A damage function used for prediction of low cyclic fatigue life

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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。     

A new distortion energy-based equivalent stress for multiaxial fatigue life prediction

A new equivalent stress amplitude expression has been developed for the assessment of fatigue life in components under multiaxial loading. The expression was generated by incorporating non-linear/plastic stress–strain relation into a mechanical energy calculation, and then applying the calculation to the distortion energy theory for a cyclic loading case. Therefore, the new uniaxial equivalent stress expression determines an appropriate stress amplitude value for multiaxial cyclic loading. The purpose of the equivalent stress value is to determine multiaxial fatigue failure using an energy-based fatigue life prediction criterion. The governing understanding behind the criterion states that the physical damage quantity for failure is equal to the accumulated strain energy in a monotonic fracture, which is also equal to the accumulated strain energy during fatigue failure. Using the new equivalent stress amplitude expression and the energy-based life prediction method, a comparison is made between prediction results and multiaxial empirical data. The multiaxial data was acquired by a vibration-based biaxial bending fatigue test and a torsion fatigue test with an assumed axial misalignment. The results of the comparison provide encouragement regarding the capability of the newly developed equivalent stress amplitude expression for fatigue life prediction.     

Fatigue life predictions by integrating EVICD fatigue damage model and an advanced cyclic plasticity theory

An event independent cumulative damage (EVICD) fatigue prediction model was previously developed for the fatigue damage prediction under general multiaxial stress state and loading conditions. The model takes the plastic strain energy as the major contributor to the fatigue damage. The application of the EVICD model does not require a cycle counting method for general random loading. In the current effort, derivations were made to explicitly and directly relate the material constants in the fatigue model to the parameters in the Manson–Coffin equations and the cyclic stress–strain curve of the material. In addition, an advanced cyclic plasticity theory was implemented for the determination of the detailed stress–strain response that was required as the input for the EVICD fatigue model. Three metallic materials were used to demonstrate the capability of the modified fatigue model for the predictions of fatigue lives under different loading conditions. The results show that the fatigue model can provide fatigue life predictions in close agreement with the experimental observations.     

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.     

A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosis

We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions—one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measurables like accumulated plastic strain is obtained.     

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。     

The effects of rate of expansion and injection of water droplets on the entropy generation of nucleating steam flow in a Laval nozzle

The entropy generation due to irreversible heat transfer between vapor and liquid phases in a nucleating steam flow in a Laval nozzle is studied. To calculate the entropy generation due to self-condensation in transonic steam flow, a thermodynamic model is presented. The calculations of nucleating steam flow and the predictions of entropy generation rely on one-dimensional two-phase model. This model shows that the most of the thermodynamic losses take place during the nucleation phenomena. The effect of rate of expansion on the exergy losses is considered by decreasing the divergent angle of nozzle. Also micro-sized pure water droplets is injected theoretically to supercooled steam right after the nozzle throat at the onset of divergent section and the effects of injected droplets on thermodynamic losses and nucleation phenomena are investigated. The results indicate that decreasing the divergent angle and also injection of droplets diminishes the pressure rise in transonic steam flow and decreases the thermal entropy generation due to nucleation.     

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled visco-plastic constitutive model

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel were observed by the tests under the uniaxial stress-controlled cyclic loading with non-zero mean stress [G.Z. Kang, Y.J. Liu, Mater. Sci. Eng. A 472 (2008) 258–268]. Based on the obtained experimental results, the evolution features of whole-life ratcheting behavior and low-cycle fatigue (LCF) damage of the material were discussed first. Then, in the framework of unified visco-plasticity and continuum damage mechanics, a damage-coupled visco-plastic cyclic constitutive model was proposed to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented in the uniaxial stress cycling with non-zero mean stress. In the proposed model, the damage was divided into two parts, i.e., elastic damage and plastic damage, which were described by the evolution equations with the same form but different constants, since the maximum applied stresses in most of loading cases were lower than the nominal yielding strength of the material. The ratcheting of the material was still described by employing a nonlinear kinematic hardening rule based on the Abdel-Karim–Ohno combined kinematic hardening model [M. Abdel Karim, N. Ohno, Int. J. Plast. 16 (2000) 225–240] but extended by considering the effect of damage. The maximum strain criterion combined with an elastic damage threshold was employed to determine the failure life of the material caused by two different failure modes, i.e., fatigue failure (caused by low-cycle fatigue due to plastic shakedown) and ductile failure (caused by large ratcheting strain). The simulated whole-life ratcheting behavior and predicted failure life of tempered 42CrMo steel are in a fairly good agreement with the experimental ones.     

