AME Unit 4 Q2

Plasticity is the property of a material to undergo permanent deformation without breaking when subjected to a force beyond its elastic limit. Once a material has yielded (reached its elastic limit), it enters the plastic region where deformation is irreversible.  

1. Plasticity | Malleability, Elasticity, Ductility – Britannica

2. Elastic Limit | Instron

Key concepts related to plasticity:

• Yield strength: The point at which a material begins to deform plastically.   1. Yield (engineering) – Wikipedia en.wikipedia.org
• Ductility: A material’s ability to undergo plastic deformation before fracture.   1. Material Deformation: Plasticity, Curve Testing, Creep – StudySmarter www.studysmarter.co.uk
• Malleability: A material’s ability to be shaped permanently by deformation.   1. Plasticity (physics) – Wikipedia en.wikipedia.org
• Strain hardening: The increase in strength of a material due to plastic deformation.

Importance of plasticity in engineering:

• Material selection: Engineers choose materials based on their plastic properties for applications like forming, bending, and shaping.
• Design: Understanding plasticity helps engineers design structures that can withstand loads without permanent deformation.   1. True Stress and Strain: Definition & Equation | StudySmarter www.studysmarter.co.uk
• Manufacturing processes: Many manufacturing processes, such as forging, rolling, and extrusion, rely on the plastic behavior of materials.

Plasticity is a fundamental property exploited in numerous engineering fields. Here are some common examples:

Manufacturing Processes

• Forging: Shaping metal by applying compressive forces.   1. 5 Common Types of Metal Forming Processes and Their Applications www.meadmetals.com
• Rolling: Producing sheet metal by passing it through rollers.   1. Navigating the Types of Rolling Processes | Ulbrich www.ulbrich.com
• Extrusion: Producing products with a uniform cross-section by forcing material through a die.   1. nglos324 – extrusion www.princeton.edu
• Drawing: Producing wires or rods by pulling material through a die.   1. Wire drawing | Cold Working, Annealing & Tempering – Britannica www.britannica.com
• Deep drawing: Forming sheet metal into complex shapes.

Structural Engineering

• Ductile materials: Used in structures to absorb energy before failure.   1. Ductility vs. Brittleness: The Key Differences – Xometry www.xometry.com
• Crashworthiness: Designing structures to deform plastically in accidents to protect occupants.

Mechanical Engineering

• Metal forming: Creating components with complex shapes.
• Spring manufacturing: Utilizing the elastic and plastic properties of materials.

Other Fields

Aerospace industry: Some components are formed using plastic deformation processes.   1. Metal Forming: Specialized Procedures for the Aircraft Industry – ResearchGate www.researchgate.net

Automotive industry: Body panels and structural components often exploit plasticity.

Shear stress is the force per unit area acting parallel to the surface of a material. Imagine trying to cut a piece of paper with scissors; the force you apply to the blades creates shear stress on the paper.

Key points:

• Force: The force applied parallel to the material’s surface.   1. Shear stress | Definition & Facts – Britannica www.britannica.com
• Area: The area of the surface being acted upon.
• Stress: The ratio of the force to the area.   1. Shearing Stress – Introduction, Formula, Units and FAQ – Vedantu www.vedantu.com

Formula:

Shear stress (τ) = Force (F) / Area (A)

Units:

Shear stress: Pascals (Pa) or N/m²

Force: Newtons (N)

Area: square meters (m²)

Young’s modulus is a measure of the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain (deformation) in the elastic region of a material. In simpler terms, it tells us how much a material will stretch or compress under a given amount of force.  

1. Young’s modulus – Wikipedia

2. www.alliedacademies.org

3. 12.3 Stress, Strain, and Elastic Modulus | University Physics Volume 1

4. Physics A level revision resource: Introduction to Young’s Modulus – University of Birmingham

Key points:

• Stiffness: A higher Young’s modulus indicates a stiffer material.   1. Shear Modulus vs Young’s Modulus: Which One to Use? – Xometry www.xometry.com
• Elastic region: The material returns to its original shape after the load is removed.   1. 12.4 Elasticity and Plasticity | University Physics Volume 1 – Courses.lumenlearning.com. courses.lumenlearning.com
• Calculation: Young’s modulus (E) = stress (σ) / strain (ε)   1. 12.3 Stress, Strain, and Elastic Modulus – University Physics Volume 1 | OpenStax openstax.org

In essence, Young’s modulus is a fundamental property of materials that helps engineers predict how materials will behave under load.

Young’s modulus is a cornerstone in engineering design, providing crucial insights into material behavior under load. Here’s how it’s utilized:  

1. How is Young’s modulus used in engineering design? – TutorChase

Structural Engineering

• Predicting deflection: Engineers calculate how much a structure, like a beam or column, will bend or deform under a given load.   1. How is Young’s modulus used in engineering design? – TutorChase www.tutorchase.com
• Material selection: Choosing materials with appropriate Young’s modulus for different structural components. For instance, high modulus materials for bridges to minimize deflection, and lower modulus materials for shock absorption.   1. How does Young’s modulus contribute to material selection in engineering? – TutorChase www.tutorchase.com2. Understanding Young’s Modulus | The Efficient Engineer efficientengineer.com
• Optimizing designs: Ensuring structures can withstand expected loads without failure.   1. How is Young’s modulus used in engineering design? – TutorChase www.tutorchase.com

Mechanical Engineering

• Spring design: Determining the stiffness of springs for various applications like suspension systems, shock absorbers, and pressure gauges.   1. How is Young’s modulus used in engineering design? – TutorChase www.tutorchase.com
• Machine component design: Selecting materials for components like shafts, axles, and gears based on required stiffness.
• Stress analysis: Calculating stresses in components under different loading conditions.

