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 Hybrid Local/Nonlocal Continuum Mechanics Modeling of Damage and Fracture in Concrete Structure at High Temperatures

This paper proposes a hybrid peridynamic and classical continuum mechanical model for the high-temperature damage and fracture analysis of concrete structures.In this model,we introduce the thermal expansion into peridynamics and then couple it with the thermoelasticity based on the Morphing method.In addition,a thermomechanical constitutive model of peridynamic bond is presented inspired by the classic Mazars model for the quasi-brittle damage evolution of concrete structures under high-temperature conditions.The validity and effectiveness of the proposed model are verified through two-dimensional numerical examples,in which the influence of temperature on the damage behavior of concrete structures is investigated.Furthermore,the thermal effects on the fracture path of concrete structures are analyzed by numerical 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.

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.

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.

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.

Progressive Damage Analysis(PDA)of Carbon Fiber Plates with Out-of-Plane Fold under Pressure

The out-of-plane fold is a common defect of composite materials during the manufacturing process and will greatly affect the compressive strength as well as the service life.Making it of great importance to investigate the influence of out-of-plane defects to the compressive strength of laminate plates of composite materials,and to understand the patterns of defect evolution.Therefore,the strip method is applied in this article to create out-of-plane defects with different aspect ratios in laminated plates of composite materials,and a compressive performance test is conducted to quantify the influence of out-of-plane defects.The result shows that the compressive strength becomes weaker with a greater aspect ratio.When the highest aspect ratio is set to 0.12 in the experiment,the compressive strength reduces by 36.1%.Then we establish a 3-D progressive damage model based on continuum mechanics,and write it into the UMAT subroutine together with the 3-D Hashin criteria and the non-linear degradation criteria of materials.3-D solid modeling is performed for the samples with an out-of-plane fold based on ABAQUS,and progressive damage analysis is conducted to acquire the inplane evolution process of initial failure strength with different laminates.The experimental results agree well with the simulation results.

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.

Identification of Damage Parameters for Intralaminar Damage Modeling in Laminated Composites Considering Transverse Stress Effects

The aim of this study is to develop an appropriate modeling methodology for the simulation of intralaminar damage in laminated composites under complex loadings. The intralaminar damages are modeled by stiffness reduction controlled by thermodynamic forces as defined in continuum damage mechanics model proposed by Ladevèze. The original method neglected transverse stress in elementary plies during the tensile tests of [45/?45]mS laminates, resulting in variations of the identified damage parameters of Ladevèze model. This study compared the identified damage parameters considering transverse stress effects with those based on the original method. The effect of transverse stress in the identification process on the damage modeling is discussed, and it is found that one of damage coupling parameters and the damage master curves significantly depend on consideration of transverse stress effects. Finally, it is demonstrated that experimental stiffness degradation is well simulated by the prediction using the identified parameters considering transverse stress effects.

基于GTN和CDM的5754铝合金板材成形极限曲线和失效行为对比分析

为探究基于不同物理机制的损伤模型对材料可成形性预测的影响,分别采用Gurson-Tvergaard-Needleman(GTN)细观损伤模型和基于热力学的连续介质损伤力学(CDM)模型对5754铝合金板材的成形极限曲线和失效行为进行了对比分析。首先,建立了5754铝合金板材单向拉伸有限元模型,对照实验结果验证了GTN细观损伤模型和基于热力学的CDM模型在表征材料力学行为上的有效性。其次,开展了不同宽度尺寸板材试样的胀形有限元模拟,提取破坏位置的主应变和次应变,绘制5754铝合金板材的成形极限。结果表明,GTN细观损伤模型预测的成形极限曲线与实验数据吻合较好,但基于热力学的CDM模型不能准确地反映成形极限曲线中材料点拉-压力学特征与拉-拉力学特征之间的区别。最后,利用基于GTN和CDM的成形极限曲线预测5754铝合金在十字拉深成形过程中的损伤分布和失效行为,结果表明,两种基于不同机制的损伤模型都能够有效地预测5754铝合金的可成形性,预测结果与实验现象具有很好的一致性。

基于连续介质损伤力学的钛合金耐压球壳极限强度分析

本文在连续介质损伤力学理论框架下,以深海载人装备耐压球壳结构为研究对象,开展Bonora损伤模型适用性研究。首先,设计TA31钛合金加载卸载试验,依据试验结果,分析Bonora模型参数对材料应力应变响应的影响规律;随后,提出一种模型参数校准方法,依据试验数据确定TA31钛合金的模型参数;最后,将Bonora模型通过VUMAT子程序的形式嵌入到有限元软件中,开展钛合金球壳结构的极限强度分析,并与传统方法进行对比。研究结果表明,在耐压球壳极限强度分析中,引入Bonora模型可以准确模拟耐压球壳结构的失效模式和破坏压力。该模型在材料本构关系中考虑了屈服强度、抗拉强度以及最大塑性应变的影响,结构失效的物理意义更加明确,对材料性能的优化与提升具有指导意义。

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.

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.

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.

基于CDM的复合材料层合板三维非线性渐进损伤分析

建立了基于连续介质损伤力学(CDM)的中等尺度复合材料层合板三维渐进损伤分析模型。模型中损伤材料本构方程采用对应于不同损伤模式的内部状态变量进行描述,材料失效准则采用三维HASHIN准则。分析了含孔复合材料层合板压缩试件,计算强度与试验数据的吻合表明该模型可用于预测含孔层合板的压缩强度,同时该模型可以预测层合板的失效模式以及损伤发生、扩展直至最终破坏的整个过程,并且该模型具有较好的计算收敛性。

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%.

基于三维CDM的复合材料开口层合板失效分析

建立了复合材料层合板三维连续介质损伤力学模型,并将该模型应用于复合材料开口层合板的损伤破坏分析中。与相关试验中开口层合板强度和损伤破坏情况对比分析表明:本文模型能够有效地模拟开口层合板从初始损伤到完全破坏的全过程,具有较高的计算精度和良好的数值模拟收敛性。基于该模型,详细分析了在单向拉伸载荷作用下开口层合板不同铺层的损伤破坏情况。