Lifetime simulation of thermo-mechanically loaded components

The estimation of the lifetime of thermo-mechanically loaded components by testing is very costly and time-consuming, since the high temperature cycle time in practical application dominates the test duration. Common frequencies for TMF (thermo-mechanical fatigue) tests are at about 0.01 Hz compared to 10–100 Hz at HCF (high cycle fatigue) and about 0.1–1 Hz at isothermal LCF (low cycle fatigue) tests. Therefore, the simulation of fatigue life is an important design step in the fast moving and competitive automotive industry, where the steady rise of engine power and the demand for lightweight construction concurrent with enhanced reliability require an optimised dimensioning process. Methods and models are usually derived from results made on tests with specimens, since it is possible to systematically and exactly define loading parameters and measurement categories. After an extensive test programme (tensile tests, creep tests, low cycle fatigue tests and thermo-mechanical fatigue tests with different influences on specimens) it was possible to develop material models for the simulation of the time- and temperature dependent stress–strain hystereses and damage models for the simulation of the TMF lifetime. Based on this knowledge the whole simulation chain to determine the TMF life of a component is introduced: thermal calculation, mechanical calculation and lifetime calculation. Furthermore the transferability of specimen based simulation models to real components (an alternative test piece and a cylinder head) is investigated.     

高温合金材料循环相关和时间相关热机械疲劳循环性能模拟

从平衡热力学不可逆系统出发，用非线性粘弹塑性运动强化莱模拟高温合金材料的应变控制热机械疲劳循环特性。讨论了温度变化和应变循环的相位关系，循环相关和时间相关热机械疲劳损伤机制，蠕变和疲劳间的相互作用。在建立本构关系和状态方程时，均考虑了温度变化所产生的影响。     

Multiaxial creep and cyclic plasticity in nickel-base superalloy C263

Physically-based constitutive equations for uniaxial creep deformation in nickel alloy C263 [Acta Mater. 50 (2002) 2917] have been generalised for multiaxial stress states using conventional von Mises type assumptions. A range of biaxial creep tests have been carried out on nickel alloy C263 in order to investigate the stress state sensitivity of creep damage evolution. The sensitivity has been quantified in C263 and embodied within the creep constitutive equations for this material. The equations have been implemented into finite element code. The resulting computed creep behaviour for a range of stress state compares well with experimental results. Creep tests have been carried out on double notched bar specimens over a range of nominal stress. The effect of the notches is to introduce multiaxial stress states local to the notches which influences creep damage evolution. Finite element models of the double notch bar specimens have been developed and used to test the ability of the model to predict correctly, or otherwise, the creep rupture lifetimes of components in which multiaxial stress states exist. Reasonable comparisons with experimental results are achieved. The γ^′ solvus temperature of C263 is about 925 °C, so that thermo-mechanical fatigue (TMF) loading in which the temperature exceeds the solvus leads to the dissolution of the γ^′ precipitate, and a resulting solution treated material. The cyclic plasticity and creep behaviour of the solution treated material is quite different to that of the material with standard heat treatment. A time-independent cyclic plasticity model with kinematic and isotropic hardening has been developed for solution treated and standard heat treated nickel-base superalloy C263. It has been combined with the physically-based creep model to provide constitutive equations for TMF in C263 over the temperature range 20–950 °C, capable of predicting deformation and life in creep cavitation-dominated TMF failure.     

Transversely isotropic viscoplasticity model for a directionally solidified Ni-base superalloy

A transversely isotropic continuum viscoplasticity model has been formulated to capture the fatigue and creep responses of a directionally solidified (DS) polycrystalline Ni-base superalloy used mainly in turbine blades. This model has been implemented as an ABAQUS User MATerial (UMAT) subroutine using a semi-implicit integration scheme. Isothermal uniaxial fatigue data from tests conducted with and without hold times and creep data are used to characterize the stress–strain response at temperatures ranging from 427 °C to 1038 °C. The scheme leads to reduction of the associated computational costs when compared to a crystal viscoplasticity model that explicitly considers 3-D grain structure. The macroscopic elastoviscoplastic model is shown to simulate the homogenized deformation response of the polycrystalline DS alloy for various isothermal histories. The predictive capability of this model is verified using both in-phase and out-of-phase TMF data, and is compared to the results of analysis of a single crystal in terms of stress concentration and stress distribution for a model problem of a plate with a central hole.     

