Using fracture mechanics for determining residual stress fields in diverse geometries
Aplicación de la mecánica de la fractura para determinar esfuerzos residuales en diversas geometrías
DOI:
https://doi.org/10.15446/ing.investig.v32n3.35935Keywords:
Crack compliance method, residual stress, non-homogeneous loading (en)Método de respuesta de grieta, esfuerzos residuales, cargas no homogéneas (es)
Component deterioration due to a crack is of the highest importance for the engineering community. Fracture mechanics have mainly been used for studying and evaluating crack or defect nucleation and propagation. This article presents a methodology based on inducing a crack (cut) into mechanical components to characterise an induced residual stress field. This research work's originality was aimed at highlighting fracture mechanics' role in detecting possible component destruction by energetic analysis of crack propagation and evaluating service-life to be used as a technique for characterising the effect of prior loading history regarding a given material. The technique presented in this work is known worldwide as the crack compliance method, based on linear elastic fracture mechanics principles developed by Vaidyanathan and Finnie. Three studies are shown (bent beam, pressurised pipe and modified SEN specimen) where components were induced with a residual stress field. The way non-homogeneous loading could introduce a residual stress field is also presented; if residual stress field acting on a specimen has been characterised, then the mechanical process can be manipulated and a beneficial effect induced into the material.
El deterioro de los componentes debido a falla es un fenómeno que ha recibido constante atención por la comunidad ingenieril. Por su parte, el estudio de la nucleación y propagación de grietas o defectos se analizan principalmente según los principios científicos de la mecánica de la fractura. En este artículo se presenta un método de evaluación desarrollado a partir de la inducción de una grieta (corte) en componentes mecánicos para determinar o caracterizar el campo de esfuerzos residuales actuante. La originalidad de este trabajo resalta en la aplicación de la mecánica de la fractura, que es una ciencia dirigida a detectar la posibilidad de destrucción de un componente mediante el análisis energético de propagación de grietas y evaluación de su vida útil, lo que es utilizado como una técnica para caracterizar el efecto ocasionado por la historia de carga previa en un material. La técnica que aquí se presenta es conocida internacionalmente como método de respuesta de grieta (crack compliance method). Dicho método está fundamentado en principios de mecánica de fractura lineal elástica y fue inicialmente desarrollado por Vaidyanathan y Finnie. En este artículo se presentan tres casos de estudio —viga flexionada, tubo presurizado y probeta SEN modificada— en los cuales los especímenes fueron inducidos con campos de esfuerzos residuales. Asimismo, se presenta la manera como la aplicación de cargas no homogéneas introduce un campo de esfuerzos residuales, al conocer la magnitud y características de este campo es posible manipular el proceso mecánico para producir un efecto benéfico en el material.
Downloads
References
Beghini, M., Bertini, L., Residual stress modeling by experimental measurements and finite element analysis., Journal of Strain Analysis for Engineering Design, Vol. 25, No. 2, 1990, pp. 103-108.
Brandes, E.A., Brook, G.B., (ed.), Smithells Metals Reference Book., 7th ed., USA, Butterworth Heinemann, 1992, pp. 22.1-22.27.
Brinksmeier, E., Cammett, J.T., König, W., Leskovar, P., Peters, J., Tönshoff, H.K., Residual stresses; Measurement and causes in machining processes., CIRP Annals-Manufacturing Technology, Vol. 31, No. 2, 1982, pp. 491-510.
Cheng, W., Finnie, I., Measurement of residual hoop stress in cylinders using the compliance method., Journal of Engineering Material and Technology, Vol. 108, 1986, pp. 87-92.
Cheng, W., Finnie, I., KI solutions for an edge cracked strip., Engineering Fracture Mechanics, Vol. 31, No. 2, 1988, pp. 201-207.
Cheng, W., Finnie, I., The Crack Compliance Method for Residual Stresses Measurement., Welding in the World, Vol. 28, 1990a, pp. 103-110.
Cheng, W., Finnie, I., A KII stress intensity solution for an edge cracked strip., Engineering Fracture Mechanics, Vol. 36, No. 2, 1990b, pp. 355-360.
Cheng, W., Finnie, I., An overview of the crack compliance method for residual stress measurement., Proceedings Fourth International Conference on Residual Stress, Baltimore, Maryland, Society for Experimental Mechanics, 1994, pp. 449-458.
Fett, T., Thun, G., Residual stresses in PVC-cylinders determined with the weight function method., Journal of Engineering Fracture Mechanics, Vol. 55, No. 5, 1996, pp. 859-863.
Fu, W.E., Cohen, P.H., Ruud, C.O., Experimental investigation of the machining induced residual stress tensor under mechanical loading., Journal of Manufacturing Processes, Vol. 11, No. 2, 2009, pp. 88-96.
Galatolo, R., Laciotti, A., Fatigue crack propagation in residual stress fields of welded plates., International Journal of Fatigue, Vol. 19, No. 1, 1997, pp. 43-49.
Gilbert, J.L., Buckley, C.A., Jacobs, J.J., Bertin, K.C., Zernich, M.R., Intergranular corrosion-fatigue failure of Cobaltalloy femoral stems; A failure analysis of two implants., Journal of Bone and Joint Surgery, Vol. 76, No. 1, 1994, pp. 110-115.
