Fatigue crack growth and life prediction of foam core sandwich composites under flexural loading

Fatigue crack growth of foam core sandwich beams loaded in flexure has been investigated. Sandwich panels were manufactured using an innovative co-injection resin transfer molding process. S2-glass fiber with epoxy resins was used as face sheets over a PVC foam core. Testing was performed in a three-point flexure mode utilizing a newly designed fixture such that the localized indentation damage was minimal. Extensive fatigue data were generated for the S–N diagram and crack growth was monitored to develop a model for life prediction. The first visible sign of damage initiation was a core–skin debond parallel to the beam axis. This debond propagated slowly along the top interface and eventually kinked into the core as shear crack and then grew in an unstable manner resulting in total specimen collapse. A fatigue model based on this crack growth has been developed and validated with experiments.     

Analysis of the sandwich DCB specimen for debond characterization

Analysis of the compliance and energy release rate of the sandwich double cantilever beam (DCB) specimen is presented. It is assumed that there is a starter crack at the upper face/core interface and that the crack remains at or near this interface during crack propagation. Beam, elastic foundation, and finite element analyses are presented and compared to experimentally measured compliance data, and compliance calibrated energy release rate over a range of crack lengths for foam cored sandwich DCB specimens. It is found that the beam analysis provides a conservative estimate on the compliance and energy release rate. The elastic foundation model is in agreement with finite element analysis and experimental compliance data. Recommendations for specimen design and an expression for an upper limiting crack length are provided.     

Fatigue crack growth model for constant amplitude loading

A fatigue crack growth model under constant amplitude loading has been developed considering energy balance during growth of the crack. The plastic energy dissipated during growth of a crack within cyclic plastic zone and area below cyclic stress–strain curve was used in the energy balance. The near crack tip elastic–plastic stress and strain were calculated on the basis of Hutchinson, Rice and Rosengren (HRR) formulations. Fatigue crack growth rate in linear and near threshold region of da/dN versus ΔK curve can be determined on the basis of the proposed model in terms of low cycle fatigue (LCF) properties determined on smooth specimen. The predictions of the model have been compared with the experimental and theoretical results available in the literature using mechanical and fatigue properties. The model compares well in the threshold and intermediate region of the da/dN versus ΔK curve for wide range of material tested.     

Accelerated fatigue crack growth simulation in a bimaterial interface

A method for accelerated simulation of fatigue crack growth in a bimaterial interface (e.g. in a face/core sandwich interface) is proposed. To simulate fatigue crack growth, a routine is incorporated in the commercial finite element program ANSYS and a method to accelerate the simulation is implemented. The proposed method (the cycle jump technique) is based on conducting finite element analysis for a set of cycles to establish a trend line, extrapolating the trend line spanning many cycles, and use the extrapolated state as initial state for additional finite element simulations. A control criterion is utilized to ensure the accuracy of the cycle jumps. The inputs of the developed scheme are the crack growth rate as a function of energy release rate for discrete mode-mixities. If these relationships are available for a specific interface, interface fatigue crack growth in any structure with the same interface can be simulated. Using this approach, fatigue crack growth in the face/core interface of a sandwich beam is simulated. Results of the simulation show that with fair accuracy, using the cycle jump technique, more than 65% reduction in computation time can be achieved. Results show that in highly nonlinear problems the control parameter needs to be chosen with care.     

Interface crack in sandwich specimen

Fracture of a sandwich specimen loaded with axial forces and bending moments is analyzed in the context of linear elastic fracture mechanics. A closed form expression for the energy release rate for interface cracking of a sandwich specimen with isotropic face sheets is found from analytical evaluation of the J-integral. An approach is applied, whereby the mode mixity for any combination of the loads can be calculated analytically when a load-independent phase angle has been determined. This load-independent phase angle is determined for a broad range of sandwich configurations of practical interest. The load-independent phase angle is determined using a novel finite element based method called the crack surface displacement extrapolation method. The expression for the energy release rate is based on the J-integral and certain stress distributions along the ends of the sandwich specimen. When the stresses from the crack tip interacts with the stresses at the ends, the present analytical calculation of the J-integral becomes inaccurate. The results show that for the analytically J-integral to be accurate the crack tip must be a certain distance away from the uncracked end of the specimen. For a sandwich specimen with face sheet/core stiffness ratio of 100, this distance is in the order 10 times the face sheet thickness. For sandwich structures with face sheet/core stiffness ratio of 1,000, the distance is 30 times the face sheet thickness.     

