Mises Yield Criterion Research Articles

Development of a thermoplastic constitutive model for steel based on the generalized Mises yield criterion

Steel is widely used in building structures, and the constitutive model that describes the steel's response to load is an essential component of structural mechanics analysis. This paper aims to investigate the thermoplastic behavior of steel at elevated temperatures. Based on the classical elastoplastic mechanics framework, this study introduces a generalized Mises yield criterion derived from energy theory, which takes into account the temperature effect. In conjunction with relevant assumptions, hardening condition, flow rule, the generalized Hooke's law, and consistency condition, we derive a novel incremental thermoplastic constitutive model for steel. And the new thermoplastic constitutive model's rationality is further verified by utilizing high-temperature steady-state tensile test data. It is encouraging that this new model can accurately describe the mechanical behavior of steel in high-temperature environment such as fire, which is of significant importance for fire safety design of building structures.

Predictive plasticity unveiled: XFEM modeling of cyclic failure in pressurized straight pipelines under three-point bending

This study presents an innovative numerical approach for predicting pressurized welded pipelines’ cyclic behavior and failure mechanisms under complex loading conditions. Focusing on X52 steel pipelines subjected to internal pressure and three-point bending, we investigate the interplay between structural integrity, weld joint positioning, and boundary conditions. Our methodology integrates advanced finite element analysis with a sophisticated material model capturing isotropic and kinematic hardening. The constitutive behavior is calibrated using the Voce model, accurately representing the material’s cyclic response. We employ the von Mises yield criterion to characterize the multiaxial stress state within the pipeline. A key innovation is our application of the eXtended Finite Element Method (XFEM) coupled with the calibrated hardening model, enabling high-fidelity simulation of crack initiation and propagation. Our model’s predictive capabilities are rigorously validated against experimental data, demonstrating excellent agreement across various loading scenarios. Through comprehensive parametric studies, we elucidate the critical influences of internal pressure, end-fixation conditions, and weld joint locations on the pipeline’s structural response. Force-displacement hysteresis curves reveal complex, nonlinear behaviors significantly impacting fatigue life and failure modes. This research advances the understanding of cyclic plasticity and fatigue in welded pressurized pipelines, providing a robust computational framework for predicting long-term performance. The insights gained have far-reaching implications for enhancing critical energy-transportation infrastructure’s safety, reliability, and longevity, potentially informing future design criteria and regulatory guidelines.

Yielding onset in FGM thick-walled spherical shells under thermo-mechanical loading

Based on von Mises yield criterion, a thermoelasto-plastic analysis of a thick-walled spherical shell composed of functionally graded material (FGM) subjected to internal pressure and thermal gradient is conducted in order to accurately predict the onset radius of yielding within the vessel wall. The modulus of elasticity, thermal conductivity and thermal expansion coefficients, and yield stress of FGM are assumed to follow power-law functions in radius according to Erdogan’s model. The equilibrium differential equation of the shell under thermo-mechanical loading in steady-state conduction heat transfer are derived analytically and then solved to determine through-thickness variations of the radial and circumferential stresses and radial displacement in elastic and perfectly plastic zones in the vessel wall. The presented approach leads to the definition of new formulation to predict the onset radius of yielding. Moreover, a neural network (NN) solution to reliable quantify the influence of all uncertain input parameters with respect to uncertain output parameter is utilized. The numerical results showed that for various FGM parameters and specific thermal gradient, the plastic zone can commence from inside radius, outside radius, simultaneously in both radii, or may be launched in the intermediate radius of the spherical shell wall.

