Tasnim Hassan

Anatomy of coupled constitutive models for ratcheting simulation

Abstract This paper critically evaluates the performance of five constitutive models in predicting ratcheting responses of carbon steel for a broad set of uniaxial and biaxial loading histories. The models proposed by Prager, Armstrong and Frederick, Chaboche, Ohno-Wang and Guionnet are examined. Reasons for success and failure in simulating ratcheting by these models are elaborated. The bilinear Prager and the nonlinear Armstrong-Frederick models are found to be inadequate in simulating ratcheting responses. The Chaboche and Ohno-Wang models perform quite well in predicting uniaxial ratcheting responses; however, they consistently overpredict the biaxial ratcheting responses. The Guionnet model simulates one set of biaxial ratcheting responses very well, but fails to simulate uniaxial and other biaxial ratcheting responses. Similar to many earlier studies, this study also indicates a strong influence of the kinematic hardening rule or backstress direction on multiaxial ratcheting simulation. Incorporation of parameters dependent on multiaxial ratcheting responses, while dormant for uniaxial responses, into Chaboche-type kinematic hardening rules may be conducive to improve their multiaxial ratcheting simulations. The uncoupling of the kinematic hardening rule from the plastic modulus calculation is another potentially viable alternative. The best option to achieve a robust model for ratcheting simulations seems to be the incorporation of yield surface shape change (formative hardening) in the cyclic plasticity model.

An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation

Abstract In a search for a constitutive model for ratcheting simulations, the models by Chaboche, Ohno–Wang, McDowell, Jiang–Sehitoglu, Voyiadjis–Basuroychowdhury and AbdelKarim–Ohno are evaluated against a set of uniaxial and biaxial ratcheting responses. With the assumption of invariant shape of the yield surface during plastic loading, the ratcheting simulations for uniaxial loading are primarily a function of the plastic modulus calculation, whereas the simulations for multiaxial loading are sensitive to the kinematic hardening rule of a model. This characteristic of the above mentioned models is elaborated in this paper. It is demonstrated that if all parameters of the kinematic hardening rule are determined from uniaxial responses only, these parameters primarily enable a better plastic modulus calculation. However, in this case the role of the kinematic hardening rule in representing the ratcheting responses for multiaxial loading is under-appreciated. This realization motivated many researchers to incorporate multiaxial load dependent terms or parameters into the kinematic hardening rule. This paper evaluates some of these modified rules and finds that none is general enough to simulate the ratcheting responses consistently for the experiments considered. A modified kinematic hardening rule is proposed using the idea of Delobelle and his co-workers in the framework of the Chaboche model. This new rule introduces only one multiaxial load dependent parameter to the Chaboche model, but performs the best in simulating all the ratcheting responses considered.

Kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation

Abstract An earlier paper by the authors evaluated the performance of several coupled models in simulating a series of uniaxial and biaxial ratcheting responses. This paper evaluates the performance of various kinematic hardening rules in an uncoupled model for the same set of ratcheting responses. A modified version of the Dafalias–Popov uncoupled model has been demonstrated to perform well for uniaxial ratcheting simulation. However, its performance in multiaxial ratcheting simulation is significantly influenced by the kinematic hardening rules employed in the model. Performances of eight different kinematic hardening rules, when engaged with the modified Dafalias–Popov model, are evaluated against a series of rate-independent multiaxial ratcheting responses of cyclically stabilized carbon steels. The kinematic hardening rules proposed by Armstrong–Frederick, Voyiadjis–Sivakumar, Phillips, Tseng–Lee, Kaneko, Xia–Ellyin, Chaboche and Ohno–Wang are examined. The Armstrong–Frederick rule performs reasonably for one type of the biaxial ratcheting response, but fails in others. The Voyiadjis–Sivakumar rule and its constituents, the Phillips and the Tseng–Lee rules, can not simulate the biaxial ratcheting responses. The Kaneko rule, composed of the Ziegler and the prestress directions, and the Xia–Ellyin rule, composed of the Ziegler and Mroz directions, also fail to simulate the biaxial ratcheting responses. The Chaboche rule, with three decomposed Armstrong–Frederick rules, performs the best for the whole set of ratcheting responses. The Ohno–Wang rule performs well for the data set, except for one biaxial response where it predicts shakedown with subsequent reversal of ratcheting.

Behaviour of intrinsic polymer optical fibre sensor for large-strain applications

This paper derives the phase response of a single-mode polymer optical fibre for large-strain applications. The role of the finite deformation of the optical fibre and nonlinear strain optic effects are derived using a second order strain assumption and shown to be important at strain magnitudes as small as 1%. In addition, the role of the core radius change on the propagation constant is derived, but it is shown to be negligible as compared to the previous effects. It is shown that four mechanical and six opto-mechanical parameters must be calibrated to apply the sensor under arbitrary axial and transverse loading. The mechanical nonlinearity of a typical single-mode polymer optical fibre is experimentally measured in axial tension and is shown to be more significant than that of their silica counterpart. The mechanical parameters of the single-mode polymer optical fibre are also measured for a variety of strain rates, from which it is demonstrated that the strain rate has a strong influence on yield stress and strain. The calibrated constants themselves are less affected by strain rate.

Large Deformation In-Fiber Polymer Optical Fiber Sensor

We demonstrate the measurement of the phase shift in a polymethylmethacrylate single-mode optical fiber interferometer, operating at a wavelength of 632.8 nm, up to 15.8% nominal strain in the fiber. The phase-displacement sensitivity is measured to be 1.39 x10 radldrm-1 for this strain range. This strain range is well beyond the yield strain of the polymer fiber and that previously measured for polymer Bragg gratings and silica optical fiber sensors.

