An Energy Based Fatigue Life Prediction Framework for In-Service Structural Components

An energy based fatigue life prediction framework has been developed for calculation of remaining fatigue life of in service gas turbine materials. The purpose of the life prediction framework is to account aging effect caused by cyclic loadings on fatigue strength of gas turbine engines structural components which are usually designed for very long life. Previous studies indicate the total strain energy dissipated during a monotonic fracture process and a cyclic process is a material property that can be determined by measuring the area underneath the monotonic true stress-strain curve and the sum of the area within each hysteresis loop in the cyclic process, respectively. The energy-based fatigue life prediction framework consists of the following entities: (1) development of a testing procedure to achieve plastic energy dissipation per life cycle and (2) incorporation of an energy-based fatigue life calculation scheme to determine the remaining fatigue life of in-service gas turbine materials. The accuracy of the remaining fatigue life prediction method was verified by comparison between model approximation and experimental results of Aluminum 6061-T6. The comparison shows promising agreement, thus validating the capability of the framework to produce accurate fatigue life prediction.     

An Energy-Based Torsional-Shear Fatigue Lifing Method

An energy-based fatigue-life prediction framework for the determination of full-life, remaining-life, and critical-life of in-service structures subjected to torsional-shear loading has been developed. This framework is developed upon the existing foundation of energy-based fatigue models crafted for the axial, uniaxial bending, and transverse-shear loading cases, which state: the total strain energy density accumulated during both a monotonic event and a cumulative cyclic process is the same material property. The modified energy-based torsional-shear fatigue-life prediction framework is composed of the following entities: (1) the development of a torsional-shear fatigue testing procedure capable of assessing strain energy density per cycle in a pure shear stress state and (2) the determination of the remaining-life and critical-life of in-service aluminum (Al) 6061-T6 structures subjected to shear fatigue through the application of the energy-based prediction method. Experimental data was shown to be affected by load-frame misalignment which was estimated and successfully incorporated into the validation results. Close correlation between adjusted experimental results and the full-life and critical-life predictions stemmed from a 3-to-2 shear-to-axial biaxial loading assumption, which was supported by crack path comparisons. Results of the study effectively demonstrated the versatility of the energy-based lifing method.     

Scaling of size/time/temperature — Part 2: Progressive damage in uniaxial compressive specimen

This work is concerned with predicting the fatigue failure initiation of a wing/fuselage bolt assembly. Accounted for in the analysis are both the influence of energy dissipation and damage accumulation as the structure is subjected to repeated cyclic loading. Results involving the location and number of cycles to initiate a fatigue crack 10⁻² in. are obtained. They agreed both qualitatively and quantitatively with the experimental findings. Also discussed is the influence of pre-torque in the bolt which tends to decrease the number of cycles to fatique crack initiation. Fatigue life may be extended by altering the load path so as to decrease the accumulation of energy near the site of failure initiation. This can be accomplished without major modification of the design. The methodology that makes use of the strain energy density criterion can be used to optimize the fatigue strength of other structural sub-assemblies by appropriate combination of material and geometry for specified load conditions.     

Hysteresis cycles and fatigue criteria using anelastic models based on fractional derivatives

The constitutive equation and the fatigue of anelastic media are described by using fractional order derivatives. The stress–strain relation, based on a generalization of the Kelvin–Voigt model, describes typical hysteresis cycles with the stress increasing as the number of cycles increases, a phenomenon known as cyclic hardening and observed in many materials such as, for instance, steel. Criteria are established to find the number of cycles which may cause fatigue for a strain with a given amplitude and frequency. They are based on the yield and fatigue stresses, on the melting temperature through the dissipated energy, and on the strain energy. In all the cases, it is seen that the number of cycles to failure is inversely proportional to the amplitude and to the frequency of the applied strain. Comparison to experimental data indicates that the model satisfies, at least qualitatively, the behavior of real materials under cyclic loading.     

