When conventionally reinforced concrete elements are subjected to fire, their carbon-steel reinforcing bars can experience a relatively long duration of modest temperature increase (up to 600 degrees C) due to the insulation pro-vided by the concrete cover before the element fails or the fire decays. Tensile tests under constant applied stress were performed on 25 M (#8 US) reinforcing bars that conform to ASTM A615 Grades 420, 520, and 690 to measure time-dependent creep at constant temperatures from 400 to 600 degrees C (i.e., up to the critical temperature per ASTM E119). Creep rates at 400 degrees C were small for all grades regardless of the applied stress level. Specimens across all grades showed an increase in secondary creep rate when applied stress and/or temperature also increased. Tertiary creep was only observed once the temperature was increased to 600 degrees C with a higher level of applied stress (similar to 40% of ambient yield). The experimental data is used to develop predictive expressions based on both the Dorn-Harmathy model and a combined time-hardening model. Both can be used as input for numerical analysis of heated reinforced concrete structures. The models are applied in two simple examples to predict cumulative creep strains when the bars are under constant stress and transiently heated from 400 to 600 degrees C.

Components that face aggressive thermomechanical loadings that are cyclic and multiaxial often employ nickelbase single crystal superalloys to achieve acceptable lifetimes. These superalloys are commonly used with firstyield design rules, however their use under inelastic design, leveraging safe elastoplastic shakedown behaviors at elevated temperatures, has remained largely unexplored. This paper is the first to combine cyclic test results with some microstructural observations to establish conditions for the macroscopic shakedown response of a 2nd generation nickel-base single crystal superalloy under tension-torsion loadings at 600 degrees C. Microstructural studies are performed to identify and compare deformation mechanisms in specimens that exhibit shakedown and ratchetting. Based on the results, directions for future materials development, to directly exploit shakedown in design, are suggested.

Life integrity assessment of industrial components often requires investigations of the cyclic inelastic response at a range of operating temperatures. Some high strength steels exhibit a well-known ambient temperature creep behaviour, which can also impact the cyclic behaviour, especially under long-term operation. In this study, a direct method known as the Linear Matching Method has been used to predict the cyclic shakedown and ratchet limits of high-strength steel (AISI 1144). The numerical predictions are compared with a recent testing campaign that was completed at room temperature to characterise the multiaxial behaviour of AISI 1144. Due to creep of the material, inelastic strain accumulation is also observed for loading conditions within the shakedown limit. The extended Direct Steady Cyclic Analysis (eDSCA) approach has been used to predict the cyclic behaviour in the presence of creep. In addition, for specific load cases of interest, a newly revised creep-ratcheting limit has been derived and compared with the experimental tests.

A new framework to utilize stereo-vision digital image correlation (DIC) as a means of identifying the multiaxial cyclic shakedown behavior of structures is demonstrated on high strength steel bars. AISI 1144 carbon steel cylindrical bars are subjected to cyclic tension with nonzero mean stress and constant torque under ambient conditions. An elastic analytical solution is used in a post-processing procedure to extract inelastic strains and estimate the accumulated inelastic strain during cycling. DIC results are used to understand the cyclic strain evolution and determine if the accumulation of plastic strain stabilizes (shakedown). The results are used to construct a load interaction diagram (Bree Diagram) that displays the loading combinations resulting in purely elastic, safe shakedown, and undesirable cyclic inelastic behavior. The manifestation of ambient creep, during the multiaxial cyclic loading, is demonstrated through dedicated experiments. The shakedown criteria has been adapted to account for the ambient creep behavior. Depending on target structural lifetimes and allowable total strains, it is found that the design space can be enhanced by allowing shakedown to occur. An illustration is given for which the design space is enlarged 1.25 times the typical yield-limited approach.

