Using Tolerance Bounds for Estimation of Characteristic Fatigue Curves for Composites with Confidence

Fatigue S–N curves provide the number of stress cycles that result in fatigue failure at stress range S and need to be measured for new engineering materials where data are not as readily available as they are for well-characterized and widely used metals. A simple statistical method for the estimation of characteristic fatigue curves defined in terms of lower-tail quantiles in probability distributions of dependent variables is presented. The method allows for the estimation of such quantiles with a specified confidence level, taking account of the statistical uncertainty caused by a limited number of experimental test results available for the estimation. The traditional general approach for estimating characteristic S–N curves by tolerance bounds is complicated and is not much used by engineers. The presented approach allows for calculating the curves with a simple spreadsheet. The only requirement is that the experimental log S data for the S–N curve are fairly uniformly distributed over a finite logS interval, where S denotes the stress range. Experimental fatigue test programs are often designed such that test data fulfil this assumption. Although developed with fatigue of composite laminates in mind, the presented statistical procedure and the presented associated charts are valid for fatigue curve estimation for any material.

RATCHETING EVALUATION OF BIOLOGICAL TISSUES OVER ASYMMETRIC LOADING CYCLES

This study intends to evaluate the ratcheting response of biological samples prepared from bovine and porcine trabecular bone, articular cartilage, meniscus, and skin tissues and tested under asymmetric (nonzero mean stress) cycles. Meniscus and skin samples were tested with stress ratios of [Formula: see text] and [Formula: see text], respectively, while other tissues were tested at [Formula: see text]. Experimental ratcheting data and related influential parameters including stress level, stress rate, and testing frequency were discussed. A parametric ratcheting equation was further calibrated to estimate the ratcheting response of tissues. The predicted ratcheting data were found to be in close agreement with the reported experimental data.

Microbial activity responses to water stress in agricultural soils from simple and complex crop rotations

Increasing climatic pressures such as drought and flooding challenge agricultural systems and their management globally. How agricultural soils respond to soil water extremes will influence biogeochemical cycles of carbon and nitrogen in these systems. We investigated the response of soils from long-term agricultural field sites under varying crop rotational complexity to either drought or flooding stress. Focusing on these contrasting stressors separately, we investigated soil heterotrophic respiration during single and repeated stress cycles in soils from four different sites along a precipitation gradient (Colorado, MAP 421 mm; South Dakota, MAP 580 mm; Michigan, MAP 893 mm; Maryland, MAP 1192 mm); each site had two crop rotational complexity treatments. At the driest (Colorado) and wettest (Maryland) of these sites, we also analyzed microbial biomass, six potential enzyme activities, and N2O production during and after individual and repeated stress cycles. In general, we found site specific responses to soil water extremes, irrespective of crop rotational complexity and precipitation history. Drought usually caused more severe changes in respiration rates and potential enzyme activities than flooding. All soils returned to control levels for most measured parameters as soon as soils returned to control water levels following drought or flood stress, suggesting that the investigated soils were highly resilient to the applied stresses. The lack of sustained responses following the removal of the stressors may be because they are well in the range of natural in situ soil water fluctuations at the investigated sites. Without the inclusion of plants in our experiment, we found that irrespective of crop rotation complexity, soil and microbial properties in the investigated agricultural soils were more resistant to flooding but highly resilient to drought and flooding during single or repeated stress pulses.

Toward the First Italian Elastocaloric Device: Projecting and Developing Steps

Nowadays about 20% of the worldwide energy consumption is attributable to refrigeration that is almost entirely based on vapor compression refrigeration. The elastocaloric refrigeration is being considered in the recent years as one of the most promising alternatives to vapour compression cooling technology. It is based on the latent heat associated with the transformation process of the martensitic phase, found in Shape Memory Alloys (SMA) when they are subjected to uniaxial stress cycles of loading and unloading. SMAs are characterized by the mechanical property of being able to return to the initial form once the uniaxial stress has been removed. Currently the prototypes of elastocaloric cooler developed in the world are less than ten units and they are not close to the industrialization and commercialization, yet. This contribution presents the design processes and the steps of development of the first Italian elastocaloric device: SSUSTAIN-EL. This research involves part of a bigger Italian project, called SUSSTAINEBLE, that involves three research institutes: University of Naples Federico II, University of Genoa and the National Research Council. The aim of research group is the developing of a demonstrative prototype of a continuously elastocaloric cooler, which can represent a fundamental step as "proof of concept".