超声载荷下TC4钛合金的疲劳寿命分析

通过计算裂纹尖端应力强度因子及疲劳裂纹扩展速率da/d N,由C.Paris模型推导出安全寿命Nf,由Bathias公式计算"哑铃"状钛合金试样的裂纹扩展寿命。通过理论计算和有限元分析超声疲劳"哑铃"状试样,得出应力最大位置。利用有限元仿真和实验数据分析TC4钛合金疲劳寿命。在20 k Hz的超声疲劳试验中,试样的断口位置表明:TC4钛合金材料内部缺陷是试样萌生裂纹使断裂位置偏离最大应力处的主要原因。并得出疲劳裂纹萌生阶段寿命决定"哑铃"状试样的疲劳寿命。     

Fatigue Performance of Sandwich Beams With Peel Stoppers

Abstract:  This paper concerns a newly developed peel stopper for sandwich structures, which may be embedded as a core insert or an edge stiffener. The major purpose of the peel stopper is to prevent large debonds/delaminations between face sheets and core in sandwich structures in the case of failure. Experimental investigations of conventional sandwich beams and beams furnished with peel stoppers, under static and fatigue loading conditions, and with temperature monitoring, were conducted. The experimental programme included investigation of crack initiation and propagation, as well as of fatigue endurance of conventional and modified sandwich beams. The results showed that although the peel stoppers did not significantly influence the fatigue life of the sandwich beams, they were exceptionally effective in re-routing the crack propagation away from the face–core interface. Moreover, one of the two peel stopper designs presented prevented face–core debonding/delamination and total failure of the sandwich beams.     

Three-dimensional finite element simulations of microstructurally small fatigue crack growth in 7075 aluminium alloy

Three‐dimensional finite element simulations were performed to study the growth of microstructurally small fatigue cracks in aluminium alloy 7075‐T651. Fatigue crack propagation through five different crystallographic orientations was simulated using crystal plasticity theory, and plasticity‐induced crack opening stresses were calculated. The computed crack opening stresses were used to construct small crack da/dN‐ΔK diagrams. The generated da/dN‐ΔK curves compared well with experimental small crack data from the literature. The variance observed among the da/dN‐ΔK results, which occurred as a consequence of the different crystallographic orientations employed, was found to be of the same order of magnitude as commonly observed variability in small fatigue crack growth data. This suggests that grain orientation is a major contributor to observed small fatigue crack data scatter.     

A modified DCB sandwich specimen for measuring mixed-mode cohesive laws

A test method is described for measuring cohesive laws for interfaces in sandwich structures. It is proposed to increase the bending stiffness of the sandwich faces by adhering steel bars onto the sandwich faces. This stiffening reduces rotations and ensures that the method is applicable for thin face sandwich specimens. Crack growth along the face/core interface is obtained by a stiffened double cantilever beam specimen loaded with uneven bending moments (DCB-UBM). The J integral is employed and the opening of the pre-crack tip is measured using a commercial optical measurement system, from which mixed-mode cohesive laws are extracted.     

Limited weld residual stress measurements in fatigue crack propagation: Part II. FEM-based fatigue crack propagation with complete residual stress fields

Using a limited set of residual stress measurements acquired by neutron diffraction and an equilibrium‐based, weighted least square algorithm to reconstruct the complete residual stress tensor field from the measured residual stress data, the effect of weld residual stress on fatigue crack propagation is investigated for 2024‐T351 aluminium alloy plate joined by friction stir welding. Through incorporation of the least squares, complete equilibrated residual stress field into a finite element model of the Friction Stir Weld (FSW) region, progressive crack growth along a direction perpendicular to the welding line is simulated as part of the analysis. Both the residual stress redistribution and the stress intensity factor due to the residual stress field, K_res, are calculated during the crack extension process. Results show that (a) incorporation of the complete, self‐equilibrated residual stress field into a finite element (FE) model of the specimen provides a robust, hybrid approach for assessing the importance of residual stress on fatigue crack propagation, (b) the calculated stress‐intensity factor due to the residual stress field, K_res, has the same trend as measured experimentally by the ‘cut‐compliance method’ and (c) the da/dN results are readily explained with reference to the effect of the residual stress field on the applied stress intensity factor.     

Fatigue crack growth at the face sheet-core interface in a discontinuous ceramic-tile cored sandwich structure

The fatigue failure mechanism of a sandwich structure with discontinuous ceramic tile core is characterized. The sandwich structure in consideration comprises ceramic core tiles bonded to composite face sheet with a compliant adhesive layer. The discontinuous nature of the core results in a non-uniform stress field under in-plane loading of the sandwich. Static tensile tests performed on sandwich coupons revealed first damage as debonding at the gaps between adjacent tiles in the core. Tension–tension fatigue tests caused debonding at the gaps followed by initiation of cracks in the adhesive layer between the face sheet and core. Experimental data for crack length versus number of cycles is collected at various load levels. Crack growth rates (da/dN) are determined based on the experimental data acquired. The energy release rate available for crack propagation is computed using an analytical model and finite element analysis. Mode separation performed using the Virtual Crack Closure Technique (VCCT) revealed that crack propagation is completely dominated by shear (mode II). Fatigue crack growth behavior for the discontinuous sandwich structure is quantified by correlating the cyclic energy release rate with the rate of crack propagation. The loss of specimen stiffness with crack propagation is quantified using an analytical model.     

