New approach based on continuum damage mechanics with simple parameter identification to fretting fatigue life prediction

A new continuum damage mechanics model for fretting fatigue life prediction is established. In this model, the damage evolution rate is described by two kinds of quantities. One is associated with the cyclic stress characteristics obtained by the finite element （FE） analysis, and the other is associated with the material fatigue property identified from the fatigue test data of standard specimens. The wear is modeled by the energy wear law to simulate the contact geometry evolution. A two-dimensional （2D） plane strain FE implementation of the damage mechanics model and the energy wear model is presented in the platform of ABAQUS to simulate the evolutions of the fatigue damage and the wear scar. The effect of the specimen thickness is also investigated. The predicted results of the crack initiation site and the fretting fatigue life agree well with available experimental data. Comparisons are made with the critical plane Smith- Watson-Topper （SWT） method.

A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.

A CONTINUUM DAMAGE MODEL OF AGING CONCRETE

There is up to now no constitutive model in the current theoriesof CDM that could give a description for the degradation of agingconcrete. The two internal state variable β and ω are intro- ducedin this paper β is called cohesion variable as an additionalkinematic parameter, reflecting the cohesion state among materialparticles. ω is called damage factor for micro-defects such s voids.Then a damage model and a series of constitutive equations aredeveloped on Continuum Mechanics. The model proposed could give avalid description for the whole-course-degradation of aging concretedue to chemical and mechanical actions. Finally, the validity of themodel is evaluated by an example and experimental results.

Ductile Fracture Characterization for Medium Carbon Steel Using Continuum Damage Mechanics

This paper presents the ductility characterization for a medium carbon steel, for two microstructural conditions, that has been evaluated using the continuum damage mechanics theory, as proposed by Kachanov and developed by Lemaitre. Tensile tests were carried out using loading-unloading cycles in order to capture the gradual deterioration of the elastic modulus, which may be linked to the ductile damage increase with increasing plastic strain. The mechanical parameters for the isotropic damage evolution equation were obtained and then used as inputs for a plasticity-damage coupled nu- merical algorithm, validated through numerical simulations of the experimental tensile tests. A comparison between the SAE 1050 steels studied and two carbon steel alloys (obtained from the literature), provided some basic understanding of the influence of the carbon level on the evolution of the damage parameters. An empiric relationship for this set of parameters, which can provide useful data for preliminary studies envisaging prediction of ductile failure in carbon steels, is also presented.

Damage evolution model of strain hardening cementitious composites under the uniaxial stress state

The deformation and damage behaviors of strain hardening cementitious composites （SHCC） under the uniaxial stress state were investigated in this paper. Two ductile failure-based constitutive models were introduced to describe the uniaxial tension and compression properties of SHCC only using a few parameters. The computation method of model parameters was developed to ease the simulation procedures. Damage evolution of the SHCC was simulated by the formulation of continuum damage mechanics subsequently. The results show that the proposed models fit the stress-strain curves reasonably well, and the damage variables show different growth rules under uniaxial tension and compression. It is concluded that the proposed method can not only simply simulate the constitutive behavior of SHCC with the reasonable accuracy but also capture the characteristic of material degradation.

Revised damage evolution equation for high cycle fatigue life prediction of aluminum alloy LC4 under uniaxial loading

The fatigue life prediction for components is a difficult task since many factors can affect the final fatigue life. Based on the damage evolution equation of Lemaitre and Desmorat, a revised two-scale damage evolution equation for high cycle fatigue is presented according to the experimental data, in which factors such as the stress amplitude and mean stress are taken into account. Then, a method is proposed to obtain the material parameters of the revised equation from the present fatigue experimental data. Finally, with the utilization of the ANSYS parametric design language （APDL） on the ANSYS platform, the coupling effect between the fatigue damage of materials and the stress distribution in structures is taken into account, and the fatigue life of specimens is predicted. The outcome shows that the numerical prediction is in accord with the experimental results, indicating that the revised two-scale damage evolution model can be well applied for the high cycle fatigue life prediction under uniaxial loading.

