Modified Yield Criterion Research Articles

Concrete failure based on a localizing gradient‐enhanced damage formulation coupled with plasticity

AbstractInvestigations of the mechanical behavior of concrete, including plastic deformability and failure mechanisms, have always been of vital importance. In this work, a modified yield criterion with three surfaces is proposed to capture the plastic yielding behavior under different loading conditions. The failure, that is, the gradual degradation and the final loss of material integrity, can be described through a damage concept. For the purpose of robust finite element (FE) implementations as well as the failure description at an appropriate scale, a localizing gradient‐enhanced damage model has been adopted. As such, one obtains mesh‐insensitive material responses, while ruling out the unphysical damage broadening observed in conventional gradient‐enhanced damage models with a constant regularization length. Following a consistent derivation, the plasticity‐damage coupled model is implemented into an in‐house FE framework, based on which an experiment‐inspired example is simulated to illustrate the capability of the proposed description in concrete modeling, especially the mixed‐mode failure. Lastly, the conclusion provides some final insights.

Deformation and mechanical responses of AZ31B magnesium alloy under combined shear-compression loading conditions

This work presents a test method and the analytical procedure for materials under complex stress/strain state without the expensive multi-axis experimental machine. The deformation and mechanical responses of Mg alloy under combined shear-compression loading are investigated through a specific loading device. The deformation process and strain path of specimens with various loading angles are discussed based on digital image correlation (DIC) technology. Results show that the combined strain/stress state can be obtained through introducing the additional shear component. However, the loading angle almost has no effect on strain/stress path. In addition, the traditional testing machine equipped with combined loading device provides a new method to carry out the proportional loading test. A modified yield criterion considers Tresca-type material and tension-compression asymmetry is proposed to capture the mechanical characteristics of AZ31b Mg alloy. Based on the investigation, the combined test procedure can be regards as an ideal method in creation of materials database which focus on accurate description about the mechanical and fracture behaviors of materials.

Effect of grain defects on the mechanical behavior of nickel-based single crystal superalloy

AbstractIn this paper, a single crystal (SC) partition model, consisting of primary grains and grain defects, is proposed to simulate the weakening effect of grain defects generated at geometric discontinuities of SC materials. The plastic deformation of SC superalloy is described with the modified yield criterion, associated flow rule and hardening law. Then a bicrystal model containing only one group of misoriented grains under uniaxial loading is constructed and analyzed in the commercial finite element software ABAQUS. The simulation results indicate that the yield strength and elastic modulus of misoriented grains, which are determined by the crystallographic orientation, have a significant effect on the stress distribution of the bicrystal model. A critical stress, which is calculated by the stress state at critical regions, is proposed to evaluate the local stress rise at the sub-boundary of primary and misoriented grains.

Yield behavior of open-cell rhombic dodecahedron Ti–6Al–4V lattice at elevated temperatures

The initial yield behavior of Ti–6Al–4V rhombic dodecahedron lattice structures under biaxial loading at different temperatures is investigated. A modified yield criterion based on the hypothesis that the yield of materials is determined by total strain energy density, is proposed to derive the biaxial yield surface of isotropic cellular materials at different temperatures. The core advantage of this model is that the multi-axial yield behavior can be predicted by uniaxial tests instead of taking multi-axial tests. Temperature is taken into consideration by adding the thermal stress term into the model, which influences the hydrostatic pressure in the yield criterion. Then the effect on the yield surface caused by the temperature is discussed. Afterwards, the yield surfaces of Ti–6Al–4V lattice at elevated temperatures are predicted by the modified model. In order to verify the analytical framework, numerical approach is used by coupling the thermal and mechanical analysis to simulate the biaxial loading process at different temperatures. The numerical results match well with the prediction of the modified model.

Application of modified yield criteria for calculation of safe pressures on the subgrade soil

Application of modified yield criteria for calculation of safe pressures on the subgrade soil

Yield Criterion and Crack Tip Plastic Zone of Nickel-Based Single Crystal

A modified Hill yield criterion considering tension-shear stress coupling was given and material parameters of nickel-based single crystal in this criterion was determined by the Least Square Method. Crack tip plastic zones of nickel-based single crystal plate were analyzed by using this modified yield criterion and the plastic zones corresponding to mixed mode I, II crack, were derived. The crack tip plastic zones of nickel-based single crystal were compared to that of isotropic material. The influences of tension-shear stress coupling, compound ratio of mixed mode I, II crack and temperature on crack tip plastic zones were discussed. The results obtained in this paper indicate that the increasing rate of crack tip plastic zones with compound ratio in the plane stress condition is greater than that in the plane strain condition for nickel-based single crystal and the temperature has greater influence on the size of crack tip plastic zones.