Time-derivative equations for fatigue crack growth in metals

Predicting fatigue crack growth in metals remains a difficult task because available models are based on cycle-derivative equations, such as the Paris law, while service loads are often far from being cyclic. The main objective of this paper is therefore to propose a set of time-derivative equations for fatigue crack growth. The model is based on the thermodynamics of dissipative processes. For this purpose, three global state variables are introduced in order to characterize the state of the crackthe crack length a, the plastic blunting at crack tip and the intensity of crack opening C. Thermodynamics counterparts are introduced for each variable. Special attention is paid to the elastic energy stored inside the crack tip plastic zone, because, in practice, residual stresses at crack tip are known to considerably influence fatigue crack growth. The stored energy is included in the energy balance equation, and this leads to the appearance of a kinematics hardening term in the yield criterion for the cracked structure. No dissipation is associated with crack opening, but to crack growth and to crack tip blunting. Finally, the model consists in two laws: a crack propagation law, which is a relationship between d dt and da/dt and which observes the inequality stemmed from the second principle, and an elastic-plastic constitutive behaviour for the cracked structure, which provides d dt versus applied-load. The model was implemented and tested. It reproduces successfully the main features of fatigue crack growth as reported in the literature, such as the Paris law, the stress-ratio effect and the overload retardation effect.     

Face/core debond fatigue crack growth characterization using the sandwich mixed mode bending specimen

Face/core fatigue crack growth in foam-cored sandwich composites is examined using the mixed mode bending (MMB) test method. The mixed mode loading at the debond crack tip is controlled by changing the load application point in the MMB test fixture. Sandwich specimens were manufactured using H45 and H100 PVC foam cores and E-glass/polyester face sheets. All specimens were pre-cracked in order to define a sharp crack front. The static debond fracture toughness for each material configuration was measured at different mode-mixity phase angles. Fatigue tests were performed at 80% of the static critical load, at load ratios of R = 0.1 and 0.2. The crack length was determined during fatigue testing using the analytical compliance expression and verified by visual measurements. Fatigue crack growth results revealed higher crack growth rates for mode I dominated loading. For specimens with H45 core, the crack grew just below the face/core interface on the core side for all mode-mixities, whereas for specimens with H100 core, the crack propagated in the core or in the face laminate depending on the mode-mixity at the debond crack tip.     

A model of corrosion fatigue crack growth in ship and offshore steels

A model describing corrosion fatigue crack growth rate da/dN has been proposed. The crack growth rate is assumed to be proportional to current flowing through the electrolyte within the crack during a loading cycle. The Shoji formula for the crack tip strain rate has been assumed in the model. The obtained formula for the corrosion fatigue crack growth rate is formally similar to the author's empirical formulae established previously. The different effects of ΔK and the fatigue loading frequency f on da/dN, in region I as compared to region II of the corrosion fatigue crack growth rate characteristics can be described by a change of one parameter only: the crack tip repassivation rate exponent.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

A multiparameter approach to the prediction of fatigue crack growth in metallic materials

A multiparameter approach is proposed for the characterization of fatigue crack growth in metallic materials. The model assesses the combined effects of identifiable multiple variables that can contribute to fatigue crack growth. Mathematical expressions are presented for the determination of fatigue crack growth rates, d a /d N , as functions of multiple variables, including stress intensity factor range, Δ K , stress ratio, R , crack closure stress intensity factor, K _cl , the maximum stress intensity factor K _max , nominal specimen thickness, t , frequency, Ω , and temperature, T . A generalized empirical methodology is proposed for the estimation of fatigue crack growth rates as a function of these variables. The validity of the methodology is then verified by making appropriate comparisons between predicted and measured fatigue crack growth data obtained from experiments on Ti–6Al–4V. The effects of stress ratio and specimen thickness on fatigue crack growth rates are then rationalized by crack closure considerations. The multiparameter model is also shown to provide a good fit to experimental data obtained for HY-80 steel, Inconel 718 polycrystal and Inconel 718 single crystal. Finally, the implications of the results are discussed for the prediction of fatigue crack growth and fatigue life.     