Preliminary Numerical Investigation on the Optimization of a Single Bunch of Elastocaloric Elements to be Employed in an Experimental Device

Nowadays about 20% of the worldwide energy consumption is attributable to refrigeration almost based on vapor compression. In the scientific literature in the class of the eco-friendly cooling technologies alternative to vapour compression there is solid state cooling. In this field, the scientific community has devoted the attention specifically toward elastocaloric refrigeration. Elastocaloric refrigeration is based on the latent heat associated with the transformation process of the martensitic phase, found in Shape Memory Alloys (SMA) when they are subjected to uniaxial stress cycles of loading and unloading. SMAs are characterized by the mechanical property of being able to return to the initial form once the uniaxial stress has been removed. By exploiting this effect in a reverse regenerative thermodynamic cycle called Active elastocaloric regenerative refrigeration cycle (AeR), a satisfactory cooling effect is achievable. In this paper, the results of a numerical investigation conducted, through a 2-D model, on a single bunch of elastocaloric elements are shown. Specifically, the heat transfer and the energy performances are studied both by varying the geometrical parameters of the elements and by varying the auxiliary fluid (air) velocity.

Modifications on A-F Hardening Rule to Assess Ratcheting Response of Materials and Its Interaction with Fatigue Damage under Uniaxial Stress Cycles

Ratcheting deformation is accumulated progressively over three distinct stages in materials undergoing asymmetrical cyclic stresses. The present thesis evaluates the triphasic ratcheting response of materials from two stand points: (i) Mechanistic approach at which stages of ratcheting progress over stress cycles was related to mechanistic parameters such as stress level, lifespan, mechanical properties and the softening/hardening response of materials. Mechanistic approach formulated in this thesis was employed to assess ratcheting strain over triphasic stages in various steel and copper alloys under uniaxial stress cycles. Good agreements were achieved between the predicted ratcheting strain values based on the proposed formulation and those of experimentally reported. (ii) Kinematic hardening rule approach at which the hardening rule was characterized by the yield surface translation mechanism and the corresponding plastic modulus calculated based on the consistency condition. Various cyclic plasticity models were employed to assess ratcheting response of materials under different loading conditions. The Armstrong-Frederick (A-F) hardening rule was taken as the backbone of ratcheting analysis developed in this thesis mainly due to less complexity and number of coefficients in the hardening rule as compared with other earlier developed hardening rules in the literature. To predict triphasic ratcheting strain over stress cycles, the A-F hardening rule has been further developed by means of new strain rate coefficients γ2 and δ. These coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting over its progressive stages. The modified hardening formulation holds the coefficients of the hardening rule to control stress-strain hysteresis loops generated over stress cycles during ratcheting process plus the ratcheting rates over stages I, II, and III. These coefficients were calibrated and defined based on the applied stress levels. The constructed calibration curves were employed to determine strain rate coefficients required to assess ratcheting response of materials under uniaxial loading conditions at various cyclic stress levels. The predicted ratcheting strain values based on the modified hardening rule were found in good agreements with the experimentally obtained ratcheting data over stages I and II under uniaxial loading conditions. The capability of the modified hardening rule to assess ratcheting deformation of materials under multi-step uniaxial loading spectra was also assessed. Subsequent load steps were considerably affected by previous load steps in multi-step loading conditions. Ratcheting strains for low-high stress steps were successfully predicted by the modified hardening rule. High-low loading sequences however resulted in an overestimated reversed ratcheting strain in the later load steps. The modified hardening rule proposed in this thesis was then employed to predict the ratcheting strain and its concurrent interaction with fatigue damage over stress cycles in steel alloys. The interaction of ratcheting and fatigue damage was defined based on mechanistic parameters involving the effects of mean stress, stress amplitude, and cyclic softening/hardening response of materials. The extent of ratcheting effect on the overall damage of steel samples was defined by means of the product of the average ratcheting strain rate over the stress cycles and the applied maximum cyclic stress, while fatigue damage was analysed based on earlier developed energy-based models of Xia-Ellyin and Smith-Watson-Topper. Overall damage induced by both ratcheting and fatigue was calibrated through a weighting factor at various ratios of mean stress/cyclic amplitude stress. The estimated lives based on the proposed algorithm at different mean stresses and stress amplitudes showed good agreements as compared with experiments.

