Advanced
Stress
Analysis -
Introduction
Prof Aamir Mubashar
Course Contents
• Introduction
• Fracture Mechanics
• Fatigue
• Creep
• Composites
• Damage
• Failure
Fracture Mechanics
• Study of the propagation of cracks in materials.
• Uses methods of analytical solid mechanics to calculate the
driving force on a crack and those of materials science to
quantify the material's resistance to fracture.
• Objective:
• To predict the conditions under which materials fail due to
crack growth. It aims to assess the safe design of structures
and to predict the service life of components.
• Key Concepts:
• How cracks start and spread in materials under stress?
• Stress Intensity Factor (K): A parameter used to describe
the stress state at the tip of a crack and predict the growth
of cracks.
• Fracture Toughness: The critical stress intensity factor
beyond which material fails.
• Applications:
• Design of safer and more reliable structures in aerospace,
automotive, civil engineering, and other sectors.
• Failure analysis in material science and engineering
• Can be used for static or dynamic loads
• Can be used for Fatigue or Creep Crack Growth
Fatigue
• Fatigue failure is a process by which a material
cracks or fails after being subjected to repeated
cyclic loads below its ultimate tensile strength.
• Importance: Essential for predicting the lifetime
of components and structures, preventing
unexpected failures
• Key Concepts:
• S-N Curve (Stress-Life Curve): A graphical
representation of the relation between the
cyclic stress amplitude and the number of
cycles to failure.
• High-Cycle vs. Low-Cycle Fatigue:
Differentiating based on the number of cycles
to failure, with low-cycle fatigue involving
higher loads and fewer cycles.
• Crack Propagation Rate: Influenced by stress
intensity factor and material properties.
• Applications: Critical in the design and
maintenance of aircraft, automotive components,
bridges, and mechanical systems where safety and
durability are paramount
https://www.youtube.com/watch?v=v7hpYJwiuIA&list=PPSV
Creep
• Creep is the time-dependent and permanent deformation of materials under a
constant load or stress. Creep failure occurs when the material eventually
fractures or fails after a period of sustained stress, especially at high
temperatures relative to the material's melting point.
• Significance: Understanding creep is essential for the design and analysis of
components that operate under high temperatures and stresses over extended
periods, such as in power plants, jet engines, and other high-temperature
applications.
• Key Concepts:
• Stages of Creep:
• Temperature Dependency: Creep rate increases significantly with temperature, becoming
notable typically above 0.4 times the melting point (in Kelvin) of the material.
• Creep Curve: A graphical representation showing the strain in the material over time under a
constant load, highlighting the three stages of creep.
• Applications: Crucial in the aerospace, power generation, and automotive
industries, where components are often exposed to high temperatures and
stresses for prolonged periods.
Composites
Composite materials are made from two or more constituent materials with significantly different physical or
chemical properties, combined to create a material with characteristics different from the individual
components.
•Components:
•Matrix (Binder): The continuous phase that holds the reinforcement in place, typically a polymer, metal, or
ceramic.
•Reinforcement: The dispersed phase, often fibres or particles, that provides the composite its strength and
stiffness.
•Types of Composites:
•Fibre-Reinforced Composites: Fibres of one material (e.g., carbon, glass) embedded in a matrix (e.g.,
polymer).
•Particulate Composites: Consist of particles or flakes within the matrix material.
•Laminated Composites: Stacked and bonded layers of different materials.
•Properties and Advantages:
•High Strength-to-Weight Ratio: Lightweight yet strong.
•Corrosion Resistance: Resistant to chemicals and environmental conditions.
•Tailorable Properties: Can be engineered for specific applications (e.g., conductivity, thermal resistance).
•Durability: Long lifespan with minimal maintenance.
Damage
• Damage mechanics is a branch of mechanics that studies the initiation, growth, and coalescence
of micro-defects in materials, such as cracks, voids, and inclusions, and their effect on the
mechanical properties and failure of materials.
• Objective: To develop predictive models that can accurately describe the progressive failure of
materials under various loading conditions, taking into account the history of the material and its
current state.
• Key Concepts:
• Microstructural Damage: Analysis of how microscopic defects within a material contribute to its overall
weakening and failure.
• Continuum Damage Mechanics (CDM): A theoretical framework that treats damage as a continuous field
variable, quantifying the effective reduction in material stiffness and strength.
• Fracture Mechanics vs. Damage Mechanics: While fracture mechanics focuses on the propagation of existing
cracks, damage mechanics deals with the entire process of degradation, including crack initiation.
• Applications:
• Structural Engineering: Assessing the durability and lifespan of buildings, bridges, and infrastructure.
• Aerospace and Automotive: Designing components that withstand cyclic loading and environmental
degradation.
• Biomechanics: Understanding injury mechanisms and improving materials for implants and prosthetics.
• Material Science: Developing new materials with tailored properties for specific applications.