高温合金材料循环相关热机械疲劳寿命预测

在变温非线性运动强化规律所描述的高温合金材料热机械寿命应力－应变循环特性的基础上，讨论了应变控制的循环相关热机械疲劳寿命预测技术，所建模型采用了由应变以密度表示的损伤参数，并且引入了温度损伤系数，考虑了温度变化范围以及温度循环和应变循环相位关系对疲劳寿命的影响，在确定模型的一些参数，采用等温力学试验和疲劳试验的数据，为了把等温疲劳研究成果推广到变温疲劳分析领域，开辟了新的途径。     

Creep,plasticity, and fatigue of single crystal superalloy

Single crystal components in gas turbine engines are subject to such extreme temperatures and stresses that life prediction becomes highly inaccurate resulting in components that can only be shown to meet their requirements through experience. Reliable life prediction methodologies are required both for design and life management. In order to address this issue we have developed a thermo-viscoplastic constitutive model for single crystal materials. Our incremental large strain formulation additively decomposes the inelastic strain rate into components along the octahedral and cubic slip planes. We have developed a crystallographic-based creep constitutive model able to predict sigmoidal creep behavior of Ni base superalloys. Inelastic shear rate along each slip system is expressed as a sum of a time dependent creep component and a rate independent plastic component. We develop a new robust, computationally efficient rate-independent crystal plasticity approach and combined it with creep flow rule calibrated for Ni-based superalloys. The transient variation of each of the inelastic components includes a back stress for kinematic hardening and latent hardening parameters to account for the stress evolution with inelastic strain as well as the evolution for dislocation densities. The complete formulation accurately predicts both monotonic and cyclic tests at different crystallographic orientations for constant and variable temperature conditions (low cycle fatigue (LCF) and thermo-mechanical fatigue (TMF) tests). Based on the test and modeling results we formulate a new life prediction criterion suitable for both LCF and TMF conditions.     

A viscoplastic constitutive model for nickel-base superalloy,part 2: modeling under anisothermal conditions

In Part 2 of this study, extensive deformation tests were carried out on the nickel-base polycrystalline superalloy IN738LC under isothermal and anisothermal conditions between 450 and 950 °C. Under the isothermal conditions, the material showed almost no rate/time-dependency below 700 °C, while it showed distinct rate/time-dependency above 800 °C. Regarding the cyclic deformation, slight cyclic hardening behavior was observed when the temperature was below 700 °C and the imposed strain rate was fast, whereas in the case of the temperature above 800 °C or under slower strain rate conditions, the cyclic hardening behavior was scarcely observed. Unique inelastic behavior was observed under in-phase and out-of-phase anisothermal conditions: with an increase in the number of cycles, the stress at higher temperatures became smaller and the stress at lower temperatures became larger in absolute value although the stress range was approximately constant during the cyclic loading. In other words, the mean stress continues to evolve cycle-by-cycle in the direction of the stress at lower temperatures. Based on the experimental results, it was assumed that evolution of the variable Y that had been incorporated into a kinematic hardening rule in Part 1 of this study is active under higher temperatures and is negligible under lower temperatures. The material constants used in the constitutive equations were determined with the isothermal data, and were expressed as functions of temperature empirically. The extended viscoplastic constitutive equations were applied to the anisothermal cyclic loading as well as the monotonic tension, stress relaxation, creep and cyclic loading under the isothermal conditions. It was demonstrated that the present viscoplastic constitutive model was successful in describing the inelastic behavior of the material adequately, including the anomalous inelastic behavior observed under the anisothermal conditions, owing to the consideration of the variable Y.     