Green, D.J., Tandon, R., Sglavo, M.V., Crack arrest and multiple cracking in glass through the use of designed residual stress profiles., Science, Vol. 283, No. 5406, 1999, pp. 1295-1297.
Hahn, G.T., Kanninen, M.F., (ed.), Crack Arrest Methodology and Applications., American Society for Testing and Materials, 1980.
Hermann, R., Crack growth and residuals stress in Al-Li metal matrix composites under far-field cyclic compression., Journal of Material Science, Vol. 30, 1995, pp. 3782-3790.
Hernández-Gómez, L.H., Urriolagoitia-Calderón, G., Urriolagoitia-Sosa, G., Sandoval-Pineda, J.M., Merchán-Cruz, E.A., Guardado-García, J.F., Assessment of the structural integrity of cracked cylindrical geometries applying the EVTUBAG program., Revista Técnica de Ingeniería de la Universidad de Zulia, Vol. 32, No. 3, 2009, pp. 190-199.
Irwin, G.R., Analysis of stresses and strains near the end of a crack traversing a plate., Journal of Applied Mechanics, Vol. 24, 1957, pp. 361-363.
John, R., Jata, K.V., Sadananda, K., Residual stress effects on near-threshold fatigue crack growth in friction stir welds in aerospace alloys., International Journal of Fatigue, Vol. 25, No. 9-11, 2003, pp. 939-948.
Jones, K.W., Dunn, M.L., Fatigue crack growth through a residual stress field introduced by plastic beam bending., Journal of Fatigue and Fracture of Engineering Materials and Structures, Vol. 31, No. 10, 2008, pp. 863-875.
Kang, K.J., Song, J.H., Earmme, Y.Y., A method for the measurement of residual stresses using a fracture mechanics approach., Journal Strain Analysis for Mechanical Design, Vol. 24, 1989, pp. 23-30.
Kohn, L.T., Corrigan, J., Donalson, M.S., (ed.), To Err is Human; Building a Safer Health System., USA, Institute of Medicine; Committee on Quality of Health Care in America, 2010, pp. 63-65.
Kudryavtsev, Y.F., Residual Stress, Springer Handbook of Experimental Solid Mechanics, W.N. Sharpe Jr., (ed.), Springer SEM, 2008, pp. 371-386.
Lai, M.O., Siew, Y.H., Fatigue properties of cold worked holes., Journal of Materials Processing Technology, Vol. 48, 1995, pp. 533-540.
Löhe, D., Lang, K.H., Vöhringer, O., (ed.), Residual stress and fatigue behavior., Handbook of Residual Stress and Deformation of Steel, USA, ASM International, 2002, pp. 27-53.
Lu, J., James, M., Roy, G., (ed.), Handbook of Measurements of Residual Stress., USA, Fairmont Press, Inc., 1996.
Molina-Ballinas, A., Evaluación y determinación experimental-numérica del endurecimiento por deformación y el efecto Bauschinger en las propiedades mecánicas de un acero inoxidable., MSc thesis SEPI-ESIME, Instituto Politécnico Nacional, México, 2010.
National Research Council, (ed.), Improving the Continued Air-worthiness of Civil Aircraft; A Strategy for the FAA´S Aircraft Certification Service., USA, National Academy Press, 1998, pp. 24.
Nervi, S., Szabó, B.A., Young, K.A., Prediction of distortion of air-frame components made from aluminum plates., AIAA Journal, Vol. 47, No. 7, 2009, pp. 1635-1641.
Nowell, D., Tochilin, S., Hills, D. A., Measurement of residual stress in beams and plates using the crack compliance technique., Journal Strain Analysis for Mechanical Design, Vol. 35, No. 4, 2000, pp. 277-285.
O'Connor, P.D.T., Newton, D., Bromley, R., (ed.), Practical Reliability Engineering., 4a ed., England, John Wiley and Sons, Inc., 2002, pp. 1-20.
Oh, J.T., Lai, M.O., Nee, A.Y.C., Stress analysis of a ballised hole., Journal of Materials Processing Technology, Vol. 37, 1993, pp. 137-147.
Orkisz, J., Skrzat, A., Reconstruction of residual stresses in railroad vehicle wheels based on enhanced saw cut measurements; Formulation and benchmark tests., Wear, Vol. 191, 1996, pp. 188-198.
Peyre, P., Scherpereel, X., Berthe, L., Carboni, C., Fabbro, R., Béranger, G., Lamaitre, C., Surface modifications induced in 316L steel by laser peening and shot-peening; Influence on pitting corrosion resistance., Materials Science and Engineering A, Vol. 280, No. 2, 2000, pp. 294-302.
Prime, M.B., Residual stress measurement by successive extension of a slot; The crack compliance method., Applied Mechanics Reviews, Vol. 52, No. 2, 1999, pp. 75-96.
Prime, M.B., Prantil, V.C., Rangaswamy, P., Garcia, F.P., Residual stress measurement and prediction in a hardened steel ring., Materials Science Forum, Vols. 347-349, 2000, pp. 223-228.
