MODELING AND VALIDATING RESIDUAL STRESSES IN THICK- WALLED CYLINDERS

Transcription

1 May 16-18, 2018, Minneapolis, MN, USA VVS MODELING AND VALIDATING RESIDUAL STRESSES IN THICK- WALLED CYLINDERS Zhong Hu, Ph.D. Professor of Mechanical Engineering Department South Dakota State University, Brookings, SD 57007, USA Phone: (605) , Fax: (605) ResearchGate Website:

2 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 2 Presentation Outlines 1. Introduction 2. Autofrettage Processes 3. Modeling Of Swage Autofrettage Processes 4. Validation by Sachs Boring Technique 5. Validation by Neutron Diffraction Measurements 6. Modeling Comparison between ANSYS and ABAQUS 7. Conclusions Acknowledgements

3 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 3 1. Introduction Piping system of a nuclear power plant Piping systems of chemical plant Gun Barrel

4 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 4 Stresses in a Thick-Walled Pressurized Cylinder Basic Assumptions: Static loads Isotropic and homogenous material Constant temperature Elasto-plastic and small deformation Open ended. Ignoring axial load (stress) Cross section keeping plane after deformation Stresses in thick-wall cylinder. (a) Thin annulus. (b) Cylindrical volume element.

5 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 5 Elastic Analysis (Lamé Equations): Equilibrium Equation Hooke s Law (stress-strain relations) Strain-Displacement Relations Stress Components under Internal and External Pressure (Lamé Equations): Strain Compatibility Condition

6 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 6 Stress Components under Internal Pressure Only Radial stress distribution Hoop (tangential) stress distribution Large tensile hoop stress will initiate crack and accelerate crack propagation and shorten the service life.

7 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 7 Hoop Stress,, Distribution in A Single Layer Thick- Wall Cylinder. 2 1 b/a = 1.5 σθ/p Normalized radial position (%) b/a = 2 p2/p1=0 p2/p1=0.5 p2/p1=1 p2/p1=1.5 p2/p1=2 σθ/p Normalized radial position (%) p2/p1=0 p2/p1=0.5 p2/p1=1 p2/p1=1.5 p2/p1=2

8 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 8 2. Autofrettage Processes To improve the performance of an internal pressurized thickwalled cylinder, favorable compressive residual stresses can be produced near the bore of the cylinder, commonly by an autofrettage process prior to use. Autofrettage is a metal fabrication technique in which a pressure vessel is subjected to enormous pressure, causing internal portions of the part to yield plastically, resulting in internal compressive residual stresses once the pressure is released. Goal of autofrettage: is to increase the durability of the final product. Inducing residual compressive stresses (hoop and axial) into materials can also increase their resistance to stress corrosion cracking. Classification of autofrettage: Hydraulic autofrettage, Double-layer autofrettage, Swage autofrettage, Explosive autofrettage, Thermal Explosive Bonded Ring autofrettage, Rotational autofrettage.

9 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 9 Hydraulic Autofrettage Process High pressure (dangerous) and partial autofrettaged (low efficient and high cost) Z. Hu and S. Puttagunta. Computer modeling of internal pressure autofrettage process of a thick-walled cylinder with the Bauschinger effect. American Transactions on Engineering & Applied Sciences, 1(2)(2012)

10 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 10 Two layer cylinder tapered in dimension so that one can slide into another, generating prestressed assembly. High cost and low improvement Double-layer Autofrettage Process With (right) or without (left) internal pressure Z. Hu. Design and modeling of internally pressurized thick-walled cylinder NDIA Conference, Dallas, TX, May 17-20, 2010

11 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 11 Explosive Autofrettage Process The large internal pressure, developed after detonation of the explosive, force the piston to accelerate radially outward at the beginning and then reverse itself inwardly. The process is hard to control, dangerous and cost. J. D. Mote, et al. Explosive autofrettage of cannon barrels. Final Report Contract DAAG46-69-C-0061, Army Materials and Mechanics Research Center, Watertown, MA, Feb. 24, 1971

