Modelling of fatigue damage progression and life of CFRP laminates

A progressive fatigue damage model has been developed for predicting damage accumulation and life of carbon fibre‐reinforced plastics (CFRP) laminates with arbitrary geometry and stacking sequence subjected to constant amplitude cyclic loading. The model comprises the components of stress analysis, fatigue failure analysis and fatigue material property degradation. Stress analysis of the composite laminate was performed by creating a three‐dimensional finite element model in the ANSYS FE code. Fatigue failure analysis was performed by using a set of Hashin‐type failure criteria and the Ye‐delamination criterion. Two types of material property degradations on the basis of element stiffness and strength were applied: a sudden degradation because of sudden failure detected by the fatigue failure criteria and a gradual degradation because of the nature of cyclic loading, which is driven by the increased number of cycles. The gradual degradation of the composite material was modelled by using functions relating the residual stiffness and residual strength of the laminate to the number of cycles. All model components have been programmed in the ANSYS FE code in order to create a user‐friendly macro‐routine. The model has been applied in two different quasi‐isotropic CFRP laminates subjected to tension–compression (T–C) fatigue and the predictions of fatigue life and damage accumulation as a function of the number of cycles were compared with experimental data available in the literature. A very good agreement was obtained.     

Modeling delamination growth in composites under fatigue loadings of varying amplitudes

A numerical model was developed to simulate the progressive delamination of a composite subjected to mode I fatigue loading regimes of varying amplitude. The model employs a cohesive zone approach, which combines damage mechanics and fracture mechanics, and requires only standard material data as input, namely the delamination toughness and the fatigue delamination growth curve. The proposed model was validated against delamination growth data obtained from a fatigue test conducted on a DCB specimen. The model predictions agree very well with the experimental results. This model is an initial step toward life prediction of composite structures subjected to complex fatigue regimes.     

Experimental determination of the mode I delamination fracture and fatigue properties of thin 3D woven composites

The mode I delamination fracture toughness and fatigue strength of thin-section three-dimensional (3D) woven composite materials is experimentally determined. The non-crimp 3D orthogonally woven carbon–epoxy composites were thin (2 mm) and consequently their through-thickness z-binder yarns were inclined at a very steep angle (about 70°) from the orthogonal direction. The steep z-binder angle has a marked effect on the delamination toughening and fatigue strengthening mechanisms. Experimental testing revealed that the fracture toughness and fatigue resistance increased progressively with the volume content of z-binders. However, the steep angle caused the z-binder yarns bridging the delamination crack to deform and fail in shear and through-thickness tension, rather than in-plane tension which usually occurs in thick 3D woven composites. Mode I pull-off tests on a single woven z-binder yarn embedded within the composite revealed that the crack bridging traction load, strain energy absorption and failure mechanism were strongly affected by the steep angle.     

层板复合材料的疲劳剩余寿命预报模型

应用可靠性分析的方法 ,导出了层板复合材料在疲劳载荷作用下的疲劳剩余寿命的预报模型。该模型已用典型层板复合材料在恒幅疲劳载荷作用下的实验数据进行了验证。实验结果表明 ,理论预测结果与实验值的接近程度是合理的     

变幅载荷下纤维金属层板的疲劳与寿命预测

文章建立了纤维金属层板等幅疲劳载荷下的疲劳裂纹扩展速率与寿命预测模型。在此基础上对玻璃纤维-铝合金层板（GLARE）的疲劳裂纹扩展与分层扩展行为进行了试验研究,探讨了层板过载疲劳行为的机理,提出了纤维金属层板变幅载荷下疲劳寿命预测的等效裂纹闭合模型,并在GLARE层板上得到了验证。     

Short‐crack thresholds and propagation in an AISI 4340 steel under the effect of SP residual stresses

The effect of residual stresses induced by shot‐peening in a high‐strength AISI 4340 steel has been studied with the purpose of deriving a consistent fatigue model incorporating the results of fatigue crack growth experiments in the threshold region for a broad range of load ratio (R‐ratio ranging from ?2.5 to 0.7), and the effect of short cracks by means of a modified El‐Haddad model. The proposed model, taking into account the effect of crack closure and being capable to assess the conditions for fatigue propagation of short cracks partially embedded in the shot‐peened surface layer, was validated against constant amplitude fatigue experiments conducted in the endurance strength region, ie, for fatigue lives up to 10⁷ cycles, with micronotched specimens in the presence of shot‐peening residual stresses. The proposed model was also validated by comparing the results of fatigue crack propagation simulations with fatigue crack growth experiments under variable amplitude loading, experimentally reproducing the combined effect of service fatigue loads and shot‐peening residual stresses.     

