Anisotropic Yield Research Articles

Modeling of Eyld2000-2d Anisotropic Yield Criterion Considering Strength Differential Effect and Analysis of Optimal Calibration Strategy.

Sheet metals usually experience various loading paths such as uniaxial tension, uniaxial compression, biaxial tension, and simple shear during the forming process. However, the existing constitutive models cannot always accurately describe blanks' anisotropic yield and plastic flow behavior of blanks under all typical stress states. Given this, this paper improves the Eyld2000-2d yield criterion by introducing hydrostatic pressure to the A-Eyld2000-2d yield criterion that can describe the strength differential effect of materials. Meanwhile, to control the curvature of the yield surface more effectively, the near-plane strain yield stresses were added in the parameter identification process to calibrate the exponent m, so that the exponent is no longer considered as a constant value. Taking the widely used AA6016-T4, AA5754-O, DP980, and QP980 blanks in the automotive stamping industry as an example, the effectiveness of the new model and different parameter identification methods was verified by predicting experimental data under various simple and complex loading paths. Subsequently, the new model employing the optimal parameter identification strategy was compared with four widely used asymmetric yield criteria under associated and non-associated flow rules, including CPB06, LHY2013, S-Y2004, and Hu & Yoon2021, to further verify the accuracy of the proposed constitutive model. The results indicate that parameter identification strategy with variable exponent can significantly improve the flexibility of the yield criterion in describing the plastic anisotropy of blanks. Compared to the other yield criteria examined in this work, the new model provides the best prediction accuracy for the yield stresses and plastic flows of all blanks, especially in the near-plane strain and simple shear stress states. Modeling under the concept of anisotropic hardening can more accurately capture the evolving plastic behavior of blanks than isotropic hardening.

Correlation between Cellular Structure Morphology and Anisotropic Yield in Additively Manufactured Stainless Steel 316L

Additively manufactured austenitic stainless steel 316L is composed of a cellular structure, which has a directionality, and is observed with a different morphology depending on the observation direction. The cellular structure morphology that appears with a high probability in grains with a specific grain orientation is determined. Taylor factor, which is calculated by considering grain orientation, is related to cellular structure morphology due to the directional cellular structure in additively manufactured austenitic stainless steel 316L. The Taylor factor affects the mechanical properties. The yield strength of additively manufactured SUS316L can be explained by the correlation between cellular structure morphology, grain orientation, and Taylor factor.

Prediction of Strain Path Changing Effect on Forming Limits of AA 6111-T4 Based on a Shear Ductile Fracture Criterion

Strain path changing is a phenomenon in the stamping of complex panels or multiple-step stamping processes. In this study, the influence of the strain path changing effect was investigated and assessed for an aluminum alloy of 6111-T4 with a shear ductile fracture criterion. Plastic deformation of the alloy was modeled by an anisotropic Drucker yield function with the assumption of normal anisotropy. Then the shear ductile fracture criterion was calibrated by the fracture strains at uniaxial tension, plane strain tension and equibiaxial tension under proportional loading conditions. The calibrated fracture criterion was utilized to predict forming limit curves (FLCs) of the alloy stretched under bilinear strain paths. The analyzed bilinear strain paths included biaxial tension after uniaxial tension, plane strain tension and equibiaxial tension. The predicted FLCs of bilinear strain paths were compared with experimental results. The comparison showed that the shear ductile fracture criterion could reasonably describe the effect of strain path changing on FLCs, but its accuracy was poor for some bilinear paths, such as uniaxial tension followed by equibiaxial tension and equibiaxial tension followed by plane strain tension. Kinematic hardening is suggested to substitute the isotropic hardening assumption for better prediction of FLCs with strain path changing effect.

Correlation between Cellular Structure Morphology and Anisotropic Yield in Additively Manufactured Austenitic Stainless Steel

Correlation between Cellular Structure Morphology and Anisotropic Yield in Additively Manufactured Austenitic Stainless Steel

Nanoscale deformation mechanisms and yield properties of hydrated bone extracellular matrix.

Bone's hierarchical architecture combines toughness and strength. To understand the governing deformation mechanisms, its postyield behaviour was analyzed at the microscale. Micropillars were compressed in physiological solution; an increased strength compared to macroscale and an influence of hydration was found. Transmission electron microscopy revealed cracks forming in regions with adverse fibril orientation in transverse pillars. In axial pillars kink bands were observed and shear cracks emerged at the interface of ordered and disordered regions. It was estimated that bone's fracture toughness for splitting between fibrils is significantly smaller than on the macroscale. This study underlines the importance of bone's hierarchical microstructure and the need to study structure-property relationships on all length scales.

