Stress intensity factors under combined tension and torsion loadings
|
|
- Muriel Jenkins
- 5 years ago
- Views:
Transcription
1 Indian Journal of Engineering & Materials Sciences Vol. 19, February 01, pp Stress intensity factors under combined tension and torsion loadings A E Ismail a *, A Ariffin b, S Abdullah b & M J Ghazali b a Department Engineering Mechanics, Faculty of Mechanical & Manufacturing, Engineering, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Johor, Malaysia b Department Mechanical & Materials Engineering, Faculty of Engineering & Built Environment, Universiti ebangsaan Malaysia, UM Bangi, Selangor, Malaysia Received 13 December 010; accepted February 01 This paper numerically discusses the stress intensity factor (SIF) calculations for surface cracks in round bars subjected to combined loadings. Different crack aspect ratios, a/b ranged from 0.0 to 1. and the relative crack depth, a/d in the range of 0.1 to 0.6 are considered. Since the loading is non-symmetrical, the whole finite element model is constructed. Then, both tension and torsion loadings are remotely applied to the finite element model and the SIFs are determined along the crack front of various crack geometries. An equivalent SIF method is then explicitly used to combine the individual SIF obtained using different loadings. A comparison is made between the combined SIFs obtained using the equivalent SIF method and finite element analysis (FEA) under similar loadings. It is found that the equivalent SIF method successfully predicted the combined SIF for Mode I. However, discrepancies between the results, which have been determined from the different approaches, occurred when F III is involved. Meanwhile, it is also noted that the predicted SIF using FEA is higher than the predicted through the equivalent SIF method due to the crack face interactions. eywords: Stress intensity factor, Surface crack, Finite element analysis, Combined loadings Cylindrical bars are generally used to transmit power from one point to another. The bars can be subjected to cyclic stresses which can cause mechanical damages and sometime experienced premature failure 1. The initiations of fatigue cracks on the surface are normally due to mechanical defects such as notches and metallurgical defects 3,4. In services, a rotating shaft can generally be subjected to combined loading due to its self-weight, which also induces a tension stress instead of torsion loadings. In fact, any arbitrary shapes of crack initiation may grow and take a semi-elliptical shape 5. Linear elastic fracture mechanics (LEFM) has been used to analyse stress intensity factors (SIFs) along the crack front. The solution of SIFs for a wide range of crack geometries under Mode I loading has been reported elsewhere in the literature However, the calculated SIFs, subjected to Mode III and the SIFs under combined loadings such as tension and torsion are rarely studied Therefore, the aim of this study is to obtain the SIFs for semi-elliptical surface cracks subjected to tension, torsion and the combination of loadings. According to the literature 1-15, the SIFs *Corresponding author ( emran@uthm.edu.my) subjected to combined loadings are rarely studied. Since the combined SIF can be obtained directly by combining the different mode of SIFs without considering the influence of crack interaction. This numerical work is carried out to investigate whether the SIFs from different modes can be explicitly combined and compared to the ones using the FEA. Finally, the result discrepancies between the two methods are also discussed in term of the mesh deformation, which mainly focused on the crack face interaction. Evaluation of Fracture Parameters Stress intensity factors The finite element method is an appropriate approach to calculate the stress intensity factor (SIF) for linear elastic fracture mechanics problems. In order to determine the SIFs, a displacement extrapolation method 17 is used in this study. Several other works have implemented a similar method are also available 18,19. In order to analyse the cracks, it is frequently modelled as a semi-elliptical crack shape. This due to the fact, any arbitrary crack shapes will grow to take semi-elliptical crack geometry 5. Figure 1 shows an arbitrary crack shape where the crack face is parallel to the x-axis and the z-axis is normal to the
2 6 INDIAN J. ENG. MATER. SCI., FEBRUARY 01 Fig. 1 Arbitrary crack shape Fig. 3 Definition of contour path to evaluate the J-integral the SIFs obtained from the analysis are converted into normalized values in order to ensure the generality of the results. A normalized SIF, F, can be defined as follows 10 F I, a I, a = (4) σ π a a F I, b I, b = (5) σ π a b F II II = (6) xy τ π a x-y plane. Figure shows an arrangement of singular finite elements around a crack tip used in this work. After obtaining the elastic finite element solution of the particular problem, nodal displacements between two crack faces are determined and used to compute the SIFs as follows: I II Fig. Singular element around the crack tip G π vb ν d G π v = = 1+ κ r 1+ κ r G π ub ud G π u = = 1+ κ r 1+ κ r (1) () wb wd w III = G π = G π (3) r r where, I, II and III are the respective mode I, II and III SIFs, v, u and w are the relative nodal displacements between two crack faces in the direction of y-axis, x-axis and z-axis, respectively, and G is the modulus of rigidity. For plain strain condition, κ= 3-4υ, where, υ is the Poisson s ratio. All F III III = (7) xy τ π a where, σ a, σ b and τ xy are the axial, bending and shear stresses, respectively and a is a crack depth. J-integral The concepts of SIFs are successfully used as a driving fracture parameter within the scope of linear elastic analysis. However, the application of this parameter breakdown when large amount of plastic deformation induced during loadings especially for the high strength and low toughness materials. Therefore, J-integral is used instead of SIF as a driving fracture parameter. It is firstly introduced by assuming a crack in two-dimensional plate 0, J-integral is defined as a contour, Γ around the crack tip. It is evaluated counter-clockwise as depicted in Fig. 3 and can be expressed as u J = Wdy T. ds (8) z Γ where, T is a outward traction vector along the contour, Γ is defined as T i = σ ij n i or it is a force per
