Modified Yield Function Research Articles

Influence of raster orientation on fracture behavior of Ti6Al4V alloy manufactured by Laser powder bed fusion

This study analyzes the fracture characteristics of Ti6Al4V alloy manufacturedby the Laser Powder Bed Fusion (LPBF) technique, specifically investigating the effect of raster orientation. A modified yield function is presented to determine the decrease in load-carrying ability attributed to shear effects. The damage variable includes both the void volume fraction and shear damage variables, taking into consideration the consequences of void interaction. The research utilizes Finite Element Analysis (FEA) together with calibrated modified GTN fracture parameters derived from Hill’s 48 parameters to accurately predict material behavior. Uniaxial tension tests are carried out on samples in different raster orientations:0°, 45°, and 90°. The Scanning Electron Microscope (SEM) is used to conduct a more thorough examination of the fracture’s characteristics. The specimens with a 90° raster orientation exhibit considerable plastic deformation with deepdimples on the fractured surface, along with irregularly shaped voids. In contrast, the sections with 45° and 0° orientations display smaller dimples and smoother cup and cone features without significant plastic deformation. The results demonstrate that the direction of the raster has a considerable impact on the plastic modulus and fracture properties of the material.

Strain amplitude-dependent cyclic softening behavior of carbide-free bainitic rail steel: Experiments and modeling

Experimental investigations of Carbide-free bainite (CFB) rail steel under different strain amplitudes are conducted to indicate the cyclic deformation feature and hysteresis loop evolution. A modified yield function with an exponential evolution coefficient is proposed to consider the strength differential effect, and a strain range-dependent coefficient is introduced to consider the transient Bauschinger effect. Moreover, a Logistic dose–response function and a cyclic softening function are introduced into the isotropic and kinematic hardening rules. Finally, the comparison between the simulated and experimental results demonstrates that the proposed model can reasonably describe the strain amplitude-dependent cyclic softening of CFB rail steel.

A modified yield function for modeling of the evolving yielding behavior and micro-mechanism in biaxial deformation of sheet metals

In-depth understanding of the evolving plastic yielding behaviors and insight into their micro-scaled mechanisms are critical for fully exploiting of the formability of sheet metals, accurately forming of the needed shape and geometries, and precisely tailoring of the needed quality and property of the deformed parts. In this research, the in-plane yielding behaviors of dual-phase steel and aluminum alloy sheets were extensively investigated by biaxial tension experiments with the original and pre-strained specimens. It is found that the profile of the experimental plastic work contours changes with the increase of plastic deformation, no matter what the proportional or complex loading condition is. This indicates that the evolving yield behavior cannot be neglected. Based on the Yld2000-2d yield function, a modified yield function with introducing a variable exponent to represent the evolving yield behavior was proposed and then employed to model the evolving yielding of the given metallic sheets. To investigate the yielding micro-mechanisms, the simulated biaxial tension tests were conducted by using the established representative volume elements (RVEs) with a crystal plasticity model. The simulation results showed that the texture of the given sheet metals has a significant effect on the profile of the yield loci. Moreover, when the hard secondary phase is added into the polycrystalline aggregate, the optimum exponent of yield function for the given RVEs is increased, instead of decrease within a certain range of the plastic strain. The micro-mechanism of the evolving yielding behavior could be attributed to the ‘pinning’ effect of hard inclusions to the polycrystalline grains, i.e. the hardly-deformable particles strengthening the kinetic constraints to the polycrystalline matrix and further obstructing the rotation and plastic deformation of the neighboring grains. This research thus provides a comprehensive understanding of the effect of microscopic structure (crystal structure, texture and secondary hard phase) on the macroscopic plastic yielding behavior of metallic materials as well as a new high-fidelity modelling technique to describe the evolving yielding behavior phenomenologically, in such a way to support the application of FE simulation in sheet metal forming processes.

