Mode I fatigue delamination growth in GFRP woven laminates at low temperatures

The cryogenic fatigue delamination behavior of glass fiber reinforced polymer woven laminates under Mode I loading has been investigated experimentally and numerically. Fatigue delamination tests were conducted using double cantilever beam specimens at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). Fracture surface examination using scanning electron microscopy revealed delamination mechanisms under fatigue loading. A finite element analysis was also employed to calculate the J-integral range and damage distributions. The effects of temperature and loading condition on the fatigue delamination growth rates were discussed.     

Finite element computation of fatigue growth rates for mode I cracks subjected to welding residual stresses

This paper presents a finite element modeling procedure for predicting fatigue crack growth rate in butt welds subject to mode I loading condition. Sequentially coupled three-dimensional thermal–mechanical finite element model to simulate welding residual stress was first developed. The weld-induced residual stress effect on the fatigue crack growth rate was then modeled by calculating the stress intensity factor due to the residual stress field based on the superposition rule of the linear elastic fracture mechanics. The results demonstrated the significance of the residual stresses in assessment of the fatigue crack growth rate in the welds.     

Role of elasto-plastic analysis under cyclic loading in fatigue crack growth studies

Linear Elastic Fracture Mechanics (LEFM) has been widely used in the past for fatigue crack growth studies, but this is acceptable only in situations which are within small scale yielding (SSY). In many practical structural components, conditions of SSY could be violated and one has to look for fracture criteria based on elasto-plastic analysis. Crack closure phenomenon, one of the most striking discoveries based on inelastic deformations during crack growth, has significant effect on fatigue crack growth rate. Numerical simulation of this phenomenon is computationally intensive and involved but has been successfully implemented. Stress intensity factors and strain energy release rates lose their meaning,J-integral (or its incremental) values are applicable only in specific situations, whereas alternate path independent integrals have been proposed in the literature for use with elasto-plastic fracture mechanics (EPFM) based criteria. This paper presents certain salient features of two independent finite element (numerical) studies of relevance to fatigue crack growth, where elasto-plastic analysis becomes significant. These problems can only be handled in the current day computational environment, and would have been only a dream just a few years ago. The work presented in this paper is supported by sponsored research projects of the Aeronautics R & D Board, Government of India and their support is acknowledged.     

Fatigue crack growth behavior of fine-grained steel S460N under proportional and non-proportional loading

In the present investigations a series of fatigue crack growth experiments has been conducted using thin-walled, hollow cylinders with a notch. The cylinders are made of fine-grained steel S460N. Cyclic tension-compression, torsion and proportional as well as non-proportional combinations of both loadings have been applied. For these experiments the crack-initiation locations and the crack growth lives as well as the crack growth curves and the crack paths have been identified. Depending on the loading type initiation of two to four cracks at different positions of the notch has been observed. The location of crack-initiation correlates well with the location of the maximum notch root stress amplitude calculated assuming elastic material behavior. The crack propagation lives vary depending on the type of loading. They are slightly longer under non-proportional loading than under proportional loading.     

Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure

We present the results of experimental work carried out in order to analyze the initiation and propagation of fatigue cracks in FeP04 steel. The tests were performed in plane specimens under cyclic tension by keeping constant the nominal load ratio R = 0. Crack paths on the basis of the tested material microstructure were observed. __________ Translated from Problemy Prochnosti, No. 1, pp. 121–124, January–February, 2008.     

Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate

The effects of applied compressive stress on the crack tip parameters and their implications on fatigue crack growth have been studied. Four center-cracked panel specimens with different crack lengths are analysed using finite element method. The results show that under tension–compression loading the local crack tip parameters are determined by two loading parameters. The two loading parameters are the maximum stress intensity and the maximum compressive stress in the applied stress cycle. Predictions of fatigue crack propagation behaviour based on the maximum stress intensity and maximum compressive stress agree well with experimental observations.     

A damage-plasticity interface approach to the meso-scale modelling of concrete subjected to cyclic compressive loading

Concrete is characterised by stiff inclusions in a soft matrix separated by weak interfacial transition zones (ITZs). Subjected to cyclic loading, this material exhibits a strongly nonlinear response, which is characterised by the occurrence of hysteresis loops. Furthermore, for cyclic loading, failure may occur before the equivalent strength for monotonic loading is reached. The present work investigates, whether the occurrence of permanent displacements in different phases of the meso-structure of quasi-brittle heterogeneous materials, such as concrete, leads to damage evolution during repeated loading.A new three-dimensional interface model based on a combination of damage mechanics and the theory of plasticity is proposed, which allows one to control the ratio of permanent and total inelastic displacements. The model is based on only a few material parameters, which can be directly determined by experiments.The interface model is applied to the plane-stress analysis of an idealised heterogeneous material with cylindrical inclusions and ITZs subjected to cyclic compressive stresses.     