12 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 12 Stress field is generated due to the temperature gradient developed between outer and inner wall of the cylinder. Thermal Autofrettage Process Left: Autofrettage elastic-plastic stresses; Middle: Residual stresses; Right: Overall stresses. S.M Kamal and U. S. Dixit. Feasibility study of thermal autofrettage process. 5th International & 26th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12th 14th, 2014, IIT Guwahati, Assam, India

13 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 13 Rotational Autofrettage Process Large enough angular velocity in a thick-walled cylinder generates centrifugal force, causing beneficial residual stress which is the prerequisite of the autofrettage process. H. R. Zare and H. Darijani. Strengthening and design of the linear hardening thick-walled cylinders using the new method of rotational autofrettage. Int J Mechanical Sciences, (2017)1-8.

14 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 14 Swage Autofrettage Process Carried out by mechanically pushing a profiled oversized mandrel (or swage) through a thick-walled cylinder, thereby gradually causing plastic deformation from one end to the other end to the inner layer by radial interference and creating a favorable compressive residual hoop stress in the inner layer of the cylinder. It requires a significantly lower pressure to drive the mandrel as compared to the hydraulic method, and is energy efficient and safe. M. C. Gibson, et al. Investigation of residual stress development during swage autofrettage, using finite element analysis. J Pressure Vessel Technology 134(2014) ~7

15 Modeling and Validating Residual Stresses in Tick-Walled Cylinders Modeling of Swage Autofrettage Process Case study: A 105mm cannon barrel, modeled as a thick-walled cylinder, made of high-pressure vessel steel ASTM A Z. Hu. Design of two-pass swage autofrettage processes of thick-walled cylinders by computer modeling. Proc IMechE Part C: J Mechanical Engineering Science, 2018 Z. Hu. and C. Penumarthy. Computer modeling and optimization of swage autofrettage process of a thick-walled cylinder incorporating Bauschinger effect. American Transactions on Engineering & Applied Sciences, 3(1)(2014)31-63.

16 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 16 Material model (nonlinear kinetic hardening with Bauschinger effect) for cannon barrel A723, and meshed finite element model for swage autofrettage process

17 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 17 Modeling Results (Radial Stress) Swage on halfway Swage removed (residual stress)

18 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 18 Modeling Results (Hoop Stress) Swage on halfway Swage removed (residual stress)

19 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 19 Modeling Results (Axial Stress) Swage on halfway Swage removed (residual stress)

20 Modeling and Validating Residual Stresses in Tick-Walled Cylinders Validation by Sachs Boring Technique Procedure of the Sachs Boring Technique Prepare (e.g. smooth and degrease) the component surface at the strain gauge locations. Glue the strain gauges to the component and attach the lead wires. Align the component to the cutting machine. Bore out or turn down the component in a series of increments. Record the new diameter and strain gauge readings for each incremental layer removed. Analyze the diameter and strain gauge data to calculate the residual stress distribution. SACHS BORING TECHNIQUE at T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

21 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 21 Fundamentals of Sachs Boring Techniques From the Lamé Equations for elastic stresses in thick-walled cylinders, the change in stress at the outer surface due to the removal of the material between a and c is given by: σ θ r = b = a2 (σ r (r = c)) b 2 a 2 r 2 + b 2 From the general elastic stress-strain relationship: σ θ r = b = E 1 υ 2 ε θ + υε z r = b = E θ Combining these equations yields: σ r r = c = E θ b2 c 2 σ θ r = c =E σ z r = c =E Where: E = 2c 2 f b f dθ f b+f df 2f f b f dλ λ df E 1 υ 2 ; θ = ε θ + υε z ; r 2 θ (r = b & a = c) λ = ε z + υε θ T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

22 True Stress (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 22 A typical AISI4340 steel tensilecompression stress-strain curves 1.5E+9 1.0E+9 5.0E+8 True stress-strain of % offset Reverse loading at 1% Reverse loading at 2% Reverse loading at 3% Reverse loading at 4% Modeling used AISI4340 steel tensile-compression stress-strain curves fitted with 0.2% offset yield strength curves 0.0E True Strain E+8-1.0E+9-1.5E+9 J. Perry, Experimental-Numerical Three-Dimensional Model for Calculating the Residual Stress Field Created by the Autofrettage Process. Ph.D. Thesis. Ben-Gurion University of the Negev, 2009.

