Finite Element Simulation of Fatigue Damage Accumulation for Repaired Component by Cold Expansion Method Abdelkrim Aid1, Mostefa Bendouba1, Mohamed Benguediab2, and Abdewahab Amrouche3 1
Laboratoire LPQ3M, B.P. 305, Universite de Mascara, Algeria
[email protected],
[email protected] 2 Département de Génie Mécanique, Université de Djilali Liabès, Sidi Bel Abèss, Algeria
[email protected] 3 Laboratoire de Génie Civil et Géo-Environnement LGCgE, EA 4515, Faculté des Sciences Appliquées FSA Béthune, Université d’Artois, France
[email protected]
Abstract. This manuscript investigates the effectiveness of applying the cold expansion process to extend the fatigue life of mechanical structures. During the cold expansion process compressive residual stresses around the expanded hole are generated. The enhancement of fatigue life and the crack initiation and growth behavior of a holed specimen were investigated by using the 6082 Aluminum alloy. The present study suggests a simple technical method for enhancement of fatigue life by a cold expansion hole of pre-cracked specimen. This technique produces beneficial high compressive residual stresses which have been predicted by means of finite element models, both 3D for proper assessment of thickness effects. Finite element models have been developed to increase their complexity, Fatigue damage accumulation of cold expanded hole in aluminum alloy which is widely used in transportation and in aeronautics was analyzed. Experimental tests were carried out using pre-cracked SENT specimens. Tests were performed in two and four block loading under constant amplitude. These tests were performed by using two and four blocks under uniaxial constant amplitude loading. The experimental results were compared to the damage calculated by the Miner’s rule and a new simple fatigue damage indicator based on an energy criterion. This comparison shows that the ‘energy criterion model’, which takes into account the loading history, yields a good estimation according to the experimental results. Keywords: cold expansion, compressive residual stress, finite element method, energies criterion, fatigue damage accumulation.
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Introduction
Over the last 25 years, the cold expansion process has been commonly used to improve the fatigue life of components containing fastener holes. Cold expansion © Springer International Publishing Switzerland 2015 M. Haddar et al. (eds.), Multiphysics Modelling and Simulation for Systems Design and Monitoring, Applied Condition Monitoring 2, DOI: 10.1007/978-3-319-14532-7_44
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is employed usually in components that are exposed only to service conditions at ambient temperature. The cold-worked process introduces beneficial residual circumferential stresses into an annular region around the hole, and the presence of this compressive residual stress inhibits the growth and propagation of cracks (Lacarac et al. 2001, Pasta 2007). In order to increase the service life of components some methods have been developed. One of these methods, which were used in this study, is to form a controlled compressive residual stress field around the hole (Chandawanich and Sharpe 1979; Su and Yan 1986). However, the improvement in fatigue life is difficult to quantify. The residual stresses resulting from the cold expansion process are not uniform through the thickness (Pavier et al. 1997). Earlier work on cold expansion has used both analytical and numerical two-dimensional models to predict residual stress (Poussard et al. 1995). Furthermore, combining the residual stress distribution with a fatigue crack growth rate calculation is difficult due to the three-dimensional nature of the problem and complicating phenomena such as crack closure (Lacarac et al. 2004). In (Bernard et al. 1995; Ghfiri et al. 2000; Semari et al. 2013; Aid et al. 2013), the authors show the sensitivity of the degree of expansion. In a first phase the residual life increases but beyond a critical value of remaining life decreases sharply and growth is extremely detrimental. In service conditions, the components or structures are subjected to random or variable block loading. Different relationships (Lacarac et al. 2004) have been proposed to calculate the effect of variable amplitude loading conditions. However, these procedures need the identification of many parameters. In literature, in the particular case of block loading, the analysis for this phenomenon is oriented only to two loading steps. Miner’s rule (Miner 1945) is very much used to evaluate the fatigue damage accumulation when the components or structures are subjected to variable block loading. In this work, the results of a study on fatigue damage accumulation of cold expanded hole in aluminum alloys subjected to block loading are presented. Tests were carried out using pre-cracked SENT specimens and inserting an expanded hole at the crack tip. The degree of the cold expansion was chosen equal to 4.3%. Tests were performed in two and four block loading under constant amplitude. The experimental results were compared to the damage calculated by the Miner’s rule and a new simple fatigue damage indicator (Aid 2006a; Aid 2011; Amrouche 2008; Aid 2006b) and a new version of this damage indicator based on energy approach (Bendouba et al. 2011; Djebli et al. 2013).