This study aims to determine the safe elastoplastic shakedown limit of type 316L stainless steel at room temperature and at an elevated temperature of 600°C. Components made of type 316L stainless steel are commonly subjected to combined thermomechanical loads in various engineering applications. Shakedown based designs can be used to expand the feasible design space under combined thermomechanical cyclic loading conditions compared to conventional yield-limited designs. Extensive experimental and numerical effort has been made to model ratchetting and cyclic hardening/softening of stainless steels under uniaxial cyclic loading but a very limited number of studies have focused on determining the shakedown limit. In this work, shakedown limits are determined experimentally and numerically. A numerical model that combines time-dependent creep deformation and time-independent hardening is used to develop Bree load-interaction diagrams. It is found that shakedown occurs at room temperature at stress levels up to two times the linear elastic limit of the material and is limited by the time-dependent creep deformation. At 600oC, an enhanced shakedown behavior is observed that expands the feasible design space up to 4 times the linear elastic limit.

Many multiaxial experimental setups rely on stereocorrelation (SC) techniques to resolve surface strains and deformations. Torsional loadings can affect the quality and accuracy of SC results due to changes in lighting conditions and the non-conservation of gray levels with the angle of twist. In this note, the gray level correction method implemented for 2D DIC cases is introduced in a 3D surface NURBS SC formalism and applied for torsional loadings. In particular, tension-torsion loading of AISI 1144 steel rods is used to demonstrate the approach. Different surface parameterizations, with and without gray level corrections, are tested in order to enhance the SC quality (defined via gray level residuals). It is found that both gray level corrections and relaxing the regularization of an overly constrained NURBS surface definition (6 vs. 36 knots), lower SC residuals.

Many industries rely on the Inconel 625 alloy to serve under thermomechanical operating conditions. Understanding the macroscopic cyclic inelastic behavior of this material is vital for accurate assessment of its load-carrying capacity at elevated temperatures. In this work, a uniaxial experimental program at 600∘C is conducted to demonstrate designing for cyclic elastoplastic behavior (shakedown) as opposed to more restrictive first-yield, while still avoiding ratchetting or alternating plasticity. In particular, a range of cyclic stress amplitudes are imposed at non-zero mean stresses while maintaining a constant maximum stress. In addition, the effect of dynamic strain aging (DSA) on the macroscopic shakedown behavior is established under load control. The inelastic work done per cycle is used as a measure of severity of the cyclic inelastic behavior, and is evaluated by monitoring the evolution of the hysteresis loop width. It is found that when the maximum stress is constant, larger mean stress tests approach shakedown behavior. Furthermore, for the range of stress amplitudes and mean stresses considered, the cyclic elastoplastic shakedown behavior is not affected by the DSA, and only depends on the mean stress and stress amplitude.

This paper outlines an elastoplastic design approach for beam and plate structures subjected to transverse pressure loads and thermal stresses. The purpose of this study is to overcome the limitations of yield-limited designs by exploiting plastic design theorems. The feasible design space of a clamped beam/plate structure subjected to combined thermomechanical loads is explored considering shakedown (stabilized plasticity) as the design criteria. Analytic and numerical solutions are developed that show that allowing shakedown to occur extends the design space and acceptable loading range. In addition, the structures considered here are also prone to buckling due to thermal loads. In this work, interactions between thermal buckling and shakedown are investigated using numerical parametric studies. It is found that buckling enhances elastoplastic shakedown performance which expands the feasible design domain significantly when high aspect ratio beams are considered. In particular it is shown that the enhancement is 2–4 times for the range of aspect ratios examined.

Nickel-base single crystal superalloy components are designed to experience extreme and often cyclic multiaxial loads. While much of the literature has provided the foundation to use these materials near critical yield conditions, their use under inelastic design, exploiting safe elastoplastic shakedown behaviors is largely unexplored. In particular, this paper focuses on establishing the conditions for the macroscopic shakedown response of a 2nd generation nickel-base superalloy under tension-torsion loadings from numerical and experimental perspectives. A numerical model is developed to more broadly evaluate shakedown limit loads and it is found that by allowing shakedown to occur, an 18% increase in feasible design load space is expected compared to traditional first-yield design criteria. Experiments on hollow cylindrical specimens are also conducted and used to assess the prediction capabilities of the numerical finite element model.

