Tresca Criterion Research Articles

Application of lubrication theory to determine yield stress in slump tests

The slump test can determine the yield stress of slurries by measuring the slump height. The convex shape in the slumped slurry profile cannot be characterised by the Tresca criterion. Lubrication theory has been widely applied to analyse the slow flow of yield stress fluids. Thus, the present study incorporates lubrication theory and the Tresca criterion to establish a generalized model for reconstructing the slurry profile based on the yield stress. The convex profile in the lower zone can be well represented by the novel method. The predicted yield stresses by the slump tests are larger than those determined using the vane method. Slump height and spread are equally accurate for predicting yield stress via the proposed method. Overall, the combination of lubrication theory and Tresca criterion yields a good prediction of yield stress based on slump height.

Trabecular Bone Component Assessment under Orthodontic Loads and Movements during Periodontal Breakdown-A Finite Elements Analysis.

This numerical analysis, by employing Tresca and Von Mises failure criteria, assessed the biomechanical behavior of a trabecular bone component subjected to 0.6, 1.2, and 2.4 N orthodontic forces under five movements (intrusion, extrusion, tipping, rotation, and translation) and during a gradual horizontal periodontal breakdown (0-8 mm). Additionally, they assessed the changes produced by bone loss, and the ischemic and resorptive risks. The analysis employed eighty-one models of nine patients in 405 simulations. Both failure criteria showed similar qualitative results, with Tresca being quantitatively higher by 1.09-1.21. No qualitative differences were seen between the three orthodontic loads. Quantitatively, a doubling (1.2 N) and quadrupling (2.4 N) were visible when compared to 0.6 N. Rotation and translation followed by tipping are the most stressful, especially for a reduced periodontium, prone to higher ischemic and resorptive risks. In an intact periodontium, 1.2 N can be safely applied but only in a reduced periodontium for extrusion and intrusion. More than 0.6 N is prone to increasing ischemic and resorptive risks for the other three movements. In an intact periodontium, stress spreads in the entire trabecular structure. In a reduced periodontium, stress concentrates (after a 4 mm loss-marker for the stress change distribution) and increases around the cervical third of the remaining alveolar socket.

Advance optimum design of multi-layer compound cylinders

The purpose of this work is to find the optimum design for two-layer compound cylinders of the same material with an open end condition by using the elimination method. The optimization method depends on reducing the number of design variables with a simultaneous yield hypothesis for all layers of the compound cylinder. A combination of von Mises and Tresca criteria is used as a yield criterion, and the superposition principle is used to evaluate the equivalent stresses for each cylinder. By considering the working pressure and the internal diameter of the inner cylinder as the design parameters (constants during optimization) and the total thickness of the compound cylinder as the objective function, the optimization algorithm has been programmed in C# with a user-friendly graphical interface. The optimization results (outer diameter, interference diameter, and shrinkage pressure) are obtained for different working pressures and compared with the optimum design, which is based only on the Tresca criterion. The total mass of the compound cylinder can be reduced by up to 50% by using the von Mises–Tresca combination criterion. The optimized results are validated numerically by using finite element analysis in the ANSYS Workbench. The theoretical result and the FEA result agree with each other with errors of about 2%. The behavior of the optimized parameters for different working pressures is also observed and presented.

Residual contact pressure for mechanically lined pipe hydroforming with carrier pipe plastification

Mechanically Lined Pipe (MLP) is a rigid carbon steel pipe internally lined with a flimsy Corrosion Resistance Alloy (CRA). This bi-metal composite structure has become an economic and flexible solution to offshore Oil & Gas (O&G) transportation of highly caustic hydrocarbon fluids. The residual contact pressure that arises from the hydraulic expansion fabrication process may prevent wrinkling and interlayer detachment when the pipe is bent or axially compressed during installation and operation. Increasing the residual contact pressure thus becomes a relevant topic for maintaining MLP integrity. The traditional MLP manufacturing process retains the carrier pipe entirely elastic. Yet, a light degree of plastification of carrier pipe will enhance the mechanical adhesion. Mathematical formulations including linear and Ludwik Power Law (LPL) hardening models are here developed to describe the stress-strain behavior of partially plastified carrier pipe. The stress state analysis is performed throughout the whole fabrication process based on the Tresca criterion. Results for residual contact pressure and residual stress state are obtained analytically and numerically. It suggests that an appropriate plastification of carrier pipe favors the mechanical adhesion.