Numerical modeling of uneven thermoplastic polymers behaviour using experimental stress-strain data and pressure dependent von Mises yield criteria to improve design practices

Classical plasticity theories and yield criteria for ductile materials, such as Tresca and von Mises original formulations predict that yielding is independent on the hydrostatic stress state (pressure), which means that tensile and compressive stress-strain behaviours are considered equal and are equally treated. This approach is reasonable for ductile metallic materials but sometimes inaccurate for polymers, which commonly present larger compressive yield strength, therefore being characterized as uneven. Polymer unevenness can be of great interest for mechanical structural design since components that present regions operating under compression can be optimized taking this phenomenon into account. Compressive stress-strain data for polymers are very scarce in the literature, and as a step in this direction this work presents three key-activities: i) four selected polymers were tested under tension and compression to identify unevenness and assess its levels; ii) pressure dependent yield criteria applicable for polymers were briefly reviewed; iii) experimental results were incorporated in adapted design practices using modified yield criteria implemented in optimization and finite element computations. Results show that taking unevenness into account and implementing modified criteria in the numerical techniques for structural calculation can provide mass reductions up to ∼ 38% even with simple geometric changes, while keeping original safety and stiffness levels.

Finite Element Analysis of Pressure Influence on Densification of Titanium Alloy Powder under Hot Isostatic Pressing

To investigate the influence of pressure on densification behavior of metal powder under hot isostatic pressing (HIP), the consolidation of Ti6Al4V powder at various applied pressures during HIP processes were investigated by finite element method in this paper. The plasticity and creep phenomenon of the compact under high temperature and pressure were described by the viscoplastic Perzyna model, which integrated with a modified yield criterion for porous metal materials. The thermo-mechanical coupling analysis was carried out by the finite element code MSC.Marc. The calculated results show non-uniform density distributions for the compact, but this phenomenon decreases as increasing the applied pressure. The densification rate is significantly influenced by applied pressure. The consolidation mechanisms for powder compact were also discussed.

Numerical implementation of modified Coulomb-Mohr yield criterion for anisotropic and asymmetric materials

Development and numerical implementation for an elastoplastic constitutive model for anisotropic and asymmetric materials are presented in this paper. The Coulomb-Mohr yield criterion was modified to consider both the anisotropic and asymmetric properties. The modified yield criterion is an isotropic function of the principal values of a symmetric matrix which is linearly transformed from the Cauchy stress space. In addition to the constitutive equation, the numerical treatment for the singularity in the vertex region of yield surface and stress integration algorithm based on elastoplasticity were presented. In order to assess the accuracy of numerical algorithm, isoerror maps were considered. Also, extension of a strip with a circular hole was simulated and results compared with those obtained using the (smooth) Mises yield criterion to validate stress output for a complex stress state.

Stresses in a bulk solid in a cylindrical silo, including an analysis of ratholes and an interpretation of rathole stability criteria

A two-dimensional model for stresses in a cohesive bulk solid in a vertical, cylindrical vessel has been developed, assuming a rotated, circular arc orientation of principal stresses, after Enstad [1995. On the theory of arching in mass flow hoppers. Chemical Engineering Science 30 (10), 1273–1283] and Li [1994. Mechanics of arching in a moving bed standpipe with interstitial gas flow. Powder Technology 78, 179–187]. The model assumes that principal stresses form a spherical dome surface within the vessel. At the wall, the surface makes a constant angle with the wall normal, necessitating a progression of arc centre up the vessel. An incremental element of upper and lower surfaces with vertical height δ x at the wall has variable thickness with arc angle ε measured from the vessel centre. Positions within the vessel are located by height at which the arc cuts the vessel wall x, and arc angle ε . Rotational symmetry is assumed through azimuthal angle θ . This gives 3 principal stresses: σ R ; σ ε ; σ θ . Static vertical and horizontal force balances yielded two partial differential equations, and a third was obtained by assuming a known ratio between effective stresses σ ε ′ and σ R ′ . These equations were integrated numerically to give stress surfaces in x – ε space. The model simulated variations in the state of stress across the arc surface, and in some conditions, this lead to large variations in stress between the wall and vessel centre. The model accurately predicted the minimum outlet radius required for flow of a cohesive bulk material. The presence of a vertical, co-axial rathole was modelled with minor geometrical modifications. The rathole was assumed to be an unconfined plane of principal stress where the radial stress, σ R , acted vertically downwards and its value increased linearly with bed depth, contrary to Jenike's [1964. Storage and flow of solids, Bull. 123, University of Utah, USA] assumption of a limiting stress in deep beds. Conventional stability criteria ( σ R < = f c for stability), suggest that only shallow ratholes can exist. However, a modified yield criterion, allowing for the curvature of the rathole, enabled deep, stable ratholes to exist. Results show that the stability of deep ratholes depends upon the rathole radius and the vessel radius.