In this work, shakedown design strategies are demonstrated and tailored for concrete structural systems with reinforcement in extreme thermomechanical environments. It is found that allowing for shakedown to occur doubles the structure's mechanical load bearing capacity under constant thermal load. The proposed model also allows for proposing design parameters for shakedown purposes. Two additional test cases are illustrated in which two different rebar diameters are used, namely 6 and 12 mm. In the first case an inadmissible behavior is depicted while in the second case, for the same loading and boundary conditions, the shakedown behavior is observed.

Given the current trend in manufacturing to decrease part variability, and in order to increase product quality, dimensional tolerances are becoming more exacting. With this in mind, and with the decreased time allotted for components to progress from design to manufacture, it has become more critical that accurate models of the manufacturing process are developed. This paper investigates the changes in cross sectional area when a prismatic bar is plastically deformed into a ring of constant diameter. Through further processing, these rings are transformed into components that function to secure mechanical components, such as bearings, into assemblies. Failure of the ring can cause significant damage, or failure of the assembly. Typical thickness tolerances are on the order of +/−.002” (0.05 mm), but can be as small as +/−.0002” (0.005 mm). Also, a growing trend in manufacturing is for the final ring to have a specified thickness on the inner and outer edge within this tolerance band. The rings are produced in various metallic materials with different mechanical properties by continuously coiling prismatic bars to a specific diameter. An analytic model based on small strain theory was developed for the simple cross sections of rectangular and trapezoidal geometries. This model was then extended to include the effect of a hyperbolic rather than linear stress distribution through this simple section in order to relieve the constraints of small strain theory and adequately model the actual process. An empirical model was developed based on experimental observations. A numerical model was developed using the commercial finite element analysis (FEA) software Abaqus (SIMULIA, Providence, RI) to simulate the manufacturing process. This was compared to the empirical model developed from production parts for validation. Once the finite element model is validated, it could be used to explore the effects of design parameters (initial dimensions of the prismatic bar, material properties etc.) and create efficient designs for manufacturing. The empirical model can then be used in the design process. Additionally, the numerical simulation could be used to model more complex cross sectional areas which cannot be evaluated analytically. There was adequate agreement between the empirical and numerical models to the extent that the numerical model could be used for more complex cross sectional geometries. A further refinement of the analytic model to include finite strain theory should be used to expand on this.

While the effect of normal compression on the measured shear material properties of viscoelastic solids has been already acknowledged in rheological studies in the literature, to our knowledge, no systematic study has been conducted to investigate this effect in detail to date. In this study, we perform two sets of experiments to investigate the effect of normal strain and strain rate on the dynamic shear moduli of bovine liver. First, we apply normal compressive strain to the cylindrical bovine samples up to 20% at loading rates of v=0.000625, 0.00625, 0.0625, 0.315, 0.625 mm/s. Second, we perform torsional shear loading experiments, in the frequency range of ω=0.1–10 Hz, under varying amounts of compressive pre-strain (ε=1%, 2.5%, 5%, 7.5%, 10%, 12.5%, 15%, 17.5% and 20%) applied at the quasi-static loading rate of v=0.000625 mm/s. The results of the experiments show that the shear moduli of bovine liver increase with compressive pre-strain. A hyper-viscoelastic constitutive model is developed and fit to the experimental data to estimate the true shear moduli of bovine liver for zero pre-compression. With respect to this reference value, the mean relative error in the measurement of shear moduli of bovine liver varies between 0.2% and 243.1% for the compressive pre-strain varying from ε=1% to 20%. The dynamic shear modulus of bovine liver for compressive pre-strain values higher than ε>2.5% are found to be statistically different than the true shear moduli estimated for zero compressive strain (p<0.05).