Fatigue Crack Initiation and Propagation in Thick Multilayer Metallic Laminates

Transcription

1 Key Engineering Materials Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Fatigue Crack Initiation and Propagation in Thick Multilayer Metallic Laminates Z. Sharif Khodaei a, P.M. Baiz b and M.H. Aliabadi c Imperial College London, South Kensington Campus, London, SW7 2AZ, UK. a z.sharif-khodaei@imperial.ac.uk, b p.m.baiz@imperial.ac.uk, c m.h.aliabadi@imperial.ac.uk, Keywords: Multilayer, Aluminum Laminates, Fatigue Crack Initiation and Growth, FEM. Abstract. The objective of this study is to investigate and develop a methodology to predict fatigue crack initiation and propagation in metallic laminate structures. The fatigue crack initiation is based on strain-life approach. After a crack has initiated, Stress Intensity Factors (SIF) are obtained and the subsequent propagation is described following Paris law type equations (NASGRO). Detailed Stress-Strain distribution in each layer is obtained from FE models, including the effect of the transition from flat to slant cracks on the fatigue crack growth. Introduction Fibre metallic laminates (FMLs) are a family of hybrid metal and composite laminates for aircraft structural applications. This type of structures tends to behave as a simple metallic structure, but with added advantages of metal alloys and fibre-reinforced composites providing superior mechanical properties. Extensive amount of analytical and numerical models have been done to predict the fatigue crack growth (FCG) behaviour of FMLs (see references 9-14 in [4]). However, more work has to be conducted to investigate the combined fatigue crack initiation/migration and crack growth behaviour in these structures. Fatigue crack initiation occurs mainly in the metal layers in composite metallic laminates. The fatigue crack initiation behaviour of the Al layers in composite metallic laminates can, therefore, be compared to the behaviour of monolithic Al if the actual stress conditions at the notched edge are equivalent for both materials. Vasek et al. [10] conducted experiments for fatigue crack initiation in FML, concluding that fatigue cracks start to grow separately in individual layers, with a higher number in the inner layers but with faster crack growth rates in the surface layers. Homan [6] proposed an analytical 2D approach to estimate the fatigue crack initiation life of composite metallic laminates based on the actual stress level in the Al layers and empirical S-N data. Chang [4] considered the off-axis fatigue crack initiation life by combining laminate theory and energy based damage analysis, a simple FEM was used to predict crack paths angles. In terms of fatigue crack growth, Alderliesten [2] gave a comprehensive overview of the various relevant approaches (phenomenological, analytical and FEM) presented in the literature; outlining the need of further development for accurate description of fatigue crack growth in FML. In order to obtain the actual stress level in the Al sheets, the majority of works dealing with this topic have chosen 2D Classical Laminate Theory (CLT). This paper aims to investigate fatigue crack initiation and propagation in metal laminates by detailed FEM models, providing a careful examination of crack migration from cracked layers to un-cracked ones due to the changing geometry and cumulative damage. Fatigue Crack Initiation and Propagation in Metallic Laminates Crack Initiation. Since fatigue initiation mainly affects the metal layers in metallic laminates, the fatigue initiation process is analogous to that of the monolithic metal, using the actual stresses in the layers and applying empirical strain life curves for monolithic metallic Alloys [6, 4]. The strain life relationship is given as the sum of the elastic (linear) and plastic (non-linear) strain range [8]: All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-09/05/16,11:36:32)

2 930 Advances in Fracture and Damage Mechanics VIII 2( σ f ' σ m ) b c ε = ε el + ε pl = (2Ni ) + 2ε f '(2Ni ) (1) E where: σ f = fatigue strength coefficient, ε f = fatigue ductility coefficient, N i = number of cycles to local failure of material, σ m = local mean stress, b = fatigue strength exponent, c = fatigue ductility exponent. Cumulative Damage. After some layers have undergone damage, the local strains at the undamaged layers will change as a result of the changing geometry and boundary conditions. This change in local strain level at each metallic layer requires the damage to be accounted in a cycle by cycle manner (Miner s Linear Damage Rule [7]). Crack Propagation. After a crack has initiated in a metallic layer, subsequent fatigue crack growth can be described following Paris s postulate, which relates the crack growth rate per cycle (da/dn) to the stress intensity factor range ( K =K max -K min ). It is well known that fatigue crack propagation could be affected by many parameters (loading, temperature, environment, etc.); therefore different laws have been proposed to represent this dependence using mainly empirical fits to the test data. In the present work the formula proposed by the NASGRO team has been used [9]: Kth n 1 da 1 f K C K = q dn (2) R 1 K max 1 K c where: C, n, p, and q are empirically derived constants. Explanations of the crack opening function, f, the threshold stress intensity factor, Kth, and the critical stress intensity factor, Kc, are presented in the NASGRO Manual [9]. p Finite Element Model To predict the fatigue damage in multilayer structures, the commercial program ABAQUS [1] was used for detailed numerical simulations. The metallic layers were modelled with 20 node quadratic bricks (C3D20R) with reduced integration elements. After the crack initiation, the fracture mechanic mesh is obtained using quarter point elements around the crack tip. In ABAQUS/Standard, contour integral output (J-integral and SIFs) was requested for each crack in the multilayer assembly. As it is observed in experiments the crack front is not always flat therefore the effect of transition of flat to slant crack has also been considered in this work. Adhesive Layers. The adhesive zone was discretized with a single layer of cohesive elements (COH3D8 and COH3D6) through the thickness. Continuum and traction-separation responses were both considered. Cohesive elements are removed from the model after the adhesive shear strength is reached. Tie Constraints. In ABAQUS, surface-based tie constraint can be used to make the translational and rotational motion as well as all other active degrees of freedom equal for a pair of surfaces. In the present models, tie constraints have been used to join layers and also for joining the transition surface between coarse and refined meshes. Meshing. Numerical modelling of fracture mechanics problems (cracked bodies) presents certain difficulties with regards to obtaining accurate SIF of complex (curved) crack fronts. The problem is due to the particular shape that collapsed tip element should adopt with respect to the crack front. Both flat and slant crack fronts have been modelled in ABAQUS. Another point worth mentioning regarding mesh generation is the automatic meshing procedure adopted in the present work. Many different cracked scenarios are possible in a damaged multilayer structure. If careful examination of all possible configurations is required, a great number of different meshes should be considered. After an extensive literature review, based on its simplicity and generality, the