3 ISMAIL et al.: STRESS INTENSITY FACTOR FOR SURFACE CRACS 7 unit length, u is a displacement vector and ds is an element on the contour, Γ. While, W is a strain energy density expressed as ε T σij εij { σ} { ε} (9) W = d = d ε 0 0 whereas the axial force, F is directly applied to the direction-x on the cross-sectional area of the round bar. At the other end, the component is appropriately constrained. For combined loadings, two types of loading ratios are used, which are defined as: where, ε ij is a strain tensor and {ε} represents as a strain vector. In elastic-plastic analysis J-integral is composed of two parts, elastic J-integral, J e and plastic J-integral, J p as follows 1 J = J e + J p (10) where J e can be obtained numerically using finite element method or by the following expression J e I = (11) κ where, is the SIF, κ=e for plane stress and κ = E / (1-υ ) for plane strain. Finite Element Modelling The geometry of the crack shown in Fig. 4 can be described by the dimensionless parameters a/d and a/b, the so-called relative crack depth and crack aspect ratio, respectively, where D, a and b are the diameter of the bar, the crack depth and the major diameter of the ellipse. In this work, a/b ranged between 0.0 to , while, a/d is in the range of 0.1 to which are based on the experimental observations -5. Any arbitrary point, P on the crack front can also be normalised through the ratio of x/h, where h is the crack width, and x is the arbitrary distance of P. The outer diameter of the cylinder is 50 mm and the total length is 00 mm. A finite element model is developed using ANSYS 6, and a special attention is paid to the crack tip by employing 0-node iso-parametric quadratic brick elements. The square-root singularity of stresses and strains is modelled by shifting the mid-point nodes to the quarter-point locations around the cracktip region. A quarter finite element model is shown in Fig. 5. In order to remotely apply loadings on the bar, a rigid element or multi-point constraint (MPC) is used to connect the nodes at a circumferential line at the end of the component to an independent node. Figure 6 shows a technique of constructing the independent node connected to the model using a rigid beam element. The bending moment, M y and the torsion moment, T x are directly applied to this node, Fig. 4 Nomenclature of semi-elliptical surface crack Fig. 5 Symmetrical finite element model and the associated singular element around the crack tip Fig. 6 Remotely applied moments using MPC184 element
4 8 INDIAN J. ENG. MATER. SCI., FEBRUARY 01 ϑ σ σ b = (1) a τ xy λ = (13) σ x where ϑ is the loading ratio between the bending stress, σ b and the axial stress, σ a, and λ is the ratio between the shear stress, τ xy and the bending or axial stresses, σ x. The ratios for both Eqs (1) and (13) are 0.5, 1.0 and.0. In order to obtain a suitable finite element model, it is needed to compare the proposed model with available results in the literature 11,5,8. Figure 7 shows a comparison of the dimensionless SIFs under tension loading. Two crack aspect ratio, a/b are used for the validation purposes which are 0.0 and 1.0. It has been found that the findings of this study are in agreement with those determined by the previous models where the curves have coincident to each others. The solution of Mode III SIFs is difficult to obtain 10,1,14-16,9 and consequently compared with the present results. Therefore, it can be assumed that the present model is also suitable to analyse Mode III condition in a satisfactory way. Results and Discussion Stress intensity factors under loading Figures 8-10 respectively show F I,a, F II and F III along the crack fronts under pure tension stress and torsion moment for the selected crack conditions. The SIFs are calculated for six points along the crack front. However, the SIF at the intersection, between the crack and the surface, is not determined due to the square-root singularity problem. The uses of a quarter point finite element in that area do not generally produce reliable results. Many works have discussed such problems 6-16 where the nearest point is approximated 83% from the deepest crack point (x/h = 0.0). Figures 8a and 8b show the variations of F I,a along the crack front under the tension stress for two crack aspect ratios, a/b = 0.4 and 1.. As for a/b = 0.4, the SIF is uniformly distributed along the crack front. When x/h approached the outer surface of the bar, F I,a is found to be slightly higher than the others. It is clearly shown that the maximum F I,a always occurred at the intersection point area. Under tension stress, the crack growth started at the intersection point and the semi-elliptical crack front might be flattened as the cracks grew 5. For the case of a/b = 1., F I,a is not affected by the a/d, particularly when a/d 0.5. When F I,a reached x/h 0.6, F I,a is diverged to its individual values. Fig. 7 Validation of finite element model under bending loading Fig. 8 Behaviour of F I,a along the crack front (a) a/b = 0.4 and (b) a/b = 1.
5 ISMAIL et al.: STRESS INTENSITY FACTOR FOR SURFACE CRACS 9 By referring to F II in Fig. 9, it is found that at the deepest point (x/h = 0.0), F II = 0.0 and it is observed to steeply increase when x/h approached the outer surface. Figure 10 shows F III along the crack front subjected to torsion loading. The role of F III is strongly related to the relative crack depth, a/d. For a/d < 0.3, the maximum F III occurred at the deepest point of the crack front, and when a/d > 0.3, the maximum F III is shifted to the outer surface area. The movement of x/h is observed to move to the outer edge of the bar when a/b is increased implying different crack evolutions can be obtained during the crack growth and before the final failure. Tables 1 and show the F II and F III results obtained under pure torsion moments. Stress intensity factors under combined loadings In previous studies 14-16, it is hard to find the SIFs under combined loadings. This is because it is assumed that the combined SIFs can be obtained using a superposition technique 6. This assumption is established for a similar type of loading mode, for example mode I 16. The normalized SIFs under combined loading, F * EQ, under Mode I loadings are here obtained by the superposition method defined as F = F + ϑf (14) EQ I, a I, b where ϑ is the stress ratio defined in Eq. (1). Then, these combined SIFs are compared with the combined SIFs, F * FEA, obtained numerically using finite element analysis, with an excellent agreement as shown in Fig. 11. Further enhancement of the superposition technique is required to include F II and F III. Therefore, the equivalent SIF method 30 is used instead of a superposition method. The equivalent SIF is defined as the following expression III EQ = I + II + (15) 1 ν Fig. 9 Behaviour of F II along the crack front (a) a/b = 0.6 and (b) a/b = 1.0 Fig. 10 Behaviour of F III along the crack front (a) a/b = 0.4 and (b) a/b = 1.0
