Pseudo Stress Research Articles

Thermo-mechanical coupled incremental variational formulation for thermosetting resins subjected to curing process

This study presents an incremental variational formulation (IVF) for the thermo-mechanical problem of resin products subjected to curing, for which a dual dissipation potential (DDP) for the cure state is originally derived in conjunction with that for viscoelasticity. Following the thermodynamically consistent formulation for the time evolution equation of the degree of cure (DOC) of a thermosetting resin and the linear viscoelastic law, we derive these DDPs by way of Legendre-Fenchel transformations with respect to characteristic dissipations. The evolution of DOC is then casted into the flow rule in mathematical theory of plasticity with the introduction of the curing multiplier as a new internal state variable in an analogous fashion to Perzyna’s viscoplastic regularization theory. Then, the pseudo stress is introduced as a new internal state variable to parameterize the derived flow rule of DOC. By virtue of this pseudo stress, we naturally define an incremental variational problem constrained by the parameterized flow rule in order to construct a semi-implicit scheme for the variational constitutive update. The finite element discretization is applied to the governing equations that satisfy the stationary conditions so that we could perform thermo-mechanical analyses of a thermosetting resin subjected to curing with the strong coupling procedure. The verification analysis is conducted to confirm the validity of the numerical result obtained by the proposed method in comparison with that of the conventional framework and followed by a demonstrative numerical example to simulate the stress development and relaxation in a virtual device subjected to different thermal histories.

Notch stress-strain estimation method based on pseudo stress correction under multiaxial thermo-mechanical cyclic loading

In this paper, a notch stress correction method based on the structural yield surface is proposed, in which the actual stress increment at the notch root can be obtained by multiplying two quantities, that is, the pseudo stress increment and the ratio of the slopes of the material and structural stress-strain curves. In the proposed method, the influence of temperature on the notch stress correction can be taken into account, and no iteration is required during the calculation process. Moreover, based on the proposed notch correction method and a unified viscoplastic constitutive model at high temperature condition, a notch stress-strain estimation method is developed under multiaxial thermo-mechanical cyclic loading. In order to assess the prediction accuracy of the proposed method, the calculated results are correlated to those from thermal-structural non-linear finite element analysis under various proportional and non-proportional mechanical loadings at non-isothermal high temperature condition. The comparison between the calculated and analyzed results shows that the proposed method can precisely estimate the notch stress and strain under multiaxial thermo-mechanical cyclic loading.

Modification of exponential based hyperelastic strain energy to consider free stress initial configuration and Constitutive modeling

In this research, the exponential stretched based hyperelastic strain energy was modified to provide the unstressed initial configuration. To this end, as the first step, the model was calibrated by the experimental data to find the best material parameters. The fitting results indicated material stability in large deformations and basic loading modes. In the second step, the initial pseudo stress value (ISV) was eliminated from the hyperelastic strain energy using a function of the determinant of the deformation gradient. The modified and unmodified models were implemented in ABAQUS/VUMAT user subroutine and the deformation behavior of the natural rubber and the thermoplastic elastomer was predicted. The results obtained from the modified model represented a better agreement with the experimental data, in comparison to those gained by the unmodified model. In order to present the significance of the unstressed initial configuration in engineering applications, the stenting phenomenon in the atherosclerosis human artery was investigated. It was revealed that a uniform stress distribution could be achieved in the artery using the modified model, thereby reducing the possibility of tearing and restenosis.

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

AbstractA new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.

Elimination of Pseudo Initial Stress for Proposed Invariants based Hyper elastic Strain Energy

Elimination of Pseudo Initial Stress for Proposed Invariants based Hyper elastic Strain Energy

New pseudo stress correction method for estimating local strains at notch under multiaxial cyclic loading

A notch correction method is proposed under multiaxial cyclic loading, in which the real stress increments can be directly obtained by correcting the pseudo stress increments at the notch. Moreover, the proposed method does not inherently restrict the direction and magnitude of real backstress increment in the real stress space. Additionally, on the basis of Kanazawa et al.’s model, the proposed method utilizes pseudo notch strains in replacement of measured strains to take account of the additional hardening due to the non-proportionality of external loadings. Based on the proposed correction method integrated with constitutive equations using Garud’s hardening model, a notch stress-strain estimation methodology is developed to calculate the local elastic-plastic stress-strain responses at the notch area. The presented methodology does not require iteration. The applicability of the presented methodology was verified by the experimental data of TC21 titanium alloy notched tubular specimens in this study and SAE 1070 steel notched shaft specimens from the literature. The results showed that the calculated notch strains correlate well with the measured strains under proportional and non-proportional loadings.