A constitutive model for transversely isotropic material with anisotropic hardening

Many materials such as wood, as well as rigid and flexible foams, exhibit transverse isotropic or even anisotropic mechanical properties in terms of their elastic and inelastic responses. However, there appear to be few constitutive models that are able to appropriately and accurately describe them. In this study, constitutive model that describes transversely isotropic material displaying anisotropic hardening, based on a weak form of definition of anisotropic hardening, is proposed. This form of hardening is incorporated into a modified yield function by introducing a matrix comprising dimensionless hardening functions. A modified stress is also defined, such that the yield surface remains stationary in the associated stress space, thus enabling the proposed anisotropic hardening function to be evaluated. The model is then used to predict the stress-strain curves and deformation of a transversely isotropic polyethylene foam exhibiting transversely isotropic hardening, subjected to compression at different angles to the axis perpendicular to the plane of isotropy. Good agreement between predictions based on the proposed model and Jebur’s experimental data (Jebur, 2013) is observed; for comparison, predictions employing an earlier transversely isotropic model but with isotropic hardening (Tagarielli et al., 2005) shows noticeable deviation from the experimental data. The results substantiates the validity of the proposed anisotropic hardening model in describing the mechanical and deformation response of a transversely isotropic material exhibiting transversely isotropic hardening.

Consideration of strength differential effect in sheet metals with symmetric yield functions

A simple approach is proposed to extend symmetric yield functions for the consideration of strength differential (SD) effect in sheet metals. The SD effect is coupled with symmetric yield functions by simply adding a weighted pressure term for anisotropic materials based on the approaches of Spitzig et al. (Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Metall 1995;23:885–893), Spitzig and Richmond (The effect of pressure on the flow stress of metals. Acta Metall 1984;32:457–463) and Stoughton and Yoon (A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming, Int J Plast 2004;20:705–731). This approach is applied to the symmetric Yld2000-2d yield function (Barlat et al. Plane stress yield function for aluminum ally sheets—Part I: Theory, Int J Plast. 2003;19:1297–1319. The Yld2000-2d yield function is then modified to describe the anisotropic and asymmetric yielding of two aluminum alloys with small SD effect: Al 2008-T4 and Al 2090-T3 and four hexagon-closed packed (HCP) metals with strong SD effect: pure textured magnesium, an Mg 0.5% Th Sheet, an Mg 4% Li sheet and a Ti–4Al–1/4O2 titanium sheet. The predicted yield surfaces are compared with experimental results for the evaluation of the modified yield function. The comparison reveals that both anisotropy and asymmetry are correctly modeled by the proposed approach.

기공을 포함한 이방성 판재의 성형한계 예측

Most failures of ductile materials in metal forming processes occurred due to material damage evolution - void nucleation, growth and coalescence. In this paper. the modified yield function of Liao et al in conjunction with the Hosford’s yield criterion is studied to clarify the plastic deformation characteristic of voided anisotropic sheet metals. The void growth of an anisotropic sheet under biaxial tensile loading and damage effect of void growth on forming limits of sheet rnetals are investigated. Also the characteristic length defining the neck geometry is introduced in M-K model to incorporate the effect of triaxial stress in necked region on forming limits. The forming limits theoretically predicted are compared with experimental data. Satisfactory agreement was obtained between the predictions and experimental data.

An improved analytical description of orthotropy in metallic sheets

The correct description of initial plastic anisotropy of metallic sheets plays a key role in modelling of sheet forming processes since prediction of material flow, residual stresses and springback as well as wrinkling and limiting strains are significantly affected by the phenomenological yield function applied in the analysis. In the last decades considerable improvement of anisotropic yield criteria has been achieved. Among these, the yield criterion proposed by Paraianu et al. [An improvement of the BBC2000 yield criterion. In: Proceedings of the ESAFORM 2003 Conference] is one of most promising plane stress yield criteria available for orthotropic sheet materials. This work aims to improve this yield criterion with respect to flexibility. The capabilities of the modified yield function will be demonstrated by applications to an anisotropic aluminium alloy sheet material.

