A fatigue damage model for composite materials

Composite materials using polymer resins as matrices possess viscoelastic properties such that the fatigue behavior of the composite could be changed by different stress levels, stress ratio, stress frequency, or temperature. Based on a physical phenomenon of damage growth, this work develops a fatigue damage model including the nonlinear effects of stress ratio and stress frequency on the damage processes for carbon/epoxy composites. A damage index is defined and used to confirm the damage evolution behavior, and a series of fatigue tests of unidirectional specimens under monotonous loading and two‐stress level loading are conducted to test the proposed fatigue damage model. The results reveal that the proposed model could reasonably predict the fatigue life of composite materials under complicated loading conditions and it also includes the sequence effect of cyclic block loadings. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

疲劳/蠕变交互作用下塑木复合材料的断裂损伤

塑木复合材料在动态载荷作用下，其断裂损伤并非纯疲劳或纯蠕变作用的结果。利用交变载荷的试验方法，研究了在疲劳／蠕变交互作用下塑木复合材料的断裂损伤行为。结果表明，在交变载荷为破坏载荷的80％和60％时，其疲劳／蠕变断裂曲线为三段式曲线，即瞬时弹性变形阶段、延迟弹性变形阶段和加速断裂阶段；在交变载荷为破坏载荷的40％时，38h内其疲劳／蠕变曲线为两段式曲线。随着最大载荷保持时间的增加，塑木复合材料进入延迟弹性变形阶段越晚，弯曲挠度增加越快，断裂寿命降低。     

Accelerated fatigue properties of unidirectional carbon/epoxy composite materials

It has been confirmed that polymer matrix composites possess viscoelastic behavior. This means that one could accelerate the fatigue testing by changing the stress amplitude, frequency, or temperature. This study is to investigate the accelerated fatigue properties, which are resulted from the viscoelastic behavior, of carbon/epoxy composites and to predict their fatigue life. For this purpose, a series of fatigue tests of unidirectional specimens are conducted at room temperature under different stress ratios and stress frequencies. A group of sigmoid S‐N curves, which are suitable for the whole fatigue life, and the corresponding parameters are developed for different cyclic loading conditions. A transformation method, which can transform a reference S‐N curve to the corresponding S‐N curve of the assigned fatigue conditions, is established by the parameters. And this S‐N curve can be utilized to predict the fatigue life of the composite at the assigned stress ratio or stress frequency. The comparison between the linear and sigmoid S‐N curves is also carried out to show the advantages of the latter model in the whole fatigue life. POLYM. COMPOS., 27:138–146, 2006. © 2006 Society of Plastics Engineers     

The hygrothermal effect on the fatigue behavior of carbon fiber/ peek laminate composites (I)

The hygrothermal effects on the fatigue behavior of the Carbon/PEEK laminated composites before and after impact damage were examined in this study. The [0/45/90/-45]_2s AS-4/PEEK laminated composites were immersed in 80°C hot water for 45, 90 and 200 days,and subjected to falling weight impact with an energy of 8.58 J and then immersed in 80°C hot water for 45 days. It was found that the tensile strength of AS-4/PEEK laminated composites decreased with the increase of exposure period. The injured AS-4/PEEK composites were subjected to a static load and a tensiontension fatigue load at various levels of stress amplitudes. The effect of stress amplitude on the fatigue life was studied. The experimental fatigue life under different stress amplitude tests were estimated by the median rank order statistic cumulative distribution function. Then,the fitting curves for estimated data were analyzed by the Weibull distribution function. The S-N curves for a series of cyclic loads at various survival probabilities were presented. The damage behaviors of composites after fatigue load test were also investigated by scanning electron microscope(SEM). Results indicated the fatigue lives of immersed specimens were shorter than those without hygrothermal effect, the impact damage affects the fatigue life of composite significantly.     

四步法三维编织复合材料弯曲疲劳行为实验研究

采用MTS 810.23仪器对一种四步法三维编织复合材料结构在应力比为R(σmin/σmax)=0.1、频率为3Hz正弦波条件下进行三点弯曲疲劳测试,研究三维编织复合材料弯曲疲劳性能。通过实验仪器测试准静态三点弯曲和不同应力下三点弯曲疲劳性质得到Data数据,通过对数据分析获得σ-N曲线和最大最小挠度曲线,对比不同应力水平下材料破坏形态从而揭示材料弯曲疲劳机理。实验结果:50%应力水平下,试样经过106次以上的循环仍然没有破坏,80%、70%和60%应力下材料失效的圈数分别是12 833、50 370、101 652。材料疲劳加载下刚度降解和挠度变化趋势相似,材料弯曲疲劳极限为50%,材料σ-N曲线呈三段式,材料低应力水平下疲劳寿命离散性高于高应力水平。     