A fatigue damage model for asphalt mixtures under controlled-stress and controlled-strain modes

A fatigue damage model based on thermodynamics was deduced for asphalt mixtures under controlled-stress and controlled-strain modes. By employing modulus of resilience as the damage hardening variable, a damage variable related with dynamic modulus was extracted as the evaluation index. Then, the damage evolution law under two control modes was proposed, and it has a similar form to the Chaboche fatigue model with a nonnegative material parameter m related to its loading level. Experimental data of four loading levels were employed to calibrate the model and identify the parameter in both control modes. It is found that the parameter m shows an exponential relationship with its loading level. Besides, the difference of damage evolution under two control modes was explained by the law. The damage evolves from fast to slow under a controlled-strain mode. However, under a controlled-stress mode, the evolution rate is just the opposite. By using the damage equivalence principle to calculate the equivalent cycle numbers, the deduced model also interprets the difference of damage evolution under two control modes on the condition of multilevel loading. Under a controlled-strain mode, a loading sequence from a low level to a high level accelerates damage evolution. An inverse order under the controlled-stress mode can prolong fatigue life.

Effect of low cycle fatigue pre-damage on very high cycle fatigue

Carbon-manganese steel is often applied in components of pipes in nuclear plant. Ultrasonic fatigue tests following low cycle fatigue （LCF） cycles damaged are used to study the strength of very high cycle fatigure （VHCF）. The comparison of test results of simple VHCF and cumulative fatigue （LCF plus VHCF） shows that LCF load influences the following VHCF strength. Continuum damage mechanics model is extended to VHCF region.

Fatigue Reliability Analysis of Fiber-Reinforced Laminated Composites by Continuum Damage Mechanics

This paper investigates the reliability of composite laminates with various lay-ups under fatigue loading.The prediction of failure probability of composite laminates subjected to different loads involves many uncertainties associated with mechanical properties,loading,and boundary conditions.Failure in the composite material is truly hard to trace because there are individual faults in each ply,and we face a stochastic process due to the scatter in the mechanical properties.The continuum damage mechanics(CDM),as a powerful approach,is applied to model the damage of fiber,matrix,and fiber/matrix debonding.This method defines criteria for damage detection and determines safe zones.The material constitutive equations are executed using a subroutine inAbaqus.The first-order reliability method and second-order reliability method have been applied to examine the reliability of laminated composites.The results are compared with those of the Monte Carlo simulation.Different composite laminates under different stress levels are considered for the failure probability investigation.The limit state functions and random variables have been determined based on the CDM model.Finally,the effects of the number of cycles,applied stress,and stacking sequence of the laminate on the reliability and fatigue life in fiber-reinforced laminated composites are assessed.

Investigation of FE Model Size Definition for Surface Coating Application

An efficient prediction mechanical performance of coating structures has been a constant concern since the dawn of surface engineering. However, predictive models presented by initial research are normally based on traditional solid mechanics, and thus cannot predict coating performance accurately. Also, the high computational costs that originate from the exclusive structure of surface coating systems （a big difference in the order of coating and substrate） are not well addressed by these models. To fill the needs for accurate prediction and low computational costs, a multi-axial continuum damage mechanics （CDM）-based constitutive model is introduced for the investigation of the load bearing capacity and fracture properties of coatings. Material parameters within the proposed constitutive model are determined for a typical coating （TIN） and substrate （Cu） system. An efficient numerical subroutine is developed to implement the determined constitutive model into the commercial FE solver, ABAQUS, through the user-defined subroutine, VUMAT. By changing the geometrical sizes of FE models, a series of computations are carried out to investigate （1） loading features, （2） stress distributions, and （3） failure features of the coating system. The results show that there is a critical displacement corresponding to each FE model size, and only if the applied normal loading displacement is smaller than the critical displacement, a reasonable prediction can be achieved. Finally, a 3D map of the critical displacement is generated to provide guidance for users to determine an FE model with suitable geometrical size for surface coating simulations. This paper presents an effective modelling approach for the prediction of mechanical performance of surface coatings.

Multi-fracture interactions during two-phase flow of oil and water in deformable tight sandstone oil reservoirs

Tight oil reservoirs are complex geological materials composed of solid matrix,pore structure,and mixed multiple phases of fluids,particularly for oil reservoirs suffering from high content of in situ pressurized water found in China.In this regard,a coupled model considering two-phase flow of oil and water,as well as deformation and damage evolution of porous media,is proposed and validated using associated results,including the oil depletion process,analytical solution of stress shadow effect,and physical experiments on multi-fracture interactions and fracture propagation in unsaturated seepage fields.Then,the proposed model is used to study the behavior of multi-fracture interactions in an unsaturated reservoir in presence of water and oil.The results show that conspicuous interactions exist among multiple induced fractures.Interaction behavior varies from extracted geological profiles of the reservoir due to in situ stress anisotropy.The differential pressures of water and that of oil in different regions of reservoir affect interactions and trajectories of multi-fractures to a considerable degree.The absolute value of reservoir average pressure is a dominant factor affecting fracture interactions and in favor of enhancing fracture network complexity.In addition,difference of reservoir average pressures in different regions of reservoir would promote the fracturing effectiveness.Factors affecting fracture interactions and reservoir treatment effectiveness are quantitatively estimated through stimulated reservoir area.This study confirms the significance of incorporating the two-phase flow process in analyses of multifracture interactions and fracture trajectory predictions during tight sandstone oil reservoir developments.

