Elastic Plastic Analysis is a non-linear analysis. There are two main non-linearities involved here.

- The material model is non-linear and requires true stress strain curve as input. In contrast a linear static analysis just needs Elastic Young’s Modulus to construct the full stress strain curve. The stress-strain curve in this case is simply a line starting from origin with slope equal to the Elastic Young’s Modulus.
- Geometric non-linearity is also considered in an elastic plastic analysis by switching on large deformation effects. This allows the model to incorporate change in structures stiffness with large deformations. To understand this, consider a cantilever loaded at its end. Initially the cantilever will bend relatively easily and deformations will be proportional to the load (δ=PL
^{3}/3EI). However, it becomes more stiff (hard to bend) as deformations become large and the load vs deformation response is no longer linear. These sort of stress stiffening effects are captured by switching on large deformation effects. - The third type of non-linearity which is contact may or may not be present in the model.

Here an ASME PTB-3 Validation for “Example E5.2.3 – Elastic Plastic Analysis” to check for protection against plastic collapse per ASME Sec VIII Div 2 is carried out using ANSYS.

Problem Statement:

Evaluate the vessel top head and shell region given in Example Problem E5.2.1 for compliance with respect to the elastic-plastic analysis criteria for plastic collapse provided in paragraph 5.2.4.

For Vessel Data, Geometry, Mesh Details refer the post – ASME PTB-3 Validation – Elastic Stress Analysis

ANALYSIS SETUP

A static structural analysis was carried out with large deformation effects switched on to capture geometric non-linearities in the model.

MATERIAL PROPERTIES

An elastic plastic material model was set-up by defining true stress strain curves for the given materials using Annex 3-D of ASME Sec VIII Div 2. A multilinear isotropic hardening plasticity material model was used for this analysis. Here multilinear means the program will join the user input stress strain points on the curve with straight lines to complete the continuous curve. Isotropic Hardening means the strain hardening in the model is assumed to be same for both tension and compression. This model holds good for large strain applications such as the ones dealt with for plastic collapse analysis.

The curve is generated by defining Elastic Young’s Modulus for the linear portion of the curve (upto proportional limit). For the non-linear portion (the curve beyond proportional limit) stress vs plastic strain needs to be defined upto the ultimate stress. Beyond this point the curve is assumed to be perfectly plastic, indicating rupture failure.

Stress Strain Curve for SA 105

NOTE: Typically FEA softwares require stress vs plastic strain as input to generate this sort of curve with the plastic strain starting at zero. Here the plastic strain starts at 0.00002 which is small enough to be taken as zero.

Stress Strain Curve for SA 516 Gr 70

NOTE: Typically FEA softwares require stress vs plastic strain as input to generate this sort of curve with the plastic strain starting at zero. Here the plastic strain starts at 0.00002 which is small enough to be taken as zero.

LOADS & BOUNDARY CONDITIONS

- Factored Internal Pressure of 2.4P = 1008 psi was applied on the inner surfaces of the model as per table 5.4, ASME Sec VIII Div 2.

- Pressure Thrust of 2357.5 psi was applied on the flange face as negative pressure.

- Axial displacement was arrested at the shell base

ANALYSIS RESULTS

The analysis converged for the given load and thereby satisfy the global acceptance criteria for elastic plastic analysis as per para 5.2.4.3 of ASME Sec VIII Div 2. No service criteria was provided in this problem hence they are not checked here.

Von-Mises Stress

Von-Mises Stress from PTB-3 example

Equivalent Plastic Strain

Equivalent Plastic Strain from PTB-3 example

The results obtained shows a very good match with PTB-3 values.

Find PTB-3 Validation Elastic Stress Analysis here

Find PTB-3 Validation Limit Load Analysis here

Hi Sandip.

I appreciate your efforts. Good Work.

I have some questions to ask you, to clarify myself.

1. How the prop.limit was set. If it is based on true stress strain curve, it would be iterative method. Is there any hard and fast rule to define this limit.

2. Which Criterion of plastic collapse method you followed to converge LRFD. Either Tangent intersection or Twice slope yield method? Could you explain further on this convergence part.

3. Why local acceptance criteria for elastic plastic analysis as per table 5.5 of ASME Sec VIII Div 2 uses factor 1.7. It is well understand that 2.4 factor for global criteria was set based on UTS factor of safety.

Thanks.

1. Yes the procedure was iterative. There is no hard and fast rules to set the starting point of plastic strain. I would use typically a small value of the order of 1e-5 or 1e-6 for plastic strain below which the curve will be assumed to be elastic.

2. To determine the plastic collapse load, I’ll typically apply a high load and solve the model. The non linear solution will proceed by incrementing the load gradually from zero to 10%, 20% etc of full value. Finally beyond a point, say 70% load, the solution won’t converge. The collapse load in this case is 70% of applied load. In this methodology I am not using the tangent intersection or the twice yield method to arrive at the collapse load, rather I am getting the collapse load from the FEA directly.

3. The local acceptance criteria does not check for strength of the material, rather its a limit on the local deformations. Hence factor of 2.4 which is on strength is not applicable here.

Thanks and noted Mr. Sandip.

Upon question 1, I would like to know how who fix the initial true stress, (Proportional limit. Adjust to get plastic strain) in your case 17.4 & 19.4 for SA-105 & SA516-70 respectively. This initial value would be used in determining true strain in accordance with Annex 3-D. Your guidance is appreciated.

As I commented above, we won’t get a well defined proportional limit (the point upto which plastic strain is zero). You are free to start at any stress value as long as plastic strain at the starting point is small enough (of the order of 1e-5 or less) to be considered as zero.