Damage tolerant evaluation of cracked stiffened panels under fatigue loading

This paper presents the methodologies for damage tolerant evaluation of stiffened panels under fatigue loading. The two major objectives of damage tolerant evaluation, namely, the remaining life prediction and residual strength evaluation of stiffened panels have been discussed. Concentric and eccentric stiffeners have been considered. Stress intensity factor for a stiffened panel has been computed by using parametric equations of numerically integrated modified virtual crack closure integral technique. Various methodologies for residual strength evaluation, namely, plastic collapse condition, fracture toughness criterion and remaining life approach have been described. Effect of various stiffener sizes and stiffener type (concentric and eccentric stiffeners) on remaining life and residual strength has been studied under constant amplitude load. From the studies, it has been observed that the predicted life is significantly higher with concentric and eccentric stiffener cases compared to the respective unstiffened cases. The percentage increase in life is relatively more in the case of concentric stiffener compared to that of eccentric stiffener case for the same stiffener size and moment of inertia. From the studies, it has also been observed that the predicted residual strength using remaining life approach is lower compared to other methods, namely, plastic collapse condition and fracture toughness criterion and hence remaining life approach will govern the design. It is noted that residual strength increases with the increase of stiffener size.     

Residual fatigue life prediction based on a novel damage accumulation model considering loading history

The influence of prior low‐cycle fatigue (LCF) on the residual fatigue life was investigated experimentally. A Ni‐based alloy was cyclically loaded under stress‐controlled low‐high (LH) block loading. In the first loading step, low‐amplitude loading was performed with the stress amplitude of 283.5MPa at 710°C. Different cycles of preloading were performed, varying from 100 to 10 000. Subsequently, high‐amplitude fatigue loading was carried out with the stress amplitude of 315MPa at 800°C. Experimental results show that the previous loading was beneficial to the residual fatigue life when the consumed life fraction is below 0.2 and detrimental when the consumed life fraction is larger than 0.2. A novel nonlinear fatigue damage accumulation model was proposed to estimate the residual LCF life under LH loading path considering the effects of load sequence and preloading cycles. The proposed model provided a better life prediction than some existing models, such as Kwofie‐Rahbar model, Miner' rule, Peng model, and Ye‐Wang model. Lastly, this model was further validated using various materials under LH and high‐low block loadings.     

考虑多组件疲劳损伤的组合梁剩余承载力计算方法及试验验证

针对现行规范中无法计算钢-混凝土组合梁在疲劳后的剩余承载力问题,提出考虑多组件疲劳损伤的组合梁剩余承载力的计算方法。基于材料剩余强度理论,分别引入组合梁各组件（混凝土板、钢梁和栓钉连接件）在疲劳荷载作用下的强度衰减模型;对疲劳荷载作用下的组合梁进行受力分析,得到在既定疲劳荷载幅值下各组件的疲劳应力幅;将各组件的疲劳损伤计入钢-混凝土组合梁剩余抗弯承载力计算中,并考虑疲劳加载过程中组合梁抗剪连接度的变化,建立完全抗剪连接和部分抗剪连接两种情形下的组合梁剩余承载力计算方法,并通过6个试验梁的剩余承载力试验进行验证。研究结果表明：在疲劳荷载作用下,组合梁的抗剪连接度逐渐降低,剩余承载力退化明显且不可忽略。该文建立的组合梁剩余承载力计算方法的计算值与试验值吻合较好,具有良好的计算精度与适用性,补充并完善了现有组合梁承载力的计算方法。     

Fatigue behaviour and life prediction of fibre reinforced metal laminates under constant and variable amplitude loading

ABSTRACT Fatigue crack growth of fibre reinforced metal laminates (FRMLs) under constant and variable amplitude loading was studied through analysis and experiments. The distribution of the bridging stress along the crackline in centre‐cracked tension (CCT) specimen of FRMLs was modelled numerically, and the main factors affecting the bridging stress were identified. A test method for determining the delamination growth rates in a modified double cracked lap shear (DCLS) specimen was presented. Two models, one being fatigue‐mechanism‐based and the other phenomenological, were developed for predicting the fatigue life under constant amplitude loading. The fatigue behaviour, including crack growth and delamination growth, of glass fibre reinforced aluminium laminates (GLARE) under constant amplitude loading following a single overload was investigated experimentally, and the mechanisms for the effect of a single overload on the crack growth rates and the delamination growth rates were identified. An equivalent closure model for predicting crack‐growth in FRMLs under variable amplitude loading and spectrum loading was presented. All the models presented in this paper were verified by applying to GLARE under constant amplitude loading and Mini‐transport aircraft wing structures (TWIST) load sequence. The predicted crack growth rates are in good agreement with test results.     