Orthodontic Internal Resorption Assessment in Periodontal Breakdown-A Finite Elements Analysis (Part II).

This finite elements analysis (FEA) assessed the accuracy of maximum shear stress criteria (Tresca) in the study of orthodontic internal surface resorption and the absorption-dissipation ability of dental tissues. The present study was conducted over eighty-one models totaling 324 simulations with various bone loss levels (0-8 mm), where 0.6 N and 1.2 N were applied in the intrusion, extrusion, rotation, tipping, and translation movements. Tresca criteria displayed localized high-stress areas prone to resorption for all situations, better visible in the dentine component. The internal resorptive risks are less than external ones, seeming to increase with the progression of the periodontal breakdown, especially after 4 mm. The internal and external surface high-stress areas are strictly correlated. The qualitative stress display for both forces was almost similar. The rotation and tipping displayed the highest resorptive risks for the pulp chamber, decreasing with bone loss. The resorptive risks seem to increase along with the progression of periodontal breakdown if the same applied force is kept. The dentine resemblance to ductile based on its high absorption-dissipation ability seems correct. Tresca seems to supply a better predictability of the prone-to-resorption areas than the other failure criteria.

Determination of fracture toughness and yield strength of Inconel 718 by milling operation

This paper presents an analytical scheme to determine the fracture toughness and the yield strength of Inconel 718 by the widely used milling operation. It is noted that there exists material fracture at the tool tip and the removed layer of material undergoes plastic deformation along the primary shear plane. The fracture toughness is considered at the tool tip and the yield strength is applied on the primary shear plane. Subsequently, the modified Williams’ model and the modified Williams-minimization model are both proposed on the basis of the geometries and mechanics in the oblique cutting process. The modelling framework indicates that milling can be developed as an alternative method to determine the fracture toughness and the yield strength from the serrated chip thicknesses combined with the corresponding cutting forces. This is because the experimental method by milling is a convenient scheme as it only requires the cutting forces per unit width of cut with respect to a series of uncut chip thicknesses. In addition, the normal shear angle is predicted by applying the principle of energy minimization. Finally, milling experiments are conducted to validate the two proposed methods. Results show that the two analytical methods return similar values of fracture toughness and yield strength, respectively. Besides, it is noted that high values of yield strength are achieved based on Tresca criterion, which would indicate work hardening in the primary shear zone during the serrated chip formation. The proposed methods exhibit advantages of convenience and generality to derive the fracture toughness and the yield strength, since it is still a challenge for the traditional standard mechanical tests for Inconel 718 due to its toughness and ductility.

On the structure of poroplastic constitutive relations

The paper discusses from first principles all aspects relevant to the plasticity of porous materials. Emphasis is laid on unhomogeneous yielding, defined as the process of yielding and plastic flow under gradient-free macroscopically nonuniform deformation. The nonuniformity is represented by strain localization in one or more bands of finite thickness. A universal feature of all intrinsic yield criteria is their dependence upon the normal and shear tractions resolved on the band. When specialized to isotropy, a Mohr–Coulomb criterion and a Rankine–Tresca criterion emerge as two extremes. The latter is an ideal that typifies the yield behavior of porous materials under arbitrary loadings. The general theory stands for a finite number of bands or yield systems. Its overall structure bears some features of crystal plasticity, but with dependence upon the resolved normal stress. The evolution of microstructural parameters can be given in general terms, being solely based on the kinematic constraints of unhomogeneous yielding and matrix incompressibility. Throughout the paper, the competition with homogeneous yielding, heretofore taken for granted, is analyzed with or without strain and strain-rate hardening effects. We close by discussing the thermodynamic consistency of this new class of constitutive relations and a link to strain-gradient theories.