Improved ratcheting analysis of piping components

Abstract It is well known that ratcheting (defined as the accumulation of deformation with cycles) can reduce fatigue life or cause failure of piping components or systems subjected to seismic or other cyclic loads. This phenomenon is sometime referred to as fatigue-ratcheting, which is yet to be understood clearly. Commercial finite element codes cannot accurately simulate the ratcheting responses recorded in tests on piping components or systems. One of the reasons for this deficiency has been traced to inadequate constitutive models in the existing analysis codes. To overcome this deficiency, an improved cyclic plasticity model, composed of the Armstrong–Frederick kinematic hardening rule and the Drucker–Palgen plastic modulus equation, is incorporated into an ANSYS material model subroutine. The modified ANSYS program is verified against three sets of experimental results. The simulations from this modified ANSYS show a significant improvement over the unmodified ANSYS and the ABAQUS codes.

Uniaxial Strain and Stress-Controlled Cyclic Responses of Ultrahigh Molecular Weight Polyethylene: Experiments and Model Simulations

Thermoplastics such as ultrahigh molecular weight polyethylene (UHMWPE) are used for a wide variety of applications, such as bearing material in total replacement of knee and hip components, seals, gears, and unlubricated bearing. Accurate prediction of stresses and deformations of UHMWPE components under service conditions is essential for the design and analysis of these components. This, in turn, requires a cyclic, viscoplastic constitutive model that can simulate cyclic responses of UHMWPE under a wide variety of uniaxial and multiaxial, strain, and stress-controlled cyclic loading. Such a constitutive model validated against a broad set of experimental responses is not available mainly because of the lack of experimental data of UHMWPE. Toward achieving such a model, this study conducted a systematic set of uniaxial experiments on UHMWPE thin-walled, tubular specimens by prescribing strain and stress-controlled cyclic loading. The tubular specimen was designed so that both uniaxial and biaxial experiments can be conducted using one type of specimen. The experimental responses developed are presented for demonstrating the cyclic and ratcheting responses of UHMWPE under uniaxial loading. The responses also are scrutinized for determining the applicability of the thin-walled, tubular specimen in conducting large strain cyclic experiments. A unified state variable theory, the viscoplasticity theory based on overstress for polymers (VBOP) is implemented to simulate the recorded uniaxial responses of UHMWPE. The state of the VBOP model simulation is discussed and model improvements needed are suggested.

On the difference of fatigue strengths from rotating bending, four-point bending, and cantilever bending tests

Comparisons of piping fatigue data demonstrate that the fatigue strength from rotating bending tests is lower than that from cantilever and four-point bending tests, especially in the low-cycle fatigue life range. The lower strength from the rotating bending test is generally believed to result from the fact that in this test all the points on the piping surface are subjected to the maximum stress range. Consequently, the weakest point in the specimen always initiates and causes failure. On the contrary, in cantilever and four-point bending tests, the maximum stress range occurs only at the top and bottom extreme fibers, which may not contain the weakest point in the specimen. Hence, the pipes in rotating bending tests usually fail earlier in comparison with the other two tests. Finite element analyses for the three tests revealed another and more compelling reason for the lower fatigue strength from the rotating bending test. The results demonstrated that, for the same prescribed bending moment range, the inelastic strain range in rotating bending is higher than the ranges in four-point and cantilever bending tests. Experimental data also demonstrate a similar trend. The new observation suggests that fatigue data from these three tests should be analyzed or compared in terms of strain range, instead of nominal stress range.

Correlation coefficients for modal response combination of non-classically damped systems

Correlation coefficients to perform modal combination of responses for non-classically damped systems are studied. The frequency domain analysis method is used to calculate the coefficients for 12 earthquake records and 10 damping ratios. The response of non-classically damped systems is evaluated for a range of frequencies between completely rigid and completely non-rigid. It is found that the earlier proposed linear relationship of the rigid response coefficient with frequency on a semilogarithmic graph is not accurate and that the rigid response coefficient is a function of the damping ratio. New expressions for determining the rigid response coefficients for displacement and velocity responses are proposed. The related key frequencies are also studied and found to be different from those proposed in the earlier studies. New formulations for determining these frequencies are presented. Modified equations for correlation coefficients proposed in this study are found to yield good agreement with the numerically evaluated displacement and velocity correlation coefficients for all frequency ranges. Further investigation is needed for the cross-correlation coefficient to improve the agreement with numerical results in the high frequency range.

Calibration of a single-mode polymer optical fiber large-strain sensor

We calibrate the phase shift as a function of applied displacement in a polymethylmethacrylate (PMMA) single-mode optical fiber interferometer, operating at a wavelength of 632.8 nm. The phase sensitivity is measured up to 15.8% nominal strain in the fiber. The measured phase–displacement response is compared to a previous analytical formulation for the large deformation response of the polymer optical fiber strain sensor. The formulation includes both the finite deformation of the optical fiber and nonlinear strain-optic effects at large deformations. Using previously measured values for the linear and nonlinear mechanical response of the fiber, the nonlinear strain-optic effects are calibrated from the current experimental data. This calibration demonstrates that the nonlinearities in the strain-optic effect are of the same order of magnitude as those in the mechanical response of the PMMA optical fiber sensor.