Engineering Materials - Aircraft Design and Material Processing

General Aircraft Design Requirements

  • Definition: The general aircraft design requirements encompass the capabilities of an aircraft to:

    • Cope with aerodynamic loads for the speed it is flying.

    • Resist inertia loads from maneuvers.

    • Carry payload.

    • Operate in different environments.

    • Achieve the designed performance (range & endurance) with good fuel economy.

    • Maintain the lowest possible structural weight.

    • Ensure a stiff and strong structure with long life and a high degree of safety.

Modes of Loading

  • Types of Loading:

    • Axial tension

    • Compression

    • Beam bending: axial tension on one side and compression on the opposite side

    • Torsion

    • Bi-axial tension or compression

Airframe Loads

  • Examples:

    • Torsional moment on the fuselage from rudder load.

    • Bending moment carried based on Mym/I distribution.

  • Wing Loads

    • Wing alone: Distributed lift load.

    • Wing plus fuselage: Resultant loading.

  • Effect of Aileron

    • Twist due to moment induced by deflected aileron.

    • Lift from deflected aileron causing compression and tension.

Recall - Bending Stress

  • Bending Stress Formula:

The maximum longitudinal stress on a beam or panel in bending is given by:

\sigma = \frac{My}{I} 

*   y_m – greatest distance from the neutral axis
*   I – Second moment of area
*   M – Bending Moment
*   Z_e – elastic section modulus (Not to be confused with the elastic modulus of the material, E)

Recall - Bending Stress

  • Bending Moment Formulas & Section Properties

Section Shape

Area

Moment I

Moment K

Rectangle (b \times h)

bh

\frac{bh^3}{12}

\frac{bh^3}{3}(1 - 0.58 \frac{b}{h}) (h > b)

Circle (\pi r^2)

\pi r^2

\frac{\pi}{4} r^4

\frac{\pi}{2} r^4

Annulus (\pi (ro^2 - ri^2))

\pi (ro^2 - ri^2)

\frac{\pi}{4} (ro^4 - ri^4)

\frac{\pi}{2} (ro^4 - ri^4)

  • Bending Moment, M:

    • Cantilever beam with end load: M = FL

    • Simply supported beam with center load: M = \frac{FL}{4}

    • Fixed beam with center load: M = \frac{FL}{8}

Example 1.1

  • Problem: Calculate the maximum “extreme fiber” stress in a 300mm x 25mm x 1 mm stainless steel ruler when it is mounted as a cantilever with the X-X axis horizontal with 250 mm protruding and a weight of 10 N is hung from its end. The yield strength of stainless steel lies in the range of 200 to 1000 MPa. Compare this bending stress with the yield stress of the material and with the direct stress when a 10 N force is used to pull the ruler axially.

Recall - Torsional Stress

  • Torsional Stress Formula:

\tau_{max} = \frac{TR}{K}

  • \tau_{max} – maximum shear stress

  • T – applied torque

  • R – radius of shaft

  • K – polar second moment of area

  • \tau{max} = \frac{\sigmay}{2} if you do not know T, R or K

Example 1.2

  • Problem: A brass rod with shear modulus 40 GPa, length 200 mm, a solid circular cross-section with diameter 10 mm, and a tensile yield strength of 300 MPa. Calculate the torque at first yield of the rod.

Interaction Between Design Requirements, Material, Shape, and Process

  • Specification of shape restricts the choice of material and process.

  • Specification of process limits the materials you can use and the shape they can take.

Six Families of Materials

  • Members of a family have common features:

    • Similar properties

    • Similar processing routes

    • Similar applications

  • Hybrids are a combination of materials from other families.

Typical Material Properties

  • Mechanical Properties:

    • E – elastic modulus

    • \sigma_y – yield strength

    • K_{1c} – fracture toughness

    • \rho - density

  • Thermal & Magnetic Properties:

    • T_{max} – limiting temperature for engineering applications

    • \alpha – Thermal expansion

    • Magnetic properties

The Classes of Process

  • Process Categories:

    • Raw materials

    • Primary processes: Create shapes

    • Secondary processes: Modify shapes or properties.

Primary Processes

  • Primary Processes are to create shapes.

    • Casting methods: Sand, Die, Investment

    • Molding methods: Injection, Compression, Blow molding, Slip casting

    • Deformation methods: Rolling, Forging, Drawing

    • Powder methods: Sintering, HIPing

Secondary Processes

  • Secondary Processes are to modify shapes or properties.

    • Machining: Cut, turn, plane, drill, grind

    • Heat treat: Quench, temper, age-harden

Joining Process

  • Fastening, Riveting, Welding, Heat bonding, Snap fits, Friction bond, Adhesives, Cements

Surface Treatment

  • Polishing, Texturing, Plating, Metallizing

  • Anodize, Chromizing

  • Painting, Printing

Certainly! Let's break down the bending stress formula \sigma = \frac{My}{I} :

  • \sigma (sigma) - Bending stress: This is the stress at a specific point within the material due to bending. It's usually measured in Pascals (Pa) or pounds per square inch (psi).

  • M - Bending Moment: This is the moment acting on the cross-section of the object. It represents the sum of the moments of all external forces acting on the object. The unit is Newton-meters (Nm) or pound-feet (lb-ft).

  • y - Distance from the Neutral Axis: This is the perpendicular distance from the neutral axis to the point where the stress is being calculated. The neutral axis is the axis within the cross-section where there is no bending stress or strain. Measured in meters (m) or inches (in).

  • I - Second Moment of Area (Area Moment of Inertia): This is a property of the cross-sectional shape that indicates its resistance to bending. It depends on the shape and size of the cross-section. The unit is meters to the fourth power (m^4) or inches to the fourth power (in^4).

In essence, the formula tells us that the bending stress at any point in a beam is directly proportional to the bending moment and the distance from the neutral axis, and inversely proportional to the second moment of area.