弯曲载荷作用下孔边角裂纹的应力强度因子与疲劳扩展规律

本文运用边界元方法提出了弯曲载荷作用下,平板中孔单边角裂纹裂尖的应力强度因子(SIF)的计算式。并通过实验研究了孔单边角裂纹在交变的弯矩作用下,裂纹的形貌变化规律及裂纹扩展速率,指出角裂纹沿长度方向的扩展可以用Paris公式来描述,而沿深度方向则不然,但两者之间具有幂函数的关系。     

Fatigue behavior of acetal homopolymer

As an engineering thermoplastic acetal homopolymer is often used in the manufacture of parts subjected to fatigue. This article presents the results of flexural fatigue tests on acetal Delrin 550 under different environmental conditions, namely ambient air, forced-air ventilation at ambient temperature, or oil kept at a constant temperature at 40°C. The fatigue tests were performed on specimens cut from extruded sheets at a constant frequency of 30 Hz. Surface temperatures of the test specimens were measured either optically or electrically, depending on the environment. The test results show that both acetal stress and surface temperature of specimen, which are somehow related, vary considerably from one type of environment to another. However, results show that the fatigue life of the specimen is mainly governed by the amplitude of the initial stress and is almost independent of the environment, Another subject examined was the effect of oil on acetal's mechanical properties. It was found that prolonged contact with oil produced slight variations in tensile properties, but no significant effect on fatigue, life.     

Compressive fatigue damage and failure mechanism of fiber reinforced cementitious material with high ductility

The fiber reinforced cementitious material with high ductility has potential use in particular environments and structures that undergo repeated or fatigue loads. In this study, a series of monotonic and fatigue tests were performed to investigate the compressive fatigue behavior of this material. It is found that the fatigue life of this material is higher than that of plain concrete and steel fiber reinforced concrete under the same stress level. In addition, the failure deformation of fiber reinforced cementitious material with high ductility under fatigue load was larger than the monotonic envelope, while the envelope coincides with the monotonic loading curve for concrete or fiber reinforced concrete. The failure surface and damage process were investigated and a new failure mode of polyvinyl alcohol fiber with crushed end was discovered. The fatigue failure surface could be divided into three regions, including fatigue source region, transition region and crack extension region.     

基于疲劳损伤两段论的复合材料刚度降模型研究

本文在疲劳累积损伤模型和刚度降模型的基础上,根据疲劳损伤的两阶段理论,将复合材料的疲劳损伤划分为两个阶段,并用两种不同的函数分段描述疲劳损伤的过程,建立了疲劳损伤演化两阶段模型。利用试验数据,运用多元函数的最小二乘法,得到了模型中的各个参数的拟合值和层合板的S-N曲线。疲劳损伤演化两阶段模型计算数据与试验结果吻合较好。     

纳米碳酸钙改性再生混凝土疲劳性能

为研究纳米改性再生混凝土的疲劳性能,对其疲劳寿命进行估计并建立疲劳方程。以不同再生骨料取代率(0%、30%、50%,质量分数)与纳米CaCO₃掺量(0%、1%,质量分数)为主要影响因素,设计了不同应力水平(0.75、0.80、0.85)下的疲劳循环加载试验。结果表明:混凝土的弹性模量随再生粗骨料取代率的增大而减小,掺入纳米CaCO₃可以提高混凝土的弹性模量并优化破坏形态,有效提升整体性;循环荷载下的疲劳寿命随最大应力水平增大而快速缩短,1%的纳米CaCO₃改性可以使疲劳寿命延长60%;以双对数S-N(应力水平-疲劳寿命)曲线建立疲劳寿命方程,并推导出考虑寿命概率的P-S-N曲线,得到的相关系数随再生粗骨料取代率的增加而快速减小,经纳米改性后有所增大;再生混凝土的疲劳应变演化基本符合三阶段应变曲线发展规律,提出新方程描述再生混凝土第二阶段应变曲线,并建立变形量与循环比的关系式。     

疲劳与蠕变复合作用下聚苯乙烯的断裂行为

研究了聚苯乙烯在疲劳／蠕变复合作用下的断裂行为，研究结果表明，其疲劳／蠕变曲线与纯蠕变曲线十分相似，因蠕变加载作用时间缩短和疲劳载荷变化更频繁，导致在较小的应变下结束普弹应变阶段并进入延迟弹性变形的平台变阶段，随最大载荷加载作用时间延长，断裂寿命减小。     

Rubber fatigue life prediction using a random forest method and nonlinear cumulative fatigue damage model

In this study, a random forest machine-learning method is introduced on the basis of the analysis of measured constant amplitude stress fatigue data. This method aims to predict rubber fatigue life under constant amplitude stress. Strain mean value, strain amplitude, and strain ratio are used as independent variables, and the prediction model of rubber fatigue life under constant amplitude stress is established. A nonlinear cumulative fatigue damage model is proposed to calculate rubber fatigue life under the variable amplitude stress. Results show that the random forest method has high precision and generalization capability for rubber fatigue life prediction under constant amplitude stress and the nonlinear cumulative fatigue damage model could be employed to calculate the fatigue life of rubber under variable amplitude stress with enough accuracy according to the constant amplitude stress fatigue life data. This research can provide a reference for rubber fatigue life prediction. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48519.     