Reliability analysis of 50000 kN hydraulic support test bench under shrinkage test conditions

The large mining-height hydraulic support test-bed serves as a crucial tool for heavy hydraulic support factory inspections and type testing. With the successful development of the ZY29000/45/100D hydraulic support, the need for a large high-mining hydraulic support test-bed has become evident. This paper combines the theory of rigid-flexible coupling in virtual prototypes and ADAMS multi-body dynamic simulation technology to analyze the strength of the 50,000 kN hydraulic support test-bed. ANSYS classic modules were employed to address the flexibility of key components within the test-bed. The fatigue life of the test-bed was analyzed using NSOFT software, the von Mises yield criterion, and the Goodman modified curve. The S-N curve of material parameters for the test-bed components was used to conduct a shrinkage test. The results indicate that the lowest position is the most vulnerable during the shrinkage test. Among the key components, the stress on the pin bearing is 356.6 MPa, which is 167.9 %, 123.3 %, and 41.6 % higher than that of the pillar, movable beam, and base, respectively. The fatigue life of the base under low, medium, and high shrinkage conditions is1.1×107, 4.0×108, and 1.7×108, with damage values of 8.8×10-8, 2.5×10-9, and 5.7×10-9, respectively. The base’s life under low shrinkage conditions is the shortest, followed by that under high shrinkage conditions. These research findings provide technical guidance and an optimization foundation for the successful development of a 50000 kN hydraulic support test-bed. They also offer a new method and approach for analyzing and predicting the fatigue life of key components in large-scale industrial and mining equipment operating under complex conditions, with promising practical applications.

Peridynamic‐based modeling of elastoplasticity and fracture dynamics

AbstractThis paper introduces a particle‐based framework for simulating the behavior of elastoplastic materials and the formation of fractures, grounded in Peridynamic theory. Traditional approaches, such as the Finite Element Method (FEM) and Smoothed Particle Hydrodynamics (SPH), to modeling elastic materials have primarily relied on discretization techniques and continuous constitutive model. However, accurately capturing fracture and crack development in elastoplastic materials poses significant challenges for these conventional models. Our approach integrates a Peridynamic‐based elastic model with a density constraint, enhancing stability and realism. We adopt the Von Mises yield criterion and a bond stretch criterion to simulate plastic deformation and fracture formation, respectively. The proposed method stabilizes the elastic model through a density‐based position constraint, while plasticity is modeled using the Von Mises yield criterion within the bond of particle paris. Fracturing and the generation of fine fragments are facilitated by the fracture criterion and the application of complementarity operations to the inter‐particle connections. Our experimental results demonstrate the efficacy of our framework in realistically depicting a wide range of material behaviors, including elasticity, plasticity, and fracturing, across various scenarios.

Behavior and shear strength of prestressed steel reinforced concrete composite deep beam

In order to optimise the utilisation of material properties, simplify the construction process and enhance the industrialisation of steel reinforced concrete beams, an innovative prestressed steel reinforced concrete composite beams(PSRCC) was proposed, which was achieved by integrating prestressing technology and prefabricated technology to steel reinforced concrete structure. To investigate the shear PSRCC deep beams, a static load test was conducted on 7 PSRCC deep beams. The study investigated the effects of parameters such as shear span-depth ratio, prestressed tendons degree, form, height and application sequence on the failure mode, crack pattern, load-displacement behavior, strain response and damage evolution. A model was established to predict the shear strength of PSRCC deep beams, considering the steel-concrete interaction, using the von Mises yield criterion and the SST model, which assessed the contributions of composite strut, prestressed tendons and shear steel web for shear strength. The test results showed that the prefabricated and cast-in-situ concrete components maintained good integrity, and PSRCC deep beams eventually experienced typical diagonal compression failure. Applying prestressing and reducing the shear span-depth ratio under identical conditions would reduce the deformation capacity of PSRCC deep beams. When the shear span-depth ratio was reduced from 1.0 to 0.5, the cracking load and peak load of the specimens increased by 17.31 % and 16.53 % respectively. Increasing the prestress level from 0 to 0.3 and 0.6 increased the cracking load of the specimens by 1.41 and 2.36 times, respectively, but the peak load of the specimens increased by only 3.37 % and 8.17 %. The cracking load of the parabolic tendon specimen increased by 2.18 for the comparison specimen but was 8.33 % lower than that of the linear tendon specimen with the same degree of prestressing. Comparison of the two prestressing sequences showed that the cracking load of the specimen with tensioning prestressed tendons after pouring the entire beam section increased by 29.84 %, but the peak load increased by only 3.11 %. As the height of the prestres tendons increased, the cracking and peak loads of the specimen reduced by 5.84 % and 5.71 % respectively. Consequently, the shear strength of PSRCC deep beams was significantly influenced by the shear span-depth ratio and minimally affected by prestress-related parameters. The proposed model accurately predicted the shear strength of PSRCC deep beams compared to existing codes, offering valuable guidance for design.