Assessment of the Orthodontic External Resorption in Periodontal Breakdown-A Finite Elements Analysis (Part I).

This Finite Elements Analysis (FEA) assessed the accuracy of Tresca failure criteria (maximum shear stress) for the study of external root resorption. Additionally, the tooth absorption-dissipation ability was assessed. Overall, 81 models of the second mandibular premolar, out of a total of 324 simulations, were involved. Five orthodontic movements (intrusion, extrusion, rotation, translation, and tipping) were simulated under 0.6 N and 1.2 N in a horizontal progressive periodontal breakdown simulation of 0-8 mm. In all simulations, Tresca criteria accurately displayed the localized areas of maximum stress prone to external resorption risks, seeming to be adequate for the study of the resorptive process. The localized areas were better displayed in the radicular dentine-cementum component than in the entire tooth structure. The rotation and translation seem prone to a higher risk of external root resorption after 4 mm of loss. The resorptive risks seem to increase along with the progression of periodontal breakdown if the same amount of applied force is guarded. The localized resorption-prone areas follow the progression of bone loss. The two light forces displayed similar extensions of maximum stress areas. The stress displayed in the coronal dentine decreases along with the progression of bone loss. The absorption-dissipation ability of the tooth is about 87.99-97.99% of the stress.

A new hybrid approach model for predicting burst pressure of corroded pipelines of gas and oil

Accurate prediction of the burst pressure of corroded pipeline is of great significance to pipeline design, reliability analysis and maintenance decision. This paper presents a novel hybrid approach model for predicting the burst pressure of corroded pipelines. First, a new feature space with physical meaning is constructed based on the pipeline geometry, the size of corrosion defects, and the mechanical properties of materials. Then, a fusion mechanism combining empirical formula and ensemble learning is proposed, which makes full use of the prior knowledge in the Tresca criterion and the predictive ability of ensemble learning. The prediction model is built using the Light Gradient Boosting Machine, and the hyper-parameters are tuned using the Tree-structured Parzen Estimator algorithm. Finally, a burst pressure dataset of corroded full-scale oil and gas pipelines ranging from low strength to high strength is established to verify this model. The prediction results demonstrate that the hybrid approach model can significantly improve the prediction accuracy. And compared to other ensemble learning methods such as random forest and XGBoost, the accuracy of this model proposed in this paper is the highest. The correlation coefficient is 0.98163, the mean square error is 0.98087 MPa, the mean absolute error is 0.66500 MPa, and mean absolute percentage error is 0.04480. The model also provides feature importance, enhancing the interpretability of the model. In addition, further experiments demonstrate that this model has good adaptability to corroded pipelines of different strengths grade and obvious advantages compared with the calculation results of five traditional empirical formulas.

Finite Elements Analysis of Tooth—A Comparative Analysis of Multiple Failure Criteria

Herein Finite elements analysis (FEA) study assesses the adequacy and accuracy of five failure criteria (Von Mises (VM), Tresca, maximum principal (S1), minimum principal (S3), and Hydrostatic pressure) for the study of tooth as a structure (made of enamel, dentin, and cement), along with its stress absorption-dissipation ability. Eighty-one 3D models of the second lower premolar (with intact and 1-8 mm reduced periodontium) were subjected to five orthodontic forces (intrusion, extrusion, tipping, rotation, and translation) of 0.5 N (approx. 50 gf) (in a total of 405 FEA simulations). Only the Tresca and VM criteria showed biomechanically correct stress display during the 0-8 mm periodontal breakdown simulation, while the other three showed various unusual biomechanical stress display. All five failure criteria displayed comparable quantitative stress results (with Tresca and VM producing the highest of all), showing the rotational and translational movements to produce the highest amount of stress, while intrusion and extrusion, the lowest. The tooth structure absorbed and dissipated most of the stress produced by the orthodontic loads (from a total of 0.5 N/50 gf only 0.125 N/12.5 gf reached PDL and 0.01 N/1 gf the pulp and NVB). The Tresca criterion seems to be more accurate than Von Mises for the study of tooth as structure.