Effect of Bauschinger Effect and Yield Criterion on Residual Stress Distribution of Autofrettaged Tube

Many analytical and numerical solutions for determining the residual stress distribution in autofrettaged tube have been reported. The significance of the choice of yield criterion, the Bauschinger effect, strain hardening, and the end conditions on the predicted residual stress distribution has been discussed by many authors. There are some different autofrettage models based on different simplified material strain-hardening behaviors, such as a linear strain-hardening model, power strain-hardening model, etc. Those models give more accurate predictions than that of elastic–perfectly plastic model, and each of them suits different strain-hardening materials. In this paper, an autofrettage model considering the material strain-hardening relationship and the Bauschinger effect, based on the actual tensile-compressive stress-strain curve of material, plane-strain, and modified yield criterion, has been proposed. The predicted residual stress distributions of autofrettaged tubes from the present model are compared to the numerical results and the experimental data. The predicted residual stresses are in good agreement with the experimental data and numerical predictions. The effect of Bauschinger effect and yield criterion on residual stress is discussed based on the present model. To predict residual stress distribution accurately, it is necessary to properly model yield criterion, Bauschinger effect, and appropriate end conditions.

Determination of Residual Stress Distribution in Autofrettaged Tube Based on Modified Yielding Criterion and Tensile-Compressive Curve of Material

An autofrettage model considering the material strain-hardening behavior and the Bauschinger effect, based on the actual tensile–compressive curve of material and modified yield criterion, has been proposed. The analytic expressions of residual stress distribution and the autofrettage pressure have been obtained. This model has stronger curve fitting ability, nearly all of the strain-stress curves of materials used in making autoefrettage tubes can be fitted well by this model, and each of those models based on the simplified strain hardening relationship of material is a special case of the model. It was used to predict the residual stress distributions of an autofrettaged tube. The results show that the residual stress distributions predicted by the present model are in good agreement with the experimental data.

Finite Element Analysis of the Compaction Processes for Hollow Three-Level (Class IV) Components

The yield criterion describing asymmetric behavior of powdered metal compacts in tension and compression is introduced by modifying that used for sintered powdered metals. The plasticity theory related to the modified yield criterion is reviewed and summarized for a powdered metal compact. The constitutive equation is applied to the variational principle and its discritization is also introduced. Axisymmetric die pressings with copper powders were performed to see the deformation mechanics of hollow three-level parts. The simulation includes two different types of multiple-motion tooling compaction of a Class IV part of hollow three-level component. Predictions are made for density distributions, load-stroke relationships, average density as function of height, pressure distributions along the die-walls and punches, average compact densities at each level, and energy consumption for each pressing. The information from simulation can be used to synthesize the various punch motions in a multiple action tooling system.

Yield criteria for porous ductile sheet metals with planar anisotropy under plane stress conditions

Modified yield criteria for porous ductile sheet metals with planar anisotropic matrices are investigated by a finite element analysis. A sheet model with a centric through-thickness hole is adopted for an analysis model. A new proposed plane stress yield function accounting for rounded vertices of a yield surface, in particular, near the uniaxial and equal biaxial loading directions based on experiments is employed for the matrix surrounding the hole. Strain hardening behavior of the matrix is considered in the present study. Two different definitions of the macroscopic yield stress are implemented here. Macroscopic yield loci and macroscopic stress–strain relationships under plane stress conditions based on the finite element computational results and those based on the modified anisotropic yield criteria are then compared and found to be in reasonable agreement.

Modified Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals

The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. 1997, “Approximate Yield Criteria for Anisotropic Porous Ductile Sheet Metals,” Mech. Mater., pp. 213–226. Three fitting parameters are suggested for the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the modified anisotropic Gurson’s yield criterion under uniaxial and equal biaxial tensile loading conditions.

Mechanical Behavior of Carbon Steels in the Temperature Range of Mushy Zone.

