Abstract
The present work deals with the strength scaling to characterize size effect of the cylindrical ceramic specimen for bimodular materials. The analysis is based on Weibull statistical theory. The derived semi-analytical expressions for effective volume and effective surface area for characterizing volume and surface flaws, respectively, have been validated with the experimental based numerical model. The flexural testing on cylindrical specimens has been done. The characteristic unimodular and bimodular strength has been estimated with different estimators like linear regression and maximum likelihood estimators for two different sized flexural specimens. The strength distribution analysis is controlled by 90% of the confidence interval, and coefficient of determination has been tabulated for goodness of the fit of Weibull distribution curve. The numerical based unimodular and bimodular models have been developed and also its post-processing code has been developed to evaluate the effective volume and surface area numerically. The comparison has been made for different fracture criteria such as principal of independent action (PIA) and normal stress averaging (NSA).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
B. Saint-Venant, Notes to Navier’s Resume des lecons dela resistance des corps solids, 3rd edn. (Paris, 1864)
S. Timoshenko, Strength of Materials, Part 2, Advanced Theory and Problems, 2nd edn. (Van Nostrand, Princeton, NJ, 1941)
J. Marin, Mechanical Behavior of Engineering Materials (Prentice-Hall, Englewood Cliffs, NJ, 1962)
A.A. Ambartsumyan, S.A. Khachatryan, Elasticity for Materials with Different Resistance to Tension and Compression, Mekhanika Tverdogo Tela (in Russian), vol. 2 (1966)
S.A. Ambartsumyan, The axisymmetric problem of a circular cylindrical shell made of material with different strength in tension and compression. Izvestia. Mekhanika, vol. 4 (1965), pp. 1055–1067. http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0675312
S.A. Ambartsumyan, A.A. Khachatryan, A Multi-modulus elasticity theory. Mekhanika Tverdogo Tela 6, 64–67 (1966)
S.A. Ambartsumyan, Equations for a plane problem of the multi-modulus theory of elasticity. Isvestia An Armyaskoy SSR, Mekhanika, vol. 2 (1966)
C.W. Bert, Model for fibrous composites with different properties in tension and compression. J. Eng. Mater. Technol. ASME 99, 344–349 (1977)
C.W. Bert, F. Gordaninejad, Deflection of thick beams of multimodular materials. Int. J. Numer. Meth. Eng. 20, 479–503 (1984)
C.W. Bert, J.N. Reddy, V.S. Reddy, W.C. Chao, Bending of thick rectangular plates laminated of bimodulus composite materials. AIAA J. 19, 1342–1349 (1981). https://doi.org/10.2514/3.60068
C.W. Bert, J.N. Reddy, Mechanics of bimodular composite structures, in Mechanics of Composite Materials, Recent Advances, pp. 323–337 (1983)
A.E. Green, J.Z. Mkrtichian, Elastic solids with different moduli in tension and compression. J. Elast. 7, 369–386 (1977). https://doi.org/10.1007/BF00041729
N.G. Isabekian, A.A. Khachatryan, On the multimodulus theory of elasticity of anisotropic bodies in plane stress state. Ivestiya Akademii Nauk Armianskoi SSR, Mekhanika 22, 25–34 (1969)
R.M. Jones, Stress-strain relations for materials with different moduli and compression. AIAA 15, 16–23 (1977)
R.M. Jones, Buckling of stiffened multilayered circular cylindrical shells with different orthotropic moduli in tension and compression. AIAA 9, 917–923 (1971)
A. Bhushan, S.K. Panda, D. Khan, A. Ojha, K. Chattopadhyay, H.S. Kushwaha, I.A. Khan, Weibull effective volumes, surfaces, and strength scaling for cylindrical flexure specimens having bi-modularity. J. Test. Eval. ASTM 44, 1977–1997 (2016). https://doi.org/10.1520/JTE20150301
G.D. Quinn, Weibull strength scaling for standardized rectangular flexure specimens. J. Am. Ceram. Soc. 10, 508–510 (2003)
G.D. Quinn, Weibull effective volumes and surfaces for cylindrical rods loaded in flexure. J. Am. Ceram. Soc. 86, 475–479 (2003). https://doi.org/10.1111/j.1151-2916.2003.tb03324.x
F.T. Peirce, Tensile tests for cotton Yarns v.—“The Weakest Link” theorems on the strength of long and of composite specimens. J. Text. Inst. Trans. 17, T355–T368 (1926). https://doi.org/10.1080/19447027.1926.10599953
W. Weibull, The phenomenon of rupture in solids. Proc. R. Swed. Inst. Eng. Res. 153, 1–55 (1939)
W. Weibull, A statistical distribution function of wide applicability. J. Appl. Mech. 18, 293–297 (1951). citeulike-article-id:8491543
D.L. Shelleman, O.M. Jadaan, J.C. Conway, J.J. Mecholsky, Prediction of the strength of ceramic tubular components: part I—analysis. J. Test. Eval. 19, 192–200 (1991). https://doi.org/10.1520/JTE12556J
WeibPar V-4.3 and CARES V-9.3, WeibPar (Weibull Distribution Parameter Estimation) V-4.3 and CARES (Ceramics Analysis and Reliability Evaluation of Structures) V-9.3, Developed by Life Prediction Banch NASA Glenn Research Center, Procured by Connecticut Reserve Technologies; Inc., (n.d.)
Acknowledgements
Financial support from the Board of Research on Nuclear Sciences, Department of Atomic Energy, India (Project Sanction No. 2011/36/62-BRNS) is greatly acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Bhushan, A., Panda, S.K. (2020). Size Effect in Bimodular Flexural Cylindrical Specimens. In: Varde, P., Prakash, R., Vinod, G. (eds) Reliability, Safety and Hazard Assessment for Risk-Based Technologies. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-9008-1_33
Download citation
DOI: https://doi.org/10.1007/978-981-13-9008-1_33
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9007-4
Online ISBN: 978-981-13-9008-1
eBook Packages: EngineeringEngineering (R0)