Reid, C.N., A method of mapping residual stress in a compact tension specimen., Scripta Metallurgica, Vol. 22, No. 4, 1988, pp. 451-456.
Ritchie, D., Leggatt, R.H., The measurement of the distribution of residual stress through the thickness of a welded joint., Strain, Vol. 23, No. 2, 1987, pp. 61-70.
Romero-Ángeles, B., Aplicación de multicargas para el arresto de grietas., MSc thesis, SEPI-ESIME, Instituto Politécnico Nacional, México, 2009.
Schindler, H.J., Bertsschinger, P., Some steps towards automation of the Crack Compliance Method to measure residual stress distribution., 5th International Conference on Residual Stresses, Sweden, 1997, pp. 682-687.
Schindler, H.J., Cheng, W., Finnie, I., Measurement of the residual stress distribution in a disk or cylinder using the crack compliance method., Proceedings Fourth International Conference on Residual Stress, Baltimore, Maryland, Society for Experimental Mechanics, 1994, pp. 1266-1274.
Schindler, H.J., Landolt, R., Experimental determination of residual stress and the resulting stress intensity factors in rectangular plates., 4th European Conference on Residual Stresses (ECRS4), Cluny, France, 1997, pp. 509-517.
Schwaighofer, J., Determination of residual stresses on the surface of structural parts., Experimental Mechanics, Vol. 4, No. 2, 1964, pp. 54-56.
Todd, J.D., (ed.), Structural Integrity and Analysis., 2a ed., USA, McMillan Publishers, Ltd., 1981, pp. 181-189.
Urriolagoitia-Calderón, G., Hernández-Gómez, L.H., Villa y Rabasa, G., Urriolagoitia-Sosa, G., Medina-Velarde, J.L., Vázquez-Mendoza, H.H., León-Vega, C., Solución conceptual del comportamiento de una probeta agrietada sometida a cargas de fatiga para determinar su vida remanente., Científica, Año 1, No. 5, Sep.-Oct., 1997, pp. 39-42.
Urriolagoitia-Sosa, G., Analysis of prior strain history effect on mechanical properties and residual stresses in beams., PhD thesis presented at the University of Oxford Brookes, Oxford, Inglaterra, 2005.
Urriolagoitia-Sosa, G., Durodola, J.F., Fellows, N.A., Determination of residual stress in beams under Bauschinger effect using surface strain measurements., Strain, Vol. 39, No. 4, 2003, pp. 177-185.
Urriolagoitia-Sosa, G., Durodola, J.F., Fellows, N.A., Effect of strain hardening on residual stress distribution in beams determined using the crack compliance method., Journal Strain Analysis for Mechanical Design, Vol. 42, No. 2, 2007, pp. 115-121.
Urriolagoita-Sosa, G., Romero-Ángeles, B., Hernández-Gómez, L.H., Urriolagoita-Calderón, G., Beltrán-Fernández, J.A., Torres-Torres, C., Evaluation of the impact of residual stresses in crack initiation with the application of the Crack Compliance Method; Part I, Numerical analysis., Applied Mechanics and Materials, Vol. 24-25, 2010a, pp. 253-259.
Urriolagoita-Sosa, G., Romero-Ángeles, B., Hernández-Gómez, L.H., Urriolagoita-Calderón, G., Beltrán-Fernández, J.A., Torres-Torres, C., Evaluation of the impact of residual stresses in crack initiation with the application of the Crack Compliance Method; Part II, Experimental analysis., Applied Mechanics and Materials, Vol. 24-25, 2010b, pp. 261-266.
Urriolagoita-Sosa, G., Molina-Ballina, A., Urriolagoitia-Calderón, G., Hernández-Gómez, L.H., Sandoval-Pineda, J.M., Characterization of strain hardening behavior and residual stress induction used for crack arrest in a biocompatible material., Material Research Society, Vol. 1242, 2010c, pp. 233-239.
Urriolagoitia-Sosa, G., Sandoval-Pineda, J.M., Merchán-Cruz, E.A., Rodríguez-Cañizo, R.G., Urriolagoitia-Calderón, G., Hernández-Gómez, L.H., Rodríguez-Martínez, R., Torres-Martínez, R., Experimental application of the Crack Compliance Method in beams with hardened surfaces., Revista Mexicana de Física, Vol. 55, No. 1, 2009, pp. 30-33.
Vaidyanathan, S., Finnie, I., Determination of residual stresses from stress intensity factor measurements., Journal of Basic Engineering, Vol. 93, 1971, pp. 242-246.
Withers, P.J., Bhadeshia, H.K.D.H., Residual stress; Part 1-Measurement techniques., Journal of Materials Science and Technology, Vol. 17, No. 4, 2001, pp. 355-365.
License
Copyright (c) 2012 Guillermo Urriolagiotia Sosa, Guillermo Urriolagiotia Calderón, Beatriz Romero Ángeles, David Torres Franco, Luis Héctor Hernández Gómez, Arafat Molina Ballinas, Christopher René Torres San Miguel, Juan Pablo Campos López

This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:
1. The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;
2. The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;
3. The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;
4. The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.