23 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 23 Pa 1.00E E E E E+09 psi 1.45E E E E E E+9 5.0E+8 K1.5, FL16.7mm, 1.14% Interference, 0.472% PBE Radial Stress Axial Stress Hoop Stress 0.0E Normalized Radial Position (%) -5.0E+8-1.0E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

24 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 24 Pa 1.50E E E E E E E+09 psi 2.18E E E E E E E E+9 K1.5, FL16.7mm, 4.6% Interference, 3.8% PBE 1.0E+9 5.0E+8 Radial Stress Axial Stress Hoop Stress 0.0E+0-5.0E Normalized Radial Position (%) -1.0E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

25 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 25 Pa 1.50E E E E E E E+09 psi 2.18E E E E E E E E+9 K1.5, FL16.7mm, 6.5% Interference, 5.66% PBE 1.0E+9 Radial Stress Axial Stress Hoop Stress 5.0E+8 0.0E+0-5.0E Normalized Radial Position (%) -1.0E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

26 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 26 Pa 1.50E E E E E E E+09 psi 2.18E E E E E E E E+8 K1.9, FL16.7mm, 1% Interference, 0.398% PBE 2.5E+8 0.0E+0-2.5E Normalized Radial Position (%) -5.0E+8 Radial Stress Axial Stress Hoop Stress -7.5E+8-1.0E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

27 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 27 Pa 1.50E E E E E E E+09 psi 2.18E E E E E E E E+9 K1.9, FL16.7mm, 4.4% Interference, 3.62% PBE 5.0E+8 0.0E E+8 Normalized Radial Position (%) Radial Stress Axial Stress Hoop Stress -1.0E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

28 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 28 Pa 1.50E E E E E E E+09 psi 2.18E E E E E E E E+9 1.0E+9 K1.9, FL16.7mm, 6.3% Interference, 5.6% PBE Radial Stress Axial Stress Hoop Stress 5.0E+8 0.0E E+8 Normalized Radial Position (%) -1.0E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

29 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 29 Pa 1.50E E E E E E E+09 psi 2.18E E E E E E E E+8 K2.3, FL16.7mm, 0.95% Interference, 0.362% PBE 0.0E Normalized Radial Position (%) -5.0E+8-1.0E+9 Radial Stress Axial Stress Hoop Stress -1.5E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

30 Residual Stresses (Pa) Modeling and Validating Residual Stresses in Tick-Walled Cylinders 30 Pa 1.50E E E E E E E+09 psi 2.18E E E E E E E E+9 5.0E+8 K2.3, FL16.7mm, 3% Interference, 2.16% PBE Radial Stress Axial Stress Hoop Stress 0.0E+0-5.0E Normalized Radial Position (%) -1.0E+9-1.5E+9 T. E. Davidson, et al. Technical Report - Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain. 38 pages, Benet R&E Laboratories, Watervliet, NW, September 1963.