A Study on Yield Criteria Influence on Anisotropic Behavior and Fracture Prediction in Deep Drawing SECC Steel Cylindrical Cups.

The deep drawing process, a pivotal technique in sheet metal forming, frequently encounters challenges such as anisotropy-induced defects. This study comprehensively investigates the influence of various yield criteria on the anisotropic behavior and fracture prediction in SECC steel cylindrical cups. It integrates Hill'48R, Hill'48S, and von Mises yield criteria in conjunction with Swift's hardening law to evaluate material behavior under complex stress states. Experimental and numerical simulations assess the anisotropy effects across multiple orientations (0°, 45°, and 90°), revealing intricate relationships between stress criteria and material response. The findings indicate significant discrepancies between isotropic and anisotropic models in predicting fracture heights, emphasizing the importance of selecting appropriate yield criteria. Notably, the von Mises criterion results in lower fracture heights, suggesting higher susceptibility to fractures, while the Hill'48R model aligns closely with experimental data, validated through variations in punch corner radius and blank holder force parameters, with a maximum deviation of 3.23%. Hill'48S displays moderate plastic deformation characteristics.

Expansion of a spherical cavity in an infinite porous rigid/plastic medium

An expanding spherical cavity of a zero initial radius surrounded by an infinite porous rigid/plastic medium is considered. The material is assumed to obey the flow theory of plasticity based on a yield criterion and its associated flow rule. The yield criterion depends on the linear and quadratic stress invariants. No restriction is imposed on this dependence, except for the standard requirements imposed on the yield criteria. It is shown that the solution can be extended into the rigid region. The yield criterion approaches the von Mises yield criterion as the relative density approaches unity. Some equations contain the expression 0/0 at the rigid/plastic boundary. In this respect, the present solution is qualitatively different from available elastic/plastic solutions. However, the solution does not provide the solution for the von Mises yield criterion as a particular case. Numerical results are presented for Green’s yield criterion. These results follow physical expectations concerning the distributions of the relative density, the radial velocity, and the radial stress. The solution is adapted for expanding a cavity of a non-zero initial radius. The pressure required for expanding the cavity is calculated.

Analysis of elastic stresses in rotating cylinders made of Titanium and Bronze materials

ABSTRACT This study analytically investigated elastic stress distribution in rotating cylinders made of Titanium and Bronze material. The Von Mises yield criterion was applied under the assumption of plane strain conditions. The modelling process considered that the disc material remains unaffected by temperature variations. The thermal stresses of a thin circular disc are being studied. The determined temperatures are close to the maximum and minimum temperatures at which the material can work. The numerical analysis is one, and the results are depicted as a whole with graphs. This study also examined the changes in the temperature distribution on the stress distribution. At the end of the study, it was determined that the stresses occurring in the titanium material cylinder were higher than the bronze disc, and the pressures were inversely proportional to the increase in the grading parameter in the cylinders. Additionally, the ANSYS finite element program was utilised for validation.

Post-fire mechanical properties and constitutive model of Q690 high-strength structural steel

Fire hazard is one of the main threats to the integrity of steel structural buildings. Developing an accurate post-fire constitutive model for structural steel is crucial for enhancing the failure assessment of steel structures exposed to fire. In this study, the post-fire mechanical behavior of Q690 high-strength structural steel is investigated. Eighteen round bar specimens made of Q690 steel were heated with temperatures ranging from 20 °C to 900 °C. Tensile tests were conducted on these specimens to obtain the post-fire stress-strain curves and associated mechanical parameters of the material. To accurately characterize the post-fire behavior of Q690 steel, a temperature-dependent elastoplastic constitutive model combined with its numerical implementation algorithm is proposed. This model consists of four components: a temperature-dependent elasticity criterion, the von Mises yield criterion, an associated flow rule, and a temperature-dependent isotropic hardening law. The proposed constitutive model has a notable feature, i.e. the material parameters in the model can be defined as a function of temperature according to the test results. As a result, when utilizing this model for post-fire assessments of steel members, only three routine parameters, i.e. elastic modulus at room temperature, Poisson's ratio, and the temperature experienced by the material, are required in the numerical simulation to generate the material’s stress-strain relationships. To verify the proposed constitutive model, the new model was introduced into the numerical simulations of the tested round bar specimens after exposure to various temperature conditions. Both the load-displacement curves and local deformation of each round bar specimen obtained from the numerical simulations are compared with the test results to validate the accuracy of the new model. The constitutive model presented in this study provides a useful tool for assessing the post-fire behaviors of steel components.