6 10 INDIAN J. ENG. MATER. SCI., FEBRUARY 01 x/h a/d Table 1 List of mode II normalized SIF, F II a/b where, EQ is the equivalent SIF and ν is the Poisson s ratio. It is assumed that EQ = * where * is a combined SIF. Substituting Eqs (4) or (5), (6) and (7) into Eq. (15) yields the following expression FIIIτ xy π a = ( I, xσ x π ) + ( IIτ xy π ) + 1 ν * F a F a (16) where σ x can be represented as axial or bending stresses and F I,x can also be represented as the normalized SIF under bending or tension stress, respectively. Substituting Eq. (13) into Eq. (16), we obtain the following expression λfiii = ( σ x π ) ( I, x ) + ( λ II ) + 1 ν * a F F (17)
7 ISMAIL et al.: STRESS INTENSITY FACTOR FOR SURFACE CRACS 11 x/h a/d Table List of mode III normalized SIF, F III a/b Rearranging Eq. (17) in terms of combined dimensionless SIF, F * is given by λf III ( I, x ) ( λ II ) F = = F + F + σ ( 1 x π a ν ) (18) Eq. (18) can be divided into two separate equations given as F FE * = = F (19) I, x III, FE σ π a x λf F = ( F ) + ( λf ) + = F ( 1 ν ) III * I, x II I, x III, EQ (0)
8 1 INDIAN J. ENG. MATER. SCI., FEBRUARY 01 Fig. 11 Comparisons of combined mode I SIF, F * I (a) a/b = 0. and (b) a/b = 0.6 where F * I,x-III,FE is the normalised SIF obtained directly from finite element analysis under combined loadings, and F * I,x-III,EQ is the normalised SIF obtained explicitly by combining the individual SIFs F I,b, F I,a, F II and F III. In order to simplify the analysis, the work focused on this location at x/h = 0.0 where F II = 0.0. Therefore, Eq. (0) can be then reduced to the following expression * λf III I, x III, EQ =, + F ( FI x ) ( 1 ν ) (1) Figure 1 shows the SIFs obtained under single loading conditions at x/h = 0.0. It is indicated that, all the SIFs have decreased when a/b is increased and no significant effect on the SIFs for the relatively straight-fronted cracks (a/b 0.). For mode I conditions as shown in Fig. 11, the SIFs showed the increasing trends as a/d increased. Figure 1b on the other hand showed the SIFs under torsion moment obtained at x/h = 0.0. It is shown that lower values of F III occurred when a/b is increased. This occurrence Fig. 1 Behaviour of normalized SIF at different a/d (a) F I and (b) F III may be caused by the influence of crack geometries where the cracks become deeper are obtained using a/b = 1.. These type of cracks attained fully constraint mechanisms around the crack front and producing lower F III at x/h = 0.0. It is hard to obtain a single value of SIF directly from ANSYS. Therefore, an elastic J-integral is used by assuming that a single value of J-integral under combined loading represented the unified SIFs consisting of I, II and III. This is because in ANSYS, if J-integral is used in the elastic or plastic regions, it calculates only a single value of J-integral even under combined loadings. The elastic J-integral, J e, is as in Eq. (11) and it is rearranged in the terms of and assuming that = * FE, where * FE is a SIF under combined loadings obtained using finite element analysis, yields the following expression * FE E 1 ν = Je ()
9 ISMAIL et al.: STRESS INTENSITY FACTOR FOR SURFACE CRACS 13 Fig. 14 Deformed meshes under torsion moment (a) whole model, (b) enlarged area around the crack tip and (c) arial view of surface crack. Fig. 13 Comparisons of normalized SIF, F * I,a-III under combined loadings using two approaches, (a) a/b = 0., (b) a/b = 0.6 and (c) a/b = 1.0 Eq. () is used to convert the J-integral into the combined SIF for plain strain condition and it is substituted into Eq. (19). Then, F I,a are combined explicitly with F III through Eq. (1) using different stress ratio values, λ. The calculated F * EQ and F * FE are compared and the results are presented in Fig. 13. Figure 13 shows the plot of F * I,a-III against a/d for different a/b subjected to combined tension and torsion loadings. It is indicated that the loading ratio, γ played an important role in determining the discrepancies among the results. Reducing these ratios from.0 to 1.0, the Fig. 15 Deformed meshes under tension moment (a) whole model, (b) enlarged area around the crack tip and (c) arial view of surface crack results are almost agreed to each other. The detail of F * I,a-III,EQ and F * I,a-III,FE are given in Tables 3 and 4. The discrepancies of combined SIFs, F * between the two approaches remarkably depend on the values of a/b, a/d and λ. For all cases of a/b, F * EQ is considerably in agreement with F * FE for all values of loading ratios except for λ.0. When a/b increases, the discrepancies between the results obtained from the two different approaches are tremendously reduced, and all the F * values then converge when deeper cracks are used. Crack Deformation Mechanisms Figures present the stress distribution around the tip that is situated at the outer surface. Meanwhile,
10 14 INDIAN J. ENG. MATER. SCI., FEBRUARY 01 Table 3 List of F * I,a-III,EQ using an equivalent SIF method χ a/d a/b Table 4 List of F * I,a-III,FE using FEA χ a/d a/b