Regularized frictional contact problems with the interior point method

The aim of this paper is to present an algorithm to solve frictional contact problems by considering the Coulomb’s criterion. As it is known, the frictional contact problem using Coulomb’s criterion has no minimization principle behind. However in order to use algorithms based on minimization methods, the frictional contact problem is written as an optimization one, more specifically as a sequence of Tresca contact problems. Moreover a family of regularization functions is introduced in order to regularize the non-smooth character of the Tresca criterion, which in some cases can have an experimental justifications. As each minimization problem becomes smooth enough, the interior point method is used to solve the generated optimization problem, which has some advantages when the non-penetration constraints are imposed in a symmetrical manner.

SIMULATION OF THE STRESS-STRAIN STATE AND DETERMINATION OF THE NATURAL FREQUENCY OF THE LABORATORY CENTRIFUGE SHAFT VIBRATION USING ANSYS AND KISSSOFT

The rotor is a key element of high-speed mechanisms that are widely used in various industries, such as laboratory centrifuges used to separate mixtures of different fractions, gas turbines, industrial compressors, engines, and others. The main requirement for such mechanisms is reliability and safety during operation. To ensure the above requirements, it is necessary to determine the stress-strain state of the most loaded structural elements of the system and the dynamic characteristics. This paper presents an analysis of the stress-strain state of a rotor system using the example of a Pico21 laboratory centrifuge. The Ansys and KISSsoft software packages were used for 3D modelling of the finite element model. The system consists of a flexible shaft with a rotor, the rotor mass was changed during the simulation and supports, the role of which is performed by bearings. A comparative analysis of the obtained results of the stress-strain state is presented, which further makes it possible to carry out appropriate calculations taking into account stress concentrators to determine the durability and lifetime of high-speed mechanisms. The stresses are determined according to the von Mises and Tresca criteria. The paper also presents the results of the calculation and analyses the natural frequencies of the rotor system. Further studies, it is planned to determine the natural frequencies of vibration, taking into account gyroscopic effects, which are necessary to determine the resonant frequencies and zones of stable operation of the system.

Research on the Relation between Slump Flow and Yield Stress of Ultra-High Performance Concrete Mixtures.

The relation between slump flow and yield stress of ultra-high performance concrete (UHPC) mixtures was studied with theoretical analysis and experimentation. The relational expression between slump flow and yield stress of UHPC mixtures was built and then verified with a rheological test. The results showed that the prediction model, as a function of cone geometry of dimensionless slump flow and dimensionless yield stress of the UHPC mixtures, was constructed based on Tresca criteria, considering the geometric relation of morphological characterization parameters before and after slump of the UHPC mixtures. The rationality and applicability of the dimensionless prediction model was verified with a rheological test and a slump test of UHPC mixtures with different dosages of polycarboxylate superplasticizer. With increase in polycarboxylate superplasticizer dosage, yield stress of the two series of UHPC mixtures (large/small binding material consumption) gradually decreased, leading to a gradual increase in slump flow. Based on the prediction model of dimensionless slump flow and dimensionless yield stress, the relational expression between slump flow and yield stress of the UHPC mixtures was built. The comparison result showed that the calculated data was consistent with the experimental data, which provided a new method for predicting yield stress of UHPC mixtures with a slump test.

