Round bar notch shape optimization for tensile stress concentration testing
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Murat Ozsoy
Dr. Murat Ozsoy received his bachelor’s degree in 1996 in Mechanical Engineering from Balıkesir University, his master’s degree in 1998 and his PhD degree in 2005 in Mechanical Engineering from Sakarya University, Turkey. He is currently an associate professor in the Department of Mechanical Engineering at Sakarya University. His research interests include CAD, CAM, CAE and composite materials.
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Toros Arda Akşen
Toros Arda Akşen is a research assistant at the University of Sakarya. He received his bachelor’s degree in Mechanical Engineering in 2012 from Bursa Uludağ University and his master’s degree in Mechanical Engineering from the University of Sakarya. He started his Ph.D. education in 2017 at the University of Sakarya and continues. Ductile fracture, cyclic plasticity, and sheet metal forming are his primary topics of interest.
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Seçil Ekşi
Associate Prof. Dr. Seçil Ekşi works in the Department of Mechanical Engineering at Engineering Faculty, Sakarya University, Sakarya, Turkey. She received a B.Sc. degree and M.Sc. degree in Mechanical Engineering from Sakarya University, Sakarya, Turkey, in 2004 and 2006, respectively, and a PhD degree in Mechanical Engineering from Sakarya University, Sakarya, Turkey, in 2014. Her research interests include materials, mechanical behavior of material, composite materials, manufacturing, finite element analyses.
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Neslihan Ozsoy
Dr. Neslihan Ozsoy received her bachelor’s degree in 2006, her master’s degree in 2008 and her PhD degree in 2015 in Mechanical Engineering from Sakarya University, Turkey. She is currently an assistant professor in the Department of Mechanical Engineering at Sakarya University. Her research interests include optimization, mechanics of materials, composite materials, machining, and tribology.
and
Mehmet Firat
Dr. Mehmet Firat is a Professor at the University of Sakarya, Turkey. He received his bachelor’s degree from Middle East Technical University, his Ph.D. in Mechanical Engineering from the University of Sakarya in 2003. His research interests include cyclic plasticity, fatigue, sheet metal forming, and computational mechanics.
Abstract
Notched structures in machine parts for several reasons cause discontinuity and stress concentration. It is essential to optimize these stress concentrations in notched parts. This study determined the best notch shape by creating different notch shapes by keeping two key points fixed on the spline curve in the notched region. This paper involves optimizing the shape of a fillet in a notched tension bar. An optimal shape was aimed to minimize the notch factor without causing yield anywhere in the bar by parametrically controlling the spline of the fillet via ANSYS parametric design language code. Optimal shapes of B-spline curves were obtained for round bars subject to axial tension loadings. Changing the code can also be used for bending or combined loading conditions other than tensile loading.
About the authors
Dr. Murat Ozsoy received his bachelor’s degree in 1996 in Mechanical Engineering from Balıkesir University, his master’s degree in 1998 and his PhD degree in 2005 in Mechanical Engineering from Sakarya University, Turkey. He is currently an associate professor in the Department of Mechanical Engineering at Sakarya University. His research interests include CAD, CAM, CAE and composite materials.
Toros Arda Akşen is a research assistant at the University of Sakarya. He received his bachelor’s degree in Mechanical Engineering in 2012 from Bursa Uludağ University and his master’s degree in Mechanical Engineering from the University of Sakarya. He started his Ph.D. education in 2017 at the University of Sakarya and continues. Ductile fracture, cyclic plasticity, and sheet metal forming are his primary topics of interest.
Associate Prof. Dr. Seçil Ekşi works in the Department of Mechanical Engineering at Engineering Faculty, Sakarya University, Sakarya, Turkey. She received a B.Sc. degree and M.Sc. degree in Mechanical Engineering from Sakarya University, Sakarya, Turkey, in 2004 and 2006, respectively, and a PhD degree in Mechanical Engineering from Sakarya University, Sakarya, Turkey, in 2014. Her research interests include materials, mechanical behavior of material, composite materials, manufacturing, finite element analyses.
Dr. Neslihan Ozsoy received her bachelor’s degree in 2006, her master’s degree in 2008 and her PhD degree in 2015 in Mechanical Engineering from Sakarya University, Turkey. She is currently an assistant professor in the Department of Mechanical Engineering at Sakarya University. Her research interests include optimization, mechanics of materials, composite materials, machining, and tribology.
Dr. Mehmet Firat is a Professor at the University of Sakarya, Turkey. He received his bachelor’s degree from Middle East Technical University, his Ph.D. in Mechanical Engineering from the University of Sakarya in 2003. His research interests include cyclic plasticity, fatigue, sheet metal forming, and computational mechanics.
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Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Research funding: None declared.
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Conflict of interest statement: The authors state no conflict of interest.
Annex A: Engine code implemented to ANSYS software
The workflow of the engine code is explained below step by step.
