Damage characteristics and constitutive modeling of the 2D C/Si C composite: Part I – Experiment and analysis

This paper reports an experimental investigation on the macroscopic mechanical behaviors and damage mechanisms of the plain-woven(2D) C/Si C composite under in-plane on- and offaxis loading conditions. Specimens with 15, 30, and 45 off-axis angles were prepared and tested under monotonic and incremental cyclic tension and compression loads. The obtained results were compared with those of uniaxial tension, compression, and shear specimens. The relationships between the damage modes and the stress state were analyzed based on scanning electronic microscopy(SEM) observations and acoustic emission(AE) data. The test results reveal the remarkable axial anisotropy and unilateral behavior of the material. The off-axis tension test results show that the material is fiber-dominant and the evolution rate of damage and inelastic strain is accelerated under the corresponding combined biaxial tension and shear loads. Due to the damage impediment effect of compression stress, compression specimens show higher mechanical properties and lower damage evolution rates than tension specimens with the same off-axis angle. Under cyclic tension–compression loadings, both on-axis and off-axis specimens exhibit progressive damage deactivation behaviors in the compression range, but with different deactivation rates.     

Out of phase thermal mechanical fatigue investigation of a directionally solidified superalloy DZ125

Out of phase(OP) thermal mechanical fatigue(TMF) behavior of a directionally solidified(DS) superalloy DZ125 was experimentally and numerically studied. Two different temperature conditions, which are 500–1000 °C and 400–900 °C, were considered in the present research.Stress and strain responses as well as fatigue life results were presented and discussed. Scanning electron microscope(SEM) and metallographic analysis were used to study the damage mechanism. An oxidation assisted crack initiation and propagation phenomenon were found to explain the shorted life under TMF cycles. In order to characterize the stress and strain deformations under TMF loadings, a modified Chaboche's constitutive model was applied. Additionally, the TMF life of the material was modeled and predicted by Neu–Sehitoglu damage law with high accuracy.     

Dynamic tensile behavior of AZ31B magnesium alloy at ultra-high strain rates

The samples having {0001} parallel to extruding direction(ED) present a typical true stress–true strain curve with concave-down shape under tension at low strain rate. Ultra-rapid tensile tests were conducted at room temperature on a textured AZ31 B magnesium alloy. The dynamic tensile behavior was investigated. The results show that at ultra-high strain rates of 1.93 · 102 s 1and 1.70 · 103 s 1, the alloy behaves with a linear stress–strain response in most strain range and exhibits a brittle fracture. In this case, {10-12} 10-11 extension twinning is basic deformation mode. The brittleness is due to the macroscopic viscosity at ultra-high strain rate, for which the external critical shear stress rapidly gets high to result in a cleavage fracture before large amounts of dislocations are activated. Because {10-12} tension twinning, {10-11} compressive twinning,basal a slip, prismatic a slip and pyramidal c + a slip have different critical shear stresses(CRSS), their contributions to the degree of deformation are very differential. In addition,Schmid factor plays an important role in the activity of various deformation modes and it is the key factor for the samples with different strain rates exhibit various mechanical behavior under dynamic tensile loading.     

Stress analysis and damage evolution in individual plies of notched composite laminates subjected to in-plane loads

This work aims to investigate local stress distribution, damage evolution and failure of notched composite laminates under in-plane loads. An analytic method containing uniformed boundary equations using a complex variable approach is developed to present layer-by-layer stresses around the notch. The uniformed boundary equations established in series together with conformal mapping functions are capable of dealing with irregular boundary issues around the notch and at infinity. Stress results are employed to evaluate the damage initiation and propagation of notched composites by progressive damage analysis(PDA). A user-defined subroutine is developed in the finite element(FE) model based on coupling theories for mixed failure criteria and damage mechanics to efficiently investigate damage evolution as well as failure modes. Carbon/epoxy laminates with a stacking sequence of [45°/0°/ 60°/90°]sare used to investigate surface strains, in-plane load capacity and microstructure of failure zones to provide analytic and FE methods with strong validation. Good agreement is observed between the analytic method, the FE model and experiments in terms of the stress(strain) distributions, damage evaluation and ultimate strength, and the layerby-layer stress components vary according to a combination effect of fiber orientation and loading type, causing diverse failure modes in individuals.     