A mathematical extrapolation-based yield criterion and its application in modeling of burst pressure of defect-free straight pipes

To solve the problem of insufficient accuracy of the existing prediction models of burst pressure for defect-free straight pipes, a new yield criterion that can effectively reflect the deformation characteristics of pipeline materials is established by the mathematical extrapolation method, and a theoretical model of burst pressure for defect-free straight pipes is then derived. By comparing each yield criterion with the experimental data, the new yield criterion is found to be between the TSS criterion and the Tresca criterion, and is in good agreement with the experimental data. On this basis, a theoretical model for predicting the burst pressure of defect-free straight pipes is constructed by using this criterion, and the burst pressure under other yield criteria are also derived. The normalized burst pressures based on different yield criteria are given and compared with the full-size test data. It is found that the new yield criterion has the highest approximation degree to the test data since the average relative error is just 1.154% and the maximum error is no more than 10.801%. The model in this paper can meet the requirement of predicting the burst pressure of a defect-free straight pipe, which is of great significance to the structural design and safety assessment.

Comparative Study of Shear Fracture between Fe-based Amorphous and Ultrafine-grained Alloys Using Micro-tensile Testing

Micro-tensile tests were employed to clarify the post-plastic-instability behavior in the shear fractures of specimens with the dimensions of 18×25×50 µm3 made from iron-based amorphous (AM) and ultrafine-grained (UFG) alloys. The AM specimen yielded by localized shear bands with an inclination angle of ~52° with respect to the loading axis, followed by sliding off almost throughout the entire specimen thickness. Micro-tensile and micro-shearing tests revealed that the Mohr failure envelope of the AM specimens could be described by a quadratic equation rather than a linear equation. Therefore, the sliding-off process is assisted by the applied normal stress, which suggests that it is caused by free-volume coalescence. For the UFG specimen, yielding set in by shear band formation with an inclination angle of ~45° with respect to the loading axis, following the Tresca criterion. Necking after shear band diffusion formed a triaxial stress state, which resulted in a final shear fracture plane via void coalescence in the UFG specimens. Voids formed along the intersection of the primary shear bands with secondary shear bands during the necking process. This indicates that the deviation of the shear fracture plane in the UFG specimen was determined by the strain development process. A comparison of the post-plastic-instability behavior between the AM and UFG specimens suggests that the external control of triaxial stress conditions is key to improving the formability of AM specimens.

Mechanical analysis and parameter design of CFRP-Wrapped defected steel pipe

Externally wrapped carbon fiber reinforced polymer (CFRP) composites are effective to strengthen the defected steel pipes. However, the effects of thickness and mechanical properties of pipe substrate, CFRP, and putty are still unclear. In the present study, an analytical model based on the Tresca yield criterion and failure mode of CFRP-wrapped defected pipe was proposed to calculate the stress and yield/burst pressure. The analytical model was verified by the burst test and finite element (FE) analysis. The effects of Poisson's ratio, modulus, and thickness of the putty and CFRP on stress and load bearing capacity were analyzed quantitatively by the analytical model. The analytical model is accurate and conservative due to the Tresca criterion and the assumption of ideal elastic-plastic. For putty, a larger modulus and smaller thickness can reduce the stress of pipe substrate and improve the yield pressure. The yield and burst pressures are dominated by the CFRP thickness and modulus. A dimensionless model of yield pressure was established and the critical dimensionless CFRP modulus and thickness making the yield pressure of the strengthened pipe greater than the operating pressure of the original pipe were determined.

An insight into size effect on fracture behavior of Inconel 718 cross-scaled foils