1. The mechanical properties and the element type are described in the code as follows.
| ANTYPE, STATIC |
| /PREP7 |
| ET,1,PLANE42 |
| KEYOPT,1,1,0 |
| KEYOPT,1,2,0 |
| KEYOPT,1,3,1 |
| KEYOPT,1,5,0 |
| KEYOPT,1,6,0MP, NUXY,1,0.3 |
| ET,2, SOLID186 |
| MP, NUXY,1,0.3 |
| MP, EX,1,2E5 |
2. The intervals of the Δx and Δy are adjusted as demonstrated below.
| DLTX_MIN = 0.1 |
| DLTX_MAX = 0.9 |
| DLTY_MIN = 0.1 |
| DLTY_MAX = 0.9 |
3. The arrays of Δx and Δy are created. Ten increments are considered for disintegrating these arrays. Therefore, the distances corresponding to these increments are determined.
| N_INC = 8 |
| DLTX_MIN = 0.1 |
| DLTX_MAX = 0.9 |
| DLTY_MIN = 0.1 |
| DLTY_MAX = 0.9 |
| *DIM,DLTX,ARRAY,N_INC+1,1,1 |
| *DIM,DLTY,ARRAY,N_INC+1,1, |
| *DO,I,1,N_INC+1,1 |
| DLTX(I) = DLTX_MIN + (I-1)*(DLTX_MAX-DLTY_MIN)/N_INC |
| DLTY(I) = DLTY_MIN + (I-1)*(DLTY_MAX-DLTY_MIN)/N_INC |
| *ENDDO |
| *DIM,CASE_RES,ARRAY,N_INC+1,N_INC+1,1 |
| *DO, I,1, N_INC+1,1 |
| *DO, J,1, N_INC+1,1 |
| DELTAX = DLTX(I) |
| DELTAY = DLTY(J) |
4. The key points are assigned in order to create the geometric model. Subsequently, the lines are created through these key points.
| /PREP7 |
| K,1,12.7,0,0, |
| K,2,0,0,0, |
| K,3,0,40,0, |
| K,4,0,127,0, |
| K,5,25.4,127,0, |
| K,6,25.4,40,0, |
| K,7,25.4,12.7,0, |
| /AUTO, 1 |
| /REP |
| LSTR, 1, 2 |
| LSTR, 2, 3 |
| LSTR, 3, 4 |
| LSTR, 4, 5 |
| LSTR, 5, 6 |
| LSTR, 6, 7 |
| LSTR, 3, 6 |
| /AUTO, 1 |
| /REP |
5. For the parametric study, the dimensions of the notch root cross-section are described. The coordinates corresponding to the control points on the Bezier curve are parametrically defined.
| P1X = 12.7 |
| P1Y = 0 |
| P2X = 12.7 |
| P2Y = 12.7 − (DELTAY*12.7) |
| P3X = 12.7 + (12.7*DELTAX) |
| P3Y = 12.7 |
| P4X = 25.4 |
| P4Y = 12.7 |
6. The coefficients of the cubic Bezier curve are calculated, and the relevant curve equation is established.
| X = 0 |
| Y = 0 |
| H = 8 |
| *DO, IK,0.1,0.90,0.1 |
| H = H + 1 |
| B = (1-IK)**3 |
| c = (1-IK)**2 |
| D = (1-IK) |
| E = 3*IK*C |
| F = 3*IK**2*D |
| G = IK**3 |
| K,H,(P1X*B)+(P2X*E)+(P3X*F)+(P4X*G) ,(P1Y*B)+(P2Y*E)+(P3Y*F)+(P4Y*G) |
| *ENDDO |
7. The notch curve is discretized by the lines, and these lines are combined successively. The edge points of the notch curve are also associated with the initially generated points of the specimen.
| LSTR, 1, 9 |
| *DO,JX,9,H-1,1 |
| LSTR, JX, JX+1 |
| *ENDDO |
| LSTR, H, 7 |
| /AUTO, 1 |
| /REP |
| FLST,2, H-7,4 |
| *DO, JP,8, H,1 |
| FITEM,2, JP |
| *ENDDO |
| LCOMB, P51X, 0 |
| /AUTO, 1 |
| /REP |
8. Since a closed profile of the specimen (quarter section) was generated, the area is defined using the curves of the profile. Two areas were generated in order to create a convenient mesh layout.
| FLST,2,5,4 |
| FITEM,2,1 |
| FITEM,2,2 |
| FITEM,2,7 |
| FITEM,2,6 |
| FITEM,2,8 |
| AL, P51X |
| FLST,2,4,4 |
| FITEM,2,7 |
| FITEM,2,3 |
| FITEM,2,4 |
| FITEM,2,5 |
| AL, P51X |
| /AUTO, 1 |
| /REP |
9. The created areas were combined through glue contact type.
| FLST,2,2,5, ORDE,2 |
| FITEM,2,1 |
| FITEM,2,-2 |
| AGLUE, P51X |
| /AUTO, 1 |
| /REP |
10. The curve line divisions to create the mesh layout are determined. Since the notch is the critical zone, the element density along the notch was kept high. Subsequently, the area is meshed with plane42 elements. The meshed lines were also merged.
