MODELING OF FATIGUE CRACK GROWTH UNDER CONSTANT AND VARIABLE AMPLITUDE LOADING. S. M. Beden, S. Abdullah and A. K. Ariffin

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1 International Journal of Mechanical and Materials Engineering (IJMME, Vol. 4 (2009, No. 2, MODELING OF FATIGUE RA GROWTH UNDER ONSTANT AND VARIABLE AMPLITUDE LOADING ABSTRAT In this paper, a odeling of fatigue crack growth of thin walled tube aluinu alloy with circuferential crack under constant and variable aplitude loading are presented. Three Fatigue crack growth odels, naely Walker, Foran and NASGRO were exained. The results showed that the siulation of the fatigue crack growth under constant and variable aplitude loading in the proposed technique is an efficient tool and also the different odels gave different fatigue crack growth behavior. There are any factors affecting the fatigue crack growth in structures. rack initiation and stress ratio are studied and shown a great influence on the life of the thin walled tube. The NASGRO odel was found to be the ost appropriate odel for the variable aplitude loading. Therefore, this odel ay be suggested for use in critical applications in studying fatigue crack growth for different structures under variable aplitude loading. eywords: rack initiation, onstant and variable aplitude loading, Fatigue crack growth, Modeling, stress ratio and thin wall tube. INTRODUTION rack growth in structures depends on the aplitude, stress ratio, and frequency of the load. Due to the rando nature of variable loading, it is difficult to odel all these influential paraeters correctly. Overloads are known to retard crack growth, while underloads accelerate crack growth relative to the background rate. These interactions, which are highly dependent upon the loading sequence, ake the prediction of fatigue life under variable aplitude loading ore coplex than under constant aplitude loading. Many odels have been developed to predict the fatigue life of coponents subjected to variable aplitude loading (Paris et al., 1999; Sanan and Vasudevan, 1999; Jaes and Paterson, 1997; Taheri, The earliest of these are based on calculations of the yield zone size ahead of the crack tip and are still widely used. The Wheeler odel (Wheeler, 1972 and Willenborg et al., (1997 odel, for exaple, both fall into this category. Another category odels based on the crack closure approach, which considers plastic S. M. Beden, S. Abdullah and A.. Ariffin 1 Departent of Mechanical and Materials Engineering University ebangsaan Malaysia 43600, Bangi, Selangor, Malaysia sabah@vlsi.eng.uk.y 131 deforation and crack face interaction in the wake of the crack, was subsequently proposed by Elber (1972 have been used to odel crack growth rates under variable aplitude loads (Newan, 1984; Ray and Patanker, 2001; Newan et al., 2001; Schijve, More recent proposals include cobinations of the Wheeler odel with the Newan crack closure odel (Voorwald and Torres, 1991 and odel based on the strain energy density factor (Huang et al., However, due to the nuber and coplexity of the echaniss involved in this proble, no universal odel exists yet. ujawski (2005 clearly indicated that there is no general agreeent aong researchers regarding the significance of closure concept on fatigue crack behavior. In the present work, a fatigue crack growth (FG of thin walled aluinu alloy with circuferential crack under constant and variable aplitude loading (AL and VAL in tension was studied to show the behavior of FG with different load history. The FG odels Walker, Foran and NASGRO gives different behavior under the two types of loading. There are any factors affecting the FG. The effects of initial crack length and stress ratio on crack growth are shown with great influence. Need to study the other factors such load interaction, environents, crack angle etc. THEORETIAL BAGROUND Although a general understanding of any aspects of fatigue crack growth behavior was established in the early 1960s, a specific accuulation of age odel for coputation of growth under a wide variety of service loads was lacking. The reason for building odels is to link theoretical ideas with the observed ta to provide a good prediction of future observations. Modeling of FGR ta has enhanced the ability to create age tolerant design philosophies. The first paper was published by Paris et al, (1961 and it turned out to be a ilestone publication. The ajor liitation of the Paris law is its inability to account for the stress ratio. This drawback notified Walker (1970 to iprove the Paris odel by including the effect of stress ratio. Walker proposed a paraeter Δ, which is an equivalent zero to axiu (R 0 stress intensity

2 factor that causes the sae growth rate as the actual ax, and R cobination. It is expressed by the relationship of ( Δ R γ (1 ax 1 W Where ax Δ /(1-R, and Equation (1 becoes If the various Δ and R cobinations fall together on a straight line on a log-log plot of Q versus Δ, the Foran equation is applicable and ay be used. oparing Equations (5 and (6, the Foran equation can be represented as ( Δ y Q F (7 Δ Δ 1 γ W R Therefore, the Walker law is represented by or W ( Δ W Δ W 1 γ R W For R 0, Equation (3 is forulated to for W (3 (2 The Foran equation is capable of representing ta of various stress ratios for region II and III. Further odifications of the Foran's expression to represent region I, II and III have been accoplished by including the threshold stress intensity paraeter Δ. / /cycle Region I Region II Region III ( Δ W W (4 Which, is equivalent to the Paris law with p w and p w. Although Walker iproved the Paris odel by taking account of the stress ratio, neither odels could account for the instability of the crack growth when the stress intensity factor approaches its critical value. Foran (1972 iproved the Walker odel by suggesting a new odel, which is capable of describing region III of the fatigue rate curve and includes the stress ratio effect. The Foran law is given by the atheatical relationship F ( Δ ( R y F ( Δ R( (5 1 Δ y where c is the fracture toughness for the aterial and thickness of interest. Equation (5 indicates that as ax, approaches c & / tends to infinity. Therefore, the Foran equation is capable of representing stable interediate growth (region II and the accelerated growth rates (region III shown in Figure 1. The Foran equation is capable of representing ta for various stress ratios by coputing the following quantity for each ta point, i.e. ax Q [( 1 R Δ ] (6 132 Log Δ Fig. 1.: Typical / versus Δ curve NASGRO extends the generalized Willenborg et al. (1971 odel taking into account the reduction of retartion due to underloads and gave the following atheatical equation ( Δeff (1 R Δ eff eff Δ ( ( Δ eff ax eff in eff ax, eff in, eff ax red {( in red } ax,0, in for in > 0 for in 0 1/2 an a OL red φ ( OL ax 1 γ Pol (9 (8 ax