3 Key Engineering Materials Vols approached proposed by Dhondt [5] was implemented in the present work (only for straight flat crack fronts). This method consists of using an initial uncracked mesh that is modified only at the elements cut by the crack front using a simple meshing procedure. For the slant crack front a manual mesh was created in ABAQUS. Results In the following section two different multilayer specimens (open-hole and plain fatigue) are fatigue loaded until final failure. Material properties for fatigue crack initiation are obtained from [3] and propagation from [9]. Specimens are loaded with a fixed value of mean stress and different alternating stress levels. Fig. 1 shows life for 3 different cases: pristine specimens (no initial crack), initial crack in outer layer and initial crack in inner layer. Results show expected life reduction when initial cracks are present. Figure 1. Fatigue Life for Open-Hole Specimen (Initiation/Migration and Propagation). Figure 2. Beneficial Effect of Slant Cracks on Fatigue Crack Growth

4 932 Advances in Fracture and Damage Mechanics VIII It was observed in most of the experimental studies that cracks start in a plane strain condition (typical of thick sections), but as cracks developed a transition from plane strain to plane stress occurs. The mix mode condition helps to reduce KI and increase KIII. The final effect is a reduced effective stress intensity factor (K eff ), which has beneficial effects on fatigue crack growth. Figure 2 shows the SIF during the transition and the beneficial effect of this transition on fatigue life. Summary Detailed 3D Fracture Mechanics models of multilayered panels were establish in ABAQUS. Tie constraints are used to join layers in the assembly and also for mesh refinement purposes. A simple approach for automatic mesh generation was implemented for the straight flat crack front. Cohesive elements surrounding the crack surfaces are removed from the model after shear strength has been reached, obtaining more uniform and converged SIF solutions. Crack initiation in metallic layers has been obtained with a local strain-life approach (Morrow s Equation). A linear cumulative damage rule (Miner s rule) is considered for damage accumulation in multilayer structure. Fatigue crack propagation is modelled by Nasgro equation. Different initial scenarios are considered for fatigue life predictions: totally pristine specimens, initial crack in outer layer, initial crack in inner layer. From the present work, accurate description of fatigue life in metallic laminate structures can be achieved by following the present methodology. Future work includes the effect of residual stresses and fibre layers in the metallic laminate structure (FML). Acknowledgment. The authors would like to thanks AIRBUS UK and TSB for their financial support (Project No: TP/5/MAT/6/S/H0644G). References [1] ABAQUS User Reference Manual, V6.7. [2] Alderliesten, R.C., On the available relevant approaches for fatigue crack propagation prediction in Glare, International Journal of Fatigue, v29, pp (2007). [3] Boller, C., Seeger, T., Materials Data for Cyclic Loading, Part D: Aluminium and Titanium Alloys, Elsevier, Amsterdam (1987). [4] Chang, P.Y., Yang, J.M., Seo, H., Hahn, H.T., Off-axis Fatigue Cracking Behaviour in Notched Fibre Metal Laminates, Fatigue & Fracture of Engineering Materials & Structures, v30, pp (2007). [5] Dhondt, G., Automatic 3-D mode I Crack Propagation Calculations with Finite Elements, International Journal of Numerical Methods in Engineering, v41, pp (1998). [6] Homan, J.J., Fatigue Initiation in Fibre Metal Laminates, International Journal of Fatigue, v28, pp (2006). [7] Miner, M.A., Cumulative damage in fatigue, Trans. ASME, Journal of Applied Mechanics, v67, A159-A164 (1945). [8] Morrow, J.D., Cyclic plastic strain energy and fatigue of metals, ASTM STP, 378, pp (1965). [9] Nasgro Reference Manual v4.02, Copyright Southwest Research Institute (2002). [10] Vasek, A., Polak, J., Kozak, V., Fatigue Crack Initiation in Fibre-Metal Laminate GLARE2, Materials Science and Engineering A, , pp (1997).

5 Advances in Fracture and Damage Mechanics VIII / Fatigue Crack Initiation and Propagation in Thick Multilayer Metallic Laminates / DOI References [10] Vasek, A., Polak, J., Kozak, V., Fatigue Crack Initiation in Fibre-Metal Laminate GLARE2, Materials Science and Engineering A, , pp (1997) /S (97)