Tresca s or Mises Yield Condition in Pressure Vessel Design

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1 Tresca s or Mises Yield Condition in Pressure Vessel Design Franz Rauscher Institute for Pressure Vessels and Plant Technology Vienna University of Technology Austria

2 Why using Tresca s yield condition in a Design Check? Simulation Evaluation of real behaviour of a structure Design Check Show sufficient safety margin against relevant failure mode Conservative approach

3 EN : Unfired Pressure Vessels Part 3 Design: DBF (Design by Formulas) Fatigue Annex B: Direct Route for DBA with reference to Fatigue (DBF section) Annex C: Stress Categorisation for DBA

4 Direct Route Gross Plastic Deformation Design Check (GPD-DC) Progressive Plastic Deformation Design Check (PD-DC) Instability Design Check (I-DC) Fatigue Design Check (F-DC) Static Equilibrium Design Check (SE-DC)

5 Gross Plastic Deformation (GPD) Principle: Design actions have to be carried by a model with: First order theory A linear-elastic ideal-plastic constitutive law Tresca s yield condition and associated flow rule A maximum absolute value of the principal structural strains of 5% Yield strength = RM RM d = ( design Material strength RM ( material strength parameter) γ ( partial safety factor) R d parameter)

6 Tresca s vs. Mises yield condition Mises' yield surface with reduced yield strength Mises' yield surface σ 2 Tresca's yield surface σ 1 RM d _ M = 3 2 RM d

7 One dimensional Stress σ 2 σ σ σ 1 Rod in tension Beam in bending Limit pressure difference: 15.5%

8 Closed Cylinder with internal pressure σ σ 2 σ Closed cylinder σ 1 Limit pressure difference: 0%

9 Sphere with internal pressure σ σ σ 2 Sphere with internal pressure σ 1 Limit pressure difference: 15.5%

10 Example: Thin unwelded flat end Case Limit pressure [bar] Max. abs. value of total principal strain Iterations CPU time [s] Pure Tresca % 1011 init 23.5 x (Time for Mises) Pure Mises % 30 full Mises equivalent stress at Tresca limit Limit pressure difference: 3.4%

11 Example: Storage tank Max. principal strains at Tresca limit Internal pressure Hydrostatic pressure

12 Results for storage tank Case Limit pressure [bar] Max. abs. value of principal strain Iterations Limit pressure difference [%] Internal pressure pure Tresca % 2279 init 0.5% Internal pressure pure Mises % 15 full Hydrostatic pressure pure Tresca % 260 init 11% Hydrostatic pressure Tresca-95% Mises % Hydrostatic pressure pure Mises % 72 full

13 Example dished end Max. principal strain at Tresca limit Case Limit pressure [bar] Max. abs. value of total principal strain Iterations CPU time [s] Pure Tresca % x (Time for Mises) Pure Mises % 46 Limit pressure difference: 6.7%

14 Example: Sphere with nozzles Case Limit pressure [bar] Max. abs. value of total principal strain Pure Mises Tresca with 95% Mises % Pure Tresca (CAD-FEM) 371 5% plastic equivalent strain 371 Max principal PS max = = 309bar 1.2 strain at Tresca limit ( DBF :273.9bar) Experiment :750bar (2.5%)

15 Hydrogen Reactor M F p, M, F Pressure Limit Pressure p Moment M, Force F Time t p Material: Shell: 10CrMo9 10 Nozzle: 11CrMo 9 10 NT M = 285 knm F = 60 knm

Evaluation of Limits for Hydrogen Reactor 20 021 Elements, Solid 45: 8-node isoparametric

pressure [bar] Max. abs. value of total principal strain Iterations Pure Tresca 229 1.

16 Evaluation of Limits for Hydrogen Reactor Elements, Solid 45: 8-node isoparametric 3Dsolid, reduced integration, hourglass control Case Constant Moment Constant Force Limit pressure [bar] Max. abs. value of total principal strain Iterations Pure Tresca init 7775 Pure Mises full 1697 Limit pressure difference: 5.5% CPU time [s] PIV 2.5GHz, 1GB

17 Results: Case Tresca limit (pressure) / Mises limit (pressure) CPU time for Tresca limit / CPU-time for Mises limit Beam in tension and analytical results bending Closed Cylinder with 1 internal pressure Open cylinder with internal pressure Sphere with internal pressure Flat end Storage tank with internal pressure Storage tank with hydrostatic pressure Dished end Sphere with nozzles not noted Hydrogen Reactor

18 Conclusions: In general: Tresca limit may be up to 15.5% higher than the Mises limit When undisturbed cylinder or sphere fails under internal pressure: Closed cylinder fails: no difference Open cylinder fails: Tresca limit 15.5% higher Sphere fails: Tresca limit 15.5% higher In the considered examples: Tresca limit is between 3.5 and 12.3% higher Procedure for Tresca s yield condition would be needed in commercial FE packages.

Plastic non-symmetric bifurcation buckling of circular cylinders under uniform external hydrostatic pressure

icccbe 2010 Nottingham University Press Proceedings of the International Conference on Computing in Civil and Building Engineering W Tizani (Editor) Plastic non-symmetric bifurcation buckling of circular