31 May 16-18, 2018, Minneapolis, MN, USA 5. Validation by Neutron Diffraction Measurements Schematic of Neutron Diffraction Setup Testing sample preparation: Two 10 mm-thick disks with inner and outer radii of 60mm and 135mm, 78.7mm and 155mm, respectively, cut from swage autofrettaged cannon tubes. The predicted plastic radii for Disk1 and Disk2 are 96mm and 114mm, respectively, corresponding to the radial interference of 1.445% for Disk1 and 1.165% for Disk2, respectively. The lattice strains were measured with a beam of 3 3mm rectangular spot size in 1 mm increments from the bore to the outer diameter of the tubes. The neutron beam penetrated all the way through the steel ring thickness; therefore, the measurements were the average value throughout the thickness. The residual elastic strains were converted to residual stresses by using the elastic three-dimensional Hooke s law, by assuming a plane-stress condition. J.H. Underwood, et al. Hill stress calculations for autofrettaged tubes compared with neutron diffraction residual stresses and measured yield pressure and fatigue life. ASME 2007 Pressure Vessels and Piping Conference (PVP ), 47-52, San Antonio, TX, July A. Stacey, et al. Measurement of residual stresses by neutron diffraction. Journal of Strain Analysis, 20(2)(1985)93-100

32 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 32 Hoop Stress Change During Ring-Cutting by Modeling Before ring cutting After ring cutting Z. Hu. Design of two-pass swage autofrettage processes of thick-walled cylinders by computer modeling. Proc IMechE Part C: J Mechanical Engineering Science, 2018

33 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 33 Stress Contour Plots After Ring-Cutting by Modeling Left: Residual radial stress; Right: Residual hoop stress

34 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 34 Residual Strain Plots After Ring-Cutting by Modeling Left: Disk 1; Right: Disk 2 J.H. Underwood, et al. Hill stress calculations for autofrettaged tubes compared with neutron diffraction residual stresses and measured yield pressure and fatigue life. ASME 2007 Pressure Vessels and Piping Conference (PVP ), 47-52, San Antonio, TX, July 2007.

35 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 35 Residual Stress Plots After Ring-Cutting by Modeling Left: Disk 1; Right: Disk 2 J.H. Underwood, et al. Hill stress calculations for autofrettaged tubes compared with neutron diffraction residual stresses and measured yield pressure and fatigue life. ASME 2007 Pressure Vessels and Piping Conference (PVP ), 47-52, San Antonio, TX, July 2007.

36 Modeling and Validating Residual Stresses in Tick-Walled Cylinders Modeling Comparison between ANSYS and ABAQUS Swage Autofrettage Model Dimensions: The ram: Length: 1.0 and Outside Radius: The Mandrel: Lead-in Angle 1.5 and Lead-out Angle: 3.0 ; Length: 2.4 and Length of the Flat: The Tube (with entrance and exit transition): Length: 6.0 Outside Radius: 1.50 and 2.00 and Inside Radius: 1.00 (The ratios of Outside Radius to the Inside Radius are 1.5 and 2.0, respectively) The Radial Interference: 1% and 2% The Elements Tube: 8456 axisymmetric 8-node quadrilateral elements Mandrel: 1144 axisymmetric 8- node quadrilateral elements Ram: 256 axisymmetric 8-node quadrilateral elements Contact: 390 contact elements Total element number: 10246, and total node number: 30443

37 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 37 Residual stresses: Ri = 1, Ro/Ri = 1.5 and Interference = 1%: ABAQUS ANSYS Based on the private communication.

38 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 38 Residual stresses: Ri = 1, Ro/Ri = 1.5 and Interference = 2%: ANSYS ABAQUS Based on the private communication.

39 Modeling and Validating Residual Stresses in Tick-Walled Cylinders CONCLUSIONS To achieve a reliable modeling, proper material model, element size and density, incremental deformation steps, boundary conditions and modeling assumptions are crucial; To achieve a reliable experiment, proper assumptions, data processing and analysis are critical. Comparability between the modeling data and the experimental data are important.

40 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 40 ACKNOWLEDGEMENTS This work was supported by the State of South Dakota and Mechanical Engineering Department at South Dakota State University and inspired by the Department of Defense project (Cooperative Agreement # W15QKN ) by METLAB at South Dakota State University. Related information provided by Dr. Anthony P. Parker and computational facility technical support from the University High Performance Computing Center at South Dakota State University are gratefully acknowledged.

41 Modeling and Validating Residual Stresses in Tick-Walled Cylinders 41 THANK YOU FOR YOUR TIME!