11 ISMAIL et al.: STRESS INTENSITY FACTOR FOR SURFACE CRACS 15 Fig. 16 Deformed meshes under combined loadings (a) whole model, (b) enlarged area around the crack tip and (c) arial view of surface crack Figs 14 and 15 included the deformed meshes of the cracks subjected to pure torsion moment and tension loading, respectively. The F I,a and F III as seen in Figs 1a and 1b are explicitly combined together and then compared with the F *, FE that is directly retrieved from the FEA. The situation in Fig. 16 is then produced using the FEA subjected to a combined loading. It is clearly shown that under the pure torsion loading, the crack faces are completely closed due to the absence of Mode I loading. Under the combined loadings, opening crack faces are observed even the bar is subjected to torsion loading, implicating that the mechanism was responsible to produce the discrepancies among the obtained results using the two distinct methods. In FEA, the SIFs are calculated by referring to the relative distance between the two nodes situated on the crack faces. It is important to note that under the combined loadings, F * FE is found to be greater than F * EQ, due to the fact that longer relative node distances are produced when tension stress involved. Therefore, ANSYS has calculated greater F III compared to the F III obtained under completely closed crack faces under pure torsion loading. Conclusions Finite element analyses (FEA) are performed for semi-elliptical surface cracks in round bars under combined tension and torsion loadings. No available solutions are carried out to calculate the normalised SIFs, particularly the SIF under combined loadings. It is assumed that the SIFs can be explicitly combined together without considering the crack face interactions. Based on the findings of this study, the direct SIF combinations are rather questionable and inappropriate when different failure modes were involved. Meanwhile, the discrepancies of the results between the explicitly combined SIFs and the SIFs obtained using FEA are due to the different mechanisms of crack face interactions shown by the deformed meshes, in which the crack faces are closed under the pure torsion, and vice versa under the combined loadings. The opening crack faces under the combined loadings increased the relative node distances. ANSYS then used these relative distances to calculate the SIFs. As a result, higher F * FE is obtained, relative to the F * EQ due to the different mechanisms of crack deformations. References 1 Li Y D, Zhang H C & Lee Y, Indian J Eng Mater Sci, 16 (009) Ismail A E, Ariffin A, Abdullah S & Ghazali M J, Int J Automot Tech, 1() (011) Mahmoud M, Theo Appl Frac Mech, 48 (007) Gray G T, Thompson A W & William J C, Metall Trans, 16A (1985) Lin X B & Smith R A, Int J Fatigue, 19 (1997) Raju I S & Newman J C, Fract Mech, 17 (1986) Shiratori M, T Miyoshi, Sakay Y & Zhang G R, Analysis and application of influence coefficients for round bar with a semi-elliptical surface crack (Oxford Pergamon Press), Murakami Y & Tsuru H, Stress intensity factor equations for semi-elliptical surface crack in a shaft under bending (Oxford Pergamon Press), Carpinteri A, Fatigue Fract Eng Mater Struct, 15 (199) Fonte M D & Freitas M D, Int J Fatigue, 1 (1999) Carpinteri A, Brighenti R & S, Vantadori, Int J Fatigue, 8 (006) Shahani A R & Habibi S E, Int J Fatigue, 9(1) (007) Toribio J, Matos J C, Gonzalez B & Escuadra J, Eng Failure Anal, 16(6) (009) Ismail A E, Ariffin A, Abdullah S & Ghazali M J, Int Rev Mech Eng, 4(7) (010) Ismail A E, Ariffin A, Abdullah S & Ghazali M J, Meccanica (in-press) 16 Ismail A E, Ariffin A, Abdullah S, Ghazali M J Daud R & AbdulRazzaq M, J Zhejiang Univ Sci A, 13(1) (01) Guinea GV, Planas J & Elices M, Eng Fract Mech, 66(3) (000) Aslantas A, Int J Solids Struct, 40(6) (003) Aslantas, Ergun E & Tasgetiren S, J Mech Mater Des, 3() (006) Rice J R, Appl Mech, 35 (1968) im Y J, im J S, Shim D J & im Y J, J Strain Anal, 39 (004)
12 16 INDIAN J. ENG. MATER. SCI., FEBRUARY 01 im Y J, Shim D J, Choi J B & im Y J, Eng Fract Mech, 69 (00) Mahmoud M, Theo Appl Fract Mech, 48() (007) Lin X B & Smith R A, Int J Fatigue, 19(6) (1997) Shin CS & Cai CQ, Int J Fract, 19(3) (004) ANSYS 11.0 Documentation (010). ANSYS Company 7 Carpinteri A, Brighenti R & Vantadori S, Int J Fatigue, 8(3) (006) Carpinteri A & Vantadori S, Int J Fatigue, 31(4) (009) Ismail A E, Ariffin A, Abdullah S, Ghazali MJ & Daud R, Adv Mater Res, 14 (011) Qian J & Fatemi A, Eng Fract Mech, 55 (1996)
J-Integral Evaluation of Surface Cracks in Round Bar under Mode III Loadings
Research Journal of Applied Sciences, Engineering and Technology 7(10): 1985-1993, 2014 ISSN: 2040-7459; e-issn: 2040-7467 Maxwell Scientific Organization, 2014 Submitted: June 17, 2013 Accepted: June
More informationMODE I STRESS INTENSITY FACTORS OF SLANTED CRACKS
VOL. 1, NO. 10, MAY 017 SSN 1819-6608 ARPN Journal of ngineering and Applied Sciences 006-017 Asian Research Publishing Network (ARPN). All rights reserved. MOD STRSS NTNSTY FACTORS OF SLANTD CRACS A smail
More informationAn Overview of Fracture Mechanics with ANSYS
nternational Journal of ntegrated ngineering: Special issue 08: Mechanical ngineering, Vol. 0 No. 5 (08) p. 59-67 Penerbit UTHM DO: https://doi.org/0.30880/ie.08.0.05.00 An Overview of Fracture Mechanics
More informationFinite element analysis of longitudinal debonding between fibre and matrix interface
Indian Journal of Engineering & Materials Sciences Vol. 11, February 2004, pp. 43-48 Finite element analysis of longitudinal debonding between fibre and matrix interface K Aslantaş & S Taşgetiren Department
More informationStress Intensity Factors of Slanted Cracks in Bi- Material Plates
Journal of Physics: Conference Series PAPR OPN ACCSS Stress Intensity Factors of Slanted Cracks in Bi- Material Plates To cite this article: Al mran Ismail et al 017 J. Phys.: Conf. Ser. 914 01043 View
More informationFinite Element Analysis of J-Integral for Surface Cracks in Round Bars under Combined Mode I Loading
nternational Journal of ntegrated Engineering, Vol. 9 No. 2 (207) p. -8 Finite Element Analysis of J-ntegral for Surface Cracks in Round Bars under Combined Mode Loading A.E smail, A.K Ariffin 2, S. Abdulla
More informationElastic Crack Interaction Limit of Two Interacting Edge Cracks in Finite Body
Elastic Crack Interaction Limit of Two Interacting Edge Cracks in Finite Body R. Daud, M.A. Rojan Division of Applied Mechanics, School of Mechatronic Engineering, Pauh Putra Campus, Universiti Malaysia
More informationA modified quarter point element for fracture analysis of cracks
ndian Journal of Engineering & Materials Sciences Vol. 14, February 007, pp. 31-38 A modified quarter point element for fracture analysis of cracks Sayantan Paul & B N Rao* Structural Engineering Division,