Hysteresis loops predicted by isoenergy density theory for polycrystals. Part I: fundamentals of non-equilibrium thermal–mechanical coupling effects

When a polycrystal is stressed or strained at fifty percent of the corresponding yield value, damage will be inflicted non-homogeneously in the material due to the fact that the stress and/or strain distribution is non-uniform even if isotropy and homogeneity are assumed for the initial microstructure. This effect will be cumulated for each cycle of the load if the applied stress or strain is repeated continuously. Nucleation of microcracks can eventually lead to the propagation of a macrocrack.The process of damage accumulation in fatigue is defined to be sufficiently slow such that inhomogeneity of material behavior created by loading is a significant factor that can not be arbitrarily dismissed without a good reason. What this means specifically is that the difference of the stress and strain behavior at each point in a fatigue specimen must be accounted for in the analytical model in order to predict the correct cumulative effect. Such a requirement translates into a non-equilibrium formulation where the constitutive relations for each point and loading cycle must be determined separately. In this sense, the true problem of fatigue cannot be completely treated by the classical continuum mechanics approach that is limited to equilibrium mechanics for a closed system. Having said this, the isoenergy density theory will be applied to estimate the hysteresis loops of a hour-glass profile cylindrical bar specimen as recommended by the American Society for Testing and Materials (ASTM) for low-cycle fatigue.The work will be divided into two parts. Part I will cover the fundamentals of a non-equilibrium theory where the continuum elements are finite in size; they do not vanish in the limit. Therefore, size effects are immediately encountered as a function of time. General expressions for the rate change of volume of these elements with surface area are derived such that they can be computed from the nine displacement gradients. These elements can differ in size and must fit together without discontinuities or gaps to form the continuum. The condition of isoenergy energy density is invoked such that the size of these individual elements under large and finite deformation and rotation can be determined without loss in generality. The existence of such a space having the property of the same isoenergy density in all directions is thus proved. This enables the establishment of the one dimensional energy state with that in three dimensions without restriction, the absence of which has prevented the development of a complete non-linear theory of mechanics that can be solved in a direct fashion in contrast to the inverse method of assuming the displacement field. Illustration is provided for deriving the constitutive relation incrementally for a given location for the hour-glass specimen made of 6061-T6 aluminum. Once the specimen is loaded, each material point will follow a different stress and strain curve according to the local displacement rate. Hence, the method applies to material with non-homogeneous microstructure if their individual expressions can be assessed and fed into the computer.Part II computes for the non-equilibrium temperature and an entropy-like quantity that can be positive and negative. This implies that the system can absorb or dissipate energy with reference to the surrounding. Additional data for hysteresis loops are given for 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium. Accumulation of the local hysteresis energy per cycle is found to be the highest near the surface of the uniaxial specimen where load symmetry prevails. This is a consequence of the difference in accumulation of the energy density due to distortion in contrast to dilatation at the specimen center. This is why fatigue cracks tend to nucleate near the specimen surface, at a small distance towards the interior. Another distinct feature of fatigue is that the non-equilibrium temperature is found to oscillate about the ambient temperature while the local stress states fluctuate between tension and compression. This temperature reversal behavior is typical of non-equilibrium behavior and also occurs under monotonic loading. The space and time variations of the dissipated energy density for different materials are found to be related to the initial monotonic energy density or area under the true stress and true strain curve.What will be demonstrated is that no special consideration need to be made when applying the isoenergy density theory for analyzing the nucleation of micro and macrocracks in addition to failure of the specimen. Crack nucleation under fatigue is assumed to occur when the total hysteresis energy reaches a critical value. It is possible to establish a relation between the average hysteresis energy per cycle and the number of cycles to failure. The proposed method requires only a knowledge of the initial monotonic energy density curve for a given material. Predicted results for the fatigue of cylindrical bar specimens with hour-glass profile are given and they can be found in Part II of this work.     

