Excel Guide: Graphing Modified Goodman Diagram Easily

In the world of mechanical engineering, understanding material fatigue and the strength of components under cyclic loading is crucial. One effective tool for visualizing these stresses and predicting fatigue failure is the Modified Goodman Diagram. This diagram helps engineers assess whether a component can withstand cyclic stress variations without failing. This guide will walk you through creating a Modified Goodman Diagram in Microsoft Excel, an essential skill for any engineer working on stress analysis.

Understanding the Modified Goodman Diagram

The Modified Goodman Diagram plots alternating stress (σ_a) against mean stress (σ_m) to determine the safe region for stress cycles. Here’s what you need to know:

• σ_a (alternating stress): This is half the range of the stress cycle.
• σ_m (mean stress): This is the average stress in the cycle.

The diagram includes:

• The fatigue limit line, where failures occur due to infinite life under alternating stress.
• The ultimate tensile strength line, representing the material’s maximum strength.
• The yield strength line, beyond which plastic deformation starts.

Setting Up Excel for Graphing

Before we dive into plotting the diagram, ensure you have:

• Microsoft Excel installed with updated charts capabilities.
• Basic knowledge of Excel functions.

1. Entering Data

Create a new workbook:

• In the first column (A), enter values for mean stress (σ_m).
• In the second column (B), enter corresponding values for alternating stress (σ_a).
• Include material properties like ultimate tensile strength (S_ut), fatigue limit (S_e), and yield strength (S_y) for reference.

S_ut = 800 MPa
S_e = 350 MPa
S_y = 550 MPa

2. Creating the Goodman Diagram

To plot the Modified Goodman Diagram:

1. Select your data including headers.
2. Go to the ‘Insert’ tab, choose ‘Scatter’, then ‘Scatter with Smooth Lines and Markers’.
3. Your initial plot will appear; right-click on the chart area and select ‘Select Data’.
4. Adjust the data range if needed. Add new series for the critical lines:

• Fatigue Limit Line: Calculate σ_a as S_e (constant) for all σ_m from 0 to S_ut.
• Ultimate Tensile Strength: Line from (0, S_ut) to (S_ut, 0).
• Yield Strength: Line from (0, S_y) to (S_ut, S_y - S_ut).

3. Formatting the Graph

To enhance readability:

• Label axes appropriately (σ_a for Y-axis, σ_m for X-axis).
• Format axis labels with units (e.g., ‘Stress in MPa’).
• Customize series lines:
  • Fatigue limit line with a solid line.
  • Ultimate tensile strength line with a dashed line.
  • Yield strength line with a dotted line.
• Add data markers for any existing design points.
• Include a legend for better understanding of lines.

⚙️ Note: The plotted points represent design stresses, and any point falling outside the region bound by these lines might indicate potential failure.

Upon finishing your chart:

• Add a title like "Modified Goodman Diagram for [Material Name]" if it's relevant.
• Consider incorporating secondary axes for clarity.

💡 Note: Use Excel's formula bar for quick calculations if needed.

Summary

In this guide, we’ve explored how to create a Modified Goodman Diagram in Excel, starting from data entry, plotting critical lines, to formatting for clarity. This diagram provides invaluable insights into the fatigue behavior of materials, helping engineers design parts that are not only strong but also durable under cyclic loading conditions. By mastering this technique, you can make better decisions regarding material selection and component design, ensuring longevity and reliability in your engineering projects.