The 3D Stress Field of a Dislocation Line Outside a Cylindrical Void: A Numerical Collocation Point Method with Verification
Source abstract
Abstract
Material defects resulting from manufacturing and processing can significantly affect material properties. Voids and dislocations are material defects considered in this study, in which a numerical solution of the 3D stress field of a dislocation line (infinite or finite) outside a cylindrical void (either parallel to the cylinder axis or not) is developed using the collocation point method. The collocation point method is utilized to solve ordinary differential equations, partial differential equations, differential-algebraic equations, and integral equations by enforcing the solution at a set of spatial collocation points. Analytical solutions for such three-dimensional (3D) problems, e.g., a dislocation line or segment near an internal void of any shape, were not found. Therefore, a numerical solution for this problem has been constructed in this paper. The numerical solution developed is verified using an existing two-dimensional analytical solution. The numerical results and the 2D analytical solution are in perfect agreement as long as the cylindrical void is sufficiently long and the Saint-Venant’s principle is followed.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Numerical methods in engineering · Metal Forming Simulation Techniques · Metallurgy and Material Forming
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131, USA
References (32)
Show source-provided references
1. Critical stretch for formation of a cylindrical void in a compressible hyperelastic material
2. A review of void reduction strategies in material extrusion-based additive manufacturing
3. Additive manufacturing (3D printing): A review of materials, methods, applications and challenges10.1016/j.compositesb.2018.02.012 ↗
4. Finite-element analysis of cylindrical-void closure by flat-die forging10.2355/isijinternational.53.1420 ↗
5. Prediction of void closure in metal forming: One cylindrical through-hole10.2355/isijinternational.ISIJINT-2018-037 ↗
6. Porosity dependence of mechanical properties of solid materials10.1007/s10853-006-2871-9 ↗
7. The effects of voids on structural properties of fused deposition modelled parts: A probabilistic approach10.1007/s00170-018-2148-x ↗
8. Hull, D., and Bacon, D.J. (2011). Introduction to Dislocations, Butterworth-Heinemann. [5th ed.].10.1016/B978-0-08-096672-4.00003-7 ↗
9. Hirth, J.P., and Lothe, J. (1982). Theory of Dislocations, Krieger Publishing Company. [5th ed.].
10. Stress fields due to dislocation walls in infinite and semi-infinite bodies
11. Dislocation in an infinite poroelastic medium10.1007/BF01177176 ↗
12. Weertman, J., and Weertman, J.R. (1992). Elementary Dislocation Theory, Oxford University Press.
13. The stress field of rectangular prismatic dislocation loops10.1002/1521-396X(200206)191:2<418::AID-PSSA418>3.0.CO;2-H ↗
14. The displacement field of a rectangular Volterra dislocation loop10.1080/09500830210125770 ↗
15. A Dislocation at a Free Surface10.1080/14786436108239675 ↗
16. Interaction of dislocation loop with free surface
17. The dislocation loop near a free surface10.1080/14786437008228153 ↗
18. Analytic formulation of elastic field around edge dislocation adjacent to slanted free surface10.1098/rsos.220151 ↗
19. Hills, D.A., Kelly, P.A., Dai, D.N., and Korsunsky, A.M. (1996). Solution of Crack Problems: The Distributed Dislocation Technique, Springer.10.1007/978-94-015-8648-1 ↗
20. Dislocation dynamics simulations of the interaction between a short rigid fiber and a glide circular dislocation pile-up10.1016/S0927-0256(01)00253-1 ↗
21. Free-surface effects in 3D dislocation dynamics: Formulation and modeling10.1115/1.1479694 ↗
22. A distributed dislocation method for treating free-surface image stresses in three-dimensional dislocation dynamics simulations10.1088/0965-0393/12/4/S01 ↗
23. Numerical methodology for treating static and dynamic dislocation problems near a free surface10.1088/2399-6528/ab8ff9 ↗
24. A mesh-independent brute-force approach for traction-free corrections in dislocation problems
25. Ascher, U.M., and Petzold, L.R. (1998). Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics.10.1137/1.9781611971392 ↗
26. Three dimensional stress field expressions for straight dislocation segments10.1016/0038-1098(94)00894-9 ↗
27. Interaction between an edge dislocation and a circular inclusion10.1016/0022-5096(64)90017-1 ↗
28. Normalization techniques in training DNNs: Methodology, analysis and application10.1109/TPAMI.2023.3250241 ↗
29. The effect of the normalization method used in different sample sizes on the success of artificial neural network model10.21449/ijate.479404 ↗
30. Callister, W.D., and Rethwisch, D.G. (2018). Materials Science and Engineering: An Introduction, Wiley. [10th ed.].
31. Review of collocation methods and applications in solving science and engineering problems
32. Mémoire sur la torsion des prismes