Modifications on A-F Hardening Rule to Assess Ratcheting Response of Materials and Its Interaction with Fatigue Damage under Uniaxial Stress Cycles

Ratcheting deformation is accumulated progressively over three distinct stages in materials undergoing asymmetrical cyclic stresses. The present thesis evaluates the triphasic ratcheting response of materials from two stand points: (i) Mechanistic approach at which stages of ratcheting progress over stress cycles was related to mechanistic parameters such as stress level, lifespan, mechanical properties and the softening/hardening response of materials. Mechanistic approach formulated in this thesis was employed to assess ratcheting strain over triphasic stages in various steel and copper alloys under uniaxial stress cycles. Good agreements were achieved between the predicted ratcheting strain values based on the proposed formulation and those of experimentally reported. (ii) Kinematic hardening rule approach at which the hardening rule was characterized by the yield surface translation mechanism and the corresponding plastic modulus calculated based on the consistency condition. Various cyclic plasticity models were employed to assess ratcheting response of materials under different loading conditions. The Armstrong-Frederick (A-F) hardening rule was taken as the backbone of ratcheting analysis developed in this thesis mainly due to less complexity and number of coefficients in the hardening rule as compared with other earlier developed hardening rules in the literature. To predict triphasic ratcheting strain over stress cycles, the A-F hardening rule has been further developed by means of new strain rate coefficients γ2 and δ. These coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting over its progressive stages. The modified hardening formulation holds the coefficients of the hardening rule to control stress-strain hysteresis loops generated over stress cycles during ratcheting process plus the ratcheting rates over stages I, II, and III. These coefficients were calibrated and defined based on the applied stress levels. The constructed calibration curves were employed to determine strain rate coefficients required to assess ratcheting response of materials under uniaxial loading conditions at various cyclic stress levels. The predicted ratcheting strain values based on the modified hardening rule were found in good agreements with the experimentally obtained ratcheting data over stages I and II under uniaxial loading conditions. The capability of the modified hardening rule to assess ratcheting deformation of materials under multi-step uniaxial loading spectra was also assessed. Subsequent load steps were considerably affected by previous load steps in multi-step loading conditions. Ratcheting strains for low-high stress steps were successfully predicted by the modified hardening rule. High-low loading sequences however resulted in an overestimated reversed ratcheting strain in the later load steps. The modified hardening rule proposed in this thesis was then employed to predict the ratcheting strain and its concurrent interaction with fatigue damage over stress cycles in steel alloys. The interaction of ratcheting and fatigue damage was defined based on mechanistic parameters involving the effects of mean stress, stress amplitude, and cyclic softening/hardening response of materials. The extent of ratcheting effect on the overall damage of steel samples was defined by means of the product of the average ratcheting strain rate over the stress cycles and the applied maximum cyclic stress, while fatigue damage was analysed based on earlier developed energy-based models of Xia-Ellyin and Smith-Watson-Topper. Overall damage induced by both ratcheting and fatigue was calibrated through a weighting factor at various ratios of mean stress/cyclic amplitude stress. The estimated lives based on the proposed algorithm at different mean stresses and stress amplitudes showed good agreements as compared with experiments.