Dynamic Tensile Characterization of Vascomax® Maraging C250 and C300 Alloys

Vascomax® maraging C250 and C300 alloys were dynamically characterized in tension with Kolsky tension bar techniques. Compared with conventional Kolsky tension bar experiments, a pair of lock nuts was used to minimize the pseudo stress peak and a laser system was applied to directly measure the specimen displacement. Dynamic engineering stress–strain curves of the C250 and C300 alloys were obtained in tension at 1000 and 3000 s−1. The dynamic yield strengths for both alloys were similar, but significantly higher than those obtained from quasi-static indentation tests. Both alloys exhibited insignificant strain-rate effect on dynamic yield strength. The C300 alloy showed approximately 10 % higher in yield strength than the C250 alloy at the same strain rates. Necking was observed in both alloys right after yield. The Bridgman correction was applied to calculate the true stress and strain at failure for both alloys. The true failure stress showed a modest strain rate effect for both alloys but no significant difference between the two alloys at the same strain rate. The C250 alloy was more ductile than the C300 alloy under dynamic loading.

Long Term Use of Antipsychotics in Schizophrenia and Relation to Cortisol Level

Introduction and Aim of work Literature suggest that antipsychotic medications may decrease cortisol level, an effect that seems to be more present with second generation antipsychotic. Our study aims at assessing effect of long term use of antipsychotics on cortisol level Subjects and Methods 30 chronic schizophrenic patients on antipsychotics compared to 20 drug naif schizophrenic patients as regards serum cortisol level Results Cortisol level was significantly lower in chronic schizophrenic patients receiving antipsychotics compared to drug naif patients (P=0.002 Conclusion Antipsychotic medications seem to have the potential to decrease cortisol level in blood. Among hypothesis proposed in literature is the good control of pseudo stress due to psychotic features

An applied electro-magneto-elastic thin plate theory

The physical variational principle (PVP) in a static magneto-elastic field without source current is discussed first, and then, the PVP in a general electromagnetic field is derived. It is especially useful in the plate vibration problem. Using the PVP and the pseudo total stress principle, the electro-magneto-elastic thin plate bending theory in first order and a Mindlin-type plate bending theory for a moderate thickness plate are easily obtained. This method significantly simplifies the derivation of the governing equations of the thin and moderate plates with nonlinear electromagnetic behavior. The Maxwell stress is naturally included in the governing equation. Using the governing equation of a thin plate, the analyses of the stability and vibration of a plate in an external homogeneous magnetic field are discussed.

Fatigue Life Modeling of Anisotropic Materials Using a Multiaxial Notch Analysis

Fatigue life modeling of anisotropic materials such as directionally-solidified (DS) and single-crystal Ni-base superalloys is often complicated by the presence of notches coupled with dwells at elevated temperatures. This paper focuses on an approach for predicting low cycle fatigue that includes notch geometry effects while taking into consideration material orientation. An analytical model based on a generalization of the Neuber notch analysis to both multiaxial loading and anisotropic materials is used to determine the localized stress-inelastic strain response at the notch. The material anisotropy is captured through a multiaxial generalization of the Ramberg–Osgood relation using a Hill’s criterion. The elastic pseudo stress and pseudo strain response in the vicinity of the notch used as input in the Neuber analysis is determined from an anisotropic elastic finite element analysis. The effects of dwells at elevated temperature are captured using an equivalent strain rate. A nonlocal approach is needed to correlate the life of notched specimens to smooth specimens.

Pseudo Stress Response in Kolsky Tension Bar Experiments

An abnormal stress peak was measured in the specimen response in a Kolsky tension bar experiment. Efforts in changing specimen gage length and applying Teflon tape on the threads of both the specimen and the adapters have been conducted to address this stress peak which was found to be pseudo. The pseudo stress peak was caused by the interfacial impact of the threads on the specimen and the bar ends and must be removed from the intrinsic stress response of the specimen material. Higher impact speeds result in higher amplitudes in the peak stress. The peak stress can be significantly reduced by applying Teflon tape on the threads. At a certain strain rate, it becomes more efficient to minimize the peak stress by simultaneously using a specimen with a shorter gage length and applying Teflon tape on the threads.