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General Principal of the Method
In this study, cold expansion is achieved by inserting an oversized rigid ball from one side (entry face) of the holed plate and removing it from the other side (exit face). The degree of cold expansion DCE is defined by the relation:
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DCE % =
(D − d ) × 100 d
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(1)
A cold expansion of the hole introduces compressive residual stresses that are beneficial in terms of lifetime until a critical degree of expansion where it becomes not beneficial for structures. Both aspects are shown in Figure 1.
Fig. 1 The curve of crack initiation according to the numbers of the cycles
Where d is the diameter of the hole drilling and D is the diameter of the rigid ball. Different technique can be used to repair a cracked component. The cold working expansion process was realized by forcing a hard steel ball of 6 mm inside a predrilled hole (the initial diameters of the hole are: 5.9, 5.8, 5.75, 5.6 and 5.5 mm for aluminium alloy and 5.8, 5.75 for steel), this process is illustrated in (Aid 2006) .
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Materials and Specimens
The material used for this study was aluminum alloy Al 6082 T6, some of the mechanical properties are given in (Aid 2006). A difference gap of 10% between the characteristics of the uncracked specimens and the batch of specimens with hole was noticed. The specimens used for this investigation were conforms to ASTM standards (ASTM 1997). The geometry of the fatigue test specimen cut in the longitudinal direction (Aid 2006). For getting specimens with an expanded hole of 6 mm in diameter we drilled a hole of Ø5.75 mm at the pre-crack tip and then a cold-working expansion process was conducted by forcing a steel ball of 6 mm diameter. The fatigue tests were carried out using a 100 kN capacity Instron hydraulic machine. The loading frequency was 30 Hz and a stress ratio R of 0.57. During
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fatigue testing, a video camera with scale of 0.1 mm was used to determine the crack initiation in the entry and exit faces of specimen.
3.1
3D Finite Element Modeling
3-D FEM simulations using MSC.Marc have been used to evaluate the rigid ball during the cold expansion process. In this case the axial movement of the rigid ball through the specimen has been introduced in the model to obtain the distribution of the residual stresses through the thickness. Because of the symmetry, half of the lug is representative of the useful of the specimen. The quadrilateral element topology QUAD4 has been adopted for the analysis. Globally, the finite element model consists of 3886 elements and 5721 nodes. (see figure 2).
Fig. 2 3D FEM mesh, with rigid ball for cold-expansion and fatigue critical section
The contact between the surfaces of the steel ball and the hole is simulated by using the contact elements. Residual stress is obtained at the three surfaces (entry face, middle and exit face) to analyze the influence of cold expansion direction on the fatigue crack initiation life. During the simulation, the rigid ball was moved through the hole incrementally. The boundary conditions imposed are as following: The displacements of the nodes located on the X–Y plane are constrained in the z direction. The displacements of the nodes located on the X–Z plane are constrained in the y direction within a rectangular surface on the exit face.
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Results and Discussions of the Simulation
The figure 3 illustrates the hoop stresses at the entry, middle and exit expansion step. Portrays the finite element prediction of the tangential residual stress variation at different through thickness positions from the entrance face, this figure reveals the large variation in hoop residual stress in the region of influence.
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entry face
middle face
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xit face
Fig. 3 Circumferential residual stress distribution in the 3D model
Low hoop residual stresses on entrance and exit faces are caused by the shear stress from the axial movement of the rigid ball. The compressive residual stresses into the annular region around the hole reduce the origin of cracks. During fatigue testing, this residual stresses act to change the effective stress intensity factor at the crack tip, i.e. the crack growth rates are lower than those in absence of residual stress. The residual stress profiles are in agreement with other studies presented in previous literature (Poussard et al.1985; Pavier et al. 1999 ; De Matos et al. 2005). Figure 4 shows the FE prediction of hoop residual stresses through the thickness of the plate from the entrance face to the exit face. A significant difference in the magnitude of tangential stress is recorded between the entry side and exit side. The magnitude of hoop residual stresses on the entrance and the exit faces are lower than the stresses on the mid-thickness. These results are in accordance with recent research (Yan et al. 2012 ; Chakherlou 2012).