| FLST,5,1,4, ORDE,1 |
| FITEM,5,8 |
| CM,_Y,LINE |
| LSEL, P51X |
| CM,_Y1,LINE |
| CMSEL, _Y |
| LESIZE, _Y1, 30, 1 |
| FLST,5,6,4, ORDE,2 |
| FITEM,5,2 |
| FITEM,5,-7 |
| CM,_Y,LINE |
| LSEL, P51X |
| CM,_Y1,LINE |
| CMSEL, _Y |
| LESIZE, _Y1,1.733, 1 |
| /AUTO, 1 |
| /REP |
| FLST,2,2,4,ORDE,2 |
| FITEM,2,2 |
| FITEM,2,7 |
| LCCAT, P51X |
| FLST,5,2,5, ORDE,2 |
| FITEM,5,1 |
| FITEM,5,-2 |
| CM,_Y,AREA |
| ASEL, P51X |
| CM,_Y1,AREA |
| CHKMSH, ‘AREA’ |
| CMSEL,S,_Y |
| MSHKEY,1 |
| AMESH, _Y1 |
| MSHKEY,0 |
| CMDELE, _Y |
| CMDELE, _Y1 |
| CMDELE, _Y2 |
| /AUTO, 1 |
| /REP |
11. The boundary conditions are applied to the specimen. These boundary conditions comprise symmetry conditions and an applied pressure (Figure 5a). Since the specimen is modelled in 2D, the force is applied on the specimen as the line pressure.
| FINISH |
| /SOL |
| FLST,2,3,4,ORDE,2 |
| FITEM,2,1 |
| FITEM,2,-3 |
| DL,P51X, ,SYMM |
| /AUTO, 1 |
| /REP |
| FLST,2,1,4,ORDE,1 |
| FITEM,2,4 |
| /GO |
| SFL,P51X,PRES,-0.25 |
| /AUTO, 1 |
| /REP |
12. Finally, the FE simulation is performed. Then the post-processor was activated.
| /SOL |
| /STATUS,SOLU |
| SOLVE |
| /AUTO, 1 |
| /REP |
| /AUTO, 1 |
| /REP |
| /POST1 |
| SET,LAST |
| /EFACET,1 |
| PLNSOL, S,Y, 0,1.0 |
| /AUTO, 1 |
| /REP |
13. In the post-process section, the maximum stress values in the y direction are obtained from the simulations for different cases, and these values were written to an output file.
| *GET,NELEM,ELEM,COUNT |
| *GET,NNODES,NODE,COUNT |
| NSORT,S,Y |
| *GET,SYY_MAX,SORT,MAX |
| CASE_RES(I,J) = SYY_MAX |
| FINISH |
| /SOL |
| LSCLEAR,FE |
| FINISH |
| /PREP7 |
| FLST,2,2,5,ORDE,2 |
| FITEM,2,1 |
| FITEM,2,-2 |
| ACLEAR,P51X |
| GPLOT |
| FLST,2,2,5,ORDE,2 |
| FITEM,2,1 |
| FITEM,2,-2 |
| ADELE,P51X, 1 |
| GPLOT |
| LDELE, 2, 1 |
| GPLOT |
| *ENDDO |
| *ENDDO |
| *CFOPEN, ‘Notch_Bar_Solution_2D_1’, ‘TXT’ |
| *VWRITE,CASE_RES(1,1),CASE_RES(1,2),CASE_RES(1,3),CASE_RES(1,4),CASE_RES(1,5),CASE_RES(1,6),CASE_RES(1,7),CASE_RES(1,8),CASE_RES(1,9) |
| (11E18.5) |
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Articles in the same Issue
- Frontmatter
- Microstructure and properties of argon arc cladded CoCr x FeMoNiAl high entropy alloy coatings on Q235 steel
- Effects of different profiled pins used in friction stir welding of Al 6061 T6
- Effect of Ti3O5 addition on oxide evolution for HRB400
- Bulge test technique and digital image correlation for the determination of the biaxial behavior of polymeric films
- Effect of Cu addition on microstructure and corrosion behavior of Al–15Mg2Si composite
- Fracture failure analysis of an offshore drilling centralizer
- Influence of tool plunging rate on mechanical properties and microstructure of friction stir welded DMR249A high strength low alloy (HSLA) steel butt joints
- Modelling boron diffusion for Fe2B layer formation: comparative kinetics analysis in pack-boronized AISI 4147 steel
- Round bar notch shape optimization for tensile stress concentration testing
- Analysis of tool wear and surface roughness in machining of AISI 4462 duplex stainless steel
- Effects of build orientation and hatch spacing on high-speed milling behavior of L-PBF 316L stainless steel
- Physical and chemical properties of beads glasses
- Effect of polyurethane matrix and steel fiber in combination with glass fiber or basalt fiber on the properties of hybrid composite laminates
- Calibration of photoelastic materials with the disc under diametral compression