Development of GDDR method for ratcheting analysis of moderately thick plates

In the present paper, a previously introduced numerical method, GDDR (Generalized Differential Dynamic Relaxation), is developed to analyze ratcheting behavior of moderately thick rectangular plates. The validity of the method is verified by comparison with literature data and finite element method results. Classical Plate Theory (CPT) and First-order Shear Deformation Theory (FSDT) are utilized to define the displacement field of plates. Incremental strain equations are derived according to von Karman relations. Prandtl-Reuss flow rule and von Mises yield criterion and are used to express the behavior of the plates in the plastic region. The Armstrong-Frederick nonlinear kinematic hardening model is incorporated for elastic-plastic analyses. Finally the results of ratcheting analysis obtained by GDDR method based on two mentioned theories are compared. Results showed that higher amounts of strains are predicted when FSDT theory is employed. Moreover, the area of hysteresis loops obtained by FSDT analysis are larger than those of CPT analysis, meaning that FSDT approach predicts more energy dissipation during each cycle of loading compared with CPT approach. Finally, comparing the results for different ratios of thickness to width shows that GDDR method can predict more accurate results, especially for higher ratios, when it utilizes FSDT theory.

The Influence of Reverse Yielding on the Plastic Conditioning of Interference Fits in Power Transmission Engineering

Interference fits are very common shaft–hub connections due to their low manufacturing costs and excellent technical properties. The Plastic Conditioning of this machine element is a new and not very well-known method. During the development of this method, it was discovered that Reverse Yielding occurs in certain applications and has a negative impact on the result. This paper examines the effects of Reverse Yielding on the technology of Plastic Conditioning of interference fits in Power Transmission Engineering. Based on the Shear Stress Hypothesis (SH), the Plane Stress State (PSS), and the ideal plastic behavior of materials, established stress–mechanical relationships are used to find the influencing parameters of Reverse Yielding on the technology of Plastic Conditioning and their limits. As a result, a new computational concept is developed that allows the user to maximize Plastic Conditioning while avoiding Reverse Yielding. Analytical calculation suggestions and diagrams for practical application are provided. Furthermore, the deviations in the obtained results, taking into account other material models such as the Von Mises Yield Criterion (VMYC) and material hardening, as well as the Bauschinger effect, are examined in comparison with our own numerical results from the development of Plastic Conditioning, and the resulting need for further research is defined. In addition, the method of Plastic Conditioning of interference fits is introduced and its basic principles are briefly explained.

Characterizing the mechanical deformation response of AHSS steels: A comparative study of cyclic plasticity models under monotonic and reversal loading

This study evaluates the performance of a user-defined combined hardening modeling method for advanced high-strength steels (AHSS) under monotonic and reversal loading conditions. The plastic behavior of TWIP980 and TRIP980 AHSS sheet metals is investigated using a cyclic plasticity modeling approach. The model incorporates an isotropic von Mises yield criterion and a single-term Chaboche nonlinear kinematic hardening rule. Monotonic and reversal loading stress-strain curves are predicted and compared with experimental results. The model accurately captured the Bauschinger effect for both materials, but it needs help to effectively model the permanent softening behavior observed in TWIP980 steel. Overall, the proposed modeling method agrees well with experimental results for monotonic loading and accurately represents the Bauschinger effect and transient behavior during reversal loading. However, better improvements are needed to capture the permanent softening behavior of TWIP980 steel.