Fatigue-creep interaction based on continuum damage mechanics for AISI H13 hot work tool steel at elevated temperatures

AISI H13 （4Cr5MoSiV1） is one of the commonly used materials for extrusion tool, and it suffers from fatigue-creep damage during the hot extrusion process. Stress-controlled fatigue and creep-fatigue interaction tests were carried out at 500℃ to investigate its damage evolution. The accumulated plastic strain was selected to define the damage variable due to its clear physical meaning. A new fatigue-creep interaction damage model was proposed on the basis of continuum damage mechanics. A new equivalent impulse density for fatigue-creep tests was proposed to incorporate the holding time effect by transforming creep impulse density into fatigue impulse density. The experimental results indicated that the damage model is able to describe the damage evolution under these working conditions.

Continuum damage mechanics based modeling progressive failure of woven-fabric composite laminate under low velocity impact

A continuum damage mechanics (CDM) meso-model was derived for both intraply and interply progressive failure behaviors of a 2D woven-fabric composite laminate under a transversely low velocity impact.An in-plane anisotropic damage constitutive model of a 2D woven composite ply was derived based on CDM within a thermodynamic framework,an elastic constitutive model with damage for the fibre directions and an elastic-plastic constitutive model with damage for the shear direction.The progressive failure behavior of a 2D woven composite ply is determined by the damage internal variables in different directions with appropriate damage evolution equations.The interface between two adjacent 2D woven composite plies with different ply orientations was modeled by a traction-separation law based interface element.An isotropic damage constitutive law with CDM properties was used for the interface element,and a damage surface which combines stress and fracture mechanics failure criteria was employed to derive the damage initiation and evolution for the mixed-mode delamination of the interface elements.Numerical analysis and experiments were both carried out on a 2D woven glass fibre/epoxy laminate.The simulation results are in agreement with the experimental counterparts,verifying the progressive failure model of a woven composite laminate.The proposed model will enhance the understanding of dynamic deformation and progressive failure behavior of composite laminate structures in the low velocity impact process.

某超超临界汽轮机转子蠕变-疲劳损伤分析及寿命评估

工业用电需求使得汽轮机组进行频繁的启停,针对此情况,建立某1000MW超超临界机组汽轮机高压转子的有限元模型,基于Norton定理模拟其冷态启动和额定工况下的正常运行过程,研究转子在启动及运行过程中的危险点位置、温度和应力的变化规律。根据模拟计算结果,采用CDM(Continuum damage mechanics)模型分析该转子在每年20次冷态启动工况下的疲劳损伤、蠕变损伤及考虑两者交互的蠕变-疲劳损伤,并将结果与美国ASME及法国RCC-MR和DDS标准进行对比,表明该汽轮机转子的寿命在ASME标准下为30年,而在法国RCC-MR和DDS标准下偏于不安全。

Low-cycle fatigue lifetime estimation of Ti–6Al–4V welded joints by a continuum damage mechanics model

The low-cycle fatigue （LCF） behavior of directionally solidified nickel-based superalloy Ti-6A1-4V was studied under bare and electron beam welding condi- tions at room temperature. Results show that： （1） under the same test conditions, all the joints exhibit lower LCF lifetime than Ti-6A1-4V; （2） the failure of welded structures is mainly ascribed to the welding defect. A novel lifetime prediction methodology based on continuum damage mechanics is proposed to predict the lifetime of Ti-6A1-4V and its welded joints.

Creep life assessment of aero-engine recuperator based on continuum damage mechanics approach

The creep life of an aeroengine recuperator is investigated in terms of continuum damage mechanics by using finite element simulations.The effects of the manifold wall thickness and creep properties of brazing filler metal on the operating life of the recuperator are analyzed.Results show that the crack initiates from the brazing filler metal located on the outer surface of the manifold with the wall thickness of 2 mm and propagates throughout the whole region of the brazing filler metal when the creep time reaches 34900 h.The creep life of the recuperator meets the requirement of 40000 h continuous operation when the wall thickness increases to 3.5 mm,but its total weight increases by 15%.Decreasing the minimum creep strain rate with the enhancement of the creep strength of the brazing filler metal presents an obvious effect on the creep life of the recuperator.At the same stress level,the creep rupture time of the recuperator is enhanced by 13 times if the mismatch between the minimum creep rate of the filler and base metal is reduced by 20%.

