## Cohesive zone model based analytical solutions for adhesively bonded pipe joints under torsional loading.(English)Zbl 1236.74184

Summary: Adhesively bonded pipe joints are extensively used in pipelines. In the present work, cohesive zone model (CZM) based analytical solutions are derived for the bonded pipe joints under torsion. The concept of the minimum relative interface rotation $$\varphi_{m}$$ is introduced and used as the fundamental variable to express all other parameters, such as external torsion load, distribution of interfacial shear stress, length of elastic zone and softening zone, etc. It is found that when the bond length of the pipe joint is longer than a certain value, further increase in bond length cannot bring any significant increase in torsion load capacity. Given that the bond length of the pipe joint is long enough, the torsion load capacity is indeed independent of the shape of cohesive laws and the bond length. Consequently, simplified expressions of the torsion load capacity are derived as a function of the interface fracture energy, torsion stiffness of the pipe, and the geometric properties of the pipe joints. Depending on the torsion stiffness ratio of the pipe and the coupler, the macroscopic-debonding can initiate at the right end, left end or both ends simultaneously. It is interesting to note that the maximum torsion load capacity is achieved when the torsion stiffness of the pipe and the coupler are identical. Good agreement with finite element analysis (FEA) result validates the accuracy of the current model. Fracture energy based formulas of the torsion load capacity derived in the present work can be directly used in the design of adhesively bonded pipe joints.

### MSC:

 74K30 Junctions 74G05 Explicit solutions of equilibrium problems in solid mechanics
Full Text:

### References:

 [1] Adams, R. D.; Peppiatt, N. A.: Stress analysis of adhesive bonded tubular lap joint, Journal of adhesion 9, 1-18 (1977) [2] Atkinson, C.: Stress singularities and fracture mechanics, Applied mechanics review 32, No. 2, 123-135 (1979) [3] Barenblatt, G. I.: The formation of equilibrium cracks during brittle fracture. General ideas and hypothesis, Axisymmetrical cracks, PMM 23, 434-444 (1959) · Zbl 0095.39202 [4] Blackman, B. R. K.; Hadavinia, H.; Kinloch, A. J.; Williams, J. G.: The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints, International journal of fracture 119, 25-46 (2003) [5] Camacho, G. T.; Ortiz, M.: Computational modeling of impact damage in brittle materials, International journal of solids and structures 33, 2899-2938 (1996) · Zbl 0929.74101 [6] Chen, D.; Cheng, S.: Torsional stress in tubular lap joints, International journal of solids and structures 29, No. 7, 845-853 (1992) · Zbl 0825.73093 [7] Cheng, J. C.; Li, G.: Stress analyses of a smart pipe joint integrated with piezoelectric composite layers under torsion loading, International journal of solids and structures 45, 1153-1178 (2008) · Zbl 1169.74370 [8] Chon, C. T.: Analysis of tubular lap joint in torsion, Journal of composite materials 16, 268-284 (1982) [9] Dugdale, D. S.: Yielding of steel sheets containing slits, Journal of the mechanics and physics of solids 8, 100-104 (1960) [10] Graves, S. R.; Adams, R. D.: Analysis of bonded joint in a composite tube subjected to torsion, Journal of composite materials 15, 211-223 (1981) [11] Hilleborg, A.; Modeer, M.; Petersson, P. E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and concrete research 6, 773-782 (1976) [12] Hosseinzadeh, R.; Cheraghi, N.; Taheri, F.: An engineering approach for design and analysis of metallic pipe joints under torsion by the finite element method, Journal of strain analysis for engineering design 41, No. 6, 443-452 (2006) [13] Hutchinson, J. W.; Evans, A. G.: Mechanics of materials: topdown approaches to fracture, Acta materialia 48, 125-135 (2000) [14] Needleman, A.: A continuum model for void nucleation by inclusion debonding, ASME journal of applied mechanics 54, 525-531 (1987) · Zbl 0626.73010 [15] Ouyang, Z., Li, G., 2008. Local damage evolution of DCB specimens during crack initiation process: a natural boundary condition based method. ASME Journal of Applied Mechanics, in press. [16] Pan, J.; Leung, C. K. Y.: Debonding along the FRP-concrete interface under combined pulling/peeling effects, Engineering fracture mechanics 74, 132-150 (2007) [17] Rizzi, E.; Papa, E.; Corigliano, A.: Mechanical behavior of a syntactic foam: experiments and modeling, International journal of solids and structures 37, 5773-5794 (2000) · Zbl 0946.74502 [18] Rose, J. H.; Smith, J. R.; Ferrante, J.: Universal features of bonding in metals, Physical review B 28, 1835-1845 (1983) [19] Tvergaard, V.: Effect of fibre debonding in a whisker-reinforced metal, Material science and engineering 125, 203-213 (1990) [20] Tvergaard, V.; Hutchinson, J. W.: The relation between crack growth resistance and fracture process parameters in elastic-plastic solids, Journal of the mechanics and physics of solids 40, 1377-1397 (1992) · Zbl 0775.73218 [21] Volkersen, O.: Recherches sur la theorie des assemblages colles, Construction mttallique 4, 3-13 (1965) [22] Williams, J. G.; Hadavinia, H.: Analytical solutions for cohesive zone models, Journal of the mechanics and physics of solids 50, 809-825 (2002) · Zbl 1002.74090 [23] Wu, Z. S.; Yuan, H.; Niu, H.: Stress transfer and fracture propagation in different kinds of adhesive joints, Journal of engineering mechanics, ASCE 128, No. 5, 562-573 (2002) [24] Xu, X. P.; Needleman, A.: Void nucleation by inclusion debonding in a crystal matrix, Modeling and simulation in materials science and engineering 1, 111-132 (1993) [25] Zhao, Y.; Pang, S. S.: Stress – strain and failure analyses of pipe under torsion, Journal of pressure vessel technology 117, 273-278 (1995) [26] Zou, G. P.; Taheri, F.: Stress analysis of adhesively bonded sandwich pipe joints subjected to torsional loading, International journal of solids and structures 43, No. 20, 5953-5968 (2006) · Zbl 1120.74614
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.