 When designing structures, engineers often use the terms plastic collapse and limit load. These concepts are important for creating strong and reliable designs.

### What is plastic collapse?

Plastic collapse is a global phenomenon that occurs when a structure can no longer sustain the applied loads. This happens when the material has undergone irreversible deformation. The result may be a burst, collapse, leak, or fracture. In other words, the structure fails completely.

### How to determine the plastic collapse load?

One way to determine the plastic collapse load is to use a computer program that simulates the behavior of the structure under different loads. This program takes into account the material properties, such as its strength and stiffness, and uses this information to calculate the maximum load the structure can withstand before it collapses. Engineers use this information to design structures that are strong enough to handle the expected loads.You can read more about the various plasticity models available in ANSYS here and here is more information on how to input a stress-strain curve in ANSYS.

Here are the steps to determine the plastic collapse load using ANSYS:

1. First, choose a plasticity model that accurately represents the behavior of the material in real life. This will help ensure that the results of the analysis are as close to reality as possible.

2. Next, obtain the stress-strain curve for the material you are modeling. This can be done through physical testing or by generating a curve using the Ramberg-Osgood equations.

3. Once you have the stress-strain curve, input it into ANSYS.

4. Then, apply the loads that you are interested in studying.

5. It’s important to include load steps in your analysis so that the applied load is gradually increased. For example, if you are designing a component for a 5,000 psi operating pressure, you may want to ramp up the pressure in your analysis to above 5,000 psi in increments of 1,000 psi.

6. Determine the load at which the model fails to converge. This means that you need to check if the lack of convergence is due to a true representation of plastic collapse or if it is a numerical phenomenon causing a premature failure. You can do this by comparing the maximum stress reported by the analysis to the maximum stress on the stress-strain curve. If they are close (within 5%), it’s likely that the non-convergence is representing a true collapse situation.

7. Once you have determined the load at which the model fails to converge, plot the load-displacement curve. This curve will show the displacement of a node of interest (either total or directional displacement) versus the applied load. This plot will help you identify two important facts:

• The overall shape of the plot should be similar to the material stress-strain plot.
• At higher loads, large deformations are observed with small load increments due to the formation of a plastic hinge.

Based on the analysis, the raw plastic collapse load is 3,000 kips. However, depending on the design code being followed, the designer may need to include a factor on top of this load. For example, in the image below, the dashed line represents a design collapse load of 2,700 kips (90% of the raw plastic collapse load). Limit Load is a concept in engineering that helps to determine how much load a structure or component can take before it collapses. Engineers use a method that aims to calculate the plastic collapse load accurately. However, in reality, components may collapse at loads different from what has been predicted through analysis, making this approach less conservative.

One of the main sources of inaccuracy is the material model and stress-strain curve used. Materials have a complex plastic response, and sometimes available material models may not be conservative enough for specific situations. To address this, an elastic-perfectly plastic (EPP) material model can be used to ensure conservatism. This model doesn’t take credit for work hardening, which can be a source of error. A comparison between an elastic-plastic and elastic-perfect plastic curve can help illustrate the difference. The limit load is the plastic collapse load based on the EPP material model.

Here are some key points to note:

• In ANSYS, the Bilinear Kinematic Hardening (BKIN) material model can be used to define EPP material behavior.
• The slope of the plastic portion of the EPP curve is called the tangent modulus and must be defined manually. Some design codes allow a small slope of less than 5% for the plastic portion to help with numerical convergence of the model.
• Based on the EPP material curve, the yield and ultimate tensile strengths are the same, which simplifies the analysis.
• Determining the limit load in this way is often referred to as limit load analysis. It provides a lower bound estimate for the plastic collapse load, which is important in engineering design.

Good Luck!   