Development of a kinematic hardening rule to assess ratcheting response of materials under various multiaxial loading spectra

The present thesis develops an Armstrong-Frederick (A-F) type coupled kinematic hardening rule to assess ratcheting response of steel alloys under various multiaxial loading paths. The hardening rule is constructed on the basis of the recently proposed Ahmadzadeh-Varvani (AV) hardening rule to further evaluate the ratcheting response of materials under multiaxial loading spectra. The modified model offers a simple framework with limited number of terms and coefficients in the dynamic recovery portion of the model. The dynamic recovery further holds inner product of plastic strain increment p dand backstress unit vector a a with different directions under multiaxial stress cycles enables the model to track different directions. Term 1/ 2 n. a a taking positive values less than unity for multiaxial loading conditions is to control the accumulation rate of ratcheting strain and to prevent the modified model to experience plastic shakedown over stress cycles in stage II. Term(2 n. a a ) taking the values between 1 and 3 under multiaxial loading, magnifies the effect of coefficient γ2 to take into account the nonproportionality effect of various loading paths and further to shift down the predicted ratcheting strain over the stress cycles. The predicted ratcheting curves by the modified rule were compared with those predicted based on earlier developed hardening rules of Ohno-Wang (O-W), Jiang-Sehitoglu (J-S), McDowell, and Chen-Jiao-Kim (C-J-K) holding relatively complex framework and more number of coefficients. The O-W, the J-S, McDowell and C-J-K models mainly deviated from the experimental ratcheting strain of steel alloys for various multiaxial loading histories, while the predicted curves of the modified model closely agreed with experimental data of steel samples over ratcheting stages. The predicted ratcheting curves based on the modified model closely agreed with experimental data of steel samples under various multiaxial step-loading histories. The modified model was also found capable of predicting ratcheting in the opposite direction as the tensile axial mean stress dropped in magnitude. The O-W, J-S, McDowell and C-J-K models holding more backstress components and coefficients require longer Central Processing Unit (CPU) time. While time required for ratcheting assessment using the modified hardening rule was found to be twice shorter due to its simpler framework and limited number of coefficients.

Development of a kinematic hardening rule to assess ratcheting response of materials under various multiaxial loading spectra

The present thesis develops an Armstrong-Frederick (A-F) type coupled kinematic hardening rule to assess ratcheting response of steel alloys under various multiaxial loading paths. The hardening rule is constructed on the basis of the recently proposed Ahmadzadeh-Varvani (AV) hardening rule to further evaluate the ratcheting response of materials under multiaxial loading spectra. The modified model offers a simple framework with limited number of terms and coefficients in the dynamic recovery portion of the model. The dynamic recovery further holds inner product of plastic strain increment p dand backstress unit vector a a with different directions under multiaxial stress cycles enables the model to track different directions. Term 1/ 2 n. a a taking positive values less than unity for multiaxial loading conditions is to control the accumulation rate of ratcheting strain and to prevent the modified model to experience plastic shakedown over stress cycles in stage II. Term(2 n. a a ) taking the values between 1 and 3 under multiaxial loading, magnifies the effect of coefficient γ2 to take into account the nonproportionality effect of various loading paths and further to shift down the predicted ratcheting strain over the stress cycles. The predicted ratcheting curves by the modified rule were compared with those predicted based on earlier developed hardening rules of Ohno-Wang (O-W), Jiang-Sehitoglu (J-S), McDowell, and Chen-Jiao-Kim (C-J-K) holding relatively complex framework and more number of coefficients. The O-W, the J-S, McDowell and C-J-K models mainly deviated from the experimental ratcheting strain of steel alloys for various multiaxial loading histories, while the predicted curves of the modified model closely agreed with experimental data of steel samples over ratcheting stages. The predicted ratcheting curves based on the modified model closely agreed with experimental data of steel samples under various multiaxial step-loading histories. The modified model was also found capable of predicting ratcheting in the opposite direction as the tensile axial mean stress dropped in magnitude. The O-W, J-S, McDowell and C-J-K models holding more backstress components and coefficients require longer Central Processing Unit (CPU) time. While time required for ratcheting assessment using the modified hardening rule was found to be twice shorter due to its simpler framework and limited number of coefficients.