Prediction of fatigue crack growth and residual life using an exponential model: Part II (mode-I overload induced retardation)

Almost all load bearing components usually experience variable amplitude loading (VAL) rather than constant amplitude loading (CAL) during their service lives. A single overload cycle introduced in a constant amplitude fatigue loading retards fatigue crack growth and increases residual fatigue life. Although many models have been proposed on this subject, but life prediction under these complex situations is still under constant improvement. The present study aims at evaluating retardation in fatigue life due to application of a single tensile overload spike by adopting an exponential model. The proposed model calculates not only parameters related with overload induced retardation in fatigue crack growth, but also residual life in case of 7020-T7 and 2024-T3 aluminum alloys with reasonable accuracy without integration of rate equation. The model also covers stage-II and stage-III of post-overload period.     

Interior micro-defect induced cracking mechanism and life prediction of carburized Cr−Ni steel based on double nonlinear damage under variable amplitude loading

The constant/variable amplitude loading fatigue test with interior inclusion-fine granular area-fisheye induced failure under R=0 were carried out on carburized Cr−Ni steel. The results showed that the fatigue life under variable amplitude loading is longer than that under constant amplitude loading in very-high-cycle fatigue regime under same maximum stress level, and the surface morphology of fine granular area under variable amplitude loading is coarser than that under constant amplitude loading under same order of magnitude of fatigue life. Simultaneously, it can be determined that the formation micro-mechanism of fine granular area is caused by the continuous deboning due to stress concentration around interior micro-defects. Furthermore, the life prediction model based on double nonlinear fatigue damage, which considers the coupling effect of local equivalent stress (surface residual stress and local stress concentration effect), loading sequence, failure mechanism and nonlinear characteristics of fatigue damage under constant/variable amplitude loading is established, and predicted life has good accuracy within the factor-of-three lines.     

Fatigue life prediction for GRP subjected to variable amplitude loading

A method of predicting lifetime to failure for any glass fibre reinforced composite system subjected to a complex load–time history has been developed. The prediction first requires the generation of a model to characterize the general fatigue response of the particular composite system. Once the models are derived they can be used to predict lifetimes to failure for any load–time history using a modified Miner’s damage summation rule and rainflow analysis. Variable amplitude fatigue testing of different GRP materials, using the same load–time history, allowed a comparison to be made between predicted and actual lifetimes to failure and was useful in verifying the accuracy and robustness of the life prediction methodology employed. The results from the life prediction models for three very different GRP systems showed themselves to be accurate predictors of fatigue behaviour for the variable amplitude loading condition investigated.     

Anisomorphic constant fatigue life diagrams for a woven fabric carbon/epoxy laminate at different temperatures

The effect of temperature on the constant fatigue life (CFL) diagram for a woven fabric carbon/epoxy quasi-isotropic laminate has been examined. Constant amplitude fatigue tests are first performed at different stress ratios on coupon specimens at room temperature (RT), 100 and 150 °C, respectively. The experimental results show that the CFL diagram for the woven CFRP laminate, which is plotted in the plane of mean and alternating stresses, becomes asymmetric about the alternating stress axis, regardless of test temperature, and shrinks as temperature increases. The CFL envelopes for given constant values of life are nonlinear over the range of fatigue cycles, regardless of test temperature, and they take peaks approximately at a particular stress ratio “critical stress ratio” that is given by the ratio of compressive strength to tensile strength. Then, the experimental CFL diagram for each temperature is compared with prediction using the anisomorphic CFL diagram approach that allows constructing the asymmetric and nonlinear CFL diagram for a given composite on the basis of the static strengths in tension and compression and the reference S-N relationship for the critical stress ratio. It is demonstrated that the anisomorphic CFL diagram approach can successfully be employed for predicting the CFL diagram and thus for predicting the S-N relationships for the woven CFRP laminate at any stress ratios, regardless of test temperature.     

Non-destructive fatigue damage characterization of laminated thermosetting fibrous composites

The fatigue behaviour of the laminated thermosetting Fiberdux 6376-HTA composite material is studied experimentally for both constant and variable amplitude stress reversal loading. The fatigue-induced material degradation is correlated to non-destructive evaluation data obtained from C-scan graphs through the concept of the damage severity factor ( DSF ). The DSF is able to account for the varying severity of damage at the different specimen locations and is used to quantify the fatigue-induced damage. The concept of the DSF , introduced earlier by the authors for constant amplitude fatigue loading of thermoplastic fibrous composites, is applied to characterize fatigue damage of thermosetting fibrous composites and is extended to account for variable amplitude loading. Constant amplitude fatigue tests at various stress levels were performed to correlate fatigue damage to the change of mechanical properties, such as axial stiffness, residual tensile strength and interlaminar shear strength, and to develop expressions to relate DSF to the degradation of the mechanical properties with increasing fatigue damage. Correlation between DSF evolution and consumed fatigue life is made and fatigue damage functions involving stress amplitude dependency are formulated. These expressions together with a modified rainflow method are then used to assess fatigue life under variable amplitude fatigue loading; computed fatigue lives are compared against experimental results.     