Other Fields

Civil engineering: Designing foundations, roads, and tunnels.

Aerospace engineering: Designing aircraft components that are lightweight yet stiff.

Biomedical engineering: Analyzing the mechanical properties of biological tissues.

A safety coefficient, or factor of safety, is a numerical value that indicates how much stronger a structure or component is than it needs to be for its intended load. It’s a crucial concept in engineering to ensure safety and reliability.  

1. What Is The Factor of Safety?

Key points:

• Purpose: To account for uncertainties in material properties, loads, manufacturing processes, and environmental conditions.
• Calculation: Factor of safety = Ultimate strength / Allowable stress
• Typical values: Vary depending on the application, material, and potential consequences of failure. Higher values are used for critical structures like bridges and buildings.   1. Factor of safety – Wikipedia en.wikipedia.org

Example:

If a material has an ultimate strength of 100 MPa and the allowable stress is 20 MPa, the factor of safety is 5. This means the material can withstand five times the expected load before failure.

By incorporating a safety factor, engineers can design structures and components that are less likely to fail under unexpected conditions.

The Collapse of the Tacoma Narrows Bridge

A classic example of the critical importance of factor of safety is the collapse of the Tacoma Narrows Bridge in 1940.

Often referred to as the “Galloping Gertie,” the bridge collapsed due to aerodynamic instability, commonly known as flutter. While this was the immediate cause, underlying factors related to structural engineering and safety factors played a role.

• Insufficient stiffness: The bridge was designed with a relatively low factor of safety for stiffness. This meant it was more susceptible to vibrations.
• Underestimation of wind loads: The design calculations might have underestimated the potential wind forces the bridge could encounter.

While the primary cause of the collapse was aerodynamic instability, the bridge’s susceptibility to these forces was exacerbated by insufficient structural rigidity, which can be linked to an inadequate factor of safety.

This tragic event underscored the importance of considering all potential loads and stresses, and applying appropriate safety factors in engineering design.

While the Tacoma Narrows Bridge is a famous example, there have been other instances where inadequate safety factors contributed to structural failures:

The Challenger Disaster

While primarily a failure of material science, the Challenger disaster also highlights the importance of safety factors. The O-rings used in the space shuttle’s solid rocket boosters were not designed with sufficient safety margins to account for the extremely cold launch conditions. This led to their failure and the subsequent catastrophe.

Building Collapses

There have been numerous instances of building collapses due to inadequate safety factors. These can be caused by factors such as:

• Underestimation of loads: Buildings might not be designed to withstand the weight of additional floors or heavy equipment.
• Material defects: Weaknesses in construction materials can reduce the overall strength of the structure.
• Construction errors: Mistakes during the building process can compromise the structural integrity.

These examples emphasize the critical role of safety factors in ensuring the reliability and safety of engineered structures.

The safety coefficient, a crucial factor in engineering design, can be influenced by various factors during the operational phase. These factors can alter the original design assumptions and necessitate adjustments to the safety margin.

Operational Factors Affecting Safety Coefficient

1. Environmental Conditions:
   • Temperature: Extreme temperatures can affect material properties, reducing strength and increasing the likelihood of failure.   1. Temperature Effects: Ductility, Yield Strength & Steel – StudySmarter www.studysmarter.co.uk
   • Humidity: Corrosion and degradation of materials can reduce their load-bearing capacity.
   • Weather conditions: Wind, rain, snow, and ice can impose additional loads on structures.
2. Loading Conditions:
   • Overloading: Exceeding the design load can reduce the effective safety factor.
   • Dynamic loading: Vibrations, shocks, or impacts can induce higher stresses than static loads.   1. Impact Loading – Roy Mech roymech.org
   • Fatigue: Repeated loading can lead to material fatigue and failure, even below the static yield strength.   1. In Our Element: What Is Fatigue Failure? – Materion www.materion.com
3. Material Degradation:
   • Corrosion: Chemical reactions with the environment can weaken materials.   1. Effect of Corrosion on Tensile Strength – TFT Pneumatic tft-pneumatic.com
   • Wear and tear: Friction and abrasion can reduce material thickness and strength.
   • Aging: Materials can degrade over time due to internal changes.
4. Maintenance and Inspection:
   • Lack of maintenance: Corrosion, wear, and other forms of degradation can accelerate if not addressed.
   • Inspection frequency: Regular inspections can identify potential issues before they become critical.
5. Human Error:
   • Operational mistakes: Incorrect operation can overload components.
   • Maintenance errors: Improper repairs or modifications can compromise safety.

Additional Considerations

• Consequences of failure: The potential severity of failure impacts the required safety factor.   1. Factor of safety – Wikipedia en.wikipedia.org
• Regulatory requirements: Industry standards and regulations often dictate minimum safety factors.   1. “Factor of Safety: Definition, Examples, Formula” – StudySmarter www.studysmarter.co.uk
• Cost-benefit analysis: Balancing safety with economic considerations can influence the chosen safety factor.

By carefully considering these factors, engineers can assess the actual safety factor of a component or structure in operation and take corrective actions if necessary.