Modeling the residual strength of carbon fiber reinforced composites subjected to cyclic loading

Fatigue and residual strength data available in literature were modeled with a modified two-parameter wear-out model based on strength degradation. The model explicitly accounts for the maximum applied stress and the stress ratio and requires a limited number of experimental data to predict with accuracy the fatigue life of a series of polymer-based composites. In this paper a substantial modification of the model is proposed in order to enhance its capability in predicting the residual strength kinetics with emphasis to the “sudden drop” of strength before catastrophic failure. It is argued that the strength degradation kinetics under given loading conditions can be obtained from the statistical distribution of cycles to failure under the same loading conditions. From the new approach no new parameters are introduced, limiting to a minimum the experimental data needed to predict the residual strength. The strength degradation law reliability is verified on three different materials data sets appeared in literature. The results indicate that both the fatigue life and the residual strength are related to the statistical distribution of the static strength.     

Numerical predictions and experimental measurements of residual stresses in fatigue crack growth specimens

Controlling macro residual stress fields in a material while preserving a desired microstructure is often a challenging proposition. Processing techniques which induce or reduce residual stresses often also alter microstructural characteristics of the material through thermo-mechanical processes. A novel mechanical technique able to generate controlled residual stresses was developed. The method is based on a pin compression approach, and was used to produce well-controlled magnitudes and distributions of residual stresses in rectangular coupons and compact tension specimens typically used in fatigue crack growth testing. Residual stresses created through this method were first computationally modeled with finite element analysis, and then experimentally reproduced with various levels of pin compression. The magnitudes and distributions of residual stresses in experimental specimens were independently assessed with fracture mechanics methods and good correspondence was found between residual stresses produced using the pin compression and processing techniques. Fatigue crack growth data generated from specimens with low residual stresses, high residual stresses resulting from processing, and high residual stresses introduced through the new pin compression technique were compared and validated. The developed method is proposed to facilitate the acquisition and analysis of fatigue crack growth data generated in residual stresses, validate residual stress corrective models, and verify fatigue crack growth simulations and life predictions in the presence of residual stresses.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

Application of Numerical Method to Investigation of Fatigue Crack Behavior Through Friction Stir Welding

Fatigue crack propagation through a friction stir welded (FSW) joint of 2024-T351 Al alloy is investigated numerically. The governing relationships for predicting the crack behavior including incremental crack length, crack growth rate, and crack growth direction are presented. Stress intensity is calculated based on displacement correlation technique, and fatigue crack growth through the FSW joint is investigated under linear elastic fracture mechanics (LEFM) using the Paris model. The concepts of crack closure, residual stress, and stress relaxation are incorporated into the Paris model to support the final results. Maximum circumferential tensile stress method is applied to predict the crack growth direction. Finally, the numerical approaches are employed to the high number of elements in the framework of Fracture Analysis Code (FRANC2D/L) to simulate the fatigue crack propagation through the FSW joint including various zones with different material properties. Fatigue lifetime of the welded joint is predicted by implementing the same procedure for various loading values. The obtained numerical results are validated with the experimental work (Ali et al., Int J Fatigue 30:2030–2043, 2008).

Debonding strength of bundled glass fibers subjected to stress pulse loading

This paper reports experimental results of the debonding propagation of bundled-fibers specimens subjected to a tensile stress wave. In addition, the paper also presents a dynamic debonding model for the problem on the basis of the cohesive zone model, and verifies the model by comparing the predicted debonding to the experimental data. The established numerical model is used to study the propagation mode of the debonding, and the result suggests that in this particular specimen design and loading condition, the debonding initiated in a mixed mode condition. However, the mode II quickly increased and dominated the mode I during an early debonding propagation up to certain extend where the mode mixity became constant.     

Computations of energy release rate under monotonic and cyclic loading conditions

In case of an elastic–plastic fracture mechanics analysis, the determination of the energy release rate distribution is a crucial point. In the present paper, three numerical techniques: the virtual crack closure technique (VCCT), J-integral and energy derivative technique (EDT), are used to compute the energy release rate in a middle-crack tension specimen with the combined isotropic/kinematic hardening model. The results obtained by these methods are compared with each other under monotonic and cyclic loading conditions. Finally, it comes out that the difference of the VCCT method to the J-integral is rather insensitive to load increasing, especially when the traction >40% of yield stress, however, the deviation of the VCCT and J-integral results are within 10%, suggesting that one may use the VCCT for plastic cracked specimen analysis. The computations show that the EDT provides the same values for the monotonic as the J-integral if the plastic deformations are not large, but for high plastic loading the EDT overestimates the fracture energy. For cyclic loading case, VCCT method offers closer results as the elastic analytical results, also suggesting that the whole plastic dissipated energy in the loading process should be integrated. While EDT method gives the smaller results than the J-integral because of the energy dissipated in the unloading phase is considered in the loading process.     