Analiza elastično-plastičnog naprezanja skupljajućih debelih FGM cilindara

This paper addresses the stress analysis of shrink-fitted thick-walled cylinders made of functionally graded material (FGM). Analytical solutions are provided for the elastic-plastic behavior of shrink-fitted axisymmetric thick-walled FGM cylinders based on the linear plane elasticity theory and plasticity laws. Due to the material's functional gradation, mechanical characteristics like Young's modulus, yield stress, and plastic parameters are controlled by a power function along the wall thickness. Considering a plane strain case, elastic-perfectly plastic model and Von Mises yield criterion; theoretical solutions are obtained for both elastic and plastic phases. The radial, hoop, axial, and equivalent Von Mises stresses are obtained for up to 25%, 50%, and 75% of cylinder plasticization for the elastic and plastic zones. Stresses are given in terms of interference and geometrical and mechanical parameters of the assembly. In addition, the interferences to start plastic deformation and the full plastic collapse of the cylinder are discussed. Moreover, the effect of the gradient index on the contact pressure and both the start of yield and plastic collapse pressures are conducted. The analytical results found in the current research are compared with the numerical solutions carried out by Ansys Workbench. Both results show a good agreement.

Design of equi-strength annular disks made of functionally graded materials

This research proposes a robust method for designing functionally graded disks subject to internal and external pressures. The design objective is to find the profile of equi-strength disks. The von Mises yield criterion controls the initiation of plastic yielding. The yield stress and Young’s modulus are entirely arbitrary functions of the polar radius. Poisson’s ratio is constant. The solution is facilitated using the dimensionless yield stress as an independent variable instead of the polar radius. In particular, a numerical technique is only required to solve two ordinary differential equations. Moreover, one of these equations is independent of the other. Therefore, the equations can be solved individually, simplifying the solution method. The limitation imposed by the thickness gradient on the acceptability of plane stress conditions is considered. Particular designs are proposed assuming that the power function describes the radial distribution of material properties. A critical condition that allows for deriving relatively simple design solutions is emphasized. It is shown that this condition is satisfied for many specific material property distributions used in the literature.

An adaptive pseudo-lower bound limit analysis for fracture structures

In this study, we present a new approach to determine the limit loads of fracture structures by using the pseudo-lower bound method with adaptive quadtree meshes. A significant advantage of the pseudo-lower bound method is that calculations done with the stress field immediately solve the volumetric locking problem. Additionally, by defining quadtree meshes in the context of polygonal elements, it is possible to handle the technique of adaptive quadtree meshes, which poses a significant challenge in traditional finite elements due to the presence of hanging nodes during the refinement procedure. The von Mises yield criterion is employed, and structures containing cracks are assumed to have plane stress or plane strain conditions. The static form of the limit analysis is changed into second-order cone programming (SOCP), and the Mosek tool is then used to solve it. Numerical validation is used to illustrate the reliability and effectiveness of the proposed approach.

Analysis of functionally graded rotating disks via analytical approximation methods

Analytical solutions for functionally graded (FG) rotating disks are limited due to the functional representation of the cross-sectional geometry, the density, and the modulus of elasticity which lead to a governing differental equation with variable coefficients. Analytical solutions for such disks are limited according to the functional form chosen for the variation of the property. Hence, analytical approximation approaches gain importance for such problems. In this study, two analytical approximation approaches are proposed for the analysis FG rotating disks. The methods used are the Improved Adomian decomposition method (IADM) and the optimal homotopy asymptotic method (OHAM). The resulting solution is an analytical solution in power series form. It is assumed that the disks considered are subjected to constant angular velocity. Material properties such as modulus of elasticity, density and yield strength are assumed to vary along the radial direction according to the power law function. Stresses are obtained for different values of the gradient parameters to investigate the effects of the parameters. Von Mises yield criterion is used to determine elastic limit angular velocities. The results from this study are in very good agreement with previous results available in the literature. In addition, it is observed that OHAM converges to results much faster than IADM.