Tensile strength and ductility of carbon steels have been measured in the temperature range of mushy zone by the in-situ melting tensile test technique with Gleeble system. The specimen was melted and cooled to the test temperature before the tensile deformation in order to get the mechanical properties subject to the continuous casting process. During hot tensile test, a ceramic fiber tube was used to reduce the radial temperature gradient in the heated specimen. Tensile strength of carbon steels in the temperature range of mushy zone increased with decreasing test temperature, and was well described by the modified yield criterion for porous metals. The measured zero strength temperature (ZST) and zero ductility temperature (ZDT) were related to the solid fractions evaluated by the numerical simulation of microsegregation developed by Ueshima et al. The characteristic solid fractions of ZST and ZDT which corresponded to 0.75 and 0.99, respectively, were well described by the prediction equation on ZST and ZDT at given steel compositions and cooling rates.

Overall volume change, water volume change, and yield associated with an unsaturated compacted loess

This paper presents the overall volume change, water volume change, and yield associated with an unsaturated, compacted, low-plasticity loess from China. Two types of tests were conducted using a modified triaxial apparatus, namely isotropic compression tests with controlled suction (ICT), and triaxial shrinkage tests (TST). In the triaxial shrinkage tests, the net cell pressure is controlled and suction is allowed to increase. The results show that the stress path has a significant effect on overall volume change and the water volume change. The soil parameters related to overall volume change and the water volume change for the isotropic compression tests vary significantly in the low suction range, whereas the same soil parameters related to the triaxial shrinkage tests exhibit gradual changes. The yield net mean stress for the loading-collapse yield curve increases with suction. The yield suction is not equal to the maximum suction experienced by the soil specimen for the suction increase yield locus. Based on the test data obtained from the low-plasticity loess, a modified criterion for yield associated with suction increase is proposed. The proposed modified yield criterion should be valid for loess and silts of similar densities and plasticities.

Overall volume change, water volume change, and yield associated with an unsaturated compacted loess

This paper presents the overall volume change, water volume change, and yield associated with an unsaturated, compacted, low-plasticity loess from China. Two types of tests were conducted using a modified triaxial apparatus, namely isotropic compression tests with controlled suction (ICT), and triaxial shrinkage tests (TST). In the triaxial shrinkage tests, the net cell pressure is controlled and suction is allowed to increase. The results show that the stress path has a significant effect on overall volume change and the water volume change. The soil parameters related to overall volume change and the water volume change for the isotropic compression tests vary significantly in the low suction range, whereas the same soil parameters related to the triaxial shrinkage tests exhibit gradual changes. The yield net mean stress for the loading-collapse yield curve increases with suction. The yield suction is not equal to the maximum suction experienced by the soil specimen for the suction increase yield locus. Based on the test data obtained from the low-plasticity loess, a modified criterion for yield associated with suction increase is proposed. The proposed modified yield criterion should be valid for loess and silts of similar densities and plasticities.

Prediction of forming limits using Hosford's modified yield criterion

A new generalized anisotropic yield criterion has been suggested by Hosford. This criterion has been used in prediction of forming limits by Graf and Hosford using M-K analysis for a material with normal anisotropy. In this paper the effect of planar anisotropy has been incorporated and the procedure for calculation of forming limits has been modified using the approach suggested by Parmar and Mellor. The results are compared with those of Graf and Hosford in the case of planar isotropy to validate the model and procedure. The results are also compared with the predictions of the M-K model using Hill's old and new (after Parmar and Mellor) yield criteria as well as experimental values obtained under conditions of both in-plane and punch stretching. It is observed that the effect of planar anisotropy is negligible while the predictions are strongly dependent on exponent “ a” (exponent in yield criterion). Predictions with a = 5, 6 or 8 match the experimental results much better than predictions using the M-K model with Hill's old criterion, or even the new criterion used by Parmar and Mellor.

The biaxial deformation and yield behavior of bisphenol‐a polycarbonate: Effect of anisotropy

AbstractThe biaxial tension stress‐strain‐yield behavior of glassy bisphenol A‐polycarbonate has been investigated at constant octahedral shear stress rate and at 25°C and −40°C. The specimens possess a small amount of anisotropy. Hill′s criterion for yielding of anisotropic materials is modified to take into account the sensitivity of the yield locus to the hydrostatic stress component. This modified yield criterion fits the 25°C data quite well. However, the data at −40°C cannot be fitted using reasonable parameters.