More information436 A. Barani and G.H. Rahimi assessment models have been employed to investigate the LBB of cracked pipes that are not for combined load [8]. Yun-Jae
Scientia Iranica, Vol. 4, No. 5, pp 435{44 c Sharif University of Technology, October 27 Approximate Method for Evaluation of the J-Integral for Circumferentially Semi-Elliptical-Cracked Pipes Subjected
More informationCritical applied stresses for a crack initiation from a sharp V-notch
Focussed on: Fracture and Structural Integrity related Issues Critical applied stresses for a crack initiation from a sharp V-notch L. Náhlík, P. Hutař Institute of Physics of Materials, Academy of Sciences
More informationElastic-Plastic Fracture Mechanics. Professor S. Suresh
Elastic-Plastic Fracture Mechanics Professor S. Suresh Elastic Plastic Fracture Previously, we have analyzed problems in which the plastic zone was small compared to the specimen dimensions (small scale
More informationINVESTIGATION OF ELASTIC STRESS SHIELDING DAMAGE INTERACTION BASED ON FITNESS FOR SERVICE (FFS) CODES Pauh, Perlis, Malaysia
International Conference on Mechanical Engineering Research (ICMER03), -3 uly 03 Bukit Gambang Resort City, Kuantan, Pahang, Malaysia Organized By Faculty of Mechanical Engineering, Universiti Malaysia
More informationCracks Jacques Besson
Jacques Besson Centre des Matériaux UMR 7633 Mines ParisTech PSL Research University Institut Mines Télécom Aγνωστ oς Θεoς Outline 1 Some definitions 2 in a linear elastic material 3 in a plastic material
More informationCALCULATION OF FRACTURE MECHANICS PARAMETERS FOR AN ARBITRARY THREE-DIMENSIONAL CRACK, BY THE EQUIVALENT DOMAIN INTEGRAL METHOD 1
CALCULATION OF FRACTURE MECHANICS PARAMETERS FOR AN ARBITRARY THREE-DIMENSIONAL CRACK, BY THE EQUIVALENT DOMAIN INTEGRAL METHOD 1 G. P. NIKISHKOV 2 and S. N. ATLURI 3 Center for the Advancement of Computational
More informationMaterials and Structures
Journal of Mechanics of Materials and Structures BRITTLE FRACTURE BEYOND THE STRESS INTENSITY FACTOR C. T. Sun and Haiyang Qian Volume 4, Nº 4 April 2009 mathematical sciences publishers JOURNAL OF MECHANICS
More informationME 2570 MECHANICS OF MATERIALS
ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation
More informationG1RT-CT A. BASIC CONCEPTS F. GUTIÉRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE W P 6: TRAINING & EDUCATION
A. BASIC CONCEPTS 6 INTRODUCTION The final fracture of structural components is associated with the presence of macro or microstructural defects that affect the stress state due to the loading conditions.
More informationTransactions on Modelling and Simulation vol 9, 1995 WIT Press, ISSN X
A path-independent integral for the calculation of stress intensity factors in three-dimensional bodies C.M. Bainbridge," M.H. Aliabadi," D.P. Rooke* "Wessex Institute of Technology, Ashurst Lodge, Ashurst,
More informationThe Ultimate Load-Carrying Capacity of a Thin-Walled Shuttle Cylinder Structure with Cracks under Eccentric Compressive Force
The Ultimate Load-Carrying Capacity of a Thin-Walled Shuttle Cylinder Structure with Cracks under Eccentric Compressive Force Cai-qin Cao *, Kan Liu, Jun-zhe Dong School of Science, Xi an University of
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationPROPAGATION OF CURVED CRACKS IN HOMOGENEOUS AND GRADED MATERIALS
PROPAGATION OF CURVED CRACKS IN HOMOGENEOUS AND GRADED MATERIALS Abstract Matthew T. Tilbrook, Robert J. Moon and Mark Hoffman School of Materials Science and Engineering University of New South Wales,
More informationIMECE CRACK TUNNELING: EFFECT OF STRESS CONSTRAINT
Proceedings of IMECE04 2004 ASME International Mechanical Engineering Congress November 13-20, 2004, Anaheim, California USA IMECE2004-60700 CRACK TUNNELING: EFFECT OF STRESS CONSTRAINT Jianzheng Zuo Department
More informationDETERMINATION OF STRESS INTENSITY FACTORS ALONG CRACKED SURFACES IN PIPING ELBOWS STRUCTURES E.M.M.FONSECA*, F.Q.MELO**, R.A.F.
1 th PORTUGUESE CONFERENCE ON FRACTURE - 6 DETERMINATION OF STRESS INTENSITY FACTORS ALONG CRACKED SURFACES IN PIPING ELBOWS STRUCTURES E.M.M.FONSECA*, F.Q.MELO**, R.A.F.VALENTE** *CENUME IDMEC Instituto
More information5. STRESS CONCENTRATIONS. and strains in shafts apply only to solid and hollow circular shafts while they are in the
5. STRESS CONCENTRATIONS So far in this thesis, most of the formulas we have seen to calculate the stresses and strains in shafts apply only to solid and hollow circular shafts while they are in the elastic
More informationElastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack
Chin. Phys. B Vol. 19, No. 1 010 01610 Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack Fang Qi-Hong 方棋洪, Song Hao-Peng 宋豪鹏, and Liu You-Wen 刘又文
More informationMethod for calculating the stress intensity factor for mode-i indentation with eccentric loads
Acta Technica 6 (017), No. 4A, 481488 c 017 Institute of Thermomechanics CAS, v.v.i. Method for calculating the stress intensity factor for mode-i indentation with eccentric loads DUO Yili 1,, XIE Yujun
More informationFRACTURE MECHANICS FOR MEMBRANES
FRACTURE MECHANICS FOR MEMBRANES Chong Li, Rogelio Espinosa and Per Ståhle Solid Mechanics, Malmö University SE 205 06 Malmö, Sweden chong.li@ts.mah.se Abstract During fracture of membranes loading often
More information3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1
Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is
More informationThermal load-induced notch stress intensity factors derived from averaged strain energy density
Available online at www.sciencedirect.com Draft ScienceDirect Draft Draft Structural Integrity Procedia 00 (2016) 000 000 www.elsevier.com/locate/procedia 21st European Conference on Fracture, ECF21, 20-24
More informationMechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002
student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity
More informationDEVELOPMENT OF TEST GUIDANCE FOR COMPACT TENSION FRACTURE TOUGHNESS SPECIMENS CONTAINING NOTCHES INSTEAD OF FATIGUE PRE-CRACKS
Transactions, SMiRT-23 Division II, Paper ID 287 Fracture Mechanics and Structural Integrity DEVELOPMENT OF TEST GUIDANCE FOR COMPACT TENSION FRACTURE TOUGHNESS SPECIMENS CONTAINING NOTCHES INSTEAD OF
More informationFig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double cantilever beam (DCB) specimens.