A DAMAGE MECHANICS MODEL FOR FATIGUE LIFE PREDICTION OF FIBER REINFORCED POLYMER COMPOSITE LAMINA

A damage mechanics fatigue life prediction model for the fiber reinforced polymer lamina is established. The stiffness matrix of the lamina is derived by elastic constants of fiber and matrix. Two independent damage degrees of fiber and matrix are introduced to establish constitutive relations with damage. The damage driving forces and damage evolution equations for fiber and matrix are derived respectively. Fatigue tests on 0° and 90° unidirectional laminates are conducted respectively to identify parameters in damage evolution equations of fiber and matrix. The failure criterion of the lamina is presented. Finally, the life prediction model for lamina is proposed.

Low-cycle fatigue behavior of DZ125 superalloy under prior exposure conditions

Low-cycle fatigue(LCF) behavior of the directionally solidified(DS) nickel-based DZ125 superalloy was studied at elevated temperature(980 ℃).Specimens were,respectively,exposed for 0,2,25,50,and 100 h in air.The fatigue life of pre-exposed specimens is lower than that of unexposed specimens.The result is closely associated with fatigue crack initiation and propagation due to oxygen embrittlement and cycle loading.Detailed fractographic evaluations indicate the fatigue life is closely related to the surface microstructural modification.The resulting changes in microstructure cause the decrease in the effective area and the increase in actual stress.A methodology based on the continuum damage mechanics is developed to describe the correlation between the residual LCF life and pre-exposed time.

Determination of multiaxial stress rupture criteria for creeping materials:A critical analysis of different approaches

Materials in engineering applications are rarely uniaxially-loaded.In reality,failures under multiaxial loading has been widely observed in engineering structures.The life prediction of a component under multiaxial stresses has long been a challenging issue,particularly for high temperature applications.To distinguish the mode of failure ranging from a maximum principal stress intergranular damage to von Mises effective stress rupture mode a multiaxial stress rupture criterion(MSRC)was originally proposed by Sdobyrev and then Hayhurst and Leckie(SHL MSRC).A multiaxial-factor,α,was developed as a result which was intended to be a material constant and differentiates the bias of the MSRC between maxi-mum principal stress and effective stress.The success of the SHL MSRC relies on accurately calibrating the value ofαto quantify the multiaxial response of the material/geometry combination.To find a more suitable approach for determining MSRC,the applicability of different methods are evaluated.Given that the resulting analysis of the various approaches can be affected by the creep failure mechanism,princi-ples in the determination of MSRC with and without using continuum damage mechanics approaches are recommended.The viability of uniaxial material parameters in correlating withαthrough the analysis of available data in literature is also presented.It is found that the increase of the uniaxial creep dam-age tolerance parameterλis accompanied bythe decreaseof theα-value,whichimplies thatthe creep ductility plays an important role in affecting the multiaxial rupture behavior of materials.

Experimental and numerical investigations of the mechanical behavior of half sandwich laminate in the context of blanking

In this study,the complex mechanical behavior of an aluminum/low-density polyethylene(LDPE)half sandwich structure was investigated during the blanking process.Mechanical tests were conducted for the polymer and metal layer and the delamination behavior of the adhesive between the two layers.A new testing device was designed for detecting the delamination under tensile mode.Corresponding finite element models were established for the mechanical tests of the metal layer and the delamination of both layers for inverse parameter identifcation.Material parameters for Lemaitre-type damage,Drucker-Prager,and cohesive zone modeIs were identified for the metal,polymer,and adhesive,respectively.A finiteelement(FE)model was established for the blanking process of the sandwich structures.The experimental forcedisplacement curves,obtained in the blanking process of the half sandwich sheet,were compared with the predicted results of the FE model.The results showed that the predicted force-displacement curves and the experimental results were in good agreement.Additionally,the correlation between cutting clearance and changes in the forcedisplacement curves was obtained.Three feature values quantitatively described the imperfection of the experimental cutting edge.The effect of punch clearance on these values was studied numerically and experimentally.The results indicated that a smaller clearance generated a better cutting-edge quality.The stress state of the half sandwich structure during blanking was analyzed using the established FE model.