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．     

A thermodynamic model for electrical current induced damage

Electromigration-induced damage, which is in principal an irreversible mass diffusion under high current density, has been a concern for VLSI design for a long time. Miniaturization of electronic device sizes down to nano-scale will make electromigration a concern for all conducting components. This paper uses thermodynamics, statistical mechanics and mass transport (diffusion) principals to propose a model for electromigration process and a damage evolution model to quantify the degradation in microelectronics (and micro electromechanical system) solder joints subjected to high current densities. Entropy production in the system is used as a damage metric. The irreversible thermodynamic damage model utilized in this work has previously been successfully applied to thermo-mechanical fatigue of microelectronic solder joints. In this paper we extend this model to electromigration-induced degradation.Electromigration process is modeled by the atomic vacancy flux (mass diffusion) process. The proposed unified model is compared with several existing analytical and empirical models. A comparison of the damage evolution model proposed in here agrees well with empirical models proposed in the literature.     

Mechanothermodynamical system and its behavior

An attempt to formulate the basic principles of mechanothermodynamics of systems is made. The notion of tribo-fatigue entropy generated in a mechanical system is introduced similarly to thermodynamic entropy governed by matter and energy exchange. Interrelation of motion, damage, and information is found. It is shown that motion generates new information in the system if its damageability index is non-zero. The information is positive if the system is hardened and negative if it softened. It leads one to perceiving the principal feature of interaction of irreversible damages (effective energies and entropy) generated by effects of different nature (mechanical loads, heat flows, etc.), viz. dialectic character of interaction. Two principles of thermodynamics are formulated.     

复合材料层板疲劳损伤加载次序效应研究

从能量耗散的角度出发，建立了一种以有效循环滞回能为基础的非线性疲劳损伤累积法则，并从理论和实验两方面证明了该法则能够正确反映载荷次序效应     

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.     

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。     

Damage accumulation for growth of anti-plane crack in work-hardening material

Elastic–plastic solutions of an anti-plane crack in an infinite body are used in conjunction with a continuum damage model to describe the conditions necessary for the onset of crack instability, fatigue crack propagation due to cyclic loading, and rates of crack growth due to time dependent events. A power law relates the stress to the strain of the material. The damage, which invokes nucleation, growth and coalescence of microvoids due to elevated strain, is confined to the plastic zone surrounding the crack tip. For applied loading below the yield stress, the small-scale and large-scale yielding solutions are used to determine the influence of strain hardening on crack instability and failure. Crack growth due to cyclic loading and time-dependent deformations are studied using the small-scale yielding solution of the deformation theory of plasticity.     

Integrated numerical–experimental analysis of interfacial fatigue fracture in SnAgCu solder joints

In ball grid array (BGA) packages, solder balls are exposed to cyclic thermo-mechanical strains arising from the thermal mismatch between package components. Thermo-mechanical fatigue crack propagation in solder balls is almost always observed at the chip side of the bump/pad junction. The objective of the experimental part of this study is to characterize the bump/pad interface under fatigue loading. Fatigue specimens are prepared by reflowing Sn3.8Ag0.5Cu lead-free solder alloy on Ni/Au substrates. Obtained results show that fatigue damage evolution strongly depends on the microstructure. Applied strain and solder volume both have an influence on the fatigue damage mechanism. In the numerical part of the study, fatigue experiments are modeled using the finite element technique. A cohesive zone approach is used to predict the fatigue damage evolution in soldered connections. Crack propagation is simulated by an irreversible linear traction–separation cohesive zone law accompanied by a non-linear damage parameter. Cohesive zone elements are placed where failure is experimentally observed. Damage evolution parameters for normal and tangential interaction are scrutinized through dedicated fatigue tests in pure tensile and shear directions. The proposed cohesive zone model is quantitatively capable of describing fatigue failure in soldered joints, which can be further extended to a numerical life-time prediction tool in microelectronic packages.     

A thermodynamic theory of damage in elastic inorganic and organic solids

This contribution presents the foundations of a thermodynamic theory of damage in elastic solids, developed in collaboration with the late J. Kestin and with E. Honein and T. Honein. The theory is rooted in the so-called conservative or conventional thermodynamics of irreversible processes, where the concept of a local thermodynamic state plays a prominent role. An elastic body prone to damage is regarded as a thermodynamic system characterized by a set of extensive variables that can be defined in both equilibrium and nonequilibrium states and assigned approximately the same values in both the physical space and the abstract state space (i.e., the Gibbsian phase space of constrained equilibria). The extensive variables introduced include internal parameters which describe the damaged state of the body and whose conjugate intensive variables, or affinities, constitute a generalization of Eshelby’s concept of a “force on an elastic singularity”. The local state approximation is applied by assigning to the entropy and temperature in physical space local values which can be calculated in the Gibbsian phase space by the well-established methods of equilibrium thermodynamics. This leads to an explicit expression for the entropy production. The rate equations for the damage are then postulated in such a way as to conform to the second part of the second law of thermodynamics. The resulting theory captures many features of real inorganic material behavior in which no mass loss is sustained. By contrast, damage of organic materials, such as compact bone subject to osteoporosis, is accompanied by bone mass loss. This feature can be accommodated in the theory proposed by a suitable adjustment of the expression of the Gibbs free energy.