used. Hence the developed model is formulated within the framework of a meshfree environment. The new constitutive model allows an analysis of grain size effects on strength and dilatancy of rocks. The role and effectiveness of the new gradient terms on regularizing the underlying boundary value problems of geomechanics beyond the initiation of strain localization will be assessed in a future paper.