A Simple and Efficient Reformulation of the Classical Manson–Coffin Curve to Predict Lifetime Under Multiaxial Fatigue Loading—Part II: Notches

The present study is concerned with the use of the modified Manson–Coffin curve method to estimate the lifetime of notched components subjected to multiaxial cyclic loading. The above criterion postulates that fatigue strength under complex loading paths can efficiently be evaluated in terms of maximum shear strain amplitude, provided that the reference Manson–Coffin curve used to predict the number of cycles to failure is defined by taking into account the actual degree of multiaxiality/nonproportionality of the stress/strain state damaging the assumed crack initiation site. The accuracy and reliability of the above fatigue life estimation technique was checked by considering about 300 experimental results taken from the literature. Such data were generated by testing notched cylindrical samples made of four different metallic materials and subjected to in-phase and out-of-phase biaxial nominal loading. The accuracy of our criterion in taking into account the presence of nonzero mean stresses was also investigated in depth. To calculate the stress/strain quantities needed for the in-field use of the modified Manson–Coffin curve method, notch root stresses and strains were estimated by using not only the well-known analytical tool due to Köttgen et al. (1995, “Pseudo Stress and Pseudo Strain Based Approaches to Multiaxial Notch Analysis,” Fatigue Fract. Eng. Mater. Struct., 18(9), pp. 981–1006) (applied along with the ratchetting plasticity model devised by Jiang and Sehitoglu (1996, “Modelling of Cyclic Ratchetting Plasticity, Part I: Development and Constitutive Relations. Transactions of the ASME,” ASME J. Appl. Mech., 63, pp. 720–725; 1996, “Modelling of Cyclic Ratchetting Plasticity, Part I: Development and Constitutive Relations,” Trans. ASME J. Appl. Mech., 63, pp. 720–725)) but also by taking full advantage of the finite element method to perform some calibration analyses. The systematic use of our approach was seen to result in estimates falling within an error factor of about 3.

Size Effects of Hair-Sized Structures – Torsion

Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include the strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scaled structure [1]. This paper focus on the structural size effects on torsion of cylinders. The torsional stiffness of cylinders can be higher than conventional expectation when the cylinder size is in the nanometer - or micron-scale. Following the Saint-Venant theory of torsion, we established the equation of torsion in terms of the warping function on the basis of the nano-mechanical theory of elasticity. The torsional equations contain two higher order material length scale parameters and two conventional Lame constants. The equilibrium equation is a fourth order partial differential equation which can be reduced to two second order equations. Two formulations in terms of pseudo warping function and stress function are presented. Closed-form solutions for circular and thin wall section and series solutions for rectangular microbars have been obtained. The total torque depends only on the stresses conjugated to the strain and is only implicitly dependent on the higher order stress metrics. The solution reveals that the torsional rigidity is dependent on the higher order length scale parameters and strain gradients and increases asymptotically upward when the cylinder size is reduced to the size of the higher order length scale material parameters. The increase is most marked for thin walled cylinders, stiffening to more then 10 times the conventional value when the cylinder size is near that of the higher order length scaled parameters.

Multiaxial and time dependent behavior of a filled rubber

This paper explores the applicability of various pseudo stressand strain models for predicting the nonlinear stress-strain behavior ofa lightly filled rubber. The objectivity of the different models wasexamined and parameters were extracted on the basis of relaxation andramp loading experiments in tension. The effectiveness of the models forpredicting strip biaxial tension and compression and simple shearresponses was examined. A pseudo stress model based on Cauchy stressprovided the best agreement with experimental results. However,improvements are still needed for modeling the unloading behavior in allstress states and the normal stresses that are induced during simpleshear loading.

Viscoelastic constitutive modeling of asphalt concrete with growing damage

This paper presents a mechanistic approach to uniaxial viscoelastic constitutive modeling of asphalt concrete that accounts for damage evolution under cyclic loading conditions. An elasticviscoelastic correspondence principle in terms of pseudo variables is applied to separately evaluate viscoelasticity and time-dependent damage growth in asphalt concrete. The time-dependent damage growth in asphalt concrete is modeled by using a damage parameter based on a generalization of microcrack growth law. Internal state variables that describe the hysteretic behavior of asphalt concrete are determined. A constitutive equation in terms of stress and pseudo strain is first established for controlled-strain mode and then transformed to a controlled-stress constitutive equation by simply replacing physical stress and pseudo strain with pseudo stress and physical strain. Tensile uniaxial fatigue tests are performed under the controlled-strain mode to determine model parameters. The constitutive equations in terms of pseudo strain and pseudo stress satisfactorily predict the constitutive behavior of asphalt concrete all the way up to failure under controlled-strain and -stress modes, respectively.