Triplet state of the primary donor in reaction centers of the phototrophic bacterium Rhodobacter sphaeroides R26 with active photoinduced electron transfer

EPR characteristics of transient paramagnetic states photoinduced in isolated reaction centers of Rhodobacter sphaeroides R26 with intact electron transfer have been studied. It was demonstrated that the detected weak triplet state EPR signal belongs to the primary donor molecule and is populated via the conventional mechanism of radical pair S-T0 mixing. The distortion of the spectral shape of this signal is explained by the triplet quantum yield anisotropy brought about by the short lifetime of precursor radical pairs. The angular dependence of the anisotropy was evaluated. It was shown that the spectral shape of the triplet state of photosystem II reaction center observed in the case of singly-reduced primary quinone acceptor can also be described by the anisotropic quantum yield of the triplet, with practically the same angular dependence. These properties confirm the conclusions on the mechanism of photoinduced electron transfer in photosystem II, made in previous publications. The peculiarities in the functioning of photosystem II reaction centers are probably determined by strict limitations on the triplet state generation.

Measurement of Anisotropic Consolidation Behavior

The anisotropic behavior of bulk solids is significant for many applications in bulk solids handling like consolidation processes or silo design. A new powder tester has been developed to measure the unconfined yield strength in the uniaxial direction, which means consolidation and strength measurement in the same direction, as well as to measure the anisotropic unconfined yield strength in the biaxial direction, which means consolidation and strength measurement in orthogonal directions. In the anisotropy tester the consolidation stress is applied through movable sidewalls in the horizontal direction for measuring the anisotropic unconfined yield strength and in the vertical direction for measuring the uniaxial unconfined yield strength. The friction between the walls and the bulk solid is minimized by flexible membranes that deform uniformly with the specimen. After the consolidation step all sidewalls are removed and the freestanding specimen can be stressed in the vertical direction until failure occurs. The ratio between the anisotropic and the uniaxial unconfined yield strength yields the intensity of the anisotropic consolidation behavior. This ratio has been measured for different bulk solids and consolidation stresses σ1 ranging between 20 and 250 kPa. The design of the tester as well as the experimental results with three different bulk solids are presented.

Parametric Study on Crashworthiness of Automotive Sheet Alloy

Crashworthiness (or collision performance) is a critical design factor in optimizing automotive part products. In this study, a numerical sensitivity analysis was performed to investigate the effects of material properties on crashworthiness for automotive sheet materials. As standard material parameters, the measured mechanical properties of AA 6111-T4 sheet were considered, based on the anisotropic non-quadratic yield function, YId2004-18p, and a combination type non-linear isotropic-kinematic hardening law. The constitutive law was implemented into codes of the commercial finite element program ABAQUS, using user material subroutines. As for process simulations, spring-back after forming as well as sheet forming and collision were included in this evaluation.

Experimental investigation of the behavior of extra high strength steel

This paper comprises a study concerning the mechanical behavior of extra high strength steel. This is investigated by means of biaxial testing of flat cross-shaped specimens in the full σ1-σ2 plane, a concept developed earlier at Steel Structures, Lulea University of Technology. Furthermore, new specimen designs had to be developed to enable testing of a material with high yield strength and low ultimate over yield strength ratio, such as the extra high strength steel Weldox 1100. The tests are performed in two steps: one initial loading followed by unloading and a subsequent loading in a new direction. The test results, containing data from 15 biaxial tests, are characterized by a slightly anisotropic initial yield criterion where the proof stress in compression is consequently somewhat higher compared to the results in tension. In the subsequent loading the observed phenomena are a Bauschinger effect in the direction opposite the initial loading direction and that the transition from elastic to plastic state in subsequent loadings is gradual and direction-dependent.

Multiscale Thermodynamic Significance of the Scale Invariance Approach in Continuum Inelasticity

AbstractIn this paper, the scale invariance approach from micro- to macro-plasticity by Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach,” ASME J. Eng. Mater., 117, pp. 352–355) and Ning and Aifantis (1996, “Anisotropic Yield and Plastic Flow of Polycristalline Solids,” Int. J. Plasticity, 12, pp. 1221–1240) is investigated within Rice’s normality structure (1971, “Inelastic Constitutive Relations for Solids: An Integral Variable Theory and its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455; 1975, “Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms,” Constitutive Equations in Plasticity, A. S. Argon, ed., MIT Press, Cambridge, MA, pp. 23–79). The normality structure provides a minimal framework of multiscale thermodynamics, and the dissipation equivalence between the microscale and macroscale is ensured by a variational equation which can be further formulated into principle of maximum equivalent dissipation. It is revealed in this paper that within the framework of normality structure, the so-called hypothesis of generalized scale invariance holds for the kinetic rate laws, flow rules, and orthogonality conditions in the sense of Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach”). Stemming from Rice’s kinetic rate laws, the generalized scale invariance reflects the inherent self-consistent character of the normality structure. If the plastic work rate is assumed to be equal to the intrinsic dissipation rate, the kinematic hardening plasticity as a demonstration of the scale invariance approach by Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach”), can be well accommodated within the framework of normality structure. Therefore, the scale invariance approach is justified from a multiscale thermodynamic viewpoint. It is further shown that the maximization procedure in this approach just corresponds to the principle of maximum equivalent dissipation.

