how to graph modified goodman diagram in excel

Daniel Parker

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17-01-2025

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The Modified Goodman diagram is a crucial tool in mechanical engineering for assessing the fatigue life of components subjected to both mean and alternating stresses. Creating this diagram manually can be time-consuming. Fortunately, Excel offers a powerful and efficient way to visualize this data. This article will guide you through the process step-by-step.

Understanding the Modified Goodman Diagram

Before diving into the Excel process, let's briefly review the fundamentals. The Modified Goodman diagram graphically represents the relationship between mean stress (σ_m) and alternating stress (σ_a) for a material, considering its ultimate tensile strength (σ_u) and yield strength (σ_y). The equation defining the Modified Goodman line is:

σ_a = σ_u * (1 - σ_m/σ_u)

This equation represents the fatigue limit. Any stress combination falling below this line is considered safe, while those above suggest potential fatigue failure.

Data Preparation: Gathering Necessary Information

To construct your Modified Goodman diagram in Excel, you need the following information:

• Ultimate Tensile Strength (σ_u): This represents the maximum stress a material can withstand before fracturing.
• Yield Strength (σ_y): This is the stress level at which the material begins to deform plastically.
• Mean Stress (σ_m) values: A range of mean stress values you want to plot.
• Alternating Stress (σ_a) values: The corresponding alternating stress values for each mean stress. These are often determined experimentally or through FEA (Finite Element Analysis).

You can organize this data in a simple Excel table with columns for σ_m and σ_a.

Step-by-Step Guide to Creating the Modified Goodman Diagram in Excel

1. Inputting Data: Enter your σ_m and σ_a values into two columns of an Excel spreadsheet. Label these columns clearly.

2. Calculating the Goodman Line: In a separate column, calculate the corresponding alternating stress for each mean stress using the Goodman equation. You'll use Excel's formula capabilities for this. In a cell next to your first σ_m value, enter the formula: =σ<sub>u</sub>*(1-σ<sub>m</sub>/σ<sub>u</sub>). Replace σ<sub>u</sub> and σ<sub>m</sub> with cell references to your ultimate tensile strength and the mean stress value. Then copy this formula down to apply it to all your mean stress values. Remember to replace the placeholder values with the actual cell references from your data.

3. Creating the Chart: Select both the σ_m column and the calculated σ_a column. Go to the "Insert" tab and choose a "Scatter" chart (specifically, the "Scatter with Straight Lines and Markers" option is usually best). This will create a plot of your Goodman line.

4. Adding Data Points (Optional): If you have experimentally obtained (σ_m, σ_a) data points, select these columns as well and add them to the chart. This lets you visually compare your data with the theoretical Goodman line. They should be represented as distinct points on the graph.

5. Customizing the Chart: Enhance your chart for clarity.

   • Labels and Titles: Add appropriate axis labels (σ_m and σ_a) and a descriptive chart title (e.g., "Modified Goodman Diagram for [Material Name]").
   • Gridlines: Include gridlines for better readability.
   • Legend: If you included experimental data points, add a legend to distinguish them from the Goodman line.
   • Data Labels (Optional): Add data labels to your points for precise values.

6. Adding the Yield and Ultimate Strength Lines: To complete the Modified Goodman diagram, you also need to represent the yield and ultimate strength values.

   • Vertical Line at σ_u: Draw a vertical line at x = σ_u.
   • Horizontal Line at σ_y: Draw a horizontal line at y = σ_y/2. (Note: The intersection of this line and the Goodman line forms the end point of the safe region for the Goodman diagram. )

Interpreting the Diagram

Once the Modified Goodman diagram is constructed, you can assess the fatigue safety of components. Any operating point (σ_m, σ_a) falling below the Goodman line is considered safe; points above it suggest a potential fatigue failure.

Conclusion

Creating a Modified Goodman diagram in Excel streamlines the fatigue analysis process. By following these steps and using Excel's charting capabilities, you can efficiently visualize fatigue data and make informed decisions about the safety and reliability of your engineering designs. Remember to accurately input your material properties and experimental data for reliable results.