Creep-based characterization of nonlinear relaxation behavior of plastics

It is a matter of fact that creep experiments can be conducted more easily and accurately than stress relaxation experiments, since it is easier to maintain a stress constant (for instance by a “dead weight”) than a strain constant. Nevertheless, in practice, structural parts made of plastics (which are nonlinear viscoelastic materials) are very often loaded under stress-relaxation conditions. The present paper presents an approach to predict the behavior of a nonlinear viscoelastic material under stress-relaxation-type loading, based on data obtained from creep-type experiments. The nonlinear creep compliance is described mathematically by an exponential series with a limited number of terms and a single nonlinearity function depicting the transient behavior. The nonlinear behavior of the material under constant strain (i.e., stress relaxation) is then obtained by dividing the considered time range into very short time intervals in which constant stresses are acting, while the different values of the applied stresses are chosen in a manner that guarantees the same stain at the end of each interval. In this way, one performs a numerical nonlinear superposition of the effects of the loadings in the various intervals, leading to the desired results under stress relaxation. A comparison of theoretical results with experiments conducted on some thermoplastic materials shows good agreement.     

Fatigue analysis of piezoelectric microdevice based on a continuum damage model

The utilization of piezoelectric materials in MEMS devices under harsh environments has gained affordable appreciations due to its unique mechanical and electrical material properties. However, the reliability of MEMS devices triggered by fatigue damage remains elusive and needs to be further explored. Here, we present a continuum constitutive model for piezoelectric materials containing a substantive amount of randomly dispersed microcracks. The constitutive equation of the piezoelectric materials with microcracks is formulated via Helmholtz free energy by combining the Kachanvo damage evolution law and the Chaboche fatigue damage development to express the fatigue damage growth. A case of the fatigue damage analysis of the piezoelectric microplate with transverse matrix cracks in the status of plane stress is presented by adopting the von Karman’s plate theory. With numerical schemes employed, the effect of cyclic impulsive loadings and electrical loadings on the fatigue damage and fatigue life prediction of a piezoelectric microplate is investigated and discussed. The findings provide valuable insights into the fundamental mechanism of reliability in piezoelectric MEMS devices due to cyclic loadings, thereby offering new ways to exploit and fabricate the piezoelectric-based MEMS devices suitable for harsh conditions.     

Evaluating the fatigue resistance of notched specimens of polyethylene

The fatigue life of a linear low density polyethylene was measured as a function of stress, notch depth., and temperature under plane strain conditions. The fatigue life was precisely related to the stress intensity. The temperature dependence of the fatigue life corresponded to an activation energy of 72.5 KJ which was independent of stress level. A general equation for the fatigue lifetime was proposed for polyethylenes in terms of the material parameters, the mechanical parameters such as stress intensity, stress amplitude, frequency, and waveform.     

Fatigue behavior of continuous glass fiber composites: Effect of the matrix nature

The effect of the matrix morphology on the fatigue behavior of a continuous glass fiber/polypropylene (GF/PP) composite system was studied by means of stress‐life and mode II cyclic delamination tests. The stress‐life behavior of a GF composite is considerably affected by the nature of the matrix. A two‐stage fatigue damage curve was observed in the composite made with a PP matrix, whereas a three‐stage curve was observed in the composite made with a thermoset polyester matrix. For a fatigue stress higher than 50% of the yield stress, the PP matrix composite showed a considerably longer fatigue life than the thermoset polyester matrix composite. Mode II cyclic delamination tests showed that the morphology itself of the PP matrix also played an important role. Higher fatigue delamination growth rates, at given strain energy release rates, and lower strain energy release rates at failure were obtained for a composite showing a coarse spherulitic morphology and well‐marked interspherulitic regions than for a composite showing a finer spherulitic morphology and less‐marked interspherulitic regions. While the fatigue mode of the composite with a coarse spherulitic morphology was interspherulitic, that of the composite with a finer spherulitic morphology was transpherulitic.     