Model-Based Estimates of Equatorial Pacific Wind Stress

Abstract A Pacific basin version of the Geophysical Fluid Dynamics Laboratory ocean model is used to compare and modify wind stress fields derived from uncoupled simulations of the Center for Ocean-Land-Atmosphere Studies (COLA) Atmospheric General Circulation Model (AGCM). In an earlier study it was found that a zonal wind stress empirically derived from the zonal wind at the top of the boundary layer in the AGCM produces a better simulation than the AGCM zonal surface stress without any modifications. In addition, the statistically derived model wind stress gives ocean model simulations of sea surface temperature anomaly (SSTA) that are superior to simulations with the wind stress calculated from the Florida State University (FSU) pseudo stress. However, even with the statistical derived model wind stress, it is shown that the SSTA simulation in the eastern Pacific is particularly poor. In an attempt to improve the simulation in the eastern Pacific, an iterative procedure that modifies the zonal wind st...

Creep design analysis of silicon nitride using stress relaxation data

A new approach to tensile creep analysis of ceramics based on stress relaxation testing is described for sintered silicon nitride. The results are presented in terms of creep rate vs. stress, covering a maximum of five orders of magnitude in tests lasting less than one day. Tests for various initial stresses, and at temperatures between 1200°C and 1350°C, are analyzed, and compared with creep rates measured during conventional constant load testing. It is shown that a significant portion of the accumulated creep strain is anelastic and recoverable. This is confirmed using repeated tensile loading and unloading over a given range of temperature. Pseudo stress vs. time curves, generated from the data, show a strong rate sensitivity, which is confirmed in a low stress rate tensile test. A design analysis is made based on a characteristic stress vs. creep rate response at each temperature. This is parameterized and used as a basis for a stress-temperature curve for a projected creep life.

Thermal fatigue crack growth experiments on austenitic steel plates

A thermal cycling fatigue crack growth experiment has been performed on austenitic stainless steel plates in which a semi-elliptical surface crack grows through a surface layer experiencing cyclic plasticity. Linear elastic fracture mechanics crack growth assessments over-predict the surface growth and under-predict the through thickness growth. An alternative crack growth analysis has been performed using a pseudo stress intensity factor which is closely related to a strain intensity factor. The pseudo stress used to derive the pseudo stress intensity factor is calculated from uncracked body inelastic finite element analysis. It is demonstrated that a much improved prediction of fatigue crack shape can be made provided that the effects of crack closure are incorporated into the analysis. The method is relevant to leak-before-break and leak tightness arguments where the accurate prediction of through-thickness crack growth is particularly important.

PSEUDO STRESS AND PSEUDO STRAIN BASED APPROACHES TO MULTIAXIAL NOTCH ANALYSIS

Abstract The analysis of notch stresses and strains is one of the key parts of fatigue life prediction of components and structures, In this paper two related approaches are introduced, covering the whole field from uniaxial to multiaxial non‐proportional loading. The pseudo stress at the notch root computed by theory of elasticity is introduced as the governing variable for elastic‐plastic notch analysis. Although the pseudo stress is just a specially defined nominal stress, it eases notch analysis in comparison to using arbitrarily definable nominal stresses, especially for non‐proportional multiaxial loading. Additionally a pseudo strain based approach is introduced and compared to the stress approach. Both proportional and non‐proportional loading are discussed, and compared with the approaches of other workers.

On the description of cyclic creep and rate dependent plastic deformation

A constitutive model is proposed to describe cyclic creep and other rate dependent plastic deformation. The model is general in concept and thus applicable to a wide variety of engineering materials such as metals, polymers, concrete, rocks and soils. Effect of temperature and deformation history is also included into the basic formulation. The main feature of the model is the concept of a family of nested hypersurfaces in a pseudo stress space. The psuedo stress space is defined by combining both stress and physical time. Thus the rate dependent plastic deformation may be treated as a pseudo rate independent process.