2: Tie Rod

Introduction to Ashby Material Selection Method

  • Overview of the second lecture on Ashby material selection.

  • Focus on a specific example: designing a lightweight tie rod for tensile load carrying at minimum mass.

Establishing the Performance Function

  • Define the performance function as the ratio of the load carried to the mass used.

    • Load = Stress x Area.

    • Mass = Density x Volume.

  • Volume of a tie rod is calculated as:

    • Volume = Cross-sectional area x Length.

  • Thus, performance function can be expressed as:

    • Load/Mass = Stress/(Density x Length).

Objective of the Tie Rod Design

  • Primary goal: Minimize the mass while carrying a specified load.

  • Secondary constraint to consider: Tie rod must not yield, ensuring structural integrity.

  • Define failure as plastic yielding, requiring:

    • Stress in the tie rod ≤ Yield stress of the material.

Rearranging the Performance Function

  • Performance function becomes an expression defining mass with given parameters:

    • Mass ≥ (Load x Density x Length) / Yield Stress.

  • The inequality indicates that insufficient mass leads to component failure due to inadequate material to withstand the load.

Groups of Parameters in the Equation

  • Separate parameters into:

    • Functional Requirements:

      • Maximum load and length of the rod (constant regardless of material).

    • Material Properties:

      • Density and yield stress, which change with material selection (e.g., aluminum vs steel).

Defining the Merit Index

  • Merit index established to rank materials based on their ability to minimize mass:

    • Merit Index = Yield Stress / Density.

  • Maximizing performance is achieved by maximizing merit index, which inversely corresponds to minimizing mass.

Utilizing the Ashby Diagram

  • Introduces an Ashby diagram, plotting:

    • Strength (MPa) on the y-axis vs. Density (Mg/m^3) on the x-axis.

  • Regions represent classes of materials (metals, composites, etc.).

  • Design Guidelines:

    • The slope of the design line relates to the component’s performance characteristics, specifically:

      • Slope = Yield Stress / Density.

Analyzing Material Performance

  • Materials located above the design line are preferable; they exhibit higher strength-to-weight ratios.

  • Critical constraints include:

    • Amount of load carried, with the example specifying a minimum of 100 kN and a maximum allowable mass of 1 kg for the tie rod, with a fixed design length of 1 meter.

Calculating Minimum Merit Index

  • Apply secondary constraints in the performance function to derive a minimum value for the merit index:

    • Minimum Merit Index = 100 MPa/Mg/m^3.

Revising the Ashby Diagram for Minimum Requirements

  • Update the Ashby diagram with a new line reflecting the calculated merit index threshold.

  • Identify materials meeting or exceeding this threshold, indicating suitability for design:

    • Materials that fall below are not suitable for the design requirements.

Conclusions on Material Selection

  • Evaluate material candidates:

    • Discard zinc alloys due to inadequacy.

    • Consider strength-to-weight profiles for nickel alloys and steels, which may not meet the stringent criteria.

    • Identify titanium alloys, some aluminum, and magnesium alloys as potential best options due to suitable yield stresses and densities.

  • Emphasize the method of converting functional requirements and objectives into a merit index for quantitative material ranking.