Stress and
Types of
Stress
Structure
• Cross brace
• Supported at left edge
by two lugs
• Loaded at right hand
edge through two lugs
• Sitting in global XY
plane
Ref: http://www.digitaleng.news/de/stress-in-finite-element-analysis-part-2/
Stress in X Direction, SX
Stress in X Direction, SX
Stress in X Direction, SX
Stress in X Direction, SX
Stress in Y Direction, SY
Stress in Y Direction, SY
Local Coordinate System
• The global SX and SY
stresses provide good
indication of response of
horizontal and vertical
members Zone G
• How to investigate the
cross members at Zones Zone F
F and G?
• Global stresses SX and
SY are of no use
Local Coordinate System
• Problem can be solved by setting up a local coordinate system
• Transform stresses from global coordinate system to local coordinate
system in post-processor
• Plotting local X direction stresses at Zone F so that they align with
bottom right-hand cross member axial direction
• Requires defining a local coordinate system and transforming stresses
Local Coordinate System
Shear Stresses
• Shear stress would exist across the cutting plane, at right angle to
axial stresses
• Contour plot of shear stresses and their distribution across the cut
plane can be plotted in local coordinate system
Shear Stresses
Stress Zone G
Global Shear Stress, SXY
Stress Components
• Useful in understanding the load paths within component regions
• Helps in identifying overall response of structure
• Stress transformation can help in visualizing response of members
not aligned with global stress components
• It is important to realize that we are always describing the same
stress state
Stress Components
Stress Transformation Equations
𝜎𝑥 + 𝜎𝑦 𝜎𝑥 − 𝜎𝑦
𝜎𝑥ƴ = + cos 2𝜃 + 𝜏𝑥𝑦 sin 2𝜃
2 2
𝜎𝑥 + 𝜎𝑦 𝜎𝑥 − 𝜎𝑦
𝜎𝑦ƴ = − cos 2𝜃 − 𝜏𝑥𝑦 sin 2𝜃
2 2
𝜎𝑥 − 𝜎𝑦
𝜏𝑥ƴ 𝑦ƴ =− sin 2𝜃 + 𝜏𝑥𝑦 cos 2𝜃
2
Stress Transformation
• Pick a datum point on the structure, adjacent to the top right hand
corner lug
Stress Transformation
Maximum Principal Stress
Minimum Principal Stress
Principal Stresses
Principal Stresses
Von Mises Stress
Stress Interpretation
• Von Mises Stress: Overall indicator of stress distribution and stress
concentration region. Margins over yield
• Cartesian Stress: Indicates which type of stress dominates the
response
• Principal Stress: Gives sense of flow stress. Givens maximum tensile
or compressive stresses or maximum shear stresses
Case Study
Airbus A380 Wing Cracks
Background:
• In 2012, hairline cracks were discovered in the wing rib feet of the
Airbus A380, the world's largest passenger airliner.
• The cracks were a significant concern due to their potential impact on
the structural integrity of the aircraft.
Airbus A380 Wing Cracks
Discussion Points:
1.Design and Materials:
1. Overview of the A380's wing design and materials used (aluminum alloys, composites, etc.).
2. Discussion on how material selection impacts stress distribution and fatigue life.
2.Stress Analysis and Finite Element Modelling:
1. Exploration of the stress factors contributing to the crack initiation.
2. Finite element analysis (FEA) used in the original design and subsequent investigations.
3.Fatigue and Fracture Mechanics:
1. Understanding the role of fatigue and fracture mechanics in the development of the cracks.
2. Analysis of load cycles and stress concentrations.
4.Engineering Solutions and Modifications:
1. Review of the corrective actions taken by Airbus, including design modifications and
inspection regimes.
2. Discussion on the implications of such modifications on performance, cost, and safety.
https://www.dailymail.co.u
k/indiahome/indianews/art
icle-2099825/Airbus-A380-
More-cracks-wings-worlds-
biggest-jets.html
https://engtechmag.files.wordpres
s.com/2012/02/airbus-a380-wing-
cracks1.jpg
Reasons Identified
• Airbus had not used carbon fiber composites for wing-rib
construction on previous models and that the A380’s designers were
“pushing hard” to reduce weight
• Each A380 wing has up to 60 ribs, with about 4,000 rib feet per wing
set, although only about 20 brackets have been subject to cracking
• By using the composite material for wing-rib webs and conventional
aluminum-alloy for rib feet, the manufacturer had been able to save
about 660 pounds from the weight of each wing
Solution
• Later, the A380 featured modified wings that incorporated a revised
design for certain ribs following Airbus’s analysis of cracks discovered
in feet (or brackets) that attach the ribs to the outer skins, known as
“covers,” in Airbus parlance
• Manufacturer reverted to the use of metal in place of the composite
material chosen originally to save weight in the wing-rib panels (or
webs)
• All wing-rib feet later manufactured from 7010 Aluminum, rather
than 7449 material, making them “similar to other Airbus aircraft
https://www.ainonline.com/aviation-news/air-transport/2012-07-11/airbus-aims-put-a380-wing-crack-problem-
behind-it-final-fix
THANK YOU