Vacuum effects on fatigue crack growth in submicrometre‐thick freestanding copper films

To clarify vacuum effects on fatigue crack growth in freestanding metallic thin films, experiments were conducted on approximately 500‐nm‐thick copper films inside a field emission scanning electron microscope. Fatigue crack growth accompanied by intrusion/extrusion formation occurred in vacuum, and da/dN was smaller than in air in the middle‐ΔK region (ΔK ≈ 1.7‐3.1 MPam^1/2). Conversely, in the low‐ΔK region (ΔK ? 1.7 MPam^1/2), da/dN was larger in vacuum than in air. Further, fatigue crack growth in vacuum occurred below the fatigue threshold in air (ΔK_th,air). A nonpropagating crack after reaching ΔK_th,air continued to propagate in vacuum when the environment changed from air to vacuum. This indicates that fatigue crack growth resistance is smaller in vacuum than in air under the same effective driving force. The fatigue damage area near the crack paths in vacuum in the low‐ΔK region became wider, suggesting that the nucleation of fatigue damage was enhanced in vacuum.     

FATIGUE CRACK GROWTH IN D16T A1-ALLOY SHEET SUBJECTED TO BIAXIAL OUT-OF-PHASE LOADING

Abstract— Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under out-of-phase biaxial tension and tension-compression. In the range of the biaxial load ratios λ from ?0.5 to +0.5 and an R-ratio of 0.3, fatigue striation formation took place beyond a crack growth rate near to 4 × 10^?8 m/cycle. The striation spacing and the crack growth rate increase as the φ-angle of the out-of-phase biaxial loads increases in the range of φ-angles from 0° to 180°. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1 to 1 when da/dN is greater than 4 × 10^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 10^?6 m/cycle (N_d), and the crack growth period, N_P, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ ratios and φ angles. The value of N_d decreases as the φ angle is increased in the range from 0° to 1807deg;. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF₁(λ, R)F₂(φ). The values of F₂(φ) were determined. The calculated fatigue crack growth period, N_c, applicable up to and including the stage of fatigue striation formation (predicted by using both of the F₁(λ, R) and F₂(φ) functions) is correlated with the experimental data and the error is of the order of 15%.     

Fatigue and fracture of a Ni–P amorphous alloy thin film on the micrometer scale

Fracture and fatigue tests have been performed on micro‐sized specimens for microelectromechanical systems (MEMS) or micro system technology (MST) applications. Cantilever beam type specimens with dimensions of 10 × 12 × 50 μm³, approximately 1/1000th the size of ordinary‐sized specimens, were prepared from a Ni–P amorphous thin film by focused ion beam machining. Fatigue crack growth and fracture toughness tests were carried out in air at room temperature, using a mechanical testing machine developed for micro‐sized specimens. In fracture toughness tests, fatigue pre‐cracks were introduced ahead of the notches. Fatigue crack growth resistance curves were obtained from the measurement of striation spacing on the fatigue surface, with closure effects on the fatigue crack growth also being observed for micro‐sized specimens. Once fatigue crack growth occurs, the specimens fail within one thousand cycles. This indicates that the fatigue life of micro‐sized specimens is mainly dominated by a crack initiation process, also suggesting that even a micro‐sized surface flaw may be an initiation site for fatigue cracks which will shorten the fatigue life of micro‐sized specimens. As a result of fracture toughness tests, the values of plane strain fracture toughness, K_IC, were not obtained because the criteria of plane strain were not satisfied by this specimen size. As the plane strain requirements are determined by the stress intensity, K, and by the yield stress of the material, it is difficult for micro‐sized specimens to satisfy these requirements. Plane‐stress‐ and plane‐strain‐dominated regions were clearly observed on the fracture surfaces and their sizes were consistent with those estimated by fracture mechanics calculations. This indicates that fracture mechanics is still valid for such micro‐sized specimens. The results obtained in this investigation should be considered when designing actual MEMS/MST devices.     

Crack deflection analyses of different peel stopper designs for sandwich structures

This paper relates to a newly developed peel stopper concept for sandwich structures. The proposed concept is a specially designed core insert, which has the ability to confine face sheet debonding/delamination (peeling) by deflecting a delamination crack front away from the face/core interface into the bulk of the sandwich core, and thereby constraining the debonding/delamination to a limited prescribed area. In this paper various peel stopper designs are analysed for their ability to deflect cracks away from propagating along a face–core interface. The crack deflection ability of the studied peel stopper designs leads to design guidelines, which describes the minimum requirements regarding the relation between the two interface toughnesses. The analysis further reveals that compliant peel stopper wedges are preferred because they lead to the lowest interface toughness ratio requirement. This has been confirmed through an experiment with a sandwich beam subjected to three-point bending loading. The experiment has shown that the ability of a peel stopper to deflect cracks is highly dependent on the stiffness of the wedge.