Effect of material damage on forming limits of voided anisotropic sheet metals

Most failures of ductile materials in metal-forming processes occur due to material damage evolution (void nucleation, growth, and coalescence). The current article examines the modified yield function of Liao et al., in conjunction with Hosford’s yield criterion, to clarify the plastic-deformation characteristic of voided anisotropic sheet metals. As such, the void growth of an anisotropic sheet under biaxial tensile loading and the damage effect of void growth on the forming limits of sheet metals are investigated. Plus, the process length defining the neck geometry is included in the Marciniak and Kuczynski (M-K) model to incorporate the effect of triaxial stress in a necked region on the forming limits. The predicted forming limits were compared with experimental data, and a satisfactory agreement was obtained.

Transversely isotropic materials undergoing large deformations and application to modelling of soft tissues

Many materials such as wood, as well as rigid and flexible foams, exhibit transverse isotropic or even anisotropic mechanical properties in terms of their elastic and inelastic responses. However, there appear to be few constitutive models that are able to appropriately and accurately describe them. In this study, constitutive model that describes transversely isotropic material displaying anisotropic hardening, based on a weak form of definition of anisotropic hardening, is proposed. This form of hardening is incorporated into a modified yield function by introducing a matrix comprising dimensionless hardening functions. A modified stress is also defined, such that the yield surface remains stationary in the associated stress space, thus enabling the proposed anisotropic hardening function to be evaluated. The model is then used to predict the stress-strain curves and deformation of a transversely isotropic polyethylene foam exhibiting transversely isotropic hardening, subjected to compression at different angles to the axis perpendicular to the plane of isotropy. Good agreement between predictions based on the proposed model and Jebur’s experimental data (Jebur, 2013) is observed; for comparison, predictions employing an earlier transversely isotropic model but with isotropic hardening (Tagarielli et al., 2005) shows noticeable deviation from the experimental data. The results substantiates the validity of the proposed anisotropic hardening model in describing the mechanical and deformation response of a transversely isotropic material exhibiting transversely isotropic hardening.

Finite-element analysis of flat rolling with inclusion of anisotropy

Anisotropy is a major phenomenon which influences roll torque, roll force and distribution of pressure and shear stress on the roll—strip interface. In this paper, a model for steady-state plane strain cold rolling is presented, which takes into account anisotropic behavior of the sheet. For this purpose, a modified yield function is presented for solving plane strain problem. A parametric study has been carried out for hypothetical material parameters to study their influence on design parameters. It is established that anisotropy should be included in numerical simulation codes for getting correct estimate of design parameters.

A modified Nadreau yield function

Nadreau and Michel developed a yield criterion for polycrystalline isotropic ice based on data by Jones. It was found that the criterion in its published form had to be modified to meet some of its postulates. Based on the authors' original idea, a modified yield function is proposed which accommodates the concerns raised.

A model for assessing the impact of atmospheric deposition on regional forest inventories

A model for estimating the impact of atmospheric deposition on regional forest inventory was developed, and combines a regional inventory projection model, a modified yield function which includes crown length as a predictor variable and exogenously determined timber harvests. The effect of atmospheric deposition on forest growth is simulated by varying crown length, and the inventory impact is the difference between inventory without and with varied crown length. The model is demonstrated by projecting the Commonwealth of Virginia's softwood forest inventory in 5-year intervals to the year 2035. A one-foot reduction in crown length causes a 0·7 to 1·7% reduction in inventory, depending on ownership. Inventory reductions of 1·7 to 8·7 and 4·5 to 17·8% are estimated for 5- and 10-foot crown reductions. However, models which account for market interactions halve the reductions.

Removal of singularities in tresca and mohr–coulomb yield functions

AbstractThe Tresca and Mohr–Coulomb yield functions are used widely in metal and soil plasticity computations. Both of these criteria, however, possess angular vertices at which the gradient with respect to the stresses, and hence the elastoplastic constitutive law, is undefined. This paper describes a modified yield function which may be used to ‘round‐off’ these vertices. When used in conjunction with the parent yield function, the modified yield function results in a yield surface which is continuous and differentiable for all values of the stresses. The modified yield function is used in the vicinity of the vertices and is given in a form suitable for finite element programming.