疲劳过程中的能量耗散和疲劳寿命的预测

试验测量了A3钢和铝合金LY12CZ在疲劳过程中的耗散能密度与应力幅的关系和破坏时的临界累积耗散能密度。通过一系列不同加载频率和应力比的比较试验,结果表明耗散能密度与应力幅的关系和临界累积耗散能密度在不同加载频率下变化不大,但是受应力比的影响较大。本文还建立了临界累积耗散能密度疲劳寿命预测判据,并用此判据进行了带中心孔板条构件的疲劳寿命预测,取得了较好的结果（误差在25％以内）。这种方法对于构件局部的疲劳主要由一个方向应力控制的工程问题,使用简便有效。     

Plastic Strain Energy Model for Rock Salt Under Fatigue Loading

The fatigue test for rock salt is conducted to investigate the effects of stress amplitude, loading frequency and loading rate on the plastic strain energy, from which the evaluation rule of the plastic strain energy is analyzed, which is divided into three stages: cyclic hardening,saturation and cyclic softening. The total accumulated plastic strain energy only depends on the mechanical behavior of rock salt, but is immune to the loading conditions. A novel model for fatigue life prediction is proposed based on the invariance of the total plastic dissipation energy and the stability of the plastic energy per cycle.     

Q345低周疲劳性能与疲劳寿命预测分析

本文对结构用钢Q345的低周疲劳性能进行了试验研究。试验在常温下岛津电液伺服疲劳试验机上进行,采用轴向应变控制方法,恒定应变速率为0.005s-1,应变比为-1。试验结果表明,初始阶段,Q345在高应变幅值(0.6%)循环作用下出现循环硬化效应,而在低应变幅值(0.6%)作用下出现循环软化效应;随着加载应变幅的增加,硬化和软化率呈直线上升趋势。Q345疲劳裂纹萌生阶段占其整个寿命的60%以上,其裂纹萌生寿命与应变幅存在幂函数关系。根据Coffin-Manson公式得到了Q345的应变-寿命关系公式;采用能量预测法得到了材料的塑性应变能与疲劳寿命的关系表达式。上述结果对钢结构的设计、评估具有重要的工程应用参考价值。     

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。     

Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

Fatigue-life prediction by an order statistics treatment of acoustic-emission signals

In fatigue, both the crack-propagation rates and the cumulative acoustic-emission activity are known to be related to the applied stress-intensity range. By considering the energy balance during crack propagation and the relation of strain energy release to the acoustic-emission characteristics, a formal relation between acoustic emission amplitudes and initial fatigue-crack-propagation rates has been derived. Continuous monitoring of acoustic emission during low cycle (tension-tension) fatigue tests has been conducted on aluminum 2024-T3 and 7075-T6 alloys, until fracture. Initial crack sizes and orientations in the fatigue specimens were randomly distributed. Every few hundred cycles, the acoustic signal having the highest peak amplitude was recorded as the extreme acoustic-emission event for the elapsed period. The extreme peak amplitudes, related to extreme crack-propagation rates, were shown, by an order statistics treatment, to be extremally distributed. Statistical, nondeterministic, approach to fatigue considers that only extreme crack-propagation rates are vital to fatigue lives. Knowledge of the distribution function of propagation rates is therefore essential in design for fatigue. Such knowledge can now be obtained in a nondestructive manner, during service in real time, by analyzing the distribution of amplitudes of acoustic-emission signals emitted during cyclic stressing. The statistical treatment enables the prediction of the number of cycles left until failure. Predictions performeda posteriori, based on results gained early in each fatigue test, were in good agreement with actual fatigue lives. The amplitude distribution analysis of the acoustic signals emitted during fatigue tests has been proven to be a feasible nondestructive method for predicting fatigue life.     