Prediction and evaluation of fatigue life for mechanical components considering anelasticity‐based load spectrum

To accurately predict the degraded fatigue life of components under random loads, anelasticity effect of metal on life estimation needs to be explored. Weighting coefficient and dynamic elastic modulus are introduced to modify the calculation process of the model. By establishing an equal‐amplitude fatigue median surface and applying Miner linear fatigue cumulative damage theory, a fatigue life prediction model of the component under random loads is proposed. The model can be used to calculate the degraded fatigue life of components, which provides a theoretical basis for life estimation under random load spectrum. The two‐dimensional load spectrum is compared with the unprocessed two‐dimensional load spectrum and the one‐dimensional program spectrum in life prediction results. With the comparison of the target life and simulation life and the data calculated by the model of the automobile front stabilizer bar, it is concluded that the data obtained by the modified model are more reasonable and accurate.     

Numerical simulation of fatigue‐driven delamination using interface elements

This paper presents a computational technique for the prediction of fatigue‐driven delamination growth in composite materials. The interface element, which has been extensively applied to predict delamination growth due to static loading, has been modified to incorporate the effects of cyclic loading. Using a damage mechanics formulation, the constitutive law for the interface element has been extended by incorporating a modified version of a continuum fatigue damage model. The paper presents details of the fatigue degradation strategy and examples of the predicted fatigue delamination growth in mode I, mode II and mixed mode I/II are presented to demonstrate that the numerical model mimics the Paris law behaviour usually observed in experimental testing. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical fatigue life analysis of a high frequency mechanical impact treated industrial component based on damage mechanics models

After post weld treatment with high frequency mechanical impact (HFMI) treatment of welds, a significant increase of fatigue life (up to a factor of 10) can be achieved. During the last years numerous experimental tests of welded joints with simple geometry under constant amplitude loading have been performed to quantify the positive effect of high frequency mechanical impact treatment. Due to the lack of methods for the prediction of the high frequency mechanical impact benefits, a widespread use of this process is not the case yet. Furthermore, it is still not clear if the results of these fatigue tests can be transferred to complex geometries and complex loading conditions such as in industrial applications. Therefore, an approach to assess the fatigue life of complex welded structures under variable amplitude loading was developed. For this purpose, high frequency mechanical impact treatment and fatigue load of simple welded specimen made of S690QL steel were simulated with finite element analysis (FEA) firstly. Then, the needed damage parameters for the fatigue life correlation were evaluated from the finite element post‐processing. The calculated life time to crack initiation was in good agreement with the experimental fatigue test results. In the next step, this procedure was implemented on a welded arm of an evacuator of type EW180B of the company Volvo Construction Equipment made of S700MC. The variable amplitude load measured under real service condition was transferred to single constant amplitude load cycles using a rainflow‐counting algorithm. By simulation and damage mechanics evaluation of each load cycle the total damage sum could be calculated and compared with the experimental results from Volvo Construction Equipment.     

Residual strength prediction of composite materials: Random spectrum loading

The goal of this project is to identify if and how load order impacts residual strength in an E-glass/vinyl ester composite laminate subjected to variable amplitude fatigue loading. This paper presents results for constant amplitude loading data which, are used to fit parameters for a phenomenological model that can then applied to the spectrum loading cases. The residual strength distribution shape, in addition to median values, is modeled using Weibull statistics. Three cases are run experimentally and modeled for a 735,641 cycle spectrum containing 22 stress levels. The first two are ordered block loading, from highest stress to lowest and from lowest stress to the highest. In both cases, the model predicts the resulting residual strength distribution very accurately. A final case where the entire spectrum was randomized produced unexpected results with every specimen failing after 200,000-400,000 cycles while the model predicts identical residual strength when compared with the block loading case. This work points to a dire need for focus on developing a better understanding of load order impacts in design of composite structures based on constant amplitude fatigue tests.     

Impact and post impact behavior of composite sandwich panels

Assessing the residual mechanical properties of a sandwich structure is an important part of any impact study and determines how the structure can withstand post impact loading. The damage tolerance of a composite sandwich structure composed of woven carbon/epoxy facesheets and a PVC foam core was investigated. Sandwich panels were impacted with a falling mass from increasing heights until damage was induced. Impact damage consisted of delamination and permanent indentation in the impacted facesheets. The Compression After Impact (CAI) strength of sandwich columns sectioned from these panels was then compared with the strength of an undamaged column. Although not visually apparent, the facesheet delamination damage was found to be quite detrimental to the load bearing capacity of the sandwich panel, underscoring the need for reliable damage detection techniques for composite sandwich structures.