a). Cohesive Failure b). Interfacial Failure c). Oscillatory Failure d). Alternating Failure Fig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double
More informationFracture Mechanics, Damage and Fatigue Linear Elastic Fracture Mechanics - Energetic Approach
University of Liège Aerospace & Mechanical Engineering Fracture Mechanics, Damage and Fatigue Linear Elastic Fracture Mechanics - Energetic Approach Ludovic Noels Computational & Multiscale Mechanics of
More informationDetermination of Stress Intensity Factor for a Crack Emanating From a Rivet Hole and Approaching Another in Curved Sheet
International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) Determination of Stress Intensity Factor for a Crack Emanating From a Rivet Hole and Approaching Another in Curved Sheet Raghavendra.
More informationTentamen/Examination TMHL61
Avd Hållfasthetslära, IKP, Linköpings Universitet Tentamen/Examination TMHL61 Tentamen i Skademekanik och livslängdsanalys TMHL61 lördagen den 14/10 2000, kl 8-12 Solid Mechanics, IKP, Linköping University
More informationFinite element modelling of infinitely wide Angle-ply FRP. laminates
www.ijaser.com 2012 by the authors Licensee IJASER- Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 9442 Finite element modelling of infinitely wide Angle-ply FRP laminates
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011
Interlaminar failure analysis of FRP cross ply laminate with elliptical cutout Venkateswara Rao.S 1, Sd. Abdul Kalam 1, Srilakshmi.S 1, Bala Krishna Murthy.V 2 1 Mechanical Engineering Department, P. V.
More informationExample 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.
162 3. The linear 3-D elasticity mathematical model The 3-D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides
More informationCrack Tip Plastic Zone under Mode I Loading and the Non-singular T zz -stress
Crack Tip Plastic Zone under Mode Loading and the Non-singular T -stress Yu.G. Matvienko Mechanical Engineering Research nstitute of the Russian Academy of Sciences Email: ygmatvienko@gmail.com Abstract:
More informationEfficient 2-parameter fracture assessments of cracked shell structures
Efficient 2-parameter fracture assessments of cracked shell structures B. Skallerud, K.R. Jayadevan, C. Thaulow, E. Berg*, K. Holthe Faculty of Engineering Science The Norwegian University of Science and
More informationExperimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives
Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives Mark Oliver October 19, 2016 Adhesives and Sealants Council Fall Convention contact@veryst.com www.veryst.com Outline
More informationTOUGHNESS OF PLASTICALLY-DEFORMING ASYMMETRIC JOINTS. Ford Research Laboratory, Ford Motor Company, Dearborn, MI 48121, U.S.A. 1.
TOUGHNESS OF PLASTICALLY-DEFORMING ASYMMETRIC JOINTS M. D. Thouless, M. S. Kafkalidis, S. M. Ward and Y. Bankowski Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann
More informationBurst Pressure Prediction of Multiple Cracks in Pipelines
IOP Conference Series: Materials Science and Engineering OPEN ACCESS Burst Pressure Prediction of Multiple Cracks in Pipelines To cite this article: N A Razak et al 2013 IOP Conf. Ser.: Mater. Sci. Eng.
More informationModule 5: Theories of Failure
Module 5: Theories of Failure Objectives: The objectives/outcomes of this lecture on Theories of Failure is to enable students for 1. Recognize loading on Structural Members/Machine elements and allowable
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationNumerical methods of multiaxial fatigue life prediction for elastomers under variable amplitude loadings
ORIGINAL CONTRIBUTION doi: 10.1111/ffe.12401 Numerical methods of multiaxial fatigue life prediction for elastomers under variable amplitude loadings J. CHUNG and N. H. KIM Department of Mechanical and
More informationME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.
ME 323 - Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM-12:20PM Ghosh 2:30-3:20PM Gonzalez 12:30-1:20PM Zhao 4:30-5:20PM M (x) y 20 kip ft 0.2
More informationExperimental validation of a fracture plane model for multiaxial cyclic loading
Experimental validation of a fracture plane model for multiaxial cyclic loading A. Carpinteri, R. Brighenti, A. Spagnoli Dipartimento di Ingegneria Civile, Universita di Parma Viale delle Scienze, 431
More informationSize effect in the strength of concrete structures
Sādhanā Vol. 27 Part 4 August 2002 pp. 449 459. Printed in India Size effect in the strength of concrete structures B L KARIHALOO and Q Z XIAO Division of Civil Engineering School of Engineering Cardiff
More informationNON-LINEAR FRACTURE BEHAVIOR OF DOUBLE CANTILEVER BEAM
Engineering MECHANICS, Vol., 015, No., p. 95 10 95 NON-LINEAR FRACTURE BEHAVIOR OF DOUBLE CANTILEVER BEAM Viktor Rizov* This article describes a theoretical study of non-linear fracture behavior of the
More informationMechanical Properties of Materials
Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of
More informationComputation of Linear Elastic and Elastic Plastic Fracture Mechanics Parameters Using FEA
Computation of Linear Elastic and Elastic Plastic Fracture Mechanics Parameters Using FEA Renjin J Bright, Lokesh umar P. J Abstract Linear Elastic Fracture Mechanics (LEFM) parameter Stress intensity
More informationINFLUENCE OF TEMPERATURE ON BEHAVIOR OF THE INTERFACIAL CRACK BETWEEN THE TWO LAYERS
Djoković, J. M., et.al.: Influence of Temperature on Behavior of the Interfacial THERMAL SCIENCE: Year 010, Vol. 14, Suppl., pp. S59-S68 S59 INFLUENCE OF TEMPERATURE ON BEHAVIOR OF THE INTERFACIAL CRACK
More informationChapter 3. Load and Stress Analysis. Lecture Slides
Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.