A simple endochronic transient creep model of metals with applications to variable temperature creep

Similar to the theory of endochronic plasticity, modified by Valanis in 1980, a simple endochronic transient creep model of metals is proposed by using a definition of intrinsic time ζ, measured within the creep strain tensor space, whose metric tensor is treated as a simple power form of creep strain-rate sensitive material function. The resulting constitutive equation of creep (Endocreep) contains only three material constants whose values can be determined completely by a simple creep test. An incremental form involving isothermally constant creep stress, with or without jump, and constant stress with temperature jump, are then formulated.In the applications of Endocreep on 304SS under variable temperature creep, data of simple creep tests, provided by Ohashi et al. at 650°C, Ohno et al. at 600°C, Findley and Cho at 593°C–649°C, are employed to determine material constants. The computational results in the simulation of creep tests under step-up and step-down temperature with constant axial stress are found in very good agreement with data provided by Findley and Cho. However, the results reveal that the model is too simple to deal with the recovery response of unloading. Beside this deficiency the model and its computational method proposed have a potential in the future FEM creep analysis of general thermomechanical loading history.     

High-temperature fatigue-life estimation: Extension of a unified theory

A procedure is presented for predicting the fatigue behavior at elevated temperature by extending the unified theory of fatigue damage previously proposed for room temperature. The method predicts the experimental results of high-temperature push-pull tests under isothermal conditions, using the total strain range. The analysis is based on parameters obtained from short-term tensile tests in which the temperature and the strain rate are the same as for the fatigue test. The procedure is applied for fatigue of a stainless steel at 650°C under cyclic axial strain. It has also been applied to published data for three austenitic stainless steels. In general, the present procedure gives estimates closer to experimental results than those obtained from other known methods.     

Characterization of mechanical properties of aluminum cast alloy at elevated temperature

The tensile response, the low cycle fatigue(LCF) resistance, and the creep behavior of an aluminum(Al) cast alloy are studied at ambient and elevated temperatures.A non-contact real-time optical extensometer based on the digital image correlation(DIC)is developed to achieve strain measurements without damage to the specimen. The optical extensometer is validated and used to monitor dynamic strains during the mechanical experiments. Results show that Young's modulus of the cast alloy decreases with the increasing temperature, and the percentage elongation to fracture at 100℃ is the lowest over the temperature range evaluated from 25℃ to 300℃. In the LCF test, the fatigue strength coefficient decreases, whereas the fatigue strength exponent increases with the rising temperature. The fatigue ductility coefficient and exponent reach maximum values at 100℃. As expected, the resistance to creep decreases with the increasing temperature and changes from 200℃ to 300℃.     

The interaction of creep and fatigue for a rotor steel

Twenty tests were performed on a 1 Cr?1 Mo?1/4 V rotor steel at 1000° F (538°C) to determine the interaction of creep and low-cycle fatigue. These tests involved five different types of strain-controlled cycling: creep at constant tensile stress; linearly varying strain at different frequencies; and hold periods at maximum compressive strain, maximum tensile strain, or both. The experimental data were then used to characterize the interaction of creep and fatigue by the:

1. Frequency-modified strain-range approach of Coffin;
2. Total time to fracture vs. the time of one cycle relation as proposed by Conway and Berling;
3. Total time to fracture vs. the number of cycles to fracture characterization of Ellis and Esztergar;
4. Summation of damage fractions obtained from tests using interspersed creep and fatigue as proposed by the Metal Properties Council;
5. Strain-range-partitioning method of Manson, Halford, and Hirschberg.