A novel unified model predicting flow stress and grain size evolutions during hot working of non-uniform as-cast 42CrMo billets

The cast preformed forming process(CPFP) is increasingly considered and applied in the metal forming industries due to its short process, low cost, and environmental friendliness, especially in the aerospace field. However, how to establish a unified model of a non-uniform as-cast billet depicting the flow stress and microstructure evolution behaviors during hot working is the key to microstructure prediction and parameter optimization of the CPFP. In this work, hot compression tests are performed using a non-uniform as-cast 42 CrMo billet at 1123–1423 K and 0.01–1sà1. The effect laws of the non-uniform state of the as-cast billet with different initial grain sizes on the flow stress and microstructure are revealed deeply. Based on experimental results, a unified model of flow stress and grain size evolutions is developed by the internal variable modeling method. Verified results show that the model can well describe the responses of the flow stress and microstructure to deformation conditions and initial grain sizes. To further evaluate its reliability, the unified model is applied to FE simulation of the cast preformed ring rolling process.The predictions of the rolling force and grain size indicate that it could well describe the flow stress and microstructure evolutions during the process.     

Thermal-structural response and low-cycle fatigue damage of channel wall nozzle

To investigate the thermo-mechanical response of channel wall nozzle under cyclic working loads,the fnite volume fluid-thermal coupling calculation method and the fnite element thermal-structural coupling analysis technique are applied.In combination with the material lowcycle fatigue behavior,the modifed continuous damage model on the basics of local strain approach is adopted to analyze the fatigue damage distribution and accumulation with increasing nozzle work cycles.Simulation results have shown that the variation of the non-uniform temperature distribution of channel wall nozzle during cyclic work plays a signifcant role in the thermal-structural response by altering the material properties;the thermal-mechanical loads interaction results in serious deformation mainly in the front region of slotted liner.In particular,the maximal cyclic strains appear in the intersecting regions of liner gas side wall and symmetric planes of channel and rib,where the fatigue failure takes place initially;with the increase in nozzle work cycles,the residual plastic strain accumulates linearly,and the strain amplitude and increment in each work cycle are separately equal,but the fatigue damage grows up nonlinearly.As a result,a simplifed nonlinear damage accumulation approach has been suggested to estimate the fatigue service life of channel wall nozzle.The predicted node life is obviously conservative to the Miner＇s life.In addition,several workable methods have also been proposed to improve the channel wall nozzle durability.     

THE IMPACT PROPERTIES OF HYBRID COMPOSITES

In this paper an experimental investigation on the impact behaviour of hybrid composites is conducted by instrumental Charpy impact test. The variation of impact strength and impact toughness index of C/K and C/G hybrid composites of different matrices with hybrid ratio and interface number is revealed. The dynamic hybrid effect is also investigated from different aspects. Meanwhile, the estimating model for impact strength is established and the estimated values are in good agreement with experimented ones. The hybrid effect coefficients based on different definitions are organically related by the model. This provides a basis for the further study of the impact constitutive equation of hybrid composites.     

A new stress-based multi-scale failure criterion of composites and its validation in open hole tension tests

A new stress-based multi-scale failure criterion is proposed based on a series of off-axis tension tests, and their corresponding fiber failure modes and matrix failure modes are determined at the microscopic level. It is a physical mechanism based, three-dimensional damage analysis criterion which takes into consideration the constituent properties on the macroscopic failure behavior of the composite laminates. A complete set of stress transformation, damage determination and evolution methods are established to realize the application of the multi-scale method in failure analysis. Open-hole tension（OHT） specimens of three material systems（CCF300/5228, CCF300/5428 and T700/5428） are tested according to ASTM standard D5766, and good agreements are found between the experimental results and the numerical predictions. It is found that fiber strength is a key factor influencing the ultimate strength of the laminates, while matrix failure alleviates the stress concentration around the hole. Different matchings of fiber and matrix result in different failure modes as well as ultimate strengths.     