Failure behavior of adhesively bonded joints with a rubber modified epoxy adhesive under tensile-shear combined cyclic loading

Rubber-modified epoxy adhesives are used widely as structural adhesive owing to their properties of high fracture toughness. In many cases, these adhesively bonded joints are exposed to cyclic loading. Generally, the rubber modification decreases the static and fatigue strength of bulk adhesive without flaw. Hence, it is necessary to investigate the effect of rubber-modification on the fatigue strength of adhesively bonded joints, where industrial adhesively bonded joints usually have combined stress condition of normal and shear stresses in the adhesive layer. Therefore, it is necessary to investigate the effect of rubber-modification on the fatigue strength under combined cyclic stress conditions. Adhesively bonded butt and scarf joints provide considerably uniform normal and shear stresses in the adhesive layer except in the vicinity of the free end, where normal to shear stress ratio of these joints can cover the stress combination ratio in the adhesive layers of most adhesively bonded joints in industrial applications.

In this study, to investigate the effect of rubber modification on fatigue strength with various combined stress conditions in the adhesive layers, fatigue tests were conducted for adhesively bonded butt and scarf joints bonded with rubber modified and unmodified epoxy adhesives, wherein damage evolution in the adhesive layer was evaluated by monitoring strain the adhesive layer and the stress triaxiality parameter was used for evaluating combined stress conditions in the adhesive layer. The main experimental results are as follows: S–N characteristics of these joints showed that the maximum principal stress at the endurance limit indicated nearly constant values independent of combined stress conditions, furthermore the maximum principal stress at the endurance limit for the unmodified adhesive were nearly equal to that for the rubber modified adhesive. From the damage evolution behavior, it was observed that the initiation of the damage evolution shifted to early stage of the fatigue life with decreasing stress triaxiality in the adhesive layer, and the rubber modification accelerated the damage evolution under low stress triaxiality conditions in the adhesive layer.     

基于混凝土基体和界面过渡区性质的疲劳方程

根据混凝土材料在静态荷载与疲劳荷载作用下破坏的相似性,结合其在静态荷载作用下的破坏分析了疲劳破坏过程,通过引入基体和界面过渡区对疲劳性能的影响因子f1,f2,定义基体性质特征参数I和界面过渡区性质特征参数M,应用数学模型描述f1,f2随疲劳寿命对数值lgN的变化趋势,建立混凝土材料基体、界面过渡区性质与疲劳性能之间的定量关系,并得到基于基体与界面过渡区性质的疲劳方程.测试了水胶比为0.35,不同矿物掺合料掺量混凝土在不同应力水平下的疲劳寿命.应用所建立的疲劳方程能较好地拟合S-N关系,尤其是大矿物掺合料掺量的情况下,反映了低周疲劳向高周疲劳过渡的非线性变化.     

A New Test Methodology for Simultaneous Assessment of Monotonic and Fatigue Behaviors of Adhesive Joints

Adhesive joints are normally subjected to different working conditions in their service life. This may involve both static and cyclic loadings. In many instances, a combination of various loading conditions occurs that can be further provoked by exposure to hostile environments. This, in turn, leads to the need to characterize the joint behavior under different combinations of working conditions. Extensive experimental tests are needed in order to evaluate the joint performance under such variable working conditions. This implies the development of low cost and efficient test technique, the one that is simple and reduces the operator time as well. With this objective in mind, a novel technique in mechanical evaluation of adhesive joints was developed in the present work. Alternative monotonic and variable-amplitude cyclic loads were applied on the same double cantilever beam (DCB) specimens under cleavage mode. DCB specimens were made from aluminum bars joined together by a two-part toughened structural adhesive. On one face, a series of crack detection sensors were bonded to control the test machine for switching between monotonic and cyclic loadings. The test machine had two aligned hydraulic actuators which applied bending forces on the upper and lower arms of the DCB specimen. The effects of test frequency and applied load history were also investigated within a range of 4–20 Hz for a nominal adhesive thickness of 0.5 mm. The fatigue performance of each configuration was represented by a power-law relationship and was compared for different test conditions. The test results revealed that the fatigue damage occurred at relatively lower load levels (35%) when compared with monotonic fracture load. The power-law constants for the tested adhesive were influenced by test frequency but were not sensitive to loading order.     

Fatigue strength of vibration‐welded unreinforced nylon butt joints

The fatigue properties of vibration‐welded butt joints in two thermoplastics, nylon 6 and nylon 6,6, are examined in this work. Injection molded plaques were welded under high and low pressure conditions at 212 Hz and at an amplitude of 1.8 mm to a weld penetration of 1.5 mm. Dog‐bone coupons were machined from welded and unwelded plaques and then fatigue cycled in load control at a stress ratio of R = 0.1. The test frequency ranged from 1 to 10 Hz to avoid hysteretic heating. When the temperature rise in the weld region during testing was insignificant, no physical thermal damage was observed. It was found that the nonwelded specimens have longer fatigue lives than the welded ones, while the welded specimens appear to have similar fatigue behavior, except for nylon 6 welded in high pressure, which was slightly inferior. Vibration welding of these materials appears to be viable for structural applications requiring fatigue resistance. POLYM. ENG. SCI. 45:935–944, 2005. © 2005 Society of Plastics Engineers