In order to properly assess the strain-range-partitioning approach, seven additional tests were performed at the NASA Lewis Research Center. Visual, ultrasonic, and acoustic-emission methods of crackinitiation determination were unsuccessful. An approximate indication of crack initiation was obtained by finding the cycle N_o where the stress-cycle curve first deviated from a constant slope. Predictive methods (based on monotonic tests) for determining the fatigue life in the creep range were examined and found deficient, though they may still be useful for preliminary comparison of materials and temperatures. The extension of the frequency-modified strain-range approach to notched members was developed and the results of notched-bar tests were shown to corroborate this approach, when crack initiation for the plain and notched bars was campared.     

Thermovisco-hyperelastic behavior of elastomeric materials modified by filler nanoparticles

We present the results of experimental studies of hyperelastic and relaxation properties of polymer composites with elastomeric matrix made of hydrogenated nitrile butadiene rubber filled with nanoparticles of technical carbon in the temperature range 19–150° C. We present typical experimental diagrams of deformation of the material with constant strain rate and the stress relaxation curves at different strain levels under tension and compression conditions. We consider a possible version of constitutive relations for describing some singularities of the behavior of the material under study. We developed a method for determining all the parameters of the accepted relations on the basis of the results of uniaxial tests. We found a nonmonotone dependence of the relaxation modulus on the temperature and proposed a formula for describing this dependence in the temperature range under study. To justify the possible use of the considered constitutive relations to perform calculations under conditions of arbitrary compound stress state, we performed numerical modeling of the compression experiment for cylindrical samples. A rather satisfactory agreement between the computational results and experimental data was obtained.     

On the forms of relationship between two noncoaxial second-order tensors (the case of plane strain or a plane stress state)

A relationship between noncoaxial tensors of stress and creep strain rate is established for the case of plane strain or a plane stress state. The basis is the experimentally substantiated hypothesis on the existence of a creep surface, which is a set of loading paths in the stress space that, at any time, ensure identical values of the creep intensity for a certain chosen measure and orthogonality of the creep strain rate vector to this surface. The relation obtained completely corresponds to available experimental data for complex loading. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 135–140, March–April, 1998.     

A High-frequency High-temperature Optical Strain/Displacement Gage

This paper describes an optical method for measuring strain or crack-opening displacement at high frequencies (20 kHz) and high temperatures (590°C) on a near-real-time basis. Two small reflective markers are placed on a smooth specimen or across a crack. When illuminated with a laser, interference fringes are generated; their motion can be monitored with photomultiplier tubes. The data acquisition system acquires 200 points per 50 microsecond cycle. These are processed, displayed, and stored at a rate of 25 Hz. Applications are in the general area of very high cycle (10⁹ cycles or more) fatigue. Demonstration tests at 20 kHz at room temperature with a strain range of 0.45 percent and at 590°C with a range of 0.2 percent are presented along with room temperature displacements up to 0.7 μm across the center of a 1.4 mm long crack.     

Development of high-temperature microsample testing

Microsample tensile testing has been established as a means of evaluating the room temperature mechanical properties of specimens with gage sections that are tens to hundreds of microns thick and several hundred microns wide. The desire to characterize the mechanical response of materials at elevated temperatures has motivated the development of high-temperature microsample testing that is reported here. The design of specially insulated grips allows the microsamples to be resistively heated using approximately 2 V DC and currents ranging between 2 to 6 A. An optical pyrometer with nominal spot size of 290 μm and 12 μm diameter type K thermocouples was employed to measure and verify the temperature of the microsamples. The ability of the pyrometer to accurately measure temperature on microsamples of different thicknesses and with slightly different emissivities was established over a temperature range from 400°C to 1100°C. The temperature gradient along the length and thickness of the microsample was measured, and the temperature difference measured in the gage section used for strain measurements was found to be less than 6.5°C. Examples of elevated temperature tensile and creep tests are presented.     