Adaptation Models of Anisotropic Bone

A theoretical model and numerical methods were developed for testing different bone internal remodelling stimuli. The keystone of the study was the formulation of a stimulus based on the mechanical invariants of the stress tensor, which look into account bone non-homogeneity and anisotropy. A non-site specific remodelling rate equation was then used for the apparent density whereas anisotropy was fixed and evaluated from anatomic observations. An node-based semi-implicit algorithm with adaptive stepsize was implemented for solving the evolution equation. To preclude numerical artifacts (non-convergence, instability), a phase space description was proposed. As an illustration, the evolution of apparent density distribution surrounding the femoral stem after a Total Hip Replacement was simulated. Three stimuli were tested: the strain energy density stimulus, the octahedral shear stress stimulus, and an anisotropic plastic yield stress stimulus.

Plastic anisotropy of sheets with continuously varying anisotropic parameters and flow stress

A continuum mechanics model has been developed on the basis of Hill's theory of orthogonal anisotropy for predicting global mechanical properties of sheets with a through-thickness texture gradient and strength gradient. By the present model, the globalr value and yield and flow stresses of the entire sheet can be predicted from the local anisotropic parameters, yield and flow stresses which are given as arbitrary functions of the through-thickness position of the sheet.

Anisotropic yield and failure of shale : Niandou, H; Shao, J F; Henry, J P Proc International Symposium on Assessment and Prevention of Failure Phenomena in Rock Engineering, Istanbul, 5–7 April 1993P107–112. Publ Rotterdam: A A Balkema, 1993

Anisotropic yield and failure of shale : Niandou, H; Shao, J F; Henry, J P Proc International Symposium on Assessment and Prevention of Failure Phenomena in Rock Engineering, Istanbul, 5–7 April 1993P107–112. Publ Rotterdam: A A Balkema, 1993

Anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain

On condition that any perfectly plastic stress component at a crack tip is nothing but the function of η, by making use of equilibrium equations, anisotropic plastic stress-strain-rate relations, compatibility equations and Hill anisotropic plastic yield condition, in the present paper, we derive the generally analytical expressions of the anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain. Applying these generally analytical expressions to the mixed-model cracks, we can obtain the analytical expressions of anisotropic plastic stress fields at the tips of mixed-mode I–III, II–III and I–II–III cracks.

Anisotropic phase transition of rutile under shock compression

Shock recovery experiments for single crystal and powdered specimens of TiO2 with the rutile structure were performed in the pressure range up to 72 GPa. Single crystal specimens were shocked parallel to [100], [110] and [001] directions. X-ray powder diffraction analysis showed that the amount of α-PbO2 type TiO2 produced by shock-loading depended strongly on the shock propagation direction. The maximum yield (about 70%) was observed for shock loading to 36 GPa parallel to the [100] direction. In the [001] shock direction, the yield is much smaller than that of the [100] direction. This anisotropic yield was consistent with the observed anisotropy of the phase transition pressure in shock compression measurements. However, transformation to the α-PbO2 type cannot explain the large volume change observed above about 20 GPa. On the basis of the high pressure behavior of MnF2, we assumed that the high pressure phase was either fluorite or distorted fluorite type and that the phase conversion to the α-PbO2 type was induced spontaneously in the pressure reduction process.

A hardening model for anisotropic materials

Results from proportionate-loading experiments under plane-stress states illustrate the existence of a field of uniform-hardening potentials for the yield and creep deformation behavior of isotropic, slightly anisotropic, aelotropic and orthotropic polycrystalline materials in the initially strain-free condition. For two different plane-stress states, it is shown that a linear functional relationship holds between the plastic-strain increment ratio and the stress ratio in these materials and that, consequently, the field is adequately modeled by a uniform-hardening anisotropic function that is quadratic in the components of deviatoric stress. Anisotropic plane-stress yield functions are formulated for any stage in the deformation process by combining the uniform-hardening function with the kinematic-hardening rule. The resulting functions, which correspond to rigid translations of initial yield loci according to Ziegler's rule, provide good agreement with experimental observations on a marked Bauschinger effect and an absence of cross hardening.

A theory of linear plasticity for plane strain

A reformulation is made of the classical von Mises theory of plane strain rigid-perfect plasticity. The adoption of an anisotropic piecewise linear yield criterion results in two sets of field equations, each equivalent to the classical vibrating string equation. The development of the theory is routine. Certain properties of discontinuous stress and velocity fields are discussed, but the complete development of this aspect of the theory is not given here.