Dynamic Response Analysis of Bird Strike on Aircraft Windshield Based on Damage-modified Nonlinear Viscoelastic Constitutive Relation

Damage-modified nonlinear viscoelastic constitutive equation and failure criterion are introduced and the three-dimensional incremental forms are deduced based on the updated Lagrangian approach. A simple tensile test model and a split Hopkinson pressure bar model are built to verify the accuracy of the subroutine implemented within the non-linear finite element program LS-DYNA. A numerical model of bird strike on windshield is established to study the responses of windshield under three different bird velocities at three sites. The bird is represented by a cylinder with a hemisphere at each end and the contact-impact coupling algorithm is used in this study. It is found that the implemented subroutine can properly describe the mechanical behavior of polymethyl methacrylate under low and high strain rates and large deformation, and can be used validly.     

Coupling damage and reliability model of low-cycle fatigue and high energy impact based on the local stress–strain approach

Fatigue induced products generally bear fatigue loads accompanied by impact processes,which reduces their reliable life rapidly. This paper introduces a reliability assessment model based on a local stress–strain approach considering both low-cycle fatigue and high energy impact loads.Two coupling relationships between fatigue and impact are given with effects of an impact process on fatigue damage and effects of fatigue damage on impact performance. The analysis of the former modifies the fatigue parameters and the Manson–Coffin equation for fatigue life based on material theories. On the other hand, the latter proposes the coupling variables and the difference of fracture toughness caused by accumulative fatigue damage. To form an overall reliability model including both fatigue failure and impact failure, a competing risk model is developed. A case study of an actuator cylinder is given to validate this method.     

Modeling on mechanical behavior and damage evolution of single-lap bolted composite interference-fit joints under thermal effects

This paper reports the modeling method and outcomes of mechanical performance and damage evolution of single-lap bolted composite interference-fit joints under extreme temperatures. The anisotropic continuum damage model involving thermal effects is established on continuum damage mechanics which integrates the shear nonlinearity constitutive relations characterized by Romberg-Osgood equation. The temperature-induced modification of thermal strains and material properties is incorporated in stress-strain analysis, extended 3D failure criteria and exponential damage evolution rules. The proposed model is calibrated and employed to simulate behavior of composite joints in interference fitting, bolt preloading, thermal and bearing loading processes, during which the influence of interference-fit sizes, preload levels, laminate layups and service temperatures is thoroughly investigated. The predicated interfacial behavior, bearing response and failure modes are in good agreement with experimental tests. The numerical model is even capable of reflecting some non-intuitive experimental findings such as residual stress relaxation and matrix softening at elevated temperatures.     

基于CDM的开口复合材料层合板结构损伤问题研究

为研究含开口复合材料层合板结构在面内载荷作用下的损伤破坏问题,基于CDM基本原理,从平面应力状态下的Gibbs自由能出发,建立描述复合材料层合板结构层内断裂破坏的二维渐进损伤关系;基于ABAQUS材料用户子程序,将上述渐进损伤关系与二维Hashin失效准则相结合,开发复合材料损伤本构模型,并对含开口复合材料层合板结构在拉伸载荷作用下的破坏过程进行数值模拟;通过与文献试验数据的对比,证明该模型在平面拉伸载荷状态下可以有效预测含开口层合板结构的损伤起始与扩展过程,对层合板强度的预测误差较小。应用上述模型对三种不同开口类型层合板结构在剪切载荷作用的下损伤、破坏分析,结果表明：对于相同面积的开口,不同的开口类型会导致层合板抗剪强度产生较大的差异;而在铺层相同情况下,椭圆形开口层合板的剪切强度相对较高。     

Constitutive modelling of composite laminates under uniaxial compression

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave elasticplastically and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter.The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina,the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear material model is tested against experimental data of composite laminates subjected to uniaxial compressive loads, and good agreement is obtained.     

A constitutive model coupling damage and material anisotropy for wide stress triaxiality

A constitutive model that can describe the damage evolution of anisotropic metal sheets during the complex forming processes which experience wide stress triaxiality history is essential to accurately predict the deformation and rupture behaviors of the processes. In this study, a modified Lemaitre damage criterion which couples with the anisotropic Barlat 89 yield function is established. The effects of stress triaxiality, Lode parameter and shear stress on damage accumulation are considered in the constitutive model. The model is numerically implemented and applied to fracture prediction in tensile tests with different stress triaxialities and a complex deformation process with wide stress triaxiality history. The good consistency of predictions and experiments indicates that the modified Lemaitre damage model has excellent fracture prediction ability. Finally, the accuracy of the model is analyzed and discussed.     