3 φ φ /( (2.5 R 0.6, R < 0.25 R 1.0R 0.25 U o U U (10 σ / σ, φ 0.2 to 0.8 U UL ax, OL O The liitation of this odel is the value of φ O is to be obtained fro experientally. METHODOLOGY In this application a thin wall tube of aluinu alloy (radius500 and 50 in thickness with circuferential crack under tensile load. The echanical and fatigue properties of the aterial used are shown in Table 1. Table.1: Mechanical and fatigue properties of the aterial Yield Stress (MPa YS Ultiate Tensile Strength (MPa 455 UTS Plane Strain Fracture Toughness (MPa( 1/2 1 Plane Stress Fracture Toughness (MPa( 1/2 1 D Parte Through Fracture Toughness (MPa( 1/2 1 E Paris o-efficient (/MPa( 1/2 n E- 10 Foran Exponent n Walker Exponent 0.3 NASGRO Exponent p 0.5 oponents, structures are subjected to quite diverse load histories, their histories ay be rather siple and repetitive, at the other extree, ay be copletely rando. The variable and constant load histories used are shown in Figure 2 and 3 respectively. To account load ranges and ean of the used load history, rain flow accounting ethod was used. The odeling and siulation of the analysis were done based on Glyphwork codes. Fig.3.: Display of onstant Aplitude Loading RESULTS AND DISUSSION The effects of the above loading (AL and VAL are using the axiu value of VAL as the value of AL on FG of the shell was studied and shown in Figure 3. FG under AL gives less life than under VAL. AL account for all cycles as the axiu value, while in VAL only the peaks. Figure 4 also shows the effect of using different FG odels. Fig.4.: Fatigue rack Growth of Thin Wall Tube with AL and VAL using Different FG Models Fig. 2.: Display of Variable Aplitude Loading 133 Fig. 5.: Fatigue rack Growth for Different Initial rack Length

4 recognizes that the effect of the stress ratio on fatigue crack growth behavior is strongly aterial dependent. ONLUSIONS Fig. 6.: Fatigue Life with Different Initial rack Length Fig. 7.: Fatigue rack Growth with Different Stress Ratio For the odels with VAL, Foran odel gives longer life and ore than NASGRO odel, while Walker odel gives the lowest life. For AL, NASGRO odel gives the longer life, and Walker odel also gives the iniu life. The effect of initial crack length on FG using NASGRO odel was studied and shown in Figure 5. The interactions between the indicate that the higher value of initial crack length tend to the lower nuber of cycles for crack growth. In the sae way, the fatigue life drawn verses the initial crack length and shown Figure 6, which gives a iniu life for larger initial crack length. Most ean stress effects on crack growth have been obtained for only positive stress ratios, i.e., R 0. Figure 7 shows the variation of the nuber of fatigue loading cycles versus the corresponding crack length for different stress ratios. The Foran odel, which used here is a odification of the Paris equation that incorporates ean stress and region III fatigue crack growth behavior. It observed that the FG affected by different stress ratio, which shown on a-n curve that increasing the stress ratio (which eans increasing the ean stress has tendency to increase the crack growth rates. It should be The study of fatigue crack propagation exaines how a fatigue crack grows under cyclic load. This topic is the subject of considerable research, ainly dealing with the developent of various odels to better explain the crack propagation phenoenon. For the odern high perforance structures designed for finite service life, fatigue crack growth occurs over a significant portion of the useful life of the structures. Therefore, accurate siulation of crack propagation paths in engineering aterials is what designers and engineers are always looking for. A fatigue crack growth of thin walled aluinu alloy with circuferential crack under constant and variable aplitude loading in tension was studied and showed the behavior of FG with the different load histories. A crack growth calculation procedure based on a three different odel Walker, Foran and NASGRO based Glyphwork codes. These odels applied in both constant and variable aplitude loading situations gave different behavior under the two types of loading. Walker iproved the Paris odel by including the effect of stress ratio while, Foran iproved the Walker odel by suggesting a new odel, which is capable of describing region III of the fatigue rate curve and includes the stress ratio effect. NASGRO extended the generalized Willenborg odel by taking into account the reduction of retartion due to underloads. Aong any factors affecting the FG, the effect of initial crack and stress ratio are shown. This study indicate that the higher value of initial crack length tend to the lower nuber of cycles for crack growth, and also showed that increasing the stress ratio (which eans increasing the ean stress has tendency to increase the crack growth rates. It should be recognizes that the effect of the stress ratio on fatigue crack growth behavior is strongly aterial dependent. REFERENES Elber, W. The significance of fatigue crack closure in fatigue. ASTM STP 486: , Foran, RG. Study of fatigue crack initiation fro flaws using fracture echanics theory. Engineering Fracture Mechanics, 4(2: , Huang, XP., ui, W., and Leng, JX. A odel of fatigue crack growth under various load spectra. In: Proc of Sih G, 7th International conference of MESO, August 1 4, Montreal, ana, pp , Huang, XP., Zhang, JB., ui, W., and Leng, JX. Fatigue crack growth with overload under spectru 134

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