More informationA short review of continuum mechanics
A short review of continuum mechanics Professor Anette M. Karlsson, Department of Mechanical ngineering, UD September, 006 This is a short and arbitrary review of continuum mechanics. Most of this material
More informationJ. Sladek, V. Sladek & M. Hrina Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Slovakia
Evaluation of fracture parameters for functionally gradient materials J. Sladek, V. Sladek & M. Hrina Institute of Construction and Architecture, Slovak Academy of Sciences, 842 20 Bratislava, Slovakia
More informationTHE EFFECT OF GEOMETRY ON FATIGUE LIFE FOR BELLOWS
Advanced Materials Development and Performance (AMDP2011) International Journal of Modern Physics: Conference Series Vol. 6 (2012) 343-348 World Scientific Publishing Company DOI: 10.1142/S2010194512003418
More informationThe Rotating Inhomogeneous Elastic Cylinders of. Variable-Thickness and Density
Applied Mathematics & Information Sciences 23 2008, 237 257 An International Journal c 2008 Dixie W Publishing Corporation, U. S. A. The Rotating Inhomogeneous Elastic Cylinders of Variable-Thickness and
More informationGeometry-dependent MITC method for a 2-node iso-beam element
Structural Engineering and Mechanics, Vol. 9, No. (8) 3-3 Geometry-dependent MITC method for a -node iso-beam element Phill-Seung Lee Samsung Heavy Industries, Seocho, Seoul 37-857, Korea Hyu-Chun Noh
More informationExamination in Damage Mechanics and Life Analysis (TMHL61) LiTH Part 1
Part 1 1. (1p) Define the Kronecker delta and explain its use. The Kronecker delta δ ij is defined as δ ij = 0 if i j 1 if i = j and it is used in tensor equations to include (δ ij = 1) or "sort out" (δ
More informationFracture mechanics fundamentals. Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design
Fracture mechanics fundamentals Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design Failure modes Failure can occur in a number of modes: - plastic deformation
More informationUsing the finite element method of structural analysis, determine displacements at nodes 1 and 2.
Question 1 A pin-jointed plane frame, shown in Figure Q1, is fixed to rigid supports at nodes and 4 to prevent their nodal displacements. The frame is loaded at nodes 1 and by a horizontal and a vertical
More informationA Model for Local Plasticity Effects on Fatigue Crack Growth
A Model for Local Plasticity Effects on Fatigue Crack Growth USAF Aircraft Structural Integrity Program Conference San Antonio, Texas November 28-30, 2006 R. Craig McClung Brian M. Gardner Yi-Der Lee Fraser
More informationCRACK INITIATION CRITERIA FOR SINGULAR STRESS CONCENTRATIONS Part I: A Universal Assessment of Singular Stress Concentrations
Engineering MECHANICS, Vol. 14, 2007, No. 6, p. 399 408 399 CRACK INITIATION CRITERIA FOR SINGULAR STRESS CONCENTRATIONS Part I: A Universal Assessment of Singular Stress Concentrations Zdeněk Knésl, Jan
More informationFracture Behaviour of FRP Cross-Ply Laminate With Embedded Delamination Subjected To Transverse Load
Fracture Behaviour of FRP Cross-Ply Laminate With Embedded Delamination Subjected To Transverse Load Sriram Chintapalli 1, S.Srilakshmi 1 1 Dept. of Mech. Engg., P. V. P. Siddhartha Institute of Technology.
More informationTuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE
1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & Free-Body Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More informationACCURACY OF APPROXIMATION OF STRESS FIELD IN CRACKED BODIES FOR FAILURE ZONE EXTENT ESTIMATION
VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-8 J.G.M. Van Mier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang (Eds) ACCURACY OF APPROXIMATION OF STRESS
More informationSEMM Mechanics PhD Preliminary Exam Spring Consider a two-dimensional rigid motion, whose displacement field is given by
SEMM Mechanics PhD Preliminary Exam Spring 2014 1. Consider a two-dimensional rigid motion, whose displacement field is given by u(x) = [cos(β)x 1 + sin(β)x 2 X 1 ]e 1 + [ sin(β)x 1 + cos(β)x 2 X 2 ]e
More informationMultiaxial Fatigue. Professor Darrell F. Socie. Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign
Multiaxial Fatigue Professor Darrell F. Socie Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign 2001-2011 Darrell Socie, All Rights Reserved Contact Information
More informationFig. 1. Circular fiber and interphase between the fiber and the matrix.
Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In
More informationA parametric study on the elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends
Arch. Mech., 68, 3, pp. 03 8, Warszawa 06 A parametric study on the elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends F. YALCIN ), A. OZTURK ), M. GULGEC 3)
More informationOn the torsion of functionally graded anisotropic linearly elastic bars
IMA Journal of Applied Mathematics (2007) 72, 556 562 doi:10.1093/imamat/hxm027 Advance Access publication on September 25, 2007 edicated with admiration to Robin Knops On the torsion of functionally graded
More informationTopics in Ship Structures
Topics in Ship Structures 8 Elastic-lastic Fracture Mechanics Reference : Fracture Mechanics by T.L. Anderson Lecture Note of Eindhoven University of Technology 17. 1 by Jang, Beom Seon Oen INteractive
More informationFinite Element Method in Geotechnical Engineering
Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Statics
More informationStress intensity factor analysis for an interface crack between dissimilar isotropic materials
Stress intensity factor analysis for an interface crack between dissimilar isotropic materials under thermal stress T. Ikeda* & C. T. Sun* I Chemical Engineering Group, Department of Materials Process
More informationDHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF MECHANICAL ENGINEERING ME 6603 FINITE ELEMENT ANALYSIS PART A (2 MARKS)
DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF MECHANICAL ENGINEERING ME 6603 FINITE ELEMENT ANALYSIS UNIT I : FINITE ELEMENT FORMULATION OF BOUNDARY VALUE PART A (2 MARKS) 1. Write the types
More informationFracture Mechanics of Composites with Residual Thermal Stresses
J. A. Nairn Material Science & Engineering, University of Utah, Salt Lake City, Utah 84 Fracture Mechanics of Composites with Residual Thermal Stresses The problem of calculating the energy release rate
More informationStress Analysis of Radial and Non- Radial Nozzle Connections in Ellipsoidal Head Pressure Vessel
Journal of Mechanical Engineering Vol. 10, No. 1, 67-83, 2013 Stress Analysis of Radial and Non- Radial Nozzle Connections in Ellipsoidal Head Pressure Vessel Haszeme Abu Kasim 1, a Professor Dr. Ir. Wahyu
More informationGeneralized fracture toughness for specimens with re-entrant corners: Experiments vs. theoretical predictions
Structural Engineering and Mechanics, Vol. 32, No. 5 (2009) 609-620 609 Generalized fracture toughness for specimens with re-entrant corners: Experiments vs. theoretical predictions Alberto Carpinteri,
More informationDEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS).
DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS). Lab Director: Coordinating Staff: Mr. Muhammad Farooq (Lecturer) Mr. Liaquat Qureshi (Lab Supervisor)
More informationINFLUENCE OF THE LOCATION AND CRACK ANGLE ON THE MAGNITUDE OF STRESS INTENSITY FACTORS MODE I AND II UNDER UNIAXIAL TENSION STRESSES
INFLUENCE OF THE LOCATION AND CRACK ANGLE ON THE MAGNITUDE OF STRESS INTENSITY FACTORS MODE I AND II UNDER UNIAXIAL TENSION STRESSES Najah Rustum Mohsin Southern Technical University, Technical Institute-Nasiriya,
More informationStress and Displacement Analysis of a Rectangular Plate with Central Elliptical Hole
Stress and Displacement Analysis of a Rectangular Plate with Central Elliptical Hole Dheeraj Gunwant, J. P. Singh mailto.dheerajgunwant@gmail.com, jitenderpal2007@gmail.com, AIT, Rampur Abstract- A static
More informationArch. Metall. Mater. 62 (2017), 3,
Arch. Metall. Mater. 62 (2017), 3, 1881-1887 DOI: 10.1515/amm-2017-0285 P. RAMASWAMI* #, P. SENTHIL VELMURUGAN**, R. RAJASEKAR** EFFECT OF OVALITY IN INLET PIGTAIL PIPE BENDS UNDER COMBINED INTERNAL PRESSURE
More information5 ADVANCED FRACTURE MODELS
Essentially, all models are wrong, but some are useful George E.P. Box, (Box and Draper, 1987) 5 ADVANCED FRACTURE MODELS In the previous chapter it was shown that the MOR parameter cannot be relied upon
More informationFatigue and Fracture
Fatigue and Fracture Multiaxial Fatigue Professor Darrell F. Socie Mechanical Science and Engineering University of Illinois 2004-2013 Darrell Socie, All Rights Reserved When is Multiaxial Fatigue Important?
More informationBIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS
BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS H. Kumazawa and T. Takatoya Airframes and Structures Group, Japan Aerospace Exploration Agency 6-13-1, Ohsawa, Mitaka,
More informationA novel approach to predict the growth rate of short cracks under multiaxial loadings
A novel approach to predict the growth rate of short cracks under multiaxial loadings F. Brugier 1&2, S. Pommier 1, R. de Moura Pinho 2, C. Mary 2 and D. Soria 2 1 LMT-Cachan, ENS Cachan / CNRS / UPMC
More informationSurface crack subject to mixed mode loading
Engineering Fracture Mechanics 65 (2000) 1±14 www.elsevier.com/locate/engfracmech Surface crack subject to mixed mode loading M.Y. He a, J.W. Hutchinson b, * a Materials Engineering Department, University
More informationCHARACTERIZATION, ANALYSIS AND PREDICTION OF DELAMINATION IN COMPOSITES USING FRACTURE MECHANICS
Oral Reference Number: ICF100942OR CHARACTERIZATION, ANALYSIS AND PREDICTION OF DELAMINATION IN COMPOSITES USING FRACTURE MECHANICS T. Kevin O Brien U.S. Army Research Laboratory Vehicle Technology Directorate
More informationLife Prediction Under Multiaxial Fatigue
Lie Prediction Under Multiaxial Fatigue D. Ramesh and M.M. Mayuram Department o Mechanical Engineering Indian Institute o Technology, Madras Chennai-600 036 (India) e-mail: mayuram@iitm.ac.in ABSTRACT
More informationPrediction of geometric dimensions for cold forgings using the finite element method
Journal of Materials Processing Technology 189 (2007) 459 465 Prediction of geometric dimensions for cold forgings using the finite element method B.Y. Jun a, S.M. Kang b, M.C. Lee c, R.H. Park b, M.S.
More informationSchur decomposition in the scaled boundary finite element method in elastostatics
IOP Conference Series: Materials Science and Engineering Schur decomposition in the scaled boundary finite element method in elastostatics o cite this article: M Li et al 010 IOP Conf. Ser.: Mater. Sci.
More informationFinite element simulations of fretting contact systems
Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 45 Finite element simulations of fretting contact systems G. Shi, D. Backman & N. Bellinger Structures and Materials
More informationDiscrete Element Modelling of a Reinforced Concrete Structure
Discrete Element Modelling of a Reinforced Concrete Structure S. Hentz, L. Daudeville, F.-V. Donzé Laboratoire Sols, Solides, Structures, Domaine Universitaire, BP 38041 Grenoble Cedex 9 France sebastian.hentz@inpg.fr
More informationINFLUENCE OF FLANGE STIFFNESS ON DUCTILITY BEHAVIOUR OF PLATE GIRDER
International Journal of Civil Structural 6 Environmental And Infrastructure Engineering Research Vol.1, Issue.1 (2011) 1-15 TJPRC Pvt. Ltd.,. INFLUENCE OF FLANGE STIFFNESS ON DUCTILITY BEHAVIOUR OF PLATE
More informationChapter 4 Deflection and Stiffness
Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 4-1 Spring Rates 4-2 Tension, Compression, and Torsion 4-3 Deflection Due to Bending 4-4 Beam
More informationCOURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6
COURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 0 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 TIME SCHEDULE Module Topics Period Moment of forces Support reactions Centre
More informationLecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements
Lecture #10: 151-0735: Dynamic behavior of materials and structures Anisotropic plasticity Crashworthiness Basics of shell elements by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering,
More informationFinite Element Investigation on the Stress State at Crack Tip by Using EPFM Parameters
Finite Element Investigation on the Stress State at Crack Tip by Using EPFM Parameters FRANCESCO CAPUTO, ALESSANDRO DE LUCA, GIUSEPPE LAMANNA 1, ALESSANDRO SOPRANO Department of Industrial and Information
More information