Nonlinear inelastic analysis of space semi-rigid steel frames subjected to static load using plastic-zone method

A new hybrid element based on plastic-zone method is proposed for static nonlinear analysis of space semi-rigid steel frames. Four zero-length nonlinear rotational springs are added to the beam ends to model both in- and out-of-plane connection rotational behavior with appropriate semi-rigid connection models. The von Mises yield criteria are applied to govern material plasticity along the member length and throughout the cross-section using Newton–Cotes integration points. The modified generalized displacement control method is used to solve the system of nonlinear equilibrium equations. Some numerical examples are investigated to show the reliability and visual illustration of the proposed hybrid element.

Creep Analysis of Rotating Thick Cylinders Subjected to External and Internal Pressure: Analytical and Numerical Approach

Creep analysis is crucial when dealing with thick rotating cylinders exposed to a steady load or stress at a higher temperature. These cylinders present a fundamental constituent in a variety of dynamic engineering applications, such as pressure vessels, hydraulic cylinders, gun barrels, boilers, fuel tanks, aerospace technologies, nuclear reactors, and military equipment. Thus, severe mechanical and thermal loads cause significant creep and reduce service life. Hence, the prediction of creep in such axisymmetric components, including pressure vessels, subjected to steady load at elevated temperatures is extremely important and quite a complex task. Thus, in this study, the creep behavior in a rotating thick-walled cylinder made of Al-SiCp composite subjected to constant load as well as internal and external pressures is investigated, both analytically and numerically, using FEM. A wide range of rotational speeds effect on the process is also included. The creep behavior is assumed to follow the Norton constitutive model, and for stress failure analysis, von Mises yield criteria are adopted. The effect of internal and external pressures, as well as the rotational speed on the stresses, strains, and strain rates in the cylinder, is studied and presented. Both finite element analysis (FEA) and Lame’s theory were used to determine the radial, tangential, and longitudinal displacements and corresponding stresses, as well as the equivalent Von Mises stresses and strain rate distributions in the cylinder revolving about its own axis. It is observed that with the increase of the internal pressure in the cylinder, the strain rate increases. Meanwhile, when subjecting the cylinder to both external and internal pressures, the strain rates tend to decrease. For instance, it was also found that stress and strain rates were higher for the 1000 rad/sec rotational speed of thick cylinder in comparison with lower rotational speeds of 300 and 500 rad/sec. Also, it is noticed that the variation in these values at the inner radius was more than those found at the outer radius. All results of the stresses, strains, and strain rate distributions obtained are found to be in full agreement with the published data. Furthermore, all plotted results of the stresses, strains, and strain rate distributions obtained through the analytical approach were found to be in exceptional compliance with those solutions obtained using finite element analysis (FEA).

A large strain thermoplasticity model including recovery, recrystallisation and grain size effects

AbstractIn manufacturing, thermomechanical processes such as static annealing and hot working are commonly used to tailor the microstructure of metals to achieve favourable macroscopic material properties that meet specific application requirements. To improve sequential manufacturing processes and to accurately predict the microstructural changes of the material along the process chain, physically motivated constitutive models are required that simultaneously account for the effects of recovery and recrystallisation, as well as grain size dependencies. To this end, Cho et al. [Int. J. Plasticity 112, 123–157 (2019)] proposed a macroscopic hypo‐elasticity based large strain thermoplasticity model that aims at the unification of the effects of static and dynamic recovery and recrystallisation, as well as grain growth and refinement. In the present contribution, the hypo‐elasticity based large strain recrystallisation formulation proposed by Cho et al. is transferred to a hyper‐elasticity based large strain thermoplasticity framework to overcome the limitations typically accompanied with hypo‐elasticity based formulations. For this purpose, an isotropic temperature dependent hyper‐elastic Hencky type formulation defined in logarithmic strains is combined with a temperature dependent von Mises yield criterion. The recrystallisation modelling approach by Cho et al. is adopted, assuming a non‐associated temperature dependent proportional hardening rate in the form of an Armstrong‐Frederick type hardening minus recovery format, wherein the proportional hardening related internal variable is interpreted as a measure of dislocation density. It is shown that the hyper‐elasticity based format results in a thermodynamical consistency condition that effectively constrains the physically motivated evolutions of recrystallised volume fraction and average grain size. To investigate the capability of the model to predict the material response of unified recrystallisation thermodynamically consistently, representative thermomechanical sequential loading conditions including static annealing and hot working are studied.