Balanced Biaxial Testing of Advanced High Strength Steels in Warm Conditions

The main purpose of the present work is to measure the stress–strain behavior under warm conditions (about 100 °C) of advanced high strength steel (AHSS) sheets up to large strains compared to uniaxial tension. The test equipment consists of two main parts, i.e., a hydraulic bulge tester and a heating device. A mechanical system is attached to the test equipment for measuring the membrane stress and thickness strain at the bulge pole. The stress–strain curves were measured for three kinds of AHSS sheets with the proposed test method for various initial temperatures (10, 50 and 100 °C). The proposed method does not provide isothermal stress–strain curves because the specimen temperature increases during the test due to the effect of deformation-induced heating. A numerical scheme using thermo-mechanical finite element (FE) simulations is suggested to deconvolute the isothermal stress–strain curves.     

A crystallographic model for the orientation dependence of low cyclic fatigue property of a nickel-base single crystal superalloy

ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｃｈｗｏｒｋｈａｓｂｅｅｎｃａｒｒｉｅｄｏｕｔｔｏｉｎｖｅｓｔｉｇａｔｅｔｈｅｉｎｆｌｕｅｎｃｅｏｆｏｒｉｅｎｔａｔｉｏｎａｎｄｓｔｒａｉｎｒａｔｅｏｎｔｈｅｍｅｃｈａｎｉｃａｌｐｒｏｐｅｒｔｙｏｆｎｉｃｋｅｌ＿ｂａｓｅｓｉｎｇｌｅｃｒｙｓｔａｌｓｕｐｅｒａｌｌｏｙｓ .Ｉｎｐａｒｔｉｃｕｌａｒ,ｔｈｅａｎｏｍａｌｏｕｓｙｉｅｌｄｉｎｇｂｅｈａｖｉｏｒ,ｔｅｎｓｉｏｎ/ｃｏｍｐｒｅｓｓｉｏｎａｓｙｍｍｅｔｒｙａｎｄｏｒｉｅｎｔａｔｉｏｎｄｅｐｅｎｄｅｎｃｅｈａｖｅｂｅｅｎ…     

Critical Stresses in Spalling and Dynamic Rupture of Metals

Results of dynamic rupture tests of a series of metals obtained using a composite Hopkinson bar and shock-wave loading of plane specimens are described. It is shown that the actual rupture strength at a strain rate of 5 · 10³ sec⁻¹ is very close to the spall strength at higher strain rates. Results of testing the same metals using a composite Hopkinson bar within a temperature range of 20–350°C are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 103–107, November–December, 2005.     

Mechanical behavior of Gamma-Met PX under uniaxial loading at elevated temperatures and high strain rates

Gamma titanium aluminides have received considerable attention over the last decade. These alloys are known to have low density, good high temperature strength retention and good oxidation and corrosion resistance. However, poor ductility and low fracture toughness have been the key limiting factors in the full utilization of these alloys. More recently, a new generation of gamma titanium aluminide alloys, commonly referred to as Gamma-Met PX, has been developed by GKSS, Germany. These alloys have been observed to have superior strength and better oxidation resistance at elevated temperatures when compared with conventional gamma titanium aluminides.The present paper discusses results of a study to understand the uniaxial mechanical behavior in both compression and tension of Gamma-Met PX at elevated temperatures and high strain rates. The compression and tensile tests are conducted using a modified Split-Hopkinson Bar apparatus at test temperatures ranging from room temperature to 900 °C and strain rates of up to 3500 s⁻¹. Under uniaxial compression, in the temperature range from room to 600 °C, the flow stress is observed to be nearly independent of test temperature. However, at temperatures higher than 600 °C thermal softening is observed at all strain rates with the rate of thermal softening increasing dramatically between 800 and 900 °C. The room temperature tensile tests show negligible strain-rate dependence on both yield stress and flow stress. With an increase in test temperature from room to 900 °C, the material shows a drop in both yield and flow stress at all levels of plastic strain. However, the measured flow stress is still higher when compared to nickel based super-alloys and other gamma titanium aluminides under similar test conditions. Also, no anomaly in yield stress is observed up to 900 °C.