Product miniaturisation has increased the demand for cross-scaled components with various sized features covering the macroscale (mm-scale) and mesoscale (μm-scale). During the sheet metal forming process, the feature size of cross-scaled components, such as foil thickness, changes from macroscale to mesoscale. The fracture behavior of the cross-scaled components varies from that of the macroscale components due to the size effect, leading to a high scrap rate and unacceptable cost in manufacturing. To reveal size effect on fracture and predict the fracture occurring of the cross-scaled components is still a challenge urgently to be solved. Thus, taking Inconel 718 superalloy cross-scaled foils as the case material, firstly, the cross-scaled foils were prepared with the thicknesses from 0.05 to 1.5 mm, the ratio of thickness to grain size (t/d) from 1.07 to 24.26. Uniaxial tensile tests and in-situ tensile tests were performed to reveal the fracture mechanism of the superalloy cross-scaled foils. Then, several uncoupled fracture criteria were implemented into the crystal plasticity finite element modeling (CPFEM) with the cross-scaled geometric modeling and random texture to predict the fracture behavior of the cross-scaled components. The uncoupled fracture criteria include Freudenthal criterion, Cockcroft & Latham(C&L) criterion, Normalized C&L, Brozzo criterion, Ayada criterion, Rice & Tracy criterion, Tresca criterion, equivalent stress criterion, equivalent strain criterion and maximum principal strain criterion. The phenomenological crystal plasticity model and dislocation density-based crystal plasticity model were compared in terms of calculation accuracy and efficiency. Thirdly, the size effect related fracture mechanisms of the cross-scaled foils were revealed, and the relationship between the fracture strain, fracture stress and t/d were obtained. Generally, the fracture strain and stress drop with a decrease in t/d. Consequently, an abnormal phenomenon occurs where the plasticity and strength increase with the decrease of t/d in some areas. The random textures lead to fluctuations in the strength and plasticity of the cross-scaled foils. Finally, the equivalent stress fracture criterion (ESFC) was determined where the fracture threshold is less affected by random texture. The relationship between the fracture threshold of ESFC and t/d was found, and the CPFEM-ESFC model was established considering the random textures induced scattering of the fracture threshold due to random textures. The scattering distribution function of cross-scaled component fracture behavior under different t/d was obtained through CPFEM-ESFC model and hundreds of random textures designs. The study provides a statistical method to avoid the forming scattering and a theoretical basis for the process design of cross-scaled components.

More on Plastic Yield Criteria

The two plastic yield criteria known as MISES and TRESCA were proposed long ago. The Mises criterion is the one usually preferred by the strength of materials community, but tests have shown that Tresca’s criterion is the more accurate. We discuss here the two criteria, and based on those tests we conclude in favor of the Tresca criterion. But the two criteria are not that different, so when accuracy is not important, Mises may serve as a simple approximation to Tresca.

Plastic zone size at notch tip in mode I fracture using the modified Irwin’s model and volumetric approach

At crack tip the stress distribution has singularities (i.e the stress intensity is infinite) which is physically impossible. Irwin realised that the stresses at crack tip are finite and subsequently introduced the Stress Intensify Factor(SIF). This factor is used to determine this plastic zone size. The crack is a special case of the notch. Around the notch, the fracture needs a volume to develop according to the volumetric approach. This volume is characterised by the distance effective Xeff, the stress effective σeff and the stress intensity factor KρI . In This paper a new proposed formula called “Modified Irwin’s Model” based on Irwin’s model can be used to determine the plastic zone size. This new formula will be verified using numerical finite element simulation and validated using the Von-Mises and Tresca Criteria. The Modified Irwin’s Model can be an alternative way to estimate the fracture elaboration zone from the plastic zone.

A weighted unification yield criterion and its application in analysis of burst pressure of pipe elbow

In order to solve the problem of insufficient accuracy in predicting the burst pressure of a pipe elbow based on the existing yield criteria, a new yield criterion is established firstly and then used to analyze the plastic failure of a pipe elbow. According to this idea, the mathematical characteristics of the Tresca criterion and the Mises criterion are revealed from the perspective of square shear stress, and a new yield criterion with generality is established by introducing a weighting coefficient δ. The yield criterion can be transformed to various yield criteria with different δ, including the existing yield criteria. On this basis, the plastic failure analysis of a pipe elbow is carried out, and the analytical formula of the burst pressure is derived, in which the strain hardening effect of the material is also considered. Besides, the main parameters that affect the burst pressure are analyzed. It is shown that the theoretical burst pressures calculated by the present yield criterion with different δ can coincide well with the experimental values for different materials, and the burst pressures decrease with the increase of the strain hardening exponent, while increase with the increase of the thickness-diameter ratio. The burst pressure formula established in this paper is of great significance to the structural design and safety assessment of a pipe elbow.