Constitutive behavior and microstructural evolution in hot deformed 2297 Al-Li alloy

The microstructural evolution mechanism and constitutive behavior of 2297 Al-Li alloy were studied via thermal compression test with the constant strain rates of 0.001–1 s⁻¹ and the deformation temperatures ranging from 623 to 773 K. To verify the predictable ability of diverse constitutive models under different stress states, the hot compression experiments with stress triaxiality varying from −0.33 to 0.46 were conducted. The microstructures of the deformed specimens under diverse deformation conditions are probed to reveal the mechanism of hot deformation behavior. The experimental results indicate that the work-hardening and dynamic softening are competitive during the hot compression process, and the dynamic softening is more obvious under low deformation temperature and high strain rate. The microstructural analysis manifests that the dynamic recovery gets predominant at high deformation temperature to produce fine grains. Meanwhile, the dynamic recrystallization becomes more dominant as the strain rate decreases, which is sensitive to the stress triaxiality. In addition, both the modified Johnson-Cook model and strain-compensated Arrhenius-type function are suitable for describing the flow behavior of 2297 alloy, while the latter reveals a more accurate prediction. However, the predictability of the two kinds of models is worsened with the transformation of stress triaxiality, and the validity of the Arrhenius-type model is restricted by high stress triaxiality.     

基于连续损伤模型的复合固体推进剂力学性能研究

为了模拟复合固体推进剂本构关系,利用连续损伤力学理论并耦合线性累积损伤来建立含有损伤变量的本构模型。模型中推进剂累积损伤利用Miner线性累积损伤法则,损伤演化利用蠕变损伤演化规律,无损条件下的推进剂本构关系利用三元件波因廷模型。该模型提供了一种基于损伤本构关系来研究推进剂力学性能变化的有效方法。     

Modeling high-speed cutting of SiCp/Al composites using a semi-phenomenologically based damage model

In this paper, we attempts to investigate cutting mechanisms in high-speed cutting of Al6061/SiC_p/15p composites using a semi-phenomenologically based damage model in the equivalent homogeneous material (EHM) framework. By combining macroscale EHM modeling and underlying microscale physical mechanisms, a feasible semi-phenomenological plastic model is proposed for prediction of cutting forces and chip morphology during high-speed turning Al6061/SiC_p/15p composites. This model incorporates the modified Weibull weakest-link effect to represent the strain-based damage evolution in large deformations. This proposed semi-phenomenological constitutive model is implemented by compiling material subroutines into cutting finite element (FE) codes. The effects of the critical shear stresses on chip formation that depend on the tool-chip frictional coefficient are accounted for in the cutting FE model. The chip formation mechanism affecting material removal behaviors during high-speed turning is further investigated. The capabilities of the proposed constitutive model are evaluated by comparing cutting forces and chip morphologies between experiments and simulations at different cutting speeds associated with strain rates. The EHM-based and microstructure-based models are further compared in both computational efficiency and accuracy. The simulation results show that the developed semi-phenomenological constitutive formalism and cutting model are promising and efficient tools for further investigation of dynamic mechanical and cutting behaviors of particle-reinforced composites with different volume fraction and particle size.     

DD3 单晶粘塑性损伤本构模型研究

介绍了建立DD3单晶高温合金本构模型的理论和过程,详细推导了DD3单晶损伤演化方程,简要分析了模型的组成和特点。简单讨论了模型材料常数的标定方法,具体标定了950℃下的模型材料常数。给出了模型的预测结果和试验结果的对比曲线,从中看出,该模型能够较准确地描述DD3单晶的力学行为特点,可望用于单晶叶片的结构分析。     

针刺陶瓷基复合材料损伤本构模型及构件应力分析

基于连续介质损伤力学方法提出了适用于针刺陶瓷基复合材料的各向异性损伤本构模型.该模型考虑了拉伸与剪切损伤的影响.通过试验得到了材料的拉伸和剪切的应力-应变曲线,采用曲线拟合获得了本构模型的参数.应用用户子程序技术将本构模型写入商用有限元软件,计算所得拉伸和剪切的应力-应变曲线与试验曲线比较吻合,最大误差分别为5.62%和1.47%.使用该损伤本构模型及弹性模型计算了航空发动机尾喷管调节片在气动和温度载荷下的力学响应,两者计算所得应力分布相似,但损伤本构模型计算值明显小于弹性模型计算值.