Multiscale modeling for mechanical properties of carbon nanotube reinforced nanocomposites subjected to different types of loading

Multiscale modeling was presented for the nonlinear properties of polymer/single wall carbon nanotube (SWNT) nanocomposite under tensile, bending and torsional loading conditions. To predict the mechanical properties of both armchair and zigzag SWNTs, a finite element (FE) model based on the theory of molecular mechanics was used. For reducing the computational efforts, an equivalent cylindrical beam element was proposed, which has the unique advantage of describing the mechanical properties of SWNTs considering the nonlinearity of SWNT behavior. For a direct evaluation of the rigidities of the proposed equivalent beam, the data obtained through atomistic FE analyses of SWNT were fitted to six different equations, covering the three types of loading for both armchair and zigzag configurations. The proposed equivalent beam element was then used to build a cylindrical representative volume element (RVE) using which the effects of the interphase between SWNT and the polymer on the mechanical properties of RVE could be studied. It was found that while the interphase has a small effect on the nanocomposite stiffness, the ratio of (SWNT length)/(RVE length) dramatically affects the nanocomposite stiffness.     

Three-dimensional, parallel, finite element simulation of fatigue crack growth in a spiral bevel pinion gear

This paper summarizes new results for predicting crack shape and fatigue life for a spiral bevel pinion gear using computational fracture mechanics. The predictions are based on linear elastic fracture mechanics theories combined with the finite element method, and incorporating plasticity-induced fatigue crack closure and moving loads. We show that we can simulate arbitrarily shaped fatigue crack growth in a spiral bevel gear more efficiently and with much higher resolution than with a previous boundary-element-based approach [Spievak LE, Wawrzynek PA, Ingraffea AR, Lewicki DG. Simulating fatigue crack growth in spiral bevel gears. Engng Fract Mech 2001;68(1):53-76] using the finite element method along with a better representation of moving loads. Another very significant improvement is the decrease in solution time of the problem by employing a parallel PC-cluster, an approach that is becoming more common in both research and practice. This reduces the computation time for a complete simulation from days to a few hours. Finally, the effect of change in the flexibility of the cracking tooth on the location and magnitude of the contact loads and also on stress intensity factors and fatigue life is investigated.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part I: Material constitutive model

A life prediction algorithm and its implementation for a thick-shell finite element formulation for GFRP composites under constant or variable amplitude loading is introduced in this work. It is a distributed damage model in the sense that constitutive material response is defined in terms of meso-mechanics for the unidirectional ply. The algorithm modules for non-linear material behaviour, pseudo-static loading-unloading-reloading response, Constant Life Diagrams and strength and stiffness degradation due to cyclic loading were implemented on a robust and comprehensive experimental database for a unidirectional glass/epoxy ply. The model, based on property definition in the principal coordinate system of the constitutive ply, can be used, besides life prediction, to assess strength and stiffness of any multidirectional laminate after arbitrary, constant or variable amplitude multi-axial cyclic loading. Numerical predictions were corroborated satisfactorily by test data from constant amplitude fatigue of glass/epoxy laminates of various stacking sequences.     

Application of the dissipated energy criterion to predict fatigue crack growth of Type 304 stainless steel following a tensile overload

This paper presents the results of numerical simulations of fatigue crack growth performed using three-dimensional elastic–plastic finite element analysis. A simple node release scheme is used to simulate crack advancement. The crack front is assumed to be straight. Crack growth following a tensile overload is simulated. The total energy dissipated per cycle is calculated directly from the finite element analysis and used to predict fatigue crack growth. For comparison, fatigue crack growth rate experiments were performed on Type 304 stainless steel C(T) specimens to determine the effect of a single tensile overload. The dissipated energy per cycle is found to correlate well with the measured fatigue crack growth rate following an overload.     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

含紧固件碳纤维增强树脂复合材料在雷电流A分量下的损伤特性

为深入分析雷电环境下含紧固件碳纤维增强树脂（CFRP）复合材料的损伤机制及尺寸对损伤面积的影响规律,对两种不同尺寸含紧固件CFRP进行雷电损伤试验和仿真研究。根据热电耦合理论在ABAQUS中建立含紧固件CFRP的热-电耦合模型,得到单一雷电流A分量作用下CFRP的温度场分布规律;雷电损伤试验中采用超声C扫描方法评估试件损伤特性。试验和仿真结果表明:此雷击条件下,雷电流通过紧固件扩散到CFRP层合板整个厚度,试件在雷电流峰值不太大的情况下损伤面积较小,但随电流峰值的增大,损伤面积剧增、分层损伤严重。电流相近情况下不同尺寸的含紧固件CFRP的损伤分层、损伤形态及面积相近,尺寸对试件的损伤特性影响较小。试验和仿真研究为CFRP的结构设计提供一定的仿真和试验数据支撑。      

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part II: FE implementation and model validation

The FE implementation of FADAS, a material constitutive model capable of simulating the mechanical behaviour of GFRP composites under variable amplitude multiaxial cyclic loading, was presented. The discretization of the problem domain by means of FE is necessary for predicting the damage progression in real structures, as failure initiates at the vicinity of a stress concentrator, causing stress redistribution and the gradual spread of damage until the global failure of the structure. The implementation of the stiffness and strength degradation models in the principal material directions of the unidirectional ply was thoroughly discussed. Details were also presented on the FE models developed, the computational effort needed and the definition of final failure considered. Numerical predictions were corroborated satisfactorily by experimental data from constant amplitude uniaxial fatigue of multidirectional glass/epoxy laminates under various stress ratios. The validation of predictions included fatigue strength, stiffness degradation and residual static strength after cyclic loading.