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Damage Accumulation Based an Energy Parameters
An energy approach is presented in this paper, which forms the basis for a new damage model. The strain energy density is proposed as a parameter of the fatigue analysis. The models do not include a division of the strain energy density into elastic and plastic parts, like in all the cases of the parameters proposed by Smith– Watson–Topper (SWT) (Smith et al. 1970), Hoffman and Seeger (Hoffman and Seeger 1989), Bergman and Seeger (Bergman and Seeger 1979). In the elastic range, energy is calculated from
1 W = σε 2
(2)
For uniaxial fatigue loading, authors (Bendouba et al. 2011; Djebli et al. 2013) introduce a new damage parameter, Di, defined as the ratio of the increment of energy due to stress damage over the difference between the energy due to ultimate stress and the applied stress. The damage indicator is defined by:
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Hoop residual stress (MPa)
200 150 100 50 0 -50 0 -100 -150 -200 -250 -300
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Entry… Exit face
Distance from hole edge (mm) Fig. 4 Finite element predictions of residual hoop stress at entry face and exit face
D=
W edi −W i W u −W i
(3)
where: Wedi : energy is due to stress damage. Wi : energy is due to the applied stress. Wu : energy is due to the ultimate stress of the material.
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Fatigue Testes
The experimental conditions are given in (Aid 2006). Eight tests were carried out for increasing loading conditions and as much for decreasing loading. To evaluate the effect between these loading conditions, the Miner’s Rule was considered for damage accumulation. Endurance curves are shown in (Aid 2006). These are based on constant amplitude test and the failure was considered at the crack initiation (Aid 2006). Two and four cyclic stress levels were considered and two different sequences were applied (Aid 2006). The aim of this set of tests is to determine the influence of increasing or decreasing loading conditions on lifetime and to prove that the proposed model takes into account the history of blocks loading and the nonlinearity of the accumulated damage unlike the Miner’s rule. Figure 5 demonstrates the comparison between the prediction models (Miner’ Rule, DSM model and the energy approach) with experimental results for different loading conditions (two and four blocks with increasing and decreasing loads) for specimens pre cracked and repaired by the technical process of cold expansion. This figure confirms that the estimates results by the DSM model and the energy approach used in this investigation are in good agreement with the experimental results (Aid 2006).
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Figure 5 demonstrates the comparison between the prediction models (Miner’ Rule, DSM model and the energy approach) with experimental results for different loading conditions (two and four blocks with increasing and decreasing loads) for specimens pre cracked and repaired by the technical process of cold expansion. This figure confirms that the estimates results by the DSM model and the energy approach used in this investigation are in good agreement with the experimental results.
Fig. 5 Comparison between theoretical results and experimental results for different loading conditions
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Conclusion
At first, a modelization study on cold-expansion process by finite element method has been made. Different FE models have been defined to evaluate different characteristics as plastic strain representation, contacts simulation and material characterization has been used. Residual stresses after the cold-expansion process have been evaluated by means of FEM models using MSC Marc software. Secondly, this investigation is also set to study fatigue damage accumulation in arresting crack holes with cold expansion process was studied. In total, 24 specimens were tested, eight specimens were used to obtain the fatigue endurance curve and 16 were subjected to increasing or decreasing blocks loading. Using the Miner’s rule to calculate the cumulative life time. We found that in both cases, increasing and decreasing blocks loading, the experimental results were below prediction. The results obtained by the energy approach and model of the damage stress are compared with the experimental results and a good agreement has been found. The experimental results show that the load sequence has no significant effect on the crack reinitiating.
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It seems that in the case of drilling with a cold expansion, the combination of the geometrical and mechanical effect attributed to the stress concentration factor associated with the compressive residual stresses predominate in the life time. In the other hand the load sequence has a minor effect. In this investigation, the compressive residual stresses at the edge of the hole are around of the yielding stress. The effective local applied stress is lower than the residual stress; this observation can explain the raison why there is no significant influence of the sequence loading. Currently, we achieve tests with more important loading in order to evaluate the sequence loading effect.
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