镍基单晶合金多轴非比例加载低周疲劳研究

基于正交设计, 分别在680℃和850℃下进行DD3镍基单晶合金薄壁圆管试样([001]取向)拉/扭非比例加载低周疲劳试验, 研究等效应变范围、应变路径角、拉/扭载荷相位角、循环特性和温度诸因素对镍基单晶合金多轴低周疲劳寿命的影响作用. 疲劳试验数据的极差分析表明, 应变路径角、拉/扭载荷相位角和等效应变范围是影响疲劳寿命的主要因素. 将菱形应变加载路径区分为比例加载段和非比例加载段, 提出了表征非比例加载效应的等效应变参量, 并通过引入单晶应变三轴性因子反映拉/扭应变路径角对多轴疲劳寿命的影响. 用考虑非比例加载效应的等效应变范围和单晶应变三轴性因子构造循环塑性应变能损伤参量, 进行多元线性回归分析, 疲劳寿命回归模型与试验寿命具有很好的相关性, 所有试验数据都落在2.0倍的偏差分布带之内.      

Cyclic plastic deformation and cyclic hardening/softening behavior in 304LN stainless steel

Low cycle fatigue experiments have been conducted on 304LN stainless steel in ambient air at room temperature. Uniaxial ratcheting behavior has also been studied on this material and in both engineering and true stress controlling modes. It is shown that material’s cyclic hardening/softening behavior in low cycle fatigue and in ratcheting is dependent not only on material but also on the loading condition. Improvement of ratcheting life and mean stress dependent hardening are observed in the presence of mean stress. A method based on the strain energy density (SED) is used to represent cyclic hardening/softening behavior of the material in this work. The decrease of SED with cycles is an indication that the life in low cycle fatigue and in ratcheting is improved. The SED represents the area of the hysteresis loops.     

扭转预应变对35CrMo钢低周疲劳性能的影响

自行设计了疲劳和扭转两用的试样,通过对试件预扭转不同的角度,系统研究35CrMo钢在不同扭转预应变下的低周疲劳性能,分析了扭转预应变后35CrMo钢的循环硬化软化特性、滞后回线、塑性应变能及循环弹性模量的变化规律,并对疲劳断口进行扫描电镜分析。结果表明:4种预扭转处理过的试件均表现出明显的循环软化行为,且循环软化规律及衰减的程度基本相同;循环应力范围及疲劳寿命随着预扭转角的增大而降低;应力应变滞后回线中加卸载曲线间的宽度随着预扭转角的增大而减小;塑性应变能都随着循环次数的增大而增加,且随着预扭转角的增大其增大速率下降;循环弹性模量都随着循环次数的增加而逐渐降低,且随着预扭转角的增大其衰减趋势减缓。     

Thermal/mechanical damage of 6061-T6 aluminum tensile specimen

As a 6061-T6 aluminum coupon specimen is stretched, energy is being converted from mechanical work to heat. This irreversible process of material damage is detected experimentally by measuring the change in surface temperature. Contrary to the ordinary notion that the material would heat up when loaded, it actually cools before returning to the ambient condition. The recovery time was approximately 26 sec for a displacement rate of 8.467·10⁻⁵ m/sec and 200 sec when the displacement rate is reduced by one of magnitude. Cooling and heating is a rate dependent process. Three sets of temperature data were obtained for each of the displacement rates and they coincide with those prediced from the energy density theory that accounts for the nonhomogeneous dissipation of energy at every location in the specimen.Unlike any classical theories in mechanics, the energy density theory determines the stress and strain response of each element in the specimen only from a knowledge of the initial material stiffness and the displacement time rate. This is necessary because the local strain rates for elements near the center and edge of the specimen can differ by a wide margin. The so-called uniaxial stress and strain curve is then obtained by taking the average of all the elements. The results agreed extremely well with those measured experimentally for the 6061-T6 aluminum. Obtained analytically are also the thermal conductivity coefficients that are loading rate dependent and anisotropic in character due to stretching in the longitudinal direction. Their values tend to stabilize beyond the cooling/heating period.     

Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis.     

Failure initiation in unnotched specimens subjected to monotonic and cyclic loading

Failure initiation in unnotched cylindrical bar specimens is predicted by application of the strain energy density theory. Maximum value of the local minimum strain energy density function is calculated, the critical value of which is assumed to coincide with failure by monotonic as well as cyclic uniaxial loading. Damage is accumulated in the specimen for each increment of monotonically rising load and each cycle of repeatedly applied load. Use is made of the incremental theory of plasticity to account for permanent deformation that is nonuniformly distributed throughout the cylindrical bar. Failure initiation site is found to occur at the center of the bar for monotonic loading where dilatation is dominant and near the specimen surface for fatigue loading where distortion is more significant. The results are consistent with the experimental observations without including microstructural effects. Nonhomogeneity caused by macro-dilatation and macro-distortion is also shown to play an important role in failure initation.     

Fast prediction of the fatigue behavior of short-fiber-reinforced thermoplastics based on heat build-up measurements: application to heterogeneous cases

Short-fiber-reinforced thermoplastics components for structural applications are usually very complex parts as stiffeners, ribs and thickness variations are used to compensate the quite low material intrinsic stiffness. These complex geometries induce complex local mechanical fields but also complex microstructures due to the injection process. Accounting for these two aspects is crucial for the design in regard to fatigue of these parts, especially for automotive industry. The aim of this paper is to challenge an energetic approach, defined to evaluate quickly the fatigue lifetime, on three different heterogeneous cases: a classic dog-bone sample with a skin-core microstructure and two structural samples representative of the thickness variations observed for industrial components. First, a method to evaluate dissipated energy fields from thermal measurements is described and is applied to the three samples in order to relate the cyclic loading amplitude to the fields of cyclic dissipated energy. Then, a local analysis is detailed in order to link the energy dissipated at the failure location to the fatigue lifetime and to predict the fatigue curve from the thermomechanical response of one single sample. The predictions obtained for the three cases are compared successfully to the Wöhler curves obtained with classic fatigue tests. Finally, a discussion is proposed to compare results for the three samples in terms of dissipation fields and fatigue lifetime. This comparison illustrates that, if the approach is leading to a very relevant diagnosis on each case, the dissipated energy field is not giving a straightforward access to the lifetime cartography as the relation between fatigue failure and dissipated energy seems to be dependent on the local mechanical and microstructural state.     

Three-dimensional transverse fatigue crack growth in rail head

Results are given in terms of crack growth area and tonnage of train load. A three-dimensional finite element procedure is developed for analyzing multiple-mode transverse fatigue crack growth in a rail section. Stress and failure analysis are performed for each increment of non-self-similar crack growth up to the point of global instability that is assumed to be governed by the fracture toughness of the rail steel. The strain energy density criterion is adopted to predict the crack profiles developed from a two-stage fatigue loading cycle where both Mode I and III crack extension are present. Use is made of the material data obtained from the past and present TSC programs for predicting the remaining life of a 132 lb/ft rail head with an initial transverse circular crack of 0.50 in. in diameter. The number of cycles to failure are estimated for four different vertical load and initial crack positions.     

基于应变能的复杂应力场低周疲劳分析

塑性应变能使材料微观组织结构发生不可逆变化,从而引起等效宏观应力,该应力随循环加载而增大．假定材料疲劳源处破坏是由最大拉应力引起的,最大等效宏观应力与外加应力叠加达到材料本征断裂应力时形成微裂纹．微裂纹引起上述两部分应力变化,继续加载直至宏观裂纹出现,从而得到材料的疲劳寿命．本文所建立的多轴疲劳寿命公式包含材料参数、拉应力以及塑性应变能等,以上数据可通过单轴疲劳数据和有限元方法获得．通过对SM45C材料的计算验证,表明该模型对多轴随机应变加载低周疲劳寿命,具有良好的预测结果．